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An analysis of Okun’s law for the Spanish provinces

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Abstract

The inverse relationship between unemployment and Gross Domestic Product (GDP), commonly known as Okun’s law, has been traditionally analysed in the economic literature. Its application to Spain is particularly interesting due to the sharp effect that economic shocks have on unemployment. The purpose of this study is to analyse the relationship between unemployment and economic growth for the Spanish provinces between 1985 and 2013, a period characterized by economic booms and recessions that had a great impact on unemployment. After testing the time series properties of provincial GDP and unemployment, we specify and estimate the difference version of Okun’s law using VAR and panel VAR techniques. The obtained results point out that Spain’s provinces show large differences in their unemployment sensitivity to economic variations. In particular, provinces that show less diversified industries, a more developed services sector and higher rates of labour participation suffer from higher variations in unemployment rates.

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Notes

  1. In appendix A, we highlight the differences in regional unemployment rates for Spain over the period. Maps show that unemployment rate differences among provinces are great and persistent.

  2. Detailed information about the required data sets, the components and the sources of information are compiled in the table B.1 in the Appendix B.

  3. Using CPI as a GDP deflator is a consequence of the lack of data on GDP deflation at the provincial level for part of the considered period. Hence provincial CPIs become the most suitable indicator to remove the effect of prices from the output. CPI is only available for provinces after 1993; we use the index for the provincial capitals for the previous years.

  4. The EPA provides non homogeneous panel datasets. Occupation and participation data are furnished according to different criteria based on the time the information was collected. In this case, we follow De la Fuente (2012), who makes the required adjustments to link the 1976 to 1995 and 1996 to 2004 occupation and participation series to the 2005 to 2013 series. Differences are mainly due to sample replacement and methodological changes, such as questionnaire modifications and adjustments in the definition of occupation and unemployment. Annual and state adjustments are distributed among the provinces considering their weighting in the state occupation and labour force participation data.

  5. Okun’s seminal work defined three different versions of the empirical relationship: the gap version, the specification in first differences and the dynamic one. In our analysis, we select the version in first differences. Literature has frequently resorted to the gap version, however it requires making strong assumptions on the unobserved macroeconomic variables (potential output and NAIRU). In addition, there is no agreement on the proper procedure to extract the trend component from the series and observe the effect of the cycle. These problems lead us to resort to the difference specification. Also, it is easier to reach stationary series when this version is used. Many analyses have resorted to this version. Among them, we find Mankiw (1994), Sogner and Stiassny (2002), Perman and Tavera (2005) Kosfeld and Dreger (2006), Knotek (2007), Gali et al. (2012) and Palombi et al. (2015a, 2015b).

  6. Before estimating we need to perform unit root tests to know whether the series and panels with which we work are stationary. Stationarity ensures that the obtained results are not spurious. We obtain the panels and most series are generated by I(1) processes. Appendix C shows further information about the methodology and results obtained.

  7. In order to apply PVAR technique, we resort to the Ryan Decker program, which is an update version of the Inessa Love original package, used in Love and Zicchino (2006), among others.

  8. AIC, HQIC and SBIC are repectively the Akaike, Hannan-Quinn and Schwarz information criteria.

  9. More lags have also been included in the specification and results are mostly the same.

  10. As we orthogonalize the variables as Sims (1980) proposes and, thus, we assume that a GDP shock affect unemployment in the same period, we should express the VAR in the following way: ∆\(u_{t}\,\)= c + λ∆\(y_{t}\) + α(L) ∆\(u_{t}\,\)+ β(L) ∆\(y_{t}\,\)+ \(v_{t}^{u}\); ∆ \(y_{t}\,\) = c + γ(L) ∆ \(y_{t}\,\) + η(L) ∆ \(u_{t}\,\) +. \(v_{t}^{u}\)

  11. We have estimated the gap version of Okun’s law using the Hodrick Prescott filter in order to check our specification. We aim to know if the results obtained are comparable with those obtained by the authors that consider the gap version. Appendix D shows that both versions provides us a similar province ordering regarding the value of the coefficient.

  12. The ordering of the variables in the VAR model could determine the results obtained. For this reason, and in order to check GDP growth causes unemployment rate variations for most provinces, we show the results obtained when we change the ordering of the variables in the Appendix E.

  13. Detailed information about the required data sets, the components and the sources of information are compiled in the table B.1 in the Appendix B.

  14. Urban, south and coast are dummy variables. Urban variable takes the value 1 if one of the ten biggest Spanish municipalities is located in the province; and 0 otherwise. South variable takes the value 1 for the provinces belonging to Andalusia, Extremadura, Castile-La Mancha and Canary Islands NUTS 2 regions; and 0 otherwise. These regions are located in the south of Spain and are those that have traditionally had higher rates of unemployment over the years. Finally, coast takes the value 1 if the province is located in the coast; and 0 otherwise.

