Exhaustible Resources and the Hotelling Rule: an Empirical Test of the Hotelling Rule's Significance to Gold Production in South Africa

Exhaustible Resources and the Hotelling Rule: An Empirical Test of the Hotelling Rule's Significance to Gold Production in South Africa

COURAGE MLAMBO

200706118

PhD in Commerce Economics

in the

Faculty of Management and Commerce

University of Fort Hare

Supervisor: Prof R. Nwcadi

Co-supervisor: Prof A Tsegaye

Declaration

By submitting this research report electronically, I Courage Mlambo, declare that the entirety of the work contained therein is my own, original work, that I am the owner of the copyright thereof (unless to the extent explicitly otherwise stated) and that I have not previously in its entirety or in part submitted it for obtaining any qualification.

Courage Mlambo January 2017

DECLARATION ON PLAGIARISM

I, Courage Mlambo, student number 200706118, hereby declare that I am fully aware of the University of Fort Hare’s policy on plagiarism and I have taken every precaution to comply with the regulations.

Signature: ...... …

DECLARATION ON RESEARCH ETHICS

I, Courage Mlambo, student number, 200706118, hereby declare that I am fully aware of the University of Fort Hare’s policy on research ethics and I have taken every precaution to comply with the regulations. I have obtained an ethical clearance certificate from the University of Fort Hare’s Research Ethics Committee.

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Acknowledgements

First and foremost, my everlasting thanks to the Lord God Almighty for His steadfast and continual provision of wisdom and love which sustained me hitherto. If it was not for your love, grace, guidance, peace and protection that saw me through, I would not have reached this end.

My deepest thanks to my supervisor, Prof R Nwcadi, for his encouragement and assistance; your availability for consultation and direction made the difference in my study. May the Lord bless you abundantly. I would, also, like to thank Prof. A Tsagaye for his encouragement and support.

To my family; Tete Kudzi, Shillo, Karel and Celine thank you for being wonderful “friends”, your presence in my life contributed significantly to this piece of work, thank you very much. Lastly, I would like to thank the Department of Economics for its support and motivation.

Dedication

To my kids, Karel and Celine, I gratefully and emotionally dedicate this PhD project to you.

Thank you for being a gift and blessing from God.

Abstract

The study sought to test the applicability of the Hotelling rule in South Africa. In environmental economics, the Hotelling rule has come to be a pillar of the exhaustible resources framework and in addition to this, it has presented essential insights into the consumption and extraction of non-renewable resources. Hotelling sought to address one important question which had been unanswered regarding the depletion of exhaustible resources: How much of the natural resource in question should be consumed presently and how much of it should be stocked up for future generations? The focus was to find a solution for those involved in the exploitation of natural resources to choose between the current value of the natural resource if extracted and sold and the future increased value of the asset if left unexploited.

According to the Hotelling rule, the extraction path in competitive market economies will, under certain circumstances, be socially optimal. An extraction path that is not socially optimal compromises the welfare of future generations. The welfare of South Africa’s present population and more especially in the future will be greatly determined by the stock of natural resources available and the quality of the environment. Currently, the production processes deplete natural resources. Concern with the supposed increasing scarcity of gold in South Africa, and the possibility of running out of gold, has become a source of concern. South Africa’s gold reserves (gold in the ground that can be extracted profitably) are becoming depleted at an alarming rate. Most reserves are already exhausted; and the costs involved in mining lower-grade ore, and deposits located very deep in the ground, are becoming excessive. In light of this, this study sought to test the applicability of the Hotelling rule in South Africa.

In order to empirically test the Hotelling rule, the study was guided by previous literature that had sought to test it. In this regard, the study used both descriptive and inferential statistics. The study has three data analysis chapters. The first two presented and examined the time series properties of gold prices, gold production and gold consumption. The third data analysis chapter examined the relationship between gold price and interest rates. In the first two data analysis chapters, visual inspection, growth rates, variance ratio tests and advanced unit root tests were used to examine the time series properties of gold prices, gold production and gold consumption. Results showed that the behaviour of the gold price series and gold production series in South Africa have a behaviour that is socially optimal. This is

vi in line with the Hotelling rule. The rule predicts exponentially increasing resource prices and this result in mineral resources following the path of the positive trend. The positive trend is prompted by the increasing price reflecting the increasing scarcity of the resource. However, consumption trends were seen to be violating the Hotelling rule. The Hotelling rule predicts that the price increases until it eventually reaches the choke price, where the quantity demanded decreases to zero. However, in contrast to this, results showed that the demand for gold has been increasing instead of decreasing. This is not in line with the Hotelling rule. Furthermore the relationship between interest rate and gold price was negative and this suggested that the price of gold was not rising at the rate of the interest rate.

The results of the study suggested that gold production is not following a social optimally path. The study recommended that the government come up with measures that prolong the lifespan of the gold reserves. These included research and development to promote technological innovations in the mining sector. This may make it possible for firms to access lower-grade ores. The study also recommended that since the Hotelling rule partly applied in the gold sector, there is a need to adopt some other theoretical measures that can ensure that the proceeds from the gold taxes are used in the most effective way.

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Table of contents

Declaration ii

Acknowledgements iii

Dedication iv

Abstract v

List of tables xii

List of figures xiii

List of acronyms and abbreviations xiv

CHAPTER 1 INTRODUCTION 1

1.1. Introduction 1 1.2. Objectives of the study 4 1.3. Hypothesis of the study 4 1.4. Problem statement 4 1.5. Justification for the study 6 1.6. Outline of the chapters 7 1.7. Conclusion 7

CHAPTER 2 THE TRENDS OF GOLD PRODUCTION, DEPLETION AND GOLD PRICES IN SOUTH AFRICA 8

2.1. Introduction 8 2.2. An overview of mining and the gold sector in South Africa 8 2.3. Gold Production trends in South Africa 15 2.4. Market share in the global gold production: global share rankings 19 2.5. Gold depletion 22 2.6. Legal framework regulating the South African mining and gold sector 24

The South African mining laws 24

2.7. Gold price trends 26 2.8. Summary of the chapter 28 2.9. Conclusion 29

CHAPTER 3 LITERATURE REVIEW 30

viii

3.1. Introduction 30 3.2. Theoretical literature 30

Weak sustainability theories 31

3.2.1.1. Hotelling rule 31 3.2.1.2. Hartwick rule 42 3.2.1.3. Herfindahl rule 45 3.2.1.4. Applicability of the weak sustainability theories: From a South African perspective 46

Strong sustainability theories 46

3.2.2.1. Marxism 46 3.2.2.2. Non-declining natural capital stock approach 49 3.2.2.3. Applicability of the strong sustainability approach in South Africa 49

3.3. Empirical Literature 50

Findings from studies 50 Determinants of gold price 53

3.4. Overall assessment of literature 55 3.5. Conclusion 57

CHAPTER 4 METHODOLOGY 58

4.1. Introduction 58 4.2. Rationale for the methodology 58 4.3. Econometric techniques 59 4.4. Descriptive statistics 60

Visual inspection 61 The Hodrick-Prescott (HP) 62 Growth rate 63

4.5. Econometric estimations: Structural equations and hypothesis testing 64

Hypothesis testing 64 Stationarity 64

4.5.2.1. Variance ratio test 65 4.5.2.2. The ADF Test 66 4.5.2.3. Phillips-Peron test 67

4.5.2.4. DF-GLS test 67 4.5.2.5. KPSS test 68

Structural equation modelling 68

4.5.3.1. Model specification 68 4.5.3.2. Definition and justification of the variables 69 4.5.3.3. Expected priori 70 4.5.3.4. Data sources and analysis 71 4.5.3.5. Testing for stationarity/Unit root 71 4.5.3.6. Estimation Techniques 71 4.5.3.7. Diagnostic tests 73

4.6. Summary of the chapter 75 4.7. Conclusion 76

CHAPTER 5 DISCUSSION OF THE TRENDS, MEAN AND VARIANCE PROPERTIES OF SOUTH AFRICAN GOLD PRICES 77

5.1. Introduction 77 5.2. Presentation of results 77

Visual Tests for Stationarity 78 Correlogram 82 Formal unit root tests 84

5.2.3.1. Augmented Dickey-Fuller Test 84 5.2.3.2. Phillips-Perron 85 5.2.3.3. KPSS 86 5.2.3.4. DF-GLS test 88 5.2.3.5. Variance ratio test (Testing for mean reversion/aversion) 89 5.2.3.6. Break point unit root 92

5.3. Discussion of results 94 5.4. Conclusion 97

CHAPTER 6 DISCUSSION OF THE TREND PROPERTIES OF GOLD PRODUCTION AND CONSUMPTION 98

6.1. Introduction 98 6.2. Presentation of results 98

6.3. Graphical analysis 100

Formal unit root tests 103

6.3.1.1. Augmented Dickey-Fuller 103 6.3.1.2. Phillips-Perron Test 104 6.3.1.3. KPSS Test 106 6.3.1.4. DF-GLS test 106 6.3.1.5. Break point unit root 107

6.4. Consumption of gold 110 6.5. Discussion of results 113 6.6. Conclusion 116

CHAPTER 7 PRESENTATION AND ANALYSIS OF EMPIRICAL FINDINGS 117

7.1. Introduction 117 7.2. Unit root tests 117

Informal unit root tests 117

7.3. Cointegration Tests 120

Cointegration test results 120

7.4. Vector Error Correction Model – Short-run relationships 123 7.5. Diagnostic checks for the VECMs 125

Autocorrelation LM test 126 White heteroskedasticity test Error! Bookmark not defined. Jarque-Bera Normality test 127

7.6. Conclusion 128

CHAPTER 8 SUMMARY, IMPLICATIONS AND RECOMMENDATIONS 129

8.1. Introduction 129 8.2. Brief overview of the research study 129 8.3. Reaching the objectives 130

Analyse the trend of gold production, extraction and gold prices 130 To determine an optimal extraction path based on theoretical considerations 131 To test the relevance of the Hotelling rule in South Africa 132

8.4. Implications of the results 133

8.5. Contributions 134

Contributions to literature 134 Contribution to practice 134

8.6. Recommendations 135 8.7. Limitations of the study 136 8.8. Conclusion 137

xii

List of tables

Table 2.1: Seasonally adjusted index of the volume of mining production for 2016 by mineral group and mineral (Base: 2010=100) 14

Table 2.2: Gold production contribution to the economy 17

Table 2.1: Top 10 global gold-producing countries in 2004 20

Table 2.2: Top 10 global gold-producing countries in 2014 20

Table 5.1: Correlogram test 83

Table 5.2: Augmented Dickey-Fuller Test 85

Table 5.3: Phillips-Perron test 86

Table 5.4: KPSS Test 88

Table 5.5: DF-GLS unit root tests 89

Table 5.6: Variance ratio test 90

Table 5.7: Variance test with a null hypothesis of a random walk 91

Table 5.8: Break point unit root 93

Table 6.1: Correlogram test 102

Table 6.2: Augmented Dickey-Fuller test 104

Table 6.3: Phillips-Perron test with constant and trend 105

Table 6.4: KPSS test with constant linear trend 106

Table 6.5: DF-GLS test on GLS detrended residuals 107

Table 6.6: Break point unit root 108

Table 7.1: Lag selection 121

Table 7.2: Cointegration 122

Table 7.3: Vector Error Correction Model – Short-run relationships 124

Table 7.4: Langrange Multiplier test results 126

Table 7.5: Heteroskedasticity test Error! Bookmark not defined.

Table 7.6: Residual normality test 127

xiii

List of figures

Figure 2.1: The mining sector’s other ways of contributing to the South African economy 10

Figure 2.2: Total mining production 11

Figure 2.3: Total production (excluding gold) and gold production 13

Figure 2.3: Gold production trends 18

Figure 2.4: Years to depletion 22

Figure 2.5: Rand-denominated gold price 27

Figure 4.1: Regression with time series data: non-stationary variables 73

Figure 5.1: The Gold price series (a) and (b) 79

Figure 5.2: Graphical results from the Hodrick-Prescott filter 81

Figure 6.1: Gold production trends (a) and (b) 100

Figure 6.2: Hodrick-Prescott filter 101

Figure 6.3: Growth rate in gold production 109

Figure 6.4: Domestic gold consumption 111

Figure 6.5: Domestic gold sales 112

Figure 7.1: Graphical analysis at levels 118

Figure 7.2: Graphical analysis at first difference 119

Figure 7.3: AR Roots graph 126

xiv

List of acronyms and abbreviations

IFRS International Financial Reporting Standards

KPSS test Kwiatkowski-Phillips-Schmidt-Shin test

MC marginal cost mt millimetric ton (kg). 1 kilogram is equal to 1 millimetric ton.

MPRDA Mineral and Petroleum Resources Development Act of 2002

PGMs Platinum group metals ppm parts per million t metric ton. 1 metric ton = 1 000 kilograms

CHAPTER 1 INTRODUCTION

1.1. INTRODUCTION

Economists have long been concerned with the extraction and efficient use of non- renewable resources (Shogren, 2000 & Rodrigo, 2014). The fact that non-renewable resources decrease as they are used has made economists worry that at some point the world will run out of these resources. Non-renewable resources include fossil-fuel energy supplies such as oil, gas and coal; gold; diamonds; and minerals like copper and nickel. The crude forms of these resources are produced over very long periods of time by chemical, biological or physical processes. Their rate of formation is sufficiently slow in timescales relevant to humans that it is sensible to label such resources non-renewable or depletable resources.

Sweeney (1992) suggests that a resource is depletable if 1) its stock decreases over time whenever the resource is being used; 2) the stock never increases over time; 3) the rate of stock decrease is a monotonically increasing function of the rate of resource use; and 4) no use is possible without a positive stock. At any point in time, there exist some fixed, finite quantities of natural resources in the earth’s crust. However, it is appropriate to describe non-renewable resources or depletable resources as existing in fixed quantities and once extracted, they cannot be renewed. One question is of central importance: What is the optimal extraction path over time for any particular non-renewable resource stock? The Hotelling rule is a necessary efficiency condition that must be satisfied by any optimal extraction programme.

The Hotelling rule states that the market price for an exhaustible natural resource should rise at a rate equal to the interest rate in a market equilibrium (Hotelling, 1931). In environmental economics, the Hotelling rule has come to be a pillar of the exhaustible resources framework (Gaitan, 2004 & Rodrigo, 2014) and in addition to this, it has presented essential insights into the consumption and extraction of non-renewable resources. Heal (2007) and Minnitt (2007) concur and assert that the founder of analytical environmental and resource economics was Harold Hotelling, with his fundamental work on the economics of exhaustible resources. Harold Hotelling’s theory postulated that the most socially and economically profitable extraction track of a non-renewable resource was one in which the price of the resource, determined by the marginal net revenue from the sale of the resource, 2 increased at the rate of interest (Harold 1931). The theory proposed the time tracking of natural resource extraction that most increases the value of the resource reserve.

Hotelling sought to address one important question which had been unanswered regarding the depletion of exhaustible resources: How much of the natural resource in question should be consumed presently and how much of it should be stocked up for future generations? The aim of this was to find a solution for those involved in the exploitation of natural resources to choose between the current value of the natural resource if extracted and sold and the future increased value of the asset if left unexploited. This simple rule can be expressed by the equilibrium situation representing the optimal solution. The basic Hotelling model of non-renewable resource extraction predicts that the shadow price of the resource stock, which is an economic measure of the scarcity of the resource, should grow at the rate of interest (Hotelling, 1931).

In the Hotelling model, there is perfect information about the backstop price, the quantity of the resource, the demand for the resource, and the cost of extracting the resource (Reynolds, 1995). According to Hotelling (1931) there are three things, we can say about resource extraction for a finite resource:

1. Firms will always try to extract low-cost resources before high-cost resources, causing resource extraction costs to increase over time. 2. In general, greater scarcity caused of in-situ reserves increases the value of a resource, causing the price to increase over time. 3. Since the price of a resource increases over time, then demand and production should decrease over time.

The Hotelling rule states that the price of a non-renewable resource in a competitive market would rise at the interest rate and that the production trajectory would be monotonically declining till the resource is exhausted (Khanna, 2003). Its central result is that the extraction rate of an exhaustible resource is monotonously sinking, while its price is increasing. An implication of the continuously rising price is that the quantity extracted would be continuously falling until such time as the resource is exhausted. As the price rises the demand for the resource is slowly choked off. Eventually the price would be so high that demand would be eliminated altogether. In the basic model, this is precisely when the resource stock would also be completely exhausted. To understand why, suppose that when the price is sufficiently high to entirely choke off all the demand, resource owners are left

3 with some positive quantity of the resource. This remaining stock would be completely worthless to the owner since no one would want to buy it. Realising this, the resource owners would begin to sell off the stock at lower prices before the demand is choked off by the high prices. However, this would mean that there would be an excess supply of the resource in the market which would lower current prices. The production trajectory would be extended in time and again the price would continue to rise at r percent per year until all the stock is completely depleted.

The basic message of the Hotelling rule is that the profitable extraction path, both socially and economically, is one in which the price of the non-renewable resource increases at the same rate as the interest rate (Wagner, 2006). In other words, the Hotelling rule illustrates the time path of non-renewable resources’ extraction which maximizes the value of the natural resource stock. The Hotelling rule is a necessary efficiency condition that must be satisfied by any optimal extraction programme. The extraction path in competitive market economies will, under certain circumstances, be socially optimal. An extraction path that is not socially optimal compromises the welfare of future generations. The welfare of South Africa’s present population and more especially that of future generations will be greatly determined by the stock of natural resources available. Concern with the supposed increasing scarcity of gold in South Africa, and the possibility of running out of gold, has become a source of concern. South Africa’s gold reserves (gold in the ground that can be extracted profitably) are becoming depleted at an alarming rate (Mining Review, 2011).

The declining importance of the gold sector is also shown by gold production data. Historical values of the gold index show the extent to which production has fallen. Gold production has continued to decline over the last ten years. It declined from 522,4 metric tons in 1995 to 342,7 metric tons in 2004, "the lowest level of production since 1931" (Mantashe, 2008). In January 1980, the index was 359,0, while the volume of gold produced was far lower in January 2015, resulting in the low index of 48,4 (StatsSA, 2015). In other words, South Africa produced 87% less gold in January 2015 compared with the same month in 1980. These statistics show that the gold sector is losing the prominent place it once had in the South African economy. This is reducing gold's contribution to the South African economy. The metal contributed 3,8% to gross domestic product in 1993, falling to 1,7% in 2013. In terms of sales, gold made up 67,0% of all mineral sales in 1980, falling to 12,5% in 2014 (StatsSA, 2015). When all these statistics are taken into consideration a question arises: Is gold being

4 depleted more rapidly than the optimisation of the Hotelling rule? In light of this, this study seeks to test the applicability of the Hotelling rule in South Africa.

1.2. OBJECTIVES OF THE STUDY

This study has the following objectives:

i. To analyse the trends of gold production, extraction and gold prices in South Africa ii. To determine an optimal extraction path based on theoretical considerations. iii. To test the relevance of the Hotelling rule in South Africa. iv. To identify the extraction path that yields outcome that is socially optimal. v. To provide policy recommendations

1.3. HYPOTHESIS OF THE STUDY

The following hypotheses will be tested in this study:

Hypothesis 1

퐻0 Gold price is mean reverting

퐻1 Gold price is not mean reverting

Hypothesis 2

퐻0 Gold production is mean reverting

퐻1 gold production is not mean reverting

Hypothesis 3

퐻0 Hotelling rule is not relevant in gold production in South Africa

퐻1 Hotelling rule is relevant in gold production in South Africa.

1.4. PROBLEM STATEMENT

The prospect of an imminent depletion of non-renewable resources such as gold in South Africa prompts for economic conservation through finding the optimal extraction path. The welfare of South Africa’s present population and more especially that of future generations will be greatly determined by the stock of natural resources available. Currently, the

5 production processes generally deplete natural resources. For any non-renewable resource, a positive rate of extraction means that physical stock of the resources is reduced in size. This has raised concern over the rate with which gold is extracted in South Africa. The supposed increasing scarcity of gold in South Africa, and the possibility of running out of it, has become a source of concern (Mining Review, 2011).

South Africa’s production of gold has been declining on account of the depletion of gold reserves in the mines. The consequence of this has been a drastic fall in South Africa’s share of world gold production. The drop in South Africa’s international market share was from 17% in 2000, to 14% in 2004, 9% in 2008 and around 6% in 2013 (Baartjes & Gounden, 2012 and Williams, 2013). For a resource economy like South Africa where gold accounts for a significant proportion of export earnings, the decline in both volume and continued and rapid depletion of this non-renewable resource is undesirable. Along with this continued and rapid decline in gold production has been the gradual decline in the engineering and manufacturing operations that are directly linked to the gold industry. Accordingly, there has been the loss of South Africa’s previous substantial heavy manufacturing and engineering capacity (Leger, 2011).

A number of concerns have been raised over the future of several leading gold mines in South Africa. The exploration company Randgold Resources estimated that most of South Africa’s gold mines will have to close down during the next 12 to 14 years (Van Rensburg, 2011 in Kleynhans, 2013). Most reserves are already exhausted; and the costs involved in mining lower grade ore, and deposits located very deep in the earth, are becoming excessive (Hassan, 2012 in Kleynhans, 2013). Mantashe (2008) notes that the "depth at which gold deposits are found in South Africa is a further complicating factor. The closure of marginal mines is accelerating the decline, visible in the 8,8% decline in gold production between 2003 and 2004".

Already, several gold mines have shut down. The North West, Ergo, Tau Tona and St. Helena mines have been all closed down (USA International Business Publications, 2011). In addition to this, Harmony Gold Mining, a mining company which is ranked third in gold production in South Africa, has, in the last couple of years, closed several mine shafts. In 2009 it closed the Evander shafts numbers 2, 5, and 7 in the Mpumalanga province and several other shafts in its mines in the Free State province (Ruffin, 2010). Moreover, the rate of decline of the reserves of several mines owned by the three giants gives them less than ten years of continued production and about a tenth of these reserves are moreover in the

6 form of mine dumps from which gold is being recovered (van Rensburg (2011) in Kleynhans, 2013). South Africa’s gold reserves (gold in the ground that can be extracted profitably) are becoming depleted at a rate that, within 25 to 33 years, will mean the end of the industry on which South Africa's economy has been built (Mining Review, 2011 and StatsSA, 2015). This raises questions of how much of these non-renewable resources (gold) should be extracted today and how much should be saved for future use or for future generations. How should we allocate this limited resource between current and future time periods?

1.5. JUSTIFICATION FOR THE STUDY

This study contributes to the literature by examining the South African gold industry’s ability to allocate the extraction of gold over time in an efficient manner. The South African gold industry appears set to continue on a path of decline due to the continued and rapid depletion of gold reserves. Insightful and intense changes are required to the non-renewable resource framework if what remains of the gold mining sector is not to be entirely dissipated, with the subsequent loss of the economic value of the gold sector to the country. This study will, therefore, complement and contribute to the expansion of knowledge on opportunities for addressing the prevailing problem of the optimum extraction path of gold in South Africa. In a wider sense, it will facilitate an understanding of the relationship, interdependence and interaction between the price of gold and the changes in the interest rate. The results of this study will assist policy makers within a scope of environmental economics to design effective policies that seek to address the problem of optimum extraction of gold in South Africa.

Without an optimal resource extraction path a rapid decline in the production of gold could have a major impact on the South African economy. In addition, this could have serious implications for future generations. While the ownership of resource mines has been a focus of debate, what appears equally important is the rate at which these resources, particularly gold, are extracted. The establishment of an optimum extraction path has long been of interest to economists. Given the importance of the gold industry to the South African economy, a study of the optimum extraction path in the gold industry is especially valuable.

There are no records of similar studies having been conducted in South Africa. This study makes an original contribution towards the broader scope of environmental economics.

1.6. OUTLINE OF THE CHAPTERS

This study is organised in eight chapters as follows: Chapter 1 is an introduction. Chapter 2 is an overview of the gold industry in South Africa while highlighting the core issues of this study. The third chapter provides a detailed theoretical framework and literature review on the conceptualization of exhaustible resources. The fourth chapter presents the methodology used to test the Hotelling rule and the justification of using that procedure. In Chapters 5, 6 and 7 the study presents the results. The implications of the results, policy recommendations, suggestions for further research and conclusion are contained in Chapter 8.

1.7. CONCLUSION

The aim of this chapter was to provide an introduction to the study’s area of focus and an overview of the research background. The chapter introduced the study by providing information pertaining to the context of the research. It discussed the background to the study, problem statement, aim, objectives, significance and format of the study. The chapter showed that the Hotelling rule states that the market price for an exhaustible natural resource should rise at a rate equal to the interest rate and this Hotelling rule has come to be a pillar of the exhaustible resources framework. It was also shown that gold extraction in South Africa is being depleted and extracted at a rate that might not be socially optimal according to Hotelling. This therefore makes the testing of the Hotelling rule appropriate. The next chapter will look at objective two, which is to analyse the trends of gold production, depletion and gold prices in South Africa.

CHAPTER 2 THE TRENDS OF GOLD PRODUCTION, DEPLETION AND GOLD PRICES IN SOUTH AFRICA

2.1. INTRODUCTION

This chapter seeks to address objective one, namely to analyse the trends of gold production, depletion and gold prices in South Africa. The chapter seeks to provide an overview of the South African gold sector and the gold prices. The key aim is to show how the gold sector has evolved over time and to highlight how gold prices have been trending. The chapter makes an attempt to build a comprehensive picture of the South African gold mining sector with specific focus on gold production and gold prices. This is important because it might give an insight of whether gold depletion and gold prices are following the path that was suggested by Hotelling. In order to show where the gold sector comes from, the chapter will first, briefly, introduce, the South African mine sector. The chapter will then discuss the gold mining sector examining its background, composition and production trends. The last section will look at the trends in gold prices. The chapter ends with some concluding remarks to serve as a summary of the whole chapter.

2.2. AN OVERVIEW OF MINING AND THE GOLD SECTOR IN SOUTH AFRICA

The mining sector has been and will remain the heart and nervous system of the South African economy (Antin, 2013). The discovery of world-class diamond and gold deposits in the latter half of the nineteenth century laid the foundation for the emergence of South Africa from an agricultural to a modern industrial economy. Historically, South Africa’s mining industry has been at the heart of the economy’s development – given the country’s competitive position as one of the most naturally resource-rich nations in the world. In fact, the mining industry has played a key role in attracting foreign investment and creating leading global enterprises, and remains South Africa’s most critically observed economic sector. The mining industry covers a wide spectrum of minerals in which South Africa has an exceptional mineral endowment. Mining plays a vital role as a foundation industry that stimulates key services, manufacturing and side-stream industries. Furthermore, mining provides direct employment to about half a million economically active people.

The mining sector in South Africa has traditionally occupied a principal role in the generation of output in the economy. Today, mining in South Africa is still playing a significant role in

9 the development and history of South Africa, both as a country, and as a leading economy on the African continent. South Africa is still considered to be "the country with the world’s largest mineral endowment" (Carroll 2012). In 2014, the South African mining industry contributed 7.6% to GDP and 20% of private investment (Chamber of Mines, 2015). Once indirect effects are considered, the full contribution of the mining industry comes to light. Including side-stream and downstream beneficiations, the mining industry generates approximately 18% of the economy’s activity (Chamber of Mines, 2011). The South African mining sector has provided the critical mass for a number of industries that are either suppliers to the mining industry, or users of its products. These include energy, financial services, water and engineering services, and specialist seismic geological and metallurgical services. Furthermore, the mining industry directly contributes more than 95% towards the country’s electricity generation (Department of Mineral Resources, 2010).

The mining sector also make a huge contribution in the labour market. The mining industry is also a huge employer in South Africa. It provides over 1.3 million jobs (Chamber of Mines, 2012). This shows that it contributes positively to the South African labour market. There are also other ways in which the mining sector contributes to the South African economy. Some of the contributions are shown in Figure 2.1 below.

Foreign exchange

earner – 50% of total merchandise exports

Mining One quarter of companies total annual alone paid Mining investments 17.2% of total sector are related to corporate the complex taxes

Mining shares Financial and legal

account for 29% services – which of the total value were started to of the JSE support the sector – account for 20% of GDP

Figure 2.1: The mining sector’s other ways of contributing to the South African economy

Source: Antin (2013)

Figure 2.1 shows that the mining sector is the biggest exporting industry in South Africa; approximately half of total merchandise exports come from the mining sector. Exports, in turn, bring in the much-needed foreign currency. Figure 2.1 also shows that the mining sector is a source of government revenue as it provides about 17% of total corporate taxes. The mining sector is also an investment destination; approximately 25% of total investments are related to this sector. Furthermore, mining shares account for almost a third of the total value of shares on the Johannesburg Stock Exchange. All these statistics show that the mining sector is a huge contributor to the South African economy.

Despite the mining sector being one of the cornerstones of the South Africa’s economy, it has not been performing to its full potential. The performance of the mining industry has

11 become a more modulated one. Kantor (2013) claims that when measured in constant 2005 prices, the contribution of mining to GVA and GDP has been steadily declining over many years from a large 23% share in 1960 to the current less than 6% share. Whereas in some of its traditionally pivotal roles it remains in much the same position, in most areas it is considerably less important than it used to be (Fedderke, 2002). This is shown by the declining production in the sector. A review of the trends of production in the mining sector show that the sector has had periods of slumps. Figure 2.2 shows the trends in mining production.

Total Mining Production

120

115

110

105

e 100

I 95

92 94 96 98 00 02 04 06 08 10 12 14

Year

Figure 2.2: Total mining production

Source: Graph made from figures from the SARB (2016)

Figure 2.2 shows that mining production has been volatile but began to fall significantly in 2007. Mining production had a steady trend from 1990 and 2000. During this period, mining production was volatile and it had an almost constant trend. From the year 2000 onwards, mining production began to show an upward trend but this later fell in 2005. In 2007 there was a sharp decline in the mining production index. This continued until 2009 when mining production began to rise gradually. From that period on, mining production showed a constant trend but there were periods where it fell significantly, notably in 2012. In 2012, mining production fell and it went to levels in never went in the period between 1990 and

2015. In other words mining production were on its lowest levels in 2012. The fall in production was caused by a number of factors including global economic developments.

The South African mining sector, like any other sector, is affected by global economic developments. For example, the sharp decline in production as caused by the global financial crisis. The South African economy was severely affected by the global financial crisis of 2008. When the economy went into recession then, the mining industry was heavily affected by the crisis on account of its dependence on global growth to stimulate prices and demand, liquidity in the global economy, and conservative investment strategies in times of insecurity (Bexter, 2009). Thereafter, neither the mining sector’s contribution to GDP nor its investment returned to pre-crisis levels until 2011 (Chamber of Mines of South Africa 2012). Mining production later rose gradually between 2014 and 2015.

However, it should be noted that there are other mineral sectors in the mining sector which are doing well. Since this study is focused on the gold sector it would be worthwhile to compare the gold industry’s performance to total mining performance. The gold sector has been underperforming and it has been contributing negatively to total mining production. Taking this into consideration, it would be worthwhile to examine the mining production trends without gold. This will enable us to check if the gold sector has been making a huge contribution to the mining sector. Figure 2.3 shows the comparison between the gold industry and total mining production.

Indexed montlhy production: Mining sector and Gold sector

400

300 d

l 200 u

140 o

d 100

c 120

n 0

c 100

M 60 92 94 96 98 00 02 04 06 08 10 12 14

Gold Production Mining Production excluding gold

Figure 2.3: Total production (excluding gold) and gold production

Source: Graph made from figures from the SARB (2016)

Figure 2.3 shows that gold production has been in a state of decline since the start of the period under investigation (1990). Figure 2.3 also shows that mining production excluding gold has been on the rise since the beginning of the period under investigation (1992). However, mining production excluding gold fell in 2007 and it later rose in 2011. The decrease in production was caused by a number of factors. It was during that down period of 2008 to 2011 that today’s pressing issues of underperformance, rising electricity prices, skill shortages, labour disputes, nationalisation, and the debate around the right policy approach towards the mining industry emerged (Antin, 2013). From 2011 on, the production levels were volatile but, overall, they showed a rising trend. To complement Figure 2.3, Table 2.1 shows the different sectors in the mining industry. The focus is to show each sector’s contribution to total mining production.

