OKUN’S LAW: CAN IT STILL BE A BEST RULE
OF THUMB? (A TIME-SERIES ANALYSIS)
A Thesis
Presented to the
Faculty of
California State Polytechnic University, Pomona
In Partial Fulfillment
Of the Requirements for the Degree
Master of Science
In
Economics
By
Abdullah Alkraidees &
Anees Ayaz
2014
SIGNATURE PAGE
THESIS: OKUN’S LAW: CAN IT STILL BE A BEST RULE OF THUMB? (A TIME SERIES ANALYSIS)
AUTHOR: Abdullah Alkraidees & Anees Ayaz
DATE SUBMITTED: Spring 2014
Economics Department
Dr. Carsten Lange ______Thesis Committee Chair Economics
Dr. Bruce Brown ______Economics
Dr. Craig Kerr ______Economics
ABSTRACT
Since 1962, policy makers and economists consider Okun’s law as a pillar of mainstream economics. Keeping this point into consideration, the main goal of our research project is to find out a relationship between the unemployment rate and the GDP growth rate as proposed by Okun (1960). The paper also focuses on the short-run and long-run relationship between these two variables. For this purpose a time series data from 2001 to
2013 is used, and is divided into two time periods, on quarterly basis, 2001:Q1-2007:Q4 and 2008:Q1-2013:Q4. Time-series econometric techniques are applied on each period to find an association between unemployment rate and GDP growth rate including
Augmented Dickey-Fuller (ADF) test for stationary analysis, Engle-Granger test of co- integration and Johansen test of co-integration for co-integration analysis, vector auto- regressive model (VAR), and vector auto-regressive model (VECM) for finding inter- dependencies between variables, and finally estimating a difference version of Okun’s law regression equation. The results show a long-run association between the unemployment rate and the GDP growth rate in both periods i.e. 2001:Q1-2007:Q4 and
2008:Q1-2013Q4, but no contemporaneous impact on the unemployment rate by the
GDP growth rate.
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TABLE OF CONTENTS
SIGNATURE PAGE ...... ii
ABSTRACT ...... iii
LIST OF TABLES ...... vi
LIST OF FIGURES ...... vii
CHAPTER 1 ...... 1
Introduction ...... 1
CHAPTER 2 ...... 3
1) What is Okun’s Law? ...... 3
1.1) Okun’s Law? ...... 3
1.2) Okun’s assumptions...... 3
1.3) Okun’s observation ...... 4
1.4) The other versions of Okun’s law ...... 6
2) Literature Review ...... 7
Chapter 3 ...... 10
1) Methodology ...... 11
1.1) Model Specification ...... 11
1.2) Time Series Econometric Concepts ...... 12
2) Econometric Techniques ...... 14
2.1) Augmented Dickey-Fuller Test (ADF) ...... 15
2.2) Vector-Autoregressive Model (VAR) ...... 17
2.3) Tests of Co-Integration and Error-Correction Model (ECM) ...... 20
3) Empirical Results and Discussions ...... 21
iv
3.1) 2001:Q1 – 2007Q4 ...... 21
3.2) 2008:Q1 – 2013:Q4 ...... 34
Conclusion ...... 46
REFERENCES ...... 49
v
LIST OF TABLES
Table 1 Unemployment In Levels 2001:Q1 - 2007:Q4 ...... 22
Table 2 Unemployment Rate After First Difference 2001:Q1 - 2007:Q4 ...... 23
Table 3 GDP In Levels (2001:Q1-2007:Q4) ...... 25
Table 4 GDP Growth After First Difference (2001:Q1 - 2007:Q4) ...... 26
Table 5 Residual Unit Root Analysis (2001:Q1 - 2007:Q4) ...... 28
Table 6 Lag-Length Criteria (2001:Q1 - 2007:Q4) ...... 29
Table 7 Johansen Test of Co-Integration Test Results (2001:Q1 - 2007:Q4) ...... 30
Table 8 VECM Results (2001:Q1 – 2007:Q4) ...... 32
Table 9 Wald Test Results (2001:Q1 - 2007:Q4) ...... 33
Table 10 Okun's Law Regression Results (2001:Q1 - 2007:Q4) ...... 34
Table 11 Unemployment Rate In Levels (2008:Q1 - 2013:Q4) ...... 35
Table 12 Unemployment Rate After First Difference (2008:Q1 - 2013:Q4) ...... 36
Table 13 GDP Growth Rate In Levels (2008:Q1 - 2013:Q4) ...... 38
Table 14 GDP Growth Rate After First Difference (2008:Q1 - 2013:Q4) ...... 39
Table 15 Residual Unit Root Analysis (2008:Q1-2013:Q4) ...... 40
Table 16 Lag-Length Criteria Results 2008:Q1 – 2013:Q4...... 41
Table 17 Johansen Test of Co-Integration Test Results (2008:Q1 - 2013:Q4) ...... 42
Table 18 VECM Results (2008:Q1 - 2013Q4) ...... 44
Table 19 Wald Test Results (2008:Q1 - 2013:Q4) ...... 45
Table 20 Okun's Law Regression Results (2008:Q1–2013:Q4) ...... 46
vi
LIST OF FIGURES
Figure 1 Unemployment Rate In Levels (2001:Q1 - 2007:Q4) ...... 22
Figure 2 Unemployment Rate After First Difference (2001:Q1- 2007:Q4) ...... 24
Figure 3 GDP Growth Rate In Levels (2001:Q1 - 20017Q4) ...... 24
Figure 4 GDP Growth After First Difference (2001:Q1 - 2007:Q4) ...... 27
Figure 5 Unemployment Rate In Levels (2008:Q1 - 2013:Q4) ...... 35
Figure 6 Unemployment Rate After First Difference (2008:Q1 - 2013:Q4) ...... 37
Figure 7 GDP Growth Rate In Levels (2008:Q1 - 2013:Q4)...... 37
Figure 8 GDP Growth Rate After First Difference (2008:Q1 - 2013:Q13) ...... 39
vii
CHAPTER 1
Introduction
What are the main problems an economy could face? What are the main issues policy makers and economists do mostly care about? Those are three primary macroeconomic policy goals in general; economic growth – an increase in the capacity of an economy to produce goods and services from one period to another, the inflation rate – a general increase in a country’s price level of goods and services measured as an index, and the unemployment rate – the proportion of people who are actively seeking for jobs (Blanchard, 2011).
