Berger, Tino

Everaert, Gerdie

English

Ghent University Academic Bibliography

           FACULTEIT ECONOMIE EN BEDRIJFSKUNDE   TWEEKERKENSTRAAT 2 B-9000 GENT Tel. : 32 -  (0)9 – 264.34.61 Fax. : 32 -  (0)9 – 264.35.92    WORKING PAPER    Unemployment in the OECD since the 1960s. Do we really know?  Tino Berger Gerdie Everaert    November 2006  2006/425         D/2006/7012/70 Unemployment in the OECD since the 1960s.Do we really know? ∗Tino Berger† Gerdie Everaert‡November 17, 2006AbstractNickell, Nunziata and Ochel [Economic Journal, 2005] argue that unemployment ratescointegrate with labour market institutions in a panel of OECD countries. This paper repro-duces their Maddala-Wu panel cointegration test and shows that this test is only valid when(i) the number of countries tends to infinity and (ii) the underlying country-specific cointegra-tion tests are independent. Their finding of cointegration does not survive when small sampleproperties and heterogeneous cross-sectional dependencies are taken into account. This sug-gests that the estimated impact of institutions on unemployment is spurious.JEL Classification: C15, C33, E24Keywords: unemployment, panel cointegration, bootstrapping1 Replication resultsUsing a panel of yearly data for 20 OECD countries ranging from 1960 to 1995, Nickell, Nunziata,and Ochel (2005), NNO henceforth, estimate a reduced form unemployment equation includ-ing labour market institutions, interactions among these institutions and macroeconomic shocks.Using the Maddala and Wu (1999), MW henceforth, panel unit root test, calculated from Dickey-Fuller (DF) tests for the individual countries, NNO find that the unit root hypothesis cannot berejected for unemployment and for most of the explanatory variables. As such, NNO test forcointegration using the MW panel cointegration test. Their MW test statistic of 75.891 can bereplicated by (i) estimating a static version of the model2, i.e. dropping the lagged unemploymentrate, (ii) calculating p-values for the country-by-country Engle-Granger (EG) cointegration testsfrom the standard DF unit root distribution and (iii) combining these country-specific p-valuesinto the MW panel test statistic. Comparing this test statistic with the 5% critical value of 55.76∗We acknowledge financial support from the Interuniversity Attraction Poles Program - Belgian Science Policy,contract no. P5/21. The usual disclaimer applies†SHERPPA, Ghent University, Tino.Berger@UGent.be, www.sherppa.be‡SHERPPA, Ghent University, Gerdie.Everaert@UGent.be, www.sherppa.be1See NNO, Table 5, note (d).2As in NNO we estimate a fixed effects panel data model including time dummies and country-specific trendsusing iterated GLS allowing for heteroscedastic errors across countries and country-specific first order serial corre-lation.1from the χ240 distribution led NNO to conclude that there is a cointegrating relationship betweenunemployment and institutions.We challenge this result for two reasons. First, the MW panel cointegration test has a χ2distribution only if the underlying country-specific cointegration tests are independent. As bothunemployment rates and labour market institutions are highly correlated over countries3, thisassumption is clearly not satisfied. NNO acknowledge that there are cross-country dependenciesbut argue that the problem is solved by including time dummies in the empirical specification. Ashighlighted by MW these time dummies are only adequate in the presence of common time-specificeffects, i.e homogeneous correlation, but not in the presence of heterogeneous correlation. MWfurther argue that the latter is probably a more adequate description of cross-country dependenciesin most practical settings. Using Monte Carlo simulations Strauss and Yigit (2003) show that usingthe χ2 distribution under heterogeneous correlation induces a strong size bias in the MW panelunit root test. Second, calculating the p-values for the country-by-country EG cointegration testsfrom the standard DF unit root distribution relies on the assumption that the estimated residualscan be treated as ‘raw’ data. In a pure time series context this assumption is clearly violated asthe estimated residuals are obtained from minimising the sum of their squares. The appropriatedistributions for an EG cointegration test are provided by Mackinnon (1996).4 In a homogenouspanel data context, the estimated residuals can be treated as ‘raw’ data asymptotically, i.e. forthe number of countries tending to ∞, as in this case the impact of an individual country onthe estimated coefficients, and therefore on the