The relationship between output and unemployment in France and United Kingdom Gaétan Stephan 1 University of Rennes 1, CREM April 2012 (Preliminary draft) Abstract We model the relation between output and unemployment for France and United Kingdom inside a bivariate unobserved component model. Our results show that movement of real GDP and unemployment are explained in a large part by permanent movements of the series, suggesting that the cycle represents the adjustment to the permanent shocks. Morevoer, negative correlation is found between trend and cycle for both series supporting real business cycle theory. Finally, we find that Okun s coefficient is significantly lower (in absolute values) than in previous estimates. JEL Classification: C32, E32 Key-words: Business cycles, Okun s law, unobserved components 1 PhD student, Faculty of Economics 7, place Hoche CS 86514 35065 RENNES Cedex (France) Tél : +33 02 23 23 53 81 Email : gaetan.stephan@univ-rennes1.fr I am grateful to Christophe Tavéra for his helpful comments for the elaboration of this paper. 1
Section 1 Introduction Since Okun (1962) seminal contribution, the correlation between output and unemployment was widely accepted as an empirical regularity relevant for macroeconomic policy analysis. More precisely, Okun s law represents the negative correlation which holds between cyclical unemployment and cyclical output. A major problem is in the choice of the detrending method to extract cyclical components of output and unemployment for estimation of Okun s law. Among detrending methods usually used (linear trend, Hodrick-Prescott filter, band-pass filters, Harvey s structural time series approach, ) any take account potential correlation between trend and cycle (for unemployment and output) and the Okun s law is traditionally estimated by first extracting cyclical components and then estimating correlation between these components to get Okun s coefficient. In a recent paper, Sinclair (2009) proposes an alternative way to estimate Okun s coefficient using a bivariate unobserved component model. In this model, output and unemployment are divided into a permanent and a transitory component; overall, we relax assumption that trend and cycle are uncorrelated and estimate Okun s law directly within this model. Applied to France and United Kingdom, our estimates show that variations of output are largely dominated by technology shocks. The paper shows also the natural rate of unemployment is quite volatile and supports the idea that fluctuations of unemployment are strongly related to movements of the natural rate. Moreover, our estimates tend to prove that trend and cycle are negatively correlated for both series. Including structural break in permanent components does not alter qualitatively these findings. Negative correlation support the idea, defended by Stock and Watson (1988), that real or technology shocks tend to modify the long-run trend growth of output and the natural rate of unemployment, suggesting that short-run fluctuations reflect overall adjustments of variable to their newsteady state values. Also, we observe that adjustment seems slower for unemployment than for real GDP in both countries. Concerning Okun s law coefficients, our estimates show that unemployment and output are negatively correlated through their transitory and permanents components. Overall, our results indicate that Okun s coefficient associated to transitory components is lower (in 2
absolute values) than estimates using traditional detrending methods. Whereas Okun s coefficient for permanent movements is very close to traditional estimates of Okun s coefficients. This negative correlation between permanents components of output and unemployment should enhance theories which highlight the negative impact of productivity growth on unemployment. The paper is organized as follows. Section 2 describes the bivariate unobserved components used in the paper. Section 3 presents data and estimates of the model. Section 4 concludes. Section 2 Econometric Model We model output and unemployment as the sum of an unobserved permanent component and an unobserved transitory component. The permanent component of output represents the long-run trend growth and the permanent component of unemployment can be viewed like natural rate of unemployment or NAIRU. Transitory components can be seen as the cyclical component of output and unemployment, i.e. deviations from trend. The model may be written as follows: Each of the trend component is assumed to be a random walk to allow for permanent movements in the series. We also include a drift for the permanent movement of output and unemployment: Following Sinclair (2009), Sinclair and Mitra (2012) and Clark (1989), we model each transitory component as an AR(2) process: 3
