A Panel VAR Approach for Internal Migration Modelling and Regional Labor Market Dynamics in Germany

Abstract

This chapter analyzes the causal linkages between regional labor market variables and internal migration flows among German states between 1991 and 2006. We adopt a Panel VAR approach to identify the feedback effects among the variables and analyse the dynamic properties of the system through impulse–response functions. We also use the model to track the evolution of the particular East–West migration since re-unification aiming to shed more light on the East German “empirical puzzle”, characterized by lower migration responses than expected from the regional labor market position relative to the West. Indeed, we get evidence for such a puzzle throughout the mid-1990s, which is likely to be caused by huge West–East income transfers, a fast exogenously driven wage convergence and the possibility of East–West commuting. However, we also observe an inversion of this relationship for later periods: That is, along with a second wave of East–West movements around 2001 net flows out of East Germany were much higher than expected after controlling for its weak labor market and macroeconomic performance. Since this second wave is also accompanied by a gradual fading out of economic distortions and a downward adjustment of expectations about the speed of East–West convergence in standards of living, this supports the view of ‘repressed’ migration flows for that period.

A shorter version of this chapter has been previously published as “Internal Migration, Regional Labour Market Dynamics and Implications for German East–West Disparities – Results from a Panel VAR”, in: Jahrbuch für Regionalwissenschaften/Review of Regional Research, Vol. 30, No. 2 (2010), pp. 159–189. We kindly acknowledge the permission of Springer to reprint the article in this monograph.

Jointly with Björn Alecke and Gerhard Untiedt. Björn Alecke, Gesellschaft für Finanz- und Regionalanalysen (GEFRA), e-mail: Alecke@gefra-muenster.de; Gerhard Untiedt, GEFRA & Technical University Clausthal, e-mail: Untiedt@gefra-muenster.de.

Appendices

Appendix A: Testing for Instrument Validity in the Migration Equation

The inclusion of valid instrumental variables (IV) in the regression model is of vital importance for consistency of the obtained results. A statistical tool to guide IV selection is the Sargan (1958)/Hansen (1982) overidentification test (also denoted as J-statistic). As pointed out by Bowsher (2002) and Roodman (2009), one has to carefully interpret Hansen’s J-statistic since it has shrinking power with increasing number of instruments. That is, numerous instruments can over fit the instrumented variables, failing to expunge their endogenous components and biasing coefficient estimates towards those from non-instrumented estimators. In a series of Monte Carlo simulations Bowsher (2002) shows that the J-statistic based on the full instrument set essentially never rejects the null when T becomes too large for a given value of N. The author proposes to reduce the number of lag length employed for estimation in order to improve the size properties of the test.

Alternatively, Roodman (2009) argues in favor of using ‘collapsed’ instruments, which has the potential advantage of retaining more information since no lags are dropped as instruments. This strategy is equivalent to imposing certain coefficient homogeneity assumptions on the IV set and thus makes the instrument count linear in T. The author further shows that for cases where the ‘no conditional heteroscedasticity’ (NCH) assumption holds, the simple Sargan (1958) statistic may be used as an appropriate indicator to check for IV consistency, which does not suffer does not suffer from the above problem since it does not depend on an estimate of the optimal weighting matrix in the two-step GMM approach. Nevertheless, the problem with the Sargan statistic is that the latter performs weak for non normal errors. Our solution to these shortcomings is to combine both test statistics in an IV downward testing approach from the full instrument set to an specification that satisfies both the Sargan as well as Hansen’s J-statistic.

Our resulting IV downward testing approach using the long-run migration equation as an example is shown in Table 2.5. In the first column of the table we apply the full set of available instruments according to (2.10) and (2.14). Among lagged net migration (nm _ij,t−1) as right hand side regressor we include regional differences in real wages ($\widetilde{wr}_{ij,t-1}$), unemployment rates ($\widetilde{ur}_{ij,t-1}$), labor productivity growth ($\Delta \widetilde{ylr}_{ij,t-1}$), labor participation ($\tilde{q}_{ij,t-1}$) and human capital ($\widetilde{hc}_{ij,t-1}$). We also control for the distortion in the migration pattern for Lower Saxony due to German resettlers by the inclusion of a dummy variable (D _NIE ).

Table 2.5 Downward testing approach for instrument validity in PVAR model

We see that the Sargan (1958) and Hansen (1982) overidentification tests yield clearly contrasting testing results: While Hansen’s J-statistic does not reject the null hypothesis of the joint validity of the included IV set, the Sargan statistic casts serious doubts on the consistency of the latter. As discussed above, the reason for the divergence in the testing results is the huge number of instruments employed for estimation (a total of 459), which lowers the power of the J-statistic. The huge number of potentially available instruments in the SYS-GMM approach is due to the exponential growth of instrumental variables with increasing time horizon T according to the standard moment condition in (2.10). In order to minimize this problem, in column 2 of Table 2.5 we therefore employ the collapsed IV set, which reduces the number of instruments to 90.

For this specification the Hansen J-statistic now clearly rejects the null of joint validity of the IV set and is thus in line with the Sargan (1958) statistic. This result underlines the point raised by Bowsher (2002) and Roodman (2009) that the J-statistic has no power with increasing number of instruments, while the Sargan test still has. Finally, based on the collapsed IV set we further reduce the number of instruments using a C-statistic based algorithm, which is able to subsequently identify those IV subsets with the highest test results (see Mitze 2009, for details). This gives us a model with a total of 20 instruments, which passes both the Sargan and Hansen J-stat. criteria as reported in Table 2.5.

The regression results show that the estimated parameter coefficients are qualitatively in line with the full IV set specification in column 1. Moreover, the downward tested model also shows to have the smallest RMSE and does not show any sign of heteroscedasticity in the residuals.¹⁷ We finally apply the same estimation strategy for the whole PVAR(1) system, which reduces the number of instruments to 222 (out of a maximum of 2382 in the full ‘uncollapsed’ IV case).

Appendix B: Impulse–Response Functions and In-Sample PVAR(1) Predictions for East–West Net Migration

Fig. 2.8

Impulse–responses for PVAR(1), $\widetilde{hc}_{ij,t}, \tilde {q}_{ij,t}, \Delta\widetilde{ylr}_{ij,t}, \widetilde{wr}_{ij,t}, \tilde {ur}_{ij,t}, nm_{ij,t}$]. Note: With nm _ij,t = lnmr _i, $\widetilde {ur}_{ij,t} =$ ldur _ij, $\widetilde{wr}_{ij,t} =$ ldwager _ij, $\Delta\widetilde{ylr}_{ij,t} =$ ldyrl _fd _ij, $\tilde{q}_{ij,t} =$ ldq _ij, $\widetilde{hc}_{ij,t} =$ ldhc6 _ij

Fig. 2.9

Actual and fitted net migration between East and West German state pairs. Note: For details about the computation see text. BW = Baden-Württemberg, BAY = Bavaria, BRE = Bremen, HH = Hamburg, HES = Hessen, NIE = Lower Saxony, NRW = North Rhine-Westphalia, RHP = Rhineland-Palatine, SAAR = Saarland, SH = Schleswig-Holstein