estimated residuals, becomes infinitely small. Thepanel data set used in NNO only includes 20 (highly correlated) countries, though.5Taking stock, the distribution of both the country-by-country EG cointegration test and theMW panel cointegration test should be simulated taking into account the properties of the paneldata set, i.e. the number of countries included and the observed cross-country correlation. Forthis purpose, we set up a bootstrap procedure in the next section.2 A bootstrap approachUnder the null of no cointegration, we assume that the data generating process (DGP) for theunemployment rate Uit is given byUit = 100 (1 + exp(−U ′it))−1 , i = 1, . . . , N ; t = 3, . . . , T (1)U ′it = βU′it−1 + (1− β)U ′it−2 + µit, (2)3The cross-country correlation for changes in the unemployment rate for instance ranges from -0.35 to 0.84.4For 30 time series observations, the 5% critical value of a standard DF unit root test including a constant anda trend is -3.58. For a unit root test on the residuals estimated from a regression including a constant, a trend and20 explanatory variables (which is about the number of explanatory variables in NNO), this critical value drops to-10.03.5A small Monte Carlo experiment shows that for a panel of 20 countries including 30 time series observations, the5% critical value of a unit root test on the residuals estimated from a homogeneous regression including country-specific constants and trends, time dummies and 20 explanatory variables equals -3.89. Adding heterogeneouscross-country correlation of about the magnitude observed in unemployment rates, this critical value drops to -4.23.2where N is the number of countries, T is the number of time series observations and µit is a meanzero disturbance term, for which we assumeE[µtµ′t] = Ω ∀t, E[µtµ′s] = 0 ∀s 6= t, (3)where µt = [µ1t, . . . , µNt]′ and the variance-covariance matrix Ω is, besides positive definiteness,left unrestricted to allow for (i) heteroscedasticity across countries and (ii) heterogeneous cross-country correlation.Two aspects of this DGP are worth emphasising. First, although observed unemployment ratesare found to exhibit a unit root, we cannot simply generate Uit from a random walk process asthis would fail to preserve the restriction that it is bounded to lie between 0 and 100%. Thereforewe impose this restriction on the DGP by means of a logistic transformation, i.e. equation (1)translates the possible range [−∞,∞] for the unit root process U ′it into a range [0, 100] for Uit.6Second, NNO assume that the cross-sectional dependencies in the data are caused by commontime-specific effects, i.e. µit = λt + εit where εit is an idiosyncratic random component. In thiscase, λt can be eliminated by including time dummies. Following MW we allow for a more generalform of cross-sectional dependence, i.e. Ω is left unrestricted. In this case including time dummieswould not control for (all of) the cross-sectional correlation and hence the MW test would nothave a χ2 distribution.To obtain a bootstrap sample U˜it we first estimate equation (2) using OLS to obtain theestimate βˆ and the estimated (rescaled) residuals µˆit for i = 1, . . . , N and t = 3, . . . , T.7 Next,we resample µˆit to obtain µ˜it for t = 3, . . . , T , and generate U˜it from equations (1) and (2) withinitialisation U˜ ′i1 = U′i1 and U˜′i2 = U′i2. With respect to resampling µˆit we need to take into accountits structure as implied by equation (3). As resampling from the cross-sectional dimension wouldfail to preserve the cross-country dependencies and heteroscedasticity, we resample from the timeseries dimension only, keeping the cross-section index fixed, i.e. a bootstrap sample of residualsµ˜it is obtained asµ˜it = (µˆit3 , . . . , µˆitT )′, i = 1, . . . , N, , (4)where the (T − 2)× 1 vector of indices (t3, . . . , tT )′ is obtained by drawing with replacement fromthe index (3, . . . , T )′.The bootstrapped unemployment rates are then linked to the observed explanatory variablesby estimating the static version of the model, again using the same GLS estimator as in NNO.Next we perform a DF test on the country-specific residuals. After repeating this 10.000 timeswe obtain country-specific empirical distributions for the EG cointegration test. The panel av-erage 5% critical value of this empirical distribution is -4.61 (compared to the 5% critical valueof -3.58 from the standard DF distribution used by NNO). From the obtained country-specific6Using a MW panel unit root test, the null hypothesis that the transformed unemployment rate U ′it =−ln (100/Uit − 1) exhibits a