Table 2.1: Seasonally adjusted index of the volume of mining production for 2016 by mineral group and mineral (Base: 2010=100)

Mineral group May–Jul Aug–Oct 2016 % change Contribution and mineral 2016 between (%) to the % May 2016 and change in Aug–Oct 2016 total mining production

Gold 76,7 72,2 -5,9 -0.7

Iron ore 111,3 127,0 14,1 2,3

Chromium ore 132,2 138,4 4,7 0.2

Copper 54,2 99,7 83,9 0,6

Manganese ore 188,4 202.0 7,2 0.4

PGMs 103,7 93.2 -10,1 -2.3

Nickel 116.1 123,6 6.5 0.1

Other metallic 80,2 81.9 2,1 0.0 minerals

Diamonds 87,7 97.5 11,2 0.4

Coal 99,0 97.5 -1.5 -0.4

Building 118.1 117,0 -0.9 0.0 materials

Other non- 65,7 68.5 4.3 0.1 metallic minerals

Total 99,3 100.0 0.7 0.7

Source: Stats SA (2016)

Statistics from Table 2.1 show that iron ore made the biggest contribution to the change in total mining production. It had a change of 2.3 % between May and October 2016. Other sectors that made positive changes include chromium ore, copper, manganese ore, nickel, diamonds and other metallic minerals. Table 2.1 also shows that of all the minerals produced in SA, the gold production and PGMs recorded negative growth rates in the period under investigation (May–August 2016). Gold production had a negative 5.9% change and it also contributed negatively to total mining production (0.7%). This shows that the gold sector continued to have a negative trend in 2016. This was caused by a number of factors. The impacts of various challenges, including escalating costs, labour availability, and labour utilisation in the mining industry, and the gold sector in particular, are quite evident (Neingo and Tholana, 2016). This had been established by EY (2014), who stated that productivity on cost and volume bases had been declining since 2000, and various companies had engaged in different cost-cutting exercises. A deeper analysis of gold trends and factors influencing gold performance will be discussed in the next section.

2.3. GOLD PRODUCTION TRENDS IN SOUTH AFRICA

Gold was discovered in the Witwatersrand in 1886, and it soon became evident that the area covered the world's largest and richest gold deposits. The discovery of the Witwatersrand goldfields led to the development of South Africa’s world-class gold mining industry which dominated the world’s gold mining scene for 120 years (Gold in South Africa, 2006). The development of gold mining on the Witwatersrand led to burgeoning economic activity in the area and the establishment of institutions to support the nascent industry. Gold and diamond mining laid the foundation for the emergence of South Africa from an essentially agricultural to a modern industrial economy (Graduate School of Business of the University of Cape Town, 2000). "It presaged the emergence of the modern South African industrial state." (GCIS, 2012). By 1886, gold and diamond rushes were quickly turning mining in South Africa into the nation’s staple economy.

The discovery of gold in the Witwatersrand changed the face of mining in South Africa. No longer could gold be recovered by simple panning, as the gold was embedded deep in rock d high-level technology was needed to be able to extract and recover it (Gold in South Africa, 2007). This meant that mining gold required huge sums of capital, and only large-scale mining companies could continue mining under these conditions. In fact, the Witwatersrand goldfields will probably remain the greatest goldfield ever discovered, surpassing all others by several orders of magnitude. Since records of production were first collected in 1884 until

2004 the South African gold mining sector has produced 50,055 t of gold which accounts for some 33% of all the gold estimated above surface (Gold in South Africa, 2006).

The gold mining sector has led to certain economic developments in South Africa. For example, the establishment of the Johannesburg Stock Exchange followed swiftly after the discovery of the Witwatersrand gold deposits (Gold in South Africa, 2007). The JSE was founded by Benjamin Woollan in 1887 and subsequently became the largest stock exchange on the African continent. Gold mining has also played a major role in the establishment of infrastructure in South Africa, on foreign exchange and on employment and has led to the establishment of metropolitan centres such as Johannesburg, Welkom, Orkney, Springs, Benoni, Witbank and Klerksdorp. The gold mining sector has been a major contributor to the South African economy since commercial mining began on the Witwatersrand gold fields in the 1880s. Some of the gold mining sector contributions are shown in Table 2.2 below.

Table 2.2: Gold production contribution to the economy

2007 2008 2009 2010 2011 2012 2013 2014 Change

Mineral sales 38 46 48.7 53.1 68.9 76.8 57.2 46.8 -3.9% (Billions R)

Taxes Paid 1.0 3.7 1.5 0.3 1.8 2.1 0.9 1.6 5.8% (Billions R)

Remuneration 14.7 16 17.4 19.9 20.9 22 23.4 23.4 34.5% (Billions R)

Capital 8.1 8.8 10.3 11.1 11.8 13.6 11.8 9.4 -8.2% Expenditure (Billions R)

Employees 169.1 166.4 159.9 157 145.6 142.2 132.2 119.1 -25.5% (Thousands)

Gold Production 254.7 217.6 204.9 191.4 186.7 167.2 167 168.7 -17.7% (Index)

Free cash flow 6.2 10.5 10.1 12.8 19.7 10.7 12.2 10.4 2.3% margin (%)

Source: PWC South Africa (2015)

Table 2.2 shows that mineral sales have declining by 3.9% per annum between 2007 and 2014. This may suggest that the importance of the gold sector is declining. It also goes in line with the decline in employment. There was a decrease of -25.5% in the period under investigation. When sales are declining, firms are forced to cut back on employees and this explains why there has been a decrease in employment in the gold sector. This is confirmed by GCIS (2012) which stated that gold has fallen from its eminent position as the main contributor to mineral sales, as a result of which employment in the mining industry has contracted significantly since 1986. Table 2.2 shows that the gold sector has a huge but declining capital investment in infrastructure. In 2014 it stood at 9.4 billion. Capital expenditure investment had shown a decrease of -8.2% in the period under investigation. However, Table 2.2 shows that the gold sector still has potential as shown by the positive

18 change in the free cash flow margin1 (2.3%). However, it should be noted that free cash flow margin has been in a state of decline since 2011 when it stood at 19.7. It fell in 2012 and it has been low since then. It is as a result of the troubled labour situation and the resulting political insecurity that are scaring investors away. Threats of nationalisation have damaged the carefully built-up investor trust and have hindered the realisation of necessary long-term investments.

Table 2.2 also shows that gold production has declined by -17.7% between 2007 and 2014. The gold sector has been in a state of decline since the 1980s. The continued decline in South Africa's gold production has resulted in the country dropping in production ranking from the largest producer in the world in 2007. The declining profile of gold production over a much more longer period is shown in Figure 2.3 below.

Gold Production

700

600

500

n 400

300

200

100

90 92 94 96 98 00 02 04 06 08 10 12

Years

Figure 2.3: Gold production trends

Source: graph made from figures from the SARB (2016)

1 Whilst this approach is clearly not acceptable under IFRS, it does provide a good indication of the performance of a mining company and its ability to invest in future growth or to reward stakeholders.

Figure 2.3 shows that although the gold mining industry in South Africa is essentially mature (as shown by the huge production outputs) the production tonnage is showing a declining profile. Figure 2.3 shows that the declining profile of gold production started in 1993 and it has followed this declining trend ever since. However, it should be noted that this declining profile started before 1980. A closer look at the rapidly decreasing importance of gold mining in SA shows gold production came down by 57% for the period between 2003 and 2013. The decrease in production is mainly as a result of the mining of lower-grade ore, influenced by higher rand gold prices, and temporary closure of shafts to maintain infrastructure (Environmental Economic Accounts Compendium, 2015). South Africa's gold mining industry works at deeper levels and under more difficult conditions than any other mining industry in the world. The decline in gold mining is, therefore, due to structural factors in the sector, rather than changes in the gold price.

According to Phillips (2013) there has been a steady decline in production since 1970, and although the trend is clear in hindsight, few people predicted the seriousness of the fall in production or the grave situation of the industry today. In 2005, South Africa produced 297.3 mt of fine gold, which declined to 275.1 mt in 2006 - the lowest level of production in 84 years (Gold in South Africa, 2006). South Africa's gold production (extraction) decreased in 2009 due to the global economic crisis in 2009, which resulted in a declining demand for commodities. The rise in electrical costs for mining operations in the country and the decline in the value of gold and other precious minerals within South Africa over the years have only made things worse. In addition to the further tax burden of a 2% to 3% revenue-based royalty that became effective from the beginning of March, the country has to raise its electricity prices significantly to pay for new generation capacity (Engineering and Mining Journal, 2010)

2.4. MARKET SHARE IN THE GLOBAL GOLD PRODUCTION: GLOBAL SHARE RANKINGS

The previous section showed that gold production has been decreasing. This has implications on South Africa’s global market share. A review of the global market share is done in this section. Production of gold in South Africa as a share of global output has been declining consistently for a decade. South Africa was a globally dominant gold producer in the twentieth century. For many decades South Africa was the world’s largest gold producer, but production has declined precipitously over the past two decades in particular. Since 2012, mineral sales have fallen 40% (SA Gold, 2015). Statistics further reveal that gold

20 production declined consistently in the last three decades and with that also South Africa’s share in the total world gold production. In 1970 South Africa produced 79% of the world’s gold ad this declined to 19,2% in 2002 and now it accounts for around just 5% of global output (Krugell, 2013 and Cairns, 2015). This has led to South Africa dropping from the top spot of world biggest producer. This is shown in Table 2.1 and Table 2.2 below.

Table 2.1: Top 10 global gold-producing countries in 2004

Country 2004 (t)

South Africa 342

USA 260

Australia 253

China 220

Peru 173

Russia 159

Canada 129

Indonesia 100

Uzbekistan 90

Papua New Guinea 71

Table 2.2: Top 10 global gold-producing countries in 2014

Country 2014 (t)

China 450

Australia 274

Russia 247

United States 210

Canada 152

Peru 140

South Africa 125

Mexico 118

Uzbekistan 100

Ghana 91

Source: US Geological Survey’s (2016)

Table 2.1 and 2.2 show that South Africa has fallen in global gold production rankings. They also show that between 2004 and 2014 China doubled its gold mining production and rose to the top slot, while South Africa cut its production in half and fell from first to seventh. This shows that South Africa is falling on the global market. Most of the other large gold producing countries have increased their output. By contrast, South Africa’s rate of production over the past decade shows the highest rate of decline out of the world’s top ten producing countries.

Prior to 2007, the country held the number one spot as the top gold producer in the world. By 2014, South Africa had dropped to seventh place falling behind other countries such as Peru, USA, Australia, and Russia. China is currently the world’s top gold producer. The gold mining industry in South Africa is reaching a mature stage and new areas of competitive production have emerged in China, Russia, Indonesia, Uzbekistan, Peru, Papua New Guinea, Mali and Tanzania (VULA, 2012). Factors that have led to the scaling down of South African gold production in the last two years include increasing mine depth and declining grades, as well as higher material input costs. These factors have been hampering activities in the gold sector. Nonetheless, the gold mining industry continues to be an important player in the South African economy. The sector accounts for roughly one-third of the market capitalisation of the JSE, and continues to act as a magnet for foreign investment in the country. It is also a foreign currency earner and an employment creator.

2.5. GOLD DEPLETION

Gold reserves in South Africa are declining fast (Krugell, 2013). This was confirmed by StatSA (2009) when it stated that South Africa had about 30 years of production in the gold sector remaining, a forecast that fluctuates based on the day's modifying factors. The exploration company Randgold Resources estimated that most of South Africa’s gold mines will have to close down during the next 12 to 14 years (Van Rensburg, 2011 cited in Kleynhan, 2013). Several mines are already closing down and mines are operating at deep levels, a sign of depleting gold resources. Figure 2.4 show the gold depletion trends between 1990 and 2014.

Years to Depletion

e 32

s 28

90 92 94 96 98 00 02 04 06 08 10 12

Years

Figure 2.4: Years to depletion

Source: Stats SA (2016)

Figure 2.4 shows that the years to depletion was ranged between 20 and 24 years between 1990 and 2006. However, by 2014, the years to depletion was 37 years. This suggests that, other things being constant, South Africa has 37 years left to extract gold before it is depleted. The expectation, therefore, is that if gold continues to be extracted at the rate with which it is extracted at the moment, South Africa is likely to run out of gold in 2054. Although

South Africa still possesses some gold reserves, most of it is of a too low a grade to mine profitably. Most reserves are already exhausted; and the costs involved in mining lower- grade ore, and deposits located very deep, are becoming excessive (Hassan, 2012 cited in Kleynhan, 2013).

The government2 is the custodian of resources and as such it is required to ensure that resources are extracted optimally. However, since the late 1990s there has been little effort focused on developing depletion models for mineral resources. This can firstly be attributed to the general expectations within the industry that knowledge and technology will address any shortfalls in production (e.g. the ability to maintain high production output even when ore grades are declining). Secondly, the historical record of growing global resource quantities with the globalisation of mining has made physical constraints at the national level less important beside considerations of how future needs will be supplied (Willett 2002 and Tilton 2003). However, several concerns have been raised with regard to the current rate of resource consumption. These concerns are rooted in the fear that if the world continues to remain dependent on non-renewable resources, it runs the risk of economic (and military) collapse once these resources are no longer available. This has led to calls for governments to actively intervene and aid in the development of renewable alternatives.

Mantashe (2008) noted that because the decline had reached crisis level, gold mining received a disproportionately higher level of attention. The Gold Crisis Committee was set up in 1998. This culminated in the Mining Summit of 2000, with the sole objective of looking into the long‐term survival of the industry, with particular focus on employment trends (Mantashe, 2008). However, these concerns were focused on employment trends rather than on the decreasing importance of the gold sector and the fast depletion of gold resources. When little is done to ensure that resources are properly and optimally extracted, the government should make efforts to regulate the extraction of resources. This is the focus of the next section.

2 In order to be neutral any other player(s) in the mining sector can play a huge role in ensuring that resources are extracted in a sustainable way. The government is usually seen as an obstacle to the effective performance of any market from a Classical point of view (Hotelling rule falls in the Classical economics category).

2.6. LEGAL FRAMEWORK REGULATING THE SOUTH AFRICAN MINING AND GOLD SECTOR

This section looks the laws and policies put in place to govern the mining sector. In order to better understand the production and depletion trends of any mineral, it is important to assess the conditions in which such a sector operates. A critical assessment of the trends of gold production, depletion requires knowledge of the political economic and legal constraints in which the mining market operates. In this regard, an understanding of the political and legal context is essential. The government has a huge role to play in resource management and sustainability. Furthermore, many analysts conclude that depleted reserves could be effectively extended through regulatory interventions by government or private entities. In light of this, this section will look at the role of government in the gold mining industry and mining sector at large. The important questions that the section seeks to address are:

i. Do the current laws and policies ensure the sustainable extraction of mineral resources in South Africa? ii. Are these laws in line with the Hotelling rule or any other resource management theory?

Although the Hotelling rule does not explicitly place political factors into the pricing of a natural resource (Omoregie, 2015), studies have shown that political factors can play a role in either making the Hotelling rule applicable or making it invalid. For instance, Chakravorty et al. (2009) note that in reality an increase in the price of non-renewable sources may not persist as many short-run factors such as regulation and speculation in commodity markets may come into play, resulting in alternative phases of upward and downward price movements.

The South African mining laws

The Constitution, which is the supreme law in South Africa points to the importance of sustainability in resource management. Section 24 states that everyone has the right:

a. to an environment that is not harmful to their health or well-being and b. to have the environment protected, for the benefit of present and future generations, through reasonable legislative and other measures that - i. prevent pollution and ecological degradation

ii. promote conservation; and iii. secure ecologically sustainable development and use of natural resources while promoting justifiable economic and social development

Section 24 of the Constitution clearly shows that the state has an obligation to promote conservation of resources and to ensure that there is sustainable use of resources. This extends to resource extraction as it is directly related to resource conservation. The government of South Africa has drafted and implemented legislations and policies that give effect to section 24 of the South African Constitution. Policy governing mining and mineral extraction vests primarily in the Department of Minerals and Energy. Legislation most relevant to resource extraction include:

i. The Mining Rights Act of 1967 The Mining Rights Act of 1967 regulates the possession and trade of gold in businesses making use of gold as a raw material. One of the distinguishing features of the South African gold business, compared with other countries, is that South Africans are effectively prohibited from owning gold other than in bullion coins or jewellery.

ii. The Mineral and Petroleum Resources Development Act of 2002 (MPRDA); The objects of this Act are, among other things, to—

 Recognise the internationally accepted right of the State to exercise sovereignty over all the mineral and petroleum resources within the Republic;  Give effect to the principle of the State’s custodianship of the nation’s mineral and petroleum resources;  Promote equitable access to the nation’s mineral and petroleum resources to all the people of South Africa;  Substantially and meaningfully expand opportunities for historically disadvantaged persons, including women, to enter the mineral and petroleum industries and to benefit from the exploitation of the nation’s mineral and petroleum resources;  Promote economic growth and mineral and petroleum resources development in the Republic;  Promote employment and advance the social and economic welfare of all South Africans;  Provide for security of tenure in respect of prospecting, exploration, mining and production operations.

The MPRDA is based on the principle of state custodianship of mineral resources and abolishes the previous regime of private mineral rights. Applications for prospecting, exploration and mining rights are made to the state. Transitional provisions in the act allow for the conversion of existing rights, referred to as ‘old-order’ to ‘new-order’ prospecting and mining rights.

From the above brief analysis of the legislation in South Africa it can be realised that the laws do not really place any emphasis on the depletion of non-renewable mineral resources. South African environmental law describes the legal rules in South Africa relating to the social, economic, philosophical and jurisprudential issues raised by attempts to protect and conserve the environment in South Africa. The legislation does not look at resource extraction as this is left to the market to determine. Like many other market economies, the extraction of gold is left to the market to determine. However, this seems to cast a blind eye on the rate at which the gold would be depleted. The depletion rate is alarming and it warrants attention. Phillips (2013) states that there has been a steady decline in production since 1970, and, although the trend is clear in hindsight, few people predicted the seriousness of the fall in production or the grave situation of the industry today. The annual decline of Witwatersrand production has averaged 20 t of gold per year since 1994 and at this rate, Witwatersrand gold mining will end in mid-2022 (Phillips, 2013).

2.7. GOLD PRICE TRENDS

The price of gold has been rising over the years. The surge in gold prices has resulted in many people purchasing gold to diversify their investment portfolios. People are turning to gold as it provides long-term security and a hedge against inflation (Lear, 2016). Gold prices are essentially determined by the demand and supply of this precious metal. The price of gold is on the rise continually due to its high demand and finite supply. Apart from an investment instrument, it is also used widely for industrial purposes due to its high resistance to corrosion and thermal conductivity. In light of the supply, persistent increase in demand causes the price to go up and vice versa. There has been a drastic increase in the price of gold over the last two decades. This is shown by Figure 2.5 below.

Rand denominate gold price

16,000

12,000

8,000

4,000

92 94 96 98 00 02 04 06 08 10 12 14

Years

Figure 2.5: Rand-denominated gold price

Source: Quantec (2016)

Figure 2.5 shows that the rand-denominated gold price has been increasing since 1990. It showed a slow and gradually increasing trend from 1990 until 2005. The gold price had a sharp and significant increase in 2006 but it later fell between 2007 and 2008. The decrease in the gold price was short-lived as it later rose in 2009 and 2010. The gold price maintained its rising trend from 2010 onwards. However it later fell abruptly in 2012 and later increased in 2013 and 2014. A myriad of other global factors affect the price of gold (Pierdzioch et al., 2014), which in turn, can be primarily classified into six categories: The business cycle factor; the nominal factor; the interest rate factor; the commodity factor; the exchange rate market factor; and the stock price factor.

The increasing trend in the gold price is in line with the predictions of the Hotelling rule. Resource rent is responsive to changes in the underlying economic scarcity. The resource rent reflects the opportunity cost of current resource extraction, that is, the trade off between resource extraction now and resource extraction in the future. It is a measure of the anticipated scarcity of the resource. Rising resource rents would indicate rising scarcity,

28 whereas falling resource rents would indicate falling scarcity and no rise or fall would suggest no change in scarcity (Neumaye, 2013).

2.8. SUMMARY OF THE CHAPTER

The main objective of this chapter was to address objective one, namely to analyse the trends of gold production, depletion and gold prices in South Africa. The chapter used official documents to achieve its objective. In terms of key findings, the following characterisations appear to be relevant:

i. Results showed that the gold sector makes a significant contribution to economic activity, job creation and foreign exchange earnings. The gold mining sector has been a major contributor to the South African economy since commercial mining began on the Witwatersrand goldfields in the 1880s. Between 1950 and 2006, gold accounted for an average of 6.9% of GDP (reaching a peak of 16.7% in 1980) and 31.8% of merchandise exports. ii. Despite the mining sector being one of the cornerstones of the South Africa’s economy, it has not been performing to its full potential. The performance of the mining industry has become a more modulated one. Whereas in some of its traditionally pivotal roles it remains in much the same position, in most areas it is considerably less important than it used to be (Fedderke, 2002). This is shown by the declining production in the sector. A review of the trends of production in the mining sector shows that the sector has had periods of slumps. iii. Gold production has been in a state of decline in South Africa. This has affected mineral sales and employment. South Africa's gold production has decreased, resulting in the country dropping in production ranking from the second-largest to the fourth-largest producer in the world. The decrease in production is mainly as a result of the mining of lower-grade ore, influenced by higher rand gold prices, and temporary closure of shafts to maintain infrastructure. The declining gold production is in line with the predictions of the Hotelling rule. Hotelling predicted that due to scarcity, there should be declining production. iv. Gold reserves in South Africa are declining fast (Krugell, 2013). This was confirmed by StatSA (2009) when it stated that South Africa had about 30 years of production remaining in the gold sector. The exploration company Randgold Resources estimated that most of South Africa’s gold mines will have to close down during the next 12 to 14 years (Van Rensburg, 2011). This is consistent with

what Hotelling predicted. Hotelling has predicted that there should be increasing scarcity in a non-renewable resource. In other words, there is a positive relationship between extraction of a resource and its depletion. As long as a non- renewable resource is extracted it will decline in terms of reserves. v. The price of gold has been rising over the years. The surge in gold prices has resulted in many people purchasing gold to diversify their investment portfolios. The increasing trend in gold price is in line with the predictions of the Hotelling rule. Resource rent is responsive to changes in the underlying economic scarcity. The resource rent reflects the opportunity cost of current resource extraction, that is, the trade-off between resource extraction now and resource extraction in the future. It is a measure of anticipated scarcity of the resource.

2.9. CONCLUSION

This chapter sought to address objective one, namely to analyse the trends of gold production, depletion and gold prices in South Africa. The chapter provided an overview of the South African gold sector and the gold price. The key aim was to show how the gold sector has evolved over time and to highlight how gold prices have been trending. It was shown that the South African mining sector is a one of the cornerstones of economic growth and development in South Africa. Over the years, the mining sector has been underperforming. The gold sector, like the mining sector, has been underperforming. This was shown by the declining production trends.

CHAPTER 3 LITERATURE REVIEW

3.1. INTRODUCTION

This chapter seeks to achieve the second objective of this study; to determine an optimal extraction path based on theoretical considerations. In order to achieve this objective, the chapter examines theories and empirical work associated with the examination of sustainable resource extraction and optimal exhaustible resource use. The focus will be on certain key theoretical and empirical issues which lie at the heart of any analysis of sustainable and optimal exhaustible resource use.

The chapter will first explore theoretical literature, with considerations being made to the Hotelling rule, Hartwick rule, Herfindahl rule, Marx’s strong sustainability theory and the theory of Non-declining stock of natural capital. The second part of this chapter will look at the empirical literature that sought to find the sustainable and optimum extraction path. The focus was on getting an insight on how to sustain the exhaustible resources in which they proposed that technical development in resource extraction and recycling as well as the availability of substitutes are major factors in the resources’ sustainability and meeting the increasing demands of the non-renewable natural resources.

3.2. THEORETICAL LITERATURE

The theoretical section of this study discusses the theories that sought to explain how sustainability can be achieved and how an optimum extraction path can be established. Although economists have long been concerned with the extraction of natural resources, there is no theoretical consensus on how to get an optimum extraction path. The efficient use of scarce natural resources, both renewable and non-renewable, has long been a concern of natural resource economics (Shogren, 2000). For example, Adam Smith, Ricardo, and Robert Malthus raised concern about the dangers of population growth, asserting that the increasing population was likely to preclude the endless progress towards a utopian society (Barnett & Morse, 1963) raised concern about the consequences of coal depletion on population growth.

Several models have been forwarded to address these issues. These models were developed over time to study the natural resources’ sustainability as well as depletion, by

Hotelling, Hartwick, Solow, Dasgupta and Heal, and several other scholars. These models and studies worked on developing methods on how to sustain the exhaustible resources, in which they proposed that technical development in resource extraction and recycling as well as the availability of substitutes are major factors in the resources’ sustainability and meeting the increasing demands of the non-renewable natural resources.

For the purposes of this study, the theoretical literature section will be divided into two sections. The first section will look at the strong sustainability theories and the second section will look at the weak sustainability theories. Kuhlman and Farrington (2010) stated that when assessing sustainability and models of optimum extraction path, a distinction should be made between strong and weak sustainability. Strong sustainability is concerned with the non-declining stock of capital in which the environmental constraints are met at every point in time (Perman, 2003). This viewpoint lays emphasis on development not leading to irretrievable loss of resources. On the other hand, the weak sustainability rule presupposes that natural capital and man-made capital can be traded off against one another.

Weak sustainability theories

Weak sustainability tends to place more faith in market values to reflect the full long-term value of capital (in particular natural capital) stocks. The main implication of this literature is that maintaining the value of the aggregate capital stock should be sufficient to maintain consumption, or well-being. This study will focus on the Hotelling rule, the Hartwick rule and the Herfindal rule.

3.2.1.1. Hotelling rule

Hotelling's rule states that in a competitive market, the price of a depletable resource must increase at the same rate as the discount rate. Arbitrage will remove any deviation of the future prices. The theory for this special case was worked out in the classic paper of Hotelling

(1931). Krautkraemer’s (199) notes that "Hotelling’s formal analysis of non-renewable resource depletion generates some basic implications for how the finite availability of a non- renewable resource affects the resource price and extraction paths".

An intuitive explanation of the Hotelling rule is as follows. Consider a competitive market with identical producers having depletable resources on the ground. Any production level will see the eventual depletion of the resources, and the producer has to decide how best to optimise production between now or the future so as to maximise profits (Tham, 2010). Suppose he increases his production sufficiently high, increasing present supply and lowering present prices. This causes his resource stocks to deplete at a faster rate, and the rate of future price increases γ to be high. In this case, γ > r (discount rate). However, his competitor may find it more optimal to not follow his lead. This will enable them to enjoy future higher prices, which grow higher than the discount rate. As such, equilibrium sets in such that the producer will lower his production enough so that γ = r (Tham, 2010). Again, suppose that he limits his production, so that present prices become higher whilst stocks are depleted more slowly. Future price increases now become less, such that γ < r. Competitors now find it more optimal to increase their production, and invest the money into the money market for a higher return. As such, equilibrium sets in such that the producer will increase his production enough so that γ = r.

Hotelling’s rule primarily addresses one basic question of the owner or agent involved in the exploitation of the non-renewable resource: How much of the asset should I consume now and how much should I store for the future? (Kuhlman and Farrington, 2010). In other words, the agent has to choose between the current value of the asset if extracted and sold and the future increased value of the asset if left unexploited. This simple rule can be expressed by the equilibrium situation representing the optimal solution.

푃′(푡) = 휎 ……………………………………………………………………..(i) 푃 (푡) when P(t) is the unit profit at time t and δ is the discount rate (the inverse of rate of return). The stock of a non-renewable resource, being an asset, holds a market value which yields returns to its owner at a certain rate. This rate of return can be determined by three components:

1. Flow of product generated by the marginal unit of the resource, Marginal Productivity or Dividend rate.

2. Change in the physical characteristics of the asset over time. 3. The rate at which market value of the asset will change over time.

The equality of this rate of return to the rate of return of alternative investments (i.e., if the yield obtained from asset’s sale is invested elsewhere), determines the asset market’s equilibrium (Kuhlman and Farrington, 2010). Considering a non-renewable resource, say a stock of oil in the ground, which is subject to two characteristics; one, it has a fixed size which cannot be increased over time and two, the in situ asset is unproductive. This makes the first component, marginal productivity, nil. Assuming that holding the asset in situ will not lead to its depreciation, even the second component is rendered zero. Remainder is the rate of appreciation of the asset’s value which is, hence, the only determinant of rate of return of the stock of oil (Torin, 1998). This is the famous Hotelling’s rule which states the asset market equilibrium condition. It states that the net price of the natural resource must grow at the rate of interest. Assuming that the marginal cost of extracting the resource does not depend on the rate of extraction and does not vary over time, then the market price of the asset over time would be:

푃′(푡) 푐 = r (1 - ) …………………………………………………………(ii) 푃 (푡) 푝 (푡)

An optimal extraction path is one that maximises the present value of the net benefits from extraction subject to the constraint that cumulative extraction cannot exceed the initial stock of the resource. An optimal path is characterised by three necessary conditions (Sandroni, 1999). First, the marginal static benefits of resource extraction must equal its marginal static costs. Marginal benefits are equal to the price of the resource. Marginal static costs consist of extraction costs and an opportunity cost which represents the fact that future exploitation opportunities are reduced if the resource is extracted today. The latter has frequently been referred to as the user cost or the in situ value of the resource.

The second condition refers to dynamic efficiency. The resource stock is viewed as an asset which generates a rate of return that needs to be compared to the returns from other assets. Asset market equilibrium requires that the return to holding a marginal unit of the resource is equal to the returns from any other asset considered (Rouwenhorst, 1995). The return to "other" assets is measured by the rate of interest, which is treated as exogenous in a partial equilibrium context. The return to the in situ resource stock comprises capital gains and the marginal net benefits from holding a unit of the resource stock. Capital gains comprise increases in the user cost of the resource (Sandroni, 1999). Marginal net benefits from

34 holding the resource stock are generally referred to as stock effects. They arise e.g. if extraction costs increase as the resource stock declines. Holding one more unit of a resource stock then represents a benefit because it leads to lower extraction costs.

The third condition is a transversality condition. It implies that, at the end of the time horizon considered, the remaining resource stock is either exhausted or worthless (i.e. its in situ value is zero). In other words, efficiency requires that the entire resource stock is used up as long as it is valuable. If the time horizon is infinite, the transversality condition implies that the present value of the in situ value of the resource stock converges to zero in infinite time. In the simplified case where extraction costs are zero and stock effects are absent, the first condition implies that the resource price is equal to its user cost ((Rouwenhorst, 1995). The second condition implies that the in situ value of the resource increases at the rate of interest.This result is referred to as Hotelling’s rule.

Both conditions together imply that the resource price also rises at the rate of interest. If the demand structure is stationary, the quantity extracted declines over time at a rate that depends on the properties of the demand curve. If the transversality condition is fulfilled and the time horizon is infinite, the resource stock is exhausted in infinite time One of the most important prerequisites for Hotelling’s rule to be valid is a precise idea of a given known resource stock or at least of a given probability distribution of future exploration possibilities ((Rouwenhorst, 1995). The Hotelling rule is an efficient condition that must be satisfied by any optimal extraction programme regardless of utilitarian social welfare and competitive market economies.

According to Hotelling (1931), there are five main factors determining a non-renewable natural resource price: the marginal cost of extraction, the back stop price of the next best substitute, demand, the resource reserves and the discount rate. The Hotelling rule states that the market price for an exhaustible natural resource should rise at a rate equal to the interest rate in a market equlibrum (Hotelling, 1931). In environmental economics, the Hotelling rule has come to be a pillar of the exhaustible resources framework and in addition to this, it has presented essential insights into the consumption and extraction of non- renewable resources. The price of any non-renewable resource, in a competitive economy, should rise at a rate that is equal to the interest rate (Hotelling, 1931). The basic assumption that underpinned Hotelling’s reasoning was constant marginal extraction costs (Devarajan and Fisher, 1982).

This simple rule can be expressed by the equilibrium situation representing the optimal solution. The basic Hotelling model of non-renewable resource extraction predicts that the shadow price of the resource stock, which is an economic measure of the scarcity of the resource, should grow at the rate of interest (Hotelling, 1931). If the natural resource market is perfectly competitive, then the Hotelling rule implies that the market price minus marginal costs must grow at the rate of interest, and therefore that the natural resource price should be increasing over time if marginal costs are constant. A numerical example that has been modified from Salant (1995:98) shows this condition well. With an interest rate of ten percent and the net price per ounce of gold at $300 an ounce, if the gold price is expected to be at a price below $330 in the next period, it pays to extract more gold in the current year, because the income will earn ten percent interest. This is because no asset holder would wish to hold resources in the ground and all production would be shifted to the current period. On the other hand, if the net price is expected to be above $330 and thus grow faster than the rate of interest, gold miners will have no incentive to mine gold in the current period. By delaying production, suppliers place pressure on the gold price to rise. In this case, resource deposits left in the ground would be a superior way of holding wealth. From this analysis, it is observed that there is a natural tendency for the net price of exhaustible mineral deposits to appreciate at the rate equal to the rate of interest prevalent in the economy, maintained by producers adjusting their production based on the expected future gold price.