Arthur Melvin Okun (1962) was the first economist who developed an economic model where he empirically connected the variations in the unemployment rate to the changes in the state of the economy captured by changes in the GNP by using quarterly data from 1947:II to 1960:IV (Dimitrios, 2006). This correlation between the two important economic variables is famously known as Okun’s law, and since then it has been used as a benchmark by policy makers to measure the cost of higher unemployment and vice versa.
The association between changes in the output and the unemployment rate is of crucial interest during times of economic recession and recovery; therefore the primary goal of research project is to find such an association, if exists,
(according to Okun’s law), and to know whether it can still be used as a best rule of thumb. For this purpose, quarterly data from 2001:Q1 to 2013:Q4 is used. The data range is divided into two periods, 2001:Q1 to 2007:Q4, and 2008:Q1 to
2013:Q4. The conclusion is based on the results obtained as a result of the
1
application of various econometric techniques including stationary tests, tests of co-integration, and the tests to check the inter-dependencies between these two variables. These econometric techniques are discussed in Chapter III of this paper.
2
CHAPTER 2
This chapter consists of two sections; the first section sheds light on the original paper, findings of Arthur Mervin Okun, and the other versions of Okun’s law. The second section discusses the findings of researchers that took the same concept of Okun, expanded further by including more elements that Okun omitted in his analysis, and also applied on other time periods and countries (literature review).
1) What is Okun’s Law?1
1.1) Okun’s Law?
Arthur Melvin Okun (1962) empirically connected variations in the unemployment rate to the changes in the state of the economy captured by changes in the GNP using quarterly data from 1947:QII to 1960:QIV. In his original paper, published in
1961, he presented two empirical relationships between the unemployment rate and the real output; the difference approach, and the gap approach. His findings are discussed below.
1.2) Okun’s assumptions
In his paper, Okun believed that a four percent unemployment rate is a reasonable target to achieve full employment, where an economy could produce maximum production without any inflationary pressure. Unemployment rate reflects the number of hours worked, and labor force participation. In other
1 See Okun, Arthur M. “Potential GNP: Its Measurement and Significance”. Section. Alexandria, VA: American Statistical Association, 1962, pp. 98-103. Reprinted as Cowles Foundation Paper 190.
3
words, lower unemployment rate means more labor is being used in the economy for production, and vice versa. On the other side, in estimating potential
GNP, factors such as technological knowledge, the labor skills and education, natural resources are taken as given under the present economic conditions.
1.3) Okun’s observation
In Okun’s original paper that was published in 1961, he presented two empirical relationships between the unemployment rate and the real output, the difference approach, and the gap approach. His findings are discussed below.
The difference version: Okun’s first relationship captures how changes in the unemployment rate affect growth in real output by using quarterly data from
1947:Q2 to 1960:Q4.
The Okun’s difference version equation is given below:
In this approach, quarterly changes in the unemployment rate, , expressed in percentage points, are related to quarterly percentage changes in real GNP,
The constant in the equation (1) shows a mean change in the unemployment rate when the economy does not grow. The coefficient is the
Okun’s law coefficient (OLC). The regression results obtained by Okun after applying the ordinary least square (OLS) techniques are shown below:
4
̂
According to these results, the unemployment rate will rise by 0.3 points from one quarter to another quarter if no growth occurs. A one percent increase in real
GNP is associated with 0.3 percentage points decrease in the unemployment rate from one period to another (shown by a negative sign with Okun’s co- efficient in equation 2). This approach is used in our research project.
The gap version: The second version is the gap version approach. In this approach, certain exponential paths of potential output are chosen based on the agreement that these potential GNP should be equal to actual GNP when the unemployment rate level is four percent in the economy. The gap version regression equation is given below:
The constant in equation (3) is the unemployment rate associated with full employment. Okun obtained the following regression equation results using the data,
The results implies that the unemployment rate associated with a zero gap is
5
3.72 percentage points, which is close to four percentage points that Okun assumed to be a reasonable target to produce maximum output without any inflationary pressure. Moreover a one percent increase in unemployment is associated with 2.8 percent loss of potential output, or simply an economy is producing below potential level.
