Testing the Stability of Okuns Law - Term Paper Example

Testing the Stability of Okun’s Law Testing the Stability of Okun’s Law Introduction Macroeconomics, since its inception, has been concerned with the study of variables that affect the behavior of the economy as a whole. Two of the most important variables that attract the attention of economists and policymakers is the growth in output or real GDP and the unemployment rate. Typically, economists and policy makers would expect the two variables to be inversely related but evidence from the real world point to the fact that real GDP growth and the unemployment rate may not be always inversely related. For example, between the first quarter of 2003 and the first quarter of 2006, the average annual growth rate in real Gross Domestic Product in the United States was 3.4 percent and the rate of unemployment during that period fell considerably (Knotek, 2007). However, this inverse relationship was not replicated in the year that followed. In other words, while average growth in real Gross Domestic Product slowed down in the year that followed, the downward trend in the unemployment rate continued. Many economists could easily view this situation as an anomaly. Given the importance of economic growth and job creation to both policy makers and the citizenry, it is important to study the relationship between the two in order to ensure a more effective and efficient decision-making. Okun (1962) made the first attempt to study this relationship and he found that real GDP and unemployment are inversely related to each other and this has come to be known as the Okun’s Law. More specifically, a 2% rise in output is associated with a 1% decline in the unemployment rate. In another version, a 3% rise in the Gross National Product is associated with a 1% decline in the unemployment rate. While the relationship determined by Okun appears to have some empirical deficiencies, it, nonetheless, serves as a guide to policymakers in making crucial economic decisions. This paper seeks to determine whether or not there is some variability in the relationship between changes in real GDP growth rate and changes in the unemployment rate over an extended period. It is done by means of a recursive Ordinary Least Squares or rolling regression techniques. The first section provides a review of the literature on the subject and compares their results. This is followed by an explanation of the relationship estimated by Okun (1962). The third section describes the data and the methodology used. The fourth section presents the results and the final section concludes. Literature Review Arthur Okun’s empirical negative relationship between changes in the growth of output and the corresponding changes in the unemployment rate has attracted the attention of several writers to the subject. Different estimates of the Okun’s coefficient have yielded different results. While some authors suggest the relationship is not stable over time (for example Knotek, 2007; Owyang and Sekhposyan, 2012) others find some level of stability in the relationship (for example, Freeman, 2000; Ball et al, 2013). Knotek (2007) finds that the relationship between changes in unemployment rate and growth in real output varies considerably over time and across countries. The author attributes the relative instability in the relationship to the state of the business cycle. For example, while Prachowny (1993) estimates a 3% decline in real output for every 1% increase in unemployment, Abel and Bernanke (2005) a 2% decrease in output is associated with a 1% increase in the unemployment rate. The relative instability in the relationship notwithstanding, Knotek (2007) argues that the Okun’s law is still useful as a forecasting tool especially when one considers its relative instability. In a related argument, Owyang and Sekhposyan (2012) also find that the Okun’s relationship is unstable largely. The authors find that on average, high unemployment rates are usually observed during recessions and these high unemployment rates are highly correlated with the increased sensitivity of the unemployment rate to output. However, they add that these shifts do not always lead to significant changes. In conclusion, the authors suggest that the Okun’s law “should not be taken too seriously but rather as an approximation taken with a grain of salt.” In a sharp contrast, Freeman (2000) finds that the value of Okun’s coefficient is stable around 2 for all time periods and across regions in the United States regardless of how equilibrium output and employment are measured. The author finds that the original estimates of 3% change in real output for every 1% change in the