estimating and forecasting european migration: methods...

Estimating and forecasting European migration:methods, problems and results1

Herbert Brücker and Boriss Siliverstovs

The specification of macro migration models and, hence, forecasts of migration poten-tials differ largely in the literature. Two main differences characterise macro migrationmodels: first, whether migration flows or stocks are used as the dependent variable,and, second, whether the heterogeneity in the migration behaviour across countries isconsidered. This paper addresses both issues empirically using German migration datafrom 18 European source countries in the period 1967Ð2001. It finds first that panelunit-root and cointegration tests reject the hypothesis that the variables of the flowmodel form a cointegrated set, while the hypothesis of cointegration is not rejected forthe stock model. The second finding is that standard fixed effects estimators dominatethe forecasting performance of both pooled OLS and heterogeneous estimators. Ap-plying the preferred fixed effects estimator, the migration potential from the Centraland Eastern European accession countries is estimated at 2.3Ð2.5 million persons forGermany, which implies a migration potential of 3.8Ð3.9 million persons for the EU-15. Finally, our estimates indicate that the migration potential in the EU-15 is alreadyexhausted and that the migration potential from Turkey is relatively small.

Contents

1 Introduction

2 Stock versus flow models

3 Comparing alternative estimationprocedures

4 Potential migration in an enlargedEU

5 Conclusion and policy-implica-tions

References

1 This paper benefited substantially from comments and suggestions by Michael Fertig, the editor ElmarHönekopp and two anonymous referees. The authors alone are however responsible for any remainingerrors.

ZAF 1/2006, S. 35Ð56 35

Estimating and forecasting European migration Herbert Brücker and Boriss Siliverstovs

1 Introduction

International migration is the “great absentee”(Faini et al. 1999) in the liberalisation of globalgoods and factor markets. While the barriers to in-ternational trade and capital mobility are alreadylargely removed, the opening of labour markets lagsfar behind. Moreover, most regional trade areas inthe world exclude labour markets from the removalof barriers to trade and factor movements. The Eu-ropean Union (EU) forms a notable exception inthis context. The free mobility of labour and otherpersons is defined as one of the four fundamentalfreedoms of the Common Market since the Treatyof Rome, which established the Community in 1957.The free movement started in a community of sixcountries with a joint population of 185 millions in1968, and has been step by step extended to the EU-15 and the three other members of the EuropeanEconomic Association (EEA) with a joint popula-tion of 380 million persons until the mid of the1990s. Another eight countries from Central andEastern Europe together with Cyprus and Maltahave become members of the EU in May 2004.Moreover, Bulgaria and Romania will probably jointhe Community in 2007. Altogether, the current ex-tension of the EU to the East will increase its popu-lation by some 102 million persons. However, transi-tional periods for the free movement of labour havebeen agreed which allow the individual MemberStates to dispense free labour mobility up to a maxi-mum period of seven years.

At least from a global perspective, the EU and theEEA formed a club of rich countries with relativehomogeneous per capita income levels in the past.Even in the case of the EU’s Southern enlargement,the per capita income of Greece, Portugal and Spainhave already converged to 65Ð70% of the averagelevel of the old Member States, when EU member-ship was granted (Maddison 1995). Consequently,less than one-third of the foreign population in theEU stems from other Member States. The mainsource of migrants are middle- and low incomecountries in the neighbouring regions of the EU, i.e.Northern Africa (Algeria, Morocco, Tunisia) andSouth-eastern Europe (Turkey and the Balkancountries).

The current enlargement round changes the pictureof the EU as a club of rich countries with homoge-neous income levels. The average GDP per capitameasured at purchasing power parities (PPP) of theeight accession countries from Central and EasternEurope which are admitted in this enlargementround is estimated by Eurostat (2003) at almost 50

36 ZAF 1/2006

per cent of that in the EU-15. If Bulgaria and Roma-nia join the EU, the average PPP-GDP per capita ofthe accession countries will decline to 45 per cent ofthe EU-15 level. At current exchange rates, the percapita GDP of the accession countries is, at 20 percent of that in the EU-15, even lower. This incomegap is larger than in any other of the previous en-largement rounds of the Community. Nevertheless,the accession countries from Central and EasternEurope are middle income countries from a globalperspective, and their income levels are twice ashigh as that of the remaining neighbours of the EUin Northern Africa, South-eastern Europe and theCommonwealth of Independent States (CIS) (seeFigure 1).

Given the unprecedented income differences be-tween the old and the new Member States of theEU, the uncertainty on the migration potential islarge. Starting with the seminal contribution of Lay-ard et al. (1992), numerous studies have tried to re-duce this uncertainty. Basically we can distinguishthree approaches to estimate the migration potentialfrom the East in the literature: representative sur-veys, extrapolations of South-North migration toEast-West migration, and forecasts based on econo-metric studies.

Representative surveys of the population are af-fected by three problems, which make it hard todraw quantitative inferences from them. First, it isdifficult to assess the extent to which the migrationintentions revealed in surveys later materialise intoactual movements of individuals or households. Sec-ond, surveys capture only the supply side and ignoredemand-side factors such as job opportunities andthe availability of housing. Third, surveys cannot ap-propriately capture the temporary dimension of mi-gration. Since only a minority of migrants stay ina foreign country permanently, a large number ofindividuals who will migrate at a certain point oftheir life may coexist with a small number of personswho are living abroad at a particular point in time.As a consequence, findings from surveys of the pop-ulation from the accession countries vary widely: in-dividuals intending to migrate range from 2Ð30%of the population, depending on the questionnairesemployed and the interpretation of the answers.2

Note that the correlation between migration inten-tions and actual migration is rather weak: for exam-ple, according to the German Socio-Economic Panel(GSOEP), more than 10% of the East German pop-

2 The careful studies by Fassmann/Hintermann (1997), IOM(1998), and Krieger (2003) obtain results at the lower end of thisspectrum. However, their results depend critically on the interpre-tation and weighting of the answers.

