Estimating Road Transport Fuel Demand Elasticities in the Uk: an Empirical Investigation of Response Heterogeneity

ESTIMATING ROAD TRANSPORT FUEL DEMAND ELASTICITIES IN THE UK: AN EMPIRICAL INVESTIGATION OF RESPONSE HETEROGENEITY

Ahmad Razi Ramli

Centre for Transport Studies Department of Civil and Environmental Engineering Imperial College London

Submitted for the Diploma of the Imperial College (DIC), PhD degree of Imperial College London

March 2014

DECLARATION OF ORIGINALITY

I hereby declare that I am the sole author of this thesis and have personally carried out the work contained within. The contribution of my supervisor was only supervisory and editorial. I further declare that all sources cited or quoted are indicated and acknowledged in the list of references in this thesis.

……………………………………………… Ahmad Razi Ramli

‘The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work’.

ABSTRACT

The main aim of this dissertation is to estimate fuel demand elasticities for the UK road transport sector. Despite being extensively studied, there is a renewed need for the estimation of fuel demand elasticities so that they might be more reflective of recent trends and changes in consumption patterns. At present, understanding the fuel demand sensitivities is especially important for policy making purposes.

A review of the empirical literature on fuel demand revealed three important areas of concern. First, fuel demand estimates tend to vary greatly in magnitude. The effect- size differences observed are probably related to the diversity of study-characteristics and data factors. Second, the reliability of past estimates may be questionable due to shortcomings in the modelling methodology employed. Obtaining reliable estimates does not only require the use of recent data but, beyond that, it is also important for the model to be based on sound methodological and theoretical foundations. Third, studies have often relied on the elasticity of petrol to define road transport fuel demand, assuming the absence of fuel type heterogeneity among road transport fuels. This is severely restrictive, however, since demand sensitivities are likely to vary between the respective fuels.

This thesis undertakes a series of empirical analyses aimed at improving the current understanding of fuel demand for the UK road transport sector. Through meta- regression analysis, this research examines the underlying factors that can help explain the between-study variations found in the literature. The research then examines the sensitivity of fuel demand through the use of both time series and panel data econometric models. Special attention has been given to methodological issues and the use of recent econometric techniques to ensure the reliability of the estimates. In addition, this thesis does not assume that demand elasticity is homogenous for each respective transport fuels. To that end, fuel demand elasticities are estimated separately for each fuel type.

ACKNOWLEDGEMENTS

This thesis was not what I originally intended at the beginning of the PhD. Despite that, I am really glad that it turned out the way it has. For this I am extremely grateful to my supervisor, Professor Daniel Graham, who has been tireless in encouraging me to move away from my comfort zone and who has continuously stressed the importance of thinking critically and conducting meaningful research. His knowledge and positive guidance throughout my PhD has allowed me to develop a greater understanding of the theoretical and fundamental ideas of my research and a stronger appreciation of the intricacies of econometric techniques and modelling.

The journey through my PhD has also been made easier by the support and encouragement that I received from friends and colleagues in CTS. In particular, special thanks goes to the ‘gang of 602’: Patricia Melo, Hamed Jahromi, Bani Anvari, Jacek Pawlak, and Kriangkrai Arunotayanun; for simply being there every morning when I get to the office and for the meaningful discussions and friendship offered. I would like to extend my appreciation also to Ramin Moradi, Thalis Zis, Rocky Li Haojie, and K. C. Pien. Many thanks also to Jackie Sime and Fionnuala Dhonabhain, whose continued administrative support has made my stay in Imperial certainly easier.

It would not have been possible for me to cope with the PhD on my own. On that account, I am extremely fortunate for having the support of my family. I am extremely indebted to my wife, for her continuous belief in me and for helping to manage the family when I was totally engrossed with the PhD. Her loving and nagging certainly helped me get through this journey. In addition, I am thankful also to my daughters: Aliah, Arissa, Aafreen, Aaira, and Alanis; for being such great supporters of everything that I do and for reminding me that there are other important things in life apart from work. My gratitude also goes to my parents and in-laws as well as my siblings for their understanding and crucial support over the last four years.

Last but not least, I am also thankful for the scholarship and assistance from Universiti Teknologi MARA, without which, the dream of undertaking my PhD in Imperial would never have been possible to begin with.

Ahmad Razi Ramli Centre for Transport Studies Imperial College London March 2014

TABLE OF CONTENTS

Declaration of Originality 2 Copyright Declaration 3 Abstract 4 Acknowledgements 5 Table of Contents 7 List of Figures 11 List of Tables 12 List of Acronyms 14

CHAPTER 1 INTRODUCTION 16 1.1 Introduction 16 1.2 Background and Motivation 18 1.3 Problem Statement, Objectives and Scope of the Thesis 25 1.4 Structure and Overview of the Thesis 28

CHAPTER 2 ROAD TRANSPORT FUEL DEMAND: TRENDS AND STATISTICAL 31 BACKGROUND 2.1 Introduction 31 2.2 Road Transport Fuel Consumption Trends 32 2.3 Road Vehicles Statistics: Characteristics and Usage 34 2.3.1 Behavioural Differences: Fact of Fiction? 36 2.4 Summary 39

CHAPTER 3 FUEL DEMAND ELASTICITY MODELLING: A REVIEW OF ECONOMETRICS 40 AND METHODOLOGICAL ISSUES 3.1 Introduction 40 3.2 Model Specification 42 3.3 Data Characteristics 49 3.4 Contextual Characteristics 51 3.5 Time Series Models: Recent Estimation Issues 52 8

3.5.1 Non-stationarity, Co-integration and Error Correction Models 52 3.6 Panel Data Regression Models 56 3.6.1 Dynamic Panel Data Models: Estimation Issues 62 3.7 Summary 64

CHAPTER 4 ROAD TRANSPORT FUEL DEMAND ELASTICITIES: A REVIEW OF THE 65 LITERATURE 4.1 Introduction 65 4.2 Fuel Demand Elasticities: Overview of Empirical Evidence 67 4.3 Summary of Elasticities 72 4.3.1 Overall Summary of Elasticities Results 80 4.3.2 Variations between Time Series and Panel Data Models 82 4.3.3 Variations due to Estimation Techniques 84 4.4 Summary 86

CHAPTER 5 A META-REGRESSION ANALYSIS OF ROAD TRANSPORT FUEL DEMAND 88 5.1 Introduction 88 5.2 Meta-Regression: A General Discussion 90 5.3 Scope of the Meta-Regression 92 5.3.1 Meta-sample 95 5.4 Design of the Meta-Regression Analysis 99 5.5 Meta-Regression Results 103 5.5.1 Price Elasticity 103 5.5.2 Income Elasticity 109 5.6 Publication Bias 115 5.7 Summary 121

CHAPTER 6 ESTIMATION OF FUEL DEMAND ELASTICITIES USING ANNUAL TIME 122 SERIES DATA 6.1 Introduction 122 6.2 Time Series Data Sources 124 9

6.2.1 Dataset Construction 126 6.2.2 Dataset Limitations 127 6.3 Fuel Demand Model Specification 128 6.3.1 Extended Model 129 6.4 Time Series Cointegration Estimation Methodology 131 6.4.1 First Difference Regression 137 6.5 Estimation Results 138 6.5.1 Stationarity Tests 138 6.5.2 Model Cointegration Tests 139 6.5.3 Estimation Results for the Base Models 143 6.5.4 Estimation Results for the Extended Models 150 6.6 Summary of Elasticities 152 6.7 Summary 156

CHAPTER 7 AGGREGATE PANEL DATA ANALYSIS OF FUEL DEMAND ELASTICITIES 158 7.1 Introduction 158 7.2 Panel Data Sources and Variable Description 160 7.2.1 Dataset Construction 163 7.3 The Panel Data Model Specification 165 7.3.1 Static Model 167 7.3.2 Dynamic Model 168 7.4 Panel Data Estimation Techniques 169 7.4.1 Additional Estimation Validity Checks 172 7.5 Estimation Results 175 7.5.1 Diesel Fuel Estimates 175 7.5.2 Petrol Fuel Estimates 178 7.5.3 Total Fuel Estimates 181 7.6 Summary of Elasticities 185 7.7 Summary 189

CHAPTER 8 CONCLUSIONS 191 8.1 Introduction 191 10

8.2 Summary of the Main Findings 192 8.3 Research Contributions 197 8.4 Implications of the Research 199 8.4.1 Summary of Estimation Results 199 8.4.2 Methodological Implications 201 8.4.3 Policy Implications 203 8.4.4 Forecast of Road Transport Fuel Demand in the UK 204 8.5 Limitations of Study 210 8.6 Directions for Future Research 212

REFERENCES 214

APPENDICES 221

PUBLICATIONS 226

LIST OF FIGURES

Figure 2.1 Road transport fuel consumption in the UK 33 Figure 2.2 Road transport vehicle stock categorised by fuel type 34 Figure 4.1 Short-run price elasticity of fuel demand 79 Figure 4.2 Long-run price elasticity of fuel demand 79 Figure 4.3 Short-run income elasticity of fuel demand 79 Figure 4.4 Long-run income elasticity of fuel demand 79 Figure 5.1 Relationship between price elasticity estimates (in absolute values) and their standard errors 117 Figure 5.2 Relationship between income elasticity estimates (in absolute values) and their standard errors 118 Figure 8.1 Road transport petrol consumption forecasts for the UK 206 Figure 8.2 Road transport diesel consumption forecasts for the UK 207

LIST OF TABLES

Table 1.1 Price and income elasticities from previous fuel demand studies in the UK 19 Table 1.2 Fuel demand elasticities estimated in this research 27 Table 2.1 Share of petrol and diesel vehicles in the UK vehicle fleet 35 Table 2.2 Diesel car share statistics 35 Table 2.3 Annual vehicle-km of cars categorised by fuel type 36 Table 2.4 Percentage share of licensed diesel cars categorised by engine capacity 37 Table 2.5 Percentage share of licensed petrol cars categorised by engine capacity 37 Table 4.1 Summary of price and income elasticities 69 Table 4.2 Price and income elasticities from time series cointegration studies 73 Table 4.3 Price and income elasticities from time series dynamic partial adjustment studies 75 Table 4.4 Price and income elasticities from panel data studies 77 Table 4.5 Summary statistics of elasticity estimates from the literature reviewed 81 Table 4.6 Elasticity estimates produced by time series and panel data models 82 Table 4.7 Elasticity estimates produced by cointegration and dynamic models (time series only) 84 Table 5.1 List of primary studies used in the meta-regression analysis 94 Table 5.2 Summary of price elasticity variables included in the meta-regression analysis 97 Table 5.3 Summary of income elasticity variables included in the meta-regression analysis 98 Table 5.4 Summary of moderator variables considered in the meta-regression analysis 102 Table 5.5 Meta-regression results – short-run price elasticity 107 Table 5.6 Meta-regression results – long-run price elasticity 108 Table 5.7 Meta-regression results – short-run income elasticity 113 Table 5.8 Meta-regression results – long-run income elasticity 114 13

Table 5.9 Publication bias tests for price elasticity 120 Table 5.10 Publication bias tests for income elasticity 120 Table 6.1 Description of time series variables, data sources and descriptive statistics 125 Table 6.2 Tests for stationarity of the variables 140 Table 6.3 Cointegration test results for the base and extended fuel demand models 142 Table 6.4 Long-run elasticity estimates of the cointegrating regressions (base models) 143 Table 6.5 Dynamic OLS ARDL estimation results for diesel fuel (base model) 145 Table 6.6 Dynamic OLS ARDL estimation results for total fuel (base model) 146 Table 6.7 Short-run results from the ECM of diesel consumption (base model) 147 Table 6.8 Short-run results from the ECM of total fuel consumption (base model) 148 Table 6.9 Difference regression estimation results for petrol (base model) 149 Table 6.10 First difference regression results for the extended fuel demand models 150 Table 6.11 Summary of elasticities from the preferred estimators 152 Table 7.1 Description of panel data variables, data sources and descriptive statistics 162 Table 7.2 Variation in data 164 Table 7.3 Estimation results for the panel data diesel fuel models 176 Table 7.4 Estimation results for the panel data petrol fuel models 180 Table 7.5 Estimation results for the panel data total fuel models 182 Table 7.6 Elasticity estimates from the LSDVc estimator 185 Table 8.1 Comparison of estimated elasticities 200 Table 8.2 Forecasts of road transport fuel consumption (Million tonnes of fuel) 205

LIST OF ACRONYMS

2SLS Two-Stage Least Squares ADF Augmented Dickey–Fuller ARDL Autoregressive distributed lag CNG Compressed Natural Gas DECC Department of Energy and Climate Change DERV Diesel Engined Road Vehicles DfT Department for Transport DUKES Digest of United Kingdom Energy Statistics ECM Error Correction Model/Mechanism ECUK Energy Consumption in the UK EG–ADF Engle–Granger ADF FD First-Differences GMM Generalized Methods of Moments GOR Government Office Regions IV Instrumental Variable LPG Liquefied Petroleum Gas LSDV Least Squares Dummy Variables LSDCVc Least Squares Dummy Variables corrected NUTS 1 Nomenclature of Territorial Units for Statistics 1 (12 UK regions) ONS Office for National Statistics OLS Ordinary Least Squares PAM Partial Adjustment Model UECM Unrestricted Error Correction Model VKM Vehicle-Kilometre

‘If I have seen further it is by standing on the shoulders of giants’. Sir Isaac Newton

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION The study of fuel demand and the estimation of its elasticities are not something new. Since the early 1970s, there has been strong interest in understanding the pattern and factors that influence energy consumption in the transport sector. It can be argued that in the area of empirical economics, few topics have been the subject of more research interest while at the same time also being of interest to a wide spectrum of the society.

This dissertation is a further continuation of that interest. From 1970 to the present, the road transport sector in particular (and society as a whole) has experienced numerous structural and behavioural changes and as such it would be natural to expect that fuel consumption sensitivity has also evolved. In this context, this thesis plays an important role since it aims to contribute to the current state of knowledge by providing up-to-date and reliable estimates of fuel demand elasticity for the road transport sector using recent econometric methodologies. This thesis also aims to extend the scope of understanding further, beyond the usual price and income elasticities, by including additional factors deemed relevant to consumption. Furthermore, unlike in previous studies, this thesis does not assume that demand elasticity is homogenous for the different transport fuels or that petrol elasticity estimates alone are adequate to explain the trends in energy consumption. Instead, demand sensitivity is assumed to be heterogeneous and this is reflected in empirical analyses in which fuel elasticities are estimated separately for petrol, diesel and total fuel. In addition to the above, the work undertaken in the thesis also contributes to the development of the methodological aspect of fuel demand estimation. 17

This chapter serves to provide an overview to the issues of fuel demand modelling and the context of the research. In the next section, the motivation and contextual background for the research are further explored. This covers issues such as the application of transport fuel demand elasticities and the reasons as to why investigation into the sensitivity of different road transport fuels is necessary. This is followed in Section 1.3 by a statement of the problem, objectives and scope of the research. Section 1.4 outlines the structure of the thesis.

1.2 BACKGROUND AND MOTIVATION Fuel demand is central to many policy issues. Starting with the energy crisis in the 1970s, the policy focus has evolved to encompass energy security, depletion of supplies and conservation and, now, the link between emissions and global warming. An essential element in building an understanding of fuel demand that can inform these policy interests is through the study and estimation of price and income elasticities for transport fuel. Dahl (2012) asserted that interest is drawn towards the estimation of elasticities simply because they have numerous real world applications.

Similarly, in the UK, the understanding and management of fuel demand has attracted interest from a broad sector of society. This understanding is essential because it affects not only decisions at the highest levels of government but also touches upon the daily lives of individuals. In practice, this understanding (via the use of elasticities) has been used to affect numerous policy issues. At the road transport level, these range from setting the level of fuel and motoring taxation (see Leicester, 2005; Smith, 2000) , to understanding travel behaviour and distributional implications (see Santos and Catchesides, 2005) as well as developing policies to curb consumption and emissions from the road transport sector (see Parliament. House of Commons, 2006), to name a few.

If the policy objectives above are to be achieved successfully, then there is a need for fuel demand studies and associated elasticity estimates that reflect current behavioural and structural realities in consumption. As such, it is important for future studies to factor in the changing fuel consumption patterns observed in the road transport sector. Specifically, this means recognising the increasing (and perhaps greater) role being played by diesel fuel in road transportation. This is particularly important considering that diesel has now replaced petrol as the dominant road transport fuel. In 2009, 55.8% of all petroleum-based fuel consumed by the sector can be accounted to diesel fuel (DECC, 2011).1

1 Chapter 2 provides further statistical perspectives on road transport fuel demand trends in the UK. 19

Table 1.1 Price and income elasticities from previous fuel demand studies in the UK

Price Elasticity Income Elasticity Authors Fuel Type Data Type Period Frequency Context of Analysis Short-Run Long-Run Short-Run Long-Run Virley (1993) Petrol & Time Series 1950–1990 Annual –0.09 –0.46 0.54 1.22 Road Transport diesel (No additional exogenous variables) Dargay (1993) Petrol Time Series 1950–1991 Annual –0.17 –0.45 0.10 1.00 Road Transport (Car price) Petrol Time Series 1950–1991 Annual – –0.70 to –1.40 – 1.50 Private Transport (No additional exogenous variables) Franzen and Petrol Time Series 1960-1988 Annual –0.11 –0.4 to –1.4 0.36 1.47 to 1.6 Road Transport Sterner (1995) (No additional exogenous variables) Fouquet et al. Petrol Time Series 1960–1993 Annual – – 0.37 to 0.45 1.95 to 2.05 Road Transport (1997) (Not stated) Hanly et al. Petrol & Time Series 1960–2000 Annual –0.06 to –0.10 –0.23 to –0.67 0.04 to 0.45 0.44 to 1.15 Road Transport (2002) diesel (No additional exogenous variables) Hunt & Petroleum Time Series 1971–1997 Quarterly – –0.12 – 0.80 Transport Sector Ninomiya (2003) Fuel (No additional exogenous variables) Notes: 1) Disaggregate studies using panel data models were excluded since they were applied in the context of estimating the elasticities of vehicle miles travelled (VMT). 2) The elasticity of fuel demand for private transport in Dargay (1993) was obtained through a structural model. 3) The estimates for Hanly et al. (2002) are from dynamic partial adjustment models. 20

One of the first areas that were looked into before proceeding with the research was the current state of knowledge with regards to fuel demand, particularly for the road transport sector. A search of the literature was conducted and this found that there appear to be gaps in the literature that invite an attempt at an up-to- date estimation of elasticities.

First, while fuel demand studies are certainly available, to the best of our knowledge, none have been conducted recently (i.e. in the past 5 years). Secondly, the literature review indicated that (in the context of the UK) aggregate data studies appear to be based on time series data with panel models only being used to produce estimates at the disaggregate level. This, according to Basso and Oum (2007), raises the question of comparability between the estimates.2 The presence of these gaps serves to validate the undertaking of this research. Apart from providing an up-to-date estimate, an additional contribution is the use of a panel model to produce an aggregate level estimate.

Our survey of the literature also reveals an additional issue that has often been overlooked in the empirical studies of fuel demand. While there are numerous studies focusing on elasticities in the road transport sector, most have either looked at petrol (gasoline) demand or have used (albeit significantly less frequently) total road transport fuel demand. This is rather surprising given that, apart from the ubiquitous petrol, there are also other road transport fuel types available, namely diesel, liquefied petroleum gas (LPG), compressed natural gas (CNG) and, recently, biofuel. While, admittedly, the proportion made up by the last three fuels in the list is relatively negligible, this does not explain why diesel has not received more attention in the empirical literature. This phenomenon was also noted by Sterner (2007), who stated that despite the obvious (in reference to the lack of diesel elasticities); practically all demand sensitivity studies were focused on petrol.

2 In addition, the disaggregate studies found for the UK were also conducted in the context of estimating the elasticity of vehicle-km travelled (VMT). Although related, these are not directly comparable to the estimates of fuel demand elasticities, which is the focus of this research. 21

In a similar vein, Schipper et al. (1993) strongly question the uncritical use of petrol as the de facto measure, although their context was in reference to the use of total gasoline fuel as a proxy to estimate automobile fuel elasticity. They assert that, since the composition of fuel consumed is expected to vary over time, the continuation of such a practice is likely to lead to serious error in the estimates.3 Basso and Oum (2007), conscious of the importance of this issue, further stress the need for empirical studies to be clear on the context of what is actually being analysed and what is being used as a measure.4

A natural extension to the discussion, then, would be whether fuel elasticity based on an aggregated measure of total road transport fuel would be a more appropriate way to capture the sensitivity of road transport fuel demand with respect to price and income. While this was one of the possible solutions suggested by Schipper et al. (1993), in contrast, Dargay (1993) cautioned against simply relying on such estimates. This is especially so if there are differences in the sensitivities in demand between the individual groups. Dargay reasoned that, in such a situation, elasticity estimates based on an aggregated measure would produce average elasticities, which would neither be representative of the individual groups nor useful for meaningful policy analysis.

This leads us to the next question as to whether there are reasons to believe that demand sensitivities could be different between the fuels. In general, based on historical patterns of utilization, it is plausible that the sensitivity of fuel consumption between the two fuels is likely to differ. Diesel demand, within the road transport sector, in the past, was largely attributed to public service and

3 A natural extension to this argument can also be in the case of petrol being the proxy for road transport fuel demand as a whole. This particular problem is further aggravated if the fuel mix has changed to the extent that the fuel being used as a reference is no longer the dominant type consumed. 4 This appears to be the problem with the work of Hunt and Ninomiya (see Table 1.1) as the context was not made very clear. In their study, they used fuel data for the transportation sector, but their explanation for the observed results was largely based on road transport. The issue with the use of such data is that petroleum products for the transport sector as whole also include fuels for air transport (i.e. aviation spirit and turbine fuel) as well rail transport (i.e. gas oil). See Final Consumption of Petroleum Product in the DECC’s Digest of Energy Consumption in the UK for the exact composition of petroleum fuel in the transport sector. 22

freight vehicles while in contrast petrol was predominantly consumed by private vehicles (i.e. cars and motorcycles). As such it can be expected, due to the differences in the underlying purpose of travel between the users of these fuels, that the relationship (as well as the sensitivity) to fuel demand is not the same.

Recent data, however, indicates that the pattern of consumption that was previously seen has changed. While petrol demand has continued to be dominated by private vehicles, diesel consumption on the other hand has experienced a dramatic change in terms of the mix of users, particularly due to the influx of private vehicle users. In the road transport sector, the dramatic shift seen in diesel demand from private consumers is largely due to policy measures favouring diesel.

The dieselisation of the car fleet is largely the result of the EU Voluntary Agreement (VA) with the European Automobile Manufacturers’ Association (ACEA) (Whitmarsh and Köhler, 2010). In many countries, dieselisation was singled out as the most important factor in reducing the average car emissions and as an extension, total

CO2 emissions (Jeong et al., 2009; Schipper and Fulton, 2009; Zervas, 2006). In the UK, increasing diesel penetration was also actively encouraged as a means of improving fuel efficiency and one definitive outcome from the adoption of the VA package was the dieselisation of the car fleet (Bonilla, 2009). Today, the extent to which diesel fuel is consumed as a proportion of total road transport fuel clearly shows that a decisive shift away from petrol vehicles has taken place. In the context of diesel particularly, this shift has also resulted in cars now becoming the dominant consumer of the fuel.

From the above, one cannot help but wonder if the sensitivity is now the same for both fuels. Since private vehicle are now dominating diesel consumption, would it be plausible that the estimated aggregate diesel elasticity would reflect the change in the relative share as well? This would imply that diesel sensitivity would now be relatively similar to petrol, making the estimates for the latter applicable to the former as well.

The review of the literature, however, appears to suggest the contrary. It appears from a comparative perspective, there is some evidence to suggest a different magnitude of response in diesel sensitivity compared to petrol. Studies by Hivert (2011), Schipper (2011) and Schipper and Fulton (2009) suggest that diesel vehicle users may have different behaviour-utilisation considerations compared to the users of petrol powered vehicles. This may result in dissimilar responses to changes in price and income. While some of this can be attributed to a self-selection process, the studies have also pointed to tendencies, when replacing vehicles, of switching to a bigger and more powerful diesel vehicle instead of matched pairs and also to differences in how diesel vehicles are used. For example, Schipper (2011) cited a direct survey in France that found ‘new dieselists’ drive their diesel cars further than their former petrol cars. This behaviour is also observed in the UK, with data from the National Travel Survey indicating that the average diesel car’s mileage for private trip purposes is approximately 24.5% higher than its petrol counterpart (DfT, 2010). Due to these differences, it is plausible to assume that the elasticity estimates would also be different.5 Thus, by estimating separately the response sensitivity of the fuels, a better understanding can be achieved with regards to the demand relationship of these fuels.

In the context of rising diesel consumption, it is clear from the above that the reliability of petrol estimates as a proxy for road transport fuel response sensitivity is likely to be seriously compromised. Unfortunately, as seen for the UK in Table 1.1 (and similarly in our sample of international studies later in Tables 4.2–4.4), elasticity estimates have largely been and continue to be based on petrol fuel. Since the use of unreliable demand elasticities would probably hamper the efficacy of any policy decisions, this provides additional (perhaps the driving) motivation for the undertaking of this research.

5 It is also possible that demand sensitivities between the different groups of diesel users are opposite to the extent that the average diesel elasticity obtained is representative of none of the groups. However, this is beyond the scope of the research and is suggested as a potential area to be investigated. 24

In principle, based on the above, it is apparent that the ideal solution is to estimate separately fuel demand elasticities for each respective fuel. In addition, the reliability of the estimates will also be dependent on whether the models take into account methodological and econometric issues (which may not have been thoroughly investigated in past studies). While this will not be elaborated here, understanding the methodological issues, as well as identifying recent estimation techniques, is also an important motivator driving this research. In our view, an important contribution of this research is therefore also in the use of recent econometric techniques to ensure the reliability of the estimates. As such, although the primary focus is on obtaining separate fuel demand elasticities for the transport sector, an equal focus was also directed to the means through which it was ensured that the said estimates are methodologically robust and reliable. Due to this, a substantial portion of this research also involves work with regards to the methodological and econometric estimation issues related to fuel demand modelling. The objective and focus of the research is further elaborated in the next section.

1.3 PROBLEM STATEMENT, OBJECTIVES AND SCOPE OF THE THESIS Despite having been extensively studied, there is a renewed need for the estimation of fuel demand elasticities to be undertaken in order to ensure that these elasticities are more reflective of recent trends and changes in consumption patterns. At present, understanding the sensitivity of fuel demand is no less important than in the past for policy making purposes, and is possibly even more

essential considering the relationship between fuel consumption and CO2 emissions and especially in the context of the need to meet the targets set by the Climate Change Act.6

An additional concern when relying on past estimates relates to the adequacy of the modelling methodology employed. Obtaining reliable estimates does not only mean the use of recent data but is also dependent on the model being based on sound methodological and theoretical foundations. The investigation of the literature on fuel demand indicates that the reliability of empirical estimates derived in the past may be compromised due to the failure to take into account important methodological issues. These include, the possibility of spurious parameters due to non-stationarity in time series data and the potential of biased estimates due to the issue of endogeneity in dynamic panel econometric models. Since the research is aimed at providing reliable empirical estimates of fuel demand elasiticities, particular attention has been given to the extent to which the existing literature adheres to the latest methodological and econometric estimation techniques.

From the review of the academic literature, it was also revealed that there are gaps and limitations in the studies undertaken in the past that may limit the capacity for a comprehensive understanding of fuel demand elasticities. In particular, important questions, such as whether demand sensitivity is homogenous across different road fuels or whether other factors, apart from price and income, also influence

6 The Climate Change Act is a legally binding target set by the Government for the reduction of CO2 emissions. The act explicitly states that the UK will have to find ways of reducing CO2 emissions by 80% from the level recorded in 1990 by the year 2050 (DECC/DEFRA, 2009). 26

consumption patterns need to be looked into. These, amongst others, are the important areas that will be explored further in this research.

Research Objectives This research contribute to the essential issue of understanding fuel demand in the road transport sector. Although some of the focus (as stated above) will be on the estimation methodologies, the driving theme of the research is to improve the current understanding of fuel demand by empirically exploring how certain factors may exert an influence on its consumption in the road transport sector. Specifically, the analyses in the research are conducted with the aim of meeting the following objectives:

1. To understand whether the sensitivity of fuel demand is affected by fuel type heterogeneity. This is achieved by estimating the elasticities separately for each respective road transport fuel.

2. To understand the econometric and methodological considerations in undertaking fuel demand elasticity modelling. This is achieved by conducting an extensive review of the survey literature and empirical studies on road transport fuel demand.

3. To understand the underlying factors that lead to variations in the magnitude of elasticities reported in the literature. An empirical assessment via the method of meta-regression analysis is undertaken to identify objectively the factors that affect empirical estimation of fuel demand elasticities.

4. To identify the determinants of road transport fuel demand in the United Kingdom, and estimate their effects. Apart from price and income, additional determinants of fuel demand are also included in the estimation models to enable their effects to be statistically tested and quantified.

This research is focused on obtaining separate elasticity estimates for road transport fuel in the UK. Specifically, it involves only the estimation of the aggregated petrol, diesel and total fuel demand elasticities respectively without further separating the consumption by users.7

For comparability purposes, the econometric models of fuel demand in this research are limited to obtaining elasticity estimates at the aggregate level. While previous time series studies tend to be at the aggregate level, panel data models have often been conducted using disaggregate data. For this purpose to be achieved, the research utilizes both aggregate time series and panel datasets. To the best of our knowledge, this is the first time that such panel datasets are used in the context of fuel demand elasticity estimation in the UK.

Despite the above, the use of the differing datasets does impose certain limitations. Firstly, due to the recent availability of this type of data, the panel dataset covers a shorter time period compared to the time series data. Additionally, due to the length of the time series observations, the data used for the covariates may not be directly comparable. This is particularly so in the context of the cross-price elasticity of fuel demand. The elasticities estimated in this research are shown in Table 1.2 below:

Table 1.2 Fuel demand elasticities estimated in this research

with respect to Elasticity of Public Technology demand for Own Price Income Vehicle Stock Bus Fare Transport Fare Share Petrol    TS PD  PD Diesel     TS  PD  PD Total Fuel     TS  PD  PD Notes: 1) The respective elasticities are estimated for both time series and panel data models unless noted otherwise. 2) The superscripts TS and PD indicate time series and panel data models respectively.

7 The term total fuel used in this research is defined as the sum of petrol and diesel fuel. 28

1.4 STRUCTURE AND OVERVIEW OF THE THESIS This section highlights the structure of the PhD thesis. The thesis is comprised of eight chapters, with three of these containing the empirical work. The chapters follow a standard presentation format with each having an introduction, followed by the content discussion and concluded by a chapter summary. The thesis structure, as well as an overview for each of the individual chapters, is detailed below:

Chapter 1: Introduction This chapter provides an introduction to the issue of the estimation of road transport fuel demand elasticities estimation and the context of the research. An overview to the motivation, objectives and considerations behind undertaking the research is also provided.

Chapter 2: Road Transport Fuel Demand: Trends and Statistical Background The second chapter gives a broad review of the background literature related to the research. It covers the issue of changing fuel consumption trends in the United Kingdom and provides a statistical context as to why demand elasticities may differ between road transport fuels.

Chapter 3: Fuel Demand Elasticity Modelling: A Review of Econometric and Methodological Issues The chapter presents a detailed review of the econometric and methodological approaches that have been used in the fuel demand literature. It begins by assessing the general considerations often encountered in modelling fuel demand. The differences as well as the relative advantages of time series and panel data estimation techniques are also discussed. This is then followed by an additional examination of the key methodological issues that arise from the use of the differing techniques, such as non-stationarity in time series estimation and endogeneity in the case of dynamic panel models.

Chapter 4: Road Transport Fuel Demand Elasticities: A Review of the Literature This chapter focuses on a review of the literature and the vast empirical studies on fuel demand elasticities. It describes the a priori economic expectations and discusses the differences in estimation outcomes that may arise due to empirical specifications. This is then followed by a survey of recent international fuel demand elasticity estimates, with an equal focus on time series models as well panel data studies. The chapter then summarizes the elasticities and conclude with a narrative review of the results.

Chapter 5: A Meta-Regression Analysis of Fuel Demand Modelling This is the first empirical chapter and an essential continuation of the literature review undertaken in Chapter 4. Central to the chapter is the meta-regression analyses which aim to provide a quantitative and objective assessment of the underlying factors causing the variations between studies seen in the literature. Additionally, the chapter – through various tests – also looks for evidence as to whether empirical studies of fuel demand are affected by publication bias.

Chapter 6: Estimation of Fuel Demand Elasticities Using Annual Time Series Data This chapter estimates road transport fuel demand elasticities using time series data. Using recently available data, separate demand elasticities are estimated for petrol and diesel (the major road transport fuels consumed in the UK) as well as for the composite measure, total fuel. The dataset has never been applied before in this context and contains series with an observation period of 29 years. The estimation employs both static and dynamic cointegration methodologies as well as first difference regression to overcome the issue of non-stationarity.

Chapter 7: Aggregate Panel Data Analysis of Fuel Demand Elasticities The final empirical chapter estimates similar fuel demand elasticities but through the application of panel data. The dataset consists of observations at the NUTS 1 30

level for the period ranging from 2005 to 2011.8 The issues of unobserved regional heterogeneity, as well as endogeneity in dynamic panel models, are addressed through the use of appropriate econometric techniques.

Chapter 8: Conclusions The final thesis chapter provides a conclusion drawn from the outcome of the empirical chapters. Suggestions are provided based on the limitations found in the research and further research directions are identified for future studies.

8 NUTS is an abbreviation for Nomenclature of Units for Territorial Statistics. See Chapter 7 for further details on the specific regions. 31

CHAPTER 2 ROAD TRANSPORT FUEL DEMAND: TRENDS AND

STATISTICAL BACKGROUND

2.1 INTRODUCTION The objective of this chapter is to provide context and statistical background on fuel consumption and the related underlying factors that are taking place in the road transport sector. This is crucial, since if a research study is to be effective, an important part of the research process involves understanding the context underlying the issue that is being investigated.

This chapter is structured as follows. Section 2.2 provides background information and discusses the changes with regards to fuel consumption trends in the road transport sector. This is then followed by Section 2.3 that looks into changes that are taking place in the road vehicle fleet. Some statistics on driving and car ownership pattern are also discussed. A brief summary of the findings in the chapter is then provided in Section 2.4.

2.2 ROAD TRANSPORT FUEL CONSUMPTION TRENDS Transport accounted for 39% of all final energy consumption in the UK, using approximately 56.5 million tonnes of oil equivalent in 2009. Unlike other segments of the economy, 97% of the energy consumed by the sector came through the use of petroleum. As a whole the transport sector’s usage represents 75% of the total oil consumption in the UK.

Road transport is the biggest energy consumer within the transport sector, accounting for 72% of the total energy used. Although usage of biofuels has been increasing since the introduction of the Renewable Transport Fuels Obligation in 2008, its utilization is still relatively limited, making up 2.7% of road transport fuel consumed. While there has been an overall decline in petroleum based fuel consumed by the road transport sector, it is still responsible for 54.7% of final consumption of petroleum product in 2009 (DECC, 2010).

Figure 2.1 provides details of road transport fuel consumption in the UK for the period spanning 1970-2009. Fuel usage by the sector has increased significantly by 186% since 1970, reaching 35.93 million tonnes in 2009. Demand grew sharply between 1970 and 1990 but then at a relatively moderate pace in the succeeding periods to 2007. The total fuel consumed declined after 2007, coinciding with the economic crisis. Road transport fuel demand in 2009 is 7.3% lower than the peak of 38.78 million tonnes recorded in 2007.

A much more interesting aspect can be glimpsed by looking at the changing consumption pattern of the different petroleum based fuels. Road transport fuel has historically consisted primarily of petrol and diesel. Although liquefied petroleum gas (LPG) has been used as an alternative transport fuel, its share in terms of consumption in 2009 is only about 0.3%. Petrol usage peaked at 24.3 million tonnes in 1990 but has since been continuously on a downward trend. In 2009, the consumption of petrol was 35.2% lower than the peak level recorded. While historically, therefore, road transport fuel has been dominated by petrol, this trend has recently changed. 33

Figure 2.1 Road transport fuel consumption in the UK Source: Department of Energy and Climate Change

There has been a substantial change in fuel consumption trends that reflects a long-term shift towards diesel. After plateauing during the 1970s and early 1980s, diesel utilization has been on an increasing trend until 2007. Consumption of diesel reached a peak of 21.07 million tonnes in 2007 before declining by 4.8% in 2009. The outcome of the diverging trends in petrol and diesel usage has resulted in diesel fuel deliveries surpassing petrol in terms of mass in 2005 making diesel the primary road transport fuel consumed. This trend has since continued into 2009 and diesel consumption now accounts for 55.8% of all petroleum based fuel consumed in the road transport sector.

2.3 ROAD VEHICLES STATISTICS: CHARACTERISTICS AND USAGE The change in the fuel consumption trend discussed in the previous section can largely be attributed to the growth of the diesel vehicle fleet. As a proportion, diesel vehicle share has been on the rise since 1982. The main reason for the increasing penetration of diesel vehicles in terms of market share is due to the technical advantage that diesel vehicles have over their petrol counterparts (Jeong et al., 2009). In principle, diesel vehicles are much more efficient if compared directly to petrol vehicles of a similar output. On a matched pair basis, Schipper and Fulton (2009) pointed out that diesel vehicles have an average efficiency advantage of about 25%.

Figure 2.2 Road transport vehicle stock categorised by fuel type Source: Department for Transport

As can be seen from Figure 2.2, the amount of diesel vehicles as a proportion of the road transport fleet has been increasing on an annual basis. Even after the 2007 economic crisis, where total vehicle growth began to plateau, diesel vehicle stock growth has remained consistent. In comparison, petrol vehicle stock peaked at an all-time high of 24.56 million vehicles in 2004 before falling continuously in the following years up to 2009. 35

Table 2.1 Share of petrol and diesel vehicles in the UK vehicle fleet

1980 1990 2000 2009 Total vehicle stock 19,209,870 23,673,450 28,897,600 34,257,529 % share of petrol 93.26 89.33 79.02 64.82 vehicles % share of diesel 6.46 10.48 20.84 34.66 vehicles Source: Own calculations

Table 2.1 shows a comparative perspective of the total road transport fleet. It can be seen that the growth in diesel vehicles has come at the expense of the petrol fleet. As a proportion, the share of petrol vehicles has declined from a high of 93.26% in 1980 to 64.82% of the vehicle fleet in 2009. On the other hand, the share of diesel vehicles in the vehicle fleet has increased significantly, rising to 34.66% in 2009 from 6.46% in 1980. The shift in the share of diesel vehicles accelerated in 2004 when the petrol vehicle stock started to record a decline. A probable reason for the decline in petrol vehicle stock is possibly the result of substitution due to consumers’ preference for diesel vehicle. In addition, the economic downturn may have also contributed in accelerating the process.

Table 2.2 Diesel car share statistics

Annual 1994 2000 2004 2009 growth Diesel car stock ( x 1,000) 1,576.2 3,152.7 5,010.6 7,641.4 11.11% % share of diesel fleet 42.89 52.34 58.06 64.36 - % share of car fleet 7.44 12.92 18.54 27.05 - Source: Department for Transport

The dieselisation of the vehicle fleet was largely driven by the rapid increase in the diesel car stock. The data from Table 2.2 shows that between 1994 and 2009, the number of diesel cars increased by nearly 485%, or at an average growth rate of 11.1% annually. In the same period, petrol cars recorded an increment of 4.4%, with the amount of petrol cars peaking at 2004 before continuously declining in the following years. Dieselisation of the car fleet has also resulted in it becoming a major factor in the vehicle stock. As a proportion, it has grown from only 7.44% of 36

the car fleet in 1994 to more than a quarter (27.05%) in 2009. Currently, diesel cars account for 64.4% of all diesel vehicles.

2.3.1 Behavioural Differences: Fact or Fiction? In §1.2, the possibility of behavioural differences between petrol and diesel vehicle users was discussed. It was suggested that this dissimilarity is likely to cause differences in the demand response when price and income changes. In their analysis of automobile use in Europe, Schipper (2011) noted that diesel buyers do not buy matched pairs, instead they buy larger and more powerful vehicles. In addition to the above, diesel users apparently drive their cars further.

Based on the points above, we look for similar signs of behavioural differences in the UK by examining the driving patterns as well as whether the tendency of switching to bigger vehicles exists. Table 2.3 provides a comparison of annual car mileage differentiated by the fuel type consumed.