1.4) The other versions of Okun’s law
The dynamic version: In the dynamic version of Okun’s law, the current and past values of real output growth rate, and past changes in the unemployment rate are introduced in the model.2 The Okun’s dynamic version (Knotek: 2007) is given below:
The drawback of dynamic version is that it lacks the original concept of Okun’s law, which focuses originally on the contemporaneous impact of changes in real output growth on changes in the unemployment rate. However, it still has similarities to the original version of Okun’s law (Knotek: 2007).
The production–function version: The production function approach is also known as a theoretical approach to the Okun’s law. In this version, analysis of the effects of a combination of technology, labor and capital is observed in the
2 Including past values eliminates the issue of serial correlation from the model.
6
production of output. The production function version can be expressed as
(Prachowny, 1993),
Where y is output, k is the capital input, and c is its utilization rate, n represents the number of workers, h is the number of hours worked; and are output elasticities, and and are the combinations of workers and weekly hours to the total labor input; and is a disembodied technology factor. One of the drawbacks of this approach is that both capital and technology are difficult to measure.
One other production function was modeled by (Gordan, 1984) as shown below,
Where Q is real GNP, E / L is the employment rate; H hours per employee; Q /
EH is labor productivity; L / N is the labor force participation; and N is the population.
2) Literature Review
In case of the United States, the Okun’s (1962) relationship of three-to-one output-unemployment association appears to attenuate over time. Since his publication, economists and researchers have been investigating the Okun’s law
7
by using data from different time periods to confirm the relationship between changes in unemployment and output for various periods of times.
Laurence Ball, Daniel Leigh, and Prakash Loungani (2012) investigated how
Okun’s law has fitted short-run unemployment movements in the United States since 1948, and in twenty advanced economies since 1980. They found that the
Okun’s law co-efficient (OLC) varies across countries, and there is a strong and stable relationship between the unemployment rate and real GDP growth in most of the countries.
Christian Pierdzioch, Jan-Christoph Rulke and Georg Stadtmann (2008) used survey data for the G7 countries using the classical linear version of Okun’s law, and found that forecasts of changes in the unemployment rate and the real output growth rate are consistent with Okun’s law.
Edward S. Knotek (2007) investigated Okun’s law relationship by using three versions of Okun’s law; the difference version: to estimate the unemployment rate on a quarterly basis, the gap version: to measure the gap between actual output and potential output, and the dynamic version: where he introduced the past level of output, current level of output and past level of employment to analyze the effects on unemployment.
Sinclair (2004) used the gap version of Okun’s law to examine bivariate correlation between unemployment and output. In his paper, Sinclair divided the two macro-economic variables into a permanent and a transitory component, and then he estimated correlation of these components. He found that fluctuations in both output and unemployment are largely permanent, and there exists a negative relationship between these components that was similar to the Okun’s
8
law relationship between the transitory components. (Permanent and Transitory
Movements in Output and Unemployment: Okun’s Law Persists – Tara M.
Sinclair).
Kwami Adanu (2002) estimated Okun’s coefficient for ten provinces of Canada applying Hodrick-Prescott de-trending method and quadratic de-trending method using real GDP and unemployment rate data. He found a stability of the coefficients across the two de-trending methods.
Brian Silverstone and Richard Harris (2001) used a symmetric between changes in the unemployment rate and real output growth rate for seven OECD countries
(Australia, Canada, Germany, Japan, New Zealand, the United Kingdom and the
United States). He used gap version of Okun’s law, and tested the co-integration between unemployment and output in countries such as the United States and
New Zealand. They also find a short-run output and unemployment adjustments to disequilibrium.
During the last couple of years, especially after 2001 and the financial crisis of
2008, Okun’s law faced serious challenges. Various studies have shown a positive economic growth with no improvement in unemployment, which is famously known as jobless growth. This is because the global financial crisis deeply impacted the labor markets globally including the United States.
Marly Daly and Hobjijn (2010) found that Okun’s law has departed from the rule of thumb in the second half of 2009.
Robert J. Gordon (2010) mentioned in his paper that the last three recessions in the United States (1990-1991, 2001, and 2007-2009) have been followed by a
9
jobless recovery (a positive output growth with no improvement in labor markets).
Moreover, Gordon said,” Labor has always been the prime victim of recessions3.
There are numerous other empirical studies where researchers applied the same concept of Okun’s law in different scenarios by using the gap, dynamic and production-function versions to find out whether Okun’s law still can be used as a pillar of mainstream economics by policy makers and economic advisors or not.
3 See A Broken Economic Law by LOUIS UCHITELLE, February 22, 2010 - http://economix.blogs.nytimes.com/2010/02/22/a-broken-economic-law/
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CHAPTER 3
This chapter consists of three sections. The first section discusses the methodology of research project, and a brief discussion about the important time series econometric concepts. The second section discusses the econometric techniques that are used in our research project. The third section discusses the empirical results obtained as a result of the application of the econometric techniques discussed in section 2 of this chapter.
1) Methodology
1.1) Model Specification
The difference version of Okun’s law is used in the research paper. For this purpose, data range is selected from 2001:Q1 to 2013:Q4, and is divided into two time-periods, from 2001:Q1 to 2007:Q4, and 2008:Q1 to 2013:Q4.