unit root cannot be rejected (p-value = 0.90).7By applying the Baltagi and Li (1995) test the null of an AR(1) or MA(1) structure in the residuals can berejected at the 10% and 5% level respectively.3empirical distributions we can now calculate the p-values for the country-specific EG cointegra-tion test statistic obtained from the original data and calculate the MW panel cointegration teststatistic. Table 1 reports the result. The MW test statistic drops from 75.89 as in NNO to 47.91.For each of the bootstrapped samples we also calculate the MW panel cointegration test. Thisyields its distribution under the null hypothesis of no cointegration. The 5% critical value fromthis simulated distribution is 72.21. Comparing the simulated MW panel test statistic with thesimulated distribution of this test shows that in contrast to NNO’s finding unemployment doesnot cointegrate with labour market institutions. The same result is obtained when we relax theassumption that the AR coefficient in equation (2) is homogeneous (see bottom line Table 1).Table 1: Maddala-WU panel cointegration teststest statistic critical value p-valueNickell et al. (2005) 75.89 55.76 0.00Bootstrap approach (a) 47.91 72.21 0.21Bootstrap approach (b) 48.35 75.26 0.21Bootstrap approach (a) assumes β in equation (2) to be homogeneous overthe panel while (b) allows for country-specific βs.3 DiscussionThe finding of no panel cointegration neither implies that there is no relation between unem-ployment and labour market institutions nor that the results reported by NNO are invalid. First,economic theory relates the equilibrium rate of unemployment to a large variety of factors, some ofthem being difficult to measure or even unobservable, e.g. the reservation wage which is a functionof, among others, the value of leisure. By inducing a unit root component in the residuals, bothmissing non-stationary variables and measurement error in non-stationary variables turn an oth-erwise cointegrating relation into a spurious regression.8 Second, although panel cointegration isrejected this does not necessarily invalidate the results reported in NNO. Phillips and Moon (1999)show that for a spurious panel regression, different from a pure time series context, the pooledleast squares estimator is√N -consistent. The intuition behind this result is that the informationin independent cross-section data carries a stronger signal compared to the pure time series case.The data set used in NNO includes (highly) correlated data for only 20 countries, though. Solarge N asymptotics are probably a poor guide to the small sample properties. Therefore, we testin each of our bootstrap iterations over the static model whether the null of no relation betweenthe unemployment rate and the institution variables can be rejected at the 5% level of significanceusing a standard t-test. Although we set the nominal size equal to 5%, this hypothesis could not8Note that Engel (2000) has shown that in the presence of a permanent component in the residuals, standardcointegration tests have a large size bias, i.e. they find cointegration in too many cases. This suggests that thecritical values reported in Table 1 should be seen as upper bounds on the real critical values if there is a relationbetween unemployment and institutions but there is a permanent component left in the residuals. This furtherweakens the case of cointegration.4be rejected only in about 60% of the cases.ReferencesBaltagi, B. H., Li, Q., 1995. Testing ar(1) against ma(1) disturbances in an error componentmodel. Journal of Econometrics 68 (1), 133–151.Engel, C., 2000. Long-run ppp may not hold after all. Journal of International Economics 51 (2),243–273.Mackinnon, J. G., 1996. Numerical distribution functions for unit root and cointegration tests.Journal of Applied Econometrics 11 (6), 601–618.Maddala, G. S., Wu, S., 1999. A comparative study of unit root tests with panel data and a newsimple test. Oxford Bulletin of Economics and Statistics 61, 631–52.Nickell, S., Nunziata, L., Ochel, W., 2005. Unemployment in the oecd since the 1960s. what dowe know? Economic Journal 115 (500), 1–27.Phillips, P. C. B., Moon, H. R., 1999. Linear regression limit theory for nonstationary panel data.Econometrica 67 (5), 1057–1112.Strauss, J., Yigit, T., 2003. Shortfalls of panel unit root testing. Economics Letters 81 (3), 309–313.5

Unemployment in the OECD since the 1960s: do we really know?

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Unemployment in the OECD since the 1960s: do we really know?

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