Table 2.3 Annual vehicle-km of cars categorised by fuel type

Year Petrol Diesel Petrol and diesel 1995/97 14,677 25,621 15,595 1998/00 14,581 21,903 15,369 2002 13,808 20,600 14,758 2003 13,663 21,292 14,838 2004 13,470 21,404 14,726 2005 13,100 20,793 14,500 2006 12,553 20,342 14,098 2007 12,601 20,519 14,275 2008 12,360 19,586 13,953 2009 11,957 18,620 13,551 2010 11,861 18,572 13,551 Source: DfT National Travel Survey

From the table above, it appears that there are differences in the driving trends as measured in terms of vehicle-km between petrol and diesel users. At its peak, diesel cars are driven 76% more per year than a petrol car. Although the average 37

driving distance in 2010 has declined from the peaks recorded in 1995/97, on average a diesel car is still driven further, at a distance of 18,572km as compared to 11,861km reported for petrol cars.

Table 2.4 Percentage share of licensed diesel cars categorised by engine capacity

1- 1,001- 1,551- 2,001- 2,501- 3,001cc+ Unknown Total 1,000cc 1,550cc 2,000cc 2,500cc 3,000cc 1994 0.3 6.1 77.5 12.0 2.8 1.3 - 100 2000 0.1 5.9 75.8 12.6 4.4 1.3 - 100 2005 0.1 7.6 69.5 14.2 7.0 1.6 - 100 2009 0.1 9.6 65.7 14.4 8.8 1.4 - 100 Source: DfT Vehicle Licensing Statistics

Apart from the fact that diesel cars are found to be driven further, there is some evidence that the tendency of switching to a much bigger diesel powered car (instead of a matched pairs) as previously seen in Europe.9 For example, 83.9% of all licensed diesel powered cars were of the 1 – 2,000cc engine capacity categories in 1994. However, this figure has declined to 75.4% in 2009 indicating that there is the probability that preference has indeed changed towards bigger diesel cars.

Table 2.5 Percentage share of licensed petrol cars categorised by engine capacity

1- 1,001- 1,551- 2,001- 2,501- 3,001cc+ Unknown Total 1,000cc 1,550cc 2,000cc 2,500cc 3,000cc 1994 10.3 40.1 42.7 3.0 2.3 1.5 - 100 2000 7.1 38.8 45.6 3.8 2.5 2.2 - 100 2005 5.8 38.2 46.0 4.5 2.6 2.8 - 100 2009 6.1 39.6 44.7 4.1 2.5 3.0 - 100 Source: DfT Vehicle Licensing Statistics

When we extend the analysis to include petrol vehicles, a similar pattern as observed with diesel car appears to exist. We found in 1994, 93.1% of all licensed petrol cars fell under the 1 – 2,000cc categories. In comparison, the figure declined slightly to 90.4% in 2009. From the data, it looks like the shift towards bigger and

9 Zachariadis (2011) defines the term ‘matched pairs’ as two model versions with similar attributes such as mass, engine size, power, torque with the difference being the type of engine being used i.e. diesel or petrol. 38

more powerful cars is not exclusively limited to diesel cars only, although in the case of petrol cars, the shift is less profound.

It is difficult to decide conclusively, whether such behavioural-utilisation differences, really exists based solely on the data above. This is because, in comparison to the analysis of Schipper (2011) and Schipper and Fulton (2009), the statistics above are not as comprehensive. On the surface, the results, give the impression that there is some evidence to believe that diesel users behave differently as compared to their petrol counterpart. At the very least, analysis of the data confirm that the trends Schipper observed in France and Germany do appear to exist in the UK as well.

2.4 SUMMARY This chapter provides some context and statistical background to the changing trends affecting the road transport sector. It touches upon the changing fuel consumption trends as well on the underlying changes in the market structure of vehicle ownership. The main feature that can be observed is that there are structural changes taking place.

First, it is important to note that there appears to be a clear shift away from petrol fuel in the transport sector. While petrol fuel consumption continues to fall, the opposite is taking place with the consumption of diesel fuel. As a result of these contrasting trends, diesel has now become the dominant fuel (in terms of mass) in the road transport sector. The statistics also indicate that the driving factor for the change in fuel demand is the shift in consumers’ preference towards diesel powered vehicles. This is particularly apparent if taken from the pace of growth in the diesel car fleet.

The chapter also reviewed some statistics with regards to driving and car ownership trends. Although it cannot be conclusively confirmed, the data does provide some evidence of behavioural differences between petrol and diesel users. In terms of this research, the chapter provides an important context for the issue being investigated. Since structural and behavioural changes in fuel consumption appear to exist, it provides grounds to continue the estimation of separate elasticities for road transport fuel.

CHAPTER 3 FUEL DEMAND ELASTICITY MODELLING: A REVIEW OF

ECONOMETRICS AND METHODOLOGICAL ISSUES

3.1 INTRODUCTION This chapter presents a review of the econometric approaches and methodological issues in road transport fuel demand modelling. Because of the relevance to this research of obtaining fuel demand elasticity estimates, this chapter will review the method through which these estimates are derived, especially with respect to price and income. Since demand for road transport fuel affects a broad range of policy issues there are a wide variety of estimates in the literature, each approaching the task of estimation from these differing policy perspectives. Depending on the research context, variation in the estimates can be attributed to the use of different functional forms, estimation techniques, independent and dependent variables, types of data and environmental characteristics (Basso and Oum, 2007).

Since the validity and confidence in the forthcoming analysis of fuel demand responses in the UK is critically dependent on the adoption of a sound methodological approach to the estimation of fuel demand elasticities, it is clear that establishing the appropriate ways of modelling these elasticities must take precedence. Apart from the above, the objective of this review chapter is also to identify the most appropriate model specification for use in this research for estimating fuel demand elasticities, both for the time series and panel data models.

Since the literature is replete with numerous models, applying differing specifications and estimation techniques, this chapter approaches the issue by highlighting the important criteria to be considered when modelling fuel demand. The structure of the chapter follows the precedence set by previous 41

methodological review studies in which the estimation of fuel demand is distinguished through three different measures, namely: the demand model specification; the data characteristics; and the contextual characteristics (see Basso and Oum, 2007; Wohlgemuth, 1997; Blum et al., 1988). In addition, we also look at estimation issues with regards to both the time series and panel data models.

The chapter is therefore structured as follows. Section 3.2 provides a detailed review of the issue of model specification. This section is further divided into subsections that focus on matters such as the choices of quantity measures and the functional forms that can be applied. Concerns regarding data and contextual characteristics are addressed in Sections 3.3 and 3.4. In Section 3.5, issues with time series models are discussed, while matters regarding panel data models are explored in Section 3.6. Finally, Section 3.7 concludes the review on the methodology and econometric approaches to fuel demand modelling.

3.2 MODEL SPECIFICATION The process of model specification is usually preceded by the selection of the measure in which fuel demand is to be quantified. In the literature, numerous measurements for the dependent variable have been used for modelling fuel demand. The most commonly found quantity measures include fuel consumption per capita (see Bentzen, 1994; Ramanathan, 1999; Wadud et al., 2009a) , total (aggregate) fuel consumption (see Birol and Guerer, 1993; De Vita et al., 2006; Li et al., 2010), fuel consumption per vehicle (see Baltagi et al., 2003; Crôtte et al., 2010; Pock, 2010), fuel per household (see Santos and Catchesides, 2005; Wadud et al., 2009b) and, to a lesser extent, fuel consumption per kilometre (see Johansson and Schipper, 1997; Barla et al., 2009; and Karathodorou et al., 2010).10

The first step in deriving an estimate begins by specifying the econometric equation. According to Studenmund (2010) the process of specifying an equation involves choosing the potentially correct independent variables, the correct functional form and the correct form of the stochastic error term. In most of the literature, however, there is a focus on the first two factors since issues with the stochastic error term can often be resolved through the use of appropriate independent variable and econometric estimation and testing techniques.

The primary consideration in deciding whether an independent variable belongs in an equation is whether the variable is essential on the basis of theory. In road transport fuel demand estimation, the independent variables used have primarily revolved around variants of own price, substitute price and income.11 Depending on the context, the explanatory variables have also included measures of automobile ownership, vehicle characteristics and dummy variables, as well certain geographical and demographic characteristics (Blum et al., 1988; Espey, 1998).

10 According to Espey (1998), the quantity measure applied does not appear to result in a significant variation in the estimates. Some reviewers, however, prefer the per capita measure on the basis that this accounts for the effect of population growth, especially in models without any form of population variable (see Chapter 6 for further details). 11 For example, the income variable has been represented by GDP, GDP per capita, disposable income, expenditure, etc. 43

The inclusion of additional exogenous variables is not without issues, however. Basso and Oum (2007) suggest that care must be taken when including additional exogenous variables since there is evidence that they may only capture short-run elasticities. On the other hand, excluding them may not be without issues either, since this may result in their effect being captured by price and income elasticities (Blum et al., 1988). Worse still, exclusion of important explanatory variables may lead to the serious problem of omitted variable bias. As such, selecting the appropriate independent variables has always been an important dilemma to be faced early in the model specification process.

In the estimation of fuel demand elasticities, the preferred approach in both the academic and non-academic literature has been reduced-form demand models using aggregate data (Hughes et al., 2008; Basso and Oum, 2007).12 This is favoured because its application is extremely practical. The simplest form of a reduced-form model, as in Equation (3.1), basically implies that fuel demand (F) is a function of price (P) and income (Y).

퐹 = 푓(푃, 푌) (3.1)

In terms of application, the reduced form model gives a direct but static estimation of fuel demand. The model can be extended to include other determinants (X) of fuel demand, but price and income variables are always included in some form since models without them are considered to be mis-specified (Dahl and Sterner, 1991).

퐹 = 푓(푃, 푌, 푋) (3.2)

12 Alternatively, fuel demand can also be indirectly estimated through what is termed as a structural equation approach. In a structural model, the right-hand components of fuel demand (i.e. driving distance, vehicle stock and fuel efficiency) are decomposed into separate but interdependent models, with fuel demand then estimated indirectly. In the literature, studies using the structural model are less prevalent compared to the reduced-form demand model. While they are certainly more informative in providing information on the response process, this approach is data intensive and, as such less, popular among researchers. In the meta- analysis by Espey (1998), less than 3% of the elasticity estimates analysed used the indirect approach. Nonetheless, Espey found no statistically significant difference between the results derived from indirect and direct reduced-form models. 44

The main limitation of the static model is that it assumes that the equilibrium between fuel demand and the independent variables takes place instantaneously, whereas in actuality this may not necessarily be the case. Because behavioural changes, in this case fuel consumption, may take time to take effect when its determinant changes (e.g. an increase in price); static models would not fully capture the adjustments.13 This has led to authors classifying estimates of the elasticity from static models as intermediate-run in nature (Goodwin, 1992).

If we are to assume that changes do not occur immediately, and that today’s fuel consumption is also a function of earlier changes in income and price, then the appropriate way of modelling this would be through the use of dynamic models. The dynamic model in Equation (3.3) is used when it is believed that response to fuel demand will take time.

퐹푡 = 푓(푃, 푃푡−푖, 푌, 푌푡−푖푋, 푋푡−푖) (3.3)

The simplest way of capturing this temporal aspect of behavioural inertia is through a dynamic model called the partial adjustment model. The partial adjustment model is currently widely used in estimations involving dynamic behaviour. A popular way of modelling the temporal aspect of adjustments is by including a lagged fuel demand (endogenous) variable on the right-hand side of a fuel demand equation, as in Equation (3.4). The model known as the lagged endogenous model is particularly popular in the literature. In a log-linear functional form, the coefficients 훽 and 훾 conveniently give the short-run elasticities, while the long run elasticities can be obtained by dividing them with (1 − 훿) (Basso and Oum, 2007).

퐹푡 = 훼 + 훽 ⋅ 푃푡 + 훾 ⋅ 푌푡 + 훿 ⋅ 퐹푡−1 (3.4)

13 The assumption that there is inertia in fuel consumption when there are changes to exogenous variables such as price and income is perfectly rational. In the short-run, consumers’ response options may be limited but over the long-run it is reasonable to expect response to include a wide variety of measures such as replacing vehicles and moving residential location. 45

Another form of the dynamic model is the distributed lag model, as specified in Equation (3.5). This model assumes that the current value of fuel consumption

(퐹푡) is a function of the current and past values of price (푃푡−1) and income (푌푡−1). The benefits of this model are that it gives more flexibility in estimating the impact of inertia and also allows for the short-run and long-run elasticity to be obtained and distinguished (Basso and Oum, 2007). Its drawback, however, is that estimation can be restricted when the sample size is small, especially when involving too many parameters. The model can also suffer from severe multicollinearity, thus affecting the precision of estimates (Studenmund, 2010; Kennedy, 2008). Although there are various forms of the distributed lag model, its usage has been limited by the use of the more convenient lagged endogenous model.

푞 푟

퐹푡 = 훼 + ∑ 훽푖 ⋅ 푃푡−푖 + ∑ 훾푖 ⋅ 푌푡−푖 (3.5) 푖=0 푖=0

It is also quite common in fuel demand literature using aggregate data to see the inclusion of an exogenous variable to represent the effect of vehicles on fuel demand. Some authors have hypothesised that since driving distance, vehicle number (V) and vehicle characteristics (VC) affect fuel demand behaviour, such factors should be included in any fuel demand equations (Graham and Glaister, 2002; Baltagi and Griffin, 1983). This model is often referred to as the vehicle stock or vehicle characteristics model and it takes these aspects into account by including variables such as car ownership, vehicle characteristics (in the form of fuel efficiency, engine size or weight) and even the usage of alternative transport (Graham and Glaister, 2002; Espey, 1998; Dahl and Sterner, 1991).

퐹 = 푓(푃, 푌, 푋, 푉, 푉퐶) (3.6)

The next consideration in specifying the model will be in deciding the functional form of the relationship between the independent and the dependent variables 46

(Studenmund, 2010).14 Similar to selecting the explanatory variables, choosing the correct functional forms depends very much on the theoretical considerations. Apart from providing the mathematical basis of the relationship, the functional form selected may also affect the derivation of the elasticity estimates from the model. Additionally, the chosen functional form imposes certain constraints on how the parameter of interest varies in response to any changes to the explanatory variables. Although there is no clear cut direction on the matter of the selection of the functional form, a propensity towards the use of the log-linear form is evident in the literature on the estimation of fuel elasticity.

Applying the log-linear functional form to the fuel demand function as in Eq. (3.1), the model can now be expressed as:

ln퐹푡 = 훼 + 훽 ⋅ ln푃푡 + 훾 ⋅ ln푌푡 + 휀푡 (3.7)

As described above, the log-linear functional form appears to be the most widely used formulation in the literature. This is due to its ease of use in terms of estimation, and because it allows the parameters to be straightforwardly interpreted as elasticity. In the model, the parameters 훽 and 훾 represent the

elasticity of fuel demand with respect to price (휂푝) and income (휂푌).

The main criticism levelled at the log-linear form is that it is restrictive from a theoretical perspective since it assumes that the elasticities estimated remain constant for all values of price and income. Although the log-linear model may seem restrictive, Pesaran et al. (1999) argued that it often provides good approximation of the observed data (in energy demand models) and generally outperforms specifications that are more complex.

The linear functional form model is an alternative to the log-linear formulation that allows for the estimation of non-constant fuel demand elasticities. The linear

14 The functional forms that can be used to describe the relationship between the dependent and independent variables include the log-linear, linear, semi-log and translog forms. 47

functional form assumes that fuel demand elasticities will vary linearly to price and income and inversely to consumption. The linear model can be specified as:

퐹푡 = 훼 + 훽 ⋅ 푃푡 + 훾 ⋅ 푌푡 + 휀푡 (3.8)

In the linear model, the price and income elasticities of fuel demand are:

푃 푌 휂 = 훽 ∙ 푎푛푑 휂 = 훾 ∙ (3.9) 푝 퐹 푌 퐹

As with the log-linear model, the linear model is also restrictive from a theoretical perspective since the value of both price and income elasticities are assumed to continuously increase as both variables increase in value. It is therefore common in the literature to see both models referred to as ad-hoc models, to acknowledge their limited theoretical foundation (Zarnikau, 2003).

An alternative specification that has greater flexibility and that may also have some theoretical basis, is the translog model. The translog model for fuel demand is specified as:

2 2 ln퐹푡 = 훼 + 훽1 ⋅ ln푃푡 + 훽2 ∙ (ln푃푡) + 훾1 ⋅ ln푌푡 + 훾2 ∙ (ln푌푡) + 휓 ∙ (ln푃푡 ∙ ln푌푡) + 휀푡 (3.10)

The translog model includes additional terms for the explanatory variables in quadratic formulation, as well as an interaction between the variables. The inclusion of the quadratic form is useful since, in the literature, it is often applied to capture the decreasing or increasing effects of an increment in the explanatory variables (Asteriou and Hall, 2011; Wooldridge, 2009). For example, the quadratic formulation has a theoretical basis since it has been argued that income elasticity tends to decline at a higher level of income (Kayser, 2000). Similarly, the inclusion of the interaction term in the translog model can also be theoretically justified on 48

the basis that the elasticity of fuel demand with respect to price, for example, will also depend on the magnitude of income, and vice versa.

For the translog functional form, the price and income elasticities are:

휂푝 = 훽1 + 2훽2ln푃푡 + 휓ln푌푡 푎푛푑 휂푌 = 훾1 + 2훾2ln푌푡 + 휓ln푃푡 (3.11)

Basso and Oum (2007) stated that in fuel demand elasticity models there is flexibility of choice since the form used has not been a major issue. Evidence from Sterner and Dahl (1992) and Espey (1998) indicates there is little difference between estimates arrived at using different functional forms. In practice, the log- linear functional form is mostly used in preference to the linear form because it directly computes elasticity and may provide a better fit than linear equations (Dahl, 1995).

3.3 DATA CHARACTERISTICS Apart from model specification, the fuel demand literature also highlights the importance of data. It is well understood that empirical models depend on the availability and quality of the data but, additionally, in fuel demand estimation, the type of data being used will also have influence on the estimates (Basso and Oum, 2007; Goodwin et al., 2004; Espey, 1998; Dahl and Sterner, 1991).

Data types can be divided into time series, cross-section or panel. Time series data comprises of observations over a long period of time (e.g. UK fuel demand over 20 years); cross-sectional data is data of a variable collected across different subjects in a period of time (e.g. fuel demand for European countries in a single year); panel data, which is also known as cross-sectional time-series data, is a combination of both the elements of time series and cross-section data (e.g. fuel demand for various European countries over 20 years). The appropriateness of each type of data depends on the nature of the study being conducted. For example, Basso and Oum (2007) stated that cross-sectional data may not be appropriate for models that take time into account, a factor that is not a hindrance for time series and panel data.

Another way of categorising data is through its quantity measure: aggregate (the combination of various individual elements of data, e.g. national level fuel consumption) or disaggregate (data made up at the individual/household level). In terms of application in the literature, time series studies are normally aggregate in nature and are used to study demand responsiveness at the national or regional level. Disaggregate data on the other hand enables researchers to understand behavioural response due to socio-economic factors. Since aggregate data is often readily available as compared to the others, time series based studies are much more common in the literature.

Apart from the above, the data type used can also be categorised in terms of the periodicity/interval. Especially in time series studies, it is quite normal to see the data being distinguished as being monthly, quarterly and yearly. There are 50

contrasting findings, however, in terms of the effects of the use of different periodicity data on the elasticity estimates. Dahl and Sterner (1991) concluded that seasonal data is inappropriate for long-run adjustments, but this conclusion is not shared by Espey (1998), who theorised that the effects seen by Dahl and Sterner may be more related to model specification rather than the data periodicity. In practice, however, the use of monthly or quarterly data does introduce seasonal variations and, as such, care must be taken when using them in a model.

To conclude, it is important to be aware that any estimates produced are highly dependent on the type of data used. These variances in the estimates can be attributed to the characteristics of the data used. Although scholars differ on the influence of these data characteristics the contribution of survey literature such as Basso and Oum (2007), Goodwin et al. (2004) and Graham and Glaister (2002), are still invaluable since they provide an idea as to the outcome that may be obtained.

3.4 CONTEXTUAL CHARACTERISTICS It can also be observed that elasticity estimates tend to differ according to the contextual characteristics of the study.15 Espey (1998) and Goodwin et al. (2004) highlighted this in their literature surveys, suggesting that it is inappropriate to make generalised assumptions when it comes to fuel demand elasticity.

Among the environmental characteristics that differentiate studies are the level of the data (e.g. panel, state, regional or national level data), the geographical locations and the time frame of the datasets (e.g. before 1974, between 1974 to 1981 and after 1981). For example, Goodwin et al. (2004) found in their survey that price elasticities were higher during the 1974-1981 period compared to periods after it. A similar outcome was also noticed by Hughes et al. (2008) when looking at the shift in fuel elasticities in the US, and Hughes et al. go on to stress the need to consider the temporal aspects of elasticity studies, pointing out that there has been a huge change in consumer responsiveness due to behavioural and structural factors. It is interesting to add that estimates between countries also differ quite considerably, as shown in a recent survey by Dahl (2011) that catalogues elasticity estimates in 124 countries.

In summary, the spatial and temporal aspects of studies, or what is usually defined as the contextual characteristics, indicate that fuel demand elasticities are subject to change. In the context of this research, this implies that it is worthwhile attempting to estimate fuel demand elasticity in order to capture the changes in responsiveness due to current structural and behavioural factors.

15 Espey (1998) uses the term environmental characteristics to similarly describe the contextual nature of the data. Accordingly, the words environmental characteristics and contextual characteristics are used interchangeably in this thesis. 52

3.5 TIME SERIES MODELS: RECENT ESTIMATION ISSUES Based on the survey of the literature presented here, it is evident that fuel demand estimation appears generally to be dominated by time series models. This is not surprising, since as stated before, the greater availability of time series data makes it easier for researchers to utilise time series models. Upon further investigation however, it is also evident that estimates derived from these earlier studies may be questionable.

Recent studies, for example, have highlighted concerns in regard to the estimation of fuel demand elasticities using time series data. These revolve around the tendency of time-series data, especially in large samples, to produce spurious outcomes if trends and stationarity are not tested for and taken account of (Wooldridge, 2009; Hendry and Juselius, 2000). Our review of the literature appears to indicate that this issue might raise significant doubts about the validity of past estimates, since it appears that, traditionally, time series studies have often been contingent on the assumption of stationarity (see Banaszak et al., 1999; Al- Faris, 1997; Birol and Guerer, 1993). In light of this, we feel that it is appropriate that this issue is given further attention and the next subsection is therefore dedicated to providing additional discussion on this matter.

3.5.1 Non-stationarity, Co-integration and Error Correction Models Time-series data, especially in economics and finance, have a tendency of growing over time. The use of dependent and independent variables that are affected by the same underlying trend may result in regression that appears to be significant, leading to a false (spurious) conclusion of a causal relationship. Running a regression on spuriously correlated series will often result in an overstated, and ultimately unreliable, fit.

Econometric theory assumes that observed data is stationary. In a stationary time series, the mean and variance would remain constant and that the covariance between two points is dependent on the time distant between them and not on the time period itself (Basso and Oum, 2007; Hendry and Juselius, 2000). If one or 53

more of these properties are not met, then the series is non-stationary and the problem is referred to as non-stationarity (Wooldridge, 2009; Kennedy, 2008).

In order to overcome spurious regression, non-stationary series can be made to be stationary through an appropriate process of transformation. This depends on whether the series are difference stationary or trend stationary (Wooldridge, 2009). A difference stationary series can be made to be stationary by differencing the series. If stationarity is achieved after the first differencing, the series is integrated to the order of 1 or denoted as I(1). In the event that it takes two lots of differencing to induce stationarity, the series is integrated to the order of 2 or I(2). A trend stationary series, on the other hand, is stationary around a trend line. To make it stationary, the series is simply time detrended. As mentioned, the transformation process should be based on the series’ stationary process since mishandling the treatment will result in specification errors. A time series that is difference stationary but is detrended results in under-differencing, while a time series that is trend stationary but is differenced will cause over-differencing (Gujarati and Porter, 2009).

In the estimation of fuel demand elasticities, the presence of non-stationarity poses a challenge. If both the dependent variable and independent variable series are I(1), regressing them may lead to the spurious regression problem. While differencing may induce stationarity, it creates another problem since we now lose the ability to obtain a level estimation of the relationship between the variables. Fortunately, recent work on time-series suggests that this can be avoided if both the series are co-integrated (see Engle and Granger, 1987).

Empirical studies into the properties of time-series indicate that it is possible for the underlying stochastic trend to be shared by two variables with the effect that regressing them is not necessarily spurious. This implies that although the variables are individually I(1), their linear combination is I(0) or, in another words, stationary. In such an event, the variables are said to be co-integrated, and this implies that 54

they have an equilibrium relationship in the long-run (Hendry and Juselius, 2000); Engle and Granger, 1987).

This finding is important and has a convenient implication in the context of fuel demand estimation. First of all, if variables are co-integrated, we are able to avoid the problems associated with non-stationarity; regressing these variables will now be valid and will also convey important economic information (e.g. there is a long- run equilibrium relationship). From the context of estimation, regressing cointegrated variables is also convenient because the parameters can be interpreted as the long-run elasticities and the estimate will be super consistent. Furthermore, co-integrated variables exhibit an error correction mechanism which, when used with an Error Correction Model (ECM), will enable not only the estimation of the short-run elasticity but also the speed of adjustment. The following is an example of an ECM for estimating fuel demand elasticity:

Δln퐹푡 = 훼 + 훽 ⋅ Δln푃푡 + 훾 ⋅ Δln푌푡 + 휆 ⋅ 푒푡−1 + 휀푡 (3.12)

where 푒푡−1 is the error obtained from regressing F with P and Y (i.e. 푒푡−1 =

ln퐹푡−1 − 훼 − 훽ln푃푡−1 − 훾ln푌푡−1) and 휀푡 is a white noise term.

Equation (3.12) states that Δln퐹푡 is dependent not only with Δln푃푡 and Δln푌푡 but

also with the equilibrium error term, 푒푡−1. As such, when the variables are cointegrated, the ECM equation (3.12) exhibits both the long-run and short-run properties of the relationship. The coefficients 훽 and 훾 are the impact multipliers that measure, in this case, the short-run elasticity of price and income respectively.

The long-run property of the relationship is represented by the inclusion of 푒푡−1, in which 휆 (the adjustment coefficient) signifies the speed of adjustment that takes place to correct the disequilibrium towards the long-run equilibrium.16

16 For the properties to remain valid in the ECM, we assume that the coefficient 휆 < 0 and is statistically significant. 55

In terms of interpretation, the properties exhibited by the ECM are also sensible from an economic equilibrium concept. For example, suppose that both 훽 = 0 and 훾 = 0 but the equilibrium error term is not, then the model is out of equilibrium. In the case that 푒푡−1 is negative, it implies that there is disequilibrium, where ln퐹푡−1 is below its equilibrium level of ln퐹푡−1 − 훼 − 훽ln푃푡−1 − 훾ln푌푡−1. However, since 휆 is negative, the term 휆푒푡−1 will be positive and, as such, Δln퐹푡 will also be positive, serving to revert to the equilibrium. This shows that if ln퐹푡−1 is below the equilibrium then, through the ECM mechanism, ln퐹푡−1 will increase in the next period to correct the equilibrium error; hence the term error correction model (Asteriou and Hall, 2011; Koop, 2009). The opposite will also hold true in the event that 푒푡−1 is positive.

3.6 PANEL DATA REGRESSION MODELS Another feature that has been observed relatively recently in the literature on the estimation of fuel demand elasticity is the growing use of panel data regression. The panel data model, which allows for the inclusion of data for 푇 time periods (e.g. months, quarters, years, etc.) and 푁 cross-sections (e.g. individuals, firms, countries, etc.) is being increasingly widely used since it is considered to be a much more efficient analytical method for handling econometric data (Baltagi, 2008).17 A simple panel model can be specified as:

퐹푖푡 = 훼 + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + 푣푖푡 (3.13) 𝑖 = 1, 2, … , 푁 푡 = 1, 2, … , 푇

where i is the ith cross-sectional units and t is the time period for the variables F, P and Y previously defined.

The panel model specified by Equation (3.13) is also known as the pooled OLS regression, or constant coefficients, model. The use of panel data as in the model specified is problematic, however, and may in fact be no more preferable than a time series regression (Basso and Oum, 2007). As the name implies, the model assumes that the coefficients are common (homogeneous) for all cross-sectional units (i.e. household groups) and for all years. No distinction is made to account for any uniqueness (heterogeneity) that may exist since the model subsumes any

heterogeneity in the disturbance error term, 푣푖푡 (Gujarati and Porter, 2009). Although this may be useful if the data set is assumed a priori to be homogeneous, it is quite restrictive, especially in the context of this research. Pesaran and Smith (1995) argued that such an assumption is highly implausible for energy consumption while Basso and Oum (2007) stated that the model’s usefulness in policy analysis may be limited if the heterogeneity of any group is not captured.

17 There are variations in the types of panel data (e.g. pooled time series – cross-sectional data, micropanel data, longitudinal data, etc.) but, in general, they all consist of observations of cross-sectional units over time. 57

In terms of estimation, subsuming the heterogeneity in 푣푖푡 is also not without its consequences. In a lot of cases, it is possible that these (heterogeneity) factors have an important influence on the response elicited when there are changes to P and Y. Some of these factors may be readily apparent, such as gender and age (for individuals) or geographical size and natural resources (for countries), but there may also be other unobserved factors that may be difficult to account and control for (Wooldridge, 2009).18 In such cases, the coefficients estimated in Equation (3.13) may be biased and inconsistent since the equation implies that the error 19 term, 푣푖푡 is correlated with the regressors.

Assuming that there is a time-constant unobserved effect that needs to be accounted for, an indirect way to account for this is by specifying Equation (3.13) as:

퐹푖푡 = 훼 + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + 휖푖 + 푢푖푡 (3.14)

where the disturbance error term, 푣푖푡 = 휖푖 + 푢푖푡 is a composite error containing 휖푖,

the unobserved heterogeneity (time-constant) effect and 푢푖푡, the remainder disturbance (a classical error term).20

In Equation (3.14), the variable 휖푖 is time-constant and captures all unobserved

cross-sectional specific effects that affect 퐹푖푡. For example, if the cross-sectional units are countries, these unobserved effects can be their respective land area or geographical features which, although they might differ between the units, are unlikely to change over time. Although Equation (3.14) manages to account for the

unobserved heterogeneity, however, there is a possibility that 휖푖 is correlated with

푃푖푡 and 푌푖푡, resulting to what is defined as heterogeneity bias (Wooldridge, 2009).

18 There are two types of unobserved factors: those that are cross-sectional specific (constant over time) and time-specific (constant over cross-sections). 19 This goes against the Classical Assumption which states that all regressors are uncorrelated with the error term. 20 The composite error 푣푖푡 = 휖푖 + 푢푖푡 is also known as the one-way error component model. Similarly, a two- way error component can also be utilised where the composite error, 푣푖푡 = 휖푖 + 휆푡 +푢푖푡 in which 휆푡 is an unobserved time-specific (cross-sectional constant) effect. 58

Since this violates the Classical Assumption of the linear regression model, in order to fully overcome the problem of unobserved heterogeneity, two alternative (and more appropriate) approaches, known as the fixed effects model and the random effects model, can be utilised.

The fixed effects model is appropriate if the focus is on a specific set of N cross- sectional units (e.g. firms, countries or, in this research, different household- income groups) and if the inference is restricted to the behaviour of these cross- sectional units (Baltagi, 2008). Gujarati and Porter (2009) argued that the fixed effect model is also more efficient if 휖푖 and the regressors are assumed to be correlated and when N is small and T is large.

There are three approaches to the fixed effects regression. The first, which is known as the least-squares dummy variable (LSDV) model allows for heterogeneity by explicitly incorporating the unobserved effect in the form of an individual intercept for each cross-sectional unit. This can be shown by rewriting Equation (3.14) as:

퐹푖푡 = 휖1 + 휖2 ∙ 퐷2푖 + … + 휖푁 ∙ 퐷푁푖 + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + 푢푖푡 (3.15)

where the intercept dummy 퐷2푖 = 1 for a cross-sectional unit 2 and 0 otherwise, and where 퐷푁푖 = 1 for the N-th cross-sectional unit and 0 otherwise. In Equation

(3.15), 휖1 is treated as the base, representing the intercept of cross-sectional unit 1 and the sum (휖1 + 휖푁) provides the intercept value for the N-th cross-sectional unit.

An alternative approach to the LSDV model is the within-group (WG) estimator. In this approach, the unobserved heterogeneity effects are eliminated by expressing the values of the dependent and explanatory variables of the cross-sectional units as deviations from their respective mean values (Gujarati and Porter, 2009). This can be written as:

퐹푖푡̈ = 훽 ∙ 푃푖푡̈ + 훾 ∙ 푌푖푡̈ + 푢̈ 푖푡 (3.16)

where 퐹푖푡̈ = 푡ℎ푒 푡𝑖푚푒 푑푒푚푒푎푛푒푑 퐹 = 퐹푖푡 − 퐹̅푖, 푃푖푡̈ = 푡ℎ푒 푡𝑖푚푒 푑푒푚푒푎푛푒푑 푃 =

푃푖푡 − 푃̅푖 and similarly for 푌푖푡̈ and 푢̈ 푖푡 respectively.

It should be noted that although the within-group estimator in Equation (3.16) may appear to be similar to the pooled OLS model in Equation (3.13), the important difference is that the former takes heterogeneity into account by removing the unobserved effects, whereas the latter ignores them altogether. A drawback of the within-group estimator is that although it produces consistent slope estimates they may not be efficient. More importantly, the removal of the time-constant heterogeneity effect means that the model can no longer include any (important) explanatory variables that are constant over time (Wooldridge, 2009).

The third fixed effects approach is known as the first-differenced estimator. In this approach the unobserved effect, 휖푖, is similarly removed as with the within-group method. As the name implies, however, this is done by differencing away (i.e. subtracting the first observation of a variable for a given cross-sectional unit from the second observation).

Δ퐹푖푡 = 훽 ∙ Δ푃푖푡 + 훾 ∙ Δ푌푖푡 + Δ푢푖푡 (3.17)

where Δ퐹it = 퐹푖푡 − 퐹푖푡−1 and similarly for Δ푃푖푡, Δ푌푖푡 and Δ푢푖푡 respectively.

As with the within-group estimator, the first-differenced estimator in Equation (3.17) is not without its problems. Similarly, as before, the differencing procedure removes the possibility of including any time-constant explanatory variables in the model. Furthermore, although the original disturbance term (푢푖푡) may not be autocorrelated, the differencing procedures means that ∆푢푖푡 is, since ∆푢푖푡 = 푢푖푡 −

푢푖푡−1 (Gujarati and Porter, 2009). This poses an estimation problem, although if the 60

explanatory variables are strictly exogenous,21 the first-difference method is unbiased and would be preferable when compared to the within-group estimator (Wooldridge, 2009).

Based on the various approaches to the fixed effects model discussed above, it is apparent that it has two major drawbacks. The first is that the inclusion of too many parameters to be estimated (e.g. in the LSDV model) – resulting in the loss of degrees of freedom – may not be necessary considering that the trade-off involves a loss of efficiency in estimating the common slope (Baltagi, 2008; Kennedy, 2008). The second is that by eliminating those explanatory variables that do not vary with time (e.g. gender, race, land size, etc.), the fixed effects model may no longer be effective since the slope coefficients of those variables can no longer be estimated (Wooldridge, 2009; Kennedy, 2008).

An alternative way to model panel data without facing the same drawbacks is through the random effects model. This is appropriate if it is assumed that the panel data draws N cross-sectional units randomly from a large population so that 2 the heterogeneity effect is also random. In this case 휖푖 ∼ 퐼퐼퐷(0, 휎휖 ), 푢푖푡 ∼ 2 퐼퐼퐷(0, 휎휖 ) and the 휖푖 are independent of the 푢푖푡. In addition, the explanatory

variables (푃푖푡 and 푌푖푡) are assumed to be independent of the 휖푖 and the 푢푖푡, for all i and t (Wooldridge, 2009; Baltagi, 2008).

The random effects model differs from the fixed effects model in that it handles the constants (intercepts) for each cross-sectional unit not as being fixed but as having been drawn from a bowl of possible intercepts, making it a random variable and as such treated as part of the error term (Asteriou and Hall, 2011; Kennedy, 2008). In the random effects model, the intercept for each cross-sectional unit can be expressed as:

21 A variable is said to be strictly exogenous if it does not depend on current, past and future values of the error term 푢푖푡. 61

훼푖 = 훼 + 휖푖 (3.18)

2 where 휖푖 is a zero mean random error term and a variance of 휎휖 .

What this implies is that since the cross-sectional units are drawn randomly from a large population, they essentially have a common mean value for the intercept, with any individual differences being reflected as the error term, 휖푖. Now assume Equation (3.18) is substituted in the following panel equation:

퐹푖푡 = 훼 + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + 푢푖푡 (3.19)

Therefore:

퐹푖푡 = (훼 + 휖푖) + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + 푢푖푡 = 훼 + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + (휖푖 + 푢푖푡) (3.20) where Equation (3.20) is the random effects model.

The random effects model has some advantages over the fixed effects model in that there are fewer parameters to estimate and it allows for the use of time- constant variables in the model. The main drawback, however, is that it requires the assumptions for 휖푖 made earlier to be strictly met. In cases where the panel involves cross-sectional units that are at an aggregated level (e.g. countries, regions or even differing income groups) such an assumption may not be tenable. In practice, this makes the use of the random effects model rather limited.

3.6.1 Dynamic Panel Data Models: Estimation Issues As discussed previously in §3.2, the use of a static model places a rather restrictive implied assumption (i.e. that demand adjustments takes place instantaneously), which may not be plausible. Since economic relationships are almost always dynamic in nature, it is also important for the model applied to capture the process of adjustment that takes place over time. In such cases, excluding the dynamics in the model may result in an omitted variable bias.

The availability of a time dimension in panel data is advantageous, since it allows the effect of time to be incorporated through the use of a dynamic panel data model. The use of this approach to model an economic relationship may not only avoid the problem of omitted variable bias but also allow the researcher to better understand the dynamics of the adjustments (Baltagi, 2008). Bond (2002) states that allowing for dynamics is important in obtaining consistent model estimates, even when the dynamics (i.e. the lagged variables) are not of direct interest.

To account for the dynamic relationship in a panel data framework, a model can be specified in the following form:

퐹푖푡 = 훼 + 훽 ∙ 푃푖푡 + 훾 ∙ 푌푖푡 + 훿 ∙ 퐹푖,푡−1 + 휖푖 + 푢푖푡 (3.21) where the speed of adjustment towards equilibrium is represented by the adjustment coefficient 훿 with 0 ≤ 훿 ≤ 1, in order for the dynamic relationship to be stable.

The inclusion of the lagged dependent variable in the context of the dynamic panel model is not without its own problems, however, especially when involving the most commonly applied estimators (i.e. the OLS, the fixed-effects and the random effects estimators). The presence of the lagged dependent variable causes biased and inconsistent parameter estimates to be produced, due to the correlation between the lagged dependent variable and the error.

Baltagi (2008) pointed out that in the case of the OLS, since 퐹푖,푡 is a function of 휖푖, the lagged dependent variable 퐹푖,푡−1 will be correlated with the error term, as by extension 퐹푖,푡−1 is also a function of 휖푖, making the OLS estimator biased and inconsistent. With the fixed effects estimator, Nickell (1981) showed that a similar problem (dubbed the Nickell bias) also arises because although the 휖푖 is wiped out by the within transformation, the demeaned lagged dependent variable

(퐹푖,푡−1 − 퐹̅푖,푡−1) will still be correlated with the demeaned error (휖푖,푡−1 − 휖푖,푡−1), since by construction 퐹푖,푡−1 is correlated with 휖푖̅ . This bias does not disappear even as the number of cross-sectional units increases, making the estimator inconsistent, especially in the context of models with large N and small T. The random effects estimator in the context of a dynamic panel data model is also biased and inconsistent as similar complications arise from the correlation between the lagged endogenous variable and the compound error.

In the context of the dynamic panel data model, therefore, the main issue that needs to be addressed in order to obtain consistent and unbiased estimates is the correlation between the lagged dependent variable and the error term. Fortunately, in the literature on dynamic panel data models, several alternative estimators have been suggested to overcome this difficulty. The properties and the approach of these estimators will be discussed further in Chapter 7.