The Okun’s equation used is given as:
Where,
is the change in the unemployment rate;
is the change in the GDP growth rate;
is the Okun’s Law Coefficient (OLC);
is the unemployment rate when the economy does not grow;
represents the error term, where ); and
t = 1.....T.
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1.2) Time Series Econometric Concepts
The time-series econometric concepts that are applied throughout the paper are discussed below:
1.2.1) Stationary Analysis
A key concept underlying time series processes is that of stationary, which forms a basic foundation of time-series analysis. A time series variable is said to be stationary when it consists the following three characteristics:
• It exhibits mean reversion in that it fluctuates around a constant long-run mean;
• It has a finite variance that is time-invariant; and
• It has a theoretical correlogram that diminishes as the lag-length increases.
In mathematical terms, a time series variable is said to be stationary if:
• = constant for all time periods t;
• = constant for all time periods t;
• = constant for all time periods t and all , or in other words if its mean, its variance and its covariances remain constant over time.
From the above discussion, we mean that a time-series variable remains the same whether observations are from, for example, 1990 to 2000 or from 2000 to
2013. Stationary concept is important in time-series analysis because if a time series is non-stationary, then all typical results of a classical regression analysis are not valid, and therefore the regression would be a false or fake regression.
Hence regressions with non-stationary series have no meaning. One more
12
important point to mention is that shocks to a stationary time-series are necessarily temporary; over time, the effects of the shocks will disappear, and the series will revert back to its long-run mean.
1.2.2) Simultaneity
In economics, there are cases in building economic models where some variables are not only explanatory variables for a given dependent variable, but they are also explained by the variables that they are used to determine. In such cases we deal with simultaneous models where we use to identify which variables to use as endogenous variable(s), and which variable to use as exogenous variable(s); hence we could face an identification problem.
Christopher A. Sims criticized this concept of differentiation among variables, and said that if there is simultaneity among a number of variables, then there should be no distinction between endogenous and exogenous variables, thus all the variables are treated the same (Sims, 1980).
1.2.3) Co-integration
Co-integration is an important concept in time-series analysis, therefore is widely used in finding long-run relationships. As discussed above that most macroeconomic variables are trended and therefore are non-stationary, thus fake regression is highly likely to exist in cases. In order to resolve such an issue, difference is applied to the series until stationary is achieved, and then the stationary series is used for regression analysis. But the problem with differencing is that it leads to the loss of long run properties (as economists are more likely interested in long run relationships).
13
But it is possible to have models that can be measured in their levels, combines both short-run and long-run properties, and which at the same time can maintain stationary in the variables. This gives the concept of co-integration. In other words, if there is a long-run relationship between variables, then although the variables are trended but there is a common trend that links them together. If, for example, if we have two non-stationary variables, and )) , and the linear combination between them is given by the regression equation4.
If we take the residuals and run the following regression as,
̂ ̂ ̂
Now if ̂ is stationary, ̂ , then the variables Y and X are said to be co- integrated or a long-run relationship is said to exist between these two variables.
If a series exhibits such property, then the series is said to be co-integrated.
2) Econometric Techniques
Time-series econometric techniques that are used in this paper are discussed below:
4 See Gujrati, Damodar N..’Basic Econometrics’. 4th Edition, page 822.
14
2.1) Augmented Dickey-Fuller Test (ADF)
There are various methods for unit root analysis. Augmented Dickey-Fuller Test
(ADF) is used to check whether the data series is stationary or not in the data series5.
Unemployment Rate,
The ADF test consists of estimating the following regressions:
6 ∑
Where = ( , = ( , and is pure white noise term. The number of augmented lag terms is determined by minimizing the
Schwartz Bayesian Information (SBI) criterion or minimizing the Akaike
Information Criterion (AIC), or the lags are dropped until the last lag is statistically significant.
The Null-Hypothesis in this case is:
i.e. the time-series data has a unit-root (non-stationary), and therefore needs to be differenced to make it stationary.
5 The reason for using ADF test for unit root analysis in our paper is to remove the issue of serial correlation. 6 See Gujrati, Damodar N..’Basic Econometrics’. 4th Edition, page 817.
15
The Alternative-Hypothesis is:
i.e. the data series has no unit-root (stationary), and therefore doesn’t need to be differenced.
GDP Growth Rate,
The ADF test consists of estimating the following regressions:
7 ∑
Where = ( , = ( , and is pure white noise term. The number of augmented lag terms is determined by minimizing the Schwartz Bayesian Information (SBI) criterion or minimizing the
Akaike Information Criterion (AIC), or the lags are dropped until the last lag is statistically significant.
The Null-Hypothesis in this case is:
i.e. the data series has a unit-root (non-stationary), and therefore needs to be differenced to make it stationary.
7 See Gujrati, Damodar N..Basic Econometrics. 4th Edition, page 817.
16
The Alternative-Hypothesis is:
i.e. the data series has no unit-root (stationary), and therefore doesn’t need to be differenced.
2.2) Vector-Autoregressive Model (VAR)
Vector-Autoregressive (VAR) model approach is used to find inter-relationship between variables (in our case unemployment rate and GDP growth rate). All variables are treated the same, i.e. there is no need to identify variables. In VAR model, we do not try to estimate the exact coefficients, but instead find out if there is any relationship among the variables or not. Why our main concern is to find out any inter-relationships among variables but not there coefficients? The answer is that the obtained coefficients of the VAR model are difficult to interpret as they are a-theoretical and have no economic meaning.