The model can be cast in state-space form by making the transition observation equation an identity and treating both trend and cycle as state variable. We use Kalman filter for maximum likelihood estimation of the parameters as well as for the permanent and transitory components. In our correlated unobserved component model, the important point is that the matrix of variance/covariance allows for correlation within permanent and transitory shocks and cross-series correlation between unemployment and output. In fact, the key assumption is that we impose no restrictions on the variance/covariance matrix. In our bivariate unobserved component model, the matrix can be written as: Σ Using this framework, we can estimate Okun s law (1962) which states that a decrease of cyclical unemployment is associated with an increase of cyclical output. Recents estimates, see Freeman (2001) for instance, point out this tradeoff is now about a two to one. A version of this relationship may be written by the following: Where represents the Okun s coefficient. Sinclair (2009) proposes the following method to estimate Okun s coefficient basing on the correlations of the matrix of variance/covariance of unobserved component model. We substitute transitory components of output and unemployment by their innovations (if we cannot reject the hypothesis that the autoregressive parameters are the same for GDP and unemployment). We can rewrite: And assuming that innovations are jointly normally distributed and is an independent normal random variable. Multiplying both sides by and taking expectations, leads to: 4
Where is Okun s coefficient for transitory innovations. Similarly, we can also examine the relationship between permanent innovations of real GDP and unemployment in the same way. We call the Okun coefficient for permanent innovations, can be written as: Section 3 Data and Results Data are taken from OECD.stat from 1969:1 to 2011:2 for France and from 1971:1 to 2011:2 for UK, using quarterly data. We use unemployment rate and logarithm of real GDP (millions of national currency, chained volume estimates, national reference year and seasonally adjusted) multiplied by 100. We check if output and unemployment have a unit root in their series. To do so, we implement the standard ADF test, the ERS test (1996) and Zivot-Andrews test (1992). For ADF test and ERS test, the null hypothesis corresponds to a unit root process against a stationary process. In Zivot-Andrews test, the null hypothesis describes a unit root process against a break-stationary process where the break is endogenously calculated. Results are drawn in table 1 and 2. Our results provide convergent findings and show that we can reject the null hypothesis of a unit root process for each series in both countries. So, we can describe our macroeconomic series as a non-stationary (permanent component) and a stationary component (transitory). We implement our bivariate unobserved component model using Kalman filter. Preliminary estimates have shown that including a drift in permanent movement of unemployment was not significant, so it is not include in the present estimates. Maximum likelihood estimates of our bivariate unobserved component model are reported in Table 3 and 4 for France and United Kingdom. Figures 1 and 2 plots estimates of permanent components and transitory components for France; Figures 3 and 4 plots estimates of permanent components and transitory components for United Kingdom. For both countries, we can see in Figures 1 and 3 that the permanent component of output is clearly not a smooth trend. In fact, movements of real GDP are very close to movements of 5
permanent component of output. As the standard deviation of the permanent innovation (1,2934 for France and 1,4632 for United Kingdom) is greater than the standard deviation of transitory innovation (1,0701 for France and 0,9746 for United Kingdom) and the standard deviation of the first difference of the real GDP series (0,6056 for France and 0,9779 for United Kingdom). These results are in accordance with Morley, Nelson and Zivot (2003) where permanent component rather than transitory component accounts for most of variations in output, implying that fluctuations of real GDP are largely permanent. We also note that the ratio of standard deviation of permanent innovation to transitory innovations is greater than 1 and more important in United Kingdom (1,50) that in France (1,20). We plot the recessions (shaded areas on Figures) calculated using Bry-Boschan algorithm for quarterly data. We see that recessions are associated with a fall of the permanent component of output, indicating that recessions have long-lasting effects on real GDP. All these results are in line with real business cycle theory where movements in output are related to technology shocks; see for instance Prescott (1987). The transitory component