From an estimation perspective, (apart from the model utilised) it is also important to have awareness of the contextual factors mentioned earlier, since a multitude of factors affect elasticity estimates. One way of improving awareness is by comparing existing estimates of fuel demand elasticity. This is essential, since it provides a reference point to verify findings. To this end, the following chapters build upon the findings of the methodological review highlighted here by attempting to collate and systematically assess some of the fuel demand estimates available.

3.7 SUMMARY This chapter has reviewed the methodological and econometric approaches for road transport fuel demand modelling. It has shown that factors such as model specifications, data characteristics, periodicity, contextual characteristics and estimation techniques will have an effect on the magnitude of the elasticity estimated. At the aggregate level in particular, demographic/environmental factors have strong effects on the estimated elasticity. This is particularly important since it implies that elasticity does change over time as factors such as travel satiation and the relative price of fuel to income take effect. Furthermore, it appears that our planned approach of utilising both time series and panel data to estimate the fuel demand elasticities will not only ensure the optimal use of recently available data but also result in a higher level of confidence in the parameters derived.

From the perspective of this research, the evaluation of the modelling approaches has also been fruitful since it has served to highlight some of the methodological problems and issues that were not addressed in earlier studies; i.e. non-stationarity in time series models and the problem of endogeneity of the lagged fuel consumption variable in dynamic panel models. In this aspect, the effort expended here has proven to be invaluable since it allows similar mistakes to be avoided and necessary precautions to be undertaken during the later fuel modelling and estimation stage.

To build upon the findings highlighted in this chapter, Chapters 4 and 5 are dedicated to further expand our comprehension of the area of road transport fuel demand modelling by taking into account and systematically assessing the estimates available in the literature. This is to ensure that not only will we be able to form a coherent understanding on the subject matter but that our estimations in Chapters 6 and 7 succeed in providing a meaningful contribution to the current body of knowledge.

CHAPTER 4 ROAD TRANSPORT FUEL DEMAND ELASTICITIES: A REVIEW

OF THE LITERATURE

4.1 INTRODUCTION Health service expert, Sir Ian Chalmers, in his seminal talk entitled ‘The scandalous failure of scientists to cumulate scientifically’, pointed out – in the context of unnecessary deaths from clinical drugs trials – the ethical imperative for a systematic review of the body of evidence to be conducted before a new clinical trial is implemented (see Chalmers, 2006). Although this research deals with a situation of less immediate gravity, the wisdom of Chalmers’ underlying argument, i.e. to first examine the existing research evidence, is compelling. Similarly, for this research, the process of model estimation can greatly benefit from looking at the body of evidence already available in the literature.

This chapter, in a sense, is a companion to the review presented in Chapter 3. While the latter presents a review of the modelling and methodological issues in fuel demand estimation, it does not explore the phenomenon being investigated. As Kennedy (2002) points out in his paper, in applied econometrics, it is easy to put too much focus on the tools (i.e. techniques and methodologies) and forget about the perspective for the statistical reasoning (i.e. economic theory). As such, the purpose of this chapter is to bridge that gap, by providing a context to the regression models. The objective here is to review the overall empirical evidence with a focus particularly on the income and price elasticity of fuel demand, obtain a priori knowledge on the expected outcome as well as to identify additional estimation issues that may arise. In other words, the aim is to attain the big picture of what is to be expected so that the modelling outcome later can be assessed in terms of its accordance to the conventional view. 66

In addition to the above, this review chapter will also highlight and summarise some the results from recent aggregate studies using the cointegration and dynamic partial adjustment models, both for time series and panel data. The chapter is structured as follows. Section 4.2 provides an overview of fuel demand elasticities with respect to price and income. The section also touches on the issues of time frame and the interpretation when other exogenous variables are included. Section 4.3 involves a survey of the estimation outcomes of recent fuel demand studies. This is then followed by a summary of the elasticities. Section 4.4 concludes the review of the literature on fuel demand elasticities.

4.2 FUEL DEMAND ELASTICITIES: OVERVIEW OF EMPIRICAL EVIDENCE There are a large number of studies dedicated to the understanding of fuel demand in the road transport sector. Since road transport fuel demand affects a broad range of policy issues the literature contains various estimates, each aiming at analysing differing issues, with a resulting wide variety of elasticity values.22 Depending on the research context, variation in the estimates can be attributed to the use of different functional forms, estimation techniques, independent and dependent variables, types of data and environmental characteristics (Basso and Oum, 2007). Due to this, inferring the meaning of these elasticity estimates can be a difficult task.

In fact, this diversity has led to the publication of literature reviews which attempt to catalogue the way these elasticities were derived and explain the estimates and the variations seen in them. In general, these literature reviews can be classified into surveys (see Dahl and Sterner, 1991; Graham and Glaister, 2002; Graham and Glaister, 2004; Goodwin et al., 2004; Basso and Oum, 2007) and meta-analyses (see Espey, 1998; Brons et al., 2008).23 In the area of fuel demand estimation, as in empirical economics as a whole, these review articles are important since they provide the rationale and perspective to the estimation, thus providing a basis for inference and comparisons. In this chapter, however, we rely more on the literature surveys since they tend to have a relatively stronger focus (in our opinion) on the context and theoretical perspective of fuel demand estimation and as such, correspond to the objectives of the chapter.

Despite the variations in the estimates reported, there appears to be some consensus on a few issues. Firstly, in terms of specification, fuel demand models, as expected from basic economic theory, should contain proxies to measure the

22 Over the years, interest in this area has been driven by various factors; from the issue of energy conservation and energy security (in the 70s and the 80s) to the current concerns regarding emissions and global warming. 23 Roberts (2005) classifies surveys as literature that usually employ some form of statistics but largely apply a narrative approach to reviewing empirical results, while meta-analyses make use of quantitative techniques to synthesise the findings. 68

effects of price and income. Fuel demand models without variables representing income and price are considered to be mis-specified (Dahl and Sterner, 1991).

While the above statement by Dahl and Sterner (1991) has a strong underpinning from economic theory, it is also important to have some perspective on how the relationship functions in the real world. In our opinion, Sterner and Dahl (1992) provided what is perhaps the best cogent reasoning for this relationship. They describe that while, on the surface, fuel demand is directly related to the vehicle stock; in essence it is actually a derived demand. The end outcome that we observe is essentially an end product to a series of gradual decision making processes. Initially, these may involve issues such as whether to purchase the vehicle or not and on the type purchased. This then gradually evolves to include interdependent factors such as the level of usage expected and the frequency as well as the distance of travel. These relationships are the basis of the structural models described in Chapter 3.

In the reduced-form models, the above processes are simplified. Since the decisions are strongly correlated to price and income, therefore it is plausible to allow all of the effects to be captured just through price and income. For example, changes in price impose constraint on budgets which then affects decisions such as the distance driven, driving behaviour and fuel efficiency (Basso and Oum, 2007). Income on the other hand enters the equation because it heavily influences decisions regarding vehicle ownership and characteristics (Espey, 1998).

In the literature, it is common for empirical models to specify fuel demand as a function only of price and income because this specification both has solid theoretical grounds and represents a parsimonious way of capturing the overall effects (especially from vehicle factors but also from other exogenous variables) which are often the focus in policy analysis (Basso and Oum, 2007).24 It therefore comes as no surprise that the estimates of price and income elasticity dominate the

24 Such a model specification is also termed as the basic model. 69

literature. Table 4.1 provides a summary of the elasticities from some of the literature surveys mentioned.

Table 4.1 Summary of price and income elasticities

Authors Price elasticity Income elasticity Short-run Long-run Short-run Long-run

Dahl and Sterner (1991)1 –0.13 to –0.24 –0.23 to –0.88 0.20 to 0.58 0.64 to 1.31 Espey (1998) –0.26 –0.58 0.47 0.88 Graham and Glaister (2002) –0.20 to –0.30 –0.60 to –0.80 0.35 to 0.55 1.10 to 1.30 Graham and Glaister (2004) –0.25 –0.77 0.47 0.93 Goodwin et. al (2004)1 –0.25 –0.64 0.39 1.08 Basso and Oum (2007) –0.20 to –0.30 –0.60 to –0.80 0.30 to 0.50 0.90 to 1.30 Notes: 1) Estimates derived from dynamic estimation models only.

Unsurprisingly, the overall picture from the literature review reveals, as expected from basic economic theory, that price will have a negative effect on consumption while the effect of income will be positive. An important outcome that is consistently seen from the surveys is that there are clear differences in magnitude between price and income elasticity. From the surveys, income elasticities are consistently higher than the price elasticities, both in the short- and long-run. This means that if consumption is to be retained at the current level, fuel price would have to be increased at a significantly higher rate to account for the higher income effect (Graham and Glaister, 2002). For the UK, this finding has important implications, especially in the context of the effectiveness of taxation in managing transport fuel consumption.

Another common insight gained from the literature surveys is that of the clear differences between the short- and long-run fuel demand elasticities with respect to both price and income.25 In these surveys, the absolute values of the long-run elasticities are consistently higher than in the short-run. Graham and Glaister (2002) report long-run price (income) elasticities of between –0.6 to –0.8 (1.1 and 1.3). In contrast, they find the short-run elasticities for price as ranging from –0.2 to –0.3 while for income as being between 0.3 and 0.5. The survey by Basso and Oum

25 This is not surprising and is again consistent with the general theoretical expectation. Additionally, the same outcome is also applicable to other elasticities. 70

(2007) reports an identical price elasticity range with long-run values of between – 0.6 to –0.8 and short-run ones of between –0.2 to –0.3. For income elasticities, they find long-run estimates to be between 0.9 to 1.3 while values in the short run were in the range of 0.3 and 0.5.

In the short-run, the response to any changes to price and income available to fuel consumers are rather limited thus making them rather inelastic. For example, an increase in price will in general result in an adaptive behavioural process: consumers will try to drive less or at lower speed, while businesses may resort to consolidating delivery consignments or scheduling deliveries to off peak hours. Over the long run, however, a wider range of response options may come into consideration. These may include the replacement of vehicles, changing the mode of transport or even relocating the residence or workplace altogether. As seen in Chapter 2, it is plausible that the long-term response may go even further, that vehicle stock replacement also involves fuel substitution i.e. from petrol to diesel.

Since fuel demand is influenced directly by vehicular factors, models that include variables that measure some of these aspects are also quite common (see §3.2 for a description of these factors).26 The inclusion of such variables is not without issues, however. The main concern with regards to vehicle stock and vehicle characteristics models, as stated in the literature (see Dahl and Sterner, 1991; Sterner and Dahl, 1992; Espey, 1998), is that such models are unlikely to capture long-run responses. From an estimation perspective, the inclusion of these variables means that such factors are held constant, thus resulting in the model not being able to capture the adaptation process through vehicle stock replacement. Since price and income have a significant influence on the vehicle replacement process, it is likely in vehicle models, for the price and income elasticity to reflect only the short-run (direct) effects of price and income on fuel consumption. In such a case, Espey (1991) postulated that price and income measure the changes due to driving only.

26 Fuel demand models which are specified as such are sometimes termed as vehicle stock or vehicle characteristics models. 71

Hence, when it comes to the inclusion of vehicle variables, Basso and Oum (2007) asserted that the researcher would have to contend with a dilemma: whether to omit these factors from the fuel demand model or to include them. With omission, their effects could possibly be (indirectly) captured by price and income, thus enabling the long-run effects to be estimated. On the other hand, there is no guarantee that all of the effects attributable to the vehicle variables could be accounted for, and by omitting them, the researcher would then run the risk of introducing bias into the model. In terms of estimation, the inclusion of vehicle factors into the basic fuel demand model would result in a lower magnitude (in absolute value) of price and income elasticities (Espey, 1998).

At the aggregate level, we have also encountered fuel demand models that include some measure to account for alternative forms of travel such as public transport fare and availability (see Blum, 1988; Crôtte et al., 2010; Sene, 2012) as well as to account for the shift towards other fuel substitutes (see Polemis, 2006; Pock, 2010). In this chapter, however, we will not discuss the expected effects of the factors above because they are too numerous to be covered adequately. Furthermore, their expected signs are likely to differ depending on the context of the dependent variable (i.e. fuel being consumed). As pointed out by Basso and Oum (2007), it is important to think through the variables being introduced in the model properly since some of their effects can be ambiguous, particularly when it is unclear what they are actually measuring.

4.3 SUMMARY OF ELASTICITIES As stated earlier, elasticity estimates from the literature reviewed are essential to this research because they represent the current understanding and practice in the area of transport fuel demand and provide a basis for guiding the methodology and subsequently the expectations as to the outcome of the models applied. As such, this section is structured around highlighting the estimates available in recent literature and then proceeding to describe the characteristics found in these studies.

To this end, 438 elasticity observations from 30 primary studies have been collected, a majority from published journals obtained through the use of publication databases such as ScienceDirect and ISI Web of Knowledge, as well as Google Scholar.27 Care has also been taken to ensure that the majority of these studies are recent (i.e. published not earlier than 1990) and that the estimation methodologies used to derive the estimates are related to the econometric techniques employed in this thesis. For example, the time series samples are based both on the cointegration and the partial adjustment model while our panel data samples are largely composed of the partial adjustment methodology. An effort has been made to ensure that the studies differ from what has been used in earlier survey literatures in order to assess whether similar outcomes as described in §4.2 are noticeable, although this is not entirely feasible for those based on the cointegration model due to their relatively limited availability and recent application for deriving transport fuel demand elasticity.

This section has adopted a similar presentation format for the literature materials listed in Tables 4.2–4.4 as that commonly seen in the survey literature. Summary statistics comprising the mean, standard deviation, range and sample sizes of the collated results are presented in Tables 4.5–4.7. Figures 4.1–4.4 are graphs that combine histogram and box-plots showing the distribution of the elasticity estimates, categorised into short- and long-run elasticity for both price and income.

27 This is the number of estimates used for the summary statistics. They are comprised only of results which are statistically significant. Tables 4.2–4.4 on the other hand also report non-significant estimates. 73

Table 4.2 Price and income elasticities from time series cointegration studies

Other Exogenous Periodicity Price Elasticity Income Elasticity Authors Fuel Type Data Method Variables (Country) Short-Run Long-Run Short-Run Long-Run Bentzen (1994) Gasoline T/S 1948-91 Annual Cointegration –0.32 –0.41 0.89p 1.04p Vehicles per capita, (Denmark) trend Eltony & Al- Gasoline T/S 1970-89 Annual Cointegration –0.37 –0.46 0.47 0.92 None Muntairi (1995) (Kuwait) Samimi (1995) Gasoline & T/S 1980-93 Quarterly Cointegration –0.2ns –0.12 0.25p 0.52p None diesel (Australia) Ramanathan Gasoline T/S 1972-94 Annual Cointegration –0.21 –0.32 1.18 2.68 None (1999) (India) Dahl & Kurtubi Gasoline T/S 1970-95 Annual Cointegration –0.04ns –0.63 0.19ns 1.29 None (2001) (Indonesia) Diesel T/S 1970-95 Annual Cointegration –0.13ns –0.67 2.15 2.16 None (Indonesia) Barns (2002) Gasoline T/S 1989-2001 Quarterly Cointegration –0.20 –0.07 - - Seasonal dummy (New Zealand) Alves & Bueno Gasoline T/S 1974-99 Annual Cointegration –0.09 –0.46 0.12 0.12 Alcohol price, quadratic (2003) (Brazil) trend Ramanathan et al. Gasoline T/S 1979-2000 Annual Cointegration –0.05 –0.52 0.35 0.96 None (2003) (Oman) Cheung & Gasoline T/S 1980-1999 Annual Cointegration –0.19 –0.56 1.64 0.97 None Thomson (2004) (China) Polemis, M. L. Gasoline T/S 1978-2003 Annual Cointegration –0.10 –0.38 0.36 0.79 Diesel price, trend (2006) (Greece) Diesel T/S 1978-2003 Annual Cointegration –0.07 –0.44 0.42 1.18 Gasoline price, diesel (Greece) fleet per capita Akinboade et al. Gasoline T/S 1978-2005 Annual Cointegration - –0.47 - 0.36 None (2008) (South Africa) Notes: 1) ns indicates result is not significant. 2) p indicates studies which used proxies for income where Bentzen (1994) used vehicle per capita while Samimi (1995) used road transport output. 3) T/S signifies time series studies.

Table 4.2 Price and income elasticities from time series cointegration studies (continued)

Other Exogenous Periodicity Price Elasticity Income Elasticity Authors Fuel Type Data Method Variables (Country) Short-Run Long-Run Short-Run Long-Run Wadud et al. Annual Gasoline T/S 1979-2004 Cointegration –0.07 to –0.09 –0.10 to –0.12 0.47 to 0.52 0.57 to 0.59 None (2009a) (USA) Annual Vehicles per capita, Crôtte et al. (2010) Gasoline T/S 1980-2006 Cointegration –0.06 to –0.10 –0.06 to –0.29 0.43 to 0.78 0.53 to 0.76 (Mexico) metro fares Quarterly Lim et al. (2012) Diesel T/S 1986-2010 Cointegration –0.36 –0.55 1.59 1.48 None (South Korea) Notes: 1) ns indicates result is not significant. 2) p indicates studies which used proxies for income where Bentzen (1994) used vehicle per capita while Samimi (1995) used road transport output. 3) T/S signifies time series studies.

Table 4.3 Price and income elasticities from time series dynamic partial adjustment studies

Other Exogenous Periodicity Price Elasticity Income Elasticity Authors Fuel Type Data Method Variables (Country) Short-Run Long-Run Short-Run Long-Run Al-Faris (1997) Gasoline T/S 1970-1991 Annual PAM –0.16 –1.78# 0.11 1.22# None (Bahrain) Gasoline T/S 1970-1991 Annual PAM –0.10 –1.67# 0.07 1.17# None (Kuwait) Gasoline T/S 1970-1991 Annual PAM –0.29 –1.21# 0.27 1.16# None (Oman) Gasoline T/S 1970-1991 Annual PAM –0.14 –0.70# 0.02 0.10# None (Qatar) Gasoline T/S 1970-1991 Annual PAM –0.09 –0.32# 0.03 0.11# None (Saudi Arabia) Gasoline T/S 1970-1991 Annual PAM –0.08 –0.28# 0.28 0.97# None (UAE) Banaszak et al. Gasoline & T/S 1973-1992 Annual PAM –0.12 –0.52 0.23 0.98 None (1999) diesel (Taiwan) Gasoline & T/S 1973-1992 Annual PAM –0.39 –0.87 0.44 0.99 None diesel (South Korea) Hanly et al. (2002) Gasoline & T/S 1960-2000 Annual PAM –0.07 –0.44 0.13 0.88 None diesel (United PAM (lin-lin) –0.09 –0.66 0.1 0.94 None Kingdom) PAM (log-lin) –0.06 –0.67 0.04 0.44 None PAM (lin-log) –0.1 –0.32 0.38 1.15 None Kennedy & Wallis Gasoline T/S 1974-2005 Annual PAM –0.11 –0.18 0.07 0.11 None (2007) (New Zealand) Koshal et al. Gasoline T/S 1957-1999 Annual PAM –0.12 –0.41 0.30 1.06 CPI, Time dummy (2007) (Japan) Notes: 1) ns indicates the result is not significant. 2) # indicates elasticity values manually derived using the lagged endogenous coefficient given in the studies. 3) T/S and PAM signify time series and partial adjustment models respectively.

Table 4.3 Price and income elasticities from time series dynamic partial adjustment studies (continued)

Other Exogenous Periodicity Price Elasticity Income Elasticity Authors Fuel Type Data Method Variables (Country) Short-Run Long-Run Short-Run Long-Run Hughes et al. Gasoline T/S 1975-1980 Monthly PAM –0.30 –0.34 0.41 0.46 Monthly dummies (2008) (USA) T/S 2001-2006 Monthly PAM –0.03 –0.05 0.39 0.58c Monthly dummies (USA) Li et al. (2010) Gasoline T/S 1977-2005 Quarterly PAM –0.22 –0.29 0.27 0.36 Seasonal dummies (Australia) Gasoline T/S 1977-2005 Annual PAM –0.08 –0.12 0.23 0.36 None (Australia) Sene (2012) Gasoline T/S 1970-2008 Annual PAM –0.12ns –0.30ns 0.46 1.14 Population, public (Senegal) transport index Notes: 1) ns indicates the result is not significant. 2) # indicates elasticity values manually derived using the lagged endogenous coefficient given in the studies. 3) T/S and PAM signify time series and partial adjustment models respectively.

Table 4.4 Price and income elasticities from panel data studies

Other Exogenous Periodicity Price Elasticity Income Elasticity Authors Fuel Type Data Method Variables (Country) Short-Run Long-Run Short-Run Long-Run

Baltagi & Griffin Gasoline PD N = 18 Annual PAM –0.07 to –0.29 –0.24 to –1.42 0.19 to 0.55 –0.46 to 0.33 Cars per capita 1,2 (1997) 1960-1990 (OECD) Eskeland & Gasoline PD N = 31 Annual PAM –1.04 –1.39 0.63 0.84 Car price, highway 1 Feyzioglu (1997) 1982-1988 (Mexico) length per car Baltagi et al. Gasoline PD N = 21 Annual PAM –0.02 to –0.19 –0.14 to –0.72 –0.03 to 0.52 –0.80 to 1.91 Cars per capita 1,2 (2003) 1973-1998 (France) Pock (2010)1,2 Gasoline PD N = 14 Annual PAM –0.21 to 0.02 –0.24 to –2.66 0.00 to 0.47 0.88 to 6.06 Total cars per driver 1990-2004 (OECD) PAM –0.03 to –0.19 –0.31 to –0.84 0.04 to 0.24 0.17 to 0.61 Gasoline cars per driver, diesel cars per driver Crotte et al. Gasoline PD N = 30 Annual PAM –0.09 to –0.19 –0.39 0.02 to 0.61 1.187 Vehicle stock per capita, 1,2 (2010) 1993-2004 (Mexico) metro fares, year dummy Gasoline PD N = 16 Annual PAM –0.11 to –0.39 –0.22 –0.44 to 0.69 0.50 Vehicle stock per capita, 2001-2004 (Mexico City) metro fares, fuel efficiency Danesin & Linares Gasoline PD N = 15 Annual PAM –0.17 to –0.30 –0.41 to –2.78 –0.02 to 0.53 –0.21 to 0.87 Gasoline cars per capita, 1,2 (2011) 2000-2007 (Spain) diesel share ratio Diesel PD N = 15 Annual PAM –0.17 to –0.29 –0.39 to –0.54 0.01 to 0.88 1.99 to 4.52 Diesel cars per capita, 2000-2007 (Spain) diesel share ratio Total Fuel PD N = 15 Annual PAM –0.19 to –0.32 –0.52 to –0.81 0.01 to 0.79 1.87 to 2.49 Total cars per capita, 2000-2007 (Spain) diesel share ratio Gasoline PD N = 15 Annual PAM –0.13 to –0.39 –0.10 to –2.64 –0.02 to 0.11 –0.21 to 0.27 Gasoline cars per capita 2000-2007 (Spain) Diesel PD N = 15 Annual PAM –0.10 to –0.23 –2.17 to – 0.02 to 0.47 1.69 to 4.51 Diesel cars per capita 2000-2007 (Spain) 20.48 Total Fuel PD N = 15 Annual PAM –0.18 to –0.28 –0.58 to –0.91 0.01 to 0.62 1.45 to 1.84 Total cars per capita 2000-2007 (Spain) Notes: 1) 1 indicates studies that used fuel per vehicle as the dependent variable. 2) 2 Author(s) applied multiple estimators. Results reported here are from homogeneous panel estimators only. 3) # indicates elasticity values manually derived using the lagged endogenous coefficient given in the studies. 4) PD and PAM signify panel data and partial adjustment models respectively.

Table 4.4 Price and income elasticities from panel data studies (continued)

Other Exogenous Periodicity Price Elasticity Income Elasticity Authors Fuel Type Data Method Variables (Country) Short-Run Long-Run Short-Run Long-Run Liddle (2012) Gasoline PD N = 14 Annual Cointegration –0.16 –0.19 to –0.43 0.28 0.20 to 0.34 Car ownership per 1978-2005 (OECD) capita Gonzalez-Marrero Gasoline PD N = 15 Annual PAM –0.29 to –0.42 –0.57 to – –0.01 to 0.29 –0.03 to 0.45# Diesel price, gasoline & 1,2 # et al. (2012) 1998-2006 (Spain) 2.84 diesel fleet per capita, road saturation Diesel PD N = 15 Annual PAM –0.03 to –0.08 –0.14 to – 0.00 to 0.48 0.33 to 0.90 Gasoline price, gasoline # 1998-2006 (Spain) 0.20 & diesel fleet per capita, road saturation Santos (2013)2 Gasoline PD N = 27 Quarterly PAM –0.32 to –0.43 –1.19 0.16 to 0.21 0.52 Ethanol & CNG prices, 2001-2010 (Brazil) dummy variables Ethanol PD N = 27 Quarterly PAM –0.96 to –1.39 –8.47 0.46 to 0.56 3.72 Gasoline & CNG prices, 2001-2010 (Brazil) dummy variables CNG PD N = 27 Quarterly PAM –0.12 to –0.19 –1.03 0.06 to 0.14 0.81 Gasoline & ethanol 2001-2010 (Brazil) prices, dummy variables Notes: 1) 1 indicates studies that used fuel per vehicle as the dependent variable. 2) 2 Author(s) applied multiple estimators. Results reported here are from homogeneous panel estimators only. 3) # indicates elasticity values manually derived using the lagged endogenous coefficient given in the studies. 4) PD and PAM signify panel data and partial adjustment models respectively.

60 80 60 40 40 Frequency Frequency 20 20 0 0

-1.5 -1.2 -.9 -.6 -.3 0 -9 -7.5 -6 -4.5 -3 -1.5 0 Elasticity Elasticity

Figure 4.1 Short-run price elasticity of fuel demand Figure 4.2 Long-run price elasticity of fuel demand 50 40 40 30 30 20 Frequency Frequency 20 10 10 0 0

0 .5 1 1.5 2 0 1.5 3 4.5 6 Elasticity Elasticity

Figure 4.3 Short-run income elasticity of fuel demand Figure 4.4 Long-run income elasticity of fuel demand

4.3.1 Overall Summary of Elasticity Results It can be seen that the short-run price elasticity of the fuel demand estimates from the literature reviewed ranges from –1.31 to 0.02 with a mean elasticity of –0.24. The long-run price elasticity estimates reflect the trend normally observed, in having a bigger magnitude compared to the short-run estimates, ranging from – 8.47 to –0.05 and a mean of –0.72. Although the magnitude of range reported for the estimates appeared to be quite wide with a similarly large standard deviation as compared to the means, this is not entirely uncommon.28 In fact from Table 4.5, a similar outcome is also noted from the literature reviewed in respect to the short- run and long-run income elasticity of fuel demand estimates.

The common explanation for the wide variation seen is that the differences in elasticity estimates arise due both to the estimation technique being used and the influence of the wide ranging contextual assumptions in the literature. Graham and Glaister (2004) provided a similar explanation although they also stressed the importance of the modelling approach and the level of data aggregation in influencing the estimate produced.

Further informative insights can also be glimpsed from Tables 4.5–4.7 which show the results of the analysis of the estimates from the literature reviewed through the use of summary statistics. The first is that long-run elasticity estimates are consistently higher than the short-run estimates, which is similar to the findings in other survey literatures. In this literature review, the mean long-run price and income elasticities are –0.72 and 0.90 respectively, compared to –0.24 and 0.37 for both the mean short-run price and income elasticities. However, these values appear to be inflated when compared with the official UK elasticity values. Based on official documents, the long-run price and income elasticities were set equal to – 0.60 and 0.40 respectively. In comparison, the short-run price elasticity is reported to be –0.14 (see DECC, 2013; OBR, 2010).

28 The wide range reported can largely be attributed to elasticity estimates derived from the panel data methodology. Estimates of fuel types other than petrol also contribute further to the large variation seen.

Table 4.5 Summary statistics of elasticity estimates from the literature reviewed

Elasticity Total Short-Run Long-Run

Price Mean elasticity –0.452 –0.274 –0.719 Standard deviation 0.695 0.303 0.981 Range –8.465, 0.015 –1.391, 0.015 –8.465, –0.049 Number of estimates 236 142 94

Income Mean elasticity 0.590 0.367 0.902 Standard deviation 0.690 0.322 0.916 Range –0.460, 6.056 0.003, 2.149 –0.460, 6.056 Number of estimates 202 118 84

Note: The term ‘total’ above indicates that the statistics are comprised of both the short- and long-run elasticities.

Additionally, the elasticity estimates also generally displayed the expected signs, with a change in price having a negative effect on fuel demand while the opposite is observed for income. Although there are instances when the estimates reported indicate signs contrary to a priori expectations, the frequency of such occurrences are rare and in all such cases arise solely from panel data sources. These contradictory results stemming from panel data estimates will be highlighted further in Table 4.6.

A matter that is much more substantial from the summary statistics in Table 4.5 is the magnitude of the mean elasticity estimates. The mean long-run price elasticity appears to be lower (in absolute value) while on the other hand, the evidence indicates the income elasticity magnitude has remained relatively similar in comparison to the mean values reported Graham and Glaister (2004). For example, in their survey, the mean long-run price and income elasticities, as reported by Graham and Glaister (2004), were –0.77 and 0.93. This signifies that the decline in price elasticity is not being matched similarly by income; surely a discouraging result in the context of the effectiveness of tax to decouple income growth with consumption.

If analysed only from the context of income elasticities, however, some positives can be taken from the outcome. The results indicate that the mean short-run and

long-run income elasticities of 0.37 and 0.90 are lower in absolute value compared to the estimates given in Graham and Glaister (2004) and Goodwin et al. (2004). This is encouraging since it somewhat supports the general assumption that income elasticity will decline over time due to satiation. Apart from travel satiation, Goodwin et al. (2004) also argued that the lower values can be due to the fact that as income rises, car usage and thus fuel demand will come from non-workers, who normally travel less. Taken together, it is likely that road transport fuel consumption will not grow as much as it had in the past even as income continues to rise.

4.3.2 Variations between Time Series and Panel Data Models The influence of data types on estimation results is highlighted in Table 4.6. It can be seen that the time series estimates in the sample reviewed produce patterns familiar from previous studies in which all of the estimation results conform to the theoretical expectations (i.e. displays expected signs, short-term effects differ from long-term effects). The only exception that can be highlighted is perhaps the slightly larger range for the income elasticities reported. This can be explained by the inclusion of estimates from developing countries in which the estimates reflect how the growth of income is fuelling rapid motorisation of travel.

Table 4.6 Elasticity estimates produced by time series and panel data models

Price Elasticities Income Elasticities Short-Run Long-Run Short-Run Long-Run

Time Series Mean elasticity –0.155 –0.497 0.464 0.863 Standard deviation -0.104 -0.390 0.491 0.537 Range –0.385, –0.033 –1.780, –0.049 0.020, 2.149 0.10, 2.682 Number of estimates 30 35 34 36

Panel Data Mean elasticity –0.306 –0.852 0.328 0.931 Standard deviation -0.329 -1.186 0.212 1.124 Range –1.391, 0.015 –8.465, –0.137 0.003, 0.875 –0.460, 6.056 Number of estimates 112 59 84 48

While the well-established features in fuel demand studies are present in the panel data estimates, the results from the sample do contain some unexpected observations. Note that the means reported are mostly larger than the time series estimates (i.e. by a factor of 1.7 to 2 for both short-run and long-run price elasticities) and some results for the short-run price and long-run income estimates contain signs contrary to expectations. Additionally, summary statistics for the panel model also indicate quite a wide range of results with large standard deviations compared to the means.

Although some of the observations appear to stand out, they are in general not at all surprising. As mentioned earlier, since the estimates are derived from varied sources, the results are influenced by a lot of factors. One source of variation in the panel data statistics is the inclusion of results for alternative fuels such as ethanol and compressed natural gas (CNG). For example, the study by Santos (2013) indicated an unusually high long-run price (income) elasticity of –8.47 (3.42) for ethanol. If fuels other than petrol were excluded from the sample, the variance reported would have been smaller.

Another source of variation in the panel data estimates is due to the use of multiple estimators when presenting the results. Since estimates from the commonly applied panel data estimators are biased and inconsistent when applied in a dynamic context (i.e. partial adjustment model), it is usual for researchers in panel model papers to present results from multiple alternative estimators. These single studies with multiple estimators applied (e.g. Baltagi & Griffin, 1997; Pock, 2010) often have a wide variance in the reported parameters (largely due to the inclusion of results from biased estimators) and their inclusion in the review sample results in a similar effect on the summary statistics.

The type and level of data may also have an influence on the wide variation observed in the panel data model. Espey (1998) found that panel data estimates tend to be more elastic. She attributed this to the greater level of detail and

variation available in panel studies, thus allowing for more subtle responses to be captured, hence resulting in the more elastic estimates.

Additionally, the level of aggregation used in the panel data model may also influence the range of the estimates. While we have only included aggregate panel data models in the review sample, there still remain differences in the level of data used between these studies.29 For example, OECD level studies rely on country level data, while country level estimates involve data aggregated at the regional or state level. As such, it is plausible that such differences may result in the wide ranging variation observed.

4.3.3 Variations due to Estimation Techniques In order to account for the possible variations due to the estimation techniques being used, Table 4.7 provides the summary statistics to compare the elasticity estimates from the cointegration and dynamic partial adjustment models. Since the results from the panel data models are mostly based on the partial adjustment model (PAM), however, these are excluded from this summary analysis.

Table 4.7 Elasticity estimates produced by cointegration and dynamic models (time series only)

Price Elasticities Income Elasticities Short-Run Long-Run Short-Run Long-Run

Cointegration Mean elasticity –0.184 –0.403 0.792 1.041 Standard deviation -0.120 -0.183 0.617 0.656 Range –0.370, –0.050 –0.670, –0.065 0.122, 2.149 0.122, 2.682 Number of estimates 11 16 14 16

Dynamic (PAM) Mean elasticity –0.138 –0.575 0.234 0.736 Standard deviation -0.093 -0.496 0.154 0.392 Range –0.385, –0.330 –1.780, –0.049 0.020, 0.458 0.10, 1.22 Number of estimates 19 19 20 20

29 See Kayser (2000), Nicol (2003) and Romero-Jordán et al. (2010) for panel data estimates of fuel consumption at the disaggregate level.

It can be seen that for income, the mean elasticities for both short-run (0.79) and long-run (1.04) estimates produced from the cointegration model are somewhat higher in absolute value than the ones from the dynamic model. It is difficult to come to a strong conclusion as to whether this reflects the true relationship since the outcomes from literature surveys varied in this respect. This may simply reflect that the mean seen here is affected by the sample, since the majority of estimates are from developing countries (which tend to display large income elasticities).

Consistency with previously reported literature surveys, on the other hand, is seen with the cointegration estimates for long-run price elasticity. Goodwin et al. (2004) and Espey (1998) observed that dynamic specifications tend to deliver long-run price elasticities that are higher compared to static cointegration models. In this review sample, it can be seen that the mean long-run price elasticity of –0.4 from the static models is smaller than the dynamic estimation mean elasticity by a ratio of 0.7; an observation which is similar to that reported by Basso and Oum (2007).

4.4 SUMMARY This chapter provides an overview and some perspectives on the road transport fuel demand elasticities reported in the literature. There was a focus on the empirical estimates of price and income elasticity. The review shows that in general price and income elasticities tend to conform to the a priori expectations. As expected, from basic economic theory, the price effect will be negative while the income effect will be positive on fuel demand. Furthermore, the literature surveys indicate that factors such as model specifications, data characteristics, periodicity, contextual characteristics and estimation techniques will have an effect on the magnitude of the elasticity estimated.

Our own review of the aggregate empirical studies appears to confirm the findings of the literature surveys. In our survey sample, we observe wide variation in the estimates. When the sample is stratified, the resemblance to some of the often analysed observations described in the review literature is apparent. While this is comforting, the outcome also brings to light additional issues not only on the results of the estimation but also on the framework of the survey process itself.

One issue is whether other factors in the study design affect the estimates? For example, none of the surveys appear thoroughly to investigate whether fuel type differences affect the price and income elasticity estimates. Additionally, while the survey framework appears to work well in explaining the variation in the estimates when applied to certain aspects of studies that are well defined (e.g. short-run over long-run effect, magnitude of price elasticity against income elasticity), when the area of interest involves differences in the study design that are less clear cut (i.e. fuel type, geographical effects, technique used) then it becomes clear that the framework of the survey approach is severely limited. As Roberts (2005) argued, when faced with a mass of empirical results the survey framework is unlikely to be able to produce objective and reliable answers. As an alternative, he suggests that survey of empirical studies should rely on a more robust procedure called meta- regression analysis.

To conclude, the work in this chapter has been useful in providing an overview of the theory and expectations in regard to the estimation outcomes for the price and income elasticity of fuel demand. The review of the empirical studies, however, has revealed that there are gaps that have not yet been well researched. These include, particularly, whether the variations observed are attributable to other factors. In the case of this research, this issue focuses on the influence of fuel type and the model specification of the estimates. This suggests that further investigation should perhaps be undertaken to analyse this matter. In the following chapter, therefore, we pursue this issue further through the application of meta-regression analysis.

CHAPTER 5 A META-REGRESSION ANALYSIS OF ROAD TRANSPORT FUEL

DEMAND

5.1 INTRODUCTION The numerous econometric studies of fuel demand that were reviewed in Chapter 4 appear to confirm that, in general, price and income elasticity estimates tend to be consistent with the a priori economic expectations. In addition, however, the literature review and the accompanying survey on fuel demand elasticities also revealed two important observations: that fuel demand estimates vary greatly, and that these variations are probably due to the influences of the characteristics of the empirical model.

Whilst the work undertaken in Chapter 4 has been beneficial in increasing our grasp of fuel demand modelling and our ability to assess the likely outcome from such an exercise, there remain important gaps that cannot be answered through such approach. The presentation of summary statistics in §4.3 serves in particular to highlight this limitation and, indeed, raises more questions than can be answered through a narrative review of the literature. For example, what further variations can be expected due to model specifications? Do the contextual characteristics of a study exert a similar influence on the estimates obtained?

Additionally, there is an increasing concern regarding the framework upon which the inference of a narrative review is based on. Among the criticisms often levelled at narrative reviews is that they are often subjective and based on casual judgement (Stanley, 2001). DeCoster (2004) stated that even when it is carried out with exceptional rigour there is a strong tendency for the narrative to be predisposed to the author’s whim. Significantly, however, the absence of statistical aid in narrative

reviews makes them ill-suited for analysing and quantifying the impact of methodological variations on the parameter of interest, especially when faced with a mass of empirical results (Roberts, 2005).

In this chapter, we attempt to overcome the limitations of the narrative reviews undertaken previously by incorporating a much more quantitative and objective review of the literature using a meta-analysis method. Meta-analysis is a body of statistical methods and procedures for integrating and analysing a large collection of empirical results (Nijkamp and Pepping, 1998). A key element of meta-analysis which lends it an objectivity not found in narrative reviews lies in the statistical synthesis of empirical studies, which allows for study-to-study variations to be empirically quantified and tested.

Notwithstanding the above, the implementation of the meta-analysis here should be seen as a continuation of the objective stated earlier in Chapter 4, such that, instead of superseding the earlier results, the meta-analysis acts as a further integral component in expanding the overall understanding of the factors contributing to the range of elasticity values observed previously. It is anticipated that this understanding will help, not only to provide additional guidance for the fuel demand estimation implemented later in this work, but also potentially to contribute to work already undertaken in this area.

The chapter continues in Section 5.2 by providing a description of the meta- regression approach taken to synthesize the literature review. Section 5.3 outlines the scope of the meta-regression and meta-sample used. Section 5.4 highlights the key moderating factors that we consider important in explaining the variation found in the fuel demand literature. Section 5.5 presents the results of the meta-regression analysis while, in Section 5.6., we test for the presence of publication bias. The conclusion of the chapter is presented in Section 5.7.

5.2 META-REGRESSION: A GENERAL DISCUSSION A meta-analysis – unlike a narrative review – is a quantitative research synthesis. Ellis (2010) describes meta-analysis as the statistical analysis of statistical analyses. As described earlier, the shortcomings of narrative reviews has resulted in a move towards a more objective approach of synthesizing results. Beginning initially in the field of medicine and psychology, the application of meta-analysis has since taken root in other field of studies and is now the accepted standard upon which the review and integration of empirical studies is based.

Before proceeding further, it is important to clarify that the process of meta-analysis is not tied to a single methodology but rather reflects a multitude of statistical approaches to synthesize research results.30 In this chapter, the evaluation of the empirical results reported previously is performed through the method of meta- regression analysis. Since the focus is not only on the effect size per se, but also on understanding the extent to which specification and contextual factors affect the parameters estimated, the use of meta-regression is deemed to be suitable in this context.