3.2.1.1.1 Empirical validity of the Hotelling rule The Hotelling rule has been presented in the previous section but the question arises; how well does Hotelling’s framework fit the real world? To answer this question, the study surveyed literature that attempted to test the theory. Some studies have also attempted to use empirical data to test the validity of Hotelling’s theory. These studies offer valuable insights into the validity of the Hotelling rule.

Economists have argued that Hotelling’s theoretical prediction of a rise in scarcity and relative prices of non-renewable resources over time is not borne out by facts (Watkins 1992). The Hotelling rule has been seen to not be in line with the statistics observed over more than a century in the United States. Statistics concerning US price data for the period 1870–2004 for copper, lead, zinc, coal, and petroleum, 1880–2004 for tin, 1900–2004 for aluminium and nickel and 1920–2004 for natural gas, reveal the rate of change of prices of these resources being influenced by a high degree of volatility (Gérard, 2007). But the more important phenomenon is that the volatility seemed to be centered at 0. In fact in none of

36 the ten cases was the mean rate of change of price considerably different from 0. Thus the actual price of the resources did not seem to be following a particular trend and definitely not the path of the positive trend as recommended by Hotelling’s rule (Gérard, 2007). While the rule predicts exponentially increasing resource prices, the results of the empirical studies were not in tandem with the rule. The results so far showed either declining or constant resource prices over time.

Devarajan and Fisher (1981) noted that Hotelling's work was unusual in being the sole origin of an entire formal field of economics. The literature it spawned appears at an ever more- rapid pace (Farzin, 1984 and Romer and Sasaki, 1985). It is even more notable that such a body of work exists at all, however, let alone flourishes. Hotelling's analysis has no descriptive or prescriptive power, because it is founded on a contrary-to-fact assumption – that the price of the supposedly-exhaustible resource will rise secularly. The fact that all natural resources have fallen rather than risen in price throughout history is inconsistent with Hotelling's starting-point assumption – that the indefinite maintenance of a steady rate of production is a physical impossibility.

There is a respectable amount of literature on the optimal consumption of non-renewable resources, based on the work by Harold Hotelling (1931). This literature argues that in the social optimum the price of a non-renewable resource should be rising at the rate of interest, a requirement known as the Hotelling rule (Lasserre, 1991). Furthermore, resource consumption should decline over time, asymptotically falling to zero (Dasgupta and Heal, 1974). Weinstein and Zeckhauser (1975) argued that a competitive market will follow these rules under certain conditions, thus producing the socially optimal outcome. In reality, however, neither the Hotelling rule nor the declining consumption requirement appears to be fulfilled. Some economists have responded to this by firmly rejecting the Hotelling approach in favour of a more realistic one (Banks, 2004), whereas others – including Pindyck (1978), Farzin (1984), and more recently André and Smulders (2004) – modified it by adding some more realistic features.

Kronenberg (2008) argued that the simple Hotelling rule does not hold in reality because a number of its assumptions are violated. He held that if the deviations from the simple Hotelling rule were caused by marginal extraction costs, which could be rising due to stock effects or falling due to technical progress, this did not pose a serious problem. Under such conditions it is socially optimal to follow a modified Hotelling rule, and that is what the market will do, so the market solution is efficient. If, however, uncertain property rights or strategic

37 interaction were the causes for the failure of the Hotelling rule, this was quite unfortunate because it implied that the market would not lead to an efficient solution.

The conditions on which Hotellings’s rule is based rarely prevail in reality (Binswanger & Chakraborty, 2000). Technological change can reduce extraction costs, which makes it profitable to extract more resource units than if extraction costs were higher. As a result, the resource price may fall over a certain time interval. Ultimately, however, rising in situ values cause the resource price to increase again, which gives rise to a U-shaped time path of the resource price. Change in extraction technology is one of the reasons why the historical prices of non-renewable resource have not increased continuously over time. Binswanger & Chakraborty (2000) believe that markets in the real world generally do not generate optimal extraction paths for non-renewable resources. Considered in isolation, resource prices are not reliable as scarcity indicators. Although resource prices must ultimately rise when the existing resource stock is close to exhaustion, the price increase may come too late and too fast for an economy to adjust smoothly. It is therefore important to think about how to identify sustainable extraction paths for non-renewable resources.

Slade (1982) found empirical evidence for such a U-shaped price path for several mineral resources. André and Smulders (2004) present a model with endogenous technological progress in extraction, which also produces a U-shaped price path for non-renewable resources. A more complicated picture arose in Farzin (1992), who focused on the rent component of price, rather than the price itself. In addition to technological change he allowed for diminishing returns to extraction and stock effects finding that the time path of scarcity rent may be non-monotonous. That is, it may be rising for some interval, then falling, then rising again, and so on. This model shows that the simple Hotelling rule of rising scarcity rents is too simple, and that U-shaped time paths may also still be too simple.

Krautkraemer (1998) argues that for the most part, Hotelling’s theoretical predictions have been inconsistent with empirical studies of non-renewable resource prices and in situ values. Over the past 100 years or so, there hasn’t been a persistent increase in the prices of non- renewable resources. In fact, economic indicators have shown that there has been growth in non-renewable resource supply as new deposits continue to be discovered and the extraction technology continues to progress (Krautkraemer 1998). Xiaoyan (2012) found there is increasing concern for scarcity of natural resources and deterioration of the environment due to economic activity. Although theoretically the Hotelling rule not only provides an optimal extraction for the resource owner's profit maximisation problem but also

38 provides the optimal solution for society as a whole, the rule fails to fit the facts and only applies to the idealised world for which it was constructed. In particular, when the resource firm realises it can affect its price depending on extraction, shareholders will disagree on the extraction rate.

However, some studies have shown that the Hotelling rule is valid in the real world. They have shown that studies that did not agree to Hotelling’s rule are flawed. For example Krautkramer’s analysis was conducted at the global level (Wright & Czelusta 2002). Although it may seem appropriate to test Hotelling's predictions at the global level, such analysis leaves open the possibility that the depletion may have been staved off at the global level through the discovery of new and underexplored territories (Wright & Czelusta 2002). Using data on the oil market from 1970 to 2004, Lin and Wagner (2007) incorporated stock effects and the technological progress in the theoretical Hotelling model and show that the oil price is consistent with the Hotelling model.

In their conclusion Devarajan and Fisher (1981) state that Hotelling’s 1931 article is the sole source of work in a vigorously growing branch of economics. It has formed the conceptual and theoretical framework used by economists to model the supply and the prices of non- renewable resources. More so, it has contributed to the conservationist movement. The volume of literature that has proliferated on the diverse aspects of the economics of exhaustible resources, suggests it is an academically appealing theory. Herein lies the problem. It is principally a theoretical economic construct that provides huge insight into a realm of modelled economics where everything behaves in an ‘economic’ manner. His elegant analysis, asides, conjectures and canonical model provide economists with a structure to build on that is almost a generation ahead of its time.

Solow (1974) stated that, "Good theory is usually trying to tell you something, even if it is not the literal truth". So although the economics of exhaustible resources does not invade the real world of mining and mineral extraction to any large extent, it is still worthwhile to re- examine the theory. Perman et al. (2003) argued that although some empirical failures of the Hotelling rule do not make it false as a theory, it does mean that the rule only applies to the idealized world for which it was constructed. Consequently, the same applies to all models which use the Hotelling rule as a shortcut. Such models are still valuable, but it must be made perfectly clear that because they do not ‘fit the facts’ of the real world, they cannot be used to explain or predict real world phenomena. They can only be used to explain phenomena that occur in the ‘idealized world’ of the Hotelling rule.

3.2.1.1.2 Studies that sought to reconcile the Hotelling rule with reality Since Hotelling (1931), optimal extraction problems of exhaustible resources have been studied by many researchers. They described the patterns of resources depletion under different assumptions about resources demand and availability, market structure, the possibility of backstop resources, and so forth. Some authors have acknowledged the validity of the Hotelling rule but have stressed that there are factors that may cause prices not to rise at the same rate as the interest rate. The literature introduces a number of factors into the Hotelling model for non-renewable resources extraction aiming to arrive at a more general characterisation of the optimal royalty. Several studies have expanded Hotelling’s basic theoretical framework to allow for more realistic features.

Pindyck (1978) and Livernois and Uhler (1987) suggested that bringing new deposits into production as the result of exploration produces a U-shaped price path. Slade (1982) proposed a U-shaped price trend due to technological advances early in production and scarcity rents late in production. Similarly, Arrow and Chang (1982) proposed models of exploration that produced a saw-tooth price curve. A more complicated picture arose in Farzin (1992), who focused on the rent component of price, rather than the price itself. Cairns and Van Quyen (1998) proposed a model that combined exploration and stock effects in which the price trend is downward for most of the stock lifetime, but rises to the choke price at the end.

Slade (1984) developed a model for assessing the effects of taxation on resource extraction for a vertically integrated extractive firm incorporating various sorts of taxes and subsidies at different stages of production. After estimation of a US copper-mining firm which had only one mine, the solutions were compared with those solutions in tax-free situations with respect to the magnitude and time pattern of distortions. He showed that taxation affects the extraction path and cumulative ore extraction as well as cumulative metal production. Only the first effect can be observed. However, in practice, the latter two effects dominate. Moreover, taxies and subsidies can change ultimate ore extraction and metal processing intensities in opposite ways depending on the stages of production at which the tax is imposed.

Krautkramer (1990) developed a model for examining the effects of taxation on resource depletion when ore quality varies within deposits and ore quality selection is constrained. He concludes that tax policy is less conserving of the resource when ore quality is heterogeneous within deposits. In particular a constant severance tax can induce faster

40 depletion, reduce the life of the mine and increase the production of metal when extraction is feasible. The simple Hotelling rule was derived under the assumption that resources can be extracted at zero cost. Sinclair (1994) argues that this may be an acceptable approximation in the case of oil-abundant countries like Saudi-Arabia, but in the case of oil drilling in the North Sea or Alaska, extraction costs are clearly different from zero. Therefore, it may be reasonable to allow for positive marginal extraction costs. Specifically, we assume that extraction costs are proportional to output, so marginal costs (MC) are constant.

Gaudet et al. (1995) considered the effects of asymmetric information on extraction costs and analysed optimal non-renewable resource royalty contracts (payment and extraction path). They showed the asymmetry of the information constraints the government’s effort to recuperate the resource rent via a royalty payment imposed on the firms exploiting the resource. In comparison with full information extraction, when the resource stock is required to be exhausted in two periods by optimal contracts, information asymmetry decreases the production in the first period for all types of firms except the most efficient. Moreover, even the output of the lowest cost firm is distorted when exhaustion in two periods is not warranted.

Krautkraemer (1998) presents theoretical extensions to the Hotelling model to take into account variable stock levels due to exploration, cost of capital, capacity constraints, ore quality, and market imperfections. Krautkraemer (1998) was able to make general statements about the stock cost term by breaking the base case into a benefit term and a cost term, but did not carry the theoretical development into the extensions. Technical progress can thus explain a U-shaped price development, where prices are at first falling and then rising over time (Krautkraemer, 1998). Perman et al. (2003) analysed the effect of revenue tax or subsidy on resource royalties. They showed that imposition of revenue tax (revenue subsidy) is equivalent to an increase (decrease) in extraction cost. Therefore taxies and subsidies can change ultimate ore extraction in opposite directions. In contrast to revenue tax, revenue subsidy may lead to lower initial gross price and shorten the time to exhaust the stock.

André and Smulders (2004) presented a model with endogenous technological progress in extraction, which also produced a U-shaped price path for non-renewable resources. The principal barrier to theoretical expansion of the Hotelling model is that dynamic optimisation is difficult to characterise in general terms. Hotelling found it necessary to resort to specific demand functions in order to explore implications of the base, costless model. Managi et al.

(2005) tested the impact of technological change on offshore oil and gas exploration- discovery and of drilling cost in the Gulf of Mexico from 1947 to 1998, both at field level and at regional level. They used the number and significance of technological innovations as a proxy for technological change. The results showed that technological change had played a very significant role in increasing reserves and lowering cost over the past 50 years. (Livernois, 2009) notes that the Hotelling model becomes complex when extended to include factors like resource degradation.

Particularly in oil markets, the shortcomings of the Hotelling approach are evident as for over 100 years real oil prices were basically constant, in marked contrast to the prediction that rents should rise at the rate of interest (Mason and Veld, 2013). A number of explanations have been offered, including the steady flow of newly found deposits and technological advances that might have continually shifted the price path out, thereby obscuring what would otherwise have been the trend towards higher prices. While these aspects are no doubt important the conventional explanation misses what we believe to be a crucial ingredient, namely production constraints that inhibit agents' ability to shift production forward in time (Mason and Veld, 2013).

Taken at face value, rejection of the empirical validity of the theory of exhaustible resources would imply that normative conclusions drawn from the theory’s predictions of market outcomes have little or no practical relevance (Halvorsen, 2008). There are three plausible explanations for the negative results. First, the econometric studies are subject to criticism in terms of the quality of the available data and the necessarily large number of maintained hypotheses (for example, Berck, 1995). Second, even if these problems did not exist, econometric studies are necessarily conducted on ex-post data that reflect uncertain events that could not be anticipated by market participants, including shocks to demand, input prices, reserve estimates and technology. Even if the Hotelling rule provides market participants the best available prediction of future resource prices, unanticipated changes in expectations due to the arrival of information will cause the actual time paths of resource prices to deviate from the Hotelling predictions (Swierzbinski & Mendelsohn, 1989). Third, the net price, or user cost, for the exhaustible resources considered in the econometric studies may be too small to dominate the decisions of the resource-owning firms. For example, the average user cost for nickel has been estimated in three studies applying different methodologies to similar data.

3.2.1.2. Hartwick rule

The Hartwick rule, in contrast, was formulated for a production economy where consumption at any point of time t depends not only on the extraction of natural capital but also on the stock of man-made capital available at t . Hartwick (1977) showed that, given the Hotelling rule as condition for local efficiency, a zero value of aggregate net investment will entail constant consumption over time. This result was the heart of what was later on called the Hartwick rule. Hartwick’s rule – that continuously zero net investment in human-made capital and natural resources in a dynamically efficient economy results in continuously constant utility – has been extensively developed since its first appearance in Hartwick (1977). Hartwick (1997) suggested that a (continuously) zero net investment rule leads to constant utility in the context of PV-optimal development, but did not note that such development produces a utility path which is generally not constant. He used a PV-optimal control problem to derive the Hotelling-like asset price rules used in the proof, but the rules also come from a maximisation exercise like above with general, unspecified discounting.

Hartwick’s rule states that if on an efficient path the value of net investments is zero at each point in time, then utility is constant. This rule was established for a very general class of models in an elegant and important piece of work by Dixit et al. (1980). In one consumption a good economy endowed with two stocks, a stock of an exhaustible non-renewable resource and a stock of man-made capital, Hartwick’s rule means that if the accumulation of man-made capital always exactly compensates in value for the resource depletion, then consumption remains constant at the maximum sustainable level. The Hartwick rule (Hartwick 1977; Solow 1986) offers a rule of thumb for sustainability in exhaustible-resource economies – a constant level of consumption can be sustained if the value of investment equals the value of rents on extracted resources at each point in time.

Hartwick showed that, if resource rents were reinvested in physical capital according to Hartwick’s rule, consumption could be sustained. The Hartwick rule illustrates the quantity of investment in produced capital that is required to accurately counteract falling reserves of exhaustible resources. This investment should be undertaken to ensure that the standard of living of future generations does not fall as the society moves into the future. One way to come up with a sustainable consumption and extraction path for an economy is to accrue produced capital adequately so that the pinch of the shrinking non-renewable resource stock is accurately countered by the services from the enlarged produced capital (Solow, 1974). Hartwick's rule – often abbreviated as "invest resource rents" – requires that a nation invest

43 all rent earned from exhaustible resources currently extracted, where "rent" is defined along paths that maximise returns to owners of the resource stock (Seierstad and Sydsæter, 1987). The rule extends to the case of many types of capital goods, including a vector of stocks of natural capital.

For countries dependent on such wasting assets, this rule offers a prescription for sustainable development, a prescription that Botswana, in particular, has followed with its diamond wealth (Lange and Wright 2004). Applying the standard Hartwick rule as development policy would be extreme. It implies a commitment to zero net saving for all time. Conversely, the constant genuine saving rule embodies a commitment to building wealth at each point in time. In a risky world this may be a more palatable development policy. The savings rules presented here are appealing in their simplicity. Maintaining a constant positive level of genuine saving will yield a development path where consumption grows without bound, even as exhaustible resource stocks are run down. The real world is more complex. Poor countries place a premium on maintaining consumption levels, with negative effects on saving – the alternative may be starvation. At the same time financial crises, social instability, and natural disasters all have deleterious effects on saving. Holding to a simple policy rule in such circumstances would be no small feat.

3.2.1.2.1 Empirical validity of the Hartwick rule The Hartwick rule is seen as one of the most important classical views on environmental economics. Hartwick’s rule became so attractive because it gave an extension to a basic message of neoclassical resource economics (Solow (1974): Exhaustible natural resource inputs can be substituted by manmade capital in a way that depleting these natural resources does not harm future generations. Substitutability between natural and man-made capital thus, in spite of the exhaustibility of natural resources, may allow for equitable consumption for all generations, and Hartwick (1977) seemed to have found the investment policy that would bring about sustainability in this way.

However, doubts have been raised concerning the true status of Hartwick’s results and thus of the Hartwick rule. Following Asheim (1994) and Pezzey (1994) it has been claimed that the Hartwick rule is, contrary to the first impression, not a prescriptive but rather a descriptive rule (Toman, Pezzey & Krautkraemer (1995:147). But the wording of the investment policy underlying the Hartwick rule undoubtedly gives a prescription. And even if one tends to see the Hartwick rule as a description, it is not exactly clear what is described by it. More than 20 years after Hartwick’s pioneering work everyone in resource economics will have some

44 understanding of the Hartwick rule, but astonishingly there is no real consensus on what the Hartwick rule in fact is. This is partly a semantic problem, which can be solved by more precise formulations, including all specific assumptions. Beyond that, however, the ambiguous status of the Hartwick rule has also led to false beliefs concerning the material content of the rule. In order to give a correct interpretation of the Hartwick rule, we will confront two myths on this rule that are pertinent in the literature.

Hartwick (1977) concentrated his attention on economics where substitution of man-made capital and resource extraction is feasible. In the wake of his contribution an impression appears to have been formed to the effect that the Hartwick rule for sustainability requires that man-made capital can substitute for natural capital; i.e. that the production possibilities are consistent with the beliefs held by the proponents of ‘weak sustainability’ (the citation from Spash and Clayton (1997) reproduced in the introduction). If, on the other hand, natural capital has to be conserved in order for utility to be sustained (the world is as envisioned by the proponents of ‘strong sustainability’), then – it is claimed – the Hartwick rule for sustainability does not apply.’ Becker (1982) suggested that Hartwick’s rule could be enforced by governments permitting borrowing and lending of consumption at an interest rate equal to the (varying) utility discount rate that supports constant utility, but he did not investigate the detailed mechanisms of such a policy. How intergenerational equity can be achieved was examined under different scenarios, and especially of interest to us is the economy with exhaustible resources (Solow; 1974 and 1986).

Hanley (1995) notes that the criticisms of the Hartwick rule are twofold. First, consumption may not be the only input in the utility function. For example, if appreciation of aesthetic natural scenarios is included in utility functions, then non-declining consumption may not necessarily lead to non-declining utility. However, there are no compelling reasons for us to believe that appreciation of aesthetic natural scenarios should be included in the utility function as much as it should not be included. The second criticism is that natural and man- made capital may not be as substitutable as assumed in the model. This is especially true when we are referring to ecosystem services such as natural floodplains, oxygen cycle, etc. (Perman, et al., 2003). The Hartwick rule is a particular case whereby there is no technological progress and constant population. Hence the result of "invest all rents from natural capital into renewable capital" only suffices in illustrating the usefulness of the Hartwick rule in this type of economy. A more general version of the Hartwick rule is needed

45 to explain for the increasing per capita consumption the world has experienced (Maddison, 1995).

3.2.1.3. Herfindahl rule

The Herfindahl rule states that extraction of identical deposits of a non-renewable resource should be in the order of their unit costs of extraction (Herfindahl (1967), Solow and Wan (1976), Lewis (1982). In the theory of non-renewable resources, Herfindahl’s rule states that a resource firm should extract deposits of a resource in the order of unit extraction costs (Herfindahl, 1967). Even with multiple non-renewable resources (not deposits of the same resource) the extraction profile is determined exogenously according to the sum of extraction and conversion costs for each resource (Chakravorty, et al., 2005). It applies to the case of multiple non-renewable resources, such as oil, gas and coal, with extraction costs that can unambiguously be ordered. It says that the cheaper resource will be depleted before the more expensive one is taken into exploitation. Moreover, this is optimal from a social welfare point of view if there are no externalities, such as the greenhouse effect. Hence, in the case at hand, the cheaper oil is extracted before the expensive solar energy is taken into production.

If the resource-extracting industry is perfectly competitive, and deposits differ only with respect to marginal extraction costs, which are assumed to be independent of extraction rates, it can be shown that the order of extraction must obey Herfindahl’s rule: exhaust the least-cost deposit before moving on to the second lowest-cost one, and so on. The equilibrium price path is continuous even at points of transition from one deposit to the next. There are exceptions to this rule. If there are constraints on labour supply, and if the economy also has a renewable resource, with higher labour requirement per unit of extraction, the optimal order of extraction may not follow Herfindahl’s rule (Chakravorty, et al. 2005). Within limits, the order of extraction can be a matter of indifference. Another exception is that if a set-up cost must be incurred before one can exploit a deposit, it is no longer the case that the price path is continuous. In fact, the price will jump down each time after the set-up cost is incurred. The general time path of price can thus display the saw- tooth pattern (Hartwick, Kemp and Long, 1986). Herfindahl’s rule is based on the assumption that deposits differ only with respect to their marginal extraction costs. If they differ in other dimensions as well as in marginal costs, it is clear that the rule must be modified. One kind of cost which is not included in the standard definition of marginal cost is the potential of supply interruption.

3.2.1.4. Applicability of the weak sustainability theories: From a South African perspective

In South Africa the question has been on natural resources such as gold and has focused on who should extract them rather than on the sustainable extraction path. In other words the whole issue of mineral resources has been politicised so that the issue of optimum extraction is neglected. However it should be noted that although politicising the issue of natural resources is justifiable, the issue of finding a sustainable extraction path and use of mineral resources such as gold is equally important. There is a strong need to give regard to intergenerational equity. However, the question that arises is how South Africa can find a sustainable extraction path of mineral resources such as gold. Will the weak sustainability theories offer a sustainable extraction path? This question will be answered through the testing of the Hotelling rule.

Strong sustainability theories

This section presents the theories that fall under the strong sustainability view. Strong sustainability theories aim to ensure sustainability of human well-being in a more direct way. This view maintains that environmental sustainability, as maintenance of the services most fundamental to human life and well-being must be ensured as a first step by limiting the depletion and degradation of the environment to within levels at which essential environmental services can be maintained (Mason and Markandya, 2004). The section presents two strong sustainability theories; the Marxism approach and the non-declining stock of capital approach.

3.2.2.1. Marxism

The environmental Marxist perspective questions the very possibility of an environmentally sustainable capitalist economy, arguing that economic growth relies upon exploitation of natural and social capital and the avoidance of wealth redistribution (or equity) both at the national and international level (GovScot, 2015). Therefore, by its very nature, capitalist development does not foster the goals of environmental sustainability, cultural diversity or more equitable social development where poverty is eradicated. The Marxian understanding of the environment-economic relationship is crucial for a complete discussion of the ecological destruction occurring in society today. Several theories in environmental economics do not challenge the basic premises of capitalism, and as such the solutions offered by these approaches cannot ameliorate the ecological effects of the system (Summers, 2006). For Marx and his followers, to understand the specificity of ecological

47 destruction in society, it is necessary to examine the historical materialist conditions, modes of production/reproduction, and the nature of capital within society.

In the Marxian analysis of the environment-economic relation, nature and society cannot be viewed as two independent bodies. Rather, they must be viewed as co-evolutionary, each changing the other in a dynamic process. For Marx and Marxists, the way humanity treats the environment is formed through social and historical forces. With respect to the environment-economic relation, historical materialism contends that social and economic life takes on a specific form based on the dynamic interrelation of the contextual conditions, resource materials, energy sources and unintended consequences in the environment where social-economic forms develop (GovScot, 2006). Thus, each form of social and economic life must be understood in terms of its own specific conditions and limits. What differentiates humans from other species is that human’s master nature through labour, and labour is applied by humans in order to produce their means of subsistence.

Humans create their own distinct historical relation and understanding of nature through production. For Marx, humans also act through the material praxis creating a distinct human- nature relation so that they can transcend the alienation from nature they experience when producing their means of subsistence (Steger, 2005). Contemporary Marxists have applied Marx’s historical materialism to the ecological crisis and assert that the current stage of history is characterised by structural forces that systematically degrade and exceed the capacity of nature, thus setting into motion ecosystem breakdowns.

For Marxists the ecological crisis is not just a crisis of nature, but also a crisis of society, created by the specific structures of production and reproduction applied by contemporary society (Fotopoulos, 2007). Relating to Marx’s co-evolutionary approach, contemporary Marxists argue that humanity is not just the perpetrator of the crisis but is also a victim of the crisis, evident in instances of malnutrition, social alienation, and the systematic poisoning of the very environment on which humans depend. For Marx and Marxists, capitalism was and is a specific historical form. Moreover, antagonism to nature is a specificity of capitalism that can be demonstrated by studying the spheres of production and reproduction, notions of value, and the nature of capital as they occur in capitalism. For Marx and Marxists, production is part of the economic dynamic that develops under specific historical forms. Capitalist production is specific from other forms of production since it rests upon a specific structure of exploitation and appropriation, made possible by various historical forces (Fotopoulos, 2007). In particular, capitalism relies on a system of private property which

48 increasingly removes the natural resources from the land. Nature has been placed in the hands of private property owners, whose main purpose of ownership was to pursue profits. Castro (2004) develops this position from 'an environmental Marxist' perspective, arguing that sustainable development as it is currently defined in the present literature is basically economic growth on capitalist terms.

For Marxists the solution to the existing ecological crisis is markedly different from that of the other schools of political economic thought. First, Marxists condemn the assumption that capitalism is part of human nature. Marxists assert that capitalism is a specific historical and social form which relates to a specific understanding of material conditions (Fotopoulos, 2007). An understanding of how society conceives and connects to nature is fundamental to changing the processes by which ecologies are destroyed. Secondly, since the ecological crisis is rooted in the social spheres of existence, the solution must involve the transformation of the historical relationship between humans and nature to a relation between nature and society which is ecologically sustainable (Steger, 2009). The struggle for ecologically rational production must be part of the struggle to overcome capitalist exploitation and the capitalist expression of nature and labour in the commodity form.

3.2.2.1.1 Empirical validity of the Marxist approach With respect to the environment, eco-socialism, Marxism and Marx have all been criticised from external economic approaches. These criticisms are largely based on the evident and obvious failure of the communist states with respect to the environment. These critics claim that the 70-year socialist experiment of Russia and the 45-year experiment of Eastern Europe were disastrous for the environment, leaving a legacy of excessive land and air pollution and insurmountable damage to waterways such as the draining of the Aral Sea and nuclear pollution in the White Sea (Fotopoulos, 2007). Thus, critics claim that Marx, by focusing on contradiction, was led to an overly optimistic environmental view of the classless society arising out of revolution. There are many counterarguments to present against this naïve criticism of Marxism. One counterargument is that the Soviet Union was not an unadulterated application of Marxist ideology (Kaika, 2006). The Soviet states and the communist states which exist today ignore a fundamental element of Marx—that free development is a necessary condition for the realisation of a classless society. None of the communist states to date had freedom as a criterion of their political systems. Thus, the ecological destruction prevalent in these states probably has less to do with socialism and

49 more to do with the fact that the governments, who ran and run theses states, totally neglect the needs of their society and place supply-side production targets above all else.

3.2.2.2. Non-declining natural capital stock approach

Another different approach to the limited degree of substitutability between natural capital (Kn) and man-made capital (Km) is that of the approach suggested by Pearce et al (1996). Here the view was taken that, whilst some substitution is possible between certain elements of natural capital and human capital (for example, better machinery, meaning that less raw materials are used to produce certain products), many elements of natural capital provide non-substitutable services to the economy. The idea here was that, if it is necessary to maintain some amount of the natural capital stock constant in order to allow future generations to reach the same level of utility as the average held by this generation, this holding constant of the natural capital stock becomes a rule for sustainable development (Envis, 2016). The three views for holding Kn constant were: (1) the existing level, (2) the level consistent with maintaining the critical element of Kn, (3). A rule for sustainable development suggested preventing reductions in the level of Kn below some constraint value. If natural capital were held constant in physical terms, the level at which the category is defined will become all-important. All the three alternatives, however, assume that we can measure the value of Kn at any point of time; in other words that the different elements of Kn can be aggregated together in comparable units (Pearce at al. 1996).

3.2.2.3. Applicability of the strong sustainability approach in South Africa

The strong sustainability approach to resource extraction seems attractive to the current state in South Africa where mineral resources are being depleted at faster rates. Strong sustainability theories require the preservation of the integrity of all natural resources. However, it has some limitations because South Africa is still developing and it requires mining to boast economic growth and development. In the South African context, the social development agenda is dominated by the need to address the vast socio-economic disparities between income levels, employment levels, basic services provision, health and nutrition, and skills and education levels. Currently, the funds that are channelled for the public good are derived from an unsustainable growth path that will result in the faster erosion of critically threatened resources, and an economy that is unable to adapt to its limits to growth.

3.3. EMPIRICAL LITERATURE

In this section of the study a brief empirical literature review relating to the empirical significance of the Hotelling rule is presented. This review is intended to show a critical analysis of previous work in the area of exhaustible resources and the Hotelling rule, the methods of analysis used, the spectrum of issues covered and the vacuum in terms of what remains to be explored in the literature. Empirical literature can play a critical role by practically examining the validity of theories as well as testing the applicability of economic theories in the world. Empirical literature also offers reasons why some theories do not hold in certain circumstances. More precisely, empirical literature can scrutinise the theoretical setting and show a clear picture. After discussing the different theories of modelling exhaustible resources, it is important to focus on dealing with previous studies carried out to investigate the Hotelling rule in different countries. This is the focus of this section.

The task of literature scrutiny is to develop a well-founded judgement that can guide to a reasoned decision on the issues of the optimum extraction path and sustainability. The judging process takes place with due consideration of the studies that were done to test the Hotelling rule and to find a sustainable extraction path. This section will first investigate the studies that tested the Hotelling rule. The section will also explore the determinants of gold price. It is common knowledge that the price of gold is not determined only by the interest rate. It is therefore worthwhile to examine the factors that influence the price of gold.

Findings from studies

Barnett and Morse (1963) collected time series data on the price of a resource and explored whether the proportionate growth rate of the price is constant. The results indicated that resource prices including iron, copper, silver and timber fell over time, which is a disconcerting result for proponents of the Hotelling rule. Pindyck (1978) demonstrated that optimal exploratory activity and production were simultaneously determined in the context of a continuous-time model under certainty. He considered that potential resource reserves were unlimited. A conclusion was reached that the price paths will be U-shaped, because when the initial reserves endowment is small, at first production will increase as reserves are developed, and later it will decline as both exploratory activity and the discovery rate fall. For non-renewable natural resources exploitation, government as the owner of the resource (called the principal) will delegate the extraction of the resource to a firm or firms (called the agent). If both the government and the delegated firm can perfectly observe the resource price and the extraction costs, the observed extraction path will satisfy the Hotelling rule of

51 non-renewable resources' optimal extraction. Then the royalty schedule must induce the mining firm to deplete the mine in a way that marginal net benefits increase at the rate of interest (Gaudet et al., 1995).