of real GDP presents some interesting facts. Indeed, as shown by Figures 1 and 3, we observe a positive transitory component during recession; this is clearly different from traditional business cycle where recessions are associated with negative cyclical output. We find also, a result similar to Morley, Nelson and Zivot (2003) and Sinclair (2009) that permanent and transitory components of output are significantly negatively correlated (-0,97 in France and -0,82 in United Kingdom). This important finding suggests that the trend/cycle decomposition has to take into account the correlation between longrun growth and business cycle and cast doubt on papers that separate fluctuations from GDP growth, as well as models which treat business cycle as exclusively temporary (Hodrick- Prescott filter, band-pass filters, ). According to Morley, Nelson and Zivot (2003) and Stock and Watson (1988), the negative correlation between innovations of permanent and transitory components of real GDP implies that cycle represents the adjustment of output to permanent shocks which shift real GDP. For instance, in real business cycle theory, adjustment arises from real shocks which require more than one period for the construction of new capital. For unemployment, we can see in Figures 2 and 4 that the permanent component of unemployment is obviously similar to the path of unemployment in both countries. It is clear 6
that movements of unemployment reflect movements, for the most part, movements of the natural rate. We observe that standard deviation of permanent unemployment is twice larger in United Kingdom than in France. Conversely to real GDP, the standard deviation of the permanent innovation (0,4965 for France and 0,8649 for United Kingdom) is very close to the standard deviation of transitory innovation (0,5299 for France and 0,8620 for United Kingdom). It highlights the importance of cyclical unemployment in the variability of unemployment rate, indeed the persistence of cyclical unemployment measured by the sum of the two autoregressive parameters is found to be very high (0,7692 for France and 0,8108 for UK) relatively to cyclical output (0,6850 for France and 0,7703 for UK) and compared to results of Sinclair (2009) for United States (0,5221 for cyclical unemployment and 0,4429 for cyclical output). So, transitory component of unemployment appears more persistent than transitory component of real GDP. It suggests that adjustment of permanent shocks to their new steady-state values seems slower for unemployment than for real GDP. The difference with GDP also can be seen with the ratio of standard deviation of permanent innovation to that of transitory innovations. This ratio is close to unity for United Kingdom and below for France. Correlation between permanent and transitory component of unemployment rate could help to discriminate among alternative labor market theories. For instance, the hysteresis phenomenon introduced by Blanchard and Summers (1986) arising from human capital depreciation or insiders-outsiders channels, where a positive shock on transitory unemployment becomes permanent on unemployment; implying a positive correlation between components of unemployment. In our model, as for permanent and transitory component of output, we find that unemployment trend and cycle are negatively correlated in both countries. This negative correlation points out that hysteresis does not seem to play an important role in unemployment fluctuations in France and United Kingdom. Negative correlation in components of unemployment could also mean that creative destruction accounts in the fluctuations of the natural rate, see Aghion and Howitt (1994). Using correlation provided by estimates of our model, we can provide Okun s coefficient for both countries. Before, we test the null hypothesis that the autoregressive parameters are the same for GDP and unemployment using a likelihood ratio test with two restrictions. With 7
a p-value of 0,54 for France and 0,20 for United Kingdom, we cannot reject this null hypothesis. We find a Okun s coefficient of -1,2 for France and -0,9 for United Kingdom. For France, it implies that an increase of 1% of transitory output is associated with a fall of 1,2% of transitory unemployment. These coefficients are below (in absolute values) estimates of Okun s law using more traditional filters. For instance, using Hodrick-Prescott and band-pass filter, we find an Okun coefficient of -1,7 for France and -1,4 for United Kingdom. Estimate of Okun s coefficient of permanent innovations provide coefficients larger than Okun s coefficients of transitory innovations. Indeed, we find an of -1.6 for France and -1.4 for United Kingdom, more in line with Okun s coefficients using more traditional detrending method. For France, it implies that an increase of 1% of permanent output