Meta-regression is a form of meta-analysis especially designed to investigate empirical research in economics (Stanley, 2001). The method is essentially the same as in primary studies where the relationship between the dependent variable and the covariates is assessed via a regression model. Unlike in primary studies, however, the variables in a meta-regression are drawn at the level of the study rather than the level of the data (Borenstein et al., 2009). The dependent variable in a meta- regression is the output from a primary study, usually an effect size or summary statistics, such as the estimated value of travel time or, in our particular case, the regression parameters representing price and income elasticities. Likewise, the moderator (independent) variables are often the variation inducing features such as the data and contextual characteristics as well the model specification used in the primary studies.

30 Borenstein et al. (2009) and Cumming (2012) provides excellent descriptions of the various meta-analytical techniques for the purpose of quantitative literature reviews.

A typical meta-regression random effects model can be described as follows (see also Mohammad et al., 2013; Melo et al., 2009; Nelson and Kennedy, 2009):

퐾

휀푖푗̂ = 훼0 + ∑ 훽푘퐷푖푗,푘 + 휖푗 + 푢푖푗 (5.1) 푘=1

where 휀푖푗̂ is the dependent variable with i indicating the individual elasticity estimate from a given study j, 퐷푖푗,푘 is a dummy variable for the meta-independent variable 푘 while 훽푘 is the meta-regression coefficient which explains the effect of meta- independent variable 푘. The constant, 훼0 represents the ‘true’ value of the parameter of interest, 휖푗 is the randomly distributed study-specific effect with mean 2 0 and variance 휎휖 , and 푢푖푗 is the white noise term.

From the above, it is not difficult to see why a quantitative approach to reviewing literature provides a more appealing alternative to the traditional narrative approach. Meta-regression enables not only the statistical identification of the factors that cause variations found in the studies but also quantifies the effects of these variables on the value under investigation (Nelson and Kennedy, 2009). Most importantly, meta-regression (when clearly defined) provides a statistical framework upon which summaries and inferences from previously undertaken literature reviews can be replicated (Stanley, 2001).

Although the application of meta-analysis was initially slower in the field of economics, in recent years many more meta-analyses have been undertaken. In the context of transport studies, meta-regression analysis has been applied to, among others, the area of travel time valuation (see Abrantes and Wardman, 2011; Wardman, 2001), public transport demand (see Holmgren, 2007; Nijkamp and Pepping, 1998), the impact of rail projects on property values (see Mohammad et al., 2013), the technical efficiency of seaports (see Odeck and Bråthen, 2012) and fuel demand (see Brons et al., 2008; Hanly et al., 2002; Espey, 1998).

5.3 SCOPE OF THE META-REGRESSION To reiterate, the objective of the meta-regression analysis in this study is not to supersede the work in the previous chapter but rather to complement it in developing a fuller understanding of the issue at hand. Specifically, the meta- regression is intended to discern systematically and statistically the effects of the differing characteristics in the empirical results reported in the primary studies, and to provide an additional reference point for the time series and panel data fuel demand modelling that will follow.

Despite its benefits, meta-regression is not without its own limitations. Just like any statistical tool, the procedure is open to abuse and misuse and as such certain pre- estimation rules need to be adhered to ensure its validity. To achieve this, we have followed the ‘best-practice’ guidelines as described by Nelson and Kennedy (2009) and Stanley (2001). In addition, we follow DeCoster (2004) in highlighting the estimation issues that we have faced and the decisions taken in conducting the analysis.

In a meta-regression, it is crucial to ensure that the dependent variable of the analysis is measuring the same economic concept (Nelson and Kennedy, 2009). There are two aspects that need to be satisfied in regard to the above. The first is in the form of effect size uniformity, since primary studies may use different units of measurement (e.g. different metrics; units or percentage value). Second, attention must also be given to the context of the effect size. While the effect size may be uniform it is possible that the underlying economic context that was measured by these primary studies was different. For example, diesel demand is also used for industrial purposes and primary studies can be ambiguous in clarifying the contextual aspect of their data. In this eventuality, the inclusion of these empirical results in a transport fuel demand meta-analysis is inconsistent with the context of the analysis.31

31 This problem is often encountered in the general energy/energy economics literature, especially when it comes to non-gasoline fuel types. For example, see the diesel estimates in Al-Faris (1997) and De Vita et al. (2006) and the context of oil consumption in Moosa (1998).

The cogency of the meta-analysis can also be compromised by publication bias.32 Stanley (2005) argued that since researchers and editors tend to be predisposed towards results that conform to conventional expectations and that are statistically significant in order to be published, there is a strong likelihood that this bias will be carried into and thus distort the meta-analysis.

In addition, problems may also arise due to the number estimates reported by a study. This is highly likely in economic literature where the use of different specifications and estimators result in more than one estimate for the effect of interest. There are several options that can be considered but none is devoid of potential problems. If just one estimate is chosen per study, the meta-analysis may be susceptible to substantial bias arising from the choice of observation/estimates included in the sample. In fact, this basically runs the risk of re-introducing the same kind of subjectivity seen in the oft-criticised narrative reviews. In contrast, if all of the results from studies with multiple estimates are included as part of the meta- sample, however, there is a risk of over-representation and subsequently distortion to the analysis (Melo et al., 2013). In addition, the meta-regression estimates will also be affected due to the likely correlation of results from the same study.

Finally, the results of the meta-analysis will also be affected by the specification (i.e. the study characteristics/moderator variables) selected, just like any econometric model. Since there are no guidelines over which study characteristics are supposed to be consequential, the leeway afforded can also give rise to some subjectivity issues. In such an eventuality, the options are either to rely on the judgement of the researcher – in which case understanding the key issues related to the matter at hand is fundamental – or to follow the conventions established in previous work. DeCoster (2004) defines the latter option as the shared subjectivity in meta-analysis review. The obvious benefit of following the convention is that the replicability allows for inferences from previews reviews to be tested as well.

32 This issue has also been termed as the ‘file drawer problem’.

Table 5.1 List of primary studies used in the meta-regression analysis

Author(s) Publication Year Author(s) Publication Year

Akinboade et al. 2008 Lim et al. 2012

Al-Faris 1997 Lin & Prince 2009

Alves & De Losso Bueno 2003 Lin & Zeng 2012

Baltagi et al. 2003 Pock 2010

Baltagi & Griffin 1997 Polemis 2006

Banaszak et al. 1999 Ramanathan 1999

Baranzini & Weber 2012 Ramanathan & Subramaniam 2003

Barla et al. 2009 Samimi 1995

Barns 2002 Santos 2013

Belhaj 2002 Sene 2012

Bentzen 1994 Wadud et al. 2009

Birol & Guerer 1993

Cheung & Thomson 2004

Crôtte et al. 2008

Dahl & Kurtubi 2001

Danesin & Linares 2011

De Freitas & Kaneko 2011

De Vita et al. 2006

Eltony & Al-Mutairi 1995

Eskeland & Feyzioğlu 1997

Gonzalez–Marrero et al. 2012

Hanly et al. 2002

Hughes et al. 2008

Kennedy & Wallis 2007

Koshal et al. 2007

Li et al. 2010

Liddle 2009

Liddle 2012

5.3.1 Meta-sample While meta-analyses on fuel demand have been undertaken previously, they were confined exclusively to gasoline demand. The analysis undertaken here expands upon the existing research by including other road transport fuels and – by conducting an up-to-date survey of the literature – a much more recent set of primary studies. In addition, the analysis undertaken here also differs from previous studies by taking into account current methodological issues in the estimation of elasticity (i.e. cointegration and dynamic panel data).

The meta-sample is made up of elasticity estimates from 39 studies; of which more than 75% were published after the year 2000 (see Table 5.1). Due to the scope that have been highlighted above, when compared to the work of Espey (1998), only three of the papers included in the meta-sample here are similar with the rest being unique to this analysis.33

In order to ensure the validity of the analysis, steps were taken to overcome the issues highlighted earlier. First, to ensure the comparability of the effect size, only studies that report unit-free fuel demand elasticity were included. The studies were also screened to ensure that these elasticities were estimated in the context of road transport fuel demand. In addition, separate analyses were conducted for both price and income elasticities.

The meta-sample presented here included elasticity estimates from both published and unpublished studies. This is not only to account for the issue of publication bias but also to ensure that the analysis benefits from a much more comprehensive coverage of the literature. An additional benefit is that it also becomes possible to test for publication bias. It was also decided to include multiple-estimates from a

33 The studies which have been included in Espey (1998) are those by Baltagi and Griffin (1997), Bentzen (1994) and Eltony and Al-Mutairi (1995).

single study in the meta-sample. Apart from increasing the sample size, using multiple-estimates avoids the introduction of bias in the analysis.34

Frequency statistics of the meta-sample are provided in Tables 5.2 and 5.3. It should be noted that there is a large disparity between the frequencies of observations for the short- and long-run elasticities. This is largely due to the fact that panel data studies, in practice, tend to present short-run estimates from various different estimators but in the contrary only report long-run estimates based on a preferred estimator. The disparity also arises from time series studies which take into account the issue of non-stationarity of the data. In this case, if cointegration is not present, only short-run estimates can be obtained and therefore reported in the study.

In conducting our meta-regression, we use the convention set by Espey (1998) and Nelson and Kennedy (2009). In particular, an outlier analysis was also conducted to ensure unrepresentative or overly influential observations are discarded. Finally, we conduct sensitivity analysis by using two different meta-regression specifications to assess the robustness of the meta-regression results.

34 Bijmolt and Pieters (2001) argued in favour of keeping multiple observations from a single study in a meta- analysis. Through their Monte Carlo study, they found that discarding the additional observations resulted in a substantial loss of power and in generally unsatisfactory outcomes in the meta-analytic procedures.

Table 5.2 Summary of price elasticity variables included in the meta-regression analysis

Dimension Number of observations Short-run Long-run Methodological Characteristics Model specification Vehicle stock/ownership included 98 63 Public transport fare included 13 6 Other variables included 104 55 Functional form Double log 192 116 Linear 1 3 Semi-log 2 4 Translog 3 2 Lag structure ECM 19 – Partial adjustment 176 81 Static 3 44 Results type Non-significant 42 17 Significant 150 89 Unstated 6 19

Data Characteristics Quantity measure Aggregate 27 13 Per capita 88 57 Per household – – Per kilometre 2 2 Per vehicle 81 53 Time interval Annual 148 98 Monthly 4 17 Quarterly 46 10 Data type Cross section – – Panel data 126 59 Time series 72 66 Fuel type CNG 12 1 Diesel 27 10 Ethanol 12 3 Petrol/Gasoline 126 100 Total fuel 21 12 Aggregation level City/borough 6 2 National 136 89 State/regional/province 56 34

Environmental Characteristics Geographical regions Australia and New Zealand 9 4 East Asia and the Pacific 15 19 Eastern Europe and Central Asia 2 – Latin America and the Caribbean 50 11 Middle East and North Africa 17 4 North America 15 24 OECD 11 12 South Asia 3 1 Sub-Saharan Africa 1 4 Western Europe 75 46 Income status High income 122 92 Low income – – Lower-middle income 15 8 Upper-middle income 61 25 Time period Pre-1990 69 55 1990 and beyond 129 70

Total 198 125

Table 5.3 Summary of income elasticity variables included in the meta-regression analysis

Dimension Number of observations Short-run Long-run Methodological Characteristics Model specification Vehicle stock/ownership included 97 64 Public transport fare included 13 6 Other variables included 103 54 Functional form Double log 188 113 Linear 1 3 Semi-log 2 4 Translog 3 2 Lag structure ECM 18 – Partial adjustment 173 80 Static 3 42 Results type Non-significant 64 28 Significant 121 78 Unstated 9 16

Data Characteristics Quantity measure Aggregate 27 13 Per capita 84 49 Per household – – Per kilometre 2 2 Per vehicle 81 58 Time interval Annual 146 96 Monthly 2 16 Quarterly 46 10 Data type Cross section – – Panel data 126 64 Time series 68 58 Fuel type CNG 12 1 Diesel 27 10 Ethanol 12 3 Petrol/Gasoline 122 96 Total fuel 21 12 Aggregation level City/borough 6 2 National 135 82 State/regional/province 53 38

Environmental Characteristics Geographical regions Australia and New Zealand 9 3 East Asia and the Pacific 15 16 Eastern Europe and Central Asia 2 – Latin America and the Caribbean 50 11 Middle East and North Africa 17 2 North America 12 23 OECD 11 12 South Asia 3 1 Sub-Saharan Africa 1 4 Western Europe 74 50 Income status High income 118 94 Low income – – Lower-middle income 15 6 Upper-middle income 61 22 Time period Pre-1990 67 51 1990 and beyond 127 71

Total 194 122

5.4 DESIGN OF THE META-REGRESSION ANALYSIS The objective of the meta-regression analysis was to identify the underlying factors (i.e. model specification and contextual characteristics) that cause the wide study-to- study variations in the empirical results. One defining aspect of the meta-analysis undertaken in this chapter is the inclusion of various road fuel types as part of the meta-sample. By including a range of road fuel types it becomes possible to test the assumption that some of the variations seen in the elasticity estimates are attributable to the different fuel types. This will not only contribute towards a better understanding of the way model specifications affect estimates but will also allow a better assessment of the results of our econometric models.

Four meta-regression models were estimated. As stated previously, price and income elasticities of fuel demand were estimated separately and each were further divided based on the time period in which the response takes effect, i.e. short- or long-run. In the meta-analysis, it was postulated that the variation found in the fuel demand literature can be attributed to three broad study/model factors: (1) methodological factors, (2) data factors, and (3) environmental factors. Following the literature review conducted in Chapters 3 and 4, these underlying study characteristics were further divided into more focused related factors. Table 5.4 describes the moderating variables/covariates included in the meta-regression.

Methodological characteristics broadly refer to the specification adopted for the econometric model used in the estimation of the fuel demand elasticities. First, it was considered whether there are other variables included in the estimation apart from price and income. Specific attention was given to the inclusion of vehicle stock and public transport fare in the estimation model, since the effects of these variables might be expected to be captured by price and income elasticities if excluded (Blum et al., 1988). The influence of functional forms on elasticity estimates was also investigated. Four different functional forms were found in the meta-sample. In the meta-regression models, the double-log form was used as the reference case with separate dummy variables assigned each for the linear, semi-log and translog forms. The influence of lag structure was also tested for. In the sample, the dynamic models

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were almost exclusively comprised of the partial adjustment model. The only exception was when the estimation was based on the Engle–Granger procedure, in which we find the dynamic process in the short-run modelled through an ECM (i.e. including the lag of the residuals). Finally, it was also investigated whether statistical significance exerts an influence on the empirical results.

Factors classified under data characteristics included the quantity measure, the time interval, the type of data used and the fuel type consumed. Quantity measure refers to the manner in which the dependent variable is quantified (refer to §3.2). The meta-sample used here was made up entirely of studies using time series and panel data. Despite our best efforts, however, we were unable to find estimations based on cross-sectional data for the publication time period under focus. With the growing availability of more informative datasets in the form of the panel data, and the preference for dynamic methods of estimation, it is likely – as evidenced here – that cross-sectional data may no longer be favoured.

The influence on the empirical results of the level of aggregation of the data was also considered. To clarify, the aggregation level refers to the unit in which the data used is measured, i.e., whether at the borough or city level, at state or regional level, and at the national level. Finally, the presence of the different road fuel types in the meta-sample also made it possible to test – albeit indirectly – the assumption that demand responses vary according to the fuel consumed. To distinguish the impact of the various fuels, moderator variables were used for each fuel type included, with petrol fuel chosen as the reference case.

Environmental characteristics include information that provides the contextual differences to the elasticities estimated. In the literature, this usually involves some spatial and temporal aspects of the study. The first factor considered was the geographical aspect. We also applied a set of moderators to control for the influence of income level. The reason for this classification is that there is compelling evidence in the literature to suggest that the type of travel and travel pattern is distinctly influenced by the level of wealth of the population. For example, it is suggested that

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low- and middle-income economies tend to experience a strong rate of motorization which will be reflected in the income elasticity estimate. In contrast, developed economies are hypothesised to experience travel saturation. This leads to a relatively low fuel demand income elasticity magnitude. The final factor investigated was whether fuel demand elasticities have remained consistent or whether they have varied over time. This has important implications as it has been suggested by Hughes et al. (2008), that the latter outcome is likely since such a responsiveness would tend to reflect the structural and behavioural changes that take place in real life. To test for this, a dummy variable was included for estimates that used primarily data from 1990 and later, with the reference case being studies that primarily consisted of pre- 1990 data.35

35 One particular problem in controlling for the variation due to the time span of the data is that the majority of the studies in the meta-sample tend to have datasets that overlap the boundary mentioned above. In this event, the categorisation adopted (i.e. pre-1990 or otherwise) was based on the number of observations that dominate the dataset of the study.

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Table 5.4 Summary of moderator variables considered in the meta-regression analysis

Dimension Variable Definition Reference case Methodological factors

Model specification DVS 1 if vehicle stock is included, 0 otherwise Study use price and income only DPT 1 if public transport fare is included, 0 otherwise DOther 1 if other variables included, 0 otherwise

Functional form DL 1 if the functional form is linear, 0 otherwise Functional form is double log DSL 1 if the functional form is semi-log, 0 otherwise DTL 1 if the functional form is translog, 0 otherwise

Lag structure DPA 1 if the model is partial adjustment, 0 otherwise Lag structure is static DStatic 1 if the model static, 0 otherwise

Results type DNS 1 if the result is non-significant, 0 otherwise Result type is significant DUnstated 1 if the result is unstated, 0 otherwise

Data factors

Quantity measure DAgg 1 if qty measure is aggregate, 0 otherwise Quantity measure is per capita DPH 1 if qty measure is per household, 0 otherwise DPKM 1 if qty measure is per kilometre, 0 otherwise DPV 1 if qty measure is per vehicle, 0 otherwise

Time interval DMonthly 1 if time interval is monthly, 0 otherwise Time interval is annually DQuarterly 1 if time interval is quarterly, 0 otherwise

Data type DCS 1 if data type is cross section, 0 otherwise Data type is time series DPD 1 if data type is panel data, 0 otherwise

Fuel type DCNG 1 if fuel type is CNG, 0 otherwise Fuel type is petrol/gasoline DDiesel 1 if fuel type is diesel, 0 otherwise DEth 1 if fuel type is ethanol, 0 otherwise DTF 1 if fuel type is total, 0 otherwise

Aggregation level DC/B 1 if aggregated at city/boroughs, 0 otherwise Data aggregation at national level DS/R 1 if aggregated at state/region, 0 otherwise

Environmental factors

Geographical regions DANZ 1 if Australia and New Zealand, 0 otherwise Estimates are for Western Europe DEAP 1 if East Asia and the Pacific, 0 otherwise and OECD DEECA 1 if Eastern Europe and Central Asia, 0 otherwise DLAC 1 if Latin America and the Caribbean, 0 otherwise DMENA 1 if Middle East and North Africa, 0 otherwise DNA 1 if North America, 0 otherwise DSA 1 if South Asia, 0 otherwise DSSA 1 if Sub-Saharan Africa, 0 otherwise

Income Status DLow 1 if low income country, 0 otherwise Study is in high income country DLow-Mid 1 if lower-middle income country, 0 otherwise DUp-Mid 1 if upper-middle income country, 0 otherwise

Time period of analysis D>90 1 if time period is after 1990, 0 otherwise Period is for years before 1990 Notes: 1) The geographical regions’ classification adopted is largely based on the World Bank’s country grouping methodology. Please refer to http://data.worldbank.org/about/country-classifications/country-and-lending-groups for further details.

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5.5 META-REGRESSION RESULTS The results of the meta-regression analysis are reported in Tables 5.5–5.8. Three different random-effects models were estimated. Model (1) includes all of the model factors, Model (2) focuses on the methodological and data factors while Model (3) looks solely at the effects of fuel type heterogeneity on demand responses. Due to the nature of the data, dummy variables for income status are excluded in Model 1, since they appear to be correlated with the geographical regions variable. Similarly, the dummy for time period does not appear to have any significant effect and is therefore not included in the models presented.

The interpretation of the meta-regression requires care. Since all of the covariates are dummy variables, the constant in the meta-regression represents the mean elasticity for a particular reference case, i.e. the expected elasticity value when all the dummy variables are zero. As such, the coefficient of a dummy variable (when it is not zero) represents the deviation from the default reference case that can be attributed to a particular factor.

5.5.1 Price Elasticity We start by examining the results of the meta-regression models on price elasticity. From the results reported in Tables 5.5 and 5.6, striking similarities were observed, not only between the different models but also between the short- and long-run estimates. This high degree of consistency in the meta-regression models indicates the robustness of the results.

Looking at the results for short-run price elasticity, it can be seen that most of the geographical regions have a larger response to changes in petrol price compared to the Western Europe/OECD region. Hughes et al. (2008) states that price elasticity in the short-run reflects changes in driving behaviour. In the short-run, behaviour response could include better vehicle maintenance, reduction of driving distance, and adoption of milder driving manners. Another hypothesis is that the less developed nature of the other regions may mean that travel destinations are relatively smaller in terms of distance and as such switching modes may be viable.

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Alternatively, it can also be attributed to what is described by Goodwin et al. (2004) as the differential effect, whereby less efficient vehicles are likely to be left at home in favour of smaller or more efficient vehicles. For example, it is common for households in South-East Asian countries to own motorcycles as well as cars, thus making switching to a less fuel intensive mode far more likely. Additionally, it is possible that the larger variation seen in the other regions reflects a lower level of dependency on motorized forms of transportation altogether.

Surprisingly, the regional heterogeneity effect appears, in some cases, to be the opposite in the long-run. Our results suggest that Australia and New Zealand, North America and South Asia seem to exhibit smaller long-run price elasticity. Although counterintuitive, the individual results can also be attributed to a variety of factors. For example in the case of South Asia, the lower response might reflect the effects of a long term trend of rising income among consumers. In theory, this means that fuel consumption would represent less of a burden in terms of budget share thus resulting in the lower level of response seen. On the other hand, the evidence that Australia and New Zealand and North America are less price responsive appears to confirm the results reported by Espey (1998). On the surface, it supports her assertion that these regions have differing driving characteristics compared to Western European countries.

Turning to the methodological design factors, there appears to be some evidence to support the assertion by Blum et al. (1988) that the effects of exogenous variables may be captured by the price elasticity if excluded from the model. This seems to be the case in the long-run estimates, especially in regard to the inclusion of vehicle stock. In both models, the inclusion of this variable appears to imply a reduction of between 56–77% in the long-run price elasticity.

We found contrasting results when it comes to the influence of the functional form adopted. For the long-run price elasticity, our models indicate the absence of a significant variation in the effect of functional form heterogeneity. On the other hand, the coefficient of the translog functional form is significant in both short-run

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models, indicating that their adoption in estimating fuel demand will result in more elastic estimates. The evidence is less conclusive, however, when it comes to the semi-log functional form, with a significant effect apparent in Model 1 but this is not replicated in Model 2.

A similar effect is evident when it comes to the influence of the choice of lag structure. For the long-run estimates, both meta-regression models appear to confirm that there are no significant differences between the results from static and dynamic models. Significant differences were evident, however, when it comes to the short-run price elasticity. In Model 1, the results corroborate those found by Espey (1998), in which dynamic and ECM models appear to produce less price-elastic estimates compared to the static model. Significantly, this outcome was also reported by Dahl and Sterner (1991) and, therefore, our results appear to support their hypothesis that static models produce estimates that are more intermediate- run in nature.

Interestingly, the results also reveal some important outcomes on the effect of data factors on price elasticity estimates. Looking at the type of quantity measure used, the results appear to imply that models specified as per kilometre appear to produce larger price elasticity for both the short- and long-run estimates. Additionally, the results from Model 1 appear to suggest that a similar outcome can also be seen in the long-run for the per vehicle specification. This was not corroborated by Model 2, however. Since the same outcome was also not repeated in the short-run models, we cannot come to a definitive conclusion on the effect of the per vehicle specification.

There was no significant difference found between the short-run estimates using time series data and those using panel data. Contrastingly, when it comes to the long-run estimates, however, panel data studies appear to produce estimates that are significantly more price elastic compared to those found in pure time series studies. To an extent, this is not surprising since the use of panel data may allow the greater data variations, compared to time series data, to be captured, thus resulting

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in more elastic estimates. Additionally, our results indicate that the level of data aggregation could result in significant variation in the short-run price elasticity estimate. In Model 1, data aggregated at the city (state) level produced price elasticity that is approximately 4 (12) percentage points larger compared to the reference elasticity value. This could be due to the fact that, at a lower level of aggregation, the data captures more subtle responses due to the larger heterogeneity of responses/choices (Nijkamp and Pepping, 1998). Surprisingly, the same outcome could not be confirmed for the long-run estimates since the coefficients for both the city and state dummy variables were not statistically significant.

Finally, the type of fuel consumed appears to have a significant influence on the variation seen in the price elasticity estimates produced from the studies. Unlike some of the results discussed earlier, the fuel heterogeneity effects are apparently consistent across all of the meta-regression models. This is particularly so for the short-run models, where the magnitude of the effects by each of the fuel types falls within a relatively narrow range. For the long-run models, although consistency was observed in terms of the sign of the effects, the exclusion of other modelling factors in Model 3 appears to produce relatively deflated effect parameters.

With the exception of ethanol, all of the fuels investigated seem to be less sensitive to price changes in the short-run compared to petrol. In the case of diesel and CNG, this reduced sensitivity could be explained by the fact that, due to the data time frame of the studies in the meta-sample, they were predominantly consumed by the road freight sector. In contrast, it makes sense for petrol price elasticity to be higher in comparison, since this is largely consumed by private consumers, who are likely to be more price-sensitive compared to businesses. In the long-run however, the effect appears to be inverted. We found the coefficients for the dummy variables representing diesel and ethanol to be statistically significant at the 1% level suggesting that these fuels are significantly more price elastic. On the other hand, while the coefficients representing CNG and total fuel display similar signs, their statistical significance cannot be confirmed by both meta-regression models.

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Table 5.5 Meta-regression results – short-run price elasticity

Model factors Dimensions Variables Model 1 Model 2 Model 3 Coefficient Std. Coefficient Std. Coefficient Std. Error Error Error

Constant 훼0 –0.176*** 0.067 –0.168*** 0.034 –0.192*** 0.030

Methodological Model specification DVS –0.044 0.037 –0.122 0.090 DPT –0.356 0.553 –0.013 0.050 DOther –0.016 0.012 –0.028 0.023

Functional form DL –0.007 0.022 –0.067 0.056 DSL –0.051** 0.023 –0.011 0.021 DTL –0.272*** 0.011 –0.271*** 0.011

Lag structure DDPA –0.157*** 0.057 –0.018 0.044 DECM –0.110** 0.054 –0.063 0.048

Results type DNS –0.123*** 0.017 –0.113*** 0.017 DUnstated –0.109** 0.055 –0.133 0.094

Data Quantity measure DAggregate –0.015 0.028 –0.045 0.043 DPKM –0.156** 0.067 –0.333*** 0.101 DPV –0.064 0.079 –0.038 0.093

Time interval DMonthly –0.048 0.240 –0.034 0.034 DQuarterly –0.014 0.047 –0.034 0.035

Data type DPD –0.020 0.043 –0.076 0.055

Fuel type DCNG –0.232*** 0.007 –0.222*** 0.009 –0.252*** 0.001 DDiesel –0.072** 0.031 –0.064* 0.033 –0.099*** 0.035 DEthanol –0.825*** 0.006 –0.834*** 0.005 –0.824*** 0.001 DTF –0.046*** 0.018 –0.048** 0.020 –0.053** 0.017

Aggregation level DC/B –0.044*** 0.016 –0.020 0.024 DS/R –0.125* 0.067 –0.077 0.086

Environmental Geographical DANZ –0.111** 0.049 regions DEAP –0.226*** 0.054 DEECA –0.108** 0.049 DLAC –0.364*** 0.139 DMENA –0.158*** 0.051 DNA –0.009 0.055 DSA –0.092* 0.051 DSSA –0.549*** 0.167

Observations 198 198 198 R2 (total) 0.904 0.867 0.726 R2 (within) 0.905 0.895 0.863 R2 (between) 0.746 0.649 0.101 Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Standard errors are robust to heteroskedasticity and adjusted for intra-study dependence.

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Table 5.6 Meta-regression results – long-run price elasticity

Model factors Dimensions Variables Model 1 Model 2 Model 3 Coefficient Std. Coefficient Std. Coefficient Std. Error Error Error

Constant 훼0 –0.441*** 0.071 –0.328*** 0.077 –0.428*** 0.056

Methodological Model specification DVS –0.249* 0.129 –0.252* 0.132 DPT –0.343*** 0.183 –0.159 0.160 DOther –0.103* 0.057 –0.025 0.072

Functional form DL –0.061 0.043 –0.088 0.077 DSL –0.058 0.050 –0.066 0.074 DTL –0.000 0.028 –0.015 0.046

Lag structure DDPA –0.135 0.087 –0.006 0.115 DECM

Results type DNS –0.051 0.185 –0.015 0.182 DUnstated –0.295*** 0.108 –0.139 0.143

Data Quantity measure DAggregate –0.087 0.115 –0.095 0.134 DPKM –0.002 0.158 –0.476** 0.198 DPV –0.332* 0.171 –0.213 0.188

Time interval DMonthly –0.084 0.055 –0.145 0.107 DQuarterly –0.221 0.138 –0.182 0.136

Data type DPD –0.254* 0.144 –0.364** 0.170

Fuel type DCNG –0.059 0.179 –0.167 0.215 –0.379*** 0.039 DDiesel –0.266** 0.112 –0.314*** 0.085 –0.191** 0.084 DEthanol –0.972*** 0.349 –1.440*** 0.231 –1.105*** 0.056 DTF –0.069 0.076 –0.088 0.086 –0.023 0.067

Aggregation level DC/B –0.105 0.139 –0.173 0.149 DS/R –0.057 0.130 –0.082 0.120

Environmental Geographical DANZ –0.433*** 0.111 regions DEAP –0.095 0.138 DEECA DLAC –0.279* 0.171 DMENA –0.078 0.076 DNA –0.295*** 0.099 DSA –0.122* 0.071 DSSA –0.413** 0.177

Observations 125 125 125 R2 (total) 0.510 0.420 0.178 R2 (within) 0.053 0.023 0.007 R2 (between) 0.779 0.567 0.319 Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Standard errors are robust to heteroskedasticity and adjusted for intra-study dependence.

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5.5.2 Income Elasticity The meta-regression analysis on income elasticity appears to reveal similarities as well as differences in the underlying factors that cause variations between the short- and long-run estimates. In general, we found evidence that in both cases, the variation seen in the estimates can be attributed to regional heterogeneity. Additionally, the differences in the magnitude of price elasticity seen can also be explained by the type of fuel modelled in the study.

Starting with the methodological factors of a study, we observe that model specification does have some influence on the estimated income elasticities. First, the inclusion of the vehicle stock variable seems to result in a smaller level of income elasticity. This is due to the positive correlation that exists between vehicle ownership and income as well as with petrol consumption. The result is consistent with what was described by Blum et al. (1988) and Basso and Oum (2007), that exclusion of the vehicle stock variable will result in an upward bias in income elasticity. Interestingly, the coefficients for the public transport fare dummy variables suggest that their inclusion will have a significantly positive impact on the income elasticity estimates for petrol demand. In general, this is plausible since public transport fares are likely to be negatively correlated with income. The exclusion of public transport fares would, therefore, likely cause its effect to be captured by the income coefficient, thus biasing the estimate downwards. Finally, there is some evidence that the income elasticity estimates might also capture the effect of other exogenous factors, as described by Blum et al. (1988). This was only statistically significant for the long-run estimates, however, while the effect was not corroborated in the short-run models.

There appear to be contrasting outcomes when it comes to the influence of the functional form on the income elasticity estimates. Translog models tend to produce significantly lower long-run income elasticity compared to the reference i.e. double- log models. On the other hand, no significant difference was found between the translog models and the double-log models in the short-run estimates.

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Contrary to the findings of Espey (1998), the results indicate that partial adjustment models do not lead to significantly lower income elasticity estimates either in the short- or long-run. As for the effect of the ECM models, the results imply that this specification tends to produce more income-elastic estimates in the short-run, although the relatively large difference in the order of magnitude attributed to the ECM models may not reflect the true underlying effect size but rather the relatively low short-run static observations in the meta-sample.

The controls for results type suggest that significant estimates tend to be higher than the non-significant estimates reported in the studies. This is interesting since it may indicate the possibility of publication bias in the reported estimates. By considering the source of the estimates (i.e. published and unpublished papers) as well as the relationship between the income elasticity and their respective standard errors, it is possible to identify whether the values reported in the studies are affected by reporting bias. The matter of publication bias will be further considered in the following section.

As with the price elasticity estimates, studies using per kilometre quantity measures tend to produce a significant difference compared to those measuring consumption in per capita terms. One possible explanation for this negative effect is that higher income may stimulate faster replacement of the older vehicle stock with more efficient ones. In this way, the per kilometre fuel consumption will decrease as income increases (Barla et al., 2009). On the other hand, there was no significant difference between studies using the per capita measure with those using either the aggregate or the per vehicle measure.

Differences in the time interval of the data used in the studies do not appear to have any significant influence on the estimated income elasticity either in the short- or the long-run. Similarly, studies using panel data have no significant effect on the magnitude of the income elasticity estimates, which is opposite to the results for price elasticity. There appears to be a strong consensus with regards to the effect of data aggregation for both the short- and the long-run income elasticity estimates. In

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particular, we found the coefficient accounting for data aggregated at the city level to be statistically significant at the 5% level in both meta-regression models. The results imply that, in such models, the income estimate will be less elastic compared to models using data aggregated at the national level. The use of data at the regional level, however, does not appear to produce a similar statistically significant effect.

Fuel type heterogeneity appears to influence the results of the estimation of income elasticity strongly. Just like the price elasticity estimates, there is a high level of consistency in terms of the results reported for income elasticity by the short-run meta-regression models. In the long-run models, however, the effects appear to be more varied. We observe that although the parameters for each of the fuel type variables are consistently displaying a positive sign (i.e. inclusion of these fuels will result in an inflated long-run income elasticity), the magnitude of their effects can differ widely between the meta-regression models. For Model 3 in particular, the exclusion of other moderating variables appears to strongly diminish the magnitude of the parameter for ethanol. In addition, the coefficient for the dummy variable for CNG is now statistically significant at the 1% level.

The results indicate that diesel, ethanol and total fuel models will produce significantly higher income elasticity compared to petrol fuel models. In the short run, the difference appears to be relatively small, however. Without controlling for regional heterogeneity in Model 2, the results suggest that the income elasticity of diesel demand is 40% higher. A similar outcome was observed in both the ethanol and total fuel models with income responses being higher by approximately 83% and 26%, respectively. The effects are analogous for the long-run elasticity estimate, although the variations in the magnitude are relatively higher. In general, this appears to reaffirm the problem of what one is really measuring if a petrol or total fuel estimate is used, as described by Schipper et al. (1993). Based on the results observed, there is a strong basis to support their argument that it is probably better to estimate demand elasticity separately for each fuel type.

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Finally, regional heterogeneity seems to play an important role in explaining the variation in the elasticity estimates seen across studies. In the short run, all of the regional coefficients are positive and significant, with the exception of those for Australia and New Zealand and Latin American and the Caribbean. This implies that studies using European data would tend to report lower short-run income elasticity. However, the results also indicate that only the geographical regions of East Asia and the Pacific, Middle East and North African and South Asia are likely to be more income-elastic than Europe in the long run.

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Table 5.7 Meta-regression results – short-run income elasticity

Model factors Dimensions Variables Model 1 Model 2 Model 3 Coefficient Std. Coefficient Std. Coefficient Std. Error Error Error

Constant 훼0 –0.007 0.202 –0.387*** 0.043 –0.338*** 0.054

Methodological Model specification DVS –0.085 0.121 –0.247* 0.134 DPT –0.208 0.154 –0.312** 0.155 DOther –0.066** 0.027 –0.054* 0.032

Functional form DL –0.037 0.046 –0.071** 0.031 DSL –0.132** 0.057 –0.007 0.029 DTL –0.003 0.010 –0.011 0.014

Lag structure DDPA –0.101 0.081 –0.045 0.101 DECM –0.351* 0.182 –0.348* 0.179

Results type DNS –0.382*** 0.090 –0.381*** 0.086 DUnstated –0.029 0.029 –0.064 0.054

Data Quantity measure DAggregate –0.065 0.120 –0.090 0.137 DPKM –0.369** 0.144 –0.235** 0.118 DPV –0.206 0.126 –0.038 0.134

Time interval DMonthly –0.059 0.082 –0.003 0.121 DQuarterly –0.000 0.156 –0.083 0.125

Data type DPD –0.273 0.176 –0.131 0.173

Fuel type DCNG –0.013 0.023 –0.002 0.020 –0.087*** 0.023 DDiesel –0.149* 0.091 –0.157* 0.093 –0.172* 0.089 DEthanol –0.329*** 0.004 –0.320*** 0.004 –0.321*** 0.023 DTF –0.099** 0.042 –0.099** 0.038 –0.114** 0.055

Aggregation level DC/B –0.093*** 0.015 –0.072** 0.028 DS/R –0.129 0.086 –0.080 0.072

Environmental Geographical DANZ –0.306 0.245 regions DEAP –0.581*** 0.182 DEECA –0.801*** 0.154 DLAC –0.084 0.140 DMENA –0.339** 0.156 DNA –0.368** 0.177 DSA –0.830*** 0.141 DSSA –0.725*** 0.261

Observations 194 194 194 R2 (total) 0.599 0.400 0.081 R2 (within) 0.569 0.530 0.145 R2 (between) 0.653 0.353 0.026 Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Standard errors are robust to heteroskedasticity and adjusted for intra-study dependence.

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Table 5.8 Meta-regression results – long-run income elasticity

Model factors Dimensions Variables Model 1 Model 2 Model 3 Coefficient Std. Coefficient Std. Coefficient Std. Error Error Error

Constant 훼0 –0.323 0.302 –0.772*** 0.205 –0.550*** 0.115

Methodological Model specification DVS –0.267 0.293 –0.586*** 0.173 DPT –0.802** 0.342 –0.688*** 0.262 DOther –0.199 0.199 –0.045 0.252

Functional form DL –0.007 0.064 –0.038 0.038 DSL –0.117 0.109 –0.162 0.145 DTL –0.179*** 0.049 –0.210*** 0.051

Lag structure DDPA –0.102 0.153 –0.090 0.164 DECM

Results type DNS –0.419* 0.216 –0.404** 0.203 DUnstated –0.255 0.164 –0.232 0.199

Data Quantity measure DAggregate –0.090 0.239 –0.313 0.240 DPKM –0.782** 0.395 –0.854** 0.417 DPV –0.001 0.330 –0.067 0.275

Time interval DMonthly –0.036 0.171 –0.179 0.127 DQuarterly –0.014 0.230 –0.218 0.239

Data type DPD –0.326 0.198 –0.351 0.244

Fuel type DCNG –0.123 0.172 –0.101 0.128 –0.272*** 0.061 DDiesel –1.016*** 0.166 –1.112*** 0.149 –1.056*** 0.162 DEthanol –0.645 0.689 –0.994** 0.387 –0.307*** 0.115 DTF –0.801** 0.361 –1.019*** 0.308 –0.991** 0.461

Aggregation level DC/B –0.950*** 0.228 –0.910*** 0.265 DS/R –0.194 0.266 –0.025 0.275

Environmental Geographical DANZ –0.108 0.373 regions DEAP –0.574** 0.288 DEECA DLAC –0.228 0.299 DMENA –0.617** 0.302 DNA –0.032 0.309 DSA –2.359*** 0.302 DSSA –0.232 0.398

Observations 122 122 122 R2 (total) 0.573 0.397 0.271 R2 (within) 0.488 0.518 0.401 R2 (between) 0.823 0.239 0.104 Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Standard errors are robust to heteroskedasticity and adjusted for intra-study dependence.

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5.6 PUBLICATION BIAS

‘Publication bias is leading to a new formulation of Gresham’s law – like bad money, bad research drives out good’. (Bland, 1988)

Despite the advantages of meta-regression analysis, it is important to realise that the cogency of its output is very much dependent on the sources of information it is required to synthesize. A frequent criticism of meta-analysis is that it is highly susceptible to the issue of publication bias (Stanley, 2005). It is therefore essential to check for the presence of publication bias when undertaking any meta-analysis.

