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.
Similar content being viewed by others
References
Alecke B, Huber P, Untiedt G (2001) What a difference a constant makes. How predictable are international migration flows? In: OECD (ed) Migration policies and EU-enlargement, the case of central and eastern Europe. OECD, Paris, pp 63–78
Alvarez-Plata P, Brücker H, Siliverstovs B (2003) Potential migration from central and eastern Europe into the EU-15-an update. Report for the European Commission, DG Employment and Social Affairs, Berlin: German Institute for Economic Research (DIW Berlin)
Anderson TW, Hsiao C (1982) Estimation of dynamic panel models with error components. J Am Stat Assoc 76:74–82
Arellano M, Bond SR (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev Econ Stud, 58:277–297
Arellano M, Bover O (1995) Another look at the instrumental-variable estimation of error-components models. J Econom 68:29–52
Baevre K, Ries C, Thonstad T (2001) Norwegian cohort emigration. J Popul Econ 14(3):473–489
Baltagi BH, Griffin JM (1997) Pooled estimators vs. their heterogeneous counterparts in the context of dynamic demand for gasoline. J Econom 77:303–327
Baltagi BH, Griffin JM, Xiong W (2000) To pool or not to pool: homogeneous versus heterogeneous estimators applied to cigarette demand. Rev Econ Stat 82(1):117–126
Baltagi BH, Bresson G, Pirotte A (2002) Comparison of forecast for homogeneous, heterogeneous and shrinkage estimators. Some empirical evidence for US electricity and natural-gas consumption. Econ Lett 76:375–382
Baltagi BH, Bresson G, Griffin JM, Pirotte A (2003a) Econometric analysis of panel data, 2nd edition. Wiley, Chichester
Baltagi BH, Bresson G, Griffin JM, Pirotte A (2003b) Homogeneous, heterogenous or shrinkage estimators? Some empirical evidence from French regional gasoline consumption. Empir Econ 28:795–811
Baltagi BH, Bresson G, Pirotte A (2004) Tobin q: forecast performance for hierarchical Bayes, shrinkage, heterogeneous and homogeneous panel data estimators. Empr Econ 29:107–113
Banerjee B, Kanbur SMR (1981) On the specification and estimation of macro rural–urban migration functions with an application to Indian data. Oxf Bull Econ Stat 43(1):7–29
Bauer T, Zimmermann KF (1999) Assessment of possible migration pressure and its labour market impact following EU enlargement to Central and Eastern Europe. Institute for the Study of Labor (IZA), Bonn
Boeri T, Brücker H et al (2001) The impact of eastern enlargement on employment and labour markets in the EU member states. Report for European Commission, DG Employment and Social Affairs, Brussels
Brücker H (2001) Die Folgen der Freizügigkeit für die OST-West-Migration. Schlussfolgerungen aus einer Zeitreihenanalyse der Migration nach Deutschland, 1967 bis 1998. Konjukturpolitik, 52(supplement):17–54
Brücker H, Schröder PJH (2005) International migration with heteregeneous agents: theory and evidence. Mimeo, DIW Berlin
Burda MC (1995) Migration and the option value of waiting. Econ Soc Rev 27(1):1–19
Doornik JA, Arellano M, Bond SR (2002) Panel data estimation using DPD for Ox. Manual, available online: http://www.nuff.ox.ac.uk//users//doornik
Faini R, Venturini A (1995) Migration and growth: the experience of Southern Europe. CEPR discussion paper No. 964
Flaig G (2001) Zur Abschätzung der Migrationspotentiale der Osteuropäischan EU-Beitrittsländer. Konjunkturpolitik, Supplement 52:55–76
Greene WH (2002) Econometric analysis, 5th edition. Prentice Hall
Harris J, Todaro M (1970) Migration, unemployment, and development: a two-sector analysis. Am Econ Rev 60:126–142
Hatton TJ (1995) A model of UK migration 1870–1913. Rev Econ Stat 77(3):407–415
Hicks J (1932) The theory of wages. McMillan, London
Hille H, Straubhaar T (2001) The impact of EU-enlargement on migration movements and economic integration: results of recent studies. In: OECD (ed) Migration policies and EU-enlargement, the case of Central and Eastern Europe. OECD, Paris, pp 79–100
Hsiao C, Pesaran MH, Tahmiscioglu AK (1999) Bayes estimation of short-run coefficients in dynamic panel data models. In: Hsiao C, Lahiri K, Lee L-F, Pesaran MH (eds) Analysis of panels and limited dependent variable models. Cambridge University Press, Cambridge, pp 268–296
Judson RA, Owen AK (1999) Estimating dynamic panel data models: a guide for macroeconomists. Econ Lett 65:9–15
Kiviet JF (1995) On bias, inconsistency and efficiency of some estimators in dynamic panel data models. J Econom 68:53–78
Layard R, Blanchard OJ, Dornbusch R, Krugman P (1992) East–West migration: the alternatives. MIT, Cambridge, MA
Maddala GS, Li Hongyi, Srivastava VK (2001) A comparative study of different shrinkage estimators for panel data models. Ann Econ Financ 2:1–30
Maddison A (1995) Monitoring the World Economy 1820–1992. OECD, Paris
Nickell S (1981) Biases in dynamic models with fixed effects. Econometrica 49:1417–1426
Pesaran HM, Smith R (1995) Estimating long-run relationships from dynamic heterogeneous panels. J Econom 68:79–113
Phillips PCB, Sul D (2004) Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence. Cowles Foundation Discussion Paper No. 1438
Robertson D, Symons J (1992) Some strange properties of panel data estimators. J Appl Econom 7:175–189
Sinn H-W, Flaig G, Werding M, Munz S, Düll N, Hoffmann H (2001) EU-Erweiterung und Arbeitskräftemigration. Wege zu einer schrittweisen Annäherung der Arbeitsmärkte. Ifo-Institut für Wirtschaftsforschung, München
Sjaastad L (1962) The costs and returns of human migration. J Polit Econ 70:80–93
Stark O (1991) The migration of labour. Basil Blackwell, Cambridge, MA
Stark O, Taylor JE (1991) Migration incentives, migration types: the role of relative deprivation. Econ J 101(408):1163–1178
Statistisches Bundesamt (1989) Fachserie 18. Statistisches Bundesamt, Wiesbaden
Statistisches Bundesamt (1999) Fachserie 18. Statistisches Bundesamt, Wiesbaden
Straubhaar T (2002) Ost-West Migrationspotenzial: Wie gross ist es? Jahrb Natl ökon Stat 222(1):21–42
Swamy PAVB, Arora SS (1972) The exact finite sample properties of the estimators of coefficients in the error component regression models. Econometrica, 40:261–275
Wallace TD, Hussain A (1969) The use of error components model in combining cross-section and time-series data. Econometrica 37:55–72
Windmeijer F (2000) Moment conditions for fixed effects count data models with endogeneous regressors. Economic Letters, 68:21–24
World Bank (2002) World Development Indicators. Worldbank, Washington D.C.
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.
Author information
Authors and Affiliations
Corresponding author
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.:
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.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00181-005-0049-y