Slade (1982) examined the effect of technological change on the exhaustible-resource industry particularly on market prices. The author argued that marginal extraction costs fall over time as technology improves thereby market prices can fall early on when scarcity rents are small. However, as reserves deplete, prices eventually rise and the price path is U- shaped. Similarly, Arrow and Chang (1982) proposed models of exploration that produced a saw-tooth price curve. Livernois and Uhler (1987) suggested that bringing new deposits into production as the result of exploration produces a U-shaped price path. Fortune (1987) related the expected interest rate to the price of gold, assuming that interest-bearing bonds are a substitute for gold. An expected increase of interest rates causes a negative adjustment in the price of gold, since it is relatively more worthwhile for individuals to sell gold and obtain assets with higher interest rates. This hypothesis is supported by their results. While central banks can circumnavigate this problem of foregone interest on gold by using lease constructions, the author finds a significant negative relation between the expected interest rate and the price of gold. Cairns and Quyen (1998) proposed a model that combined exploration and stock effects in which the price trend is downward for most of the stock's lifetime, but rises to the choke price at the end.

Agbeyegde (1989) used the CAPM model to test the interaction between prices and non- renewable resources. The study constructed an arbitrage model for copper, lead, tin and zinc and show that changes in interest rates are likely to determine the resource price. Halvorsen and Smith (1991) examined the Canadian metal mining industry on an aggregate level and used a generalised Cobb-Douglas cost function as well. They strongly rejected the Hotelling rule. They suggested further research on disaggregated data and uncertainty in a world of imperfect arbitrage. Moazzami and Anderson (1994), estimated an error-correction model and found evidence of U-shaped price paths, whereas Berck and Roberts (1996), who estimated both difference and trend–stationary models, found evidence of U-shapes under the former but not the latter.

Chermak and Patrick (1997) examined the market for natural gas in the US using monthly data from 29 tight gas sand wells. They employed a generalised Cobb-Douglas cost function, giving monthly costs as a function of gas produced, remaining reserves and a time trend. They also allowed for cost differences between firms. They found that the Hotelling

52 rule cannot be rejected for high interest rates, which, as they argue, might be applicable to the firms under consideration. For further research they suggested to incorporate uncertainty into the firm’s decision problem. Banks (2004) found evidence that rejected the Hotelling rule; findings from the study concluded that the Hubbert Curve Approach was much more relevant in explaining the behaviour of prices of non-renewable resources than the Hotelling rule. Andre and Smulders (2004) provided extensions of the Hotelling rule and they proved that the Hotelling rule was relevant.

Livernois, Thille, and Zhang (2006) examined old-growth timber, which is non-renewable, and use stumpaged price bids in timber auctions as their measure of shadow prices. Their structural tests were fairly supportive of Hotelling’s model. Gaudet (2007) investigated US price data for the period 1870–2004 for copper, lead, zinc, coal and petroleum, 1880–2004 for tin, 1900–2004 for aluminium and nickel and 1920–2004 for natural gas and plotted the rate of change of price of each of those seven non-renewable minerals and three non- renewable fossil fuels. Findings showed high volatility in the rate of change of those prices. But more significantly, this volatility appeared to be centred at zero. In fact, in none of the ten cases was the mean rate of change of price significantly different from zero. It was very hard to detect any trend in the actual price levels of those resources. All in all, there was no clear picture of whether resource prices typically rose or fell over time. This neither supported nor rejected the Hotelling rule.

Chakravorty, Leach and Moreaux's (2009) results suggest that in the long run, resource prices may exhibit significant structural variations driven by regulatory policy and market forces that may result in alternating phases with secular upward or downward price movements. They found that resource prices are stationary around deterministic trends with structural breaks in slope and intercept. In other words, prices may show upward and downward trends, these trends broken by the endogenous structural breakpoints. They may not just be rising or falling, as predicted by the textbook Hotelling model. Specifically, their results suggested that the same Hotelling model, when subjected to regulation and learning effects, may predict alternating bands of rising and falling prices, and not a secular trend as is commonly assumed. In this sense, the results obtained had a direct bearing on the literature that aimed to empirically verify the predictions of the Hotelling model. It suggested that testing for a secular trend in prices may be akin to testing a misspecified Hotelling model. The main implication of their results is that testing for secular price trends as predicted by the textbook Hotelling model may lead to incorrect conclusions regarding the

53 predictive power of the theory of non-renewable resource economics. Mason and Veld, (2013) found that in oil markets, the shortcomings of the Hotelling approach are evident. For over 100 years real oil prices were basically constant, in marked contrast to the prediction that rents should rise at the rate of interest (Mason and Veld, 2013). A number of explanations have been offered, including the steady flow of newly found deposits and technological advances that might have continually shifted the price path out, thereby obscuring what otherwise would have been the trend towards higher prices.

Determinants of gold price

This research is intended to examine the driving forces of the gold price. By exploring the determinants of the gold price, this study can bring an explanation of what is driving the gold price. This will assist in validating the Hotelling rule. If interest rates are seen to be influencing the gold price, then the Hotelling rule would be valid. Exploring factors that influence the gold price will also assist in developing a model for this study. The study will modify the models used in previous studies to develop its model. The section will therefore explore the determinants of the gold price. There are several macroeconomic variables that influence the gold price. Various studies have shown that there are other determinants of gold price. These studies will be discussed in this subsection.

Investors and central banks view gold as an inflation hedge (Christie-David et al., 2000; Faugere & Van Erlach 2006; Starr & Tran, 2008; Theal, 2009; Tkacz 2007). These gold holdings are especially useful in emerging countries whose economic situation can be highly uncertain. Empirical research supports this hypothesis (Starr and Tran, 2008). Faugere and Van Erlach (2006) hold that the yield of gold must vary inversely to the yield of a portfolio of other assets, to provide a hedge against price fluctuations of other assets. The data of Ghosh et al. (2004) supports the idea of gold being a long run inflation hedge. While rising income could indicate expected inflation and an increase in gold prices, Starr and Tran (2008) did not find a significant relation between the two. Christie-David et al. (2000) studied the effects of announcements on the price of gold. Their results suggest that the gross domestic product and the producer price index are positively related to the price of gold, which might be the result of investors looking for an inflation hedge.

Fortune (1987) related the expected interest rate to the price of gold, assuming that interest- bearing bonds are a substitute for gold. An expected increase of interest rates causes a negative adjustment in the price of gold, since it is relatively more worthwhile for individuals to sell gold and obtain assets with higher interest rates. This hypothesis is supported by their

54 results. While central banks can circumnavigate this problem of foregone interest on gold by using lease constructions, the author finds a significant negative relation between the expected interest rate and the price of gold. Sjaastad and Scacciavillani (1996) looked into the effects of exchange rate movements in accordance with the gold price which is usually denominated in US dollars. They found significant price movements of gold as an effect of exchange rate movements. Also, gold demand tends to be negatively related to US dollar exchange rates. This, since gold becomes less expensive to non-US denominated countries when the US dollar depreciates against other currencies (Tully and Lucey, 2005).

There is an arbitrage relationship (see Levin, Abhyankar and Ghosh, 1994) that drives the physical interest rate (the gold lease rate) into equality with the real interest rate. Theoretically, in equilibrium, a mine is indifferent between extracting gold now and selling the mined gold now, and leasing gold now, selling the leased gold now, investing the proceeds of the sale in a bond, selling the bond in one year and using the proceeds including interest to pay for extracting the gold plus the physical interest rate. If the cost of extraction rises at the general rate of inflation, the gold lease rate is equal to the real interest rate. The gold lease rate, therefore, can be used as an empirical proxy for the real interest rate in the empirical analysis of the short-run gold price. The theoretical analysis of the short-run gold price implies that there will be fluctuations in the gold price caused by political and financial turmoil as well as changes in real interest rates and the beta for gold that will cause divergences from the long-run inflation hedge price.

Keyfitz (2004) and Capie, Mills, and Wood, (2004) established that fluctuations in exchange rates have a significant effect on the gold price. Sjaastad and Scacciavillani (1996:884) found that, for the period 1982–1990, "European countries heavily dominate the international market for gold and hence movements in European exchange rates against the US dollar impact heavily on the dollar price of gold." Capie, Mills, and Wood (2004) examined the relationship between gold, and exchange rates of various currencies against the dollar and how well gold has performed as a hedge, with respect to exchange rate fluctuations. This paper revealed that there is a negative correlation, which is not statistically significant, between the gold price and the dollar exchange rate.

Sjaastad and Scacciavillani (1996) looked into the effects of exchange rate movements in accordance with the gold price which is usually denominated in US dollars. They found significant price movements of gold as an effect of exchange rate movements. Also gold demand tends to be negatively related to US dollar exchange rates. This is since gold

55 becomes less expensive to non-US denominated countries when the US dollar depreciates against other currencies (Tully and Lucey, 2005). Ghosh, Levin, Macmillan, and Wright (2002) examined the short- and long-term determinants of the gold price. Their main findings revealed that gold is mostly an inflationary hedge in the long run. Furthermore they state that the short-run price fluctuations in the gold price are due to changes in the real interest rate, US dollar exchange rate, and the leasing of bullion by central banks, all of which, according to Ghosh et al. (2002:1), "can disturb this equilibrium relationship and generate short-run price volatility".

Levin and Wright (2004) attempted to identify key determinants for the price of gold. They used cointegration techniques and they found a positive relationship between the US price level and the price of gold in the long run. They found the same result in the short run; a direct positive link was revealed between the US price level and gold price. The study also applied an error correction mechanism and it was found that the price of gold and the US price level moved together in the long run.

3.4. OVERALL ASSESSMENT OF LITERATURE

An analysis of the theories above showed that economic theory offers some guidance concerning the principles of non-renewable resource allocation over time. All of the theories that were discussed above are relevant to this study. The chapter showed that there are two views to addressing the issue of resource extraction and use. These two views have been called weak and strong sustainability, respectively. The main distinction between weak and strong sustainability lies in the extent to which environmental resources are assumed to be substitutable by other types of asset.

The fundamental debate regarding sustainable development is whether we choose to adopt a strong or a weak conception of sustainability (Pelenc, Ballet & Dedeurwaerdere, 2015). Although the difference between them led to a heated debate, there is a place for both of them. Some resources must fall under the requirement of strong sustainability, others under the weak variety. Which of the two it is will depend on the degree to which they can be substituted by capital. The depletion of fossil fuels, for instance, is an issue of weak sustainability: provided other sources of energy are developed instead, we are not obliged to leave our descendants an undiminished stock of petroleum. An extinct species, on the other hand, cannot, at the current state of scientific knowledge, be recovered, and must therefore be considered a loss in terms of strong sustainability (Kuhlman and Farrington.

2010). However the question that arises in this study is where gold can be classified in this case in the South African context.

This question is essentially empirical, and little empirical work has been done on substitutability. Most of the work that has been done has focused on substitutability between capital, labour and energy. Depletion of resources, breaking down of ecosystems and species extinction can be compensated for if this takes place in a process that supports opportunities for continued maintenance or expansion of economic opportunities. Weak sustainability postulates the full substitutability of natural capital whereas the strong conception demonstrates that this substitutability should be severely seriously limited due to the existence of critical elements that natural capital provides for human existence and well-being. However, the strong and the weak sustainability aim at achieving constant consumption overtime.

The theory (Hotelling rule) that this study wants to test fall under the weak sustainability theories. The Hotelling theory has contributed to the economics of non-renewable resources. It has formed the conceptual and theoretical framework used by economists to model the supply and the prices of non-renewable resources. More so, it has contributed to the conservationist movement. However, studies seem to see the Hotelling theory, though elegant, as somewhat misplaced. These studies claim that the model points out to a rise in trajectory of net prices of non-renewable resources along with the rate of interest yet there is a lack of empirical evidence to back this pricing behaviour. Moreover, the assumption of an increase in scarcity of non-renewable resources is highly debatable.

The studies consulted in this empirical literature review section are a sample of the variety of investigations applied to the Hotelling rule. The literature reviews showed that there are mixed views regarding the applicability of the Hotelling rule. The empirical failure of the Hotelling rule has been credited in part to technical changes. On the one hand, new techniques and processes may obtain synthetic substitutes for non-renewable resources. On the other, improvements in technology may facilitate more efficient exploration and production, thereby potentially offsetting the depletion effect on resource prices. Hotelling (1931) established several economic assumptions for his extractive model for natural resources that simply do not reflect truth in the real world of minerals extraction. In response to this contrast, many economists and researchers tried to bridge this gap by plugging in more variables to see their influence on resource price.

These studies argue that the failure of Hotelling's rule to predict price behaviour has been attributed to the restrictiveness of many of its underlying assumptions and may not reflect any inconsistency with intertemporal optimisation. Several of these assumptions – no extraction costs, known reserves, no technological change – were examined. Possible explanations for the lack of a trend in prices, such as changes in demand, discoveries of new reserves, and technological change were explored in this section.

However, there are other studies that found that the Hotelling rule is valid and applicable in several countries. They believe that the Hotelling rule predicts the behaviour of exhaustible resources. Empirical literature above showed that researchers, looking at different resources or different time periods, have come up with a variety of results. There is no clear picture of whether resource prices follow the Hotelling rule. It was found that very little has been done in developing countries on the relevance of the Hotelling rule. It can thus be said that the ability of the theory of exhaustible resources to describe and predict the actual behaviour of resource markets remains an open question in countries in the developing world, like South Africa. In light of this, this study makes an attempt to validate the Hotelling rule (and other associated parts of resource depletion theory) within a South African context. To the study’s knowledge; this is the first study to investigate the validity of the Hotelling rule in South Africa.

3.5. CONCLUSION

Summarising the results of the above-mentioned literature, the study comes to the following conclusions: (a) there are various schools of thought that seek to establish the sustainable extraction of natural resources; (b) there seems to be no settled opinion with regard to the optimal extraction of natural resources; (c) the Hotelling rule has been tested empirically but there is no settled opinion as to whether it is relevant in the mineral sector; (d) furthermore there is no previous study that has attempted to examine the applicability of the Hotelling rule in South Africa.

CHAPTER 4 METHODOLOGY

4.1. INTRODUCTION

This chapter provides the methodology employed in achieving the main objective of this study – to test the relevance of the Hotelling rule. The chapter justifies the selection of the particular methods of data collection, by discussing how the previous research supports their use (either theoretically or practically), for obtaining data about the research question of the study. The structure of this chapter will be as follows: Section 4.2 provides the rationale for choosing the selected research methods. Section 4.3 discusses the research techniques used to achieve the study’s objectives. Following that, Section 4.4 identifies the descriptive tests that were used. Then Section 4.5 which discusses the procedures used in hypothesis testing and structural modelling. Lastly, Section 4.6 concludes the chapter.

4.2. RATIONALE FOR THE METHODOLOGY

The study employed several methods to test the applicability of the Hotelling rule. Type of methodology influences the results so it's better to use different methodologies and then compare the results (Slade, 1997). The study also used different estimation techniques to minimise (if not eliminate) the problems that are faced when estimating the Hotelling rule. These problems include:

i. First, the econometric studies are subject to criticism in terms of the quality of the available data and the necessarily large number of maintained hypotheses (Halvorsen, 2008). ii. Second, even if these problems did not exist, econometric studies are necessarily conducted on ex-post data that reflect uncertain events that could not be anticipated by market participants, including shocks to demand, input prices, reserve estimates and technology. Even if the Hotelling rule provides market participants the best available prediction of future resource prices, unanticipated changes in expectations due to the arrival of information will cause the actual time paths of resource prices to deviate from the Hotelling predictions (Swierzbinski & Mendelsohn, 1989).

iii. Third, the net price, or user cost, for the exhaustible resources considered in the econometric studies may be too small to dominate the decisions of the resource- owning firms (Halvorsen, 2008). iv. Measurement of the net price – obtaining scarcity rent data is a challenge for mineral resources (Livernois, 2008, Thille, 2010).

Motivated by these considerations, this study applied different estimation techniques to assess and test the relevance of the Hotelling rule. Both qualitative and quantitative methods were used to achieve the objectives of the study. To undertake this research the study employed relevant econometric methods which complement and extend those previously employed in the literature. According to Neumann (2014) four different types of testing approaches have been used in literature and these are:

i. First, there are descriptive studies which examine the price behaviour ii. Second, a specific model can be tested by estimating equations. This approach relies on econometric estimations. iii. The third approach refers to a reformulation of the Hotelling rule in the form of the HVP. This study focuses on 1 (descriptive) and 2 (econometrics estimations). The study complemented quantitative research methods with qualitative research methods by using previous work done by scholars, government, private institutions and other independent sources. Qualitative secondary sources were used to criticise and support certain arguments and they were also used to analyse the gaps that exist in literature. Qualitative secondary sources were used in Chapter 2 where the study sought to address objective one, namely to analyse the trends of gold production, depletion and gold prices in South Africa. Approximately 40 sources were consulted in the drafting of Chapter 2. All the sources were from the internet and random sampling was used to select these articles. Chapter 3 also made use of qualitative secondary sources. More than 100 previous studies that sought to investigate the applicability of the Hotelling rule were consulted. These articles were consulted and selected randomly on internet search engines.

4.3. ECONOMETRIC TECHNIQUES

The previous section highlighted that the study adopted descriptive and structural methods to achieve its objective. The tests that have been performed have mainly been of two sorts: descriptive and structural. The first class is descriptive statistics. Descriptive statistics is the

60 term given to the analysis of data that helps describe, show or summarise data in a meaningful way such that, for example, patterns might emerge from the data (Brown, 2016). Its advantage is that there is no need to commit to a specific model. Instead, one can assess which models are consistent with the data and which are not. Its shortcoming is that one cannot perform formal tests. Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made (Palaiologou et al., 2015). They are simply a way to describe data.

The second class tested a specific model by estimating some equations. Its strength is that formal tests can be performed. The study used both classes to ensure the delivery of robust and reliable results.

4.4. DESCRIPTIVE STATISTICS

Most descriptive studies have examined the behaviour of mineral commodity prices (Slade, 2009). Moreover, since the predictions of Hotelling’s model are long-run, many tests make use of a century or more of data on the prices of different fuel and non-fuel minerals. Descriptive statistics are the numerical and graphical techniques used to organise, present and analyse data. Descriptive statistics are used to describe the basic features of the data in a study. Descriptive statistics is the term given to the analysis of data that helps describe, show or summarise data in a meaningful way so that, for example, patterns might emerge from the data (Brown, 2016). They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.

The motivation for using descriptive statistics in this study is that by identifying the actual properties of the data series, it would be easier to comment on whether or not these resources are subject to increasing degrees of resource scarcity. According to Hotelling (1931) there are three things we can say about resource extraction for a finite resource:

1. Firms will always try to extract low-cost resources before high-cost resources causing resource extraction costs to increase over time. 2. In general, greater scarcity caused of in situ reserves increases the value of a resource causing the price to increase over time. 3. Since the price of a resource increases over time, then demand and production should decrease over time.

The study tested the second and third principles and descriptive statistics played a huge role in testing these principles on gold price, gold production and gold consumption. The study made use of descriptive statistics to understand the nature of gold price, production and consumption path. Understanding the nature of resource price, production and consumption paths was important for several reasons. Theoretically speaking, Ahrens and Sharma (1997) for example, note that regarding both a simple and more general Hotelling model as described in Slade (1988) "price movement is still systematic and may be modeled appropriately as a deterministic trend". In contrast, in a world with uncertainty "in which speculative motives drive the behavior of extracting firms or unanticipated events largely characterize the market, resource prices may be generated by a random walk process". Thus, knowing the correct time series behaviour of natural resource prices can be vital to testing the validity of the Hotelling rule. In order to test whether (i) the gold price increases over time and (ii) demand and production decreases over time, the study made use of visual inspection (graphical analysis), Hodrick-Prescott (HP) filter and Correlogram tests. This is discussed in the next subsection.

Visual inspection

The objective was to provide a comprehensive description of long-term trends in the gold price, and to compare this description to theoretical predictions of the Hotelling rule. Literature has examined a wide variety of specifications for the time series behaviour of prices. Much of this work is concerned with whether the trend is taken to be deterministic or stochastic. Price path that follows the Hotelling rule means that stock is just exhausted when quantity demanded drops to zero.

Studies like that of Slade used visual inspection to analyse the trends of resource prices. This study also used graphical analysis to assess the trends and time series properties of gold price and production. "Visual inspection looks for evidence of trend in mean, variance, autocorrelation and seasonality in a time series. If any such patterns are present then these are signs of non-stationarity and different mechanisms exist to turn the series into a stationary one" (Metes, 2005). Visual inspection is defined as a process of using the unaided eye, alone or in conjunction with various aids, as the sensing mechanism from which judgements may be made about the condition of a unit to be inspected (Federal Aviation Administration, 2016).

Visual inspection was done through inspecting the time series behaviour of gold price and gold production on a graph. A graph is a method of presenting statistical data in visual form. The main purpose of any chart is to give a quick, easy-to-read-and-interpret pictorial representation of data which is more difficult to obtain from a table or a complete listing of the data. The type of chart or graphical presentation used and the format of its construction is incidental to its main purpose. Some basic rules for the construction of a statistical chart are listed below: a. Every graph must have a clear and concise title which gives enough identification of the graph. b. Each scale must have a scale caption indicating the units used. c. The zero point should be indicated on the coordinate scale. If, however, lack of space makes it inconvenient to use the zero point line, a scale break may be inserted to indicate its omission. d. Each item presented in the graph must be clearly labelled and legible even in black and white reprint (University of Barcelona, 2016). All these rules were adhered to in this study to ensure that the graphs and figures plotted produced reliable and valid presentations.

The Hotelling rule’s central result is that the extraction rate of an exhaustible resource is monotonously sinking, while its price is increasing. Graphs were used to examine if extraction of gold is sinking and also to see if there is an upward trend in the gold price. Unfortunately, visual analysis is not always so clear. In fact, often the interpretation of graphs is much more ambigious. As a result, there was need for utilising multiple measures. If changes are discernible by visual inspection of the graph, confirmation that the changes are not the result of chance variations but are statistically significantly can be determined using relatively simple statistical tests. Visually ambiguous results may be clearer as well if analysed with statistical tests (Vonk, Tripodi & Irwin, 2007). In this regard the study complemented visual inspection with the Hodrick-Prescott filter, estimating growth rates and Correlogram tests.

The Hodrick-Prescott (HP)

The Hodrick-Prescott (HP) filter is a commonly used tool in macroeconomics, and is used to extract a trend component from a time series (de Jong, 2016). The Hodrick-Prescott (HP)

63 filter is the standard technique in macroeconomics for separating the long-run trend in a data series from short-run fluctuations. While it seems intuitively clear that no smoothing technique should be equally well applicable to all types of trended macroeconomic data, the HP filter is universally used in macroeconomics, and while different types of criticism can be found in the literature on the HP filter, as Ravn and Uhlig (2002) state, "the HP-filter has withstood the test of time and the fire of discussion remarkably well."

In this study the Hodrick-Prescott filter was used to identify the presence and/or absence of a trend in the gold price and gold production series. The presence of a trend in the mean can be further examined by applying a Hodrick-Prescott filter to the time series. If the result is a series that does not resemble a roughly flat, horizontal line then a trend in mean is present in the initial series. Empirics on long-term mineral price behaviour should allow for variable trends – that is, the gradual evolution in LT trends without constraining the trends to be constant (or U-shaped) over time (de Jong, 2016). Band-pass filters, which decompose an economic time series into trend and cyclical components, provides one way of doing this if the objective is data description and historical analysis, rather than hypothesis testing.

Economists have a long-standing interest in decomposing various economic time series into trends and cycles. Empirical economists often use data filters to isolate features of interest and eliminate elements that are a nuisance from the point of view of the theoretical models they are studying. Explaining how data filters work, Cogley (2007:70) notes: "The starting point is the Cramer representation theorem which provides a basis for decomposing xt and its variance by frequency. It is perfectly sensible to speak of long- and short-run variation by identifying the long run with low-frequency components and the short run with high frequency oscillations." For economists working in the time (rather than frequency) domain, the cyclical component is a two-sided moving average with infinitely many leads and lags.

Growth rate

The study also looks at the growth rate of certain variables. Growth rates refer to the percentage change of a specific variable within a specific time period, given a certain context. The idea of using a growth rate is to test it with a certain theoretical assumption. The growth rate in X could be calculated as:

Present−Past 퐺푅 = ( ) ……………………………………………………………...4.1 Past

Where GR is the growth rate, Present is the present value of the variable, past is the past value of the variable in question.

In this study the growth rates were used to check if gold prices and gold production have been increasing over time. This was done to see if the trends of these variables are in line with the predictions of the Hotelling rule. For gold price a positive growth rate was expected because the Hotelling rule predicts that a price of a depletable resource should rise over time. For gold production, a negative growth rate was expected. This would be in line with the Hotelling rule. According to Hotelling rule, for the owner of a non-renewable resource the equivalent condition is price = MC + the opportunity cost of depletion, implying that less of the resource will be extracted in any period, than if it were renewable (Minnitt, 2007).

4.5. ECONOMETRIC ESTIMATIONS: STRUCTURAL EQUATIONS AND HYPOTHESIS TESTING

The second class tested a specific model by estimating some equations and testing certain hypotheses. Its strength is that formal tests can be performed and hypothesis can be tested.

Hypothesis testing

A hypothesis test is a statistical test that is used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true (Weisstein, 2004). A hypothesis test examines two opposing hypotheses about a population: the null hypothesis and the alternative hypothesis. In this study this method was used to empirically test some unit root hypotheses.

Stationarity

The importance of time series properties in the data has gradually been recognised in the literature. More recent studies also deal with the temporal properties of non-renewable resource prices testing whether prices exhibit deterministic or stochastic trends. Slade (1988), Berck and Roberts (1996), Ahrens and Sharma (1997) and Lee et al. (2006) have focused on the time series properties of natural resource prices. They used advances in unit root testing to examine the time paths of these non-renewable commodity prices. This study followed the same procedures and techniques that were used by these studies. The study used econometric techniques that examine whether a series is mean reverting or mean

65 averting. The preferred technique, in this regard, was the variance ratio test. In addition to this, formal stationarity tests complemented the visual inspections to test for the unit root properties of the gold price and gold production series. This was in line with what had been done previously.

Much of the literature focused on estimating either Trend Stationary (TS) or Difference Stationary (DS) specifications in order to estimate the constant long-term trend (Cuddington & Nülle, 2013). The Hotelling rule predicts that resource prices should rise over time and as a result they should follow a deterministic trend. The rule also predicts that production should decrease over time and as a result it should follow a downward (deterministic trend). The study sought to test this by answering the following questions: do gold price and gold production follow a stochastic or deterministic trend? The answer to this question was discerned through hypothesis testing using the following techniques:

i. Variance ratio test ii. Augmented Dickey-Fuller Test iii. Phillips-Perron, iv. KPSS and v. The DF-GLS test The methods employed in the study enabled: i. The estimation of the variance ratio to determine if the data is mean reverting or mean averting. ii. Reliable inference regarding the presence of a unit root. These methods also allowed the study to discern if the gold price and gold production paths were consistent with the Hotelling rule.

4.5.2.1. Variance ratio test

The Lo and MacKinlay (1988, 1989) overlapping variance ratio test, examines the predictability of time series data by comparing variances of differences of the data (returns) calculated over different intervals. If we assume that the data follow a random walk, the variance of a 푞−period difference should be q times the variance of the one-period difference. Evaluating the empirical evidence for or against this restriction is the basis of the variance ratio test. EViews allows you to perform the Lo and MacKinlay variance ratio test for homoskedastic and heteroskedastic random walks, using the asymptotic normal distribution (Lo & MacKinlay, 1988) or wild bootstrap (Kim, 2006) to evaluate statistical

66 significance. Lo and MacKinlay (1988) formulate two test statistics for the random walk properties that are applicable under different sets of null hypothesis assumptions about 휀푡:

First, Lo and MacKinlay make the strong assumption that the 휀푡 are i.i.d. Gaussian with variance 휎2 (though the normality assumption is not strictly necessary). Lo and MacKinlay term this the homoskedastic random walk hypothesis, though others refer to this as the i.i.d. null. Alternately, Lo and MacKinlay outline a heteroskedastic random walk hypothesis where they weaken the i.i.d. assumption and allow for fairly general forms of conditional heteroskedasticity and dependence. This hypothesis is sometimes termed the martingale null, since it offers a set of sufficient (but not necessary), conditions for 휀푡 to be a martingale difference sequence (m.d.s.).

4.5.2.2. The ADF Test

Mernard (2008:585) held that the Dickey-Fuller tests calculate an autoregressive model and test whether the coefficient ∅1 is statistically different from one. If it is not, it will be necessary to difference the series to achieve stationarity. The Dickey-Fuller test is of the model:

∆ 푌푡 = 훼 + 훾 푌푡−1 + 휀푡…………………………………………………………….(4.2)

Where 훾 = 휌 − 1 and the null alternative hypotheses are:

퐻0 ∶ 훾 = 0

퐻1 ∶ 훾 > 1

A major problem with ordinary DF test is that their critical values are biased if there is autocorrelation in the residuals of the DF regression. To correct this, Dickey and Fuller (1981) came up with the augmented version of the Dickey-Fuller Test. They included as many lagged variables as necessary to remove any autocorrelation in the residuals. The ADF approach controls for higher-order correlation by adding lagged differences terms of the dependent variables to the right-hand side of the regression (Sarkar, 2012:19). Mishra and Sethi (2008:573) held that the Augmented Dickey-Fuller will then take the form:

∆ 푌푡 = 훼 + 훾 푌푡−1 + 훿1 ∆ 푌푡−1 + 훿2 ∆ 푌푡−2 + … … . + 훿푝 ∆ 푌푡−푝 + 휀푡………………….(4.3)

This augmented specification is then tested for:

퐻0: 훾 = 0

퐻1:훾 > 1

For the purposes of this study the Augmented Dickey-Fuller was used.

4.5.2.3. Phillips-Peron test

Although the ADF is one of the most commonly used tests3, it sometimes behaves poorly, especially in the presence of serial correlation. As a result of this, Phillips and Peron developed a more comprehensive theory of unit root non-stationarity. The tests are similar to the ADF tests, but they incorporated automatic correction to the DF procedure to allow for autocorrelated residuals. The Phillips-Peron test performs better than (or at least as well as) the ADF test in terms of comparative power and yields tighter confidence intervals (Cashins & McDermott, 2003:328). In addition to this, the Phillips and Peron tests are non- parametic tests of the null of the unit root and are considered more powerful, as they use consistent estimators of the variance. (Sarris & Hallan, 2006:202). The Phillips-Perron unit root test differs from the ADF tests mainly in how they deal with serial correlation and heteroscedasticity in the errors. The Phillips-Peron test is based on the model:

푋푡 = 휂 + 훽푡 + 휋 푋푡−1 + 휓푡………………………………………………..……….(4.4)

With the unit root null hypothesis expressed by 퐻0 : 휋 = 1; the stationary process 휓푡 is not assumed to be white noise and serial correlation and heteroscedasticity in the 휓푡 term are handled in the test statistic (Donner & Barbosa, 2008:160).

4.5.2.4. DF-GLS test

The study also applied a more efficient univariate DF-GLS test for autoregressive unit root recommended by Elliot, Rothenberg, and Stock (ERS, 1996). The test is a simple modification of the conventional augmented Dickey-Fuller (ADF) t-test as it applies generalised least squares (GLS) detrending prior to running the ADF test regression. Compared with the ADF tests, the DF-GLS test has the best overall performance in terms of sample size and power. It "has substantially improved power when an unknown mean or trend is present" (ERS, 1996). The test regression included both a constant and trend for the log-levels and a constant with no trend for the first differences of the variables.

3 Farag (2009)

The null hypothesis is a random walk with a possible drift with two specific alternative hypotheses: the series is stationary around a linear time trend, or the series is stationary around a possible non-zero mean with no time trend.

4.5.2.5. KPSS test

Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests are used for testing a null hypothesis that an observable time series is stationary around a deterministic trend (trend stationary) against the alternative of a unit root. Contrary to most unit roots, the presence of a unit root is not the null hypothesis but the alternative. The work of Kwiatkowski et al. (1992) was motivated by the fact that unit root tests developed by Dickey and Fuller (1979), Dickey and Fuller (1981), and Said and Dickey (1984) indicated that most aggregate economic series had a unit root. In these tests, the null hypothesis is that the series has a unit root. Since such tests have low power in samples of sizes occurring in many applications, Kwiatkowski et al. (1992) proposed that trend stationarity should be considered as the null hypothesis, and the unit root should be the alternative. Rejection of the null of trend stationarity could then be viewed as convincing evidence in favour of a unit root.

It was soon realised that the KPSS test of Kwiatkowski et al. (1992) has a much broader utility. For example, Lee and Schmidt (1996) and Giraitis et al. (2003) used it to detect long memory, with short memory as the null hypothesis; while de Jong et al. (1997) developed a robust version of the KPSS test. The work of Lo (1991) is crucial because he observed that under temporal dependence, to obtain parameter free limit null distributions, statistics similar to the KPSS statistic must be normalised by the long-run variance rather than by the sample variance.