Publication bias is defined as the phenomenon in which the pattern and variation of published results is influenced by the predisposition and requirements particular to academic publishing (Knell and Stix, 2005). Stanley (2005) and Card and Krueger (1995) describe several instances which may lead to publication bias. First, it may be due to the penchant of academic editors in choosing to publish statistically significant results in preference to non-significant ones. Second, there might be a tendency among editors and reviewers to “play it safe”, i.e. by not favouring studies that contradict the conventional view of the expected result. Finally, this culminates in forcing researchers to conduct specification searches and self-censorship in order to meet the factors described earlier, thus continuing the cycle of publication bias. From the above, it is not hard to see how meta-regression analysis can fail, since if the empirical results in a particular field are already biased, then the output of a meta-analysis is also likely be skewed and unreliable.

In the meta-analysis conducted earlier, we have included non-published work in order to lessen the possible effect of publication bias.36 Even this may not be adequate as there is no guarantee that unpublished works are themselves free of

36 Categorising studies into published and unpublished can also be problematic. This is particularly so when publication status may possibly change over time. In our meta-sample, we have encountered cases where unpublished working papers which we initially collected during the preliminary stages of the literature review have now become published in academic journals. Examples of such cases are the original studies by Baranzini and Weber (2012) and Lin & Zeng (2012) which have now been published as Baranzini and Weber (2013) and Lin & Zeng (2013).

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selection bias. In fact, if the unpublished work is intended for publication then self- censorship is likely to result into selection bias as well.37 To test whether our meta- sample is affected, we therefore conducted tests for publication bias.

The detection of publication bias was performed by analysing the relationship between the price and income elasticity estimates with their respective standard errors (see Stanley, 2008; Stanley, 2005; Gorg and Strobl, 2001). This requirement, however, meant that not all studies from our meta-analysis could be included since some did not contain information on their standard errors. Consequently, the publication bias test was conducted on a smaller sample of only 33 studies (out of 39 originally in the meta-sample).

The test for publication bias was conducted separately for both price and income elasticities, but to compensate for the smaller sample size we combined both the short- and the long-run estimates together. There are 271 observations in our price elasticity sample, 188 of which are from published sources with the remaining 83 obtained from unpublished articles. Published and unpublished sources account for 183 and 85 observations respectively, making up for a total income elasticity sample size of 268. From a statistical perspective, combining both published and unpublished observations is beneficial as it allows for an efficient estimate of the coefficients during the formal test of publication bias implemented later in this section.

Card and Krueger (1995) proposed an informal but intuitive graphical analysis as a way of detecting publication bias. In their paper, they suggested that if publication bias were absent, then there would be no systematic relationship between the estimates and their standard error. In contrast when there is publication bias, there will be a tendency for the t-value to be above 2 (in absolute terms) thus resulting in a positive relationship between the two variables. Consequently, by plotting the

37 In the meta-sample, estimates which were originally taken from the unpublished studies and categorised as so will continue to retain the original classification as long as there are no differences in comparison to its’ published version.

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estimates with their respective standard errors, one can assess whether such a relationship exists.

Figures 5.1 and 5.2 present scatter diagrams that illustrate the mentioned relationship. In the diagrams, a line signifying the theoretical statistical threshold of where the t-ratio value equals 2 is also included. In both cases, it can be observed that there appears to be a tendency for many of the estimates to cluster above the line signifying that publication bias is likely to be present. The visual evidence also suggests that the non-published works may also be affected by selection bias. This comes as no surprise, since, as has been noted, some of these unpublished works have gone on to be published, so it is possible that some form of self-censorship was incorporated into the work to ensure conformity with the status quo.

2.4 t-stat = 2

1.8

1.2

Priceelasticity(Absolute value) .6

0 0 .3 .6 .9 1.2 1.5 Standard Error

Published Unpublished

Figure 5.1 Relationship between price elasticity estimates (in absolute values) and their standard errors

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3 t-stat = 2

2.5 2 1.5 1 Incomeelasticity(Absolute value) .5 0

0 .3 .6 .9 1.2 1.5 Standard Error

Published Unpublished

Figure 5.2 Relationship between income elasticity estimates (in absolute values) and their standard errors

The graphical analysis, although useful, can be susceptible to subjective interpretation. To overcome this, publication bias can be tested formally by a regression of the elasticity estimates with their standard errors (see Melo et al., 2013; Stanley, 2005; Gorg and Strobl, 2001). We can test for the presence of the ‘file drawer’ effect (i.e. statistically significant and having the expected sign) through the regression model:

휀푖푗̂ = 휀0 + 훽0푠푒(휀푖푗̂ ) + 휖푗+푢푖푗 (5.2)

where 휀푖푗̂ is the estimated elasticity, 휀0 is the constant term, 푠푒(휀푖푗̂ ) is the standard

error, 훽0 measures the magnitude of publication bias while 휖푗 and 푢푖푗 are the study specific effects and the usual disturbance term respectively.

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Regressing the estimated elasticities on its standard error may provide evidence of a systematic relationship between these two variables (i.e. publication bias). In theory, if publication bias is absent, one would not expect a significant 훽0 estimate and that the estimated effects would only randomly diverge from the average underlying elasticity, 휀0. Hence, if the null of 훽0 = 0 cannot be rejected, then we accept that no systematic relationship exists between the elasticity estimates and their standard errors and conclude that publication bias is not present.

Additionally, Stanley (2005) mentioned that a subset of selection bias can be that of which is independent of the effects’ direction but otherwise require a statistically significant effect only. In such case, this can be tested through the following:

|휀푖푗̂ | = 휀0 + 훽0푠푒(휀푖푗̂ ) + 휖푗+푢푖푗 (5.3)

where |휀푖푗̂ | is the absolute value of the estimated elasticity.

Finally, a more flexible model that allows for the separate detection of publication bias in published and unpublished works can be performed using the regression of the form:

휀푖푗̂ = 휀0 + 훽푃퐷푃푠푒(휀푖푗̂ ) + 훽푈퐷푈푠푒(휀푖푗̂ ) + 휖푗+푢푖푗 (5.4)

where 퐷푃 (퐷푈) takes the value of 1 if the estimate is from published (unpublished) studies and 0 otherwise.

In Tables 5.9 and 5.10, the results of Eqs. (5.2) to (5.4) are presented as Models 1–3 respectively.

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Table 5.9 Publication bias tests for price elasticity

Variable Model 1 Std. Error Model 2 Std. Error Model 3 Std. Error

휀0 –0.245*** 0.052 –0.249*** 0.052 –0.211*** 0.041

훽0 –0.429** 0.207 –0.431** 0.207

훽푃 –0.253*** 0.076

훽푈 –1.421*** 0.264

N 271 271 271 R2 (total) 0.129 0.131 0.187 R2 (within) 0.117 0.117 0.287 R2 (between) 0.096 0.097 0.002 Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Standard errors are robust to heteroskedasticity and adjusted for intra-study dependence.

Performing the regression models on price elasticity, there appears to be evidence of publication bias, thus confirming the informal test earlier (see Figure 5.1). From the results, we can conclude that there is a tendency for estimates that are statistically significant to be reported. Unpublished works are similarly affected by selection bias.

Table 5.10 Publication bias tests for income elasticity

Variable Model 1 Std. Error Model 2 Std. Error Model 3 Std. Error

휀0 –0.298*** 0.063 –0.312*** 0.060 –0.323*** 0.055

훽0 –1.406*** 0.262 –1.433*** 0.242

훽푃 –1.136*** 0.250

훽푈 –1.796*** 0.083

N 268 268 268 R2 (total) 0.268 0.313 0.265 R2 (within) 0.310 0.362 0.334 R2 (between) 0.259 0.264 0.222 Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Standard errors are robust to heteroskedasticity and adjusted for intra-study dependence.

A similar outcome can be observed from the test of publication bias on the income elasticity estimates. The results in Table 5.10 suggest the presence of publication bias since the coefficient 훽0 is statistically significant at the 1% level in both Models 1 and 2. To conclude, the outcome from the tests above appear to indicate that there is bias towards reporting statistically significant results in the literature of road transport fuel demand included in the meta-sample.

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5.7 SUMMARY In this chapter, the variations in price and income elasticity estimates found in the empirical studies of road transport fuel demand were analysed through the use of meta-regression models. Apart from using more recent studies, a defining aspect of the meta-analysis carried out here is the investigation of whether the underlying variation can be attributed to fuel type heterogeneity. To that end, a meta-sample derived from 39 primary studies which contained price and income demand elasticities, not only for petrol, but also other road fuels, such as diesel, ethanol and CNG, has been constructed.

The results from the meta-regression analysis provide evidence that some aspects of the study characteristics can indeed influence the estimates obtained in empirical studies. For both price and income elasiticities, it was found that regional and fuel type heterogeneity can have a considerable effect on the magnitude of the estimates reported. To a lesser extent, the variation found can also be attributed to the model specification adopted by a study.

Besides the above, another aspect considered in the chapter is whether empirical studies of fuel demand are affected by publication bias. Unfortunately, our results suggest that there is evidence of selection bias towards statistically significant results in the studies that we have included. This has potentially serious implications since limiting empirical evidence to what is statistically significant may hinder the overall understanding of the area of road transport fuel demand since it is based on information which may be unrepresentative of the real state of affairs.

Finally, the analyses conducted have proven to be invaluable in providing additional understanding with regards to fuel demand modelling. Taken together with the literature review conducted in Chapters 3 and 4, this analysis provides additional confidence in undertaking the actual fuel demand modelling in the following chapters.

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CHAPTER 6 ESTIMATION OF FUEL DEMAND ELASTICITIES USING

ANNUAL TIME SERIES DATA

6.1 INTRODUCTION This chapter presents and analyses the estimation results of the fuel demand model for the different fuel types using time series data. The discussion in Chapter 1 and the review of the literature presented in Chapter 3 reveal that few topics have drawn more interest from a wide spectrum of decision makers than the understanding and management of fuel demand. To this end, intensive research on transportation fuel demand estimates has been undertaken and this is reflected in the existence of an extensive literature on fuel demand elasticity. The literature review found that despite the various types of data used to produce these estimates, the use of aggregated time series data remains the most widespread and has dominated understanding on the issue (Dahl, 2012). Additionally, it was noted that there is also a wide variation in terms of the magnitude estimated. While elasticity estimates tend to differ due to the specification of the model and the type of data used, differences can also arise due to the structural changes affecting the consumption pattern in the fuel itself (Hughes et al., 2008). Estimation using more recent data allows elasticity estimates to capture such structural effects thus enabling much more reliable policy decisions.

The literature review also revealed that despite the extensive literature, the term total fuel demand elasticity has actually been a misnomer. This is because such estimates have often been confined to the use of petrol as a proxy for total fuel demand (Basso and Oum, 2007). The rising consumption of diesel demand, together with the differences in usage patterns, as highlighted in the previous chapter, indicates that there might be heterogeneous response for each fuel type. A

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continued reliance on fuel demand estimates using petrol as a proxy may not, therefore, capture the inherent responses attributed to diesel and may be a source of bias in the estimates as diesel consumption comes to take a larger proportion of the total transport fuel demand. In this context, Schipper et al. (1993) suggest that the appropriate approach is to either model each fuel separately or to use a weighted fuel model that includes both petrol and diesel consumption in estimating total transport fuel demand.

From the literature, however, it was found that studies that focused on modelling these differences were relatively few in number, even though they did tend to find evidence of heterogeneity in response for the different fuels. This chapter, therefore, adopts both of the approaches suggested by Schipper et al (1993), thus allowing for a comparative perspective in terms of fuel demand estimates. The chapter continues in Section 6.2 by providing a description of the data used as well as the development of a weighted total fuel dataset. Section 6.3 explains the fuel demand models, while Section 6.4 describes in detail the time series estimation procedures applied. The results of the annual time-series model for each fuel type are presented in Section 6.5 and a comparative summary of the results in Section 6.6. The chapter is concluded in Section 6.7.

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6.2 TIME SERIES DATA SOURCES In this chapter, the data used is aggregate annual data obtained from several of the UK government departments covering the period from 1982 to 2009. The advantage of using the aggregate time series data is that, traditionally, it has been utilised for national policy making purposes and as such is readily available. In the UK, revisions to time series statistics are retroactively undertaken, allowing not only for an improved quality of data but also consistency in the data obtained.

The primary data for fuel consumption and conversion factors was obtained from the Department of Energy and Climate Change (DECC). In the analysis, the fuel consumption statistics from the DECC’s publications, Energy Consumption in the UK (ECUK) and Digest of United Kingdom Energy Statistics (DUKES) are used. The ECUK data tables contain a breakdown of statistics for fuel consumption (in weight terms) by type and by end users (e.g. cars, buses, HGV). On the other hand, the DUKES publication provides annual fuel conversion factors and a further breakdown of fuel categories by type of fuel (e.g. premium unleaded, unleaded, lead replacement petrol, etc.) which is used in the construction of the weighted fuel consumption and price datasets.

The annual fuel price data in nominal terms (which is the average of the monthly fuel price for each year) was obtained from the DECC’s Oil and Petroleum Products Statistical Dataset. In the analysis, the data used as a proxy for income is the Gross Disposable Household Income (GDHI) which was sourced from the Office for National Statistics’ (ONS) The Blue Book (BB) annual publication. The deflator data, which was used to construct the real fuel price and real income dataset, was also taken from the Blue Book. Further descriptions of the variables and their sources are provided in Table 6.1.

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Table 6.1 Description of time series variables, data sources and descriptive statistics

Variables Definition Units Data N Mean Median SD Min Max Source Petrol Fuel Petrol fuel consumption per Litres per capita a, b, c 28 489.468 497.385 60.899 347.219 573.294 capita Diesel Fuel Diesel fuel consumption per Litres per capita a, b, c 28 273.421 283.113 91.562 120.067 414.144 capita Total Fuel Total fuel consumption per Litres per capita a, b, c 28 762.889 795.165 72.382 579.616 820.929 capita Petrol Price Weighted average real UK pence per litre a, b, d, e 28 80.770 81.926 12.199 64.278 107.488 petrol price Diesel Price Real diesel price UK pence per litre d, e 28 79.818 78.678 15.858 58.465 117.511 Fuel Price Weighted average real fuel UK pence per litre d, e 28 80.773 81.227 13.603 62.765 112.709 price Income Per capita real gross UK £ per capita c, e 28 11,338.79 11,179.10 2,693.878 7,051.612 14,891.09 domestic household income (GDHI) Bus Fare Average real bus fares UK pence per trip e, f 28 0.702 0.692 0.099 0.558 0.868 Petrol Vehicle Per capita petrol vehicle Vehicles per capita c, g 28 0.372 0.376 0.018 0.328 0.395 Diesel Vehicle Per capita diesel vehicle Vehicles per capita c, g 28 0.085 0.074 0.055 0.022 0.192 Total Vehicle Per capita diesel and petrol Vehicles per capita c, g 28 0.458 0.444 0.066 0.350 0.555 vehicle Note: All price and income variables are deflated to 2008 values. a Department of Energy & Climate Change (DECC) Energy Consumption in the United Kingdom Statistics, b Department of Energy & Climate Change (DECC) Digest of United Kingdom Energy Statistics, c The World Bank Open Data Catalog, d Department of Energy & Climate Change (DECC) Monthly and Annual Prices of Road Fuels and Petroleum Products, e Office for National Statistics (ONS) Blue Book Dataset (deflator & income), f Department for Transport (DfT) Transport Statistics Great Britain, g Department for Transport (DfT) Vehicle Statistics.

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6.2.1 Dataset Construction In order to perform the econometric analysis, some modifications were made to the data mentioned above. Fuel data was converted into litre quantities in order to correspond to the retail fuel price, which is reported on a per litres basis. Since the fuel stock density affects the volume delivered for retail consumption, we have used the annual conversion factor for each individual fuel in preparing the data instead of applying a standard conversion factor for all the fuels, so as to minimise the introduction of error into the data.38 For each type of fuel, the volume in litres consumed was calculated as:

퐹푖,푡 = 푊푖,푡퐶푖,푡 (6.1)

where F represents consumption of fuel i in litres in year t; W the mass of fuel i consumed in metric tonnes in year t; and C is the conversion factor for fuel i in year t. This method was extended to obtain the value of the total amount of transport fuel consumed, where:

푇표푡푎푙 퐹푢푒푙푖,푡 = ∑ 푊푖,푡 퐶푖,푡 (6.2)

In order to perform the analysis, further adjustments had to be made to some of the fuel price data obtained from the DECC. While diesel price can be directly used, this is not the case for petrol price (due to the availability of different types of petrol fuel) and total fuel price (for the total fuel model). For petrol and total fuel, the weighted average price for a given year was calculated as:

∑푖 푓푖푝푖 푥푝 = (6.3) ∑푖 푓푖

where 푥̅푝 represents the weighted average fuel price for fuel i.

38 Fuel stock density differs not only for each transport fuel (e.g. diesel, petrol) but also by the type of base fuel used to produce them. As such the annual conversion factor for a particular transport fuel may differ by quite a margin, making the use of a standard conversion factor unsuitable.

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In order to account for inflation, both the nominal GDHI and fuel prices are deflated into real terms using the following equation:

퐷푒푓푏푎푠푒 푅푉푡 = 푁푉푡 × (6.4) 퐷푒푓푡

Where RVt is the value of GDHI or fuel price in constant prices at time period t, NVt is the current value of GDHI or fuel price in year t, Defbase is the base year deflator (with

2008 as the base year) and Deft is the value of the deflator in year t.

6.2.2 Dataset Limitations A major drawback that limits the analysis from going further back in time is due to the use of different data sources to construct the dataset as described above. While fuel data categorised by the main types (e.g. petrol, diesel, etc.) is available from the year 1970 in the ECUK data tables, further breakdown into their constituent types as required by the analysis (i.e. especially in the case of petrol) is only available through the DUKES dataset. The same can also be applied for other important data that was required to construct the described data set such as fuel price and vehicle stock which were obtained separately from the DECC and DfT.

In addition to the above, the analysis was also constrained by the inability to obtain a continuous time-series of similar length for each of the data sets. For example, while the fuel data by type is available from 1970, the online DUKES data set for the constituent fuel types only contains information beginning from 1997. Although the data collection effort was augmented through searches in physical sources such as reports and official documents, it was not without its’ own issues and difficulties as well. Among the difficulties are physical searches can be time and resource intensive and it also became progressively difficult to obtain some of the reports the further back in time that we went. Furthermore, it was also found that some of the data was not consistently reproduced in the reports, thus further hampering the data collection effort.

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6.3 FUEL DEMAND MODEL SPECIFICATION In this section, we define the econometric model used for the time series analysis and the a priori theoretical expectation of the regressors with fuel consumption. Reflecting the discussion in §3.2, the times series model will be based on the reduced form demand model. As pointed out by Basso and Oum (2007), the reduced form model is the most popular approach for modelling fuel demand in the academic and non-academic literature. The advantage of the reduced form approach is that it allows for direct estimation of fuel demand through a single econometric model, thus minimizing the data requirements, in contrast to a structural model. Due to this, the reduced form procedure is preferable and therefore adopted for our analysis.

The choice of the explanatory variables in the econometric model specification applied here was influenced by the literature surveys presented in Chapters 3 and 4 (see Dahl and Sterner, 1991 and Graham and Glaister, 2002). In this chapter, the quantity measure adopted for the econometric model was the per capita form (see for example the works of Polemis, 2006; Hughes et al., 2008; Liddle, 2009; Park and Zhao, 2010).39 The main advantage of using the per capita form is that the specification allows the econometric model to take into account consumption that is attributable to a changing population.40

Using the Cobb–Douglas functional form, the general fuel demand model for the analysis can be specifically defined as:

훽푃 훽푌 퐹푡 = 훼푃푡 푌푡 (6.5)

39 The aggregate quantity measure was also applied in a previous version of this chapter. The results based on that specification was submitted as a paper entitled ‘Road Transport Fuel Consumption Trends in the United Kingdom: Empirical Analysis of Diesel Demand’ for presentation at the Transportation Research Board 92nd Annual Meeting. The paper (Ramli and Graham, 2012) is available online at http://amonline.trb.org/ 40 From the literature reviewed, the per capita form is also the most widely used quantity measure in time series fuel demand models.

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Taking the natural logarithm of Eq. (6.5) on both sides, the general fuel demand model becomes:

ln퐹푡 = 훼 + 훽푃 ⋅ ln푃푡 + 훽푌 ⋅ ln푌푡 + 휀푡 (6.6)

Since we are interested in estimating different fuel types, we add the subscript notation i to specify the exact fuel being modelled

ln퐹푖푡 = 훼푖 + 훽푃푖 ⋅ ln푃푖푡 + 훽푌푖 ⋅ ln푌푡 + 휀푖푡 (6.7)

where 퐹푖푡 is the per capita consumption of the ith fuel type in year t; 푃푖푡 is the annual real fuel price (UK pence/litre); Yt is the real GDHI in year t; 휀푖푡 is the residual. The subscript notations i and t indicate the different fuel types being modelled, i.e. petrol (G), diesel (D) and total fuel (T), and time period respectively.

The functional form of the econometric model is based on the log-linear (double-log) formulation. While the log-linear functional form is not without its critics (see §3.2), it remains the most widely used specification in the literature and is convenient as a

basis for comparison with previous estimates. In the model, the parameters 훽푃푖 and

훽푌푖 represent the elasticity of fuel demand with respect to price (휂푝) and

income (휂푌). 훽푃푖 would be expected to have a negative sign, indicating a negative

effect on fuel demand, while 훽푌푖 would be expected to have a positive sign, indicating a positive effect on fuel demand for all the fuel types.

6.3.1 Extended Model The use of an alternative form of the variables in the model, as specified earlier, provides a good way to check for the robustness of the estimates. According to Hughes et al. (2008), however, this robustness check can be extended further by using alternative specifications that include additional exogenous variables as well as different modelling techniques (e.g. static, dynamic models).

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Following this, the econometric model given by Eq. (6.6) was extended to include additional variables that may affect fuel demand. The general extended fuel demand model is now specified as:

ln퐹푡 = 훼 + 훽푃 ⋅ ln푃푡 + 훽푌 ⋅ ln푌푡 + 훽퐵퐹 ⋅ ln퐵퐹푡 + 훽푉 ⋅ ln푉푡 + 휀푡 (6.8)

with 푉푡 and 퐵퐹푡 representing the additional independent variables, own-vehicle stock per capita and real bus fare, respectively. The vehicle stock per capita is considered to have a direct relationship and would therefore be expected to exert a positive effect on fuel consumption. The sign for the cross-price bus fare elasticity is expected to be positive as well. Since a bus service is considered as a substitute form of transportation, an increase in the bus fare would result in an increase in fuel demand via an increase in private vehicle usage.41

As discussed previously, the use of the static equation, as in Equations (6.6) and (6.8), is a reflection of the concerns with regard to the non-stationarity and cointegration of variables in time series analysis. An unintended effect of the concerns highlighted in the early cointegration literature is that short- and long-run parameter estimations are now almost invariably done through the use of the Engle– Granger (static) two-step cointegration procedure; severely restricting the model estimation techniques that can be applied. Recent findings in the literature, however, have highlighted the potential problems of the Engle–Granger approach and have suggested alternative methods that could be more appropriate, while still taking into account the cointegration issue (see Hendry and Juselius, 2000; Inder, 1993). Following this, the next section develops these points further with additional discussion on the problems of the Engle–Granger methodology as well as on the alternative approximation techniques to address the matter.

41 We acknowledge that the relationship of bus fare with diesel fuel may not necessarily be the same as what is described above. Since diesel is the main fuel for public service vehicles, the sign for the parameter could also be the opposite.

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6.4 TIME SERIES COINTEGRATION ESTIMATION METHODOLOGY This section introduces and describes the various cointegration estimation methodologies applied for the time series model. Although the cointegration technique provides a valid estimation in non-stationarity time series data, it is still important to investigate the properties of the variables, i.e. establish the order of integration of the variables. This is because the validity of the cointegration procedure largely depends on the assumption that the variables are integrated of order one. Due to this, it can be observed that most traditional cointegration procedure adheres to a particular road map in order to validate the estimation.

The first step in a cointegration test is to check the stationarity and the order of integration of the variables by performing unit root tests. If the variables are found to have unit roots that are of the same order of integration, only then is it possible to proceed to estimate the model and test whether these series have an equilibrium (stationary) relationship.

We begin by describing the classic Engle–Granger two-step procedure (static EG OLS). The Engle–Granger approach involves estimating a static model (Equation 6.6)

by OLS in order to obtain the long-run parameters and the residual 휀푡. After estimating the static model, we then need to investigate the existence of cointegration among the regressors. If cointegration is confirmed, the long-term

relationship among the variables is now established and the parameter estimates 훽푃

and 훽푌 can be conveniently interpreted as the long-run price and income elasticities respectively.

The existence of cointegration in the Engle–Granger framework requires the

residual, 휀푡 in Eq. (6.6) to be stationary. Thus, a test of cointegration is actually a test

of the stationarity of 휀푡. If the residual, 휀푡 is stationary then their linear combination is stationary, making the parameter estimates in Eq. (6.6) to be valid. The test for cointegration can be conducted using the same stationary tests procedure

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mentioned earlier, and to that end we have applied the ADF test.42 To get a more definitive conclusion, if the EG–ADF test detects cointegration on the static model we have also applied the non-residual based test of cointegration by Hansen (1992).43

Engle and Granger (1987) pointed out that cointegrated variables exhibit an error correction mechanism enabling the inference of short-run behaviour. Through the use of an Error Correction Model (ECM), the short-run elasticity and the speed of adjustment towards the equilibrium state can also be obtained. The ECM for the fuel consumption model can be estimated as:

푙 푚 푛

∆ln퐹푡 = 훼0 + ∑ 훼푃푖 ∆ln푃푡−1 + ∑ 훼푌푖 ∆ln푌푡−1 + ∑ 훼퐹푖 ∆ln퐹푡−푖−1 + 훼휀휀푡−1 + 푒푡 푖=0 푖=0 푖=0 (6.9)

where, ∆ is the difference operator; F, P and Y are fuel consumption, real price and real GDHI respectively. The number of lagged order l, m and n are chosen as such so

that 푒푡 is white noise and 휀푡−1 is the error obtained from regressing F with P and Y:

휀푡−1 = ln퐹푡−1 − 훽0 − 훽푃ln푃푡−1 − 훽푌ln푌푡−1 (6.10)

The coefficients 훼푃,0 and 훼푌,0 are the impact multipliers that measure the short-run

price and income elasticity while 훼휀 is the adjustment coefficient. In terms of interpretation, the properties exhibited by the ECM are also sensible from an

economic equilibrium perspective. The coefficient 훼휀 signifies the speed of

adjustment that takes place in correcting the disequilibrium in the short-run and 휀푡−1 can be interpreted as the equilibrium error, which is zero at equilibrium. If fuel

42 The ADF test in the context of cointegration is formally known as the augmented Engle–Granger (EG–ADF) test. Unlike the unit root tests, tests for cointegration differ as they deal with the relationship among a group of variables. It is worth noting that the critical values used in the ADF test for cointegration also differ from the critical values used for the unit root test. 43 Unlike the residual-based tests, Hansen’s test is based upon evaluating the stability of the parameters estimated. If the null of cointegration is not rejected, the regression coefficients converge uniformly to the cointegrating relationship and one should not expect to see parameter instability (Hansen, 1992).

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consumption is not in equilibrium, then 휀푡−1 is non-zero. This shows that consumption will respond accordingly in the following period to correct the equilibrium error, hence the term error correction model.

As discussed in Harris and Sollis (2005), if the variables are cointegrated, using ordinary least squares (OLS) produces a consistent estimate of the long-run relationship between the variables in the model. In finite samples, however, the OLS estimator in a cointegrating regression has a non-normal distribution and the lack of dynamics renders the standard errors and t-statistics biased and misleading, thus invalidating the standard inferential test (Amarawickrama and Hunt, 2008, Harris and Sollis, 2005). Additionally, using the static model causes the omitted dynamics to be captured by the residual which may then consequently result in autocorrelation (Hendry and Juselius, 2000).

If the static model is to be retained, Stock and Watson (2003) suggest the use of alternative estimators to address the problem in estimating the cointegrating coefficients. One such estimator is the dynamic ordinary least squares (DOLS) estimator (Stock and Watson, 1993). This entails using an over-parameterised dynamic model involving the leads and lags of first difference explanatory variables in the regression and then applying the heteroskedastic and autocorrelation consistent standard errors (Newey–West standard errors). An alternative estimator to the DOLS is the fully modified ordinary least squares (FMOLS) developed by Philips and Hansen (1990). The FMOLS circumvents the inference problem by adjusting the OLS estimator through a nonparametric approach, in order to account for the possible impact of residual autocorrelation and endogeneity, thus making t-tests for the long-run coefficients valid. Despite, the correction procedures described above, the shortcomings noted in the static Engle–Granger approach have led to calls for the revival of the dynamic autoregressive distributed lag procedure (ARDL) (see Hendry and Juselius, 2000; Bentzen and Engsted, 2001).

Banerjee et al. (1986) provided an alternative approach to cointegration testing and estimation by using a dynamic model both to overcome the drawbacks of the Engle–

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Granger static model as well as to test for cointegration. In their method, the dynamics are included in the cointegration estimation procedure through the use of the unrestricted autoregressive distributed lag (ARDL) model:

푙 푚 푛

ln 퐹푡 = 훾0 + ∑ 훾푃푖 ln 푃푡−푖 + ∑ 훾푌푖 ln 푌푡−푖 + ∑ 훾퐹푖 ln 퐹푡−푖−1 + 푒푡 (6.11) 푖=0 푖=0 푖=0

The residual 푒푡 will be serially uncorrelated if the number of lagged order l, m and n are correctly specified. Both the short-run and long-run elasticities can be estimated

based on Eq. (6.11). The corresponding coefficients 훾1,0 and 훾2,0 are the short-run

elasticities while the long-run elasticities are calculated as 훽 = ∑훾/(1 − ∑훾3).

The ARDL procedure represents an improvement over the static model by accounting for the left-out dynamics and thus producing unbiased, and therefore more precise, estimates of the long-run relationship. Inder (1993) has shown that even when the model is over-specified, the dynamic estimator still performs better than the static OLS and FMOLS. Statistical hypothesis testing can also be conducted since the t-statistics are now standard. In addition, the dynamic model allows for a more powerful t-type unit root test of the null of no cointegration (Harris and Sollis, 2005). Banerjee et al. (1998) in their paper, denoted the cointegration test for the ARDL model as an error-correction mechanism (ECM) test with the procedure depending upon the significance of the lagged dependent variable(s) compared to the critical values given.

The ECM test is essentially a test of dynamic stability. For dynamic convergence to be

present, the sum of the lagged consumption coefficient (훾3) must be less than one. As such, to test the null hypothesis of no cointegration in the ECM test, the t-type

test statistic can be obtained by dividing (1 - ∑ 훾3) with the standard errors of their sum (Harris and Sollis, 2005).44

44 The standard errors to calculate the test statistics is obtained through PcGive 14: OxMetrics module. Doornik and Hendry (2013) remind us that in obtaining the t-statistics, it is important to realise that the standard error of the sum is not simply the sum of the standard errors.

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Significantly, another testing and estimation option that takes into account the above is the relatively new cointegrating technique called the Unrestricted Error Correction Model (UECM) bounds testing approach advanced by Pesaran and Shin (1999) and Pesaran et al. (2001). Apart from incorporating the missing dynamics, the bounds testing methodology offers additional advantages over the traditional cointegration procedure. First, it avoids the pre-testing procedure as it is applicable even when involving a mixture of I(0), I(1) or even fractionally integrated variables.45 Second, the bounds testing procedure is shown to have superior small sample properties. Third, the simultaneous estimation of the short- and long-run parameters not only enables the effects to be assessed together but also avoids the autocorrelation problem from pushing the dynamics into the error term. Consequently, this leads to efficient and unbiased long-run parameter estimates with valid t-statistics. Finally, the approach leads to valid estimation even when the variables are possibly endogenous (Pesaran et al., 2001).

The first step in implementing the bounds testing procedure is to estimate an error correction version of the ARDL, which Pesaran et al. (2001) termed as the unrestricted error-correction model (UECM):

푙 푚 푛

∆ln퐹푡 = 훼0 + ∑ 훼푃푖 ∆ln푃푡−1 + ∑ 훼푌푖 ∆ln푌푡−1 + ∑ 훼퐹푖 ∆ln퐹푡−푖 + 휙푃푙푛푃푡−1 푖=0 푖=0 푖=1

+ 휙푌푙푛푌푡−1 + 휙퐹푙푛퐹푡−1 + 푒푡 (6.12)

It can be seen that the first part of the UECM equation (i.e. the parameters 훼푃, 훼푌

and 훼퐹) represents the short-run dynamics. At the same time, the long-run

(cointegrating) dynamics are also present through the parameters 휙푃, 휙푌 and 휙퐹 in the second part of the equation.

45 However, the critical value bounds provided by Pesaran et al. (2001) are not valid for I(2) variables .

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In the bounds test procedure, testing the null hypothesis of no cointegration is basically none other than an undertaking of a F-test for the joint significance of the coefficients of the lagged levels in the UECM, that is 퐻0: 휙푃 = 휙푌 = 휙퐹 = 0. Failure to reject the null indicates the absence of a long-run equilibrium, while a rejection implies that a long-run relationship does exist between the variables. The computed F-statistic has a non-standard distribution irrespective of whether the variables are I(0) or I(1) (Pesaran and Pesaran, 2009). Instead of a single critical value, Pesaran et al. (2001) supply two critical values which signify the lower and upper bound of significance covering all possible combinations of the I(0) and I(1) variables. If the computed F-statistic is below the lower bound then the null hypothesis of no cointegration cannot be rejected. In contrast, we can conclude that there is a long- run equilibrium if the F-statistic falls beyond the upper bound. Additionally, if the F- statistic falls in-between the bounds, the test is inconclusive and unit root tests should now be conducted to investigate the order of integration of the variables in the model.

In the event that the bounds test procedure indicates cointegration, the long-run relationship as shown in Equation (6.6) is valid. Instead of reverting to the static model, however, the long-run coefficients should be obtained through a dynamic specification. There are two alternatives for doing this. According to Pesaran et al. (2001), since the UECM is basically a reformulation of the ARDL model, the long-run coefficients could be extracted by re-estimating the variables in an ARDL model as in Equation (6.11). Alternatively, the second approach is to derive the long-run coefficients directly from the UECM, as suggested by Bårdsen (1989), where the respective long-run price and income coefficients are −(휙푃/휙퐹) and −(휙푌/휙퐹) (see also Akinboade et al., 2008; and De Vita et al., 2006). The short-run elasticity is obtained through the same error correction model (Equation (6.10)) but with the residual series 휀푡−1 now being from the derived long-run equilibrium coefficients of the dynamic model (Pesaran and Pesaran, 2009, Amarawickrama and Hunt, 2008).

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To check the robustness and sensitivity of the point estimates with respect to model specification, in this chapter both the static and dynamic cointegration techniques described above are applied to estimate the fuel models. In addition, the results from the alternative estimators for the static model are also presented.

6.4.1 First Difference Regression The first difference model is an alternative approach to obtain valid regression estimates when the variables in the model are not cointegrated. It has been elaborated that the use of I(1) variables in a regression where the residual is not I(0) is invalid since it results in a spurious estimate. The first difference regression overcomes this spurious regression problem of non-stationary variables by taking their first difference to make them into I(0). Differencing these variables will often induce stationarity and therefore their regression in the first difference form will now be valid. The first difference form of Equation (6.6) can be specified as:

푙 푚

∆ln퐹푡 = 훼0 + ∑ 훼푃푖 ∆ln푃푡−1 + ∑ 훼푌푖 ∆ln푌푡−1 + 푒푡 (6.13) 푖=0 푖=0

The main advantage of the first difference regression is that the results obtained are almost similar to the ECM and the parameters estimated can be interpreted as the short-run elasticities.46 The first difference form also provides incidental benefits such as reducing the severity of multicollinearity and removing autocorrelation in equations with serially correlated residuals (Baltagi, 2008). The exclusion of the lagged residuals, however, means that unlike the ECM model, the first difference regression will not be able to provide long-term estimates of the relationship.

46 Rearranging Eq. (6.13) so that, 퐹푡 = 훼 + 훼푃(푙푛푃푡 − 푙푛푃푡−1) + 훼푌(푙푛푌푡 − 푙푛푌푡−1) − 푙푛퐹푡−1 + 푒푡 , it can be seen that the parameters (훼푃 and 훼푌) obtained from the regression are none other than the short-run impact elasticities.

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6.5 ESTIMATION RESULTS In this section, the results for the aggregate fuel consumption models based on the cointegration approach are presented. In obtaining the estimates, the sequenced testing procedure, as adopted in the Engle-Granger cointegration methodology, was observed. As discussed in §6.4, the presence of cointegration validates the regression performed on the (non-stationary) variables. That said, finding that the variables are not cointegrated does not preclude the estimation of non-spurious regression. A simple workaround to the problem is to first make the variables stationary. As will be shown later, although information from the level estimation is lost, the first difference regression will still allow non-spurious short-run elasticity estimates to be obtained.

6.5.1 Stationarity Tests Following the literature review in Chapter 3, which explored the effects of estimating with non-stationary data, the analysis initially begins by testing the variables for stationarity. To undertake this, the logarithmic form of the variables is checked for the presence of unit roots. Before conducting the formal test, a graphical analysis of the data was carried out but it was not possible to come to a conclusion as to whether the series were I(0) or I(1).

In the fuel demand literature, the most commonly applied diagnostic tests to examine the presence of a unit root are the Augmented Dickey–Fuller (ADF) and the Phillips–Perron (PP). Recent developments in the field of unit root testing, however, suggest that these traditional or first generation tests may not be reliable. Schwert (1989) pointed out that these tests are sensitive to lag specifications and warned of their test size distortion problem. Maddala and Kim (1998), citing various sources, conclude that their low power often results in the acceptance of the null of unit root and as such suggest discarding these tests in favour of better unit root tests.47

47 The power of a test is its ability to detect a false null hypothesis and is measured by the probability of rejecting the null when it is false (Seddighi, 2011).

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Maddala and Lahiri (2009) suggest that the DF-GLS test, developed by Elliott et al. (1996), is an alternative that overcomes the problems associated with the ADF and PP tests. Baum (2005) echoed this by pointing out that the DF-GLS should be the unit-root test of choice since it is approximately more powerful and therefore likely to be more robust for inference purposes. Following this, the DF-GLS test is applied here for the purpose of unit root testing.

The results of the unit root tests are presented in Table 6.2. The table displays the t- statistics of the variables in levels and first-differences from the DF-GLS test. It can be observed that the DF-GLS fails to reject the null of non-stationarity for the variables in levels, confirming the suspicion that they are not stationary. In contrast, after differencing the non-stationary series, the t-statistics of the transformed variables are statistically significant, indicating that they are now stationary. Similar results were also found when a deterministic trend was included to the difference variables.

6.5.2 Model Cointegration Tests The next step is to investigate whether there exists a cointegrating relationship in the models as shown in Equation (6.6). As discussed earlier, although the series may not be stationary individually it is possible that the variables are cointegrated, that is their linear combination may be I(0). Engle and Granger (1987) suggested that in such cases an equilibrium relationship exists between the series to the effect that regressing the variables will not necessarily be spurious.

There are different types of cointegration tests but the most commonly followed is the Engle–Granger two-step procedure single equation residual-based tests (Maddala and Kim, 1998). Engle and Granger (1987) found that using the ADF test to test for unit roots in the residuals was the best approach among the first generation tests for static specification. In light of this, the Engle and Granger ADF (EG–ADF) procedure is applied here as our initial cointegration test.

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Table 6.2 Tests for stationarity of the variables

DF-GLS Test

Variables Constant Trend

Levels First-differences Levels First-differences

푙푛 퐹푃 –0.093 [1] –1.708 [0] *** –0.898 [1] –4.602 [0] ***

푙푛 퐹퐷 –0.828 [1] –1.925 [0] *** –0.896 [1] –3.590 [0] ***

푙푛 퐹퐹 –1.377 [1] –1.929 [0] *** –0.837 [1] –4.302 [0] ***

푙푛 푃푃 –0.640 [0] –4.584 [0] *** –1.726 [0] –4.782 [0] ***

푙푛 푃퐷 –0.562 [0] –4.385 [0] *** –1.818 [0] –4.813 [0] ***

푙푛 푃퐹 –0.607 [0] –4.609 [0] *** –1.754 [0] –4.855 [0] ***

푙푛 푌 –0.457 [1] –3.003 [0] *** –1.122 [1] –4.294 [0] ***

푙푛 푉푃 –1.447 [0] –3.695 [0] *** –0.886 [0] –5.287 [0] ***

푙푛 푉퐷 –1.468 [1] –2.447 [1] *** –1.052 [2] –3.369 [1] ***

푙푛 푉퐹 –0.809 [3] –4.888 [0] *** –1.931 [0] –5.258 [0] ***

푙푛 퐵퐹 –0.059 [0] –4.489 [0] *** –2.392 [0] –4.548 [0] ***

Notes: The numbers inside the bracket represents the lags. The optimal lag length was automatically chosen in EViews using the Schwarz information criterion. *** indicates significant at the 10% level *** indicates significant at the 5% level *** indicates significant at the 1% level

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Testing the existence of cointegration in the EG–ADF context involves a similar process to the unit root testing procedure in §6.5.1. The main difference is that the residuals from the equilibrium equation are tested instead and must be stationary to confirm the existence of cointegration. If the residuals are found to be stationary, the parameters estimated by the regression model shown in Equation (6.6) are valid and can therefore be interpreted as long-run elasticities.