is associated with a fall of 1,6% of permanent unemployment. For United Kingdom, this estimate (-1,4) is in line with previous findings on Okun s coefficient, see Attfield and Silverstone (1998) and Freeman (2001). Overall, we find that Okun s coefficients of permanents movements are larger (in absolute values) than Okun s coefficients for transitory movements. This negative correlation between permanents components of output and unemployment enhance theories which highlight the negative impact of productivity or TFP growth on unemployment as in Pissarides (2000) and Pissarides and Vallanti (2007). In a recent paper, Perron and Wada (2009) challenge the results found by Morley, Nelson and Zivot (2003) about the negative correlation between transitory and permanents movements of US output. Perron and Wada (2009) show that including a dummy break in the trend output function, we find a transitory component more in line with NBER business cycle chronology and the negative correlation between trend and cycle disappears. Previous studies, Sinclair (2009), Sinclair and Mitra (2012) and Basistha (2007), also include a break in trend function of output, so this issue is important. Before, we check if there is a structural break in GDP growth and unemployment variations implementing Bai and Perron (1998, 2003) procedure. Results of Bai-Perron procedure for output growth and unemployment variations in the case of France are drawn in table 6 (for UK, no significant break was found for real GDP and unemployment rate). For GDP growth the tests are all significant at the 5% level for k between 1 and 5 and for unemployment variations for k between 1 and 2. We can conclude that at least one 8
break is present in our series. The sequential procedure, the BIC and the modified Schwarz criterion (LWZ) select one significant break. For GDP growth, the break found is 1979:2 and for unemployment variations, the break found is 1994:2. We include a dummy break in the drift of the permanent component of output and unemployment. Results of the model with break are drawn in table 7. It appears that the dummies associated with break are clearly significant. For output growth, the drift is estimated to 0,9438 before 1979 and 0,4633 after, which corresponds to a real GDP growth of 3,77% and 1,85% respectively. This evolution seems to correspond to the slowdown of productivity growth observed in industrialized countries during seventies. For unemployment rate, we find that dummy associated to the break is significant. Indeed, the drift in permanent component of unemployment is estimated to 0.09 and is significant on the period 1969-1994; our model seems to capture the steadily trend in French unemployment rate during seventies and eighties. Conversely, after 1994, the drift is no significant, which means we can model unemployment with a random walk without drift on this period. Overall, include breaks in our permanent components does not alter the qualitative interpretation of our findings. Indeed, we still find a negative correlation between permanent and transitory component and permanent component account for a large part in fluctuations for both series. Using this model, we can also estimate Okun s coefficient for transitory and permanent movements (a likelihood ratio test indicates that we cannot reject the null hypothesis that the autoregressive coefficients are the same for output and unemployment at the 5% level). For transitory movements, the estimated coefficient is -1,5 and for permanent movements the coefficient found is -2.3. Our previous findings remain robust as we show that the Okun s coefficient for permanent innovations is larger (in absolute values) than for transitory innovations. As in Sinclair (2009), these findings suggest that most business cycle fluctuations of real GDP and unemployment are due to permanent component rather than transitory component. Section 4 Conclusion In this paper, we model Okun s law for France and United Kingdom inside a bivariate unobserved component model without impose restrictions within and between correlations of the two series. 9
We find that permanent movement account for a large part of movement of the series, especially for output; this results support real business cycle theory for fluctuations of output. Moreover, the innovations of the transitory component and permanent component negatively correlated for both series. This negative correlation suggests that transitory movements reflect the adjustment of variable to their new steady-state values. This adjustment seems slower for unemployment rate than for real GDP as we find strong persistence of the transitory movement of unemployment rate in both countries. Finally, Okun s coefficient for permanent movements is stronger than Okun s coefficients for transitory movements in both countries. ANNEX Table 1: Unit Root for France ADF ERS Zivot-Andrews constant trend constant trend constant breakpoint trend breakpoint output -3,31* -3,21 2,33-0,29-3,78 2005 :1-4,35 2005 :1 unemployment -1,58-1,39-0,04-1,32-3,61 1999 :2-3,88 1983 :4 Notes: (*) significant at the 5% level Table 2: Unit Root for United Kingdom ADF ERS Zivot-Andrews constant trend constant trend constant breakpoint trend breakpoint output -0,71-1,13 1,58-2,50-3,79 1979 :3-3,63 1979 :3 unemployment -2,24-2,23-1,15-1,91-4,06 1979 :2-4,39 1980 :1 Notes: (*) significant at the 5% level Table 6 Bai-Perron test for GDP growth in France 1 37,00* 2 22,36* 3 16,00* 4 12,57* 5 10,04* 1 0 2 1 37,00* 6,69 BIC = 1 LWZ = 1 3 2 3,00 4 3 2,23 5 4 0,40 10
