Augmenting Okun s Law with Earnings and the Unemployment Puzzle of 2011

Augmenting Okun s Law with Earnings and the Unemployment Puzzle of 2011 Kurt G. Lunsford University of Wisconsin Madison January 2013 Abstract I propose an augmented version of Okun s law that regresses the change in the unemployment rate on the percent change in the nominal GDP to hourly earnings ratio. The standard Okun s regression, which regresses the change in unemployment on the percent change in real GDP, suggests that the drop in the unemployment rate was 1.19% larger than expected in 2011. In contrast, the augmented Okun s regression, using the nominal GDP to hourly earnings ratio, suggests that the drop in the unemployment rate was only only 0.79% larger than expected in 2011. Keywords: Okun s Law, Unemployment, Earnings JEL Codes: E24, E32, J30, J60 I am grateful to Kenneth D. West for numerous helpful comments. All errors are my own. Email: klunsford@wisc.edu. 1

1 Introduction In a 2012 speech, Ben S. Bernanke noted something of a puzzle in the U.S. labor market: the drop in the unemployment rate in 2011 was much larger than expected given the growth in real GDP. Panel (a) of Figure 1 summarizes Bernanke s puzzle. It displays a scatter plot of Q4 to Q4 changes in unemployment versus Q4 to Q4 percent changes in real output from 1990 to 2011 and the corresponding least squares regression line. 1 The location of the 2011 data point is well below the regression line, and the regression line suggests that unemployment should have increased, not decreased, in 2011. The statistical relationship between real GDP growth and unemployment changes was famously examined by Okun (1962), and I will refer to regressions of unemployment changes on GDP growth as Okun s law or Okun regressions. To explain the deviation from Okun s law in 2011 observed by Bernanke (2012), I propose an augmented Okun s law that uses the percent change in the ratio of nominal GDP to nominal hourly earnings of employees, which I denote by % (Yt N /w t ), as the regressor in an Okun regression instead of the percent change in real GDP. Because nominal output is the dollar value of the sales of all final goods, Yt N /w t summarizes the average sales to compensation ratio in the economy, and it can be thought of as a measure of the profitability of labor. In a standard labor market model such as Mortensen and Pissarides (1994), an increase in labor profitability motivates firms to post vacancies, which reduces the unemployment rate. Thus, Yt N /w t is a natural variable to include in an Okun regression. I call the statistical relationship between the unemployment rate changes and % (Yt N /w t ) an augmented Okun s law because when nominal GDP is decomposed into real GDP and a price level, then % (Yt N /w t ) is approximately equal to % Y t % (w t /P t ), which embeds real earnings into a standard Okun regression. For the 1990 to 2011 period, the augmented Okun s law is displayed in panel (b) of Figure 1. With the augmented Okun s law, the magnitude of the regression error is 33% smaller in 2011 than the error produced by the standard Okun s law. A sizeable literature has studied changes to Okun s law. However, unlike this paper, they focused on the production relationship between output and 1 To be consistent with Bernanke (2012), I maintain his sample period of 1990 to 2011 and follow his use of Q4 to Q4 percent changes throughout the body of this paper. In the Appendix, I show that using quarterly percent changes does not alter the qualitative results. 2

Figure 1: Panel (a) displays a scatterplot of Q4 to Q4 changes in the unemployment rate on Q4 to Q4 percent changes in real GDP from 1990 to 2011. Panel (b) displays a scatterplot of Q4 to Q4 changes in the unemployment rate on Q4 to Q4 percent changes in Yt N /w t from 1990 to 2011. In both panels, years 1990 to 2007 are displayed as dots, and years 2008 to 2011 are labelled and displayed as boxes. A least squares regression line is displayed for each plot. Details of the data and regressions are provided in Section 2. labor, which Knotek (2007) refers to as production-function versions of Okun s law. Gordon (1984, 2010) includes several additional variables into the Okun relationship, such as hours per employee, labor productivity, and the labor force participation rate, Prachowny (1993) also adds capital utilization, and Malley and Molana (2008) consider production with high-effort and low-effort states. Thus, by using Yt N /w t, this paper takes a unique approach to studying Okun s law. Further, by keeping the augmented Okun regression parsimonious, I maintain the simplicity that Knotek (2007) described as [p]art of the enduring appeal of Okun s law. 3