We have two variables, and therefore it means that we will be having two equations in our VAR model. The details are given below.
The time-series unemployment rate ( is affected by current and past values of
GDP ( , and simultaneously, the time-series GDP growth rate , to be a series that is affected by both current and past values of the ( . The structural
VAR (p) model in our case is given as below8 on next page,
8 See Asteriou, Dimitrios. Applied Econometrics - A Modern Approach using E-
17
In the above the two equations, a contemporaneous impact on , and has a contemporaneous impact on . The above two equations can also be written in matrix-form as shown below:
( ) ( )
( ) ( ) ( ) ( ) ( )
( )
By multiplying both sides by ( ) , we get
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( )
Views and Microfit. Palgrove Macmillan, page 298.
18
Where
( )
( ) ( ),
( ) ( ) ( ) ( ) ( ) ( )
( ) ( )
Here it is important to note that mention that the new error terms, and , are
composites of the two shocks, and . This can be shown below:
( ) ( )
( ) ( )
( )
From the above two equations, it can be seen that ; this is the problem of reduced from of VAR (p) model.
19
2.3) Tests of Co-Integration and Error-Correction Model (ECM)
Both Engle-Granger and Johansen test of co-integration is used to confirm long- term association between the variables. The difference version of Okun’s law is given as:
According to Engle-Granger test, run the above equation as it is, take the residuals, and then run the following equation:
̂
If the error term is found to be stationary I(0), then and are said to be co-integrated. The relationship between and can also be expressed in terms of error correction model (ECM).
̂
Where
̂ ̂ ̂
The advantage of the equation (11) is that it captures both the short-run and the long-run effects. In the ECM model mentioned above, b captures the immediate impact of GDP growth rate on the unemployment rate (known as short-term
20
effect). On the other hand, 9 is the feedback effect, or the adjustment effect; it shows how much of the disequilibrium is being corrected, i.e the extent to which any disequilibrium in the previous period effects any adjustment in the period.
Johansen test of co-integration approach is also used to find such a long-run relationship. Johansen (1988a, 1991) derived distribution when the co-integrated system is parameterized as a vector correction model (VECM). Trace test statistic and Maximum Eigen value statistic is used to check the number of co- integrating vectors. The results from both the tests of co-integration are expressed in the empirical results section of this chapter.
3) Empirical Results and Discussions
In this section, the empirical results obtained after the application of econometric techniques on each time range, 2001Q1-2007Q4 and 2007Q1-2013Q4, are discussed.
3.1) 2001:Q1 – 2007Q4
3.1.1) Stationary Analysis
Unemployment Rate,
The graphical analysis gives a visual examination about the data series. The graph of unemployment rate in its levels is shown figure 1 on next page:
9 The coefficient of must be negative.
21
Figure 1. Unemployment rate in levels (2001:Q1-2007:Q4)
Augmented Dickey-Fuller (ADF) test is applied on this time series, and the results are shown in table (1) below:
Table 1
Unemployment Rate In Levels (2001:Q1-2007:Q4)
t-statistics p-value
ADF Test 0.818995 0.9994 Statistic
Test Critical 1% Level -4.467895 Values
5% Level -3.644963
10% Level -3.261452
22
According to the results shown in Table I, The p-value 0.9994 is greater than 5% level. Thus, the null hypothesis cannot be rejected; this means that the unemployment rate is non-stationary in levels, and therefore needs to be differenced. The results after first difference are shown in Table II below,
Table 2
Unemployment Rate After First Difference (2001:Q1-2007:Q4)
t-statistics p-value
ADF Test -6.184951 0.0003 Statistic
Test Critical 1% Level -4.467895 Values
5% Level -3.644963
10% Level -3.261452
According to the results shown in Table II, the p-value 0.0003 is less than 5% level. Thus, we have enough evidence to reject the null hypothesis. This means that the unemployment rate becomes stationary after first difference. This is shown in figure (b). The graph clearly depicts that the unemployment rate becomes stationary after first difference.
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Figure 2. Unemployment rate after first difference (2001:Q1-2007:Q4)
GDP Growth Rate, )
The graph of GDP growth rate in its levels is shown in figure 3 below,
Figure 3. GDP growth rate in levels (2001:Q1-20017Q4)
After applying ADF test on GDP growth rate series, the following results are obtained shown in Table 3 on next page,
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Table 3
GDP Growth Rate In Levels (2001:Q1-2007:Q4)
t-statistic p-value
ADF Test
Statistic -0.604264 0.4458
Test Critical -
Values 1% Level 2.656915
5% Level -1.954414
10% Level -1.609329
According to the results shown in Table III, the ADF test statistics -0.604264 is less than the test critical values at all levels. Also the p-value is greater than 5% level. Thus, the null hypothesis cannot be rejected, which means that the GDP growth rate is non-stationary in levels, and therefore needs to be differenced.
The results after first difference are shown in Table 4 on next page:
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Table 4
GDP Growth Rate After First Difference (2001:Q1-2007Q4)
t-statistic p-value
ADF Test
Statistic -8.915549 0.0000
Test Critical
Values 1% Level -2.656915
5% Level -1.954414
10% Level -1.609329
The p-value associated to the ADF test statistic 0.0000 is less than 5% level.
