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On the estimation and forecasting of international migration: how relevant is heterogeneity across countries?

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Abstract

This paper performs a comparative analysis of estimation as well as of out-of-sample forecasting results of more than 20 estimators common in the panel data literature using the data on migration to Germany from 18 source countries in the period 1967–2001. Our results suggest that the choice of an estimation procedure has a substantial impact on the parameter estimates of the migration function. Out-of-sample forecasting results indicate the following: (1) the standard fixed effects estimators clearly outperforms the pooled OLS estimator, (2) both the fixed effects estimators and the hierarchical Bayes estimator exhibit the superior forecast performance, (3) the fixed effects estimators outperform GMM and other instrumental variables estimators, (4) forecasting performance of heterogenous estimators is mediocre in our data set.

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Acknowledgments

The authors wish to thank the editor Badi H. Baltagi, Paul Gregory, Konstantin A. Kholodilin, two anonymous referees as well as participants of the ‘Aarhus Econometrics’ seminar (Svinkløv, Denmark) for valuable comments and discussion of an earlier version of this paper. The authors are also indebted to Li Hongyi and A. Kamil Tahmiscioglu for providing the computer code for the shrinkage and the hierarchical Bayes estimators, respectively. The usual disclaimer applies.

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Correspondence to Herbert Brücker.

Appendix: Data Description

Appendix: Data Description

The sample used for the econometric analysis in this paper contains 18 source countries (Austria, Belgium, Denmark, Finland, France, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, United Kingdom). This sample covers the European source countries of migration to Germany almost completely, with the exception of the countries of the former COMECON and the (former) Yugoslavia. The COMECON countries have been excluded since the ‘iron curtain’ effectively prevented migration for the main period of analysis, and the former Yugoslavia has been excluded as well since the civil wars have heavily affected migration from there.

The dependent variable is the share of foreign citizens residing in Germany as a percentage of the home population. Foreign nationals are defined by their citizenship. Note that citizenship is granted on basis of the concept of ethnicity in Germany, such that the large majority of second-and third-generation migrants still possess foreign citizenship. Data on the foreign-born population are not available in the German statistics. The data on foreign residents stem from the Federal Statistical Office (Statistisches Bundesamt, Fachserie 1). Foreign residents have been reported in Germany since 1967 on an annual basis by the local municipalities, and have been counted by the central register of foreign nationals (Ausländerzentralregister) in Cologne since 1972. In general, the foreigner statistics in Germany tend to overreport the number of legal migrants slightly, since return migration is not completely recorded in the official figures.

In the sample period, we observe two statistical breaks: First, the transition of paper-based counting of foreign nationals by the local municipalities to computer-based counting by the central register of foreigners in 1972 produced a minor statistical break in case of some source countries (Statistisches Bundesamt, 1999, p. 5). The second break emerged after a revision of the foreigner statistics in the course of the population census of 1987, which reduced foreigner figures significantly for a period of three years (Statistisches Bundesamt,1989, p. 594). After three years, the statistics were based again on the non-revised figures of the central register of foreigners, however. In order to control for the first break, we included a dummy variable in the regressions, but this turned out to be insignificant. We thus decided to ignore this break. With respect to the second break, we recalculated the number of foreign residents on the basis of net migration figures for the three years affected by the revisions of the Federal Statistical Office.

The migration stock variable is normalized by the population of the home countries. Population figures are taken from the World Bank (2002). The dependent variable in the econometric analysis is the change in the migration stock as a percentage of the home population. By definition, this deviates from the net migration rate by the rate of natural population growth of the migrant population relative to that of the home population and the rate of naturalisations, i.e.:

$$\Delta mst_{t} = m_{t} + \frac{{n_{{ft}} - n_{{ht}} - \delta }}{{1 + n_{{ht}} }}mst_{{t - 1}} ,$$
(5)

where mst is defined as the ratio of the stock of residents to the home population, m as the ratio of net migration to the home population, n f as the rate of natural population growth in the migrant population, n h as the rate of natural population growth in the home population, δ the rate of naturalisations in the migrant population, and t the time index. Thus, the change in the migrant stock equals the net migration rate if the rate of natural population growth in the migrant population equals the sum of the rate of natural population growth in the home country and the rate of naturalisations. In our sample, the difference between the net migration rate and the change in migration stocks is moderate.

The explanatory variables in our model are per capita income and employment rates in Germany and the source countries. Consistent wage variables are not available for our country sample. Following the literature we thus use GDP per capita measured at purchasing power parity as an approximation for the income level. The per capita GDP at purchasing power parity (PPP-GDP) series is taken from Maddison (1995) for the period 1967–1994 and has been extrapolated with the real growth rate of the PPP-GDP per capita. The latter has been taken again from the OECD Main Economic Indicators and Historical Statistics and is complemented by national sources for countries not covered by the OECD series.

The employment rate in the econometric analysis is calculated as one minus the unemployment rate. The ILO-definition for the unemployment rates have been used; time series for the unemployment rates stem from the OECD and are complemented by national statistical sources.

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Brücker, H., Siliverstovs, B. On the estimation and forecasting of international migration: how relevant is heterogeneity across countries?. Empirical Economics 31, 735–754 (2006). https://doi.org/10.1007/s00181-005-0049-y

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