2 Augmented Versions of Okun s Law Okun regressions commonly take the form u t = α 0 + α 1 % Y t + ε t, (1) where u t is the change in the unemployment rate and % Y t is the percent change in real GDP. Knotek (2007) refers to Equation (1) as the difference version of Okun s law. In contrast to Equation (1), I consider the form ( u t = β 0 + β 1 % Y ) t N + η t, (2) w t where w t is nominal earnings and Yt N is nominal output. As noted in the Introduction, Equation (2) augments Equation (1) by embedding real earnings within a standard Okun regression. By decomposing nominal GDP into the product of real GDP and the price level, P t, it is the case that % (Yt N /w t ) = % Y t % w t /P t, when percent changes are measured as log deviations. This means that Equation (2) can be rewritten as ( u t = β 0 + β 1 % Y t β 1 % w ) t + η t, P t which is a standard Okun regression with real earnings. One feature to note about Equation (2) is that the coefficients on the percent change of real GDP and the percent change on real earnings are equal and opposite. Thus, to measure the effects of real earnings independently from real GDP, I also consider a regression that includes real earnings a separate regressor with its own coefficient: ( u t = γ 0 + γ 1 % Y t + γ 2 % w ) t + ξ t. (3) P t To estimate these equations, I use real GDP, nominal GDP and the GDP deflator from the Bureau of Economic Analysis as Y t, Yt N and P t, respectively. I also use the quarterly average of total private average hourly earnings of production and nonsupervisory employees and the civilian unemployment rate from the Federal Reserve Bank of St. Louis s FRED database for w t and u t, respectively. Because I am using Q4 to Q4 changes for any data series x t, I use x t = x t x t 4 and % x t = ln(x t ) ln(x t 4 ). I estimate all 4

Table 1: Estimated Coefficients for Equations (1), (2) and (3) Equation (1) Equation (2) Equation (3) Constant 1.093 0.736 0.872 (0.233) (0.160) (0.198) % Y t 0.394 0.408 (0.067) (0.063) % (Yt N /w t ) 0.387 (0.067) % (w t /P t ) 0.289 (0.131) R 2 0.534 0.611 0.599 Standard errors, presented in parentheses, use Newey and West (1987) with one lag. Two stars indicates significance at the 0.05 level, and three stars indicate significance at the 0.01 level. equations on data from 1990 to 2011, and the results of the regressions are presented in Table 1. The estimated coefficients for Equation (1) trace out the regression line displayed in panel (a) of Figure 1. The estimated constant suggests that the unemployment rate increases by 1.09% when real GDP growth is zero. Combined, the constant and the slope on % Y t suggest that output growth of 2.77% is consistent with a stable unemployment rate. The estimated coefficients for Equation (2) trace out the regression line displayed in panel (b) of Figure 1. In Equation (2), the estimated constant suggests that the unemployment rate increases by 0.74% when the nominal GDP to hourly earnings ratio is constant. Combined, the constant and the slope on % (Yt N /w t ) suggest that nominal GDP to hourly earnings growth of 1.90% is consistent with a stable unemployment rate. When real hourly earnings is added as a separate regressor to Okun s law, the coefficient on % Y t is nearly identical to when % Y t is the only regressor. However, the coefficient on % (w t /P t ) is both positive and statistically significant, suggesting that a 1% increase in real hourly earnings is associated with a 0.29% increase in the unemployment rate for a given level of real GDP growth. 5