Herbert Brücker and Boriss Siliverstovs Estimating and forecasting European migration

ulation intended to migrate to Western Germany in1991, but only 5% of those who expressed the inten-tion to migrate had actually moved five years later.

Several studies have extrapolated the number ofSouth-North migrants in the 1960s and early 1970sto East-West migration. The income gap betweenthe Southern and the Northern European countriesin the 1960s was similar to the gap between the EU-15 and the accession countries today. Moreover, al-though the Southern European countries were notEU Members at that time, bilateral guestworkeragreements led to the de facto opening of NorthernEuropean labour markets and supported labour mi-gration until the first oil price shock of 1973. In gen-eral, these extrapolation studies find a long-run mi-gration potential of around 3% of the population(e.g. Layard et al. 1992). However, in stark contrastto the conditions for South-North migration in theearly 1960s and 1970s, the conditions for East-Westmigration today are affected by imbalances in boththe labour markets of the receiving and sendingcountries, incomplete recovery from the transitionshock, and close geographical proximity. Thus, ex-trapolation studies can provide no more than a hintat plausible orders of magnitude.

The majority of the forecasts of East-West migrationare based on econometric estimates, which usuallyexplain migration flows or stocks by variables such

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as the income differential, (un-)employment rates,and some institutional variables. Although moststudies employ the same set of explanatory varia-bles, the estimates of the parameters, and, hence, ofmigration potentials differ considerably in the litera-ture. Table 1 presents an overview3 on a number ofeconometric studies, which have tried to estimatethe migration potential from the East either forGermany or the EU-15.4 Since the forecasts refer todifferent Central and Eastern European countries,their findings have been expressed here as a per-centage of the population in the sending countries.

As can be seen in Table 1, the forecasts for the initialnet migration range from 0.02Ð0.64% of the popu-lation in the sending countries for Germany, whichcorresponds to a figure of 20,000Ð640,000 personsper annum. Analogously, the results for the long-runmigration stock range from 2.3Ð7.2% for Germany,or, if we assume that the present regional distribu-tion of migrants from the accession countries re-mains constant, from 3.8Ð12.0% for the EU-15.Given the policy relevance of the issue, it is worth-

3 This overview is far from complete, for surveys of the literaturesee Hönekopp (2000) and Straubhaar (2002).4 Note that the focus on Germany in these studies is not acciden-tal, since Germany absorbs around 60 % of the migrants from theCentral and Eastern European accession countries in the EU-15(Alvarez-Plata et al. 2003).


while to study the causes of these differences indepth.

Beyond different data sources, two main aspects dis-tinguishes the approaches in the econometric fore-casts: The first difference refers to the choice of thedependent variable. The major part of the studiesfollows the standard approach in the literature anduse migration flows as the dependent variable. Sinceforecasts of the additional labour supply through mi-gration can hardly be based on gross inflows, netmigration rates are usually employed. In contrast,another part of the studies use migration stocks asthe dependent variable. The choice of the depend-ent variable has important consequences for model-ling the dynamics of the migration process. The flowmodel implicitly assumes that migration will con-tinue until (expected) income levels converge to acertain threshold level, where the costs of migrationexceeds the benefits, while the stock model predictsthat net migration will eventually come to a halteven if large income differentials persist. The twomodels have different micro foundations. While theflow model relies on the concept of a representativeagent, the stock model is based on the assumptionthat preferences or human capital characteristics of

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individuals differ, such that the benefits and costs ofmigration are not equal across individuals.

The question whether stock or flow models are ade-quate to model macro migration functions is notpurely of academic interest. In the case of Southernenlargement, the introduction of free movement hasnot resulted in increasing migration stocks, althoughthe income of the Southern Member Statesamounted to no more than 65Ð70% of the EU aver-age at that time. In terms of the stock model, thisphenomenon can be explained by the fact that mi-gration stocks had already achieved their equilib-rium levels when the free movement was intro-duced.

The second important difference between the stud-ies refers to the estimation method. It is uncontro-versial that country-specific factors such as culture,language, history, geography, etc. affect the benefitsand costs of migration, and consequently, the migra-tion propensity across countries. These factors areonly partly observable and can therefore not be in-cluded completely in migration models. The hetero-geneity across countries is however only partiallyconsidered by the migration models presented in Ta-


ble 1 Ð if at all. A number of studies apply pooledOLS estimators, assuming that both the interceptand the slope parameters are homogenous acrosscountries. Another part of the studies use fixed ef-fects models, assuming that the intercept differsacross countries, while the slope parameters are ho-mogenous. For the out-of-country forecasts the fixedeffects are explained in an auxiliary regression bytime-invariant variables (e.g. Boeri/Brücker 2001;Fertig 2001). The quantitative results of these twoapproaches differ considerably. As an example,while Boeri/Brücker (2001), Brücker (2001) and thefollow-up study by Alvarez-Plata et al. (2003) fore-cast for Germany a long-run migration potential of2.3Ð2.5% of the population from the accessioncountries using a fixed effects estimator, Sinn et al.(2001) and Flaig (2001) estimate the long-run migra-tion potential at 7.2% on basis of a pooled OLSmodel.