Hence, we have enough evidence to reject the null-hypothesis of unit root, and therefore conclude that GDP growth rate becomes stationary after first difference. This is shown in the figure 4 on next page, which clearly depicts that the GDP growth becomes stationary after first difference.
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Figure 4. GDP growth after first difference (2001:Q1-2007:Q4)
3.1.2) Co-Integration Analysis
Engle-Granger Approach To Co-integration
Engle-Granger test of co-integration is a simple, and a two-step procedure.
In the first step, regression is applied on variables (unemployment rate and GDP growth rate) in levels; the regression results are shown below:
Augmented Dickey-Fuller test is applied on the residuals; the results are shown in the table 5 on next page,
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Table 5
Residual Unit Root Analysis (2001:Q1-2007:Q4)
t-statistic p-value
ADF
Test Statistic -4.645604 0.0010
Test Critical
Values 1% Level -3.699871
5% Level -2.976263
10% Level -2.627420
The p-value 0.0010 is also less than 5% level. Hence we have enough evidence to reject the null-hypothesis, and therefore conclude that the error term is stationary in levels. This means that both the variables have a long run association, and are therefore co-integrated.
Johansen Test Of Co-Integration
In order to apply Johansen test of co-integration, we make certain assumptions.
The first assumption is that both variables are stationary in their levels, I(0), and if non-stationary then both variables must be integrated of the same order. From our results obtained after applying unit-root tests, we found that both of our variables are integrated of the same order, hence we can apply Johansen test of co-integration.
Before applying the test, we need to know lag length. There are several criteria for choosing a specific lag-length, for-example, sequential modified LR test-
28
statistic, Final prediction error (FPE), Akaike Information Criterion (AIC), Schwarz
Information Criterion (SIC), and Hanna-Quinn Information Criterion (HQ). All the criteria are equally good. The lag-structure criteria is applied, and the results are shown in table 6 below,
Table 6
Lag-Length Criteria (2001:Q1-2007:Q4)
Lag Log-L LR FPE AIC SC HQ
0 -8.39825 NA 0.00762 0.79986 0.89664* 0.82773
1 -2.02675 11.2726* 0.00636 0.61744 0.90777 0.70104*
2 2.289516 6.97243 0.00626* 0.59211* 1.07699 0.73245
According to the results, maximum two lags can be used in Johansen test of co- integration, and vector error correction model (VECM). The test result of
Johansen test of co-integration are shown in the table 7 on next page,
29
Table 7
Johansen Test of Co-Integration Test Results (2001:Q1-2007:Q4)
Co-
integration
Rank Test
(Trace)
Hypothesized Eigenvalue Trace Stat Critical Value p-value
No. of C.E(s) 0.05
None* 0.455338 20.70831 15.49471 0.0075
At most 1* 0.198077 5.518559 3.841466 0.0188
Co-
integration
Rank Test
(Max.
Eigenvalue)
Hypothesized Eigenvalue Max-Eigen Critical Value p-value
No. of C.E(s) Stat 0.05
None* 0.455338 15.18975 14.26460 0.0356
At most 1* 0.198077 5.518559 3.841466 0.0188
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The trace test and the max-eigenvalue test statistics are greater than critical value at 0.05 level; results indicates that there are two co-integrating equation(s).
(*means rejection of hypothesis at the 0.05 level). Hence we can conclude that there is a long-run relationship between unemployment rate and GDP growth rate).
3.1.3) Vector Error Correction Model (VECM)
Vector Error Correction Model (VECM) is used for period 2001:Q1-2007:Q4; since both variables are non-stationary in levels, and are integrated of the same order i.e. I(1) . The error correction model with two lags is given below,
10 ̂
̂ ̂ ̂
The estimated VECM is given below:
̂
̂
10 Asteriou, Dimitrios. ‘Applied Econometrics, A Modern Approach using E-Views and Microfit’. Palgrove Macmillan, page 331.
31
Table 8 on next page shows the relevant statistics related to the vector error correction model (VECM):
Table 8
VECM Results (2001:Q1-2007:Q4)
Coefficients t-statistic p-value
-3.2459715 0.0041
-0.570800 0.5748
0.944101 0.3570
0.944101 0.3660
1.295996 0.2105
-0.385789 0.7039
0.671858
The t-statistic value of is -3.245, and the associated p-value is 0.0041. This means that is statistically significant. Also real GDP growth rate has long run causality on unemployment rate (the error term in the previous period).
Unemployment rate would adjust at a speed of 1.027 times to the equilibrium as a result of deviation from the equilibrium.
To check a short run association between the unemployment rate and GDP growth, the Wald test is applied.
The Null Hypothesis is this case is:
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The Alternative Hypothesis in this case is:
The Wald test results are shown in Table 9 below,
Table 9
Wald Test Results (2001:Q1-2007:Q4)
Test Statistics Value p-value
F-statistic 0.839804 0.4472
Chi-Square 1.679608 0.4318
From the results, the p-value is 0.4318, which is greater than 5% level; hence we cannot reject the null hypothesis. Thus and jointly have no impact on . This model suggests that both unemployment rate and GDP growth rate have no short run association, but do have a long run association.