Figure 2: Panel (a) compares the regression errors from Equation (2) to Equation (1) for years 2008 to 2011. Panel (b) compares the regression errors of Equation (3) to Equation (1) for years 2008 to 2011. Over the 1990 to 2011 sample, both Equations (2) and (3) provide a better fit of the data than Equation (1) as measured by R 2. However, this measure alone does not indicate the fit for 2011. Panel (a) of Figure 2, compares the regression errors of the augmented Okun s law in Equation (2) to the standard Okun s law in Equation (1) for 2008 to 2011. The standard Okun s law has a smaller error in 2008, but the augmented Okun s law provides a better fit for 2009 through 2011. The standard Okun s law suggests that the change in the unemployment rate was 1.19% lower than expected in 2011. In contrast, the augmented Okun s law suggests that the change in the unemployment rate was only 0.79% lower than expected in 2011 a one third reduction. Bernanke (2012) hypothesized that the unexpected drop in the unemployment rate in 2011 was due to employers making up for the unexpectedly large increase in the unemployment rate in 2009 a hypothesis endorsed 6

Table 2: 1990 to 2011 Sample Averages and 2008 to 2011 Data Observations % Y t % (Y N t /w t ) % (w t /P t ) 1990-2011 Average 2.39 1.51 0.88 2008-3.38-4.99 1.66 2009-0.08-2.22 2.06 2010 2.37 1.96 0.39 2011 1.95 2.09-0.15 in a separate speech by Yellen (2012). Panel (a) of Figure 2 shows that the regression error of Equation (1) in 2009 is 1.94%. It also shows that the regression error of Equation (2) in 2009 is 1.47%. Thus, the augmented Okun s law does not refute the hypothesis put forward by Bernanke (2012); rather, it suggests that unemployment changes in 2009 and 2011 were not as abnormal as indicated by a standard Okun regression. Table 2 summarizes the 1990 to 2011 sample average for % Y t, % (Yt N /w t ) and % (w t /P t ), as well as the observations for each variable from 2008 to 2011. The superior fit of Equation (2) relative to Equation (1) in 2011 results from the fact that the growth rate of the Yt n /w t ratio was 2.09% in 2011, which was higher than the 1990 to 2011 average of 1.51% and consistent with a falling unemployment rate. This contrasts with 2011 real GDP growth, which was 0.44% lower than its 1990 to 2011 average and consistent with rising unemployment. Panel (b) of Figure 2, compares the regression errors of Okun s law with real hourly earnings in Equation (3) to the standard Okun s law in Equation (1). As with the augmented Okun s law in Equation (2), including real hourly earnings reduces the magnitude of the errors in 2009 and 2011. This suggests that accounting for fluctuations in real earnings, either through Equation (2) or Equation (3), helps account for a large portion of the change in the unemployment rate not explained by real GDP in 2009 and 2011. The improved fit of Equation (3) relative to Equation (1) in 2009 and 2011 stems from the large deviations in real earnings growth from average in those years. From 1990 to 2011, real hourly earnings growth averaged 0.88%. However, in 2009, the growth of real hourly earnings was 2.06%, more then double its average rate. In 2011, real hourly earnings growth was -0.15%, indicating 7