  15. In addition to these variables, we consider wages, levels of education, trade unions and the employment share in the public sector as independent variables in the analysis. Results point out that these variables do not significantly affect unemployment sensitivity.

  16. Diversification index is expressed as: \(\mathrm{D}_{\mathrm{i}}=\, -\overset{\mathrm{J}}{\underset{\mathrm{j}=1}\sum }\left [\frac{\mathrm{X}_{\mathrm{ij}}}{\mathrm{X}_{\mathrm{i}}}\ln \left (\, \frac{\mathrm{X}_{\mathrm{ij}}}{\mathrm{X}_{\mathrm{i}}}\right )\right ]\), where \(\mathrm{X}_{\mathrm{ij}}\) represents the total employment in industry j and province i, whereas \(\mathrm{X}_{\mathrm{i}}\) is the total employment in province i.

  17. This number of lags is given by the following formula: int{4(T/100)2/9}.

  18. Other criteria are also used in order to obtain robust results. We consider the AIC criterion in the Levin Lin Chu and Im Pesaran Shin tests to select the lag length.

  19. Unit root tests of the variables in levels are available from the author on request.

  20. In Fig. E.1, for each province we show two graphs. The second graph is the graph that was represented in Fig. 5. Meanwhile, the first graph represents the Impulse Response Functions when variables are orthogonalized in the opposite direction. Thus, the first graph represent the effect that an economic growth shock has on unemployment rate variation after one period as it is indicated in the following equation: ∆ \(u_{t}\,\) = c + α(L) ∆ \(u_{t}\,\) + β(L) ∆ \(y_{t}\,\) + \(v_{t}^{u}\) ; ∆ \(y_{t}\,\) = c + λ∆ \(u_{t}\,\) + γ(L) ∆ \(y_{t}\,\) + η(L) ∆ \(u_{t}\,\) +. \(v_{t}^{u}\)

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Acknowledgements

I gratefully acknowledge helpful comments and suggestions from Raul Ramos and Vicente Royuela and three anonymous referees. I am also grateful to the participants of the 55th ERSA Congress (Lisbon, Portugal), XVIII Encuentro de Economía Aplicada (Alicante, Spain), V Time Series Workshop (Zaragoza, Spain), XL Reunión de Estudios Regionales (Zaragoza, Spain) and UB Economics Workshop (Barcelona, Spain). I acknowledge financial support from the Catalan government. All the remaining errors are mine.

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Authors and Affiliations

  1. AQR-IREA, Universitat de Barcelona, Barcelona, Spain

    Celia Melguizo

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Correspondence to Celia Melguizo.

Appendices

Appendix A

 

Fig. A.1
figure 6

Regional unemployment rates

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Appendix B

 

Table B.1 Sources of information
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Appendix C

3.1 Unit root testing methodology

Unit root testing allows us to know whether the processes generated are stationary and guarantees that the obtained results have economic sense. The Augmented Dickey-Fuller (ADF) and Philips-Perron (PP) tests are two of the most often applied. However, these traditional unit root tests do not consider the existence of structural breaks in the series. In the presence of structural breaks, the ADF and PP tests tend to have low power. Glynn et al. (2007) establish that structural breaks generate a bias in the ADF and PP tests that reduces their ability to reject a false unit root hypothesis. Perron (1989) was the first author to mention this, and he developed a procedure based on the ADF test that accounted for only one exogenous break. However, the Perron procedure is severely criticised by many economists. Among the critics, Christiano (1992) established that a pre-test analysis of the data could lead to bias in the unit root test. Zivot and Andrews (1992) proposed an endogenous determination of the break to reduce this bias. The Zivot-Andrews test allows for an endogenous structural break, which is registered the time period in which the ADF t-statistic is the minimum. Later versions, such as Perron and Vogelsang (1992), distinguish between additive and innovative outliers. Clemente et al. (1998) contemplate this break distinction, but go further to consider the existence of two breaks. In our study, we conduct the ADF and PP traditional tests, but we also apply the Zivot-Andrews and Clemente-Montañés-Reyes tests. Applying both sets of tests guarantees robustness in determining if the series are stationary. The lag length selection criterion differs for each test. For the ADF test, we check that for every province the lags are significant at the 90% level, and we chose the maximum number of significant lags. Meanwhile, we resort to the default number of Newey-West lags to calculate the standard error for the PP test.Footnote 17

After conducting individual unit root tests, panel-data unit root tests are applied to complete our analysis and obtain an overall view of the GDP and the unemployment rate of the Spanish provinces. The test results provide additional information and increase the value of unit root tests based on single series.