The use of the EG–ADF is not without its critics, however. Firstly, since the EG–ADF test is based on the Augmented Dickey–Fuller (ADF) unit root procedure, it inherits similar problems as those described earlier for the ADF test.48 To compound matters further, it was found that the use of residuals to test for cointegration further compromises the power of the EG–ADF test (an issue which is applicable to other residual based tests). Since the residuals are derived from the static estimation procedure, it is also likely to be affected by the omitted dynamics issue. Kremer et al. (1992) pointed out that the problem of low power in residual based tests stems from the omission of these equation dynamics and suggested that cointegration tests should instead be based on ECM statistics.

From the above, it appears that the inclusion of dynamics in the model not only provides an improvement in estimation (as described in §6.4) but also turns out to be desirable since it enables the application of more powerful ECM-based cointegration tests. Since these tests can be done together with the dynamic estimation procedure described earlier, we therefore employ both the ECM test and the UECM bounds test to check for cointegration between the variables. To recap, the ECM test is based on the t-test procedure and the test statistics are derived from the t-ratio of the lagged dependent variable(s). The bounds test, as stated previously, utilizes the F-test approach and cointegration relies on the joint

48 For further discussion of the issues in residual-based cointegration tests, please refer to Maddala and Kim (1998, pp.202–205, 218–219).

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significance of the lagged level variables in the UECM equation.49 Table 6.3 presents the results of the cointegration tests for the models estimated.

Table 6.3 Cointegration test results for the base and extended fuel demand models

Cointegration Tests Statistics Model Dependent variable EG–ADF ECM test UECM Bounds Test Base Petrol –1.286 –0.949 –2.251 (0.936) Diesel –4.207** –3.603* –4.089* (0.042) Total Fuel –3.224 –3.485* –4.617** (0.210)

Extended Petrol –2.846 –2.619 –2.581 (0.692) Diesel –3.262 –1.251 –2.327 (0.504) Total Fuel –3.330 –2.881 –3.069 (0.474) Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The numbers in the parentheses are p-values. 3) The optimal lag length for the EG–ADF test was automatically chosen in EViews using the Schwarz information criterion.

It can be seen from the results that cointegration can be confirmed only for the base model of diesel and total fuel. Note that the null of no-cointegration was unanimously rejected by the cointegration tests at the usual level of significance for the diesel base model. In the case of the total fuel base model, cointegration was confirmed by both the ECM-based tests, although the EG–ADF test was not able to reject the null even at the 10% level. This may be indicative of the low power problem inherent to the residual-based tests described earlier. Maddala and Kim (1998) suggest the use of a much higher level of significance of 25% to remedy this and at this level rejection of the null is confirmed by the EG–ADF test.50

Even allowing for the higher significance level for the EG–ADF test, the residuals for all other models proved to be non-stationary. Since the outcomes from the ECM-

49 It is important to note that while both ECM tests employ the standard F- and t-statistics, they do have a non- standard distribution in testing the significance of the lagged level variables. 50 As stated previously, due to the low power issue, we perform the Hansen test as an additional confirmatory diagnostic on the static specification whenever the null of no-cointegration is rejected by the EG–ADF. Fortunately, the Hansen test confirms the initial results as it fails to reject the null of cointegration for both diesel (Lc statistics = 0.242, p-value > 0.20) and total fuel (Lc statistics = 0.156, p-value > 0.20).

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based tests also indicate similar non-rejection of the null, we therefore conclude that an equilibrium relationship does not exist for all the other models. The outcome of the tests indicate that a long-run relationship exists only for diesel and total fuel and only in the base model, but cannot be confirmed when additional variables were included. In the case of petrol fuel, there appears to be no equilibrium relationship in either the base or extended model, suggesting that petrol consumption is likely to be influenced only by short-run dynamics.

Following the outcome of the test, the results of the base models are presented in §6.5.3 With the exception of petrol fuel, this will involve both static and dynamic estimation models for the cointegrating relationship found for diesel and total fuel. In contrast, for the extended models, although equilibrium cannot be established, it is still possible to estimate the short-run relationship between the variables. In §6.5.4, estimation based on the first differenced regression is discussed.

6.5.3 Estimation Results for the Base Models The results of the cointegrated regression model are presented in Table 6.4. From the context of estimation, Equation (6.6) for diesel and total fuel is now valid and the estimated coefficients (ln 푃 and ln 푌) represent the long-run price and income elasticities of consumption respectively.

Table 6.4 Long-run elasticity estimates of the cointegrating regressions (base models)

Diesel Total Fuel Models Price Income Price Income Static OLS –0.208*** –1.593*** –0.448*** –0.515*** (0.055) (0.048) (0.029) (0.020) Static FMOLS –0.193** –1.557*** –0.453*** –0.497*** (0.085) (0.071) (0.035) (0.025) Static DOLS –0.204** –1.516*** –0.377*** –0.468*** (0.080) (0.076) (0.032) (0.026) Dynamic OLS –0.253** –1.499*** –0.436*** –0.449*** (0.111) (0.109) (0.041) (0.040) Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The numbers in the parentheses are standard errors. 3) The dynamic OLS results are derived from the ARDL model.

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The table above displays the long-run estimates from both the static and dynamic models. For the standard OLS model, the Newey–West procedure has been applied to control for autocorrelation and heteroskedasticity. To test the robustness and for inference purposes, we have also employed the DOLS and FMOLS estimators on the static cointegrating regression. While the static long-run elasticities are directly estimated, the dynamic OLS results are derived through the ARDL models specified in Tables 6.5 and 6.6.

Looking at the diesel estimates in Table 6.4, what is noticeable is that models that exclude the dynamics in the relationship tend to produce relatively higher values in the estimated income parameter. The opposite is apparent, however, when it comes to the price elasticity estimates, with the static models now delivering lower values compared to the dynamic model. Despite the variations, we derive confidence in the estimates since the values do fall within a relatively narrow range.51 From the evidence presented, the long-run price elasticity of diesel consumption appears to be between –0.19 and –0.25 while income elasticity is in the range of 1.50 and 1.59.

When it comes to the total fuel models, we note that again there appear to be relatively small differences in the values between the estimated parameters. The elasticity coefficients are all significant, with long-run values in the range of –0.38 and –0.45 for price, and between 0.45 and 0.52 for income. A degree of consistency with the diesel model was also observed when it comes to the long-run total fuel income elasticities; the static models continued to yield higher parameter values than those of the dynamic model. However, this similarity does not extend to the long-run price estimates of the total fuel model.

Further examination of the static models appears to reveal the tell-tale sign of bias arising from the suppression of the dynamics, as had been shown by Banerjee et al.

51 The diesel estimates presented here suggest that the use of different quantity measures do not appear to result in a drastically different estimation outcome. Previously published work by Ramli & Graham (2014) using an aggregate quantity measure (instead of the per capita form applied here) found almost similar results with long-run price (income) elasticity values of –0.21 to –0.30 (1.50–1.58). For further details, see: Ramli, A. R. & Graham D. J. 2014. The demand for road transport diesel fuel in the UK: Empirical evidence from static and dynamic cointegration techniques. Transportation Research Part D 26, 60–66.

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(1986) and Inder (1993). In the static model, the omitted dynamics manifested itself in a downward bias in the standard error resulting in an overestimated t-value (Hendry and Juselius, 2000). Applying the alternative static estimators, we observe that there is some improvement to the size of the standard errors. In a finite sample, however, there is the possibility that these estimators may be inadequate to deal with the bias. On the other hand, the standard errors produced by the dynamic estimator are even bigger compared to those from the FMOLS and DOLS estimators; affirming their relatively poor finite sample performance. In comparison to the static OLS, the dynamic estimator yields standard errors with values that are approximately 100–127% (57–100%) bigger in the case of diesel (total fuel) model.

Table 6.5 Dynamic OLS ARDL estimation results for diesel fuel (base model)

Dependent variable ln 퐹(퐷푖푒푠푒푙),푡 Explanatory variables Coefficient Std. Error

푙푛 푃푡 –0.080** 0.029 푙푛 푌푡 –0.477*** 0.146

푙푛 퐹퐷푖푒푠푒푙,푡−1 –1.069*** 0.190

푙푛 퐹퐷푖푒푠푒푙,푡−2 –0.387** 0.178 Constant –2.309** 0.837

Test diagnostics Adjusted R2 0.996 Breusch–Godfrey LM test 0.401 [0.675] Durbin’s alternative test 0.074 [0.788] Engle’s LM ARCH test 1.939 [0.177] Breusch–Pagan test 0.380 [0.546] Shapiro–Wilk W test 0.941 [0.146] Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The heteroskedasticity and auto-correlation robust (Newey–West) standard errors are reported. 3) The numbers in the brackets are p-values.

We now turn our attention to the results from the dynamic ARDL estimator applied to both diesel and total fuel demand. In both instances, the modelling process progressed from the general-to-specific approach, as suggested by Doornik and Hendry (2013). Starting from an over-parameterised lag structure, the preferred specification was chosen after going through the sequential simplification procedure and passing the necessary model validity diagnostics. In Table 6.5, it can be seen that the coefficients in the diesel regression appear to be well determined. From the results, the short-run price elasticity is –0.08 while the income elasticity is 0.48. The

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value of 0.32 for the adjustment coefficient (휆) indicates relatively strong habit persistence in diesel consumption with adjustment taking approximately 3.1 years.

Correspondingly, the ARDL model for total fuel also appears to be well determined (see Table 6.6).52 Short-run price, income and the lagged consumption coefficients (–0.11, 0.75 and 0.42) are significant, reasonable in magnitude and display the expected sign. Extracting 휆 from the model yields a value of 0.58, which in comparison to diesel consumption, is indicative of a smaller consumption inertia. At that rate of adjustment, long-run equilibrium is achieved in 1.5 years.

Table 6.6 Dynamic OLS ARDL estimation results for total fuel (base model)

Dependent variable ln 퐹(푇표푡푎푙 퐹푢푒푙),푡 Explanatory variables Coefficient Std. Error

푙푛 푃푡 –0.105* 0.061 푙푛 푃푡−1 –0.147 0.086 푙푛 푌푡 –0.749*** 0.099 푙푛 푌푡−1 –0.489*** 0.096

푙푛 퐹푇표푡푎푙 퐹푢푒푙,푡−1 –0.421*** 0.079 Constant –2.516*** 0.343

Test diagnostics Adjusted R2 0.975 Breusch–Godfrey LM test 0.154 [0.858] Durbin’s alternative test 0.083 [0.776] Engle’s LM ARCH test 0.938 [0.342] Breusch–Pagan test 0.002 [0.983] Shapiro–Wilk W test 0.947 [0.182] Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The heteroskedasticity and auto-correlation robust (Newey–West) standard errors are reported. 3) The numbers in the brackets are p-values.

The ECM regressions for the static models are presented in Tables 6.7 and 6.8. Once the cointegrating relationship has been confirmed, the final step is to estimate the ECM for the fuel consumption equation. The coefficients of ln 푃 and ln 푌 in the ECM model give the short-run price and income elasticity while the coefficient of

휀푡−1 represents the adjustments that take place to restore to the long-run equilibirium. The ECM regression is also helpful since it provides an additional confirmatory test of the cointegration found by the initial static models. In the event

52 The lagged fuel price coefficient based on the Newey–West procedure is retained as it has a borderline p- value of (0.104). If using normal standard errors, the coefficient is significant with a t-statistics of –1.904 (p- value = 0.071).

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that long-run equilibrium is present, the coefficient of the lagged residuals (휀푡−1) are expected to have a negative sign and be statistically significant from zero.

The short-run diesel fuel elasticities from the ECM model are summarised in Table 6.7. It can be seen that the results obtained are consistent with the a priori expectations. The signs for the impact elasticities are consistent with economic theory while the values of the short-run coefficients are smaller than their long-run counterparts. As one would expect, the magnitudes of the income elasticity estimated are also higher than the price elasticity, providing further support for the consistency of the ECM estimates.

Table 6.7 Short-run results from the ECM of diesel consumption (base model)

Dependent variable ∆ 퐷𝑖푒푠푒푙 Explanatory variables OLS FMOLS DOLS ARDL

∆푙푛 푃푡 –0.128*** –0.118*** –0.140*** –0.080*** (0.098) (0.052) (0.051) (0.034)

∆푙푛 푌푡 –0.715*** –0.681*** –0.635*** –0.477*** (0.234) (0.235) (0.213) (0.146)

∆푙푛 퐹퐷푖푒푠푒푙,푡−1 –0.554*** –0.524*** –0.620*** –0.387*** (0.118) (0.114) (0.122) (0.178)

휀푡−1 –0.277*** –0.286*** –0.354*** –0.318*** (0.098) (0.094) (0.090) (0.088) Constant –0.002*** –0.000*** –0.003*** - (0.009) (0.009) (0.009)

Test diagnostics Adjusted R2 0.620 0.624 0.651 0.627 Breusch–Godfrey LM test 0.624 [0.546] 0.581 [0.569] 0.530 [0.597] - Durbin’s alternative test 0.389 [0.540] 0.324 [0.575] 1.061 [0.315] - Engle’s LM ARCH test 2.124 [0.143] 2.101 [0.146] 2.531 [0.125] - Breusch–Pagan test 0.150 [0.699] 0.200 [0.660] 0.640 [0.431] - Shapiro–Wilk W test 0.971 [0.645] 0.972 [0.675] 0.970 [0.614] - Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The heteroskedasticity and auto-correlation robust (Newey–West) standard errors are applied for the ECM from the static models. 3) The numbers in the parentheses and brackets are standard errors and p-values respectively. 4) The representation of the dynamic OLS ARDL model in the ECM formulation was implemented using Microfit.

There is a strong degree of similarity in the results obtained from the ECM of the static estimates. The variance is relatively small between the values obtained for the short-run price elasticity, ranging between –0.12 and –0.14. This indicates that the short-run price elasticity is inelastic; increasing the fuel price by 1% will only produce a reduction in diesel consumption of between 0.12% and 0.14%. In terms of the

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income elasticity, there seem to be a bigger variance in the value of the coefficients obtained. The estimated static OLS ECM income parameter (0.715) is relatively larger when compared to those from the ECM of the FMOLS (0.681) and DOLS (0.635). The speed of adjustment indicates that between 28% to 35% of the consumption adjustment takes place within the first year whenever there is a disequilibrium.

The static ECM appears to produce parameters for the differenced income, price and lagged consumption variables that are biased upwards when compared with the error correction representation associated with the ARDL model. A similar outcome is not evident with the adjustment parameter, however.

Table 6.8 Short-run results from the ECM of total fuel consumption (base model)

Dependent variable ∆ 푇표푡푎푙 퐹푢푒푙 Explanatory variables OLS FMOLS DOLS ARDL

∆푙푛 푃푡 –0.152*** –0.143*** –0.120*** –0.105*** (0.056) (0.056) (0.053) (0.049)

∆푙푛 푃푡−1 - - –0.212*** - (0.046)

∆푙푛 푌푡 –0.789*** –0.739*** –0.765*** –0.749*** (0.149) (0.150) (0.165) (0.222)

∆푙푛 퐹푇표푡푎푙 퐹푢푒푙,푡−1 –0.330*** –0.260*** - - (0.143) (0.142)

휀푡−1 –0.582*** –0.581*** –0.802*** –0.579*** (0.118) (0.109) (0.199) (0.166) Constant –0.014*** –0.010*** –0.011*** - (0.006) (0.006) (0.089)

Test diagnostics Adjusted R2 0.732 0.743 0.736 0.728 Breusch–Godfrey LM test 0.243 [0.786] 0.149 [0.863] 0.162 [0.852] - Durbin’s alternative test 0.314 [0.581] 0.121 [0.731] 0.101 [0.754] - Engle’s LM ARCH test 1.934 [0.177] 1.874 [0.184] 0.959 [0.338] - Breusch–Pagan test 0.660 [0.423] 1.030 [0.319] 0.420 [0.525] - Shapiro–Wilk W test 0.950 [0.232] 0.962 [0.424] 0.981 [0.900] - Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The heteroskedasticity and auto-correlation robust (Newey–West) standard errors are applied for the ECM from the static models. 3) The numbers in the parentheses and brackets are standard errors and p-values respectively. 4) The representation of the dynamic OLS ARDL model in the ECM formulation was implemented using Microfit.

We now discuss the ECM estimates from the static total fuel model. The ECM models appear to be well specified, passing all the diagnostic tests, as well as having a stronger model fit. As seen previously, the results suggest an inelastic response to price changes, with price elasticity estimated to be between –0.12 to –0.15.

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Although similarly inelastic, as expected, income has a greater influence on total fuel consumption. While the static models reveal relatively small differences in values for the short-run price and income elasticities, there appears to be a slight departure from the norm in the context of the adjustment coefficient, with the DOLS parameter seeming to be overestimated. In general, there appear to be somewhat consistent results, even when including the estimates from the ARDL ECM representation. Due to the high degree of consistency, we derive confidence in the robustness of our estimated short-run total fuel demand elasticities.

Table 6.9 presents the first difference regression results for the petrol base model. As stated in §6.4.1, the first difference regression is valid as the differenced variables are now stationary. In terms of estimation, the model is similar to the ECM with the main exception being that there is no static residual included.

Table 6.9 Difference regression estimation results for petrol (base model)

Dependent variable ∆ 푃푒푡푟표푙 Explanatory variables Coefficient Std. Error

∆푙푛 푃푡 –0.162** 0.051 ∆푙푛 푃푡−1 –0.140** 0.068 ∆푙푛 푌푡 –0.802*** 0.233

∆푙푛 퐹푃푒푡푟표푙,푡−1 –0.302 0.185 Constant –0.029*** 0.007

Test diagnostics Adjusted R2 0.703 Breusch–Godfrey LM test 0.573 [0.573] Durbin’s alternative test 0.826 [0.374] Engle’s LM ARCH test 0.107 [0.747] Breusch–Pagan test 0.290 [0.594] Shapiro–Wilk W test 0.975 [0.757] Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The heteroskedasticity and auto-correlation robust (Newey–West) standard errors are reported. 3) The numbers in the brackets are p-values.

From the results, it can be seen that the coefficients in the regression appear to be well determined. The price and income coefficients are consistent with the a priori economic expectations. Price has a negative effect on short-run petrol consumption while income exhibits a stronger but positive effect. In the basic model, the short- run price and income elasticities are –0.16 and 0.802 respectively.

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6.5.4 Estimation Results for the Extended Models To recapitulate, evidence from the cointegration tests indicate that long-run equilibrium cannot be established for all the fuel types when the fuel demand model was extended to include the additional vehicles and bus fare variables. As explained previously, the workaround for valid regression estimation for non-stationary variables that are not cointegrated is to resort to a first difference variables regression (refer to Table 6.10).

At first glance, the models appear to be properly specified with the test diagnostics apparently supporting the validity of the specification selected. Across all of the models, it can be observed that the short-run price, income, vehicle stock and lagged consumption coefficients are significant and show the expected sign. In contrast, the models unanimously reject the statistical significance of bus fare on fuel demand. Although the values of the parameters are different, they appear to be consistent with the literature survey.

Table 6.10 First difference regression results for the extended fuel demand models

Dependent Variable: ∆푃푒푡푟표푙 ∆퐷𝑖푒푠푒푙 ∆푇표푡푎푙 퐹푢푒푙 ∆퐹푢푒푙 푃푒푟 퐶푎푝𝑖푡푎푖푡

∆푃푟𝑖푐푒푖푡 –0.124*** (0.058) –0.111*** (0.060) –0.112*** (0.060) ∆퐼푛푐표푚푒 푃푒푟 퐶푎푝𝑖푡푎푡 –0.612*** (0.336) –0.545*** (0.249) –0.591*** (0.288) ∆푉푒ℎ𝑖푐푙푒푠 푃푒푟 퐶푎푝𝑖푡푎푖푡 –0.497*** (0.285) –0.797*** (0.162) –0.493*** (0.277) ∆퐵푢푠 퐹푎푟푒푡 –0.088*** (0.087) –0.197*** (0.183) –0.087*** (0.123) ∆퐹푢푒푙 푃푒푟 퐶푎푝𝑖푡푎푖,푡−1 –0.387*** (0.181) –0.250*** (0.109) –0.433*** (0.163) 퐶표푛푠푡푎푛푡 –0.025*** (0.010) –0.046*** (0.015) –0.019*** (0.008)

Test diagnostics Adjusted R2 0.733 0.729 0.656 Breusch–Godfrey LM test 1.910 [0.177] 0.944 [0.407] 1.173 [0.332] Durbin’s alternative test 3.145 [0.092] 0.789 [0.386] 1.757 [0.201] Engle’s LM ARCH test 0.323 [0.575] 1.049 [0.316] 0.759 [0.392] Breusch–Pagan test 0.000 [0.996] 0.160 [0.689] 0.130 [0.724] Shapiro–Wilk W test 0.968 [0.565] 0.971 [0.651] 0.897 [0.137] Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) The heteroskedasticity and auto-correlation robust (Newey–West) standard errors are reported. 3) The numbers in the parentheses and brackets are standard errors and p-values respectively.

Looking at the fuel demand models, it can be seen that there is strong similarity as well as differences in the values of the estimated parameters. Interestingly, the magnitude of the price effect appears to be almost similar. Fuel consumption, as

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seen before, is price inelastic with an elasticity value of between –0.111 and –0.124. In a parallel manner, income elasticity also appears to be confined to within a relatively narrow range. The upper value of the income elasticity is represented by the petrol coefficient (0.612) with the lower value bounded by the diesel fuel parameter (0.545). When it comes to the vehicle stock coefficient, however, there seems to be a noticeable variance in the values estimated. For petrol, the short-run vehicle stock elasticity is 0.497 while it is estimated to be 0.797 in the case of diesel fuel consumption.

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6.6 SUMMARY OF ELASTICITIES The results from the static cointegration estimates appear to support the contention by Hendry and Juselius (2000) and Inder (1993) that the static specification – although consistent – remains a poor modelling approach, even after the application of the alternative estimators. In a finite sample, the omitted dynamics may not be sufficiently accounted for by the correction procedures, resulting in a continued downward bias of the standard error thus raising a question as to the validity of the inferential test. Due to the sample size used, the dynamic ARDL specification seems to be more appropriate. In order to err on the side of caution, the short- and long- run results of the base model discussed here will therefore be from the dynamic ARDL estimator.

Table 6.11 Summary of elasticities from the preferred estimators

Petrol Per Capita Diesel Per Capita Total Fuel Per Capita Models Short run Long run Short run Long run Short run Long run Price –0.162** – –0.080*** –0.253** –0.105** –0.436***

Base Income –0.802*** – –0.477*** –1.499*** –0.749*** –0.449***

Price –0.124** – –0.111** – –0.112* –

Income –0.612* – –0.545*** – –0.591* –

Vehicles Per –0.497* – –0.797*** – –0.493* – Extended Capita Bus Fare –0.088 – –0.197* – –0.087 –

Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively.

In general, the results obtained seem to be in line with what is documented in the literature survey. In particular, we observe that the price, income and vehicle stock coefficients tend to behave as expected i.e. significant, display the correct sign and with a reasonable magnitude. Using the petrol elasticity estimates as the border value implied by the null, we found that all the diesel coefficients for the basic model to be significantly different at the 5% level. The opposite is apparent, however, when the test is applied to the extended model with no significant difference found between the estimated coefficients of the diesel and petrol models.

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Surprisingly, however, the cross-price effect from bus fares seems to hint at an unexpected negative effect, but this cannot be confirmed since ultimately it turns out to be unanimously statistically insignificant.53 It is difficult to conclude what this outcome actually implies since, on the surface, the absence of the bus fare effect seems to indicate that motorists – especially in the context of petrol fuel – appear to be not (indirectly) influenced by bus services. Considering the prevalence of bus services as a form of transport, it is hard to contemplate that even a complementary relationship cannot be established.54 One possible explanation for the results observed is that bus fares alone may not be adequate to capture the effect of alternative modes of transportation on fuel usage. A more appropriate approach would possibly be to use a weighted measure of public transport fares, but due to data limitations we were unable to construct such a measure for the time series analysis.55

The magnitude of the estimated price elasticity, both in the short- and long-run, appears to be within the range reported by Hanly et al. (2002). In both specifications, the short-run magnitude appears to be stable, with petrol (diesel) elasticity values falling between –0.12 and –0.16 (–0.08 and –0.11). It should also be noted that petrol price sensitivity tends to be slightly higher than that for diesel. This is to be expected since the time frame of the dataset includes a large period where the primary users of diesel were predominantly the road freight and business sector, which are likely to be less sensitive to price changes. Interestingly, total fuel elasticity seems to lie in-between the aforementioned elasticities. In the long-run, however, the variance in magnitude becomes more apparent with price elasticity being stronger for total fuel (–0.44) as compared to diesel (–0.25).

53 As noted earlier, the negative effect of bus fare, however, is probable for diesel fuel. The result seen here seem to suggest that for diesel fuel, it may be best to disaggregate the estimation further by vehicle/user type in order to properly disentangle the observed effect. 54 Bus is the main public transport mode for trips undertaken in 2012. According to the National Travel Survey, bus travel in total, accounts for 6.5% of all trips taken (DfT, 2013). 55 However, this assumption will be tested further in the panel data analysis since, due to the shorter time frame, the weighted public transport fare variable is able to be constructed.

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We now discuss the income elasticity outcomes from the basic model. In the short- run, the evidence indicates that the effect of income on petrol consumption is approximately 1.7 times greater compared to diesel. The magnitude of the income elasticity reported for petrol was unexpected since, if taken at face value, it implies that petrol users strongly increase consumption as income grows (i.e. by 8% as income grows by 10%). One plausible explanation is that this apparently inflated result could be partly due to the omission of the vehicle stock ownership variable from the model, especially since the time frame in question coincides with a period of strong growth in vehicle stock and mileage.56

A much more puzzling outcome are the estimates for the basic total fuel model; in particular, what to infer from of the odd outcome in which the long-run elasticity is smaller than the short-run income elasticity. Although improbable, this outcome has been observed before in the context of road transport fuel demand, namely by Cheung and Thomson (2004) and Lim et al. (2012), as well as by Amarawickrama and Hunt (2008), albeit, in this latter case, in the electricity sector of Sri Lanka. Amarawickrama and Hunt (2008) proposed that such a situation could arise due to inflexibility in the appliance stock available to users, so that demand rises strongly as income rises in the short run but eventually tapers off as energy efficient appliances are installed. Such an explanation seems plausible in the current context as well. It is likely that the estimate reflects the difficulty faced by consumers in replacing their vehicle stock in the short run. As more efficient technology becomes available in the long run, however, the magnitude of elasticity becomes smaller as the efficiency gains means that the same amount of travel can be achieved with a lesser amount of fuel.57

56 Blum et al. (1988) highlighted this problem of estimating income elasticity. In their estimation, which includes other exogenous factors that generate travel (e.g. weather, infrastructure and economic activities), they conclude that if such factors are excluded, income elasticity will likely capture their influence and therefore be overestimated. 57 It is worth noting that this could also be due to the ‘averaging’ effect of the coefficient seen previously on total fuel estimates. In the case of the long-run income estimate, the static (but not cointegrated) petrol OLS regression reveals a surprisingly non-significant income coefficient with a value of 0.009.

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Turning to the extended specification, it appears that the magnitude of the income coefficients for the respective fuels is now confined to a much smaller range. With the addition of the vehicle stock variable, the income effect can be interpreted as capturing the intensity of vehicle usage. Even after accounting for an increase in vehicle stock, the evidence shows that fuel users have a strong tendency to increase usage as income rises. In the short run, a 1% increase in income will lead to an increase of 0.55% in diesel fuel demand. Additionally, there appears to be some truth to the effect of the omitted vehicle stock, as discussed previously. It can be seen that the short-run elasticity values are now deflated, as in the case of petrol (0.61) and total fuel (0.59).

The results confirm that vehicle stock exerts a positive effect on fuel consumption. In general, the relatively strong effect seen is consistent with the time frame involved, which was defined by similarly strong vehicle ownership growth. This is particularly so for the diesel model, which appears to pick up the surge in vehicle stock due to the dieselisation of the car fleet (see the discussion in §2.3). Alternatively, it is also possible that the stronger effect is due to the trend for diesel vehicle owners to opt for bigger and less efficient vehicles, as reported by Schipper (2011). For diesel consumption, the vehicle stock elasticity (0.80) is larger than the income elasticity. On the other hand, the opposite is seen for petrol demand where vehicle elasticity (0.50) is less elastic.

To conclude, it is worth noting that there seems to be some inconsistency in the parameter estimate yielded by the total fuel model. While it may appear to often be in-between the petrol and diesel estimates (especially in the basic model), we have shown that the total fuel model also has a tendency to underestimate the parameter (e.g. vehicle elasticity). Occasionally, the total fuel estimate may also be skewed towards one end instead of delivering an ‘average’ effect as expected. This brings to mind the concern raised by Schipper et al. (1993) as to what is actually being measured in the total fuel estimate. From the evidence presented, it does appear that for the purpose of policy decisions (and when data is available) separate estimations are likely to be more relevant and appropriate.

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6.7 SUMMARY In the present chapter, we have shown that stationarity analysis is important, especially in the context of time series data. Since the classical assumption of stationarity is unlikely to be correct, it is imperative that empirical modelling adequately addresses this issue. Performing a regression with an invalid stationarity assumption can induce spurious conclusions since non-stationary series tend to produce an overstated estimate, even with an unreliable fit. Fortunately, a way around this problem exists since such spurious outcomes can be avoided if the variables can be proven to be cointegrated.

It also appears that we have come full circle in terms of estimation methodology. As Bentzen and Engsted (2001) highlighted, the ARDL model once dominated the field of energy demand relationships but has more recently been generally dismissed with the advent of non-stationarity. Cointegration analysis results, not only in a reversion to the traditional static model but also changes the manner in how it is interpreted.58 However, as Hendry and Juselius (2000) state, recent evidence showing that cointegration and ECM are two names for the same things means the circle is now complete and ARDL is now once again valid and preferred.

In estimating the various fuel demand models, we have taken the opportunity to explore different cointegration techniques and observed the effects they have on the elasticity results. We found that when cointegration is present, both static and dynamic estimation methodologies tend to produce identical results. We have also shown, however, that the static approach appears to suffer from the omission of the dynamics i.e. a downward bias in the standard errors. This is evident even after applying alternative estimators (e.g. the FMOLS and DOLS) and corrective procedures (i.e. Newey–West standard errors for the static OLS) to overcome the issue, raising a possible doubt as to the reliability of inference from such a specification. On the other hand, inclusion of the dynamics via the ARDL

58 Basso and Oum (2007) stressed that although, estimation-wise, the static estimation procedure remains the same, conceptually the procedure now confers a different meaning to that used previously. With cointegration, the static estimation no longer reflects an intermediate relationship (due to an incomplete adjustment), as was usually interpreted, but rather describes the long-run equilibrium relationship.

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cointegration approach does indeed lead to smaller t-values, thus affirming the deficiency of the static procedure. In light of this, and the superior finite sample performance of the ARDL approach, we derive additional confidence that the results of the dynamic procedure are more appropriate.

To summarise, our basic model specification provides evidence of cointegration when diesel and total fuel are respectively regressed against income and price. Cointegration is not evident, however, when petrol is used in a similar specification as the dependent variable. This indicates that, unlike diesel and total fuel, long-run petrol may not share the same stochastic trend as income and price, although we do find evidence (via first differenced regression) that a statistically significant relationship exists in the short term. Looking back at the cointegration estimates, it is not difficult to understand why the basic model remains the most widely adopted specification. We observe – especially in this case – that cointegration cannot be established when additional regressors are included. This is probably because, as more variables are added, the probability of finding a common trend diminishes. Hence, in the case of time series estimation, a premium is placed on parsimonious specification (although this should not be to the extent of introducing omitted variable bias).

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CHAPTER 7 AGGREGATE PANEL DATA ANALYSIS OF FUEL DEMAND

ELASTICITIES

7.1 INTRODUCTION Although an extensive literature exists on transport fuel elasticities, the review in Chapter 4 revealed that most studies are based on time series data, with only rather limited estimates based on panel data. A further examination of the panel based literature also revealed that previous panel studies have mostly relied on disaggregated data, i.e. survey data (e.g. Archibald and Gillingham, 1980; Eltony, 1993; Kayser, 2000; Santos and Catchesides, 2005). While these estimates are certainly valid, Basso and Oum (2007) question the comparability of these panel studies to the traditional aggregate time series estimates. Disaggregate models are often designed to capture responses (e.g. gender and socio-economic factors) which are dissimilar to aggregate models, and this may potentially lead to conflicting outcomes to those found elsewhere in the literature.

In order to fill this gap, the empirical analysis presented in this chapter utilizes recently available aggregate panel data to estimate fuel demand elasticity. This serves to strengthen the overall validity of the research both in the utilisation of the most recently developed panel econometric estimators, and in by providing a set of estimates against which to compare those presented in Chapter 6. Additionally, the use of panel data will allow the unobserved heterogeneous region and time specific effects to be taken into account. This will not only ensure greater efficiency in the estimated elasticity coefficient but will allow greater confidence in the robustness of the estimates. As in the previous chapter, the empirical analysis estimates separately demand elasticity for petrol, diesel and total fuel consumption in the UK road transport sector.

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Section 7.2 of this chapter outlines the data used for the panel data analysis. Section 7.3 provides a description of the econometric models, the functional form and its specification. Section 7.4 discusses the panel data estimation techniques as well as the estimators employed to overcome the limitations arising from the use of the dynamic panel (see Section 3.6.1). Estimation outputs from the various panel data econometric estimators are presented in Section 7.5. Finally, the implications from the preferred elasticity estimates are discussed and summarised in Section 7.6 before the chapter is concluded in Section 7.7.

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7.2 PANEL DATA SOURCES AND VARIABLE DESCRIPTION For our panel model, an annual balanced dataset containing 84 observations was constructed. The dataset was made up of observations for the period spanning 2005–2011 at the NUTS 1 level (12 regions within the UK comprising of nine Government Office Regions (GORs) in England, Scotland, Wales and Northern Ireland).5960

As discussed in Chapter 4, the use of aggregate level panel data to produce national level fuel demand elasticity estimate has been relatively limited. In the UK, although there are estimates using disaggregate panel data, as far as we are aware this will be the first time estimation using aggregate level data has been attempted, especially in the context of distinguishing demand elasticities for the different fuel types.

The use of the panel dataset (although limited in terms of its time span) has many advantages over time series data. Firstly, panel data provides richer and more informative data (with more variability over cross-sectional unit and over time) which may allow for more efficient estimation of fuel demand (Baltagi, 2008). Additionally, as Kennedy (2008) argues, the variability of the data may help alleviate the problem of multicollinearity that is often encountered in a time series model. From an estimation perspective, the panel data model is also advantageous since it has an increased sample size. This is useful because it allows the panel estimators to be more accurate when compared to the time series model.

The advantages outlined above are certainly applicable in the context of this research. Although we obtained some of the data from similar sources as in Chapter 6, most of these datasets are relatively new and different to the ones used previously. For example, the fuel data is now from the DECC’s Regional and Local Authority Fuel Consumption Statistics. Additionally, fuel price data at the regional level are now sourced from the Automotive Association’s Regional Monthly Fuel

59 NUTS is an abbreviation for Nomenclature of Units for Territorial Statistics. 60 The nine GORs within England are categorised as the North East, North West, Yorkshire and the Humber, East Midlands, West Midlands, East of England, London, South East and South West.

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Price report. Table 7.1 provides a further description of the variables and their sources.

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Table 7.1 Description of panel data variables, data sources and descriptive statistics

Variables Definition Units Data N Mean Median SD Min Max Source Diesel Fuel Diesel fuel consumption per Litres per vehicle a, b, c 84 2,216.28 2,191.75 323.77 1,543.94 2,966.62 diesel vehicle Petrol Fuel Petrol fuel consumption per Litres per vehicle a, b, c 84 976.61 962.52 156.88 608.03 1,492.83 petrol vehicle Total Fuel Fuel consumption per Litres per vehicle a, b, c 84 1,361.06 1,376.61 151.70 935.42 1,691.98 vehicle Diesel Price Real diesel price UK pence per litre d, e 84 109.08 103.07 9.86 98.91 127.33 Petrol Price Weighted average real UK pence per litre d, e 84 104.65 98.99 9.10 94.72 122.93 petrol price Fuel Price Weighted average real fuel UK pence per litre d, e 84 107.06 101.26 9.54 96.83 125.58 price Income Per capita real gross UK £/population e, f 84 14,269.99 13,453.96 1,808.84 12,342.79 19,225.01 domestic household income (GDHI) Public Weighted average real fares UK pence c, e, g, i 84 82.99 74.62 24.08 67.36 169.28 Transport Fare for bus, light rail and underground Diesel Vehicle Per capita diesel vehicle Vehicle/population b, c, f 84 0.19 0.19 0.05 0.07 0.32 Petrol Vehicle Per capita petrol vehicle Vehicle/population b, c, f 84 0.36 0.35 0.05 0.26 0.46 Total Vehicle Per capita diesel and petrol Vehicle/population b, c, f 84 0.55 0.58 0.07 0.37 0.65 vehicle Technology Diesel vehicle share Diesel vehicle/total b, c 84 0.64 0.65 0.07 0.45 0.81 Share vehicle Note: All price and income variables are deflated to 2008 values. a Department of Energy & Climate Change (DECC) Regional and Local Authority Road Transport Fuel Consumption Statistics, b Department for Transport (DfT) Vehicle Statistics, c Department for Regional Development (DRDNI) Northern Ireland Transport Statistics, d Automotive Association (AA) Regional Monthly Fuel Price Report, e Office for National Statistics (ONS) Blue Book Dataset (deflator & income), f ONS Regional Statistics, g DfT Transport Statistics Great Britain, i Transport Scotland (TS) Scottish Transport Statistics.

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7.2.1 Dataset Construction Fuel demand is measured in litres and is converted using the annual conversion factors provided in DUKES. While diesel conversion is made directly, the quantities used for petrol and total fuel apply the same procedure used in the time series model (see Section 6.3.1).

For fuel prices, the annual average was obtained initially from the Automotive Association’s report. A similar weighted averaging methodology to that used in Chapter 6 was then applied to the fuel price dataset to take into account the differences in the type of fuel consumed. The nominal fuel data together with per capita income are then converted into real terms by deflating them to 2008 values.

The shorter time span of the data allows additional information to be incorporated into the public transport fare variable. Since no data is available regarding the specific fares applicable, however, a similar methodology as that used by Dargay and Hanly (2002) were used. This approach uses total revenue and total passenger trip information to produce an estimate of average revenue per trip as a proxy for fare (Balcombe et al., 2004).

Where applicable, the regional public transport fare includes underground and light rail fares in addition to bus fares.61 From this information, the weighted average fare is constructed weighted by the relative frequency of trips made by each mode of public transport.

∑푖,푡,푚 퐹푎푟푒푖,푡,푚 푥 퐽표푢푟푛푒푦푖,푡,푚 푊푒𝑖푔ℎ푡푒푑 푎푣푒푟푎푔푒 푓푎푟푒푖,푡 = (7.1) ∑푖,푡,푚 퐽표푢푟푛푒푦푖,푡,푚

61 The seven NUTS 1 regions which include public transport modes other than bus are London, North East, North West, Yorkshire & the Humber, East Midlands, West Midlands and Scotland.

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Table 7.2 summarises the degree of overall, between and within variation. Between variation describes the differences across individual regions while variation over time for a given region is represented by the within variation. From the statistics it can be seen that there is more variation across regions for all of the variables except for those involving the fuel prices data.