Table 7 Bai-Perron test for unemployment variations in France 1 11,51* 2 10,18* 3 7,40 4 6,97 5 6,23 1 0 2 1 11,51* 8,40 BIC = 1 LWZ = 1 3 2 1.86 4 3 5.22 5 4 3.12 Notes: The maximums breaks is set to 5, the trimming percentage is 0,15, (*) means significance at the 5% level using Bai- Perron (1998) table critical values. Table 3 Estimates parameters for France France Parameter Estimate (standard error) LogLikelihood -38,6563 Standard Deviation of Permanent Component: GDP 1,2934 (0,2561) Standard Deviation of Transitory Component: GDP 1,0701 (0,2756) Standard Deviation of Permanent Component: Unemp. 0,4965 (0,1185) Standard Deviation of Transitory Component: Unemp. 0,5299 (0,0902) Correlation betwenn GDP Components -0,9723(0,0107) Correlation betwenn Unemp. Components -0,9096(0,0778) GDP First AR parameter 0,8795 (0,0682) GDP Second AR parameter -0,1945(0,0618) GDP Drift 0,6184 (0,0729) Unemp. First AR parameter 0,9374 (0,0886) Unemp. Second AR parameter -0,1682(0,0925) Correlation Permanent GDP/Permanent Unemp. -0,6308(0,1131) Correlation Transitory GDP/Transitory Unemp. -0,6331(0,1123) Correlation Permanent GDP/Transitory Unemp. 0,6345 (0,1123) Correlation Permanent Unemp./Transitory GDP 0,6237 (0,1227) 11
Table 4 Estimates parameters for United Kingdom United Kingdom Parameter Estimate (standard error) LogLikelihood -138,7099 Standard Deviation of Permanent Component: GDP 1,4632 (0,2257) Standard Deviation of Transitory Component: GDP 0,9746 (0,3834) Standard Deviation of Permanent Component: Unemp. 0,8649 (0,1266) Standard Deviation of Transitory Component: Unemp. 0,8620 (0,1291) Correlation betwenn GDP Components -0.8286(0,0771) Correlation betwenn Unemp. Components -0.9987(0,0103) GDP First AR parameter 1,0643 (0,1392) GDP Second AR parameter -0,2940(0,1313) GDP Drift 0,5807 (0,0625) Unemp. First AR parameter 0,8441 (0,0333) Unemp. Second AR parameter -0,0333(0.0229) Correlation Permanent GDP/Permanent Unemp. -0,8486(0,0494) Correlation Transitory GDP/Transitory Unemp. -0,6364(0,1487) Correlation Permanent GDP/Transitory Unemp. 0,8691 (0,0597) Correlation Permanent Unemp./Transitory GDP 0,5384 (0,1497) 12
Table 8 Estimates parameters with break for France France Parameter Estimate (standard error) LogLikelihood -24,3778 Standard Deviation of Permanent Component: GDP 1,0374(0,1459) Standard Deviation of Transitory Component: GDP 0,8693(0,1558) Standard Deviation of Permanent Component: Unemp. 0,4049(0,0676) Standard Deviation of Transitory Component: Unemp. 0,4611(0,0425) Correlation betwenn GDP Components -0,9729(0,0303) Correlation betwenn Unemp. Components -0,8467(0,0709) GDP First AR parameter 1,0062(0,2266) GDP Second AR parameter -0,3451(0,1441) GDP Drift (1969-1979) 0,9438(0,1130) GDP Drift (1979-2011) 0,4633(0,0876) Unemp. First AR parameter 1,0772(0,2151) Unemp. Second AR parameter -0,2953(0,1462) Unemployment drift (1969-1994) 0,0975(0,0384) Unemployment drift (1994-2011) -0,0368(0,0389) Correlation Permanent GDP/Permanent Unemp. -0.9099(0,0761) Correlation Transitory GDP/Transitory Unemp. -0,8093(0,0599) Correlation Permanent GDP/Transitory Unemp. 0.8094(0,0612) Correlation Permanent Unemp./Transitory GDP 0,9534(0,1729) 13
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Figure 1: Real GDP and estimated components in France 5 3 1-1 1320-3 1300 1280 1260 1240 1220 1200 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011 Real GDP Permanent component Transitory component Figure 2: Unemployment rate and estimated components in France 1 0-1 -2-3 12-4 10 8 6 4 2 0 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011 Unemployment rate Permanent component Transitory component 2 15
Figure 3: Real GDP and estimated components in United Kingdom 7.5 5.0 2.5 0.0 1300-2.5 1280 1260 1240 1220 1200 1180 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 Real GDP Permanent component Transitory component Figure 4: Unemployment rate and estimated components in United Kingdom 2 0-2 -4 12.5-6 10.0 7.5 5.0 2.5 0.0 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 Unemployment rate Permanent component Transitory component 16
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