Structural equation modelling

The second broad technique of the study involved modelling structural equations. Structural equation modelling (SEM) is a series of statistical methods that allow complex relationships between one or more independent variables and one or more dependent variables (Purdue, 2016). This involves a number of procedures like specifying a model and estimating a model. The procedures are explained in the subsequent sections.

4.5.3.1. Model specification

The model and variables chosen in this study, were those which have displayed empirical and theoretical links with the demand for gold, and which the author believes are responsible

69 for driving the gold price for the period January 1995 to December 2015. The study adopts Ghosh et al’s (2004) model with some modifications. Ghosh et al. (2004) analysed monthly gold price data from 1976 to 1999 using cointegration regression techniques. Their study provided empirical confirmation that gold can be regarded as a long-run inflation hedge and that the movements in the nominal price of gold are dominated by short-run influences. Their basic model was:

푃푔 = 푓 (푃푢푠푎 , 푃푤 , 푅푔, 푌, 훽푔 , 푒푟, 휃)…………………………………………………….(i)

Where 푃푔is the nominal US dollar price of gold, 푃푢푠푎 is the US price index, 푃푤 is the world price index, 푅푔is the gold lease rate, Y is world income, 훽푔 is gold’s beta, 푒푟 is the dollar/world exchange rate and 휃 are random financial and political shocks that impact on the price of gold.

This study modifies Ghosh et al’s (2004) model by replacing some variables. This study modifies equation (i) by adding some additional variables that influence gold prices. The model of this study will then have the following function:

GP = f (USINT, BDI, SAINT)………………………………………….…………(ii)

Where Rand denominated Gold Price (GP) will be a function of United States Interest rates (USINT), US-world exchange rate (BDI), South African interest rates (SAINT). The model can be expressed in its linear form as:

퐺푝 = 퐵1 푈푆퐼푁푇 + 퐵2 퐵퐷퐼 + 퐵3 푆퐴퐼푁푇 + 휀 ………………………(iii)

Where 퐺푝is gold price, USINT is the US interest rate, BDI is the US-world exchange rate and SAINT is the South African interest rate.

4.5.3.2. Definition and justification of the variables

Gold Prices (GP) – This means the rand (South African) denominated gold price. The price of gold (Pg) is the monthly average spot rand price per ounce. Gold prices were the dependent variable of the study.

Unites States Interest rate (USINT) – This study used the repo rate. The repo rate (repurchase rate) is the interest rate at which commercial banks can borrow money from the Reserve Bank. Interest rates are supposed to influence the behaviour of gold prices according to the Hotelling rule.

US/World Exchange rate – the study used the US Nominal Broad Dollar Index (BDI). Tennant (2005) used a similar analysis to examine the determinants of gold price. The US- world exchange rate (ER) was included as an explanatory variable to control for movements in the price of gold denominated in US dollars caused by exchange rate movements. The spot dollar/world currencies exchange rate controls for gold dollar price movements attributable to gold market activity outside of the dollar area caused by exchange-rate- determined changes in the non-dollar gold price. The exchange rate that was used was the "nominal major currencies dollar index". Mainardi (1999) used a similar analysis in determining the determinants of gold prices in South Africa. Earlier on Sjaastad and Scacciallani (1996) used the same proxy in investigating the gold and foreign exchange markets for the 1982–1990 period. They found that although the price of gold is usually denominated in US dollars, real appreciations or depreciations of the European currencies have profound effects on the price of gold in all other countries.

South African interest rates - The study used two different interest rates from different markets. It used the US interest rate (which represented the world interest rate) and the South African interest rate (which represented the South African and emerging markets interest rate). The reason for using two interest rates is that investors usually choose where to invest their money. In the past decade it has been the US and other emerging markets which have been attracting investment.

4.5.3.3. Expected priori

Exchange rate – A fall in the dollar/world exchange rate (ER) should raise the price of gold because a US dollar depreciation would make gold cheaper for investors outside of the dollar area that would increase the demand for gold and raise the US dollar price of gold. Levin and Wright used various cointegration regression techniques to identify key determinants for the price of gold. They found negative relationships between changes in the price of gold with changes in the US dollar trade-weighted exchange rate and the gold lease rate.

Interest rates – both the US interest rate and South African interest rate are expected to move along with interest rates (Hotelling, 1931). A positive relationship between the two variables is expected. When interest rates rise, the price of gold is expected to rise.

4.5.3.4. Data sources and analysis

Data, for the study, was obtained mainly from secondary sources including Stats SA, South African Reserve Bank, Department of Trade and Industry and from other relevant sources. Nominal figures were used for the study. The study employed monthly South African data for the period 1990–2015. The data frequency selected was monthly so as to ensure an adequate number of observations. An observation less frequent than this (yearly or quarterly) would not have provided enough observations from which a reliable conclusion could be drawn. Wherever possible, data was verified by cross-checking various sources. However, there were areas where data was not available or not verifiable, for example regarding gold production stolen from the mines.

4.5.3.5. Testing for stationarity/Unit root

Stationary tests were run to assess whether or not the underlying stochastic process of the time series could be assumed to be invariant over time. If the mean and variance of a time series are constant over time, then the time series is said to be stationary. Time series data is said to be non-stationary if the variance and/or the mean are not constant over time. This study applied the Phillips Perron test to test for unit root. The descriptions of unit root tests were discussed in Section 4.5.2.5.

4.5.3.6. Estimation Techniques

Unit root tests showed that all variables became after being differenced once (intergrated of order 1). Furthermore, a cointegration analysis revealed that there is one cointergrating relationship. As a result, it was appropriate to use the VECM model. This will be discussed in the next section. Cointegration is concerned with the analysis of long run relations between variables integrated of the same order (i.e. series made stationary at the same order of differencing) and the speed of return to equilibrium after a deviation is measured by the Error Correction Model (ECM). This is discussed in the next section.

4.5.3.6.1 VECM A vector error correction model (VECM) is a restricted VAR designed for use with non- stationary series that are known to be cointegrated. The vector autoregression (VAR) is commonly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random disturbances on the system of variables. The VAR approach sidesteps the need for structural modelling by treating every endogenous variable in the

72 system as a function of the lagged values of all of the endogenous variables in the system. According to Asteriou (2007), the ECM is important and popular for many reasons:

(1) Firstly, it is a convenient model measuring the correction from disequilibrium of the previous period which has a very good economic implication. (2) Secondly, if we have cointegration, ECM models are formulated in terms of first difference, which typically eliminate trends from the variables involved; they resolve the problem of spurious regressions. (3) A third very important advantage of ECM models is the ease with they can fit into the general-to-specific (or Hendry) approach to econometric modelling, which is a search for the best ECM model that fits the given data sets. (4) Finally the fourth and most important feature of ECM comes from the fact that the disequilibrium error term is a stationary variable. Because of this, the ECM has important implications: the fact that the two variables are cointegrated implies that there is some automatically adjustment process which prevents the errors in the long-run relationship becoming larger and larger.

This study used VECM because of all these reasons and furthermore, the use of VECM allows one to perform a variance decomposition test. According to Hill et al. (2012) the VECM model can be used under the following circumstances listed in Figure 4.1 below:

Regressions with non-stationary variables

Trend stationary Stochastic trend

Estimate an ARDL model in Cointegrated Not cointegrated levels with a trend term

included

Estimate short-run Estimate long-run Estimate ARDL error correction model equation with least model in first squares differences

Figure 4.1: Regression with time series data: non-stationary variables

Source: Hill et al (2012)

Figure 4.1 shows that the VECM can be used when the variables are cointergrated. In this study, it was fund that there was one cointergrating vector. Consequently, the study adopted a VECM model. The University of Bath (2016) concurs and asserts that if a set of variables are found to have one or more cointegrating vectors then a suitable estimation technique is a VECM (Vector Error Correction Model) which adjusts to both short run changes in variables and deviations from equilibrium.

4.5.3.7. Diagnostic tests

Gujarati (2004:516) argues that diagnostic tests should be performed so that the model finally chosen is a good model in the sense that all the estimated coefficients have the right signs, they are statistically significant on the basis of the t and F tests, and the R-Squared value is reasonably high. In this regard, this study employed the Histogram and Normality test, the Ramsey test and the Serial Correlation LM test.

i. Normality Test Jarque-Bera is a test statistic for testing whether the series is normally distributed. Machiwal and Jha (2012:48) state that the test statistic measures the difference of the skewness and kurtosis of the series with those from the normal distribution. The Jarque-Bera test is based on the fact that skewness and kurtosis of normal distribution equal zero. Therefore, the absolute value of these parameters could be a measure of deviation of the distribution from normal. Jarque and Bera proposed a normality test using classical skewness and kurtosis coefficients. The Jarque Bera test is a goodness of fit measure to departure from normality, based on the sample kurtosis and skewness. Machiwal and Jha (2012:48) state that the test statistic JB is defined as:

푘−32 푛 2+ ( ) JB= (푆 4 )……………………………………………………(4.6) 6

Where 푛 = number of observations, 푆 = sample skewness and 푘 = sample kurtosis.

The JB test is based on the result that a normally distributed random variable has skewness equal to zero and kurtosis equal to 3. In other words, the test of normality compares

74 skewness and kurtosis to 0 and 3, their values under normality. The test statistic is JB. The statistic JB has an asymptotic chi-square distribution with two degrees of freedom and can be used to test the null hypothesis that the data are from a normal distribution. Machiwal and Jha (2012:48) further maintain that for a normally distributed variable, S = 0 and K = 3 Therefore, the JB test of normality is a test of the joint hypothesis that S and K are 0 and 3 respectively. In this study, the Jarque-Bera (JB) test is used to test whether stock returns and exchange rates individually follow the normal probability distribution.

ii. Residual Diagnostics/Correlogram-Q-statistics A test whether a volatility model has adequately captured all of the persistence in the variance of returns is to look at the correlogram of the standardized squared residuals. If the model is adequate then the standardized squared residuals should be serial uncorrelated (Knight and Satchell, 2007:56). The q-statistic of squared residuals looks as follows:

휏2 (훼2 ) 푄∗ = 푇 (푇 + 2) ∑푚 푘 푡 ……………………………………………… 4.7 푘=1 푇−퐾

Where T is the sample size, m represents the maximum length and 휏푘 are the correlation coefficients. The null hypothesis is퐻0 = 훽1 = ⋯ … … … … 훽푚 = 0, where 훽푖 is the 2 coeeficient of 훼푡−1 of linear regression:

2 2 2 훼푡 = 훽0 + 훽1 훼푡−1 … . . 훽푡−푚 + 휀푡 ……………………………….……4.8 for 푡 = 푚 + 1 … … , 푇. If there is no serial correlation in the residuals, the autocorrelations and partial autocorrelations at all lags should be nearly zero, and all Q-statistics should be insignificant with large p-values (Knight and Satchell, 2007:56).

iii. Serial Correlation Test Serial correlation occurs when there is dependence between error terms. Error terms of the equation estimate must be distributed independently of each other and hence the covariance between any pair of error or residual terms must be zero (Lhabitant, 2004). Serial correlation occurs when the covariance is not zero. The use of time series data often leads to the problem of autocorrelation, which means, in this study, that after a positive stock return for one month there follows a positive stock return for the subsequent month. Serial correlation is a problem because standard errors (even heteroskedastic robusts) are not consistent, affecting statistical inferences (hypothesis testing). Durbin-Watson is the most commonly used test in time series. However, it is important to know that it is not relevant in many instances, for instance, if the error distribution is not normal, or if there is a dependent

75 variable in a lagged form as an independent variable this is not an appropriate test for autocorrelation. A test that is suggested that does not have these limitations is the Lagrange Multiplier test (LM test).

iv. LM Test Song, Witt and Li (2009:53) held that the calculation of the LM test is based on an auxiliary equation of the form:

∧ ∧ ∧ ∧ 휀푡 = 훼 + 훽1 푋1푡 + 훽2 푋2푡 + … … + 훽푘 푋푘푡 + 휌1 휀푡−1 + 휌2 휀푡 − 2 … … . + 휌푝 휀푡 − 푝 +

휇푡…………………………………………………………………………….(4,9). ∧ Where 푋푖푡s are explanatory variables, the 훽푖s and 푝푗s are parameters and the 휀푡 − 푗s are the lagged residuals from the regression model. Under the null hypothesis of no autocorrelation: 퐻표 : 푝푖 = 푝2 = ⋯ … … … … … 푝푝 = 0

Song, Witt and Li (2009:53) further maintained that the test statistic is 푛 푅2, where n is the sample size. In large samples, the test statistic has a 휒2 distribution with p degrees of freedom. If the value of 푛 푅2 exceeds the critical value of 휒2, this suggests the presence of auto-correlation.

4.6. SUMMARY OF THE CHAPTER

The conclusions of this paper can be summarised as follows:

The study used both descriptive and structural equations to achieve its objective.

i. Descriptive statistics were used because they allowed the study to analyse data properties and test the applicability of the Hotelling rule. The objective was to provide a comprehensive description of long-term trends in the gold price, and to compare this description to theoretical predictions of the Hotelling rule. The descriptive statistics focused on whether real prices of non-renewable resources rise dramatically over time, signalling increasing economic scarcity or the converse. ii. Structural equations used the VECM and hypotheses tests used unit root tests and variance ratio tests to test the applicability of the Hotelling rule. The VECM model was adopted because all the variables were of the same order of intergration (intergrated of order I) and there was one cointegrating vector in the model. Unit root tests and variance ratio were used to check and examine if the

gold price and production data had trends. This was done to compare their trends to theoretical predictions of the Hotelling rule. The use of all estimation techniques was justified by previous academic and scholarly literature. This was done to ensure validity and also to eliminate researcher bias.

4.7. CONCLUSION

The main aim of this chapter was to present the research techniques that were used to achieve the objectives of the study. The chapter presented the methodology used to analyse and present the study’s findings. The chapter also offered some justifications as to why it adopted certain research techniques. The chapter laid down the model which tested the Hotelling model's relevance in the South African gold sector. Included in this model are variables that are likely to affect the gold price. For stationarity/unit roots purposes, the model employed the Dickey-Fuller and the Phillips-Perron tests. Diagnostic tests such as the Normality test, Ramsey RESET test and the LM test were discussed. The VECM technique was chosen as the estimation technique for the relevance of the Hotelling rule in South Africa. The following three chapters will discuss preliminary examination of the data using the econometric package EVIEWS 9.

CHAPTER 5 DISCUSSION OF THE TRENDS, MEAN AND VARIANCE PROPERTIES OF SOUTH AFRICAN GOLD PRICES

5.1. INTRODUCTION

The purpose of this chapter is to present the time series properties of the gold time series. The objective is to identify the trends, mean and variance properties of the South African gold prices and see if they follow the trend according to the Hotelling rule. The focus is to identify the actual properties of the gold price series and determine whether gold in South Africa is subject to increasing scarcity. The structure of this chapter is twofold; it is descriptive and it also provides some formal tests to validate the findings from the descriptive aspect of the study. The first section of the chapter looks at graphical inspection of the gold price series and examines its trends. The second section uses stationarity tests and variance ratio tests to examine the unit root properties of the gold time series data. The last section provides an in-depth discussion of the findings from both the first section (visual inspection) and stationarity tests and variance ratio tests.

5.2. PRESENTATION OF RESULTS

Regardless of the indicator used to assess observed trends in scarcity, any statistical analysis should commence with a thorough examination of the indicator’s time series properties (Ahrens and Sharma, 1997). In this regard, the chapter examines the time series properties for gold price. Measuring trends in the real price of resources allows us to assess various economic theories, including the classic Hotelling (1931) model of non-renewable resource prices. Slade and Thille (1997) categorised the existing empirical tests as (a) price behaviour, (b) shadow price, and (c) Hotelling valuation tests. This chapter examines the price behaviour of the gold price series. The price behaviour will show whether the Hotelling rule holds in the gold mining industry. In a world of certainty, the Hotelling model predicts that non-renewable resource prices are trend stationary. The rule predicts exponentially increasing resource prices and that this result in mineral resources will follow the path of the positive trend. The positive trend is prompted by the increasing price reflecting the increasing scarcity of the resource. The price increases until it eventually reaches the choke price, where the quantity demanded decreases to zero. The theoretical literature predicts that the prices of these resources should be rising over time in accordance with the Hotelling

78 rule, and argues that this behaviour is compatible with social optimality (Kronenberg, 2004). Rising prices should reflect the increasing scarcity of a mineral resource. A rising trend in gold prices is expected if the Hotelling rule holds for the South African gold denominated price.

Most descriptive studies have examined the behaviour of mineral commodity prices (Slade, 2009). Moreover, since the predictions of Hotelling’s model are long-run, many tests make use of a century or more of data on the prices of different fuel and non-fuel minerals. Literature has examined a wide variety of specifications for the time series behaviour of prices. Much of this work is concerned with whether the trend is taken to be deterministic or stochastic. This will be the focus of this chapter. The chapter will be twofold. Firstly, it is descriptive in the sense that it examines the trends in the gold price series. In order to measure the trend of the gold price visual inspection will be used to assess the plotted graph for the gold price series. In addition to this a filter technique will also be used in visual analysis of the gold price series graphs. Band-pass filters, which decompose an economic time series into trend and cyclical components, provides one way of doing this if our objective is data description and historical analysis, rather than hypothesis testing.

Secondly, the chapter uses econometric techniques that examine whether a series is mean reverting or mean averting. The preferred technique, in this regard, is the variance ratio test. Thirdly, formal stationarity tests will complement the visual inspections to test for the unit root properties of the gold price series. Much of the literature focuses on estimating either Trend Stationary (TS) or Difference Stationary (DS) specifications in order to estimate the constant long-term trend (albeit with the possible search for occasional breaks) (Cuddington and Nülle, 2013). The methods employed in the study enable: i. robust detection of the presence/absence of trends in the data, ii. robust estimation of the variance ratio to determine if the data is mean reverting or mean averting iii. reliable inference regarding the presence of a unit root The study will be guided by literature in order to discover the time series properties of the gold price series.

Visual Tests for Stationarity

This section presents the findings from graphical analysis. The examination of the data is important as it allows the detection of any data-capturing errors and structural breaks, and

79 gives an idea of the trends and stationarity of the data set (Takendesa, 2007). One of the approaches used to apply to check for stationarity is to actually plot the time series and look for evidence of trends in mean, variance, autocorrelation and seasonality. Time series is stationary if for all values and every time period, it is true that:

i. E (푦푡) = 휇 (constant mean) 2 ii. Var (푦푡= 휎 (constant variance)

iii. Cov (푦푡, 푦푡+푠) = cov (푦푡, 푦푡−푠) = 훾푠 (covariance depends on s, not t) Most analysis uses the mean to determine whether a variable is stationary or not. Non- stationary series with non-constant means are often described as not having the property of mean reversion. Looking at the sample means of time series variables is a convenient indicator as to whether a series is stationary or not4. If any such patterns are present then these are signs of non-stationarity and different mechanisms exist to turn the series into a stationary one. The gold price series was plotted and the results are shown in Figure 5.1 (a) and (b).

Time series for Gold Prices (1990-2015) Time series for Gold Prices (1990-2015)

20,000 20,000

16,000 16,000

12,000 12,000

8,000 8,000 Fitted Trend line

4,000 4,000

0 0 92 94 96 98 00 02 04 06 08 10 12 14 92 94 96 98 00 02 04 06 08 10 12 14

Year Year

Figure 5.1: The Gold price series (a) and (b)

Source: Author’s computation based of EViews 9

4 However, it must be noted that this is a informal method of checking unit and it does not constitute a hypothesis. More formal tests that constitute hypothesis e.g. the Phillips-Perron and KPSS test can be used to formally check for unit root in time series variables.

The gold price series clearly exhibits a trend which is slowly growing upwards. From Figure 5.1 it is obvious that the gold price series is not stationary since it increased upward as time changed. However the trend is wandering a little and this may suggest that there are also some elements of stochastic properties in the time series. Figure 5.1 (b) has a trend line fitted in it to determine whether the time series for gold prices has a mean reversion. If the time series was wandering around the trend line it could have been said that the series has a mean reversion. However, the series is showing an upward trend without reverting to its mean. This may suggest that there are signs of non-constant mean in the gold price series.

The presence/absence of a trend in the mean can be further examined by applying a Hodrick-Prescott filter to the time series. The Hodrick-Prescott filter5 is a smoothing method that is widely used among macroeconomists to obtain a smooth estimate of the long-term trend component of a series (de Jong, 2013). The method was first used in a working paper (circulated in the early 1980s and published in 1997) by Hodrick and Prescott to analyse post-war US business cycles. If the result is a series that does not resemble a roughly flat, horizontal line then a trend in mean is present in the initial series. The graphical results from the Hodrick-Prescott filter are displayed in Figure 5.2 below.

5 This approach (Band-pass filters) has the advantage of allowing long-run trends rate to evolve gradually over time, rather than assuming that they are constant (perhaps with occasional structural breaks) over time ((Cuddington and N¨ulle, 2013).

Hodrick-Prescott Filter (lambda=14400)

16,000

12,000

3,000 8,000

2,000

4,000 1,000

0 0

-1,000

-2,000

90 92 94 96 98 00 02 04 06 08 10 12 14

GP Trend Cycle

Figure 5.2: Graphical results from the Hodrick-Prescott filter

Source: Author’s computation based of EViews 9

From Figure 5.2 it can be seen that the gold price series appears to be trending upward. The gold price series shows that the constant variance condition for stationarity is being violated. The vertical fluctuation of the series appears to differ from one portion of the series to the other, indicating that the mean is not constant. Furthermore an upward trend is a violation of the requirement that the mean is the same for all periods. It can thus be said that the gold price series is violating the following:

(i) E (푦푡) = 휇 (constant mean) The analysis shows that the series is following a upward trend and this is a deterministic trend. The changing mean of a non-stationary process or trend can be represented by a deterministic function of time. These models for the trend imply that the series trend evolves in a perfectly predictable way, therefore they are called deterministic trend models. In Figure 5.2 it can be seen that the series is not stationary and it has a deterministic trend. Using a related methodology – Kalman filter methods – Pindyck (1999) estimated a model where prices revert to a quadratic trend that shifts over time. On the other hand, Cuddington and Nülle, 2013) used band filters to assess the behaviour of commodity prices and found that

82 there is no "general tendency" in the negative or positive direction of long-run mineral commodity price trends. While there are examples therein illustrative of the Hotelling, Prebisch-Singer, and Pindyck/Heal/Slade U-shape models and expectations of long-term price trends, none of the seminal models emerge preeminent.

Correlogram

One way to characterize a series with respect to its dependence over time is to plot its sample autocorrelation function, which is obtained by dividing the sample autocovariance by the estimated variance. This is the correlogram test. The correlogram test is an informal test for stationarity which is based on inspection of the autocorrelation function. The correlogram test was conducted and the results are displayed in Table 5.1 below.

Table 5.1: Correlogram test

Date: 10/03/16 Time: 18:46 Sample: 1990M01 2015M12 Included observations: 312

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

1 0.988 0.988 307.48 0.000 2 0.976 0.009 608.72 0.000 3 0.965 -0.011 903.68 0.000 4 0.953 -0.002 1192.5 0.000 5 0.943 0.062 1476.1 0.000 6 0.933 0.011 1754.8 0.000 7 0.923 -0.022 2028.4 0.000 8 0.913 0.023 2297.3 0.000 9 0.904 0.003 2561.5 0.000 10 0.895 -0.005 2821.1 0.000 11 0.885 -0.008 3076.0 0.000 12 0.874 -0.053 3325.7 0.000 13 0.864 0.009 3570.2 0.000 14 0.855 0.046 3810.4 0.000 15 0.845 -0.040 4045.8 0.000 16 0.834 -0.024 4276.3 0.000 17 0.823 -0.048 4501.3 0.000 18 0.812 -0.002 4720.9 0.000 19 0.801 0.016 4935.5 0.000 20 0.791 0.002 5145.3 0.000 21 0.780 -0.016 5350.2 0.000 22 0.768 -0.071 5549.4 0.000 23 0.756 0.001 5743.1 0.000 24 0.745 0.042 5932.0 0.000 25 0.735 0.034 6116.5 0.000 26 0.725 -0.018 6296.7 0.000 27 0.716 0.010 6472.8 0.000 28 0.705 -0.039 6644.2 0.000 29 0.694 -0.018 6810.9 0.000 30 0.684 0.047 6973.7 0.000 31 0.673 -0.059 7131.8 0.000 32 0.663 -0.003 7285.4 0.000 33 0.651 -0.030 7434.1 0.000 34 0.637 -0.097 7577.2 0.000 35 0.623 -0.032 7714.7 0.000 36 0.609 -0.049 7846.2 0.000

The lags were automatically generated by E-views 9.

Source: Author’s computation based of EViews 9

Table 5.1 shows that the correlogram of the gold price series does not decline exponentially. A correlogram of a stationary series should decline exponentially, while for a non-stationary series it declines very slowly. From Table 5.1 it can be seen that the gold price series in not stationary. This confirms the non-stationarity of the gold price series. A statistical process is said to be stationary if the auto-correlation function either abruptly drops to zero at some finite lag or eventually tapers off to zero (Karasavvoglou, 2016). In this case, the autocorrelation function does not drop to zero and it can thus be said that the gold price

84 series is not stationary. What is interesting to note is that there is a trend in the gold price series data. This is shown by the autocorrelation which is declining towards zero with each additional lag. If it were fluctuating up and down as it went towards zero, it would have been said that there is no trend. But in Table 5.1 the autocorrelation is declining towards zero. This confirms the findings from the visual inspection that there is a deterministic trend in the gold price series.

Formal unit root tests

The primary statistical concern of this chapter is the appropriate characterisation of non- stationary gold price prices. Mere visual examination of a time series is insufficient to determine its stationarity properties (Hamilton cited in Ahrens and Sharma, 1997). In addition to the visual inspection of the graphical plots of the gold time series, some formal stationarity tests were conducted. Much of the literature focuses on estimating either Trend Stationary (TS) or Difference Stationary (DS) specifications in order to estimate the constant long-term trend (albeit with the possible search for occasional breaks) (Cuddington and Nülle, 2013). This study employed relevant econometric methods to test for the presence of a trend in the gold price series data. Eviews 9 was used to carry out the tests. With Eviews one can get results for three different variants of the test: without constant and trend, with constant only and with constant and trend. The study employed four stationarity tests; Augmented Dickey-Fuller Test, Phillips-Perron, KPSS and the DF-GLS test. The results are presented in the next subsection.

5.2.3.1. Augmented Dickey-Fuller Test

An augmented Dickey-Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version is used, but is usually stationary or trend stationary. Results are shown in Table 5.2.

Table 5.2: Augmented Dickey-Fuller Test

Null Hypothesis: GP has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic - based on SIC, maxlag=15)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -1.002879 0.9409 Test critical values: 1% level -3.987841 5% level -3.424340 10% level -3.135208

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(GP) Method: Least Squares Date: 09/22/16 Time: 17:41 Sample (adjusted): 1990M02 2015M12 Included observations: 311 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GP(-1) -0.007759 0.007737 -1.002879 0.3167 C -37.78002 37.17328 -1.016322 0.3103 @TREND("1990M01") 0.796164 0.399730 1.991754 0.0473

Source: Author’s computation based of EViews 9

Table 5.2 shows that gold prices were not stationary in levels. At levels, the p-values of the gold price variable (0.9409) are greater than 0.05 indicating that we could not reject the null hypothesis of the existence of unit root in levels for gold prices. Since visual inspection indicated that there might be a trend in the data, the intercept and trend option was chosen. This is in line with economic literature. Perron (1988) noted that the correct specification of the trend function is important in the context of testing for a unit root in the data. The results from the ADF Test equation confirm the presence of the trend in the data. The p-value for TREND (1990M01) is statistically significant (0.0473). This suggests that there is a trend in the data.

5.2.3.2. Phillips-Perron

The Phillips-Perron performs the Phillips–Perron (1988) test that a variable has a unit root. The null hypothesis is that the variable contains a unit root, and the alternative is that the variable was generated by a stationary process. The results are displayed in Table 5.3 below.

Table 5.3: Phillips-Perron test

Null Hypothesis: GP has a unit root Exogenous: Constant, Linear Trend Bandwidth: 3 (Newey-West automatic) using Bartlett kernel

Adj. t-Stat Prob.*

Phillips-Perron test statistic -1.063543 0.9321 Test critical values: 1% level -3.987841 5% level -3.424340 10% level -3.135208

*MacKinnon (1996) one-sided p-values.

Residual variance (no correction) 83367.66 HAC corrected variance (Bartlett kernel) 90839.39

Phillips-Perron Test Equation Dependent Variable: D(GP) Method: Least Squares Date: 09/22/16 Time: 17:42 Sample (adjusted): 1990M02 2015M12 Included observations: 311 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GP(-1) -0.007759 0.007737 -1.002879 0.3167 C -37.78002 37.17328 -1.016322 0.3103 @TREND("1990M01") 0.796164 0.399730 1.991754 0.0473

Source: Author’s computation based of EViews 9

Table 5.3 shows that gold prices were not stationary in levels. At levels, the p-values of the gold price variable (0.9321) are greater than 0.05 indicating that we could not reject the null hypothesis of the existence of unit root in levels for gold prices. A trend option was chosen in the Phillips-Perron test because visual inspection indicated that there might be a trend in the data. The results from the Phillips-Perron test equation confirm the presence of the trend in the data. The p-value for TREND (1990M01) is statistically significant (0.0473). This suggests that there is a trend in the data. The results support the trends that were displayed by the graphs. It can therefore be said that the data have a deterministic trend.

5.2.3.3. KPSS

In the past, unit root tests such as the PP and ADF tests have been criticised for their lack of power in determining the presence of unit roots. Blough (1992), for example, warns that no test can have high power against any stationary process without a correspondingly high

87 probability of falsely rejecting nearby members of the unit root null. This issue arises more often when working with data frequencies greater than quarterly, thus making them less useful in these circumstances (Maddala & Kim 2000). This poses a problem for the econometrician analysing financial time series data that tend to be either weekly, daily or intraday data. However, Kwaitkowski et al. (1992) and Choi (1994) argue that it is preferable to use a combination of tests, testing for both a unit root and for stationarity as the null hypothesis, where the KPSS tests must be used as a confirmatory analysis to that of the ADF tests (Maddala & Kim 2000).

Most of the tests in the unit root literature have as a null hypothesis the non-stationarity of the series being tested: that is,

~ 퐻0 = y 퐼 (1).

The Kwiatkowski, Phillips, Schmidt and Shin test (1992) has the opposite (and perhaps more intuitive) null: that the series being tested is stationarity,

~ 퐻0 = y 퐼 (0).

In the KPSS test a comparison is done between the test statistic value and the critical value on desired significance level. If the test statistic is higher than the critical value, one can reject the null hypothesis and when test statistic is lower than the critical value, one cannot reject the null hypothesis. The results from the KPSS test are presented in Table 5.4 below.

Table 5.4: KPSS Test

Null Hypothesis: GP is stationary Exogenous: Constant, Linear Trend Bandwidth: 14 (Newey-West automatic) using Bartlett kernel

LM-Stat.

Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.503076 Asymptotic critical values*: 1% level 0.216000 5% level 0.146000 10% level 0.119000

*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)

Residual variance (no correction) 4555131. HAC corrected variance (Bartlett kernel) 62824963

KPSS Test Equation Dependent Variable: GP Method: Least Squares Date: 09/22/16 Time: 17:39 Sample: 1990M01 2015M12 Included observations: 312

Variable Coefficient Std. Error t-Statistic Prob.

C -2194.631 241.8558 -9.074133 0.0000 @TREND("1990M01") 46.15565 1.345885 34.29391 0.0000

Source: Author’s computation based of EViews 9

Table 5.4 shows the results from the KPSS test. The test result shows that the null hypothesis is rejected, which indicates non-stationarity. The Kwiatkowski-Phillips-Schmidt- Shin (KPSS, 1992) LM test statistic is 0.503076 (allowing for constant, trend, bandwidth=9, Newey-West using Bartlett kernel), where the asymptotic critical value is 0.119 for the 10% msl. Hence, the study rejects the trend stationary null at conventional levels. This shows that the gold price variable is not trend stationary at levels.

5.2.3.4. DF-GLS test

In the past, unit root tests such as the PP and ADF tests have been criticised for their lack of power in determining the presence of unit roots. Stock (1994) evaluates the various tests and suggests using the DF-GLS test subsequently presented in detail in Elliott, Rothenberg, and Stock (1996). In this regard, the study applied a more efficient univariate DF-GLS test for autoregressive unit root recommended by Elliot, Rothenberg, and Stock (1996). The test is a simple modification of the conventional augmented Dickey-Fuller (ADF) t-test as it applies generalised least squares (GLS) detrending prior to running the ADF test regression.