falling real earnings. 3 Conclusion This paper shows that an Okun regression using the ratio of nominal GDP to hourly earnings explains a large portion of Bernanke s (2012) 2011 unemployment puzzle. Further, the augmented Okun s law and an Okun regression that includes real earnings both provide a modestly better fit of changes in the unemployment rate from 1990 to 2011 than the standard Okun s law. As discussed in Knotek (2007), dynamic versions of Okun s law and Okun regressions with time varying parameters are useful for forecasting changes in the unemployment rate. Thus, a future research agenda that incorporates the nominal GDP to hourly earnings ratio or real earnings into forecasts of unemployment rate changes may help economists better predict the behavior of the unemployment rate. Appendix In this Appendix, I estimate Equations (1), (2) and (3) by using data at a quarterly frequency so that x t = x t x t 1 and % x t = ln(x t ) ln(x t 1 ) for any variable x t. The sample period remains 1990 to 2011, and the estimated coefficients of each equation are summarized in Table 3. The estimated constant for Equation (1) implies that the unemployment rate increases by 0.85% when RGDP growth is zero for four quarters, which is lower than with the annualized data. Combined, the constant and the slope on % Y t in Equation (1) suggest that annual real GDP growth of 2.91% is consistent with a stable unemployment rate, which is slightly larger than the result with annualized data. The estimated constant for Equation (2) implies that the unemployment rate increases by 0.58% when the nominal GDP to hourly earnings ratio is constant for four quarters, which is lower than with the annualized data. Combined, the constant and the slope on % (Yt N /w t ) in Equation (2) suggest that annual growth in the nominal GDP to hourly earnings ratio of 2.03% is consistent with a stable unemployment rate, which is slightly larger than the result with annualized data. As with the annualized data, the coefficients on % Y t are nearly identical for Equations (1) and (3) with quarterly data, and the coefficient on % (w t /P t ) in Equation (3) indicates that a 1% 8

Table 3: Estimated Coefficients for Equations (1), (2) and (3) Equation (1) Equation (2) Equation (3) Constant 0.212 0.146 0.166 (0.064) (0.046) (0.048) % Y t 0.291 0.298 (0.062) (0.051) % (Yt N /w t ) 0.287 (0.055) % (w t /P t ) 0.229 (0.113) R 2 0.395 0.433 0.435 Standard errors, presented in parentheses, use Newey and West (1987) with four lags. Two stars indicates significance at the 0.05 level, and three stars indicate significance at the 0.01 level. increase in real earnings per quarter corresponds to a 0.23% increase in the unemployment rate for a given rate of real GDP growth. As with the annualized data, Equations (2) and (3) provide a better fit than Equation (1) with quarterly data as measured by R 2. The sum of the errors in 2011 for Equation (1) is -1.14%, compared to -0.85% and -0.91% for Equations (2) and (3), respectively. In 2009, the sum of the errors for Equation (1) is 2.20%, compared to 1.85% and 1.91% for Equations (2) and (3), respectively. Thus, as in the annualized data, the quarterly data suggest that accounting for fluctuations in real earnings can reduce Okun regression errors for 2009 and 2011. 9

References Bernanke, Ben S. 2012. Recent Developments in the Labor Market. Speech at the National Association for Business Economics Annual Conference, Washington, D.C. Gordon, Robert J. 1984. Unemployment and Potential Output in the 1980s. Brookings Papers on Economic Activity 1984 (2):537 568.. 2010. Okun s Law and Productivity Innovations. American Economic Review: Papers & Proceedings 100 (2):11 15. Knotek, Edward S., II. 2007. How Useful is Okun s Law? Federal Reserve Bank of Kansas City Economic Review Fourth Quarter:73 103. Malley, Jim and Hassan Molana. 2008. Output, Unemployment and Okun s Law: Some Evidence from the G7. Economics Letters 101 (2):113 115. Mortensen, Dale T. and Christopher A. Pissarides. 1994. and Job Destruction in the Theory of Unemployment. Economic Studies 61 (3):397 415. Job Creation The Review of Newey, Whitney K. and Kenneth D. West. 1987. A Simple, Positive Semi- Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica 55 (3):703 708. Okun, Arthur M. 1962. Potential GNP: Its Measurement and Significance. In Proceedings of the Business and Economics Statistics Section of the American Statistical Association. American Statistical Association. Prachowny, Martin F. J. 1993. Okun s Law: Theoretical Foundations and Revised Estimates. The Review of Economics and Statistics 75 (2):331 336. Yellen, Janet L. 2012. The Economic Outlook and Monetary Policy. Speech at the Money Marketeers of New York University, New York, New York. 10