3.1.4) Okun’s Equation (2001:Q1 – 2007:Q4)
Finally, the difference version of Okun's law is estimated for the period 2001Q1 to
2007Q4. The estimated equation is shown below:
33
The relevant statistics are shown in Table 10 below,
Table 10
Okun’s Law: Regression Results (2001:Q1-2007:Q4)
Variable t-statistics p-value
-0.2113 0.8345
-1.7100 0.10007
According to the above results, the p-value is 0.10007; hence is statistically insignificant. Therefore, the GDP growth rate has no significant contemporaneous effect on the unemployment rate over the period 2001:Q1 to
2007:Q4.
3.2) 2008:Q1 – 2013:Q4
3.2.1) Stationary Analysis
Unemployment Rate,
The graph of unemployment rate in its levels is shown in the figure 5 on the page below. From the graph, it can be seen that unemployment rate is non-stationary since its mean and variance are not constant over the period 2008Q1-2013Q4.
34
Figure 5. Unemployment rate in levels (2008:Q1-2013:Q4)
The ADF test results are shown in Table 11 below,
Table 11
Unemployment Rate In Levels (2008:Q1-2013:Q4)
t-statistics p-value
ADF Test -1.5737622 0.1067 Statistic
Test Critical 1% Level -2.669359 Values
5% Level -1.956406
10% Level -1.608495
The p-value is 0.1067, which is greater than 5% level. This allows us to accept null hypothesis of unit root, and therefore we can conclude that unemployment
35
rate is non-stationary in levels. Hence, the series needs to be differenced. The results after first difference are shown in Table 12 below,
Table 12
Unemployment Rate After First Difference (2008:Q1-2013:Q4)
t-statistics p-value
ADF Test -5.025698 0.0000 Statistic
Test Critical 1% Level -2.674290 Values
5% Level -1.957204
10% Level -1.608175
The p-value 0.0000 is also less than 5% level. Therefore we have enough evidence to reject the null-hypothesis of unit-root, and conclude that the data series becomes stationary after first difference. This can also be seen in the figure 6 on next page. The graph depicts that the unemployment rate becomes stationary after first difference.
36
Figure 6. Unemployment rate after first difference (2008:Q1-2013:Q4)
GDP Growth Rate, )
The graph of GDP growth rate in its levels is shown in figure 7 below:
Figure 7. GDP growth rate in levels (2008:Q1-2013:Q4)
The ADF test results are shown in Table 13 on next page,
37
Table 13
GDP Growth Rate in Levels (2008:Q1-2013:Q4)
t-statistics p-value
ADF Test -1.162607 0.2153 Statistic
Test Critical 1% Level -2.679735 Values
5% Level -1.958088
10% Level -1.607830
The p-value associated with it is also greater than 5%. Thus we accept null hypothesis of unit root, and therefore conclude that the GDP growth rate is non- stationary in levels. Hence, the series needs to be differenced. The results after first difference are shown in Table 14 on next page,
38
Table 14
GDP Growth Rate After First Difference (2008:Q1-2013:Q4)
t-statistics p-value
ADF Test -6.143616 0.0000 Statistic
Test Critical 1% Level -2.674290 Values
5% Level -1.957204
10% Level -1.608175
The p-value associated with it 0.0000 is also greater than 5%. Thus we have enough evidence to reject null hypothesis of unit root, and therefore conclude that the GDP growth rate becomes stationary after first difference. Figure 8 shows that the GDP growth rate becomes stationary after first difference.
Figure 8. GDP growth rate after first difference (2008:Q1-2013:Q13)
39
3.2.2) Co-Integration Analysis
Engle-Granger Test of Co-integration
Engle-Granger test of co-integration is a simple, and a two-step procedure.
In the first step, regression is applied on variables (unemployment rate and GDP growth rate) in levels.
Augmented Dickey-Fuller (ADF) test is applied on the residuals; the results are shown in the table 15 on next page,
Table 15
Residual Unit Root Analysis (2008:Q1-2013:Q4)
t-statistics p-value
ADF Test -4.794640 0.0001 Statistic
Test Critical 1% Level -2.669359 Values
5% Level -1.956406
10% Level -1.608495
40
The p-value 0.0001 is also less than 5% level. Thus we have enough evidence to reject the null-hypothesis of unit root, and therefore conclude that the error term is stationary in levels. Moreover this also means that both the variables have a long run association, and are therefore co-integrated.
Johansen Test Of Co-Integration:
In order to apply Johansen test of co-integration, we make certain assumptions.
The first assumption is that both the variables are non-stationary in their levels,
I(0), and if we first difference it, it becomes stationary or in other words both variables must be integrated of same order. From our results obtained after applying unit-root tests, we found that both of our variables are integrated of the same order, hence we can apply Johansen test of co-integration. Before applying the test, we need to know lag length. The results are shown in Table 16 below:
Table 16
Lag-Length Criteria Results (2008:Q1-2013:Q4)
Lag Log-L LR FPE AIC SC HQ
0 -34.6465 NA 0.095931 3.331506 3.43069 3.354871
1 -18.7214 27.50696* 0.032552 2.247407 2.544964* 2.317502
2 -13.0916 8.700680 0.028429* 2.099239* 2.595167 2.216064*
According to the results, maximum two lags can be used in Johansen test of co- integration, and vector error correction model.