Compared with the ADF tests, the DF-GLS test has the best overall performance in terms of sample size and power. It "has substantially improved power when an unknown mean or trend is present" (Elliot et al. 1996). Just as the standard Dickey-Fuller test may be run with or without a trend term, there are two forms of DF-GLS: GLS detrending and GLS demeaning. With GLS detrending, the series to be tested is regressed on a constant and linear trend, and the residual series is used in a standard Dickey-Fuller regression. With GLS demeaning, only a constant appears in the first stage regression; the residual series is then used as the regress and in a Dickey-Fuller regression. The DF-GLS unit root tests results for the variables reported in Table 5.5 below.

Table 5.5: DF-GLS unit root tests

Null Hypothesis: GP has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=15)

t-Statistic

Elliott-Rothenberg-Stock DF-GLS test statistic -0.552311 Test critical values: 1% level -3.471000 5% level -2.908000 10% level -2.601500

Source: Author’s computation based of EViews 9

Table 5.5 shows that the test regression included both a constant and trend for the gold price time series variable. Results show that the gold price series is non-stationary. The results also further show that there is a trend in the gold price series. This confirms all other tests which have shown that there is a deterministic trend in the gold price series data. It can thus be said that the gold price series has a deterministic trend.

5.2.3.5. Variance ratio test (Testing for mean reversion/aversion)

In this section the study follows Slade and Thille (2010) and other previous studies to assess the relevance of the Hotelling rule. Slade and Thille (2010) used a variance ratio test technique to reveal the extent to which price shocks are persistent or transitory. The variance ratio test statistics are based on a ratio of variance estimates of returns:

푡 (푡) = 푦 (푡) − 푦 (푡 − 1) and period 푞 return horizons;

푟 (푡) + ⋯ + 푟 (푡 − 푞 + 1).

Overlapping horizons increase the efficiency of the estimator and add power to the test. In this study, the variance ratio test was performed to examine whether the gold time series is mean reverting or mean averting. A difference stationary process is reverting if changes are negatively auto-correlated, that is, if a price rise is more likely to be followed by a price fall. Conversely, if a rise is more likely to be followed by another rise then the process is averting. Results are displayed in Table 5.6.

Table 5.6: Variance ratio test

Null Hypothesis: Log GP is a martingale Date: 10/03/16 Time: 18:52 Sample: 1990M01 2015M12 Included observations: 311 (after adjustments) Heteroskedasticity robust standard error estimates User-specified lags: 2 4 8 16

Joint Tests Value df Probability Max |z| (at period 2)* 2.250837 311 0.0941

Individual Tests Period Var. Ratio Std. Error z-Statistic Probability 2 1.143570 0.063785 2.250837 0.0244 4 1.169983 0.123477 1.376637 0.1686 8 1.195888 0.193339 1.013184 0.3110 16 1.272287 0.281509 0.967240 0.3334

*Probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom

Test Details (Mean = 0.0087644913602)

Period Variance Var. Ratio Obs. 1 0.00177 -- 311 2 0.00203 1.14357 310 4 0.00208 1.16998 308 8 0.00212 1.19589 304 16 0.00226 1.27229 296

Source: Author’s computation based of EViews 9

Table 5.6 shows that the approximate p-value of 0.0941 is obtained using the studentised maximum modulus with infinite degrees of freedom so that we do not reject the null of a martingale. Furthermore, the individual statistics generally do not reject the null hypothesis, though the period 2 variance ratio statistic p-value is slightly below 0.05 (0.0244). All other periods do not reject the null hypothesis. This shows that the gold price series might be following a martingale. According to Kim (2004) if the time series of an asset price follows a martingale, then its return is purely non-predictable and investors are unable to make abnormal returns consistently over time. This suggests that a series following a martingale may never be mean reverting.

The bottom portion of the output shows the intermediate results for the variance ratio test calculations. A variance ratio of 1 equals random walk, variance ratio > 1 is trending (positive autocorrelation) and variance ratio < 1 is mean reverting (negative autocorrelation). Results show that the variance ratio for all the periods is a bit more than 1. Thus gold price is a mean averting series. In other words, it is not mean reverting. Table 5.7 shows a variance test which had a null hypothesis of a random walk.

Table 5.7: Variance test with a null hypothesis of a random walk

Null Hypothesis: Log GP is a random walk Date: 10/03/16 Time: 18:52 Sample: 1990M01 2015M12 Included observations: 311 (after adjustments) Standard error estimates assume no heteroskedasticity Use biased variance estimates User-specified lags: 2 4 8 16

Joint Tests Value df Probability Max |z| (at period 2)* 2.402192 311 0.0636 Wald (Chi-Square) 6.585936 4 0.1595

Individual Tests Period Var. Ratio Std. Error z-Statistic Probability 2 1.136216 0.056705 2.402192 0.0163 4 1.147484 0.106085 1.390240 0.1645 8 1.142575 0.167735 0.850000 0.3953 16 1.152329 0.249598 0.610299 0.5417

*Probability approximation using studentized maximum modulus with parameter value 4 and infinite degrees of freedom

Test Details (Mean = 0.0087644913602)

Period Variance Var. Ratio Obs. 1 0.00177 -- 311 2 0.00201 1.13622 310 4 0.00203 1.14748 308 8 0.00202 1.14257 304 16 0.00204 1.15233 296

Source: Author’s computation based of EViews 9

Table 5.7 shows that the approximate p-value of 0.0636 is obtained using the studentised maximum modulus with infinite degrees of freedom so that we do not reject the null of a random walk. Furthermore, the individual statistics generally do not reject the null hypothesis, though the period 2 variance ratio statistic p-value is slightly below 0.05 (0.0163). This is consistent with the martingale hypothesis displayed in Table 5.6 above. All other periods do not reject the null hypothesis. This shows that the gold price series might be following an exponential random walk and consequently, the series is not mean reverting. Mean reversion is the process of the price approaching a long-term mean and this is

92 inconsistent with a random walk (Meade, 2010). Furthermore, a random walk (and a random walk with drift) is not covariance stationary because:

(i) A random walk has an undefined mean reverting level (ii) The variance of has no upper bound (Wiley, 2015) This shows that the mean of the gold price series is not stationary and its mean averts.

The bottom portion of the output in Table 5.7 shows the intermediate results for the variance ratio test calculations. A variance ratio of 1 equals random walk, variance ratio > 1 is trending (positive autocorrelation) and variance ratio < 1 is mean reverting (negative autocorrelation). Results show that the variance ratio for all the periods is a bit more than 1. Thus gold price is a mean averting series. In other words, it is not mean reverting. These results are consistent with the joint tests which did not eject the null hypothesis of random walk. If a variable follows a random walk, the variable has no mean reversion tendency (Lam et al. 2005). The results therefore suggest that any large move in the gold price series following a random walk process is permanent and there is no tendency for the price to return to a trend path over time.

5.2.3.6. Break point unit root

Since the seminal work of Perron (1989) it is well known that ignoring structural change in unit root tests will lead to a bias against rejecting the unit root null hypothesis when it should in fact be rejected. Lee and Strazicich (2010) showed that the endogenous break ADF-type unit root tests are subject to spurious rejections in the presence of a unit root with break. With this in consideration, this study did a break point unit root to avoid the false rejection of a unit root without break. Results are shown in Table 5.8

Table 5.8: Break point unit root

Null Hypothesis: GP has a unit root Trend Specification: Trend and intercept Break Specification: Intercept only Break Type: Innovational outlier

Break Date: 2009M09 Break Selection: Minimize Dickey-Fuller t-statistic Lag Length: 1 (Automatic - based on Schwarz information criterion, maxlag=15)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -2.775752 0.9576 Test critical values: 1% level -5.347598 5% level -4.859812 10% level -4.607324

*Vogelsang (1993) asymptotic one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: GP Method: Least Squares Date: 01/22/17 Time: 12:49 Sample (adjusted): 1990M03 2015M12 Included observations: 310 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GP(-1) 0.964334 0.012849 75.05017 0.0000 D(GP(-1)) 0.138136 0.056604 2.440397 0.0152 C -21.46996 37.38869 -0.574237 0.5662 TREND 1.165714 0.420021 2.775374 0.0059 INCPTBREAK 244.1558 95.22182 2.564074 0.0108 BREAKDUM -306.3063 292.7062 -1.046463 0.2962

R-squared 0.996326 Mean dependent var 5007.923 Adjusted R-squared 0.996266 S.D. dependent var 4684.840 S.E. of regression 286.2823 Akaike info criterion 14.17100 Sum squared resid 24915097 Schwarz criterion 14.24332 Log likelihood -2190.505 Hannan-Quinn criter. 14.19991 F-statistic 16488.86 Durbin-Watson stat 1.944910 Prob(F-statistic) 0.000000

Source: Author’s computation based of EViews 9

The t-statistic of -2.775752, and the corresponding p-value of 0.9576 indicates we cannot reject the hypothesis that the gold price (GP) has a unit root. Furthermore, the results show that there is a trend in the data as shown by the 0.0059 p value of the TREND. This shows that there is a trend in the data.

5.3 Natural resources and the interest rate: gold price and interest rate

One way of testing Hotelling’s rule is to collect time series data on the price of a resource, and see if the proportionate growth rate of the price is equal to  (University of Strathclyde, 2016). This was first done by Barnett and Morse (1963) and several other studies followed suit. This study will also compare the growth rate of the gold price with that of the interest rate to see if they move at the same rate. The study used two different interest rates from different markets. It used the US interest rate (which represented the world interest rate) and the South African interest rate (which represented the South African and emerging markets interest rate). The reason for using two interest rates is that investors usually choose where to invest their money. In the past decade it has been the US and other emerging markets which have been attracting investment. The results are shown in the Table below.

Table 5.1: Gold price growth rate against interest rate growth rate

Growth rate (1990-2015)

US interest rate (-0.00293)

SA interest rate (-0.00103)

Rand denominated gold price (0.008775)

Source: Source: Author’s computation based on data from Quantec (2016)

Results show that both interest rates used in this study have negative growth rates. The US interest rate has a negative growth rate of -0.00293 and the SA interest rate has a negative of -0.00103. This may suggest that interest rates have had a declining long-run trend. On the other hand, the gold price growth rate is positive. It has a positive value of 0.008775. This shows that the gold price has had a positive trend. A negative interest rate and a positive gold price growth rate show that the gold price has not been increasing at the same rate as either of the interest rates. This shows that the Hotelling rule does not hold.

5.4 DISCUSSION OF RESULTS

The chapter used different methods to assess the applicability of the Hotelling rule. Type of methodology influences the results so it is better to use different methodologies and then

95 compare the results (Slade, 2009). The study used visual inspection, filter methods, and correlogram test to assess the time series properties of gold price. The results showed that the gold time series follows a deterministic trend. In addition to these methods, the chapter used formal unit root tests to test the unit root properties of the data. In this regard, the Augmented Dickey-Fuller, Phillips-Perron, DF-GLS test and the KPSS test were used to test the unit root properties of the data. These tests showed that the gold price series has a deterministic trend. The variance ratio test was also used to examine the mean properties of the data. Results showed that the gold price series is mean averting.

The motivation for this chapter was that by identifying the actual properties of the data series the study would be able to comment on whether or not these resources are subject to increasing degrees of resource scarcity. This was prompted by the essential ideas of the Hotelling rule. The essential ideas that come from Hotelling’s work are:

 The current price of non-renewable commodities should reflect both the marginal costs of production and the scarcity rent  Real prices should rise over time to reflect increasing scarcity and the rising marginal extraction cost (Rankin, 2011) According to Neumye (2013) rising resource rents would indicate rising scarcity, whereas, falling resource rents would indicate falling scarcity and no rise or fall would suggest no change in scarcity . A review of the graphical trends of the gold price series clearly showed that the series had an upward trend. This confirms the Hotelling rule and is also consistent with empirical literature. According to literature (Ahrens, 1997) as price pulls away from marginal extraction cost, the rate of increase in price will approach the rate of interest. It is clear that in such a model, price does not revert to a fixed mean. It is also clear that such a model implies systematic increases in real price over time. However, price movement is still systematic and may be modelled appropriately as a deterministic trend. This supports this present study’s findings.

Several studies have observed a rising trend in resource prices. Agbeyegbe (1993) and Berck and Roberts (1996) extended the unit root analysis incorporating a quadratic trend, while Ahrens and Sharma (1997) and Lee et al. (2006) considered breaks and found further evidence against the unit root hypothesis. Using a different methodology – Kalman filter methods – Pindyck (1999) estimated a model where prices revert to a quadratic trend that shifts over time. Lee et al. (2006) found deterministic trends in their analyses from 1870 onwards. The results from this study are inconsistent with other studies that found trendless

96 behaviour in resources prices. For example, Smith (1979) employed an econometric analysis of annual (1900-1973) price data of four aggregate resource groups and concluded that the trend in mineral prices was negative with the rate of decline decreasing over time in absolute magnitude.

Scott and Pearse (1992) and Simon (1996), showed that all of these theoretical trends have not occurred (Reynolds, 1999). Costs of extraction and prices of natural resources have mostly decreased over time, not just in recent years but in many cases for decades. Quantities extracted and produced of most natural resources have also increased over the same long time frame. Deaton and Laroque (2003) set out a model that showed prices of commodities in developing countries can be characterized as containing no significant trend by linking commodity price determination to the Lewis (1954) model. Other studies have shown that mineral prices have either been roughly trendless over time or have been stationary around deterministic trends with infrequent structural breaks (Lin and Wagner, 2007).

Furthermore, the results are not in line with the Prebisch-Singer (PS) hypothesis. Examining long-run trends, Prebisch (1950) and Singer (1950) presented both theoretical justification and empirical evidence that there was a downward secular trend in relative primary commodities prices over the period 1870–1945. What has subsequently become popularized as the Prebisch-Singer (PS) hypothesis therefore argues that (log) relative commodity prices are steadily decreasing over time.

However, the scarcity of gold in South Africa and the rising price of gold seem to be consistent with the Hotelling rule. The gold price trends have shown a steady upward climb in line with the Hotelling rule. The gold reserves in South Africa have been seen to be low because they are depleting at a faster rate. At current production levels, South African gold resources will be exhausted in only 33 years (Statistics South Africa, 2015). This is supports Hotelling rule which argues that:

(i) In general, greater scarcity caused of in-situ reserves increases the value of a resource causing the price to increase over time. (ii) Since the price of a resource increases over time, then demand and production should decrease over time (Reynolds, 2010). The second principle has been observed in South Africa. The resource prices and the production levels have been going down. The monthly gold production index has fallen over

the years. In January 1980, the index was 359,0, while the volume of gold produced was far lower in January 2015, resulting in the low index of 48,4 (Stats SA, 2016). In other words, South Africa produced 87% less gold in January 2015 compared with the same month in 1980. General historical trends show that gold has lost the prominent place it once had in the South African economy. On the other hand, the price for gold has been increasing. This is consistent with the Hotelling rule.

5.5 CONCLUSION

The main aim of this chapter was to present the time series properties of the gold time series. The objective was to identify the trends and mean and variance properties of the South African gold prices and see if they follow the trend according to the Hotelling rule. Graphical analysis showed that there is an upward trend in the gold price series. This suggested that the gold price series is not mean reversion. Correlogram tests were also performed and they confirmed the findings from the graphical analysis; the gold time series seemed to follow a trend. Formal stationary tests were conducted and the results showed that the gold price series had a deterministic trend. Last but not least, the variance ratio test showed that the gold price series could either be following random walk or martingale. The test further revealed that the gold price series is not mean reverting. This shows that the gold price series follows the path that is consistent with Hotelling. Hotelling rule predicts resource pries to follow a rising trend. In other words, it expects resource prices to rise over time. This was confirmed by the findings in this study.

CHAPTER 6 DISCUSSION OF THE TREND PROPERTIES OF GOLD PRODUCTION AND CONSUMPTION

6.1. INTRODUCTION

Like the previous one, the structure of this chapter is twofold; it is descriptive and it also provides some formal tests to validate the findings from the descriptive aspect of the study. The purpose of this chapter is to present the time series properties of the gold production and gold consumption series. The objective is to identify the trends and properties of South African gold production and consumption to see if they follow the trend according to the Hotelling rule. The focus is to identify the actual properties of the gold production and gold consumption series and determine whether gold in South Africa is subject to increasing scarcity. The first section of the Chapter will look at gold production and examine its trends. The second section will focus on gold consumption. The last section will provide an in-depth discussion of the findings from both the first and second sections.

6.2. PRESENTATION OF RESULTS

1. Firms will always try to extract low-cost resources before high-cost resources causing resource extraction costs to increase over time. 2. In general, greater scarcity of in situ reserves increases the value of a resource causing the price to increase over time. 3. Since the price of a resource increases over time, then demand and production should decrease over time.

The previous chapter focused on the second principle. This chapter will focus on the third principle which states that production and consumption trajectory would be monotonically declining till the resource is exhausted. According to Hotelling this behaviour is compatible with social optimality. The chapter will, therefore, examine if gold production and gold consumption have been following negative or declining paths over time. Literature suggests that gold is a scarce resource in South Africa. For instance as there has been a marked decline in the discovery of new deposits, and because grades are decreasing, as higher- grade mines are exhausted gold is set to become even more scarce (This is Gold, 2015). Since the gold resource is scarce, the production path is expected to have a declining path.

In order to check whether gold production and gold consumption are following a rising, constant or declining path, several statistical and econometric techniques were used. Firstly, descriptive statistics were used to describe the basic features of the data in the study. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. Secondly, the study used hypothesis testing through econometric tests to validate the results from descriptive and graphical analysis. The variance ration test and stationarity tests were used in this regard. The methods employed in the study enable: i. Robust detection of the presence/absence of trends in the data, ii. Robust estimation of the variance ratio to determine if the data is mean reverting or mean averting The study was guided by literature in order to discover the time series properties of the gold price series. Literature showed that there has been a contentious debate as to whether resource prices followed the principles established by the Hotelling rule. The impact of exploration activities and an extension of the resource base on the Hotelling framework was first investigated by Pindyck (1978). By allowing the firm to simultaneously decide on exploration activities (with certain outcomes) and resource extraction, they found that exploration activities and the resource price and production path were related: With an increase in reserves came an increase in production (Dixon, 2012). However, as the discovery of further reserves and, hence, the exploration activity declined, production also decreased. Subsequent research on exploration in the context of non-renewable resources was surveyed by Cairns (1990) as well as Krautkraemer (1998). A noteworthy empirical application was made by Pesaran (1990). By investigating exploration and production decisions for oil on the United Kingdom continental shelf, they found a reasonable degree of support for the theoretical consideration of exploration in the Hotelling framework. This

100 study was directed by literature in examining if the trends in gold production and consumption in South Africa followed the optimal path as suggested by Hotelling.

6.3. GRAPHICAL ANALYSIS

The analysis was carried out through simple visual plots of the data. From this visual analysis trends and correlations can be seen. The advantage of this approach was that it was easy to use and has thus been widely utilised. Time series data poses a number of challenges in econometric analysis. According to Gujarati (2003:807), a graphical plot of the data can give an indication about the likely nature of the time series; however this study will rely on more formal tests of stationarity.

Gold Production Trends Gold Production

360 360 Fitted line

320 320

280 280

240 240

200 200

160 160

120 120

80 80

40 40

92 94 96 98 00 02 04 06 08 10 12 14 92 94 96 98 00 02 04 06 08 10 12 14

Years Years

Figure 6.1: Gold production trends (a) and (b)

Source: Author’s computation based of EViews 9

Results from Figure 6.1 (a) and (b) show that gold production has a downward trend and that production in South Africa is declining significantly. For many decades South Africa was the world’s largest gold producer, but production has declined precipitously over the past decade in particular. By 2013, the country’s market share had reduced to 5.3% of newly mined global supply. Figure 6.1(b) had a trend line fitted into it and the analysis showed that the gold production series might be trend stationary. The declining trend can also be examined through the Hodrick-Prescott filter shown in Figure 6.2 below.

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Hodrick-Prescott Filter (lambda=14400)

400

300

40 200

20 100

0 0

-20

-40 92 94 96 98 00 02 04 06 08 10 12 14

GPN Trend Cycle

Figure 6.2: Hodrick-Prescott filter

Source: Author’s computation based of EViews 9

The Hodrick-Prescott filter shows that gold production has been declining as shown by the declining gold production trend line in Figure 6.2. This shows that there has been a decrease in gold production over time in South Africa. This is in line with the Hotelling rule which states that resource production should decrease over time to reflect scarcity. However, some studies have found the opposite. For example, Scott and Pearse (1992) and Simon (1996), show that all of these theoretical trends have not occurred. Costs of extraction and prices of natural resources have mostly decreased over time, not just in recent years but in many cases for decades. Quantities of most natural resources extracted and produced have increased over the same long time frame. The only logical explanation is that technology and substitutes are in fact more powerful than scarcity. However, the findings from this study are consistent with the findings by Mudd (2009), who compiled historical data sets. (Mudd, 2009) showed that long-term trends for copper, gold, nickel, lead, silver and zinc ore grades in Australia are declining. In many cases, high quality ores have largely been exploited, and ores that require more complex processing remain.

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Correlogram The correlogram test is an informal test for stationarity which is based on inspection of the autocorrelation function. The correlogram test was conducted and the results are displayed in Table 6.1 below.

Table 6.1: Correlogram test

Date: 10/31/16 Time: 17:31 Sample: 1990M01 2015M12 Included observations: 312

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

1 0.990 0.990 308.52 0.000 2 0.983 0.151 613.59 0.000 3 0.976 0.043 915.50 0.000 4 0.969 -0.018 1213.9 0.000 5 0.962 0.006 1509.1 0.000 6 0.955 0.005 1801.1 0.000 7 0.947 -0.047 2089.2 0.000 8 0.940 -0.000 2373.9 0.000 9 0.932 -0.020 2654.9 0.000 10 0.925 0.002 2932.2 0.000 11 0.917 -0.028 3205.7 0.000 12 0.908 -0.056 3474.8 0.000 13 0.901 0.066 3740.5 0.000 14 0.893 0.001 4002.7 0.000 15 0.885 -0.025 4261.0 0.000 16 0.877 -0.031 4515.3 0.000 17 0.868 -0.030 4765.4 0.000 18 0.860 0.051 5012.1 0.000 19 0.852 -0.041 5254.6 0.000 20 0.843 -0.027 5493.0 0.000 21 0.835 0.015 5727.6 0.000 22 0.826 -0.036 5957.8 0.000 23 0.817 0.013 6184.1 0.000 24 0.809 0.019 6406.8 0.000 25 0.800 -0.024 6625.4 0.000 26 0.791 -0.023 6839.9 0.000 27 0.782 -0.018 7050.3 0.000 28 0.772 -0.042 7256.1 0.000 29 0.763 0.007 7457.9 0.000 30 0.755 0.033 7655.7 0.000 31 0.745 -0.048 7849.1 0.000 32 0.736 -0.005 8038.4 0.000 33 0.726 0.018 8223.7 0.000 34 0.717 -0.020 8404.9 0.000 35 0.707 -0.025 8581.9 0.000 36 0.698 0.001 8754.7 0.000

Source: Author’s computation based of EViews 9

From Table 6.1 it can be seen that the gold price series is not stationary. This confirms the non-stationarity of the gold price series. A statistical process is said to be stationary if the auto-correlation function either abruptly drops to zero at some finite lag or eventually tapers

103 off to zero (Karasavvoglou, 2016). In this case, the autocorrelation function does not drop to zero and it can thus be said that the gold price series is not stationary. What is interesting to note is that there is a trend in the gold production series data. This is shown by the autocorrelation which is declining towards zero with each additional lag. If it were fluctuating up and down as it went towards zero, it would have been said that there is no trend. But here the autocorrelation is declining towards zero. This confirms the findings from the visual inspection that there is a deterministic trend in the gold production series. This then supports the fact that gold production is decreasing in South Africa.

Formal unit root tests

The primary statistical concern of this chapter is to use hypothesis testing to verify if there is a trend in the gold production data. This seeks to complement or validate what has already been observed in the previous section. Mere visual examination of a time series is insufficient to determine its stationarity properties (Hamilton cited in Ahrens & Sharma, 1997). Accordingly, in addition to the visual inspection of the graphical plots of the gold time series, some formal stationarity tests were conducted.

6.3.1.1. Augmented Dickey-Fuller

An augmented Dickey-Fuller test (ADF) tests the null hypothesis of a unit root is present in a time series sample. With Eviews one can get results for three different variants of the test: without constant and trend, with constant only and with constant and trend. The test was conducted with the variant with constant and trend. This was done because a trend was observed in the graphical analysis of the gold production series.

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Table 6.2: Augmented Dickey-Fuller test

Null Hypothesis: GPN has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Automatic - based on SIC, maxlag=15)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -2.538107 0.3095 Test critical values: 1% level -3.988036 5% level -3.424435 10% level -3.135264

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(GPN) Method: Least Squares Date: 10/18/16 Time: 14:07 Sample (adjusted): 1990M04 2015M12 Included observations: 309 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GPN(-1) -0.079457 0.031306 -2.538107 0.0116 D(GPN(-1)) -0.420873 0.058190 -7.232732 0.0000 D(GPN(-2)) -0.247677 0.055717 -4.445248 0.0000 C 26.04252 10.87455 2.394813 0.0172 @TREND("1990M01") -0.075350 0.030294 -2.487296 0.0134

Source: Author’s computation based of EViews 9

Results from the Augmented Dickey-Fuller test show that the gold production series is not stationary and that it has a deterministic trend. This is seen by the 0.0134 p value on the trend coefficient. This shows that the gold price series has a trend. This supports the results from the graphical analysis which showed that the gold price series has a downward trend.

6.3.1.2. Phillips-Perron Test

With E-views one can get results for three different variants of the test: without constant and trend, with constant only and with constant and trend. The test was conducted with the variant with constant and trend. This was done because a trend was observed in the graphical analysis of the gold production series. Results are shown in Figure 6.3 below.

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Table 6.3: Phillips-Perron test with constant and trend

Null Hypothesis: GPN has a unit root Exogenous: Constant, Linear Trend Bandwidth: 2 (Newey-West automatic) using Bartlett kernel

Adj. t-Stat Prob.*

Phillips-Perron test statistic -4.051770 0.0082 Test critical values: 1% level -3.987841 5% level -3.424340 10% level -3.135208

*MacKinnon (1996) one-sided p-values.

Residual variance (no correction) 51.86967 HAC corrected variance (Bartlett kernel) 32.73077

Phillips-Perron Test Equation Dependent Variable: D(GPN) Method: Least Squares Date: 10/18/16 Time: 14:11 Sample (adjusted): 1990M02 2015M12 Included observations: 311 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GPN(-1) -0.157440 0.031412 -5.012163 0.0000 C 53.37728 10.86979 4.910608 0.0000 @TREND("1990M01") -0.149406 0.030344 -4.923787 0.0000

Source: Author’s computation based of EViews 9

Table 6.3 shows that gold prices were stationary in levels. At levels, the p-values of the gold price variable (0.0082) is smaller than 0.05 indicate the rejection of the null hypothesis of the existence of unit root in levels for gold prices. A trend option was chosen in the Phillips- Perron test because visual inspection indicated that there might be a trend in the data. The results from the Phillips-Perron test equation confirm the presence of the trend in the data. The p-value for TREND (1990M01) is statistically significant (0.0000). This suggests that there is a trend in the data. The results support the downward trend that was displayed in the graphical analysis section.

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6.3.1.3. KPSS Test

Results from the KPSS test are shown in Table 6.4 below.

Table 6.4: KPSS test with constant linear trend

Null Hypothesis: GPN is stationary Exogenous: Constant, Linear Trend Bandwidth: 14 (Newey-West automatic) using Bartlett kernel

LM-Stat.

Kwiatkowski-Phillips-Schmidt-Shin test statistic 0.176199 Asymptotic critical values*: 1% level 0.216000 5% level 0.146000 10% level 0.119000

*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)

Residual variance (no correction) 173.3341 HAC corrected variance (Bartlett kernel) 1801.555

KPSS Test Equation Dependent Variable: GPN Method: Least Squares Date: 10/18/16 Time: 14:12 Sample: 1990M01 2015M12 Included observations: 312

Variable Coefficient Std. Error t-Statistic Prob.

C 343.8950 1.491929 230.5037 0.0000 @TREND("1990M01") -0.953031 0.008302 -114.7909 0.0000

Source: Author’s computation based of EViews 9

The test result shows that the null hypothesis is rejected, which indicates non-stationarity. The Kwiatkowski-Phillips-Schmidt-Shin (KPSS, 1992) LM test statistic is 0.176199 (allowing for constant, trend, bandwidth=9, Newey-West using Bartlett kernel), where the asymptotic critical value is 0.119 for the 10% level. Hence, the study rejects the trend stationary null at conventional levels. This shows that the gold production variable is not trend stationary at levels. Results also show that there is a trend in the data. This reinforces what has been found in the graphical analysis. Graphical analysis showed that there is a downward trend in the gold production series.

6.3.1.4. DF-GLS test

In addition to the unit root tests used above, the study also applied a more efficient univariate DF-GLS test for autoregressive unit root recommended by Elliot, Rothenberg, and Stock

107

(ERS, 1996). The test is a simple modification of the conventional augmented Dickey-Fuller (ADF) t-test as it applies generalised least squares (GLS) detrending prior to running the ADF test regression. Results are shown in Table 6.5 below.

Table 6.5: DF-GLS test on GLS detrended residuals

Null Hypothesis: GPN has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Automatic - based on SIC, maxlag=15)

t-Statistic

Elliott-Rothenberg-Stock DF-GLS test statistic -2.176537 Test critical values: 1% level -3.470900 5% level -2.908200 10% level -2.601850

*Elliott-Rothenberg-Stock (1996, Table 1)

DF-GLS Test Equation on GLS Detrended Residuals Dependent Variable: D(GLSRESID) Method: Least Squares Date: 10/18/16 Time: 14:18 Sample (adjusted): 1990M04 2015M12 Included observations: 309 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GLSRESID(-1) -0.056702 0.026052 -2.176537 0.0303 D(GLSRESID(-1)) -0.435514 0.057030 -7.636549 0.0000 D(GLSRESID(-2)) -0.256494 0.055266 -4.641069 0.0000

R-squared 0.215230 Mean dependent var 0.094598 Adjusted R-squared 0.210101 S.D. dependent var 7.507341 S.E. of regression 6.672246 Akaike info criterion 6.643451 Sum squared resid 13622.77 Schwarz criterion 6.679697 Log likelihood -1023.413 Hannan-Quinn criter. 6.657943 Durbin-Watson stat 2.003979 Source: Author’s computation based of EViews 9

Results showed that the gold production series is not stationary. This is shown by the t-statistic (-2.176537) which is less than the critical value (-2.908) at 5% significance level.

6.3.1.5. Break point unit root

A break point unit root was also undertaken because the power of unit root tests is reduced significantly when the stationary alternative is true and a possible structural break is ignored. Neglecting a break in an otherwise trend stationary process can cause the spurious appearance of unit root behavior (Perron, 1989) while a neglected trend break in a difference stationary process can lead standard unit root tests to incorrectly suggest the presence of

108 stationarity (Leybourne et al., 1998). Results from the break point unit root are shown in Table 6.6.

Table 6.6: Break point unit root

Null Hypothesis: GPN has a unit root Trend Specification: Trend and intercept Break Specification: Intercept only Break Type: Innovational outlier

Break Date: 2012M11 Break Selection: Minimize Dickey-Fuller t-statistic Lag Length: 2 (Automatic - based on Schwarz information criterion, maxlag=15)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -4.437249 0.1541 Test critical values: 1% level -5.347598 5% level -4.859812 10% level -4.607324

*Vogelsang (1993) asymptotic one-sided p-values.

Augmented Dickey-Fuller Test Equation Dependent Variable: GPN Method: Least Squares Date: 01/22/17 Time: 12:53 Sample (adjusted): 1990M04 2015M12 Included observations: 309 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

GPN(-1) 0.843511 0.035267 23.91768 0.0000 D(GPN(-1)) -0.406179 0.059139 -6.868263 0.0000 D(GPN(-2)) -0.238350 0.054746 -4.353768 0.0000 C 53.74587 12.32993 4.358975 0.0000 TREND -0.163194 0.035776 -4.561548 0.0000 INCPTBREAK 6.924098 1.602950 4.319596 0.0000 BREAKDUM -9.165693 7.026966 -1.304360 0.1931

Source: Author’s computation based of EViews 9

The t-statistic of -4.437249, and the corresponding p-value of 0.1541 indicates we cannot reject the hypothesis that the gold production series (GPN) has a unit root. Furthermore, the results show that there is a trend in the data as shown by the 0.0000 p-value of the TREND. This shows that there is a trend in the data.