It is well-known that pooled OLS models can yieldbiased and inconsistent results if omitted variablesare correlated with the explanatory variables (Balt-agi 1995). Fixed effects models avoid this estimationbias, but can still result in biased and inconsistentestimates if the slope parameters differ across coun-tries (Pesaran/Smith 1995). Moreover, with dynamicfixed effects models, simultaneous equation bias canaffect the estimation results. As an alternative, het-erogeneous estimators can be applied. These hetero-geneous estimators are based on individual regres-sions. For out-of-country forecasts, averages of theestimated parameters can be used. However, in sam-ples with a limited group and time dimension, heter-ogeneous estimators can yield unstable results, suchthat homogenous panel estimators might outper-form heterogeneous estimators (see e.g. Baltagiet al. 2000).

Thus, both the adequate specification of macro mi-gration models and the choice of the appropriateestimation procedure are controversial. Althoughsome of these issues have been already discussed(see e.g. Alecke et al. 2001; Fertig/Schmidt 2001;Straubhaar 2002), a systematic analysis of these is-sues is missing in the literature. Against this back-ground, this paper pursues three objectives:

� First, to examine the appropriate specification ofmacro migration models. More specifically, it istested whether the standard hypothesis of macromigration models that a long-run equilibrium rela-tionship between migration flows and the explan-atory variables emerges is supported by our data.Alternatively, we consider the hypothesis that along-run equilibrium relationship between migra-tion stocks and the explanatory variables exists.

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� Second, to analyse the quantitative consequencesof different estimation methods and to comparethe out-of-sample forecasting performance of dif-ferent estimators in order to derive criteria for thechoice of the adequate estimation procedure. Tothis end, we employ a wide range of estimatorswhich are discussed in the econometric literature.

� Third, to forecast the migration potential from theaccession countries on basis of the analysis car-ried-out before. The empirical analysis of the pa-per is based on migration to Germany from apanel of 18 European source countries in the pe-riod 1967Ð2001.

The remainder of the paper is organised as follows:Section 2 discusses alternative specifications of ma-cro migration models and tests whether the varia-bles of the flow or the stock model form a cointe-grated set. In Section 3 we estimate the cointegrat-ing vectors and the short run dynamics of the suc-ceeding stock model and test the out-of-sampleforecasting performance of a broad range of alterna-tive estimation procedures. On basis of the pre-ferred estimation procedure, Section 4 provides aprojection of the migration potential from the acces-sion countries to the EU. Finally, Section 5 con-cludes and discusses the policy implications of ourfindings.

2 Stock versus flow models

The standard macro migration model in the empiri-cal literature is based on the fundamental assump-tion of a representative agent, which compares util-ity differences between different locations. Conse-quently, these models presume that a long-run equi-librium relationship between migration flows andthe explanatory variables emerges. Following thisline of reasoning, the long-run migration functioncan be written in general form as

mit = �p

�p Xpft + �q

γq Xqit + δ msti, tÐ1 + μi + εit, (1)

where i = 1 . . . N and t = 1 . . . T are the (source)country and time indices, the subscript f denotes thedestination country, mit is an appropriate measurefor the aggregate gross or net migration rate (i.e. thenumber of migrants as a proportion of the popula-tion at the origin), Xpft and Xqit are vectors of ob-servable and time-varying characteristics in the re-ceiving country (index p) and the sending country(index q), respectively, and msti, tÐ1 is the lagged mi-gration stock. �p, γq, and δ are (vectors of) unknownparameters, μi captures all unobservable variables


which are specific to country i and time-invariant,and εit is the error term assumed to be iid with zeromean and constant variance. Some models in the lit-erature treat the country specific effects as randomor assume that the intercept term is uniform acrosscountries, which allows to include time-invariantvariables such as geographical or linguistic distance.Examples for this type of specification of the macromigration function in the literature are Fields(1978), Lundborg (1991), Fertig/Schmidt (2001) andPederson et al. (2004).

Most models in the empirical literature consider in-come variables and employment as the main explan-atory variables in the specification of the empiricalmodel, such that estimation equation has the follow-ing form (e.g. Hatton 1995):

mit = a1 ln(wft /wit) + a2 ln(wit) + a3 ln(eft)+ a4 ln(eit) + a5msti, tÐ1 + μi + εit, (2)

where wft and wit are the wage rates in the receivingand the source country, respectively, and ef and ei

are the employment rates in the receiving andsource country, respectively. In addition, many em-pirical models include deterministic time-trends,which should capture falling transport and commu-nication costs, and dummy variables for the institu-tional and political migration conditions.

This parsimonious specification of macro migrationmodels has a long tradition in the literature. Thechoice of explanatory variables is primarily basedon the classical contributions of Ravenstein (1889),Hicks (1932), Sjaastad (1962) and Harris and Todaro(1970). More specifically, the standard model is de-rived from the following assumptions: the utility ofindividuals is inter alia determined by expectationson income levels in the respective locations. Utilityis convex in the income differential, i.e. it is implic-itly assumed that other, non-pecuniary argumentsenter the utility function as well. Expectations onincome levels are conditioned by employment op-portunities. Individuals are risk averse, but uncer-tainty focuses on employment opportunities. As aconsequence, the model expects that the coefficientfor the employment variables is larger than that forthe income variables. Moreover, since employmentopportunities of migrants in host countries are be-low those from natives, it is expected that the coeffi-cient for the employment rate in the host country islarger than that in the source country. If capital mar-kets are not perfect, liquidity constraints affect mi-gration decisions. Consequently, for a given incomedifference between the host and the source country,the income level in the source country has a positiveimpact on migration (Faini/Venturini 1995; Faini/

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Daveri 1999). Finally, it is assumed that migrationnetworks alleviate the costs of adapting to an unfa-miliar environment, such that the costs from migra-tion are expected to decline with the stock of mi-grants already existing in the host country (Masseyet al. 1984; Massey/Espana 1987). Depending on theassumptions on the utility function, the functionalform of the macro-migration function is specifiedboth in semi-log (e.g. Hatton, 1995) and in double-log form (e.g. Lundborg 1991; Faini/Venturini 1995;Pederson et al. 2004).