41
The test result of Johansen test of co-integration are shown in Table 17,
Table 17
Johansen Test Of Co-integration Test Results (2008:Q1-2013:Q4)
Co-integration
Test
Hypothesized Eigenvalue Trace Stat Critical Value p-value
No. of C.E(s) 0.05
None* 0.574153 20.49197 15.49471 0.0081
At most 1 0.198077 2.564798 3.841466 0.1093
Co-integration
Rank Test
(Max
.Eigenvalue)
Hypothesized Eigenvalue Max-Eigen Critical Value p-value
No. of C.E(s) Stat 0.05
None* 0.574153 17.92717 14.26460 0.0126
At most 1 0.114970 2.564798 3.841466 0.1093
The trace test and the max-eigenvalue test statistics are greater than critical value at 0.05 level; results also indicates that there is only one co-integrating equation. Hence we can conclude that there is a long-run relationship.
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3.2.3) Vector Error Correction Model (VECM)
Vector Error Correction Model (VECM) is used for period 2008:Q1-2013:Q4, since both variables are non-stationary in levels, and are integrated of the same order i.e. I(1) . The error correction model with two lags is given below:
̂
̂ ̂ ̂
The estimated VECM is given below:
̂
̂
Table 18 shows the relevant statistics regarding the vector error correction model
(VECM):
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Table 18
VECM Results (2008:Q1-2013:Q4)
Coefficients t-statistic p-value
-0.868239 0.3989
-0.265827 0.7940
-2.292291 0.0368
-0.991265 0.3373
-0.270893 0.7902
-0.931230 0.3665
0.597278
π
The t-statistic value of is -0.868239, and the associated p-value is 0.3989; this means that is statistically non-significant. Unemployment rate would adjust at a speed of 0.309 times to the equilibrium as a result of deviation from the equilibrium, but more evidence is needed to prove so.
To check a short run association between the unemployment rate and GDP growth, the Wald test is applied.
The Null Hypothesis is this case is:
The Alternative Hypothesis in this case is:
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The Wald test results are shown in table XIX below:
Table 19
Wald Test Results (2008:Q1-2013:Q4)
Test Statistics Value p-value
F-statistic 0.8815 0.4346
Chi-Square 1.7630 0.4142
From the results the associated p-value is 0.4142, which is greater than 5% level, hence we cannot reject the null hypothesis. Thus and jointly have no impact on .This model suggests that both unemployment rate and GDP growth rate have no short run association.
3.1.4) Okun’s Equation (2008:Q1–2013:Q4)
Finally, the difference version of Okun's law is estimated for the period 2008:Q1 to 2013:Q4. The estimated equation is shown below:
The relevant statistics are shown in Table 20 on next page,
45
Table 20
Okun’s Law Regression Results (2008:Q1-2013:Q4)
Variable t-statistics p-value
-0.318 0.352
0.753 0.727
According to the above results, the p-value of GDP growth rate is 0.727, which is greater than 5% level; also the t-statistic 0.352 is small; hence is statistically in-significant, and the results imply that there is no contemporaneous effect of GDP growth rate on the unemployment rate over the period 2008:Q1–
2013:Q4.
Conclusion
The main goal of the research project is to find out a relationship between the unemployment rate and the GDP growth rate as proposed by Okun (1962) using time-series data from 2001 to 2013. The time series data is divided into two time periods on quarterly basis, 2001:Q1-2007:Q4 and 2008:Q1-2013:Q4. The conclusion is based on time-series analysis. Time-series econometrics techniques are applied on each period to find out an association between unemployment rate and GDP growth rate.
During the period 2001:Q1 – 2007:Q4, both the variables are found to be non- stationary, and integrated of the same order I(1) using graphical analysis, and
Augmented Dickey-Fuller (ADF) test of unit-root. A long-run association has been found using both Engle-Granger test of co-integration and Johansen test of co-
46
integration; thus meaning that both the unemployment rate and the GDP growth rate are co-integrated. The results obtained from vector error correction shows that unemployment rate would adjust at a speed of 1.027 times to the equilibrium as a result of deviation from the equilibrium. Wald test shows that and
jointly had no impact on during the period 2001:Q1 to 2007:Q4. This is also reflected in our Okun’s difference version equation where we were successful to find a negative relation between both the variables but need more evidence to prove so. Hence we couldn’t find a contemporaneous effect of GDP growth rate on the unemployment rate and GDP growth over the period 2008:Q1
– 2013:Q4.
During the period 2007:Q1 – 2013:Q4, the economy went through serious economic challenges, and we expected a deviation from such a relationship.
Both the variables are found to be non-stationary, and integrated of the same order I(1) using graphical analysis and Augmented Dickey-Fuller test of unit-root.
A long-run association has been found using both Engle-Granger test of co- integration and Johansen test of co-integration; thus meaning that both the unemployment rate and the GDP growth rate are co-integrated. The results obtained from vector error correction shows that unemployment rate would adjust at a speed of 0.309 times to the equilibrium as a result of deviation from the equilibrium, but more evidence is needed to prove so. Wald test shows that
and jointly had no impact on during the period 2007:Q1 to
2013:Q4. This is also reflected in our Okun’s difference version equation. We couldn’t find a contemporaneous effect of GDP growth rate on the unemployment
47
over the period 2008:Q1 – 2013:Q4. Based on these results, we conclude that both variables can still be used in policy decision-making.
48
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