unemployment rate has been reduced to 2.0-2.5. Freeman’s position is corroborated by Ball et al (2013) who suggest that there is a high degree of stability in the Okun’s Relationship in Most Countries While acknowledging that there are instances of deviations from the Okun’s law, the authors are quick to point out that these deviations are normally modest in size and for only short periods. Ball et al also finds that while the law appears to be stable across countries, the coefficient of interest, that is, the effect of a 1% change in output on the unemployment rate differs across countries and they attribute these differences to the special features of the labor market in each country. The next section describes the Okun’s law and the various ways of estimating it. What is Okun’s law? Historically, economists have been aware of the inverse relationship between the rate of unemployment and the growth rate of real output. However, this relationship was statistically formalized by Okun (1962) who observed the actual extent to which to which a change in real output growth is inversely related to the rate of unemployment. This statistically observed relationship has come to be known as the Okun’s law. Okun (1962) used Gross National Product and unemployment data for the United States to show that a one percentage point decline (rise) in the rate of unemployment was associated with approximately a three percentage point rise (fall) I real output growth. In addition, based on past relationship between Gross National Product and unemployment, Okun attempted to predict Potential GNP by using the relationship between real GNP gap and unemployment rate gap. He was; however, quick to add that a change in the unemployment rate does not necessarily determine the magnitude of a change in real output since there may be other factors output growth, such as labor productivity. For example, a decline in the unemployment rate may cause an increase in labor force participation, an increase in the number of working hours and productivity which, ultimately, leads to an increase in real output. Mathematically, the Okun’s relationship can be specified in two different versions; the difference version and the gap version. The difference version shows how quarterly changes in the unemployment rate are related to quarterly changes in real output growth. This can be represented by the equation; U = α + βY + µ, where U is the measure of the change in unemployment rate, Y is the measure of real output growth, α and β are parameters to be estimated, and µ represents factors, other than output, that affect the unemployment rate. The parameter β is the Okun’s coefficient and for the inverse relationship between changes in unemployment rate and real output growth to hold, β must be negative. The parameter α represents the change in unemployment rate associated with stable growth in real output and the ratio –α/β is the measure of output growth consistent with stability in the unemployment rate. This version can be estimated using available data. For example, Knotek (2007) used quarterly data from second quarter of 1948 to the fourth quarter of 1960 to estimate the above equation as; U = 0.30 – 0.07Y. This means, when real output growth remains constant in a given quarter, the unemployment rate in that quarter rises by 0.30 percentage point. In addition, at a constant unemployment rate the real of growth in real output was approximately 4.3%. This implied that any growth rate in the real output above 4.3% would induce a rise in the unemployment rate. Therefore, the above regression suggests that every one percentage rises in real output growth above 4.3% induced a 0.07 percentage point decline in the unemployment rate. The gap version, on the other hand, sought to estimate the level of unemployment by determining the gap between likely and real output, where potential output refers to the amount of goods that an economy can produce under conditions of full employment. Following Abel and Bernanke (2005), the gap version can be mathematically represented as; (Y - Ῡ)/Ῡ = -c(u -ῡ), where Y is defined the actual output, Ῡ is potential output, u is the unemployment rate, ῡ is the natural rate of unemployment and cis the factor relating changes in unemployment to changes in output. Due to the problems associated with getting measurements for both potential output and the natural rate of unemployment, this paper seeks to determine the stability of the Okun’s relationship by using the difference version. Excursive Regression Analysis Recursive Regression Graph A arrow represent a direct link between Real GNP and unemployment rate, an arc represents correlated errors in the data-generating