There exist numerous micro-economic models of themigration decision in the literature which go far be-yond these considerations. Inter alia, these modelsanalyse the role of portfolio diversification of fami-lies in the absence of perfect capital markets (Stark1991), the role of relative deprivation (Stark 1984),and the impact of uncertainty about future wage andemployment conditions on the migration decision inthe presence of fixed migration costs (Burda 1995;Bauer 1995). However, few of these theoretical con-tributions have developed macro migration func-tions which can be applied empirically. Moreover,the estimation of more complex macro models ishindered by data limitations. As an example, timeseries information on variables such as the incomedistribution in the receiving and sending countries israrely available for longer time spans, which hindersthe macro analysis of e.g. the role of risk aversion,risk pooling in households and the relative depriva-tion in migration decisions.

Thus, although the choice of variables and the func-tional form of the model in equation (2) relies ona number of arbitrary assumptions, there exist fewalternatives to this macro migration function in theempirical literature. In this paper, however, one fun-damental assumption of the standard model is calledinto question: as shown above, the standard modelassumes that a log-linear relationship between mi-gration flows and the economic variables exists inthe long-run equilibrium. This implies that migra-tion ceases not before (expected) income levels be-tween the host and the source country, as deter-mined by the wage and the employment variableson the right hand side of equation (2), have con-verged to a certain threshold level, which is deter-mined by the costs of migration. In case of persistentdifferences in (expected) income levels, either thetotal population will eventually migrate or migrationwill not happen at all from the beginning. Note thatthis is a consequence of deriving macro migrationfunctions from the concept of a representativeagent, i.e. of assuming that individuals are homoge-neous.


Consider as an alternative that agents are heteroge-neous with respect to their preferences such that thecosts of living abroad differ across individuals. De-pending on their preferences, some individuals willstay at home, migrate temporarily and permanentlyat a given income differential. Moreover, the lengthof migration differs across temporary migrants. Thishas important consequences for the mechanics ofmigration stocks and flows: In the long-run, an equi-librium between migration stocks and the (ex-pected) income differential emerges, while the netmigration rate ceases to zero- at least if we assumethat population growth rates are equal in the homeand the migrant population. However, gross and re-turn migration remains a positive function of the in-come differential in the long-run equilibrium as aconsequence of temporary migration (Brücker/Schröder 2005).

Thus, under the assumption that individuals are het-erogeneous, an equilibrium between migrationstocks instead of migration flows and the differencein (expected) income levels in the respective loca-tions emerges. We conceive therefore here as an al-ternative to the standard model in equation (2), thefollowing specification for the long-run migrationfunction:

mstit = b1 ln(wft /wit) + b2 ln(wit) + b3 ln(eft)+ b4 ln(eit) + μi + εit. (3)

The estimation of the migration functions in (2) and(3) can be affected by spurious correlation effects, ifthe regressions involve non-stationary variables(Granger/Newbold 1974). The notable exception isthe situation when non-stationary dependent andexplanatory variables form a cointegration set (En-gle/Granger 1987). While it is a general agreementthat macro-economic variables such as income levelsand employment rates are integrated of the first or-der (i.e. I(1) variables), there still is limited evidenceon the time series properties of the migration flow-and corresponding migrant stock variables. Hatton(1995) provides in his analysis of the UK-US migra-tion episode between 1870 and 1913 evidence thatall variables in equation are I(1), but it is unclearwhether this is supported also by other data sets.Particularly puzzling is the fact that both the migra-tion flow and the migration stock variables are in-cluded in equation (2). Since migration flows can beconceived as (almost) the first difference of migra-tion stocks, they can hardly be I(1) variables if mi-gration stocks are supposed to be I(1) variables aswell. In contrast, under the theoretical considera-tions of the stock model, it can be expected that mi-gration stocks are I(1) variables, while the (net) mi-gration rate can be approximated by an I(0) process.This is tested below.

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Data

The empirical analysis is based on two samples. Thefirst sample comprises the migration data from 18European source countries to Germany from 1967to 2001.5 This sample covers all European sourcecountries with the exception of the countries of theformer COMECON and Albania, and the successorstates of the Yugoslavia. The first group of countrieshas been excluded since the ‘iron curtain’ has effect-ively restricted migration from there for most of thesample period, and the second group since the (civil)wars in the former Yugoslavia hinders a meaningfulanalysis of the economic forces which drive migra-tion. Germany has been chosen as the destinationcountry for two reasons. First, it is, at some 40% ofthe foreign residents in the EU, the largest destina-tion for migrants in the Community. Second, Ger-many is one of the few European countries whichreport both migration stock and flow data by coun-try of origin since 1967, which allows to apply thetools of modern time-series econometrics.