There is some literature about panel-data unit root tests and many attempts to remove cross-sectional dependence such as Pesaran (2007), Moon and Perron (2004), Maddala and Wu (1999), Levin-Lin (2002), and Im Pesaran Shin (2003). In our work we apply the Fisher-type, Levin Lin Chu, Im Pesaran Shin, and Hadri LM tests. In the first three tests, the null hypothesis considers the presence of unit roots in, at least, one of the series that form the panel and stationarity is assumed under the alternative hypothesis. The Hadri LM test considers in its null hypothesis that the series are generated by stationary processes.

In all the tests the lag lengthFootnote 18 is chosen according to Österholm (2004), who selects the maximum number of lags from individual tests. The maximum significant number of lags obtained in the individual ADF test is that which we use to determine the lag length for the panel unit root tests.

3.2 Results of unit root tests

We conduct two types of tests over the variables in levelsFootnote 19 and first differences in order to check that the series with which we are working are stationary. The traditional ADF and PP tests are applied, as are the Zivot-Andrews and Clemente-Montañés-Reyes tests, which consider structural breaks.

Results from the ADF and PP tests over variables in first differences are shown in Table C.1. In this table, we can observe the model that we consider, which is individually chosen, and the statistical value of the test, which allows us to accept or reject the null hypothesis. In light of the results, both tests lead us to reject the null hypothesis of the presence of unit roots for most provincial series in first differences at the conventional levels of significance. When we test the first differenced unemployment rate variable, we find that none of tests can reject the null hypothesis of the presence of unit roots for any province. In the case of GDP, in 18 of the 50 provinces both tests find problems in rejecting the null hypothesis. These exceptions may be due to the presence of structural breaks in the series that are not detected by the ADF and PP tests. We apply the Zivot-Andrews and Clemente-Montañés-Reyes tests in order to check whether the results remain the same or change when structural breaks are taken into account. Tables C.2 and C.3 show the results of the Zivot-Andrews and Clemente-Montañés-Reyes tests for the variables in the first differences. According to these results, the unemployment rate and GDP provincial series are mostly stationary in first differences. The same occurs for the national data series. After performing Clemente-Montañés-Reyes tests, we observe that both GDP and unemployment rate series can be considered stationay if we take into account an innovative break in 2006, This allows us to estimate the relationship between the variables considered, as seen in most of the literature.

We also carry out panel unit root tests. Results are shown in Table C.4. They confirm the results obtained for provincial series: unit root processes are found in the levels of the variables, but we cannot reject stationarity in first differences. In particular, the Levin Lin Chu, Im Pesaran Shin, and Fisher Type (conducted as an ADF test) tests reject the null hypothesis of unit root processes in the first differenced variables at a 99% confidence level. Meanwhile, the Hadri LM test cannot reject stationarity at any of the conventional confidence levels.

Table C.1 ADF and PP unit root tests over variables in FD
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Table C.2 Unit root tests over first differenced UR
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Table C.3 Unit root tests assuming structural breaks over FD GDP (NL)
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Table C.4 Panel unit root tests over first differenced variables
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Appendix D

As can be observed in Fig. D.1, Okun’s law gap version provides a similar ordering of provinces to the version in first differences and the VAR model estimated with the first differenced data. When we compare gap and first differences specifications, we can only observe sizable differences for the Álava (VI), Albacete (AB) and Huelva (H) provinces. Gap version estimates for Albacete and Huelva a higher coefficient. The opposite occurs for Álava. With respect to the differences between the gap specification results and the results of the IRF obtained using a VAR model, we can observe notable differences for the Albacete (AB) and Guadalajara (GU). For the first province, the coefficient estimated by Okun’s law gap version points out to a higher unemployment response than the results of IRFs whereas the opposite is obtained for Guadalajara.

Fig. D.1
figure 7

Comparing the estimation results to gap specification results

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Appendix E

We aim to know if the results obtained in Fig. 5 differ from those obtained when we consider that economic growth shocks affect unemployment rate variation with a lag. We compare these resultsFootnote 20 in Fig. E.1. The orthogonalization of variables in the opposite direction than previously assumed implies that shocks similarly affect unemployment rate variation for most provinces, but after one period. There are clear exceptions such as: Illes Balears, Málaga, Murcia and Valencia. They are unaffected by the GDP shocks when the order of the variables is changed. In these provinces, GDP shocks do not cause unemployment variations. We cannot observe a causality relationship in this way in the sense of Granger.

Fig. E.1
figure 8

Orthogonalizing the variables in two directions. Effects on unemployment rate changes when gdp growth shocks occurs

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Melguizo, C. An analysis of Okun’s law for the Spanish provinces. Rev Reg Res 37, 59–90 (2017). https://doi.org/10.1007/s10037-016-0110-7

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