process for Unemployment Rate and Real GNP source ss df ms Number of obs 271 Model 117.7193 1 117.7093 F( 1, 269) 232.5 Residual 136.1901 269 0.506286 Prob > F 0 Total 253.8993 270 0.940368 R-squared 0.4636 Adj R-squared 0.4616 Root MSE 0.71154 From the ANOVA table, 46.16% of the difference in real GNP is explained by the unemployment rate. This implies that unemployment rate influences the GNP. The model for the prediction of real GNP is significant (F1, 269) 232.5, p=0.000). rgnp coef std.Err T P>t [95% Conf. Interval] unrate -1.67128 0.109608 -15.25 0 -1.88708 -1.45548 _cons 0.802978 0.043227 18.58 0 0.717871 0.888084 From the coefficient table unemployment rate (p=0.0000, -1.67128) is significant, constant (p=0.000, 0.802978) Real GNP =0.802978-1.67128employment rate Predicted value of real GNP and regressed against employment rate Source SS Df MS Number of obs 271 F( 1, 269) 232.5 Model 4.199129 1 4.199129 Prob > F 0 Residual 4.858409 269 0.018061 R-squared 0.4636 Adj R-squared 0.4616 Total 9.057538 270 0.033546 Root MSE 0.13439 From the ANOVA table, real GNP explains 46.16% of the variation in the unemployment rates. This implies that Real GNP greatly influence the unemployment rate. The model for predicting real unemployment rate is significant (F1, 269) 232.5, p=0.000) this model can be used to calculate predicted unemployment rates in order to run a recursive least squares regression. unrate Coef. Std. Err. T P>t [95% Conf. Interval] rgnp -0.2774 0.018192 -15.25 0 -0.31321 -0.24158 _cons 0.225712 0.022773 9.91 0 0.180876 0.270547 From the coefficient table gross national product (p=0.0000, -2274) is significant, constant (p=0.000, 0.0.227512) Okuns law =0.255712 -0.2274Y +0.13439 Predicted variable unrate_hat is predicted by real GNP and regressed with real GNP to find the instrumental coefficients in predicting the unemployment rate. Source SS df MS Number of obs = 271 F( 1, 269) = 232.5 Model 9.057538 1 9.05753799 Prob > F = 0 Residual 10.47961 269 0.038957647 R-squared = 0.4636 Adj R-squared = 0.4616 Total 19.53715 270 0.072359796 Root MSE = 0.19738 From the ANOVA table 46.16% of the variation in predicted unemployment rate is explained by real GNP. This implies that Real GNP affects the unemployment rate. The model for predicting real unemployment rate is significant (F1, 269) 232.5, p=0.000) this model can be used to determine recursive least squares regression unrate_hat Coef. Std. Err. T P>t [95% Conf. Interval] rgnp -0.1286 0.008434 -15.25 0 -0.14521 -0.112 _cons 0.10761 0.010558 10.19 0 0.086824 0.128396 The instrumental coefficients are real GNP (p=0.0000, -0.1286) constant (p=0.000, 0.10761). From the least estimates recursive regression the coefficients are Coef. Std. Err. T P>t [95% Conf. Interval] rgnp -0.1286 0.085272 -1.51 0.133 -0.29649 0.039282 _cons 0.10761 0.10674 1.01 0.314 -0.10254 0.317761 This implies that Okuns law can be represented as; U = 0.10761 -0.1286Y This means, when real output growth remains constant in a given quarter, the unemployment rate in that quarter rises by 0.10761 percentage point. In addition, at a constant unemployment rate the real of growth in real output was approximately 2.099%. This implied that any growth rate in the real output is above 2.099% would induce a rise in the unemployment rate. Therefore, regression analysis above suggests that every one percentage rises in real output growth above 2.099% induced a 0.1286 percentage point decline in the unemployment rate. Conclusion From the recursive regression equations Okuns law has been changing over time before becoming stable. This implies that relationship between unemployment rate and groeth in real gross national product varies by time before becoming stable. This could be attributed to changing market and global patterns that affect the quarterly GNP of various nations. For instance in the first case, at a constant unemployment rate the real of growth in real output was approximately 2.8312% which implied that that every one percentage rises in real output growth above 2.8312% induced a 0.2274 percentage point decline in the unemployment rate. In the second case instance in the first case at a constant unemployment rate the real of growth in real output was approximately 2.099% which implied that that every one percentage rises in real output growth above 2.099% induced a 0.1286 percentage point decline in the unemployment rate. This finding is supported by Knotek (2007) finds that the relationship between changes in unemployment rate and growth in real output varies considerably over time and across countries. The author attributes the relative instability in the relationship to the state of the business cycle. Read More