Both the migration stock and flow data are charac-terised by a visible structural break in 1973, i.e. theyear of the first oil-price shock. The bilateral guest-worker agreements between Germany and a num-ber of important source countries have been dis-pensed at the same year. However, the same struc-tural break is also observed for migration from theEU Member States which have not been affected bythe change in the institutional conditions. Since thisstructural break and changes in the institutional con-ditions can affect the unit-root and cointegrationtests, we perform the tests also on a second samplewhere the migration data is not affected by struc-tural breaks. This sample covers the period from1973 to 2001 and includes the founding members ofthe Community (Belgium, France, Itlay, Luxem-bourg, Netherlands), the three countries of the firstenlargement round (Denmark, Ireland, UK), andAustria and Switzerland in 1973. For the EU-mem-bers free movement was granted for the total sam-ple period, in case of the two German speakingcountries Austria and Switzerland bilateral agree-ments granted de facto free movement during thesample period.

The data on migration stocks and flows come fromthe Federal Statistical Office (‘Statistisches Bundes-amt’) in Germany. For the stock of migrants, the for-eign residents as reported by the Central Registerof Foreigners (‘Ausländerzentralregister’) are used

5 This sample comprises the 14 other members of the ‘old’ EU,Iceland, Norway, Switzerland and Turkey.


as a variable. This data is available from 1967 to2001. The stock of foreign residents is reported onDecember 31 (in some early years on September30). The number of foreign residents is slightly over-stated by the Central Register of Foreigners, sincereturn migration is not completely registered by themunicipalities. Consequently, the figures for thestock of foreign residents has been revised two timesin the wake of the population censuses in 1972 and1987. In the econometric analysis, dummy variablesare used in order to control for these breaks. More-over, after German unification, complete figures forWestern Germany are no longer available. Since thenumber of foreigners in Eastern Germany has beenfairly low, this does not affect the total figures much.The data on migration flows stem again from theCentral Register of Foreigners. The migration stockand flow variables are calculated as shares of thecorresponding home population.

Population figures are depicted from the World De-velopment Indicators 2003 (World Bank 2004). As aproxy for wages and other incomes, we employ theper capita GDP measured in purchasing power pari-ties. Before 1995, historical time-series from AngusMaddison (1995) are used, which have been extra-polated by the real growth rates of the PPP-GDPper capita from the Main Economic Indicators ofthe OECD (OECD 2003). The employment rate isdefined as one minus the unemployment rate. Un-employment rates have been taken again from theOECD Main Economic Indicators, and, if not avail-able, complemented by data from national statisticaloffices. The ILO definition has been used for all un-employment rates.

The error correction model which is estimated in thefollowing section includes three dummy variables forthe institutional conditions to migrate: (i) GUESTit,which has a value of one if a guestworker agreementbetween Germany and the respective country exists,and zero otherwise, (ii) FREEit, which is one, if mi-gration from this country is subject to free move-ment in the EU or the EEA, and zero otherwise,and (iii) DICTit, which is one, if the political systemof the respective country is characterised by dicta-torship and zero otherwise. Details on the institu-tional variables are available from the authors uponrequest.

The descriptive statistics for both samples is pre-sented in annex Table A1.

Testing for unit-roots and cointegration

In the first step of the empirical analysis, the varia-bles are tested for unit-roots for making inference

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on their order of integration. To this end, the panelunit-root test suggested by Im, Pesaran and Shin(2003) (IPS-test) is applied to the variables of thealternative migration models. Note that panel unitroot tests have a much higher power than the stand-ard Augmented Dickey Fuller (ADF)-test for indi-vidual time-series, particularly if the root is close toone. The auxiliary regressions include either an in-tercept only or an intercept together with a lineardeterministic time trend. Since trending behaviourcannot be ruled out a priori, we report for all varia-bles the results for both sets of deterministic compo-nents. The lag-length has been chosen by the modi-fied Schwarz criterion.

Table 2 reports the results of the IPS-test for thevariables of both the stock and the flow migrationmodel.6 As expected, the null hypothesis that themacroeconomic variables, i.e. the relative income ra-tio and the employment rates, follow I(1) processes,cannot be rejected.7 Moreover, the null of an I(1)process cannot be rejected for the migrant stock var-iable as well. In case of the net migration rate, it isstriking that the hypothesis of a unit root is rejectedat the 1%-significance level both in the ADF-re-gression with an intercept only and with an interceptand a deterministic trend. For both samples, i.e. forthe larger country sample which might be affectedby structural breaks, and for the smaller sample ofthe ten source countries for which free movementwas granted or de facto granted in the period 1973Ð2001, we obtain similar results.

Thus, the assumption of the standard migrationmodel that net migration flows and macroeconomicvariables such as GDP per capita levels or employ-ment rates are integrated of the same order is notsupported by the data set employed here. As a con-sequence, the flow model in equation (2) is unbal-anced as the net migration rate, which has beenfound to be an I(0) variable, is being explained bynon-stationary I(1) variables.

In order to reconcile the features of the data withthe theoretical considerations, the long-run migra-tion function of the migration stock model as speci-fied in equation (3) is employed for the further anal-ysis. According to the unit-root test results, all thevariables of equation (3) seem to be I(1), such that

6 The results of the ADF-tests for the individual time series areavailable from the authors upon request.7 For the German employment rate the individual ADF-test sta-tistic is in the regression with intercept Ð2.028 (at 2 lags), whichyields a p-value of 0.27, and in the regression with intercept anddeterministic trend Ð1.509 (without lags), which gives a p-valueof 0.80.


they can hypothetically form a cointegration set.Under the assumption of cointegration, the remain-der term εit is assumed to be an I(0) variable.