6.2.4 Growth rate in gold production

The growth rate was used to check how the gold production has been evolving over time. The focus was to check the rate of increase or decrease in the gold production rate in South Africa. If the rate is increasing, then the Hotelling rule would not hold but if it is increasing then the findings would be consistent with the Hotelling rule.

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See Figure 6.3 below.

Gold Production growth rate

1.0

0.8

0.6

0.4

0.2 Fitted line 0.0

-0.2

-0.4

-0.6

92 94 96 98 00 02 04 06 08 10 12 14

Years

Figure 6.3: Growth rate in gold production

Source: Author’s computation based of EViews 9

Results show that the growth rate has been negative in most of the periods. The growth rate has been close to zero in all the periods and it has been negative in most cases. This shows that there has not been an increase in gold production over the study period. This is in line with statistical and empirical facts. Figures from the Stats SA show that South African gold production (extraction) has decreased from 675 tons in 1980 to 198 tons in 2009, which represents a 71% decrease over a 29-year period. South Africa's gold production (extraction) year-on-year, showed a negative growth. However, although the results are in line with statistical evidence, they are not in line with what has been found in other countries. A closer statistical examination reveals that the production of non-renewable resources exhibits significantly positive growth rates in the long term.

Economic growth causes the production and use of a non-renewable resource to increase exponentially, and its production costs to stay constant in the long term. This shows that in

110 some countries there has been an increase in production. Global gold production has increased from ~2 445 metric tons in 2000 to ~2 770 metric tons in 2013 (USGS, 2014 ). This increase has been driven by personal consumption (e.g. jewellery), particularly in China and India (World Gold Council, 2012 , Cremers et al., 2013), and uncertainty in global financial markets (e.g. value of the dollar and euro) (Shafiee & Topal 2010). This increase in demand over the last 13 years has been paralleled by a dramatic increase in price (Shafiee & Topal, 2010). Over the last 13 years, the price of gold has increased from $250/ounce in 2000 to $1 300/ounce in 2013 (World Gold Council, 2012). This rise in global demand and the price of gold have stimulated new gold mining activities by multinational companies and small-scale gold miners throughout the world (Bury, 2004; Creek, 2009). But this has not been the case in South Africa. The growth rate in gold production shows that gold production is declining over time.

6.4. CONSUMPTION OF GOLD

The main aim of this section is to examine whether or not gold consumption has been declining over time. The Hotelling rule argues that in the social optimum the price of a non- renewable resource should be rising at the rate of interest (Slade, 2009). Furthermore, resource consumption should decline over time, asymptotically falling to zero (Dasgupta & Heal, 1974). This will result in an extraction path that is socially optimal according to Hotelling. This chapter however, assumes that the current consumption rate is ever- increasing. This is supported by empirical evidence. The chapter presents some evidence to show that consumption is ever-increasing. The chapter, however, does not go into this in detail because it has taken increasing consumption to be a given. The chapter looks at both domestic and international gold consumption. Results of domestic gold consumption are shown in Figure 6.4 below.

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Hodrick-Prescott Filter (lambda=14400)

2,000

1,500

1,000

500 1,200 0 800

400

-400

-800 96 98 00 02 04 06 08 10 12 14

GDC Trend Cycle

Figure 6.4: Domestic gold consumption

Source: Author’s computation based of EViews 9

The Hodrick-Prescott filter shows that there is a rising trend in domestic gold sales (gold consumption) in South Africa. This is illustrated by the trend line which has been rising steadily since 1995. The trend line shows that gold sales were slowly declining from 1995 till 2001 when it began to rise. From 2001 on there was a gradual increase in gold sales in South Africa. This is not in line with Hotelling rule which states that production and consumption of a resource should decline over time. The fact that gold consumption fell between 1994 and 2001 prompts the need to examine the growth rate under this period of investigation. This is the focus of Figure 6.5.

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Domestic Gold Sales

-1

96 98 00 02 04 06 08 10 12 14

Years

Figure 6.5: Domestic gold sales

Source: Author’s computation based of EViews 9

Figure 6.5 shows that there is a moderate degree of volatility in the rate of change of the domestic gold sales (gold consumption). More significantly for the purpose at hand, is the fact that this volatility appears to be above zero in many periods. Only in a few cases is the growth rate below zero. This shows that there was a positive growth rate in the gold price in many cases during the period under investigation (1995–2015). This is not the kind of trend that is suggested by the Hotelling rule. The Hotelling rule expects consumption to decrease over time. Global the demand for gold has been increasing, a trend that is not consistent with the Hotelling rule. Figure 6.6 shows these trends.

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Figure 6.6: HP Filter

Hodrick-Prescott Filter (lambda=100)

5,000

4,500

600 4,000

400 3,500

200 3,000

-200

-400

05 06 07 08 09 10 11 12 13 14 15

GD Trend Cycle

Source: Author’s computation based of EViews 9

Figure 6.6 shows that demand for gold has been on the increase as shown by the rising trend. Gold demand has been on the rise since 2005 and it has maintained the rising trend. However, it declined steadily around 2008. This might have been caused by the global financial crisis. The demand rose again in 2009 and then started to have a negative trend from 2013. However, the drop in 2013 and 2014 was only for a short time. Overall, it can be said that the demand for gold has been rising since 2005. The growth rate for this period is a positive 0.027538. This shows that there has been an increase in gold demand between 2005 and 2015. This is inconsistent with the Hotelling rule which predicted that the price of non-renewable resource should rise over time and this should depress demand for that commodity.

6.5. DISCUSSION OF RESULTS

The analysis above revealed that gold production has been decreasing. South Africa's gold production has decreased, resulting in the country dropping in production ranking from the second-largest to the fourth-largest producer in the world. Graphical analysis, formal

114 hypothesis tests and descriptive statistics showed that there is a downward trend in South

African gold production. In fact, most of the other large gold-producing countries have increased their output – even other mature producing countries like Australia and the USA. By contrast, South Africa’s rate of production over the past decade shows the highest rate of decline out of the world’s top 10 producing countries. According to Statistics South Africa, South Africa’s annual gold production in 2012 was close to 2206 tonnes, which is a level of gold production not seen since 1922 (GCIS, 2013).

However, the question is: is the declining gold production an indicator of a socially optimal path suggested by Hotelling? In other words is the falling gold production supporting the Hotelling rule? The decrease in production is mainly as a result of the mining of lower-grade7 ore89, influenced by higher rand gold prices, and temporary closure of shafts to maintain infrastructure (Stats SA, 2016). South African gold production (extraction) has decreased from 675 tons in 1980 to 198 tons in 2009, which represents a 71% decrease over a 29-year period. This is in line with the Hotelling rule; resource production should decrease over time to reflect resource scarcity. The findings are also in line with empirical evidence. Mudd (2009) showed that long-term trends for copper, gold, nickel, lead, silver and zinc ore grades in Australia are declining. In many cases, high quality ores have largely been exploited, and ores that require more complex processing remain.

The analysis above has shown that the declining gold production trends are in line with the Hotelling rule. According to the Hotelling rule for the owner of a non-renewable resource the equivalent condition is price = MC + the opportunity cost of depletion, implying that less of the resource will be extracted in any period, than if it were renewable (Minnitt, 2007). However the consumption trends have shown otherwise. The trends have been seen to be increasing despite the increasing gold prices. This is not in line with the Hotelling rule which expects a declining trend in the consumption of resources. Even though the production (extraction) of South African gold has been decreasing, the output (sales) have shown an

6 Only 40 years ago South Africa produced more than 1 000 tonnes of gold a year. This shows that gold production has been on a downward trend. 7 A crucial determinant of the peak minerals phenomenon is declining grade and quality – that is, the concentration of a particular mineral or metal (or metals) being mined, as well as the quality of the ore with respect to processing (prior et al. 2007) 8 Since the late 1990s there has been little effort focused on developing depletion models for mineral resources. This can firstly be attributed to the general expectations within the industry that knowledge and technology will address any shortfalls in production (e.g. the ability to maintain high production output even when ore grades are declining). 9 It is believed that when the price of gold suddenly rises, producers are afforded the opportunity to prolong the life expectancy of a mine. They do this by mining the poorer quality veins of gold first, since it is now profitable to do so. This was long noticed by Keynes who argued that the gold supply curve is backward is SA.

115 increase over the years. The output (sales) revenue of gold was R45 992 million in 2008 and this increased by 6% to R48 696 million in 2009. This hsows that demand for gold hs been increasing and the increase is likely to come from outside South Africa. Demand for gold increased in 2009, particularly from India and China (China and India have been growing so fast). This shows that the current rates of consumption are unsustainable because they do not follow the Hotelling rule's socially optimal extraction path.

In reality, however, the declining consumption requirement appears to be unfulfilled. Economic growth causes the production and use of a non-renewable resource to increase exponentially, and its production costs to stay constant in the long term. Consumption patterns continue to rise in middle- to high-income countries, and are reaching unprecedented levels in low-income countries, whose appetite for the world’s minerals reflects their rapid development (CRU International, 2001). Natural mineral resources, such as gold, play a fundamental role in our economies. They are key inputs in important industries like construction, electric materials, electronics, shipbuilding, or automobiles, among many others. This importance has contributed to the development of large industries for the extraction and processing of these minerals. Natural resources have always been the material basis of societies and their economic systems. However, in human history, the per capita level of resource consumption has changed dramatically. Humans today extract and use around 50% more natural resources than only 30 years ago, at about 60 billion tonnes of raw materials a year (Isaac et al. 2012 and FOE, 2015). People in rich countries consume up to 10 times more natural resources than those in the poorest countries. The quantity of natural resources extracted for the production of goods and services is steadily increasing.

Consumption in Asian countries and the Middle East has driven demand in recent years. Demand for gold as a monetary investment has also increased in recent years. Gold is seen as a relatively secure ‘defensive’ investment when used as a store of wealth. Investors traditionally turn to gold as a more dependable asset if economic conditions in major countries are uncertain. More recently, investment demand for gold has been driven by European debt concerns, unrest across North Africa and the Middle East, and unease in China regarding rising inflation (DFAT, 2015).

The above analysis shows that gold consumption is increasing and this violates the Hotelling rule principle which expects consumption to decrease over time. This shows that the Hotelling rule does not hold for gold consumption in South Africa. A more important question

116 is whether the failure of this Hotelling rule principle implies that the market is failing to produce a socially optimal resource consumption path. Chapter 7 contributes to answering this question.

6.6. CONCLUSION

The purpose of this chapter was to present the time series properties of the gold production and gold consumption series. The objective was to identify the trends properties of the South African gold production and consumption to see if they follow the trend according to the Hotelling rule. This was shown by the declining gold production trend. This shows that there has been a decrease in gold production over time in South Africa. It was also shown that the gold price series has a trend. This supported the results from the graphical analysis which showed that the gold price series has a downward trend. This chapter however, assumed that the current consumption rate is unsustainable and is ever-increasing. This is supported by empirical evidence. The chapter presented some evidence to show that consumption is ever-increasing.

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CHAPTER 7 PRESENTATION AND ANALYSIS OF EMPIRICAL FINDINGS

7.1. INTRODUCTION

The main objective of this chapter is to empirically test the significance of the Hotelling rule using structural equation modelling. This chapter provides an overview of the estimated results and relevant findings from previous chapters by providing an analysis of the empirical results. The chapter is only interested in the long run relationship between interest rate and gold price. The Hotelling rule focusses on the long run relationship between these two variables. The chapter is also concerned on the variance decomposition. The variance decomposition provides information about the relative importance of each random innovation in affecting the variables in the VAR. the focus shall, therefore, be on:

(i) Looking at the long run relationship between gold price and interest rates (ii) Looking at the variance decomposition to examine the relative importance of each random innovation in affecting the variables in the VAR

This chapter comprises of five subsections which start with this introductory part. Formal and informal unit root tests follow the introduction with cointegration techniques presented in the third subsection. In the fourth subsection, diagnostic checks are presented followed by variance decomposition. The sixth subsection concludes the chapter.

7.2. UNIT ROOT TESTS

The Johansen cointegration test, among other tests that were used in this study, requires variables to be tested for stationarity in order to determine their order of lag length. Each variable should prove existence of unit root. Unit root testing is important as a diagnostic tool for selecting forecasting models. In time series data it also helps because it tests for stationarity in response to the problems (spurious regression) that non-stationary time series data impose on the tested variables. An informal test of stationarity and two formal tests were employed in this study.

Informal unit root tests

The first test was carried out using graphical presentations with the aim of checking properties of the time series data. Graphical presentation is important in checking structural

118 breaks that may give biased results of the unit root tests. Figure 7.1 below displays raw data of all variables used in the model at level series.

LGP SAINT

10.0 140

9.5

120 9.0

8.5 100 8.0

7.5 80

7.0

6.5 60

90 92 94 96 98 00 02 04 06 08 10 12 14 90 92 94 96 98 00 02 04 06 08 10 12 14

USINT BDI

12 120

10 110

100

90 4

2 80

90 92 94 96 98 00 02 04 06 08 10 12 14 90 92 94 96 98 00 02 04 06 08 10 12 14

Figure 7.1: Graphical analysis at levels

Source: Author's computation using Eviews 9

All variables prove to be non-stationary at level series as they are not fluctuating around mean zero. This analysis gives inconclusive results and displayed the need to first difference data so as to attain stationarity of variables. In Figure 7.2, variables were first differenced and the graphical analysis was repeated.

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Differenced LGP Differenced SAINT

.2 15

10 .1

-.1 -5

-.2 -10

90 92 94 96 98 00 02 04 06 08 10 12 14 90 92 94 96 98 00 02 04 06 08 10 12 14

Differenced USINT Differenced BDI

.8 6

4 .4

-.4 -2

-.8 -4

90 92 94 96 98 00 02 04 06 08 10 12 14 90 92 94 96 98 00 02 04 06 08 10 12 14

Figure 7.2: Graphical analysis at first difference

Source: Author’s computation using Eviews 7

Figure 7.2 shows that after differencing once, all variables became stationary. Fluctuations around mean zero indicated that the series is stationary if integrated of order one. Results from the formal test are displayed in Table 7.1 below

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Table 7.1: Phillips Perron Tests Phillips Perron Test

Variables Level 1ST Difference

BDI -1.431176 11.33636*

GP -1.063543 -15.22684*

SAINT -2.401863 -12.70359*

INT 1.519347 12.65122*

Test Critical values: 1% level -3.451283 5% level -2.870651 10% level -2.571695

Results show that all variables were not stationary at levels. They became stationary after being differenced once.

7.3. COINTEGRATION TESTS

This study employed the Johansen likelihood approach to test for cointegration since the Johansen test captures underlying time series properties of the data. Before the cointegration tests was done several tests had to be conducted to examine the data properties. These are discussed below.

Cointegration test results

a. Order of integration Unit root testing conducted showed that all variables became stationary when first differenced. It can be concluded that all variables in the model of the study became stationary when integrated of order one. This made the application of the VAR/VECM appropriate.

b. Optimal Lag Length Selection Criteria A critical element in the specification of VAR models is the determination of the lag length of the VAR. In this regard, a VAR lag order selection criteria was performed. Table 7.2 presents the selection of an optimal lag length.

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Table 7.2: Lag selection

VAR Lag Order Selection Criteria Endogenous variables: LGP USINF USINT BDI GPN Exogenous variables: C Date: 01/26/17 Time: 04:25 Sample: 1990M01 2015M12 Included observations: 304

Lag LogL LR FPE AIC SC HQ

0 -3191.855 NA 936.8804 21.03194 21.09308 21.05640 1 -917.8640 4458.219 0.000351 6.235948 6.602760 6.382681 2 -830.8209 167.7872 0.000234 5.827769 6.500257* 6.096780* 3 -805.5298 47.91989 0.000233* 5.825854* 6.804019 6.217143 4 -789.7520 29.37577 0.000248 5.886526 7.170368 6.400093 5 -771.0129 34.27284 0.000259 5.927716 7.517235 6.563561 6 -748.0049 41.32357* 0.000263 5.940822 7.836017 6.698944 7 -736.8608 19.64886 0.000288 6.031979 8.232850 6.912379 8 -719.1914 30.57273 0.000303 6.080206 8.586755 7.082884

Source: Author’s computation based of EViews 9

Results show that the SC and HQ selected 2 lags and the AIC and FPE selected 3 lags. This study used the AIC which selected 3 lags. Thus, subsequent analyses were based on VAR with 3 lags. After the optimal lag length was determined the Johansen test was performed to examine if there was a long run relationship among the variables. Table 7.3 examines if there was cointegration in the variables.

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Table 7.3: Cointegration

Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.316066 144.0567 69.81889 0.0000 At most 1 0.046348 26.66934 47.85613 0.8665 At most 2 0.029702 12.00529 29.79707 0.9317 At most 3 0.008060 2.688390 15.49471 0.9792 At most 4 0.000608 0.187844 3.841466 0.6647

Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.**

None * 0.316066 117.3874 33.87687 0.0000 At most 1 0.046348 14.66404 27.58434 0.7743 At most 2 0.029702 9.316900 21.13162 0.8061 At most 3 0.008060 2.500546 14.26460 0.9743 At most 4 0.000608 0.187844 3.841466 0.6647

Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Source: Author’s computation based of EViews 9

Table 7.3 shows that both the Trace and Maximum Eigen tests indicated that there was at least 1 cointegrating relationship in this model. The cointegration test has proved that the variables are cointegrated, and as a result of this the VEC model can be done. One cointegrating vector in our VAR model realised from table 7.3 above is confirmed by the cointegrating graph below.

123

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00 90 92 94 96 98 00 02 04 06 08 10 12 14

Cointegrating relation 1

Source: Author’s computation using Eviews 9

It can be observed from the graph that over the period 1990 to 2015, the deviations of gold price from equilibrium were stationary. Thus, the study estimated VECMs restricted on 1 cointegrating vector.

7.4. Vector Error Correction Model – Long-Run Relationships

Since the variables were cointegrated, a VECM was used in order to determine the interrelation between them. Results from the VECM are presented in table 7.4 below.

Table 7.4: Long run relationship results Variable Coefficient Standard error t-statistic

SAINT -0.017933 0.00660 2.71923

INT -0.501446 0.04781 10.4876

BDI -2.3405 0.01084 0.00216

Source: Author’s computation using Eviews 9

Results show that there is a negative relationship between SAINT (SA interest rate) and the GP (Gold price). Furthermore, results also show that there is a negative relationship

124 between USINT (US interest rate) and the GP (Gold price). This is inconsistent with the Hotelling rule. The Hoteling rule states that the price of a resource should rise at the rate of interest rate. If this holds, then a positive relationship should be established. Results from Chapter 6 showed that gold production is decreasing and it was also seen in Chapter 5 that the price of gold has a positive growth rate whilst the interest rates have negative growth rates. This might explain why there is a negative relationship between the gold price and interest rate. According to Auty et al. (1998) extraction decreases when the rate of increase in the price of the mineral is greater than the current rate of interest. Thus, in order for a non- renewable resource be extracted in an optimal fashion, the market price should rise at the rate of interest rate. The reason why there is negative relationship may be that the gold prices are determined by global conditions. It should be noted that supply and demand conditions do not conform to world conditions of relative mineral scarcity. Therefore, the operation of the Hotelling rule would not result in an optimum production path for achieving national sustainability (Auty et al. 1998).

Results show that there is a negative relationship between BDI and interest rate. However, this relationship is insignificant as show by the 0.00216 t-statistic. Results from the error correction model are show in table 7.5 below.

Table 7.5: Vector Error Correction Model – Short-run relationships

Variable Coefficient Standard error t-statistic

D(LGP) -0.140470 0.05745 -2.44513

D(INT) 1.333126 1.42288 0.093692

D(SAINT) -0.103141 0.24695 -0.41766

D(BDI) -0.619606 0.39101 -1.58462

Source: Author’s computation using Eviews 9

In Table 7.5 below, the coefficient of D(LGP) of -0.140470 shows that the speed of adjustment is approximately 14%. This indicates that if there is a deviation from equilibrium, only 14% is corrected as the variable moves towards restoring equilibrium. The slow speed of adjustment of LGP may imply that there were variables other than the ones specified in the model that affected LGP. Most of the short-run effects from the VECM were insignificant.

125

However, this is not much of a problem because the study was not aimed at the short run relationships. More information on the short-run dynamics can be obtained from impulse response and variance decomposition analyses. However, before considering impulse response and variance decomposition analyses, there was a need to confirm that the results from the VECMs just reported were deriving from efficient models with well-behaved residuals. This was done by performing diagnostic tests on the residuals from the alternative model specifications. Diagnostic checks are discussed in the following section.

7.5. DIAGNOSTIC TESTS

Gujarati (2004:516) argues that diagnostic tests should be performed so that the model finally chosen is a good model in the sense that all the estimated coefficients have the right signs, they are statistically significant on the basis of the t and F tests. In this regard, diagnostic tests were important in validating the parameter evaluation of the outcomes achieved by the model.

AR roots test

The estimated VAR is stable (stationary) if all roots have modulus less than one and lie inside the unit circle. If the VAR is not stable, certain results (such as impulse response standard errors) are not valid. There will be roots, where is the number of endogenous variables and is the largest lag. The VAR was tested for AR Roots test the results are indicated in Figure 7.6..

Inverse Roots of AR Characteristic Polynomial

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

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Figure 7.4: AR Roots graph

Source: Author’s computation based of EViews 9

AR test assumes that the estimated VAR is stationary if all roots lie within the circle and their modules are less than one. From the table below we can conclude that the VAR model is stable since all roots lie within the circle and are less than one.

Autocorrelation LM test

In Table 7.7 LM results suggest that we cannot reject the null hypothesis of no serial correlation and conclude that there is no serial correlation among the variables in this study.

Table 7.7: Langrange Multiplier test results

Lags LM-Stat Prob

1 12.70553 0.6942 2 13.75357 0.6171 3 16.27171 0.4342 4 14.35117 0.5726 5 30.88381 0.0139 6 17.18938 0.3734 7 16.91525 0.3911 8 22.13429 0.1389 9 23.10793 0.1109 10 25.34843 0.0639 11 24.95071 0.0707 12 28.54790 0.0272 13 12.19716 0.7303 14 28.88910 0.0247 15 14.51032 0.5608 16 16.10866 0.4454 17 8.924571 0.9165 18 17.63788 0.3455 19 10.83762 0.8194 20 21.57537 0.1574 21 20.00259 0.2201 22 11.06751 0.8053 23 13.65632 0.6243 24 33.59033 0.0062 25 26.98628 0.0416 26 17.91886 0.3287 27 23.82882 0.0933 28 24.50941 0.0790 29 10.70132 0.8275 30 21.36231 0.1650

Source: Author’s computation based on EViews 9

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Jarque-Bera Normality test

Normality test was carried out using Jarque-Bera test. Table 7.8 below presents results for skewness using the Jarque-Bera test for normality.

Table 7.8: Residual normality test

Null Hypothesis: residuals are multivariate normal

Chi-sq P value

Skewness 3.436941 0.1169

Source: Author’s computation based of EViews 9

The results show that the residuals were normally distributed. This is shown by the p-value (0.1169) which is above 0.05.

Variance decomposition

The Variance decomposition was carried out using Eviews 9 and the results are shown in Figure 7.5.

Period S.E. LGP SAINT USINT BDI

1 0.041779 100.0000 0.000000 0.000000 0.000000 2 0.063820 99.46692 0.001171 0.171937 0.359971 3 0.078405 99.14719 0.156535 0.333302 0.362976 4 0.090099 98.86669 0.399762 0.419585 0.313961 5 0.100380 98.71317 0.587637 0.421742 0.277449 6 0.109689 98.62845 0.717607 0.400923 0.253022 7 0.118215 98.57742 0.802397 0.385417 0.234771 8 0.126122 98.54475 0.856278 0.379214 0.219753 9 0.133541 98.52145 0.891042 0.380079 0.207427 10 0.140564 98.50256 0.914271 0.385611 0.197562

Cholesky Ordering: LGP SAINT USINT BDI

Figure 7.5: Variance decomposition

Source: Author’s computation based of EViews 9

The forecast horizon was in months. Results show that SAINT, USINT and BDI are practically insignificant in explaining fluctuations in the gold price. This may suggest that the interest rate does not have huge impact on the gold price. This is not in line with the Hotelling

128 rule. The Hotelling rule believes that the interest rate is significant in influencing the gold price.

7.6. CONCLUSION

This chapter analysed the impact of interest rates on gold price and presented the results from econometric analysis employing the different techniques as outlined in Chapter 4. It was divided into six subsections including the introduction. After the introduction in the first section, the second subsection presented both formal and informal unit root testing methods. Under informal unit root tests, graphical presentations were made to determine stationarity of variable.

In the third subsection cointegration is discussed whereby the Johansen maximum likelihood approach was used. The information criteria approach was used for optimal lag length selection and 3 lags were used for the VAR in the study. The Johansen cointegration test was performed under the assumption of intercept and trend. The determination of the number of co-integrating vectors followed whereby the trace and maximum Eigen value cointegration tests were used. Both tests reflected that at least one cointegrating equations existed at 5% significance level. One cointegrating equation was established and this allowed for the estimation of the VECM in the third subsection. Diagnostic checks, impulsive response and variance decomposition analyses were presented in the fifth and sixth subsections respectively. To assess the suitability of the model, autocorrelation, heteroskedasticity and normality tests were used. They all pointed out that the model was suitable.

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CHAPTER 8 SUMMARY, IMPLICATIONS AND RECOMMENDATIONS

8.1. INTRODUCTION

The main aim of this chapter is to summarise the whole study and then to achieve the last objective of the study; to make policy recommendations based on the study’s findings. In this chapter there is a brief summary of theoretical and empirical literature and reflection on the main study aim, associated study objectives and its background. The chapter allows conclusions to be drawn in order to achieve the research objectives. Moreover the contribution of the study to the literature and practice are reflected upon by pointing out the limitations encountered in the study. Finally some recommendations are suggested with some prospective ideas for future research.

8.2. BRIEF OVERVIEW OF THE RESEARCH STUDY

The main aim of this study was to test the relevance of the Hotelling rule in the gold mining sector in South Africa. Since the 1980s, many economists have tried to test whether the Hotelling rule holds up to empirical scrutiny. Most, if not all, of the studies conducted to test the Hotelling rule were in developed countries. The Hotelling rule, which states that the shadow price of an exhaustible resource must grow at a rate equal to the interest rate, is recognised as the central proposition of resource economics. The Hotelling rule illustrates the time path of non-renewable resources’ extraction which maximises the value of the natural resource stock. The Hotelling rule is a necessary efficiency condition that must be satisfied by any optimal extraction programme. The extraction path in competitive market economies will, under certain circumstances, be socially optimal. An extraction path that is not socially optimal compromises the welfare of future generations.

The welfare of South Africa’s present population and more especially that of the future will be largely determined by the stock of natural resources available and the quality of the environment. The study showed that gold depletion is occurring at a faster rate than is socially optimal. Because of fewer discoveries, reduced mine life and a lower gold price, the quantity of known gold that is economically worth mining is falling. Major producers’ reserves have been on a state of decline for the last couple of decades. South Africa has slipped from dominating the global industry to being a bit player. To this end, the study examined the relevance of the Hotelling rule in South Africa. It sought to examine if the gold extraction was

130 following a socially optimal path as suggested by Hotelling. In order to do this, the study outlined several objectives which it intended to achieve. How these objectives were achieved is the focus of the next section.

8.3. REACHING THE OBJECTIVES

The study sought to achieve four objectives. They are (i) To analyse the trends of gold production, extraction and gold prices in South Africa (ii) To determine an optimal extraction path based on theoretical considerations (iii) To test the relevance of the Hotelling rule in South Africa and (iv) To identify the extraction path that yields outcome that is socially optimal. Each of these and how they were achieved is discussed below.

Analyse the trend of gold production, extraction and gold prices

This objective was achieved in Chapter 2. Chapter 2 adopted a mixed method approach (qualitative and quantitative approach) to achieve its objective. The study used both qualitative and quantitative secondary sources to analyse the trend of gold production, extraction and gold prices. Qualitative sources used consisted of previous work done by scholars, the government, private companies and other stakeholders in the gold sector. Qualitative sources were used to build, criticise and support certain arguments. In addition to this, qualitative sources complemented quantitative sources and they also gave some explanations where quantitative sources couldn’t. Quantitative sources consisted of statistical data that was extracted from various official statistical hubs such as Stats SA and the South Africa Reserve Bank. This data was used to plot graphs and calculate descriptive statistics.

The chapter achieved its objective and it came with a number of findings. The chapter showed that gold depletion has also affected gold production which has been in a state of decline since the 1990s (the start of the period under the study’s investigation). Gold production has been on a steady decline, with increasing depths of existing mines and growing costs serving as the primary impediments to growth. The decline in production has affected South Africa’s global production rankings. Production of gold in South Africa as a share of global output has been declining consistently for a decade. South Africa was a globally dominant gold producer in the twentieth century. For many decades South Africa was the world’s largest gold producer, but production has declined precipitously, over the past decade in particular.

131

The chapter also showed that gold prices have been rising since the 1990s. The price path of gold prices showed an upward trend in the time period under investigation. The increasing trend in gold price is in line with the predictions of the Hotelling rule. According to Hotelling, the price of a non-renewable resource should rise over time. This will be a reflection of its scarcity. Hotelling believed that when a non-renewable resource is extracted it declines in terms of the reserves left in the ground. This scarcity will drive the price of the resource upwards. Rising resource rents would indicate rising scarcity, whereas, falling resource rents would indicate falling scarcity and no rise or fall would suggest no change in scarcity.

To determine an optimal extraction path based on theoretical considerations

This objective was attained in Chapter 3 through a literature review providing context and theory. In order to achieve this objective, Chapter 3 examined theories and empirical work associated with the examination of sustainable resource extraction and optimal exhaustible resource use. The focus was to gain a theoretical and empirical understating of finding an optimal extraction path. The chapter used qualitative sources to achieve its objectives. It sampled at least 100 studies that sought to find the optimal extraction path of non-renewable resources. Most of these studies sought to test the Hotelling rule in an attempt to find an optimal extraction path for non-renewable resources.

The study analysed several theories and it showed that there are two schools of thought in determining the optimal extraction path. These are the weak sustainability theories and strong sustainability theories. The weak sustainability theories are to a large extent liberal and they focus on the substitutability of resources. They are also classical in nature. The Hotelling rule falls under this category. The theoretical aspect of the study showed that there is no settled opinion as to which theory is appropriate for any country. Each theory has its weaknesses and the applicability of the theories in question was seen to be an empirical issue. However, all theories studies sought to come up with an optimal extraction path for non-renewable resources.

The empirical literature section showed that several studies have been conducted in an attempt to find an optimal extraction path. These studies showed that there are mixed views regarding the applicability of the Hotelling rule.

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To test the relevance of the Hotelling rule in South Africa

This objective was achieved through empirical testing of the data. The study used different statistical and econometric techniques to achieve this objective. Previous studies had shown that the type of methodology influences the results and so it is better to use different methodologies and then compare the results. To this end, the study also used different estimation techniques to minimise (if not eliminate) the problems that are faced when estimating the Hotelling rule. The study came up with the following key findings:

(I) Visual inspection, variance ratio tests, unit root tests and growth rates showed that the gold price has been rising since 1990. This is in line with the Hotelling rule. The rule predicts exponentially increasing resource prices and this results in mineral resources following the path of the positive trend. The positive trend is prompted by the increasing price reflecting the increasing scarcity of the resource. The price increases until it eventually reaches the choke price, where the quantity demanded decreases to zero and this behaviour is compatible with social optimality. (II) Visual inspection, variance ratio tests, unit root tests and growth rates showed that gold production has been decreasing since 1990. This is in line with the Hotelling rule. The Hotelling rule claims that since the price of a resource increases over time, then demand and production should decrease over time. The rule therefore expects firms to reduce output in response to the decreased demand for mineral commodities due to rising prices. (III) Although partially done, the findings showed that gold consumption is increasing. This was also supported by qualitative sources such as previous studies. Rising consumption of a non-renewable resource violated the Hotelling rule. The Hotelling rule claims that demand and consumption should decrease over time because the price of a resource increases over time. Conventional classical economic wisdom suggests that an increase in a price of a commodity is supposed to depress its demand. The same applies to non-renewable resources.