Table 7.2 Variation in data

Variables Overall Between Within Diesel Fuel 323.77 265.58 198.47 Petrol Fuel 156.88 146.94 67.68 Total Fuel 151.70 138.19 72.79 Diesel Price 9.86 0.40 9.85 Petrol Price 9.10 0.40 9.09 Fuel Price 9.54 0.39 9.53 Income 1,808.84 1,867.17 193.97 Public Transport Fare 24.08 24.83 2.83 Diesel Vehicle 0.05 0.05 0.02 Petrol Vehicle 0.05 0.05 0.02 Total Vehicle 0.07 0.07 0.01 Diesel Share 0.07 0.06 0.03 Note: The above statistics are standard deviations.

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7.3 THE PANEL DATA MODEL SPECIFICATION This section presents the panel data econometric models for fuel demand in the UK and their estimation implications. Data limitations restricted the application of the panel cointegration model in this chapter. The relatively short length of time that the data covers (7 years) means stationarity and cointegration tests are unlikely to be computationally feasible or sufficiently powerful for application in this dataset.62,63 For panel models with large N and small T, the usual panel data procedures are recommended (Levin et al., 2002).64 In order to overcome this restriction, the static and dynamic specifications (in order to obtain the short- and long-run demand response elasticities) are applied instead, as seen in studies with similar datasets (see for example Danesin and Linares, 2011; Pock, 2010).

As in Chapter 6, the choice of explanatory variables in the econometric models applied here was informed by the panel fuel demand literature covered earlier. In particular, we follow the widely applied fuel demand specification for panel models of Baltagi and Griffin (1997) and Baltagi et al. (2003). The model is extended here, however, to include additional exogenous variables which have generally not been applied in previous studies. In this extended specification, fuel demand (F) is defined to be a log-linear function of the real income per capita (Y), real fuel price (P), vehicle stock per capita (V), public transport fare (PT) and technology share (TS). The model specification described above can be generally represented as:

ln 퐹푖푡 = 훼 + 훽1 ln 푃푖푡 + 훽2 ln 푌푖푡 + 훽3 ln 푉푖푡 + 훽4 ln 푃푇푖푡 + 훽5 ln 푇푆푖푡 + 휐푖푡 (7.2)

Due to collinearity issues between the diesel vehicle and technology share variables, however, a further slight modification has to be incorporated into the general model

62 Baltagi (2008) notes that in most non-stationary panel procedures the criteria is that T is large enough to estimate each cross-section’s regression separately. 63 Karlsson and Lothgren (2000) examine the power of unit root tests for small T panels (T = 10). For such a panel, they found that unit root tests have low power and highlight the potential risk of erroneously modelling the panel. 64 Levin et al. (2002) suggest that unit root tests are feasible only for a moderate sized panel (T between 25 and 250 and N between 10 and 250).

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for diesel fuel demand.65 As a result, the specific demand equations for each fuel type to be estimated are:

ln 퐺푖푡 = 훼 + 훽1 ln 푃(퐺)푖푡 + 훽2 ln 푌푖푡 + 훽3 ln 푉(퐺)푖푡 + 훽4 ln 푃푇푖푡 + 훽5 ln 푇푆푖푡 + 휐푖푡 (7.3)

ln 퐷푖푡 = 훼 + 훽1 ln 푃(퐷)푖푡 + 훽2 ln 푌푖푡 + 훽3 ln 푉(퐺)푖푡 + 훽4 ln 푃푇푖푡 + 훽5 ln 푇푆푖푡 + 휐푖푡 (7.4)

ln 푇푖푡 = 훼 + 훽1 ln 푃(푇)푖푡 + 훽2 ln 푌푖푡 + 훽3 ln 푉(푇)푖푡 + 훽4 ln 푃푇푖푡 + 훽5 ln 푇푆푖푡 + 휐푖푡 (7.5)

Where petrol (G), diesel (D) and total fuel (T) are the three fuel types to be estimated. It can be seen that while Equations (7.3) and (7.6) incorporate own

vehicle stock per capita, the diesel model incorporates petrol vehicle stock (푉(퐺)푖푡) as part of the equation.

As mentioned previously, the log-linear functional form means that each parameter estimated represents a particular elasticity of fuel demand. Accordingly, price and income will have the expected negative and positive effect on fuel demand. Since vehicle stock is included on both sides of the equation, the sign for the vehicle stock variable will be negative. Baltagi et al. (2003) stated that in a fuel per vehicle formulation, the vehicle stock per capita variable captures the likely effect of reduced vehicle utilization (e.g. at the household level, an increase in vehicle ownership is more likely to result in a reduced utilization of the vehicle instead of a doubling in the mileage from before).66 Public transport is viewed as a substitute and as such the cross-price fare elasticity is expected to have a positive effect on fuel consumption. The technology share variable was introduced to capture the effect of fuel substitution via technological (i.e. fuel efficiency) and vehicle fleet changes. As such, the variable is expected to have a negative effect on all petrol and total fuel

65 Estimating diesel fuel demand using the general specification led to serious multicollinearity issues resulting in the coefficients of price, income and technology share not being statistically significant. Further investigation revealed that diesel vehicle ownership is highly correlated with technology share, yielding a correlation coefficient of 0.906 (see Appendix B). 66 A workaround to make the vehicle ownership coefficient comparable to estimates in a fuel per capita formulation is to add one unit to the vehicle parameter. Hence, the elasticity of fuel demand with respect to total vehicle is (1 + 훽3). See also Pock (2010) and Crôtte et al. (2010).

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consumption. As for diesel demand, the expected negative sign reflects the effects of fuel efficiency gains stemming from the higher adoption of (newer) diesel vehicles.

7.3.1 Static Model The general demand specification seen earlier (Equation 7.2) is representative of a static fuel demand equation.

ln 퐹푖푡 = 훼 + 훽1 ln 푃푖푡 + 훽2 ln 푌푖푡 + 훽3 ln 푉푖푡 + 훽4 ln 푃푇푖푡 + 훽5 ln 푇푆푖푡 + 휐푖푡

In the equation, we assume that 휐푖푡, the disturbance term, follows a one-way error component model:

휐푖푡 = 휖푖 + 푢푖푡 (7.6)

The subscripts 𝑖 and 푡 denote cross-section or regions and time respectively. The

휖푖 component in the disturbance term is included to control for any unobservable or omitted heterogeneous (time invariant) region-specific effects (e.g. geographical factors, natural resources, etc.).

There are trade-offs and limitations that need to be considered in the application of both the static and dynamic models. Firstly, in terms of estimation, a static model is not able to produce the required short- and long-run elasticities. Additionally, as discussed in Section 4.2.1, a static specification implies that equilibrium adjustment between fuel consumption and the explanatory factors takes place instantaneously. From a theoretical perspective, this assumption is rather restrictive since in reality it is natural to expect behavioural inertia when the factors affecting fuel consumption change. For example, increasing public transport subsidy (i.e. cheaper fares) may not result in an immediate mode shift response as car users’ decisions may be hindered by imperfect information on the actual cost of travel.

Although there are limitations, including the static estimates is beneficial in two ways. Firstly, it is less problematic from an estimation point of view. Additionally, if

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not mis-specified, the results from the static model are valid and categorised to be intermediate-run in nature (Dahl and Sterner, 1991). This fact is important since it both fits well with the span of the data and facilitates the dynamic model by providing a valid point of reference to compare the resulting short- and long-run estimates.

7.3.2 Dynamic Model To account for the expected behavioural inertia, a dynamic panel fuel demand model was also applied. The dynamic fuel demand relationship differs from the static model in the inclusion of the lagged endogenous variable. The general dynamic equation follows the form:

ln 퐹푖푡 = 훼 + 훽1 ln 푃푖푡 + 훽2 ln 푌푖푡 + 훽3 ln 푉푖푡 + 훽4 ln 푃푇푖푡 + 훽5 ln 푇푆푖푡 + 훿 ln 퐹푖푡−1 + 휐푖푡 (7.7)

From the previous points mentioned, estimating fuel demand through a dynamic specification possesses several benefits. Firstly, since it is widely accepted in the fuel demand literature that consumer adjustment takes time, the use of such a model is theoretically more appropriate since it incorporates that adjustment process. Policy- wise, the dynamic model is also more informative; having the advantage of separating both short- and long-run adjustments as well as indicating the speed of the adjustment process. An equally important benefit from a model perspective is highlighted by Bond (2002) as being the avoidance of omitted variable bias and the likelihood of obtaining more consistent estimates (see Sections 3.6.1 and 6.4).

As has been discussed previously, the inclusion of the lagged dependent variable in a panel model is not without its problems, however. Measures to address this issue are discussed further in the following section.

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7.4 PANEL DATA ESTIMATION TECHNIQUES The following discussion on panel estimation techniques provides a description of the estimators as well as an overview of the factors to be considered in their application in the panel model.

A pooled estimation procedure has been adopted for performing the estimation. Although, recently, there have been some arguments in favour of a heterogeneous procedure, in this context, pooling the data across the heterogeneous units is considered appropriate, for the following reasons. Firstly, the relatively short dataset (T = 7) means that estimating heterogeneous parameters is simply not feasible. Baltagi et al. (2003) argue that homogenous panel estimators are the only viable alternative in data sets with T up to 10. Secondly, the preponderance of between variation as compared to within variation in the data (see Table 7.2) suggests that the pooled procedure (homogeneous estimators) would be more appropriate.

While estimating the static fixed effect panel model is relatively straightforward, it is well known that complications arise in the context of the dynamic model due to the inclusion of the lagged dependent variable. As discussed previously, both the OLS and FE estimators produce biased and inconsistent parameter estimates due to the correlation between the lagged dependent variable and the error term. Additionally, Nickell (1981) highlighted that although the FE estimator becomes more consistent as T gets larger, increasing the number of individual units (N) does not eliminate the problem.

A solution to overcome the problem of the endogeneity of the right-hand regressors is through the use of an instrumental variable estimator (two-stage least squares estimator/2SLS). The instrumental variable (IV) approach is a traditional econometric tool often applied to overcome the endogeneity problem. By using a valid instrument, the IV method can provide a consistent estimate of the endogenous variable. For the IV estimator to be valid, it has to satisfy two properties: the instrument must be exogenous (uncorrelated with the error) but must be highly correlated with the endogenous regressor. Additionally, the instrument used must

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also not be relevant in the original equation. As can be seen, although the IV approach provides a feasible option it places a strong assumption on the availability of a valid instrument. In practice, this is often not the case, and in this eventuality the alternative is to rely on ‘internal’ instruments (i.e. lags of the instrumented variable) (Roodman, 2006).

Among the initial 2SLS type estimators that adopted this philosophy of utilising ‘internal’ instruments to solve the endogeneity issue was the method suggested by Anderson and Hsiao (1981, 1982). Their solution involves transforming the original

model through first-differencing to eliminate the individual effects (휖푖) and then using the second and third lags of the dependent variable, either in lagged levels or differences form, to instrument the endogenous differenced lagged dependent variable. Incorporating these instruments with the earlier 2SLS technique leads to what is defined as the Anderson-Hsiao levels and difference estimators.67 The main attraction of this estimation approach is that it both solves the problem of finding a valid instrument and provides consistent estimates of the parameters. Some critics, however, argue that since all the moment conditions are not utilised the approach thus yield an estimator inefficiency problem (Baum, 2006).

Echoing the approach of Anderson and Hsiao, Holtz-Eakin et al. (1988) show that estimator efficiency can be improved by including further lags of the dependent variable as additional instruments. Although practical, the usefulness of implementing this in the standard 2SLS procedure is restricted by the trade-off imposed: the additional lag length (instruments) results in a smaller sample size. Holtz-Eakin et al. show, however, that a way around this trade-off is possible by working in the GMM framework. Their work resulted in the application of ‘GMM- style’ instruments which enable the loss of degrees freedom to be avoided (Roodman, 2006).

67 In the literature, the Anderson-Hsiao estimator is also often referred to as the first-difference 2SLS (FD-2SLS) estimator.

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Arellano and Bond (1991) took the above developments further by proposing a dynamic GMM estimator, known as the Arellano–Bond difference GMM estimator (FD-GMM). Like the Anderson–Hsiao FD-2SLS, the difference-GMM applies first- differencing on the original model to eliminate the individual effects. The endogenous first-difference lagged dependent variable is then instrumented using suitable lags of its own in levels form (i.e. twice lagged levels and beyond) and the strictly exogenous regressors. As with the original 2SLS procedure, additional instruments external to the original model can also be included. Exploiting these additional instruments makes the Arellano–Bond FD-GMM more efficient compared to the Anderson–Hsiao FD-2SLS.

Subsequent work by Arellano and Bover (1995) and Blundell and Bond (1998) revealed a potential limitation to the FD-GMM. They demonstrated that the difference GMM estimator may perform poorly with variables that are close to random walk. With persistent data, past levels convey little information about future changes, thus making level lags weak internal instruments for the first-differenced variables. To overcome this, Blundell and Bond (1998) applied a different strategy to account for the bias: instrumenting the levels with differences (i.e. transforming the instruments instead of the regressors). The resulting Blundell–Bond system-GMM estimator (sys-GMM) simultaneously performs a system of regression in first- differences with lagged levels instruments as well as in levels with lagged differences as instruments. When applied to persistent data with a small time series observation, the system-GMM estimator has been shown to provide a dramatic increase in efficiency as well as less finite sample bias (Blundell and Bond, 1998).

As with other econometric estimation methods, specification tests needs to be carried out in order to test the validity of the dynamic GMM estimators. In general, for the GMM estimators to perform as intended, they are required to conform to two main criteria (Roodman, 2006). Firstly, for the GMM estimators to be consistent, the levels equation should not contain any first-order serial correlation. To validate this, the Arellano–Bond (1991) test for serial correlation (with null hypothesis of no second-order serial correlation) is performed on the residuals in differences. By

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failing to reject the null, the test essentially confirms that there is no serial correlation in the levels equation. As with the standard IV estimation, a similar instrument validity test is applied to the dynamic GMM estimation. As such, the second specification test applied is a test of over-identifying restrictions. Here the Hansen (1982) test (with the null hypothesis of no correlation between instruments and the error) is used to check for the exogeneity of the instruments.

While dynamic GMM estimators are consistent and efficient, their desirable properties only hold true for samples with large N. Bun and Kiviet (2006) argued that in practice many datasets have values of N and T that are moderate or even small, and they therefore question the suitability of the dynamic GMM. They show that in small samples, the GMM estimates can be substantially biased and inefficient. In such situations, a recently developed bias-corrected within-groups estimator may provide a better alternative. Kiviet (1995) pointed out that, compared to the GMM and IV estimators, the LSDV although inconsistent, exhibits a smaller variance, which can be used to derive an accurate prediction of the resulting bias. The estimator proposed by Kiviet, defined as the bias-corrected within-groups estimator (LSDVc) utilizes this bias estimation procedure to correct the Nickell bias, resulting in a consistent and efficient estimate even in small samples. The superior performance of the LSDVc estimator in small samples has been confirmed by various ensuing Monte Carlo studies. Judson and Owen (1999) show that (in a balanced panel) the LSDVc performs the best when T ≤ 10 and T = 20. For T = 5, N = 20, Monte Carlo results from Buddelmeyer et al. (2008) also favour the use of the LSDVc. As a result, taking into account the size of the available dataset in this research, the LSDVc estimator is therefore applied to the panel model. For the LSDVc estimation, the coefficients based on the bias approximation term up to the order T-1 are implemented (see Bun and Kiviet (2003)) with initial values obtained from the Arellano–Bond FD-GMM estimator.

7.4.1 Additional Estimation Validity Checks In the following section, estimation results from the biased and inconsistent OLS and fixed effects LSDV estimators will also be included. Although these estimates are not

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reliable, their inclusion has been recommended as an additional validity check for the theoretically superior estimators mentioned earlier (Roodman, 2006). The correlation between the lagged dependent variable and error in the OLS estimator results in an upward bias in its coefficient estimate. On the other hand, the estimate from the LSDV estimator is biased downwards (Arellano and Bond, 1991). As Bond (2002) points out, the opposite directions of the bias are useful in providing a bounds check for the consistent estimators. As such, the estimates from the consistent estimators should lie between the upper bound and lower bound provided by the OLS and LSDV respectively.

The preponderance of consistent estimators based on the IV/GMM mould, although certainly an advantage in solving the problem of the endogeneity of the lagged dependent variable in short dynamic panels, does impose an additional risk. Roodman (2009) highlights the danger of false-positive results from relying on the difference and system GMM while Murray (2006) highlighted the issues of invalid instruments in the IV context. As such, in addition to the above, further validity checks were also performed to ensure the soundness of the estimation results displayed.

Firstly, in the context of the dynamic estimation, a test of dynamic stability should be conducted. If the dynamic adjustment assumption is to be valid, then the estimated coefficient of the lagged dependent variable (훿) should have a value below unity. The outcome of |훿| < 1, indicates a dynamic convergence and as such supports the dynamic specification of the model. An outcome where |훿| ≥ 1 suggests unstable equilibrium and therefore questions the validity of the dynamic adjustment assumption (Roodman, 2009).

Roodman (2006, 2009) also offers additional suggestions on the application of the difference and system GMM. Since both estimators tend to generate numerous instruments, one should be mindful of and report the instrument count. He cautioned against the dangers of instrument proliferation, since a large number of instruments can cause biased estimates as they overfit the instrumented variable

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and vitiate the ability of the Hansen test to detect this problem. Although there is no precise rule as to what exactly constitutes too many instruments, certain rules of thumb can be used as guidance in the application of these estimators. Firstly, instrument count should be kept as low as possible and should not surpass the number of observations (Roodman, 2009). Additionally, one can also look at the Hansen J-statistic for the tell-tale sign of overfitting; a p-value of 1.00 is indicative of this problem (Roodman, 2006).

Murray (2006) raises similar issues but in the context of the instrumental variable 2SLS estimation. He suggests that the validity of external instruments should not only be mechanistically based on statistical tests but should also include intuitive tests as an additional check. For example, a tell-tale sign of an invalid instrument is when one finds that the coefficient of the instrumental variable is counterintuitive to the a priori expectation in the reduced form regression. In addition, validated instruments should also be subjected to a weak instrument test (Murray, 2006, Baum et al., 2007).68 This is because although the IV2SLS estimation will be consistent, the use of weak instruments would result in a biased and unreliable estimator, rendering it unsuitable for econometric inference.

68 Murray (2006) provides an excellent description on the issues of invalid and weak instruments.

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7.5 ESTIMATION RESULTS In this section, the results for the aggregate panel fuel consumption models are presented. We first estimate the static estimators: the pooled OLS (which ignores individual heterogeneity) and the fixed effects LSDV. As mentioned before, if the dynamic model cannot be validated (i.e. if there is no dynamic convergence) the static estimates could then be used and interpreted as the intermediate elasticity.

For the subsequent dynamic estimation, seven alternative estimators were examined. For the IV2SLS FE in particular, we mainly follow the approach of Baltagi et al. (2003) in using the exogenous variables and their lags as instruments for the lagged dependent variable. The appeal of this particular approach is that it is theoretically intuitive and obviates the need to find other valid external instruments. In total, the estimation of the model for each fuel type involves the comparison of nine panel estimators.

7.5.1 Diesel Fuel Estimates We start by summarizing the elasticity estimates of diesel demand based on the various estimators described previously (see Table 7.3). The first two columns contain estimates from the static pooled OLS and LSDV estimators. The static OLS yields a significant price coefficient (–0.64) while finding insignificant effects for the rest of the regressors. In contrast, the LSDV estimator finds that, with the exception of public transport fare, all other factors have a significant intermediate-term effect on diesel consumption.

Turning now to the estimation results for the dynamic model, as discussed previously, both the pooled OLS and LSDV are included since they provide bounds which can be utilised to compare the results of the consistent estimators. Here it can be seen that the coefficient of the lagged dependent variable for the OLS estimator indicates a value of 0.987 (upper bound) while it is 0.246 (lower bound) for the LSDV.

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Table 7.3 Estimation results for the panel data diesel fuel models Dependent Variable: Static Dynamic Diesel/Vehicle Pooled OLS LSDV Pooled OLS LSDV IV2SLS FE FD-2SLS Diff GMM Sys GMM LSDVc

Diesel/Vehiclet-1 - - -0.987*** -0.246** -0.523** -0.334 -0.247* -0.976*** -0.333*** (0.020) (0.101) (0.251) (0.257) (0.136) (0.037) (0.106) Price -0.640* -0.687*** -0.692 -0.560*** -0.432*** -0.668*** -0.590*** -0.108** -0.502*** (0.348) (0.096) (1.094) (0.086) (0.149) (0.233) (0.200) (0.049) (0.115) Income -0.120 -0.759** -0.033 -0.475** -0.260 -0.658*** -0.270* -0.020 -0.460*** (0.269) (0.267) (0.053) (0.214) (0.235) (0.209) (0.150) (0.046) (0.166) Public Transport Fare -0.173 -0.064 -0.017 -0.004 -0.049 -0.047 -0.016 -0.004 -0.012 (0.191) (0.059) (0.036) (0.093) (0.103) (0.087) (0.118) (0.019) (0.098) Petrol Vehicle Per Capita -0.118 -1.712*** -0.019 -1.599*** -1.468*** -1.605*** -1.318** -0.011 -1.520*** (0.257) (0.326) (0.036) (0.255 (0.228) (0.262) (0.565) (0.020) (0.222) Technology Share -0.272 -1.153*** -0.016 -1.047*** -0.868*** -1.508*** -0.869*** -0.004 -0.987*** (0.249) (0.132) (0.050) (0.125) (0.178) (0.159) (0.213) (0.037) (0.099)

Observations 84 84 72 72 72 48 60 72 84 R2 0.647 0.992 0.981 0.996

Instruments - - - - 7 9 17 19 - Hansen J-test - - - - 0.185 0.000 0.688 0.807 - (p-value) Difference Hansen Test ------0.108 0.724 - (p-value) AB AR(1) ------0.550 0.178 - (p-value) AB AR(2) ------0.847 0.236 - (p-value) Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Numbers in parentheses are standard errors. 3) The standard errors reported for each estimator are robust to heteroskedasticity and adjusted for intra-region dependence with the exception of the LSDVc (bootstrapped standard errors). 4) The Kiviet’s bias corrected LSDVc estimator applies the Diff-GMM as its initial consistent estimator.

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The problem of the endogeneity of the lagged dependent variable in the diesel model is addressed by initially applying the standard instrumental variable estimators. The IV2SLS FE estimator finds a significant lagged dependent variable coefficient of 0.523. Additionally, the estimator indicates significant short-run price, substitution and technology share elasticities, although income and public transport appear not to be significant. The Anderson-Hsiao FD-2SLS reveals elasticity estimates that are much higher than those obtained by the other 2SLS estimators. However, it also reveals an improbable dynamic coefficient of –0.523, while the Hansen J-test rejects the validity of the instrument set.

The results of the Arellano–Bond Diff-GMM estimator are, in contrast, much more probable. Apart from the public transport coefficient, the other elasticities are significant with results reasonably in-line with the IV2SLS FE and LSDVc estimators. The only cause for concern is the relatively similar value of the lagged dependent variable coefficient (0.247) to the LSDV estimator, which, according to Blundell and Bond (2000), suggests that the instruments used are weak. Using additional instruments leads to an improved (larger) value of the dynamic coefficient but unfortunately caused a Hansen J-test value of 1.00 which indicates the problem of overfitting.

A similar problem is encountered with the Blundell–Bond Sys-GMM estimator. While the dynamic coefficient is within the bounds provided by the OLS and LSDV estimators, it can be observed that the value (0.976) is now biased towards the OLS. Although the Hansen J-test value is 0.807, in a small sample, this may still be indicative of an overfitting problem. Using variations with different (higher and lower) instrument counts results in either a J-test value of 1.00 or an insignificant result for all of the coefficients estimated. Furthermore, very little improvement in the dynamic coefficient was achieved using the alternative specifications.

The results from both the difference- and system-GMM estimators possibly reflect the evidence presented by Bun and Kiviet (2006) which was discussed previously: that the GMM estimators are biased and inefficient in small samples. To overcome

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this problem, therefore, the LSDVc approximation procedure is applied with the diff- GMM estimator utilised as its initial consistent values. We note that this leads to a more reasonable outcome with a higher value of 0.333 for the coefficient of the lagged dependent variable. In addition, the elasticity parameters, which are significant and within the range reported by its 2SLS counterparts, lend credence to the validity of the estimates. From the evidence shown, we feel that the coefficient estimated by the LSDVc procedure is preferable over those from other estimators in terms of representing the elasticities of diesel demand.

7.5.2 Petrol Fuel Estimates Turning to Table 7.4, we now discuss the elasticity estimates from the petrol fuel demand model. In the static regressions, it can be observed that there are significant differences between the coefficients estimated by the pooled OLS and the LSDV estimators. It appears that the OLS procedure – which ignores regional differences – tends to produce not only larger parameters but also display effects which are contrary to theoretical expectations (e.g. negative and significant income elasticity). It can be seen that, while the output from the LSDV mostly shows the expected sign, the negative and significant cross price elasticity was unexpected as it signals that public transport is a complement instead of a substitute.

The inconsistent dynamic OLS and LSDV estimators show a relatively smaller upper (0.910) and lower (0.533) bound range for the dynamic coefficient compared to those seen for diesel demand. Like its static counterpart, the dynamic OLS also appears to indicate significant income as well as technology share coefficients but with the opposite direction of effect. The price elasticity estimates produced by both estimators are, however, more in tune with what might be expected, with values between –0.146 and –0.199.

As discussed previously, in a dynamic equation, it is important for the endogeneity of the lagged dependent variable to be taken into account. Here, therefore, we present the results of our attempts to tackle the issue through the use of the IV2SLS-FE and the FD-2SLS, using as instruments the lag of the exogenous regressors. The IV2SLS-FE

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estimator yields a dynamic coefficient of 0.715, which falls within the bounds mentioned earlier. The significant short-run price, vehicle and technology share elasticities (–0.208, –0.487 and –0.390) have the expected sign and are all significant. Income, however, was found to have no significant effect on petrol consumption. In contrast, the Anderson–Hsiao FD-2SLS procedure remains problematic since, although the dynamic coefficient is now positive, its value of 0.121 is below the expected bounds. Even with the second lag in levels being used as the instrument instead, the outcome is still implausible.69 As found previously, the lagged difference and levels are often poor instruments and in both cases the validity of the instrument set was rejected by the Hansen test.

On the other hand, we obtained much more plausible results from the Arellano– Bond Diff-GMM estimator. Unlike previously, the lagged petrol consumption coefficient (0.591) is somewhat higher than that of the dynamic LSDV, suggesting that the weak instruments problem is less of an issue in the petrol model dataset. In terms of the elasticity estimates, the results obtained seems to corroborate those for petrol demand, with only price (–0.193), vehicle utilisation (–0.693) and technology share (–0.543) having significant effects. Moreover, the relative conformity in the magnitude of the elasticity effects observed compared to their counterpart estimators lends additional support to the Diff-GMM procedure.

The Blundell–Bond Sys-GMM estimator also yields reasonable estimates. The coefficient of lagged consumption (0.766) does indicate a higher habit persistence compared to those from the other consistent estimators (0.566 to 0.715), in relative terms, however, it is still far lower than the upper bound obtained from the inconsistent dynamic OLS. Mindful of the overfitting problem, we also tried different variations which minimize the instrument count; however the lower dynamic estimate achieved came with a trade-off of either insignificant elasticity coefficients,

69 Applying the Anderson–Hsiao FD-2SLS levels estimator yielded a substantially overestimated dynamic coefficient of 1.236 (robust standard error: 0.381) and statistical significance for the coefficients of price (– 0.226), vehicle ownership (–1.426) and technology share (–0.336). Although the instrument passes the Kleibergen–Paap under-identification and weak identification tests, the exogeneity of the instrument set was rejected by the Hansen J-test.

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Table 7.4 Estimation results for the panel data petrol fuel models Dependent Variable: Static Dynamic Petrol/Vehicle Pooled OLS LSDV Pooled OLS LSDV IV2SLS FE FD-2SLS Diff GMM Sys GMM LSDVc

Petrol/Vehiclet-1 - - -0.910*** -0.533*** -0.715*** -0.121 -0.591*** -0.766*** -0.674*** (0.023) (0.096) (0.103) (0.489) (0.110) (0.088) (0.112) Price -0.697*** -0.197*** -0.146*** -0.199*** -0.208*** -0.223** -0.193*** -0.154*** -0.206*** (0.169) (0.028) (0.024) (0.037) (0.037) (0.110) (0.038) (0.037) (0.041) Income -0.520** -0.029 -0.047* -0.078 -0.064 -0.361 -0.043 -0.213 -0.085 (0.189) (0.188) (0.025) (0.175) (0.142) (0.360) (0.133) (0.175) (0.157) Public Transport Fare -0.403*** -0.207** -0.027* -0.059 -0.100 -0.032 -0.088 -0.144* -0.096 (0.107) (0.085) (0.015) (0.101) (0.080) (0.085) (0.082) (0.081) (0.095) Petrol Vehicles Per Capita -0.392** -0.181 -0.018 -0.487* -0.602*** -0.232 -0.693*** -0.130 -0.546*** (0.140) (0.224) (0.018) (0.241) (0.221) (0.330) (0.186) (0.084) (0.146) Technology Share -0.196 -0.666*** -0.032* -0.470*** -0.390*** -0.557* -0.543*** -0.020 -0.401*** (0.116) (0.108) (0.015) (0.123) (0.112) (0.338) (0.121) (0.061) (0.081)

Observations 84 84 72 72 72 48 60 72 84 R2 0.845 0.992 0.990 0.995 - - - -

Instruments - - - - 8 6 19 25 - Hansen J-test - - - - 0.065 0.000 0.830 0.886 - (p-value) Difference Hansen Test ------0.574 0.678 - (p-value) AB AR(1) ------0.094 0.045 - (p-value) AB AR(2) ------0.441 0.416 - (p-value) Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Numbers in parentheses are standard errors. 3) The standard errors reported for each estimator are robust to heteroskedasticity and adjusted for intra-region dependence with the exception of the LSDVc (bootstrapped standard errors). 4) The Kiviet’s bias corrected LSDVc estimator applies the Diff-GMM as its initial consistent estimator.

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perfect J-test values or elasticity signs which are contrary to expectations.70 In terms of the elasticity, only short-run price (–0.154) and cross-price (0.144) are statistically significant from our preferred Sys-GMM specification.

We now discuss the estimate from the LSDVc estimator. From the results, it can be seen that after correcting for the Nickell bias, the dynamic coefficient (0.674) is now relatively higher compared to those from the LSDV and Diff-GMM estimator. The short-run price, vehicle utilisation and technology share elasticities (–0.206, –0.546 and –0.401) are significant and in line with the earlier results. These results appear to reaffirm the findings that income and public transport fare have insignificant effects on petrol demand.

7.5.3 Total Fuel Estimates Table 7.5 presents the empirical results for the total fuel demand model based on the various estimators described previously. The static pooled OLS yields a significant but apparently overestimated intermediate price coefficient (–0.834) whereas other regressors are not significant. In contrast, evidence from the LSDV estimator – which is widely preferred in a static specification – indicates that in the intermediate term, price (–0.354), income (0.313), cross-price (–0.107), vehicle utilisation (–0.688) and technology share (–0.185) elasticities are all significant. We observe that the magnitude of the price coefficient is also much lower (by approximately 60%). The cross-price elasticity sign was unexpected, however, since it suggests a complementary relationship between public transport and road transport usage.

Similar outcomes can be seen from the traditional but inconsistent dynamic OLS and LSDV estimators. The OLS estimator seems to find no-significant effects from most of regressors, with the exception of the dynamic and technology share coefficients. Its dynamic coefficient estimate of 1.003 appears to be overestimated and suggests an unstable dynamic equilibrium. The LSDV, on the other hand, only rejects the statistical significance of the cross-price effect.

70 The procedures used to limit the instrument count include restricting the lag ranges in generating the instrument sets and using the collapse option available in Stata as suggested in Roodman (2009).

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Table 7.5 Estimation results for the panel data total fuel models Dependent Variable: Static Dynamic Total Fuel/Vehicle Pooled OLS LSDV Pooled OLS LSDV IV2SLS FE FD-2SLS Diff GMM Sys GMM LSDVc

Total Fuel/Vehiclet-1 - - -1.003*** -0.344*** -0.350*** -0.148 -0.378*** -0.983*** -0.424*** (0.012) (0.040) (0.043) (0.298) (0.072) (0.017) (0.093) Price -0.834*** -0.354*** -0.020 -0.179*** -0.182*** -0.434*** -0.164*** -0.522 -0.139** (0.245) (0.063) (0.039) (0.021) (0.022) (0.129) (0.041) (0.946) (0.057) Income -0.234 -0.313* -0.044 -0.195*** -0.157*** -0.284** -0.121* -0.027 -0.190** (0.196) (0.145) (0.034) (0.057) (0.052) (0.139) (0.067) (0.024) (0.082) Public Transport Fare -0.063 -0.107* -0.013 -0.001 -0.018 -0.017 -0.043 -0.012 -0.001 (0.121) (0.051) (0.013) (0.037) (0.032) (0.044) (0.038) (0.017) (0.047) Total Vehicle Per Capita -0.202 -0.688*** -0.010 -0.603*** -0.583*** -0.772*** -0.519*** -0.004 -0.567*** (0.184) (0.081) (0.016) (0.031) (0.028) (0.126) (0.045) (0.022) (0.068) Technology Share -0.271 -0.185** -0.052* -0.227*** -0.226*** -0.214*** -0.229*** -0.271 -0.229*** (0.235) (0.060) (0.029) (0.022) (0.020) (0.065) (0.020) (0.275) (0.033)

Observations 84 84 72 72 72 48 60 48 84 R2 0.690 0.996 0.991 0.999 - - - - -

Instruments - - - - 7 9 15 22 - Hansen J-test - - - - 0.075 0.000 0.653 0.953 - (p-value) Difference Hansen Test ------0.744 0.719 - (p-value) AB AR(1) ------0.176 0.214 - (p-value) AB AR(2) ------0.358 0.072 - (p-value) Notes: 1) ***, **, * indicate significance at 1%, 5% and 10% respectively. 2) Numbers in parentheses are standard errors. 3) The standard errors reported for each estimator are robust to heteroskedasticity and adjusted for intra-region dependence with the exception of the LSDVc (bootstrapped standard errors). 4) The Kiviet’s bias corrected LSDVc estimator applies the Diff-GMM as its initial consistent estimator.

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The coefficient of lagged consumption of 0.344 suggests stable dynamic stability with relatively low habit persistence; adjustment towards long-run equilibrium takes approximately 1.5 years.

Next, we direct our discussion to the results from the group of consistent estimators which deal with the endogeneity issue. The IV2SLS FE estimator produces results which are somewhat similar to the dynamic LSDV estimator. The lagged consumption (0.350) and price coefficient (–0.182) are slightly larger, while the remaining significant coefficients are modestly lower. Public transport fare elasticity is insignificant. The Anderson–Hsiao FD-2SLS procedure remains dogged by what is presumably poor instrument performance related to the small sample. The dynamic coefficient of –0.148 is implausible and insignificant while the price coefficient (– 0.434) appears to be substantially overestimated.71 Although it passes the under- identification and weak identification test, the Hansen J-test rejects the validity of the instrument set which included the twice lagged differenced variable.

When the Arellano–Bond Diff-GMM estimator is employed the results are quite similar to the LSDV and IV2SLS FE. The coefficient of the lagged consumption (0.378), although larger, appears to be biased downwards towards the LSDV. Since a similar problem was encountered in the diesel dataset, its manifestation here does not come as a complete surprise. Short-run price, income, vehicle utilisation and technology share coefficients (–0.164, 0.121, –0.519 and –0.229) are significant, reasonable in magnitude and display the expected sign. Public transport fare remains insignificant.

The Blundell–Bond Sys-GMM estimator appears to display similar symptoms to those seen in the diesel model. While the dynamic coefficient (0.983) remains within the validity boundary as suggested by Bond (2002), it appears to be similarly biased upwards towards the OLS. Although the p-value of the J-test is well below 1.00,

71 The lagged total fuel coefficient is not significant although its value of 0.992 does fall within the credible range when the levels version of the FD-2SLS was implemented. Besides, the use of the twice lagged levels of the dependent variable as instrument now resulted in p-value of 0.611 and 0.000 for the under-identification and J-test indicating that the even in this specification the Anderson–Hsiao procedure remains problematic.

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overfitting appears to be an issue. This is probably because the instrument count is now nearly half of the available observation due to our specification requiring a deeper lag of the exogenous variables as instruments in order to obtain a valid and significant dynamic coefficient. In addition, none of the elasticity coefficients under the Sys-GMM procedure are statistically significant.

Acknowledging the small sample issue with the GMM estimators, the LSDVc procedure was once again used to obtain bias-corrected estimates which are more appropriate for econometric inference. When compared to the LSDV, the bias- corrected coefficient of the lagged consumption (–0.424) is now larger by approximately 25%. The magnitude of the short-run price elasticity falls from –0.179 to –0.139 while there appears to be conformity for the coefficients of income (0.190), vehicle utilisation (–0.567) and technology share (–0.229). Similar to other consistent estimators, the bias-correction procedure appears to reject the statistical significance of public transport fare on total fuel consumption. Taking account of this evidence the results from the LSDVc estimator were adopted as the preferred estimates for the total fuel model.

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7.6 SUMMARY OF ELASTICITIES Recapitulating, it can be seen from the results that the dynamic GMM procedures – especially the Blundell–Bond system-GMM estimator – appear to suffer from the small number of cross-sectional units. In such a situation, the GMM estimators may not be appropriate for econometric inference since they have been shown to be biased and inefficient. In view of this, the bias-correction procedure of the LSDVc estimator appears to be a better alternative, especially considering the small sample size of the study. The results from the LSDVc estimator are therefore preferred and will be the basis for the following discussion in the section.

Table 7.6 Elasticity estimates from the LSDVc estimator

Diesel Per Vehicle Petrol Per Vehicle Total Fuel Per Vehicle Short run Long run Short run Long run Short run Long run Price –0.502*** –0.753*** –0.206*** –0.632** –0.139** –0.241***

Income –0.460*** –0.690*** –0.085 –0.262 –0.190** –0.330**

Public Transport –0.012 –0.017 –0.096 –0.295 –0.001 –0.003 Fare Diesel Vehicles – – – – – –

Petrol Vehicles –1.520*** –2.279*** –0.546*** –1.675* – –

Total Vehicles – – – – –0.567*** –0.983***

Technology Share –0.987*** –1.479*** –0.401*** –1.230*** –0.229*** –0.397***

Notes: ***, **, * indicate significance at 1%, 5% and 10% respectively.

The short- and long-run elasticities are summarised in Table 7.6. At first glance, most of the results appear to conform to the a priori expectations. Before proceeding further though, it is important to note that there is a marked difference in terms of the level of dynamic adjustments between the two main transport fuels. While strong habit persistence is observed for petrol consumption (i.e. adjustment takes approximately 3.1 years) diesel appears to have relatively small inertia (i.e. long-run equilibrium achieved in 1.5 years). This appears to be in line with the results from Pock (2010) and from Danesin and Linares (2011).

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For the long-run estimates, there appear to be no significant differences between the elasticities from the diesel and petrol models. Significant differences were evident, however, when it comes to the short-run elasticities from the LSDVc estimator. In particular, we found the differences between the coefficients from the diesel model and the petrol model accounting for price, petrol vehicles and technology share to be statistically significant at the 1% level.72

The results confirm that price has a significant negative effect on fuel consumption. In terms of magnitude, it appears that diesel consumers have greater price sensitivity compared to petrol. In the short-run, the price elasticity for diesel is greater by approximately 2.4 times compared to petrol, although the order of difference seems to be smaller in the long-run. This result seems to affirm the selection mechanism noted by Schipper (2011). He argued that high mileage users are more likely to keep track of their fuel expenditure and are hence more inclined to switch to diesel. As such, it is plausible that the bigger sensitivity to price changes recorded here for diesel closely reflects the characteristics of such users.

A more varied response is evident when it comes to income elasticity, however. While income has a significantly positive effect on diesel consumption, the evidence suggests that petrol consumption is independent of income. In general, the results for petrol seem consistent with the hypothesis of travel saturation as seen in most developed countries.73 The finding also appears to support the selection mechanism mentioned earlier; the migration of high mileage users to diesel will leave only those with a low utilization level as the primary petrol users. Since these low-level users are most likely to use their car for basic purposes, an increase in income would not generate further usage. For total fuel, the larger income effect compared to price is consistent with the findings in the literature. In contrast, the opposite is observed for

72 The test of differences between the petrol and diesel elasticities was not performed on the income and public transport fare coefficients as they were found to be insignificant in the initial LSDVc models. 73 The unexpected negative sign for income could also be due to the inclusion of both the income and vehicle stock variables. According to Basso and Oum (2007), when both are included in the model income elasticity tends to be deflated since some of the factors attributed to vehicles are no longer captured by the income coefficient. However, the total income response is the combined effect of both variables. When this is added together, –0.085 + (1 + (–0.546)) = 0.369, the figure still indicates a positive total income response in the short- run. In the long-run, however, the total income response continues to be unexpectedly negative.