Table 3 presents two cointegration tests. The firsttest comprises the results of the two-step Engle-Granger cointegration procedure performed for thevariables of every country. The second test com-prises the panel cointegration group t-test statistic ofPedroni (1999) which aggregates the test statisticsobtained in the first place for every country in thepanel. In the larger sample, the null hypothesis of nocointegration is rejected in four out of the eighteenindividual cointegration regressions, and in thesmaller sample in three out of ten regressions. How-ever, these tests have rather low power, particularlyin case of the relatively short time-dimension of thedata at hand. The application of the more powerfulpanel cointegration test leads to the conclusion thatwe can reject the null hypothesis of no cointegrationat the 10% significance level in both samples.

Thus, the results of the cointegration tests suggestthat the country specific variables form a cointe-grated set, although the significance level is not veryhigh. This might be attributed to the rather short

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time dimension of the sample. Nevertheless, basedon the results of the unit-root and cointegrationtests, the model in equation (3) can be estimated inorder to make inference on the parameter values ofthe cointegrating relations.

3 Comparing alternative estimationprocedures

There are different procedures to estimate both thelong-run cointegration relationship and the short-run dynamics. If the variables form a cointegratedset, the cointegrating vector can be consistently esti-mated in a static regression, which completely omitsthe dynamics of the model (Engle/Granger 1987).Although the super-consistency result (Stock 1987)indicates that convergence is rather fast, the distri-bution of the least squares estimator and the associ-ated t-statistic is not normal in finite samples (seee.g. Patterson 2000, for details). Monte Carlo-evi-dence suggests that the estimation bias of the cointe-grating parameter is smaller in dynamic than instatic models (Banerjee et al. 1986). The empiricalequation is therefore here specified in form of an


error correction model (ECM), which allows to esti-mate both the long-term cointegrating vector andthe short-run dynamics. Note that the ECM is a veryflexible functional form and imposes few restrictionson the adjustment process.

Specifically, the estimation model has the form

Δmstit = �i1msti, tÐ1 + �i2 ln(wf /wi)tÐ1 + �i3 ln(wi )tÐ1

+ �i4 ln(ef)tÐ1 + �i5 ln(ei)tÐ1 + �i6Δ ln(wf /wi)t

+ �i7Δ ln(wi)t + �i8Δ ln(ef)t + �i9Δ ln(ei)t

+ �p

j=0δijΔmsti, tÐ1Ð j + ηi�zit + μi + εit, (4)

where zit is a vector of institutional variables, ηi is thecorresponding vector of coefficients, and Δ is the firstdifference operator. The parameter Ð�i1 determinesthe speed of adjustment and the long-term coeffi-

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cients of the cointegrating relationship are given by-�in /�i1, where n = 2, 3 . . .5. We consider three dummyvariables here which should capture different institu-tional conditions for migration: guestworker agree-ments between the source country and Germany, freemovement between the source country and Ger-many, and dictatorship in the source country. The firsttwo variables should capture reduced legal and ad-ministrative barriers for migration, the last variable apolitical ‘push’ factor in the source country. If possi-ble, time-invariant variables such as distance anddummy variables for geographical proximity andcommon language are considered as well.

A fundamental question for the estimation of themodel in equation (4) is whether the data should bepooled or not, i.e. whether the country specific pa-rameters are restricted to be uniform (�i = �, " �i).


Pooling can produce inconsistent and potentially mis-leading estimates of the parameter values unless theslope coefficients are identical (Pesaran/Smith 1995).However, there are few examples in the econometricliterature where the homogeneity assumption ofpooled models cannot be called into question. Sev-eral alternatives to the pooling of the data can be con-sidered. The regressions can be estimated individu-ally and the means of the estimated coefficients calcu-lated. This ‘Mean Group’ estimator produces consist-ent results if the group dimension of the panel tendsto infinity (Pesaran/Smith 1995) Ð which is howevernot the case in the sample at hand. Another alterna-tive is the ‘Pooled Mean Group’ estimator, whichconstrains the long-term coefficients to be the samebut allows for heterogeneous short-run coefficients.This estimator is an intermediate case Ð it imposesless restrictions on the adjustment process, but thesame restrictions on the long-term coefficients asstandard panel models. If the variables of the modelform a cointegrated set, similar assumptions on theconvergence of the estimated parameters as in indi-vidual regressions apply for the ‘Mean Group’ andthe ‘Pooled Mean Group’ estimators (Pesaran et al.1997).

Although the theoretical arguments against the ho-mogeneity assumption of pooled estimators are ap-pealing, there exists ample evidence that the forecast-ing performance of traditional panel estimators suchas fixed effects and pooled OLS estimators is superiorrelative to heterogeneous estimators in many empiri-cal applications (Baltagi et al. 2002; Baltagi et al.2000; Baltagi/Griffin 1997). The reason for this find-ing is that individual regressions can yield highly un-stable results if data sets have a limited time-dimen-sion.

Against this background, different pooled and heter-ogeneous estimation procedures are applied in thispaper. Six groups of estimators are considered:

� Pooled OLS (POLS) estimators;

� Fixed effects (FE) estimators;

� Random effects (RE) estimators;

� Generalized Methods of Moments (GMM) estima-tor;

� Pooled Mean Group (PMG) estimator;

� Mean Group (MG) estimator;

� Individual OLS (IOLS).