Results from structural equation modelling showed that the Hotelling rule only partly holds in the gold sector in South Africa. Results showed that there is a negative relationship between gold price and interest rates. This is inconsistent with the Hotelling rule which states that the price of a non-renewable resource should rise at the rate of interest rate. A positive

133 relationship should have been found if the Hotelling rule were to hold in the South African gold mining sector.

8.4. IMPLICATIONS OF THE RESULTS

The findings from this study have several implications. These are:

(i) The finding showed that there has been a decrease in gold production. Although this is consistent with the Hotelling rule, findings also showed that consumption and gold demand are not decreasing as predicted by the Hotelling rule. This leads to some inconsistency on the theoretical aspect of optimal depletion of the gold resource. The failure of the Hotelling rule to hold on consumption had been highlighted by other researchers. For example Mikesell states that supply and demand conditions in individual countries do not conform to world conditions of relative mineral scarcity. The implication of this is that gold extraction is following a path that is not socially optimal. Consumption of gold is likely to increase in the next couple of years because of global demand. There have been several emerging market economies like China and India who have been expanding in terms of production. These countries have also been demanding more gold in the last decade. An increase in demand and consumption of gold will lead to more production and this may lead to the rapid depletion of gold. The depletion is moving at a faster rate and this might lead to the South African mining sector running out of gold sooner10. It can thus be said that gold production is currently unsustainable and this raises the spectre of an imminent resource depletion.

(ii) The fact that results showed that the price of gold is rising over time may suggest that it is a scarce resource. As predicted by Hotelling (1931) a non-renewable resource should have an increasing price. This shows scarcity. The implications of this are that increasing scarcity may mean that the resource (gold) is getting less in terms of the quantity in the ground. This again reinforces the fact that, if there are no new discoveries, gold may run out as predicted by official statistics (in the next 30–40 years). (iii) The fact that results showed that there is a negative relationship between the gold price and interest rates. The implication of this is that gold production may be

10 The study cannot ascertain when South Africa may run out of gold reserves because it did not do an empirical forecasting of when the current gold reserves might be depleted. However, official private and government statistics show that South African may ran out in the net 30–40 years.

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following a path that is not socially optimal according to the principles of the Hotelling rule. This may lead gold to be extracted faster and consequently depleted sooner than expected.

8.5. CONTRIBUTIONS

Contributions to literature

This study contributed to the literature by examining South Africa’s gold industry’s ability to allocate the extraction of gold over time in an efficient manner. The South African gold industry appears set to continue on a path of decline due to the continued and rapid depletion of gold reserves. Very little, if anything, has been done to find an optimal extraction path in the gold mining industry. This study, therefore, made an original contribution to the expansion of knowledge on opportunities for addressing the prevailing problem of the optimum extraction path of gold in South Africa. To the best of the researcher’s knowledge, this study was the first to test the applicability of the Hotelling rule in an African country. The establishment of an optimum extraction path has long been of interest to economists. Given the importance of the gold industry to the South Africa economy, a study of the optimum extraction path in the gold industry was especially valuable. There are no records of similar studies conducted in South Africa. Recognising a gap in South African literature to test the applicability of the Hotelling rule was one of the driving forces for conducting this study. This study made an original contribution towards the broader scope of environmental economics in the South African gold mining sector.

Contribution to practice

The relationship between non-renewable resource extraction over time and depletion is so important that it warrants separate attention especially in the eyes of the government. The prospect of an imminent depletion of non-renewable resources such as gold in South Africa prompts for economic conservation through finding the optimal extraction path. The welfare of South Africa’s present population and more especially in the future will be greatly determined by the stock of natural resources available. For a resource economy like South Africa where gold and minerals account for a significant proportion of export earnings, the decline in both volume and continued and rapid depletion of non-renewable resources such as gold is undesirable. This made the conducting of this study fitting because there was a need to find a gold extraction path that is optimal.

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Taking the above into consideration this study provided insights for the government, players in the mining sectors and policy makers to help them develop more effective strategies to ensure the effective, efficient and optimal management of non-renewable mineral resources such as gold. The purpose of this research was to help players in the mining sector, gold sector, researchers and governments to better understand the role of the Hotelling rule, its usefulness and contribution to optimal resource extraction and depletion. This could make the management of non-renewable resources such as gold easier and extend the life span of these resources. The issue examined in the study is of great interest to governments and policy makers who seek an accurate description of how an extraction path is determined and managed. Through studies of this nature it is possible to measure the sustainability of gold through examining its production and depletion rates. If gold is depleted or is no longer economically viable to extract, this could have a devastating impact on the South African economy. The results of this study can, therefore, be pursued to come up with appropriate optimal resource extraction paths and management of mineral resources such as gold.

8.6. RECOMMENDATIONS

Based on the findings of this study, the following recommendations are suggested for furthering knowledge on the optimal extraction of gold and governmental mineral policy:

(i) The fact that gold depletion is occurring at a faster rate requires the government to intervene and ensure that there are new discoveries in the gold mining sector. There is a need for new discoveries to be made so that the gold reserve base can increase. There is thus a need to generate scientific knowledge and methods to discover new reserves. The government should also spend more funds and promote research and development. This could bring about more technological innovations in the mining industry. Many analysts conclude that depleted reserves could be effectively extended through regulatory interventions by government or private entities, leading for example to technology development that would allow profitable access to lower-grade ores. This could extend the lifespan of the gold resource and reduce the depletion years.

(ii) Since the Hotelling rule partly applied to the gold sector, there is a need to adopt some other theoretical measures that can ensure that the proceeds from the gold taxes is used in the most effective way. The government can use the Hartwick rule which was present in the theoretical section of Chapter 3. The Hartwick rule

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requires that proceeds from the sale of natural resources be saved for future generations. This should be adopted in the South African case where gold is fast depleting. The government needs to ensure that the tax revenue from gold is saved or used towards the development of South Africa. The South African development agenda is dominated by the need to address the vast socio- economic disparities between income levels, employment levels, basic services provision, health and nutrition, and skills and education levels. Tax revenue of the gold resource could be used to develop human capital, for example in the education sector. The proceeds can also be used to develop psychical world-class infrastructure such as roads, railways and airports. (iii) The results raise the spectre of resource depletion. This necessitates the need to begin to plan for change in the way resources are extracted. In other words there is a need for sustainable design and extended producer responsibility in the gold sector. There is a huge need to pay attention to mineral extraction and depletion statistics and take remedial action if the statistics indicate that there is a rapid erosion of non-renewable resources. (iv) There is a need to create public awareness about the meaning of resource depletion and optimal resource extraction. The public needs to know what it means to say 'resource depletion'. When statistics and studies about resource depletion are released the pubic does not pay attention. It must be noted that if the public had been aware of these matters, they would have pressurised the government and players in the mining sector to take action against the rapid depletion of natural resources such as gold. This would create some form of public resource conversation for non-renewable resources.

8.7. LIMITATIONS OF THE STUDY

The present study has included some limitations that should be taken into account. Firstly the present study focused on South Africa. It would have been better if the study had included several other countries because the gold price is determined by international factors. The study used on one non-renewable resource to test the applicability of the theory that applies to all non-renewable resources. Furthermore, the study covered the period between 1990 and 2015. Results might have been different if the study had covered a longer lifespan.

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8.8. CONCLUSION

The main aim of this study was to empirically test the Hotelling rule's significance to gold production in South Africa. The study drew attention to the fact that South Africa’s gold reserves (gold in the ground that can be extracted profitably) are becoming depleted at a rate that, within 25 to 33 years, will mean the end of the industry on which South Africa's economy has been built. This raised questions as to how much of these non-renewable resources (gold) should be extracted today and how much should be saved for future use or for future generations. Without an optimal resource extraction path a rapid decline in the production of gold could have a major impact on the South Africa economy. In addition, this could have serious implications to future generations. While the ownership of resource mines has been a focus of debate, what appears equally important is the rate at which these resources, particularly gold are extracted. The establishment of an optimum extraction path has long been of interest to economists. Given the importance of the gold industry to the South Africa economy, a study of the optimum extraction path in the gold industry is especially valuable. The study found that the extraction path is not socially optimal. Results partly supported the Hotelling rule. This suggests that the current production of gold is not sustainable. The study recommended the government intervene in the mineral sector and come up with strategies that promote sustainability.

Appendix

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SAINT GP EXCH USINT GPN USINF BDI 95.49582 1,047.1 255.62 9.9 327.7 1.03 92.8474 96.37893 1,059.3 254.52 10.2 317.5 0.47 92.9667 96.35236 1,026.2 261.3 10.27 318.1 0.55 94.1018 98.59118 992.3 265.53 10.37 312.4 0.16 94.0068 100.4044 975.9 264.48 10.48 318.3 0.23 93.0099 102.1255 937.0 266.45 10.16 322.5 0.54 93.3073 103.0168 951.2 262.95 10.04 320.9 0.38 91.6567 100.3623 1,015.6 257.33 10.1 324.6 0.92 90.2483 93.49996 999.7 257 10.18 326.5 0.84 89.349 94.40975 967.2 254.45 10.18 323.1 0.6 87.5899 92.04459 963.1 252.4 10.01 326.5 0.22 87.3577 93.31669 958.2 253.16 9.67 311.8 0 88.2319 93.91034 981.9 256.28 9.64 310.2 0.6 87.9792 90.35242 923.7 253.87 9.37 316.3 0.15 86.8807 91.95492 965.0 264.76 9.5 326.8 0.15 89.7781 88.60571 982.7 274.05 9.49 321.2 0.15 90.7463 86.02599 998.4 279.49 9.47 331 0.3 91.0742 86.07206 1,049.8 286.45 9.62 307.2 0.29 92.212 83.86399 1,058.2 288.1 9.58 324.5 0.15 91.9833 84.81397 1,022.8 287.11 9.24 329.4 0.29 91.0048 85.54772 988.2 283.61 9.01 311.3 0.44 90.0004 80.20862 1,014.2 283.05 8.86 323.5 0.15 89.3164 84.25157 1,005.8 279.49 8.71 314.3 0.29 87.9962 79.80028 998.8 276.78 8.5 308.4 0.07 87.1758 79.80033 987.9 277.93 8.43 323 0.15 86.9198 80.71541 996.2 281.53 8.76 327.9 0.36 87.994 80.11952 991.6 288.1 8.94 325.3 0.51 89.7065 79.11324 973.8 287.85 8.85 329.2 0.14 89.179 79.71177 959.6 284.74 8.67 324.5 0.14 88.2981 76.07748 956.9 280.98 8.51 326 0.36 87.141 74.03548 971.6 275.33 8.13 325.3 0.21 85.9016 72.52341 947.4 276.32 7.98 322.4 0.28 85.4079 74.3162 967.1 279.8 7.92 325.2 0.28 85.6559 81.30275 993.7 288.35 8.09 327.1 0.35 87.3199 82.56294 1,003.2 299.58 8.31 327.7 0.14 89.9165 89.66416 1,007.2 301.39 8.22 317.4 -0.07 89.9827 89.47142 1,008.6 306.84 8.02 343.3 0.49 90.6281 89.83176 1,027.2 312.01 7.68 341.2 0.35 90.7122 87.37332 1,048.7 317.86 7.5 333.9 0.35 90.0705 82.36112 1,084.9 316.76 7.47 340.5 0.28 88.2803 84.8511 1,167.0 317.56 7.47 339.7 0.14 88.1495 87.13198 1,204.4 323.38 7.42 321.9 0.14 88.3936

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86.4551 1,313.8 335.01 7.21 328 0 89.0691 88.53845 1,273.5 336.46 7.11 319.4 0.28 88.6623 90.41716 1,210.7 340.72 6.92 315.9 0.21 88.0956 85.01513 1,234.7 339.51 6.83 321.6 0.41 88.7666 82.79225 1,257.5 336.42 7.16 317.4 0.07 89.3983 81.07468 1,296.4 337.5 7.17 318.2 0 89.3136 78.92303 1,319.2 340.93 7.06 333.9 0.27 91.3648 79.16807 1,317.8 345.03 7.15 312.3 0.34 90.8174 82.86805 1,327.5 345.35 7.68 315.4 0.34 90.8181 92.48054 1,354.5 358.52 8.32 316.6 0.14 90.6812 93.12637 1,387.7 362.54 8.6 301.2 0.07 89.9185 93.41358 1,399.6 362.53 8.4 308.3 0.34 89.6065 90.11777 1,414.6 366.82 8.61 304.5 0.27 88.2908 85.49108 1,369.2 359.94 8.51 303.8 0.4 88.032 82.32145 1,392.6 355.64 8.64 305.5 0.27 87.0245 88.15859 1,380.5 353.87 8.93 297 0.07 86.3095 88.63718 1,354.9 352.41 9.17 297.2 0.13 86.493 89.64966 1,350.7 356.01 9.2 290.7 0 88.1249 91.5853 1,339.7 353.8 9.15 288.6 0.4 89.5825 91.82566 1,341.2 355.93 8.83 286.2 0.4 88.9077 91.13147 1,375.5 359.92 8.46 285.1 0.33 87.7824 88.22867 1,408.5 360.06 8.32 281.7 0.33 84.7564 91.56535 1,409.2 365.8 7.96 270.1 0.2 84.2998 95.76613 1,419.0 366.19 7.57 278.2 0.2 84.2344 100.6188 1,405.6 364.07 7.61 283.7 0 84.0489 106.074 1,396.0 364.08 7.86 274.9 0.26 85.9281 111.5987 1,402.4 366.2 7.64 276.3 0.2 86.8023 111.8518 1,398.4 365.09 7.48 279.3 0.33 86.6839 112.4178 1,405.3 364.75 7.38 259.9 -0.07 87.4431 111.7088 1,419.5 366.5 7.2 269.7 -0.07 87.6727 110.5828 1,454.2 364.1 7.03 281.2 0.59 88.2784 111.4175 1,515.7 374 7.08 275.2 0.32 88.1865 113.5595 1,556.8 392.82 7.62 266.6 0.52 88.2509 118.0341 1,656.6 420.57 7.93 265.3 0.39 88.2701 123.5496 1,712.5 437.27 8.07 276.9 0.19 88.5091 117.6085 1,676.0 435.02 8.32 259.4 0.06 88.7867 114.1804 1,684.4 438.88 8.25 261.9 0.19 88.6989 115.917 1,753.2 452.4 8 258.1 0.19 88.0994 109.0963 1,724.5 449.68 8.23 246.8 0.32 88.5077 106.4674 1,743.9 457.26 7.92 257.4 0.32 88.9773 110.3596 1,758.7 465.56 7.62 259.5 0.19 88.5368 111.8667 1,729.2 468.16 7.6 260.5 0 89.0855 110.5118 1,648.1 464.42 7.82 260.2 0.32 89.846

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105.3663 1,543.2 445.27 7.65 260.6 0.31 91.3934 106.6026 1,559.5 443.61 7.9 262.8 0.25 92.3092 105.5182 1,530.0 444.12 8.14 263.1 0.13 92.6654 106.3691 1,535.7 446.83 7.94 272.7 -0.06 91.5753 107.9095 1,533.3 449.81 7.69 258.9 0.12 91.1354 105.093 1,477.6 455.74 7.5 254.2 0.12 92.1604 106.3174 1,517.6 468.41 7.48 265.6 0.19 93.7113 108.443 1,513.6 469.01 7.43 264.1 0.25 93.9532 109.506 1,530.2 470.9 7.29 262.7 0.25 94.6141 113.6823 1,480.4 483.61 7.21 267.5 -0.06 95.9972 117.278 1,406.3 487.07 7.1 257.9 -0.12 99.3624 117.5777 1,428.5 493.91 6.99 263.5 0.19 102.108 117.0097 1,467.4 493.57 7.04 250.5 0.19 100.39 112.7669 1,471.8 497.11 7.13 237.7 0.19 100.06 113.1352 1,555.6 504.61 7.14 242.6 0.18 99.7845 115.4431 1,522.9 509.18 7.14 243.6 0.18 100.562 128.6986 1,574.5 536.09 7 250.6 0.12 102.727 136.3803 1,824.7 623.86 6.95 251.3 0.12 103.031 135.2002 1,794.1 632.26 6.92 247 0.12 104.641 132.8451 1,760.7 612.15 6.72 243.5 0.12 102.837 125.9868 1,714.8 580.71 6.71 240.1 0.24 99.946 116.8066 1,663.5 565.95 6.87 244.4 0 99.6076 117.4403 1,721.0 588.57 6.72 246.6 -0.06 98.7106 113.2724 1,718.5 598.35 6.79 239.9 0.24 98.742 109.2608 1,756.6 611.07 6.81 241.3 0.12 99.989 108.5941 1,775.7 620.9 7.04 257.1 0.3 101.076 106.4597 1,727.4 611.33 6.92 248.1 0.73 100.955 107.4073 1,710.5 618.15 7.15 244.5 0 100.715 105.5401 1,590.1 608.83 7.55 240.7 0 101.139 111.1674 1,564.5 610.6 7.63 234 0.3 101.373 116.5176 1,573.6 612.95 7.94 223.1 0.24 100.429 120.7219 1,602.5 605.93 7.82 239 0.48 100.015 120.4323 1,894.6 609.28 7.85 236.8 0.18 99.5053 119.3901 1,800.2 613.74 7.74 231.3 0.06 99.8364 117.7904 1,739.8 614.6 7.91 235.4 0 99.934 112.1498 1,742.1 611.94 8.21 226.6 0.3 99.8403 112.0808 1,894.6 631.56 8.33 252.6 0.59 101.241 106.9947 1,851.5 645.97 8.24 240.5 0.82 101.717 101.6594 1,855.2 661.2 8.15 231.2 0.06 102.25 100.438 1,937.1 702.05 8.52 221.2 0.12 104.53 100.5051 1,975.3 692.74 8.29 234.9 0.52 103.639 96.72501 1,939.6 687.62 8.15 216.3 0.23 103.872 92.75956 1,909.5 695.14 8.03 227.4 0 104.392

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92.19466 1,961.6 716.14 7.91 223.7 0.52 105.875 92.32519 2,019.4 746.73 7.8 222.8 0.17 107.346 92.68727 2,045.3 767.34 7.75 226.8 0.06 107.998 92.69875 2,078.8 763.92 7.38 217.6 -0.06 107.131 92.04605 2,063.9 777.14 7.03 212.2 0.63 107.458 89.24493 2,046.4 781.5 7.05 216.1 0.4 108.296 90.97035 2,074.9 788.33 6.95 217.7 0.23 109.882 95.4964 2,105.3 808.13 7.08 212 0.4 110.48 95.84715 2,171.2 796.71 7.15 209.8 0.45 110.565 94.27454 2,177.5 805.5 7.16 215.8 0.17 111.382 97.1108 2,193.2 819.65 7.13 212.4 -0.28 111.487 99.37321 2,262.4 830.72 6.95 192.7 0 109.545 98.66345 2,455.8 862.72 6.82 201.5 0.45 110.148 99.78484 2,625.4 926.84 6.62 204.6 -0.34 110.499 98.35844 2,688.4 971.82 6.66 205.2 -0.17 111.009 99.50901 3,194.9 1154.67 7.07 211.9 -0.39 110.934 99.00117 3,265.9 1160.8 7 215.9 0.23 112.153 96.14328 3,395.9 1148.43 6.89 211.7 0.4 112.814 96.94597 3,373.4 1149.38 7.01 212.1 0.56 112.229 93.20703 3,348.9 1107.96 6.99 219.1 0.56 112.014 93.8149 3,182.9 1014.72 6.81 214.3 0 110.574 94.12539 3,278.7 1013.92 6.65 211.9 0.06 109.136 88.18819 3,162.7 1011.37 6.49 204.1 0.11 107.534 85.3632 3,279.9 1058.94 6.29 211.4 0.33 108.873 83.88814 3,381.4 1060.44 6.09 212.4 0.17 109.71 79.42524 3,262.3 1032.8 6.11 207.5 0.17 110.482 79.95097 3,074.3 965.09 6.07 204.7 0 109.271 81.76119 2,976.2 895.97 6.05 210.9 -0.22 108.671 85.19751 3,101.9 868.16 5.92 207.7 0.44 107.34 87.63898 2,970.3 830.31 5.84 200.9 0.77 107.5 89.13799 2,737.1 804.39 5.75 202.1 0.6 106.99 95.90316 2,513.5 770.68 5.81 201.6 -0.22 105.792 97.16381 2,732.0 766.52 5.48 197.8 -0.16 102.282 96.45682 2,805.4 790.27 5.23 192.9 0.11 101.783 104.7111 2,645.3 754.81 5.63 197.3 0.11 103.017 102.3124 2,654.0 739.22 6.26 196.8 0.38 104.413 105.6253 2,766.2 732.46 6.15 195.2 0.33 103.332 112.1805 2,637.4 696.37 5.95 197.4 -0.11 100.995 121.4311 2,617.3 672.87 5.93 193.4 -0.27 100.626 121.507 2,644.2 651.59 5.88 192.1 -0.11 99.2556 124.5907 2,879.1 691.79 5.74 184 0.49 97.7671 123.4936 2,731.9 676.86 5.64 193.2 0.54 98.3874 124.1917 2,687.6 663.28 5.45 185.3 0.64 99.2971

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125.3585 2,655.4 655.37 5.83 181.4 0.32 99.8787 125.2187 2,601.4 678.21 6.27 182.9 0.59 101.657 123.2086 2,518.9 643.51 6.29 181.8 0.32 100.811 119.315 2,439.2 612.87 6.06 183 -0.16 100.014 118.7929 2,585.8 645.75 5.87 179.9 0.05 100.004 114.1702 2,648.4 654.69 5.76 173.1 0.21 99.7185 109.1002 2,686.8 638.76 5.72 171 0.53 98.5355 100.6678 2,652.3 605.58 5.73 172.6 0.05 96.337 101.3787 2,543.8 573.23 5.75 167.9 -0.37 95.1865 101.8437 2,540.7 596.98 5.71 171.6 0.21 95.5551 102.9458 2,544.1 601.61 5.63 163.6 0.58 95.8213 102.019 2,614.2 601.03 5.93 162.1 0.78 95.4297 99.55822 2,640.7 614.6 5.86 149.1 0.67 96.3591 99.3612 2,676.1 633.14 5.72 158 -0.1 96.6157 101.3244 2,904.5 675 5.58 157.7 0.05 97.4852 99.06405 2,845.6 670.35 5.7 153.4 0.46 98.1422 97.53892 2,830.7 646.5 5.82 141.3 0.51 97.3194 96.88417 2,901.6 635.78 5.77 152.1 1.22 98.201 98.1217 3,094.1 657.66 6.07 151.8 0.2 99.0799 101.4375 3,170.6 665.65 6.33 151.9 -0.8 99.2182 99.90133 3,243.4 635.91 6.27 159.9 -0.4 98.4136 99.32384 3,341.5 608.91 6.15 147.9 0.76 97.2655 99.37871 3,394.7 611.77 6.25 150.6 0.2 97.4683 101.2207 3,481.3 625.44 6.32 151.2 0.55 97.6553 101.5209 3,714.2 607.2 6.51 151.3 0.85 97.1647 98.41719 4,271.0 631.99 6.6 137.7 0.5 95.2446 95.52591 4,154.0 695.49 6.68 144 0.2 96.4896 96.70894 4,482.4 708.43 6.76 141.8 0.3 96.654 96.32267 4,389.5 695.53 6.52 140.8 0.2 96.2234 96.40894 4,450.3 740.98 6.4 144 -0.49 95.9014 96.27204 4,475.8 764.92 6.36 138.7 -0.54 95.6247 96.77702 4,549.4 725.86 6.24 139.9 -0.15 94.6433 96.39092 4,435.2 704.06 6.14 133.5 0.15 94.0288 95.56249 4,538.1 718.38 6.22 142.2 0.31 94.9518 96.21687 4,771.2 716.98 6.29 148.4 0.54 94.7953 94.1335 4,815.4 735.14 6.16 133.7 0.91 94.5388 91.60549 4,825.1 712.16 6.18 134.4 0.65 93.4108 91.69768 4,681.5 701.87 6.26 132.7 0.61 92.7491 93.29438 4,691.6 717.18 6.66 135.3 0.19 92.4838 93.53372 4,639.4 697.3 6.7 133.8 -0.03 91.1156 94.79759 4,807.8 723.34 6.57 138.9 -0.18 91.3269 93.94938 5,063.7 712.82 6.38 132.1 0.28 90.2458 93.78041 5,102.9 677.29 6.38 130.3 0.21 88.2954

143

93.61806 5,414.1 670.1 6.21 124.1 0.59 87.2538 93.44928 5,477.8 682.71 6.1 127.7 -0.07 87.886 91.2901 6,235.9 698.71 5.76 117.4 0.5 87.214 87.05542 7,066.0 763.86 5.92 115.7 0.29 86.153 84.07749 7,724.5 797.99 5.97 118.6 0.87 84.4668 86.76352 7,067.1 779.33 5.92 117.5 0.61 84.0219 86.91951 6,767.3 762.38 6.04 117.6 0.84 84.3831 85.04729 7,063.1 791.88 6.32 117.4 1.01 84.8663 83.22038 7,156.6 763.93 6.43 111.4 0.53 84.478 82.31435 6,424.1 765.78 6.48 106.2 -0.4 86.556 81.72099 6,683.7 804.72 6.04 110.5 -0.14 88.6729 86.01827 7,823.3 967.15 6.2 110.2 -1.01 93.7353 86.538 7,700.4 1011.77 6.09 107.6 -1.92 94.5679 87.56971 8,147.3 994.56 5.33 106.6 -1.03 93.068 90.88092 8,530.2 989.7 5.06 111.4 0.44 93.8506 83.45582 9,419.8 1000.62 5.13 110.4 0.5 96.4758 81.14636 9,198.4 999.32 5 110.1 0.24 96.6695 78.74085 7,985.9 901.8 4.81 104.5 0.25 94.2755 76.76122 7,788.0 837.23 4.86 106.3 0.29 91.5397 79.51932 7,605.3 805.18 5.42 101 0.86 90.9217 81.36591 7,429.5 795.13 5.22 104.4 -0.16 90.5199 81.48388 7,550.8 794.15 5.19 103.8 0.22 89.4694 81.21178 7,488.5 752.35 5.06 102.8 0.06 88.8321 82.34388 7,804.2 748.33 4.95 101.4 0.1 87.6677 82.89124 8,456.1 751.82 4.88 101 0.07 87.2221 81.56851 8,491.7 748.94 4.93 97.3 -0.18 87.4445 82.16544 8,335.6 745.27 5.03 92.2 0.34 87.4651 83.87159 8,408.9 766.12 4.99 100.5 0.02 88.4487 85.63467 8,252.6 742.58 4.97 97.5 0.41 87.5544 85.53013 8,450.5 734.34 5.1 99.9 0.17 86.9432 86.11392 9,244.1 763.32 4.89 102.2 0.08 89.1378 88.39417 9,426.1 764.73 4.74 101.2 -0.1 89.4903 89.98481 8,994.6 754.68 4.56 99.9 0.02 88.0362 90.82198 8,867.9 729.73 4.43 107.1 0.14 87.286 90.66016 9,047.1 713.89 4.35 96.2 0.06 86.3415 89.06638 9,270.8 691.77 4.23 101.2 0.12 83.9568 87.35812 9,559.3 697.2 4.3 100.3 0.04 84.0004 86.6715 9,513.9 682.94 4.71 102.7 0.17 84.6232 85.66983 9,410.9 690.21 4.76 100.7 0.48 83.5964 85.88257 9,858.9 719.11 4.95 97.6 0.49 83.0068 83.98416 9,824.5 690.86 4.84 97.8 0.98 82.3035 82.99778 9,923.0 673.24 4.84 100.9 0.64 81.0153 82.04057 10,384.6 686.1 4.64 94.3 0.47 81.036

144

80.05234 10,378.7 678.75 4.51 94.8 -0.11 80.8276 79.21822 10,682.2 679.31 4.55 97 0.09 80.2632 78.28393 12,448.6 705.98 4.27 85.2 0.28 80.8209 76.77593 13,366.3 752.14 4.11 95.9 0.15 83.2074 75.90175 13,249.9 795 4.07 95.1 -0.21 83.7571 74.9713 14,170.8 815.53 3.99 93.7 -0.08 84.2734 75.53414 13,544.4 817.45 3.96 92.7 -0.25 84.9508 74.72592 13,273.7 801.06 3.92 90.1 0.44 84.3018 75.39673 13,313.9 765.52 3.89 90.2 0.44 83.0417 75.72109 12,735.1 759.98 3.95 89 0.76 83.4098 75.3393 12,919.4 782.75 3.91 87.2 0.3 83.6173 77.31563 12,954.2 815.24 3.8 92.2 -0.12 84.8029 77.89587 13,377.7 839.62 3.68 93.2 -0.15 85.8922 79.27108 13,148.5 824.66 3.55 89.9 -0.16 85.3428 78.2118 13,436.0 827.52 3.6 88.7 0.56 84.8252 75.94602 14,413.3 827.84 3.5 85.1 0.45 83.6968 75.16644 15,112.3 864.44 3.38 47.7 -0.04 83.5034 75.35061 15,159.5 879.44 3.35 63.4 -0.47 83.791 75.0202 14,567.7 863.85 3.35 73.3 -0.27 83.0884 76.40866 14,716.2 878.57 3.41 84.1 0.3 82.9471 74.26799 14,451.8 888.27 3.53 83.4 0.82 83.8266 74.18834 14,642.6 917.47 3.57 85.6 0.26 84.2111 74.37544 13,507.0 911.25 3.45 85.2 -0.1 83.6351 75.65503 13,233.3 935.6 3.54 82.7 0.18 83.9043 75.81241 13,429.4 1003.07 4.07 79.4 0.24 84.5164 72.41046 12,756.6 991.01 4.37 93.7 0.04 84.9366 71.99127 13,555.4 1008.26 4.46 85.1 0.12 84.8632 73.95391 13,460.9 998.3 4.49 81.3 0.12 84.5762 75.86965 13,036.3 991.72 4.19 86.1 -0.26 83.6396 76.95022 13,028.6 1020 4.26 86.7 -0.2 84.2998 76.7204 12,705.0 1036.75 4.46 80.2 -0.01 84.4767 75.51678 13,551.4 1087.22 4.43 82.9 0.37 85.268 76.41102 14,247.0 1098.48 4.3 80.4 0.37 85.3879 76.14099 14,357.4 1074.68 4.34 81.5 0.64 85.2386 75.98696 13,690.8 1054.67 4.34 82.2 0.33 84.8722 73.9674 13,405.1 1039.79 4.19 80.4 0.35 84.4907 74.12383 13,666.2 1067.58 4.16 79.9 0.19 84.5252 75.58951 13,974.5 1066.28 4.13 78.9 -0.04 84.2845 75.97713 13,811.4 1066.62 4.12 79 -0.17 84.9109 78.45895 13,597.1 1095.3 4.16 79.5 0.08 86.1756 78.28414 13,519.3 1106.66 4.04 81 -0.25 87.2049 78.70508 13,040.0 1109.86 4 75.2 -0.54 88.4904 80.8628 13,810.2 1146.13 3.86 82.8 -0.57 90.2135

145

84.8661 14,464.2 1156.58 3.71 63.7 -0.47 91.7204 87.02953 14,214.4 1157.59 3.71 75 0.43 92.8036 86.50998 14,242.7 1206.44 3.77 83.1 0.6 94.3812 84.60355 14,386.8 1201.11 3.67 75.5 0.2 93.4841 84.28826 14,346.8 1196.91 3.84 77.1 0.51 92.7998 83.58557 14,537.3 1230.16 3.98 76.9 0.35 93.5186 82.90856 14,069.7 1245.15 4.05 76.5 0.01 95.0718 84.9119 14,396.2 1291.18 3.91 77.8 -0.14 96.6834 84.92277 15,369.1 1360.73 3.89 78.8 -0.16 97.3459 84.56872 15,626.5 1350.02 3.8 74.8 -0.04 96.4944 84.69757 15,364.6 1412.32 3.94 78.9 -0.21 97.9698 83.3523 15,986.4 1492.6 3.96 78.9 -0.34 98.6854

146

 CERTIFICATE OF EDITING

To whom this may concern

This is to certify that I have copy edited the thesis of

 COURAGE MLAMBO

200706118

For the degree of PhD in Commerce Economics

in the Faculty of Management and Commerce

University of Fort Hare

Topic:

"Exhaustible Resources and the Hotelling Rule: An Empirical Test of the Hotelling Rule's Significance to Gold Production in South Africa"

for spelling and grammatical errors

Date: 26 January 2017

M A Erikson BA (UKZN), BEd (Wits) Full Member of Professional Editors' Guild Member of ASAIB (Association of Southern African Indexers and Bibliographers)

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