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diesel. A 1% increase in income will increase diesel (total fuel) consumption by 0.46% (0.19%) in the short-run and by 0.69% (0.33%) in the long-run.

Interestingly, the models unanimously indicate that public transport fares have no statistically significant effect on fuel consumption. The absence of a significant cross- price effect is surprising since it implies that despite the wide extent of the public transport service in the UK, public transport is neither a substitute for nor a complement to other modes of transport for road users. It is possible that this non- significant result could be due the failure of the variable used to capture the actual effect of public transport. Road users are possibly more concerned with the level of service and hence a measure that captures this particular aspect of public transport would be more appropriate.

The elasticity of vehicle ownership for petrol and total fuel is significant and shows the expected sign. The evidence is consistent with the theoretical expectation that increased vehicle ownership results in lower utilization hence lowering per vehicle fuel consumption. The effect of a 1% increase in the number of vehicles per capita appears to be similar in magnitude for both petrol and total fuel in the short-run, i.e. fuel usage declines by 0.55% and 0.57%. In the long-run, however, the response in petrol consumption is much more elastic, decreasing by 1.68% for a percent increase in ownership, compared to 0.98% for total fuel.

As noted earlier, the inclusion of the own vehicle ownership variable for diesel appears to be highly correlated with the technology share variable and as such was replaced instead by the petrol vehicle ownership variable. Under this specification, the vehicle stock variable is also expected to be negative, although now it captures a substitution instead of utilization effect, as suggested by Pock (2010). The LSDVc estimates for diesel lead to coefficient values of –1.52 and –2.28, suggesting a strong negative substitution effect both in the short- and long-run.

Turning to the technology share elasticity, the coefficients in all models are statistically significant and have a negative effect as expected. It turns out that the

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effect is stronger with diesel fuel compared to petrol. In the short-run (long-run), a 1% increase in diesel vehicle share is associated with a decrease of 0.99% (1.48%) for diesel consumption whereas petrol usage records a relatively smaller decline of 0.40% (1.23%). To explain the stronger magnitude seen for diesel, apart from the reasons suggested in Section 7.3, it is plausible that the technology share variable captures the utilization effect which was omitted by the exclusion of the vehicle ownership variable, resulting in the more pronounced coefficient.

Finally, it is important to note that the parameters for the total fuel model tend to be either between the diesel and petrol estimates – which is expected e.g. income – or surprisingly, turn out to be completely underestimated (as in the case for the price and technology coefficients). This raises similar questions to those highlighted by Basso and Oum (2007) as to the suitability of the total fuel estimates for econometric and hence policy inference. They concluded that, when possible, it is better to distinguish in terms of fuel type when making estimations. Evidence from our panel models seems to reinforce what they posited, since the total fuel estimates do appear to be inconsistent with the ‘average’ values expected from such a specification. Notably however, evidence from our panel models does suggest structural differences between petrol and diesel consumption.

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7.7 SUMMARY As seen in the previous section, the availability of a number of consistent estimators that deal with the endogeneity problem is certainly an advantage from an empirical perspective. The main benefit, among others, is that it provides a valid basis for comparison of the results obtained, while providing a higher degree of confidence that there is conformity in the estimates (as was seen here). Inadvertently, the abundance of choice in consistent estimators may also lead to an additional issue post-estimation: that of deciding which estimator to rely on.

In this study, we have applied 2 static and 7 dynamic estimators to a small sample (12 × 7) panel dataset. Out of the four dynamic IV/GMM estimators that deal with the endogeneity issue of the lagged consumption variable, two (the FD-2SLS and Sys- GMM) tend to yield unreliable estimates. In our sample, the Anderson–Hsiao approach appears to suffer from poor instrument performance and validity issues. On the other hand, the Blundell–Bond approximation procedure often indicates the tell-tale sign of the overfitting problem, i.e. a dynamic coefficient that is biased towards the OLS. In contrast, the IV2SLS FE and Diff-GMM perform relatively well, although the latter does appear to suffer from the weak instrument problem, particularly in the diesel dataset. Finally, results from the Kiviet’s approximation approach – which takes advantage of the efficiency of the LSDV – seem to affirm the good performance of the bias corrected procedure (LSDVc) with a small sample, as proposed by Judson and Owen (1999). In view of this, the results from the LSDVc estimator are preferable and thus selected for inference.

Overall, therefore, the results show a certain level of conformity to those obtained in the literature. Diesel consumption is characterised by relatively low habit persistence but a high (absolute) coefficient magnitude in the short-run. Petrol demand is the opposite; significant inertia is observed resulting in a long-run response of 3.1 times the short-run response.74 We observe for both the diesel and total fuel models that the price, vehicle ownership and technology share coefficients have the expected

74 Similar gasoline long-run responses of the order of magnitude of 3.3 times were also noted by Dahl and Sterner (1991).

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sign and are statistically significant, while fuel consumption appears to be independent of public transport cross-price effect. As for petrol, similar results were noted with the only exception to the norm being the finding that income appears to have no significant effect on demand. Evidence from our panel models therefore appears to have revealed some important characteristics with regards to the structural differences between petrol and diesel consumption.

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CHAPTER 8

CONCLUSION

8.1 INTRODUCTION The research undertaken in this thesis was motivated by the need to understand and evaluate the sensitivity of fuel demand in relation to its determinants, by taking into account recent changes to the structural and behavioural factors in the road transport sector. Unlike traditional studies, demand sensitivities are not assumed to be homogenous for each respective road transport fuel. A distinctive aspect of this research is the separate estimation of demand elasticities for petrol, diesel and total fuel, allowing for the investigation of response heterogeneity.

This chapter serves to summarize the main findings of the research and conclude the dissertation. It is structured as follows. Section 8.2 reviews the key findings from the literature reviews and the various empirical analyses. The contributions of the research are described in Section 8.3 while its policy implications are discussed in Section 8.4. Section 8.5 draws attention to the limitations of the study. Finally, in Section 8.6, avenues for potential future research are discussed.

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8.2 SUMMARY OF THE MAIN FINDINGS This research has sought to contribute to the essential issue of understanding fuel demand in the road transport sector. Apart from the estimation of demand elasticities, substantial attention was also placed on identifying the related theoretical foundations, methodological and econometric modelling issues involved. The above was achieved through a combination of an extensive review of the literature as well as empirical analyses, both of which are viewed as equally important. This section summarizes the findings, on a chapter by chapter basis, both from the literature review and empirical chapters in the thesis.

Chapter 2: Road Transport Fuel Demand: Trends and Statistical Background This chapter provided a contextual and statistical background with regards to the current consumption trends in the road transport sector. The findings are listed as follows:

1. There has been a substantial change in fuel demand trends that reflects a long-term shift towards diesel. Diesel fuel consumption (in weight terms) has now surpassed petrol as the primary road transport fuel. In 2009, it accounted for 55.8% of all petroleum based fuel consumed by the sector.

2. This dramatic shift in the fuel consumption trend is primarily driven by the dieselisation of the car fleet. While diesel has traditionally been associated with public service and freight vehicles, the composition of diesel users has since changed. As a proportion, the amount of diesel cars has risen significantly from only 42.9% in 1994 to approximately 64.4% in 2009, making cars the largest vehicle group in the diesel vehicle fleet.

3. There is some evidence to suggest that private diesel vehicle users may have different behaviour-utilisation considerations compared to the users of petrol powered vehicles. Statistics appear to indicate that private diesel vehicles are driven further than their petrol counterparts, and there is also evidence of

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users switching to bigger and more powerful diesel vehicles instead of matched pairs.

Chapter 3: Fuel Demand Elasticity Modelling: A Review of Econometrics and Methodological Issues The methodological and econometric approaches for road transport fuel demand modelling was reviewed in this chapter. The significant conclusions drawn are:

4. There are diverse approaches to modelling fuel demand and the specification chosen is often dependent on the context of the research. Despite that, the common denominator in these models is that proxies accounting for price and income variables are always included.

5. Researchers should be aware of the methodological problems and issues associated with the use of the different econometrics models. In time series models, there is concern with the issue of non-stationarity for the observed data. In the context of dynamic panel models, the main problem to be addressed is the endogeneity from the inclusion of the lagged dependent variable which causes biased and inconsistent parameter estimates.

Chapter 4: Road Transport Fuel Demand Elasticities: A Review of the Literature This chapter reviewed the empirical evidence in order to obtain a theoretical perspective on the modelling process described earlier. A statistical summary of the reported elasticities was also performed. The resulting conclusions are:

6. While there is a solid theoretical basis for the inclusion of price and income variables, care should be taken when introducing additional variables into the fuel demand model. When new variables are included, researchers should be mindful of the overall effect they may have on the model as well as of the need to think through the expected relationship, especially by considering the context of what is being measured.

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7. The review of the empirical studies suggests that the magnitude of the price and income elasticities is probably affected by other underlying factors in the study design.

Chapter 5: A Meta-Regression Analysis of Fuel Demand Modelling This chapter used meta-regression analysis to explore the variations seen in the price and income elasticity estimates reported in the surveyed studies. In addition to that, additional tests were also performed to assess whether empirical studies of fuel demand are affected by publication bias. The conclusions are:

8. The result from the meta-regression analyses indicate that price and income elasticity estimates are affected by some aspects of the study characteristics. In the analyses, it was found that regional and fuel type heterogeneities have a considerable influence on the resulting elasticities. This is plausible since structural and demographic factors are likely to influence the consumption behaviour of consumers, and therefore be picked up by the regional dummy variables. The results also provide evidence that differences in the response sensitivity may exist between the various fuel types. This may indicate that behavioural-utilisation considerations may indeed affect the choice of consumers’ fuel preference. Finally, the variation seen, to a lesser extent, can also be attributed to the model specification adopted by the study.

9. Empirical studies of fuel demand appear to be affected by selection bias. The tests indicate that there is a tendency towards reporting statistically significant results in the literature of road transport fuel demand. This preference for results that conform to the conventional view may seriously hinder the overall understanding of the area of road transport fuel demand.

Chapter 6: Estimation of Fuel Demand Elasticities Using Annual Time Series Data This is the first fuel demand modelling chapter. Separate estimation was conducted for the respective fuel types, and additional determinants of fuel demand were also included in the time series models. The conclusions drawn are listed as follows:

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10. The results appear to support the assumption that demand sensitivities are not likely to be homogenous. In the short-run, the price elasticity of diesel fuel (in the basic model) is considerably lower compared to petrol, although this is not as apparent when it comes to the extended model.

11. Similarly, differences in the magnitude of the elasticity estimates can also be observed when it comes to the income elasticity. There is some evidence to support the contention that behaviour-utilisation considerations are not similar between consumers of the various fuels, although this cannot be consistently determined since long-run estimation is not possible when cointegration is not detected in the models. In the short-run, diesel fuel consistently exhibits the lowest response sensitivity to income, although this result is inverted when it comes to the long-run response. In the basic model, the considerable long-run magnitude of the diesel elasticity is likely to be the result of the income parameter capturing the effect of the dieselisation of the car fleet.

12. The total fuel model appears to deliver, in general, the expected ‘average’ elasticity. However, the model also exhibits signs of inconsistency since parameter estimates can also be skewed towards a particular fuel or, in some instances, underestimates the elasticity altogether. This outcome reinforces the argument for not using total fuel estimates for inference and decision making purposes.

Chapter 7: Aggregate Panel Data Analysis of Fuel Demand Elasticities This empirical chapter continues the analysis of fuel demand by modelling the relationship through the use of panel data. This is the first time that aggregate fuel demand elasticity estimates have been produced using panel data. The fuel demand models also incorporate the technology share variable to capture the effect of fuel substitution via technological and vehicle fleet changes. The main findings in the modelling exercise are:

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13. The results appear to sustain the earlier observations that response sensitivity is likely to be heterogeneous. The price elasticity of diesel is consistently greater compared to petrol, with the magnitude of the difference being a factor of 2.4 times in the short run, although this is smaller for the long-run parameter estimates. The total fuel elasticity with respect to price appears to completely underestimate the sensitivity of response towards price changes.

14. There was an unexpected outcome when it comes to the income elasticity of petrol. The results found no significant income effect on petrol consumption, suggesting that an increase in income is not statistically likely to lead to an increase in petrol consumption. This appears to be consistent with the hypothesis of travel satiation as observed in most developing countries. In contrast, a significant income effect was found for diesel fuel consumption.

15. A similar outcome was also observed across the different models when it comes to the signs of the parameter for vehicle ownership and technology share variables. Both exogenous variables were found to have a statistically significant negative effect on fuel consumption. On the other hand, the models unanimously indicated that public transport fares do not influence the consumption of fuel by road vehicle users.

16. The evidence from the panel data model appears to show similar inconsistencies in the parameter estimates of the total fuel model. The results suggest that, when data is available, road transport fuel elasticity should be modelled separately for each fuel type instead of using an aggregated measure comprising all of the fuels.

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8.3 RESEARCH CONTRIBUTIONS The research undertaken in the thesis was aimed at improving the current understanding of the essential issue of road transport fuel demand. Among the contributions of the research are that it:

1. Performs an updated investigation of the underlying factors affecting fuel demand elasticities through meta-regression analysis of recent empirical fuel demand studies. One defining aspect of the analysis undertaken in this thesis is the inclusion of a range of road fuel types other than petrol in the meta-regression model. This inclusive analysis has not been undertaken by previous surveys and this is also the first time that the influence of fuel type heterogeneity on price and income elasticities has been statistically analysed.

2. Performs the first aggregate panel data estimation of fuel demand elasticity in a UK context. The research takes advantage of recently available statistics to construct a panel dataset in order to estimate fuel demand elasticity at the aggregate level. As far as we are aware, this is the first time such a dataset has been applied in this context. The main benefit of doing this is that the effects of unobserved regional heterogeneity can now be taken into account in the estimation model. Additionally, it allows for the elasticity estimates to be validly compared with those obtained from the aggregate time series model.

3. Provides new estimates of price and income elasticities of fuel demand for the road transport sector. Apart from making use of recent data, the separate estimation of fuel demand elasticities for the two primary road transport fuels is another important contribution. As well as allowing insights into possible response heterogeneity between the fuels, the elasticity estimated has a wide application for different policy analyses, e.g. as to whether to impose differentiated fuel taxes or on carbon taxation and emissions policy.

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4. Investigates other determinants of road transport fuel demand. Unlike traditional studies, this research has made use of recent data to explore whether fuel consumption is affected by other factors apart from price and income. Even when a statistically meaningful relationship cannot be established (e.g. in the case of bus and public transport fares), the research contributes by providing future researchers with guidance; if not by recommending other alternative avenues for similar investigation, at the very least, by indicating possible shortcomings of the approach undertaken that should be taken into account in future research.

5. Improves the understanding of the application of econometric techniques and methodological considerations in the modelling of fuel demand. While this research did not develop new estimation methodologies, the extensive review of the methodological issues and econometric estimators are important contributions. Additionally, a further contribution of this research is the application of the various econometric estimators in both the time series and panel data models. This enables the estimated elasticities to be compared and allows future researchers to identify shortcomings in the econometric estimators, and thus decide on the options that are more suitable.

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8.4 IMPLICATIONS OF THE RESEARCH In this section, we begin by presenting a summary of the preferred elasticities from the various estimation techniques and then followed by a comparison and discussion of the results obtained. Apart from obtaining elasticity estimates which are applicable for policy decisions, the empirical analysis undertaken also has implications from a methodological perspective. In light of this, we feel that it is appropriate that this issue is given further attention. Since the empirical evidence has significant policy implications, a subsection is therefore dedicated to providing additional discussion on this matter. The estimated elasticities are then used to generate forecasts for diesel and petrol road transport fuel demand. These are discussed below:

8.4.1 Summary of Estimation Results The preferred elasticity estimates from the various modelling methods are summarised in Table 8.1. At first glance, the results do not appear to be dissimilar from what is reported in the literature. Overall, we observe that most of the results are consistent with the a priori economic expectations. The magnitude of the short- run elasticities is smaller as compared to their long-run counterpart with the price elasticity values also being similarly smaller relative to the income elasticity.

The results of the estimated petrol price elasticity reveal relatively small differences in values. This is particularly so for the short-run estimates, with elasticity values in the range of –0.16 to –0.21. In the long run, the estimated price elasticity magnitude shows slightly higher variation with values between –0.43 to –0.63. For income elasticity, both the short- and long-run panel data estimates were excluded since the evidence indicates no statistically significant effect on petrol consumption. The short-run time series income parameter (0.80) is significantly larger when compared to the coefficient produced by the meta-regression model (0.34).

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Table 8.1 Comparison of estimated elasticities

Fuel Type Source Price Elasticity Income Elasticity Short-Run Long-Run Short-Run Long-Run Petrol Times series model –0.162 – –0.802 – Panel data model –0.206 –0.632 – – Meta-regression model –0.192 –0.428 –0.338 –0.550 Official values – – – –

Diesel Time series model –0.080 –0.253 –0.477 –1.499 Panel data model –0.502 –0.753 –0.460 –0.690 Meta-regression model –0.093 –0.619 –0.510 –1.606 Official values – – – –

Total fuel Time series model –0.105 –0.436 –0.749 –0.449 Panel data model –0.139 –0.241 –0.190 –0.330 Meta-regression model –0.139 –0.428 –0.452 –1.541 Official values –0.140 –0.600 – –0.400 Notes: 1) The basic time series model elasticities are used in order to ensure that long-run estimates can be included. 2) The parameter estimates from meta-regression Model 3 are reported. 3) The official values are reported as total fuel elasticities since no distinction in terms of fuel type was made in DECC (2013) and OBR (2010).

We now turn our attention to the results of the diesel demand models. Using the meta-regression model to predict the diesel elasticities for the UK, it can be seen that the short-run (long-run) price and income coefficients are –0.09 (–0.62) and 0.51 (1.61) respectively. With the exception of the long-run income parameter, we notice that the time series model yielded relatively similar results when compared to the meta-regression coefficients. In comparison, the panel data model appears to produce significantly higher (lower) values in the estimated price (income) parameters.

When it comes to total fuel demand, a high degree of consistency was observed for the estimated short-run price elasticities, with values in the range of –0.11 and – 0.14. Similarly, despite the larger variations, we derive confidence in the long-run income elasticity estimates as the results appear to be robust. In both cases, the magnitude of the price effect seems to be in line with the reported official values. However, this similarity does not extend to the income elasticity estimates. There seems to be a noticeable variance in the values estimated, especially when looking at the long-run income effect. In this case, the upper value is bounded by the meta-

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regression coefficient (1.54) while the lower value of the long-run income elasticity is represented by the panel data parameter (0.33). The evidence indicates that in the short-run (long-run), a 1% increase in income would result in an increase in total fuel consumption by between 0.19–0.75% (0.33–1.54%).

Looking at the elasticity estimates in Table 8.1, what is noticeable is that the panel data method tends to produce parameter values that are more elastic as compared to those produced by the time series analysis. These results are particularly apparent in the petrol and diesel demand models. While accepting that the sample sizes used in the analysis are small, the outcome seen is not without precedence, as estimates from panel studies have been observed to display such characteristics (see the discussion in §4.3.2).

Notwithstanding the above, it is probable that the variation seen can also be attributed to other factors related to the characteristics of the data used. A source of variation could be in the level of aggregation in the data used, which is different between the panel data model (region/NUTS 1 level) as compared to the time series analysis (national level). Another factor that is highly likely to influence the outcome seen would be the time frame of the datasets employed between the two studies. Since the dataset for the panel data analysis was made up of a shorter and more recent period of observations (2005–2011), it is probable that the results indicate some evidence of a structural shift in the nature of the UK’s fuel consumption sensitivities.

8.4.2 Methodological Implications In a time series model, the assumption of stationarity for the observed variables is likely to be untenable. As such, if the time span of the dataset is sufficiently large, then formal tests to detect non-stationarity should be performed. When performing the tests, researchers should be aware of the limitations inherent in the first generation diagnostic test designed to examine the presence of the unit root. Since detecting the presence of non-stationarity is essential to the overall modelling approach taken, it is essential that the unit-root test adopted is powerful

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and sufficiently robust for inference purposes. In addition to the above, the same consideration should also be applied to the cointegration test that is to be adopted.

Another implication in terms of the time series estimation methodology is on the suitability of the classic Engle–Granger static specification, especially for inference purposes. As has been noted by Hendry and Juselius (2000), the omission of dynamics from the estimation is likely to produce a downward bias in the standard error. This phenomenon was also observed in the empirical analysis in this research, even after the application of alternative estimators. Recent developments in econometric estimation methodologies, however, have found that the dynamic ARDL specification has a valid application in the cointegration framework. Since this approach overcomes the drawback of the Engle–Granger procedure and performs better in finite samples, it should perhaps once again be adopted as the preferred approach for time series estimation.

For the dynamic panel data model, the empirical analyses have affirmed the need for the use of consistent estimators to deal with the endogeneity problem. As has been demonstrated in the empirical analyses, the use of both the OLS and FE estimators produced biased and inconsistent parameter estimates. In the case of the former, the correlation between the lagged dependent variable and the error term results in an upward bias in the coefficients estimated, while the parameter estimates for the latter are biased downwards.

Although there are a number of consistent estimators available to deal with the endogeneity problem, it is important for researchers to be aware of their respective shortcomings, especially in the context of the data at hand. It was observed from the empirical analyses, that limitations in the terms of data (e.g. a small sample panel dataset and/or the unavailability of valid instruments) impose considerable constraints on the effectiveness of the consistent estimators. Often, when those conditions are not met, the performance of the consistent estimators appears to suffer and can produce estimates that are substantially biased and inefficient. Finally, the econometric analyses undertaken appear to indicate that it

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is good practice for researchers to apply multiple (consistent) estimators in panel data estimation, as seen being practiced in the empirical literature. Apart from deriving additional confidence in the results, the practice allows researchers to develop a better understanding of the intricacies of the panel estimators and helps them to recognise additional underlying issues through the comparison of the results.

8.4.3 Policy Implications Although the research is focused more on the estimation of elasticities and the related methodological issues, the results can also be used to draw some important conclusion with regards to policy decisions.

First, it confirms earlier findings that consumers are inelastic to changes in fuel price. In terms of curbing consumption, the results imply that taxation policy will probably have a less than proportional effect on fuel consumption. At current levels, fuel taxation is unlikely to inhibit further growth in consumption especially if taken together with the stronger positive influence of income. The result also brings to mind the question posed by Johnson et al. (2012) as to whether fuel taxation is actually driven by revenue raising purposes. They note that since response is inelastic to price changes; that may be a case for taxing fuel, especially if seen in the present context.

An extension to the point above is the higher effect that income has on fuel consumption. Since fuel taxation is unlikely to be raised to totally offset the consumption attributable to income growth, there is a need for other means of decoupling the relationship that income has with fuel consumption. Perhaps this is the reason why, in the empirical literature, the approach of imposing an absolute cap on fuel consumption and encourage the use of tradable quota (i.e. tradable fuel permits) has been viewed with wide appeal. Further discussion of this matter is beyond the scope of the current research, however, and is therefore not pursued further.

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Finally, the finding that response sensitivities vary according to fuel type also poses interesting questions. In particular, should there be a differential treatment when it comes to policy preferences and the taxation of differing fuels? Since the behaviour-utilisation considerations appear to be different (e.g. longer driving distance and preference for bigger vehicles by diesel users), perhaps it is fitting for this to be taken into account when designing policy solutions. Additionally, when considering that diesel fuel is more polluting on a volumetric basis, at the very least; options should be in place to push consumers to consider fuel efficiency over other considerations, when it comes to the purchase of diesel vehicles (Mayeres and Proost, 2013; Gallo, 2011).75 This appears to underpin the argument for the imposition of a tax on the carbon content of fuels (see Bureau, 2011).

8.4.4 Forecast of Road Transport Fuel Demand in the UK The estimation of the price and income elasticities of fuel demand, as discussed in §1.2, are important as they can serve as tools for energy policy and management by allowing the prediction of fuel consumption. Using the price and income elasticity parameters from the various modelling methods reported in the previous section, a 10-year forecast of future fuel consumption for the period 2012–2020 is constructed.

In order to conduct the forecast, several assumptions were made. Firstly, since the fuel consumption literature suggest that the short term and long term response process are likely to differ, both short-run and long-run elasticities were incorporated in generating the forecast. In doing so, we adhere to the convention of Goodwin et al. (2004), with the short-run elasticity applied only to the first period of the data while using the long-run elasticity for the remaining periods.

Additionally, the future road transport fuel consumption is forecast under the assumption that the variables fuel price, real income per capita, population and stocks of petrol and diesel vehicles are highly unlikely to stay constant. With the

75 The CO2 intensity per litre of diesel fuel is 15% greater than that of petrol fuel (see DECC, 2010).

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exception of the vehicle stock variable, the annual adjustment factors and growth rates for the stated variables were obtained from the Department for Transport’s (DfT) Transport Analysis Guidance (WebTAG) data book. Finally, we assumed that the future growth for both petrol and diesel vehicle stocks would be similar to their respective compounded annual growth rate (CAGR) observed between the years 2005 and 2011. The adjustment factors and growth rates values are presented in Appendix C.

The forecast results are depicted in Figures 8.1 and 8.2. To ensure that the output from each modelling methods can be compared as objectively as possible, we have also included the actual petrol and diesel consumption for the years 2012 to 2014. These real consumption data were unavailable when the fuel demand models were estimated. As stated, the forecast output from the different econometrics model used only the estimated price and income elasticities to predict the future petrol and diesel fuel demand. However, to make matters more interesting, the forecast output of the full panel model (which made use of the additional fuel demand elasticities parameters estimated) are also included for comparison purposes. The forecast results are summarized in Table 8.2 below:

Table 8.2 Forecasts of road transport fuel consumption (Million tonnes of fuel)

Fuel Type Source 2014 2021 Forecasts Deviation (%) Forecasts Share (%) Petrol Times series model 14.59 +18.40 15.34 38.62 Meta-regression model 14.29 +15.91 12.48 38.67 Official values 14.12 +14.51 10.93 34.29 Basic panel model 13.11 +6.37 8.32 26.11 Full panel model 12.53 +1.67 6.88 26.04 Actual consumption 12.33 – – –

Diesel Times series model 22.48 –0.85 24.38 61.38 Meta-regression model 22.27 –1.77 19.80 61.33 Official values 21.63 –4.61 20.95 65.71 Basic panel model 24.24 +6.90 23.55 73.89 Full panel model 23.09 +1.83 19.54 73.96 Actual consumption 22.68 – – – Notes: 1) Deviation is the difference between the actual consumption value and the forecast value. 2) The share statistics is derived based on the assumption that road transport fuel is made up only of petrol and diesel.

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Figure 8.1 illustrates the evolution of road transport petrol consumption in the UK between 2005 and 2021. The examination of the results produces some interesting conclusions. The forecast results appear to reinforce the expectation that the decline seen in the consumption of petrol is unlikely to be reversed, with only the time series results indicating otherwise.

21 Time Series Meta-regression Official Values Basic Panel 18 Full Panel Actual Consumption

Million Million Tonnes 12

6 2005 2007 2009 2011 2013 2015 2017 2019 2021

Figure 8.1 Road transport petrol consumption forecasts for the UK

In terms of forecast performance, the panel models appear to perform exceptionally well, with the deviation in percentages from the actual consumption seen between 2012 and 2014 varying between 1.66% to 4.82% for the full panel model, and 3.94–7.67% for the basic panel model. In comparison, the forecast derived from the time series and meta-regression models produced larger deviations of 18.40% and 15.91% respectively from the observed 2014 petrol demand. On the other hand, using the official elasticity values, the forecast consumption would initially deviate by 6.04% in 2012 and progressively gets higher to 14.51% for the year 2014.

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As stated, if we are to assume that the panel models would provide the best forecast, and that the assumptions made on the growth rates and the adjustment factors remain true, then petrol consumption in 2021 would be significantly lower than the level seen at the moment. Petrol usage based on the full panel model will be 6.88 million tonnes, signifying a decrease of 50.50% from the level observed in 2011. Using the basic panel model, a similar outcome is predicted with consumption falling by 40.11% to 8.32 million tonnes.

Million Million Tonnes 20

Time Series 17 Meta-regression Official Values Basic Panel Full Panel Actual Consumption 14 2005 2007 2009 2011 2013 2015 2017 2019 2021

Figure 8.2 Road transport diesel consumption forecasts for the UK

The assessment of the various models’ forecasting effectiveness indicates that the diesel forecast results are remarkably accurate as compared to the outcome seen for their petrol counterpart. Overall, the deviation values from the observed consumption in 2012 to 2014 ranges from –4.61% to 6.90% only. When compared with the data from the actual consumption period, the time series and meta- regression model performed extremely well with forecast deviation varying between –0.66% to –1.60% and –0.68% to –1.77% respectively. In contrast, the

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residual values derived are slightly larger ranging from 2.76–6.90% for the basic panel model while for the full panel model as being between 1.49% and 3.09%.

There appears to be strong conformity in the diesel forecast results with the consumption uptrend unlikely to sustain further in the near future. Based on the basic panel model forecast, diesel demand will peak in 2015 at 24.50 million tonnes before gradually declining to 23.55 million tonnes in 2021. On the other hand, peak diesel consumption according to the forecast results from the meta-regression, official values and the full panel models appear to have already occurred in 2014. Consumption level in 2021 is predicted to be between 19.54-20.95 million tonnes. In contrast, the uptrend in diesel consumption is forecasted to continue by the time series model with demand reaching a high of 24.38 million tonnes at the end of the forecast period.

As can be seen from Figure 8.2, diesel consumption, with the exception of the time series model, is unlikely to continue its upward trend beyond the year 2015. While as a proportion it consolidates its position as the de facto road transportation fuel, the declining consumption as forecasted is unexpected. While it is likely that the structural shift towards diesel powered vehicles taking place in the UK will continue, it appears that the defining factor would be the greater impact of increased price sensitivity in the long run as estimated by the various models. Taken together with the possibility that diesel users would also eventually reach travel saturation as discussed in §7.6, the outcome seen cannot be entirely discounted.

To conclude, evaluating the forecast performance using the hold out sample reveals that the panel data models; if not the best, at the very least, are the most likely to produce more accurate forecasts. The modelling results indicate that the forecasting ability of even the basic panel model has produced better and more consistent forecasting results than the alternative estimation methodologies. However, it is difficult to come to a strong conclusion as to whether this reflects the superiority of the more econometrically sophisticated methods of the panel data

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model, considering the short period of the hold out sample. One plausible explanation is that this could be due to the differences in the specification between the estimation models, with the estimates from the time series model hampered by the omission of other exogenous variables that explain fuel consumption.

Finally, it is important to treat the forecast results with caution. The relatively accurate forecast performance notwithstanding, it would be unwise to predicate that road transport fuel consumption in general will decline. The scenario derived can largely be attributed to the rather anaemic income growth assumption coupled with a relatively stronger growth in annual fuel price as provided by the DfT’s WebTAG data book.76 Since all of the models point to a higher income effect on fuel consumption, it is likely that the outcome will be very much different in the context of medium and strong economic growth.

76 For the forecast period, income per capita and fuel price are assumed to grow annually at an average of 1.61% and 6.02% respectively. In contrast, the pre-crisis (1993–2007) average income per capita growth per annum was 2.54%.

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8.5 LIMITATIONS OF STUDY As with any other econometric studies, the research undertaken here was also constrained by various limitations that were not avoidable during the period of the thesis. Specifically, the main constraint encountered was primarily in the context of the availability and quality of data for the analysis. As the research progressed, further constraints were also encountered due to the inability to obtain the appropriate software to perform the required statistical tests and analysis. Additionally, there was also an interdependence with the constraints imposed by the timeframe of the PhD, which limited the ability to resolve the earlier issues. Finally, in terms of the findings, the following caveats should be taken into account when considering the results:

1. Comparability of the time series and panel data elasticities Although aggregate data were used in both estimation models, there is still the issue of whether the results are directly comparable. The main concern is the lack of homogeneity of the timeframe between the two datasets, which may result in each model reflecting distinct structural and behavioural factors. For example, the fairly short and recent timeframe used in the panel data model is likely to capture the growing influence of private vehicle consumption, especially in the context of diesel. On the other hand, the time series model, due to the timeframe involved, would probably reflect a consumption pattern which is largely attributable to public service and freight vehicles. Therefore, some difficulty may arise in reconciling the results observed.

2. On the representativeness of the elasticities The main aim of the empirical model is to estimate separate demand elasticities for road transport diesel and petrol fuel. As such it is important, to take the estimates as just that, as the average elasticity representing total consumption for a particular fuel. This distinction is important, as has been elaborated before, because the use of an aggregated measure would produce an ‘average’ elasticity and, as such it is unwise to associate the fuel demand sensitivities to a particular user group (see Basso and Oum, 2007; Dargay,

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1993; Schipper et al., 1993). While this is not a major problem for petrol fuel (which is primarily consumed by private vehicles), the same cannot be said about the elasticity of the diesel fuel demand.

3. Assumption of stationarity for the panel model estimate There was an assumption of stationarity for the panel data model. Due to the short length of time that the panel data covers (T = 7), conducting formal stationarity and cointegration tests were neither computationally feasible nor sufficiently powerful.

4. Symmetrical demand response assumption The fuel demand analysis is based on the assumption that the demand response observed is symmetrical, i.e. the effect observed from a rise in a particular determinant of fuel demand will be opposite but equal when a reduction occurs. Although this is the assumption usually adopted in traditional demand modelling literature, Goodwin et al. (2004) point out that there is evidence that this might not be true. For example, as income grows, consumers are likely to purchase vehicles but when the situation is reversed, it is less probable for the extent of the response to be equal. Due to inertia and habit persistence, the response would likely be to curtail travel instead of disposing of the vehicle owned.

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8.6 DIRECTIONS FOR FUTURE RESEARCH Although the research undertaken in this thesis was intended to fill the gaps existing in the literature, it is clear that there exist many issues in the field of road transport fuel demand that can be further explored and analysed. In setting the direction for potential future research, the limitations described in §8.5 can be used as a guide. Among the potential areas for future research are:

1. Analysing response sensitivity by different user groups within a fuel type It can be difficult to assess whether the demand elasticity estimated is actually meaningful in measuring the response of a particular user group within a particular fuel type. As Basso and Oum (2007) pointed out, it is difficult to draw meaningful inferences from the results if it is unclear what is being measured. This is particularly so for fuel such as diesel where the underlying purpose for travel can be significantly different between the various user groups. A potential avenue of research includes breaking down fuel demand response further by vehicle type. This will be particularly useful in developing targeted policy measures to curb fuel consumption.

2. Investigation of other determinants of fuel demand While the relationship of fuel demand with price and income has been extensively studied, its relationship with other determinants is less well understood. Dahl (2012) in particular encouraged future research work to focus on issues such as technical changes and fuel substitution. Another important aspect is to decompose income elasticity further by including exogenous variables whose effect might be captured by the elasticity, as Blum et al. (1988) had done previously.

3. Further research on the asymmetry of response sensitivities As stated earlier, the assumption of a symmetrical response is quite restrictive. Since it is probable that the adjustment process to changes in the external factors (i.e. price and income) are likely to be asymmetric, it would be truly

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useful for future research work to focus on this particular issue so that the phenomena can be properly understood.

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28. Liddle, B., The systemic, long-run relation among gasoline demand, gasoline price, income, and vehicle ownership in OECD countries: Evidence from panel cointegration and causality modeling. Transportation Research Part D: Transport and Environment, 2012. 17(4): p. 327- 331. 29. Lim, K.-M., et al., Short-run and long-run elasticities of diesel demand in Korea. Energies, 2012. 5(12): p. 5055-5064. 30. Lin, C.Y.C. and L. Prince, The optimal gas tax for California. Energy Policy, 2009. 37(12): p. 5173-5183. 31. Lin, C.Y.C. and J. Zeng The Elasticity of Demand for Gasoline in China. Institute of Transportation Studies, University of California Davis Research Report UCD-ITS-RR-12-15, 2012. 32. Pock, M., Gasoline demand in Europe: New insights. Energy Economics, 2010. 32(1): p. 54- 62. 33. Polemis, M.L., Empirical assessment of the determinants of road energy demand in Greece. Energy Economics, 2006. 28(3): p. 385-403. 34. Ramanathan, R., Short- and long-run elasticities of gasoline demand in India: An empirical analysis using cointegration techniques. Energy Economics, 1999. 21(4): p. 321-330. 35. Ramanathan, R. and G. Subramaniam, Elasticities of gasoline demand in the Sultanate of Oman. Pacific and Asian Journal of Energy, 2003. 13(2): p. 105-113. 36. Samimi, R., Road transport energy demand in Australia: A cointegration approach. Energy Economics, 1995. 17(4): p. 329-339. 37. Santos, G.F., Fuel demand in Brazil in a dynamic panel data approach. Energy Economics, 2013. 36(0): p. 229-240. 38. Sene, S.O., Estimating the demand for gasoline in developing countries: Senegal. Energy Economics, 2012. 34(1): p. 189-194. 39. Wadud, Z., D.J. Graham, and R.B. Noland, A cointegration analysis of gasoline demand in the United States. Applied Economics, 2009. 41(26): p. 3327-3336.

224

APPENDIX B

Table B1 Correlation between the variables in the panel data fuel demand model

푙푛퐹퐷 푙푛퐹푃 푙푛퐹푇 푙푛푃퐷 푙푛푃푃 푙푛푃푇 푙푛푌 푙푛푃푇 푙푛푉퐷 푙푛푉푃 푙푛푉푇 푙푛푇푆

푙푛퐹퐷 –1.0000

푙푛퐹푃 –0.0426 –1.0000

푙푛퐹푇 –0.3482 –0.8649 –1.0000

푙푛푃퐷 –0.4530 –0.3485 –0.3317 –1.0000

푙푛푃푃 –0.5086 –0.3756 –0.3764 –0.9669 –1.0000

푙푛푃푇 –0.4812 –0.3573 –0.3456 –0.9938 –0.9890 –1.0000 푙푛푌 –0.2292 –0.6062 –0.5842 –0.0235 –0.0092 –0.0241 –1.0000 푙푛푃푇 –0.5132 –0.5945 –0.2290 –0.0212 –0.0162 –0.0162 –0.2214 –1.0000

푙푛푉퐷 –0.5042 –0.6095 –0.5097 –0.2669 –0.2792 –0.2832 –0.5759 –0.4118 –1.0000

푙푛푉푃 –0.4790 –0.0263 –0.2420 –0.2648 –0.2889 –0.2788 –0.1683 –0.5264 –0.1051 –1.0000

푙푛푉푇 –0.0949 –0.4889 –0.5122 –0.0171 –0.0120 –0.0203 –0.2773 –0.0564 –0.7967 –0.6727 –1.0000 푙푛푇푆 –0.6699 –0.5611 –0.3941 –0.3663 –0.3865 –0.3873 –0.6468 –0.5761 –0.9057 –0.3187 –0.4664 –1.0000

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APPENDIX C

Table C1 Forecast assumptions: Annual adjustment factors

Income Per Diesel Vehicle Petrol Vehicle Total Vehicle Year Fuel Price Population Capita Stock Stock Stock

2011 1.000 1.000 1.000 1.000 1.000 1.000 2012 0.993 1.005 1.007 1.049 0.988 1.007 2013 1.006 1.015 1.006 1.049 0.988 1.007 2014 1.032 1.022 1.008 1.049 0.988 1.007 2015 1.062 1.017 1.007 1.049 0.988 1.007 2016 1.077 1.017 1.007 1.049 0.988 1.007 2017 1.081 1.018 1.007 1.049 0.988 1.007 2018 1.086 1.017 1.007 1.049 0.988 1.007 2019 1.089 1.016 1.006 1.049 0.988 1.007 2020 1.089 1.017 1.006 1.049 0.988 1.007 2021 1.088 1.018 1.006 1.049 0.988 1.007

226

PUBLICATIONS

Ramli, A. R. & Graham, D. J. (2014). The demand for road transport diesel fuel in the UK: Empirical evidence from static and dynamic cointegration techniques. Transportation Research Part D: Transport and Environment, 26, 60-66.

Ramli, A. R. & Graham, D. J. (2013). Road transport fuel consumption trends in the United Kingdom: Empirical analysis of diesel demand. Proceedings of the 93rd Annual Meeting of the Transportation Research Board, 13-17 January 2013, Washington DC.