ZAF 1/2006 45

The POLS estimator, which imposes homogenous in-tercept and slope coefficients, restricts not only theslope parameters, but also the intercept to be uniformacross countries. It can be applied both with and with-out time-invariant variables, the first estimator is la-belled here POLS and the second POLS(TINV). Inthe first case individual (country) specific effects arecompletely ignored, in the latter case they are onlyconsidered to the extent they are captured by thetime-invariant variables of the model.

The second group of estimators treats country spe-cific effects as fixed. The fixed effect estimator isbased on the within transformation of the data thatwipes out all time invariant variables. We employthree types of the fixed effects estimator here: onesthat allow only for the homogenous disturbances(FE), for group-wise heteroscedasticity FE(HET)and both for group-wise heteroscedasticity and cross-sectional correlation FE(HET + COR) in the disturb-ances.

The third group of estimators treat the country-spe-cific effects as random and therefore also employsvariation between the cross-sections. Depending onthe way the optimal weights are attached to thewithin and between variation, one can distinguish be-tween the random effects estimator of Wallace/Hus-sein (1969), RE(WALHUS), and the iterative GLSestimator, RE(MLE), which is equivalent to the Max-imum Likelihood Estimator. Due to insufficient de-grees of freedom in the between dimension, thestandard Swamy/Arora (1972) random effects esti-mator is not employed here.

The GMM estimator addresses the fact that simulta-neous equation bias caused by the presence of thelagged dependent variable can affect the estimationof dynamic panel models (Nickell 1981, Kiviet 1995).Although the simultaneous equation bias disappearswith the time dimension of the panel, it can still berelevant for the size of our panel with slightly morethan thirty observations over time (Judson/Owen1999). Therefore the GMM-estimator by Arellano/Bover (1995) (GMM-SYS) is applied here, which ad-dresses the simultaneous bias by using the appropri-ate set of instruments. The Arellano/Bover (1995) es-timator employs both the first differences and levelsequations. Blundell/Bond (1998) report Monte Carloevidence and empirical results which indicate that theArellano/Bond (1995) system estimator achievessubstantial efficiency improvements relative to theArellano/Bond (1991) first difference estimator.However, gains from unbiased estimation throughGMM procedures might be offset by losses in effi-ciency if the time dimension is large relative to thetime dimension of the data set (Baltagi et al. 2000).


The last three groups represent the heterogeneous es-timators. As discussed before, the Pooled MeanGroup (PMG) estimator imposes the restriction ofcommon coefficients for the long-run coefficients butallows for heterogeneous short-run coefficients,while the Mean Group (MG) estimator is based onthe averages of the coefficients in individual regres-sions. The individual OLS estimator (IOLS) allowsfor heterogeneous intercepts, short- and long-run co-efficients.

The choice of estimators here reflects three purposes:First, pooled estimators that ignore individual spe-cific effects are confronted with pooled estimatorswhich include country specific effects. This has re-sulted in considerable differences in the long-run co-efficients and, hence, in the forecasts in the migrationliterature. Second, GMM estimators which addressthe problem of simultaneous equation bias are com-pared to traditional panel estimators which ignorethis problem. Third, estimators that allow for com-plete heterogeneity amongst the different cross-sec-tions are confronted with panel estimators which relyon the fundamental assumption of homogenous slopeparameters.

Table 4 presents the estimation results for the long-run semi-elasticities for the panel estimators. The es-timation results for the short-run semi-elasticities arereported in Annex Table A2, and the long-run semi-elasticities of the individual OLS regressions in An-nex Table A3.8 Before discussing the estimation re-

8 The estimation results for the short-run semi-elasticities of theindividual OLS regressions are available from the authors uponrequest.

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sults for every group of estimators, it is worthwhilesummarising the general observations:

First, the coefficients of the lagged migration stockfull-fill the conditions for dynamic stability for allpanel and all individual OLS estimates with the ex-ception of Ireland.

Second, for a number of the estimators (POLS,POLS-TINV, RE(WALHUS)) the coefficient for thelagged migration stock variable is very close to zero,implying a very high degree of persistence of the un-derlying time series. This fact also results in extremelyhigh values of the long-run coefficient estimates Ðtheir values are around ten-times as high as those ofthe fixed-effects estimates. This corresponds to theextremely high estimates which are obtained by fore-casts of the migration potential from Central andEastern Europe based on pooled OLS estimators.

Third, the estimated coefficients for the foreign-to-home wage ratio, wf /wi, the home wage, wi, and theGerman employment rate, ef , have the expected posi-tive sign and appear significant for almost all paneldata estimators. However, for the home employmentvariable, eh, the coefficient has in some regressions anunexpected positive sign and appears frequently in-significant.

Fourth, the individual OLS regressions yield very het-erogeneous coefficient estimates. Consequently, thecoefficients of the Mean Group estimator appear in-significant for all variables except the lagged migra-tion stock.


Finally, among the institutional variables guest-worker recruitment and dictatorship have the ex-pected signs and appear significant in most panel re-gressions. However, the coefficient of the free move-ment dummy is frequently insignificant and hassometimes an unexpected sign. In principle, the im-pact of guestworker recruitment agreements appearsto be much larger than the impact of the free move-ment with the EU.

The first group of estimators include the pooled OLSwith and without the time invariant variables. Sincethese estimators ignore country-specific effects(apart from those captured by the time-invariant var-iables), the results are certainly biased if the country-specific effects are correlated with the explanatoryvariables. Note that a correlation between the laggeddependent variable and country specific effects canexplain why the coefficient of the lagged dependentvariable tends to zero (see e.g. Baltagi et al. 2000).

The second group comprises the fixed effects estima-tors: FE, FE(HET), and FE(HET + COR). As the re-gression diagnostics demonstrates, a standard F-testclearly rejects the null hypothesis of a uniform inter-cept at the 1%-significance level. Moreover, theLikelihood Ratio test results indicate that both,group-wise heteroscedasticity and cross-sectionalcorrelation in the disturbances is present in the sam-ple. As seen, the estimates based on the within trans-formation yield much higher negative values for thelagged migration stock indicating a lower persistenceover time and faster speed of adjustment to the long-run equilibrium.

The random effects estimators yield mixed results.On the one hand, the RE(WALHUS) estimates arevery close to those of the pooled OLS estimators. Thiscan be explained by the fact that the optimal weight-ing for the RE(WALHUS) is based on the OLS resid-uals (see Doornik et al. 2002). On the other hand, theRE(MLE) estimates are similar to those of the fixedeffects. This can be traced back to the fact that the im-portance of the within variation in the GLS optimalweighting scheme increases with the growing time di-mension (see Baltagi 1995).

The GMM-estimator yields similar results for thelagged migration stock as the fixed effects estimators,but much higher values for the coefficients of the ex-planatory variables such as the wage ratio. The resultsof the PMG-estimator, which imposes the same re-striction on the long-run coefficients as the panel esti-mators, but allows the parameters of the short-run variables to differ across countries, yields resultswhich are very similar to the fixed effects estimates.

ZAF 1/2006 47

Finally, the individual OLS regressions produce onaverage much larger coefficients for the lagged mi-gration stock variable relative to the panel-estima-tors, as expected by econometric theory. The MG esti-mator yields therefore an estimate for the parameterof the lagged migration stock of Ð0.255, which is thelargest among the estimators considered. However,the results for the explanatory variables are very het-erogeneous and in most cases insignificant. Given therather small time dimension of the sample, the regres-sion results are highly unstable.

Forecasting performance

For evaluation of the out-of-sample forecasting per-formance of the different models, the Root MeanSquared Forecast Error (RMSFE) is calculated in Ta-ble 5. The out-of-sample forecasting performance iscompared for two time periods: the fifth and the tenthyear ahead. For this purpose the estimated coefficientvalues on the samples 1969Ð1996, and 1969Ð1991, re-spectively, have been employed.

The ranking of the estimators based on both meas-ures of the forecast accuracy varies slightly with theforecasting horizon. The fixed effects estimatorsdominates in both cases all other estimators, but theFE(HET + COR) is replaced on the first place by theFE(HET) estimator in the longer forecasting period.The RE(MLE) estimator, which places a high weighton the within variation in the data and yields there-fore results which are close to the fixed effects estima-tors, performs relatively well in the shorter forecast-ing period, but the forecasting accuracy declines sub-stantially in the longer forecasting period. The otherrandom effects estimator, the RE(WALHUS) esti-mator, which addresses a much higher weight on thebetween variation, performs poorly in both time hori-zons. The PMG estimator, which yields similar esti-mates of the long-run coefficients as the fixed effectsestimators, has a mediocre performance in both timeperiods, with a forecasting error which is twice ashigh as that of the fixed effects estimators. TheGMM(SYS) estimator performs similar as the PMGestimator, indicating that the gains from unbiased es-timation do not offset the losses in efficiency for thedata set employed here. The pooled OLS estimators,which are popular in the literature, perform with aforecasting error which is around three time higherthan that of the fixed effects estimators at the lowerend of the estimators. Interestingly enough, the indi-vidual OLS estimator, performs poorly in the 5-yeartime period but improves the forecasting accuracy inthe 10-year time period substantially.

Nevertheless, the forecasting error is still substan-tially higher than that of the fixed effects estimators.


Finally, the mean group estimator performs ex-tremely poorly, which can be traced back to the factthat the results from the individual regressions arevery heterogeneous and unstable.

These results are comparable to those of a number ofstudies including Baltagi/Griffin (1997), Baltagi et al.(2000) and Baltagi et al. (2002), where homogenousestimators that allow for individual specific effects(e.g. fixed effects estimators) outperform heteroge-neous estimators such as individual OLS and MeanGroup estimators. This can be explained by the factthat in cases where the results of individual estimatesare relatively unstable over time and groups (i.e.countries) standard panel estimators tend to domi-nate individual estimators.

4 Potential migration in an enlargedEU

In this section we examine the migration potentialboth for countries within the sample as well as out ofthe sample, i.e. the accession countries from Centraland Eastern Europe. Within sample, the long-run co-efficients of the regressions allow to calculate thelong-run migration potential for the countries consid-ered by the estimates. The countries included in thesample comprise the members of the EEA, for whichthe free movement of labour is already granted, andTurkey.

48 ZAF 1/2006

Table 6 reports the long-run migration potential aspredicted by the different estimators for the countrieswithin sample, based on the values for the explana-tory variables in the last year of the estimation period(2001). The fixed effects estimators, which haveproved to have the best forecasting performance, sug-gest that actual migration stocks have achieved al-ready their long-run values in case of most sourcecountries.

Even in the case of Turkey, most estimators predictthat the actual migration stock is at currently 2.85 percent of the home population already relatively closeto its long-run equilibrium level. The main exceptionsare the individual OLS and the GMM estimators,which predict a long-run migration potential of 4.5and 3.85 per cent of the home population, respec-tively. However, the actual migration potential ishard to predict, since all these estimates reflect thecurrent legal and administrative restrictions to immi-gration from Turkey. A reliable estimate of the long-run migration potential for Turkey under the condi-tions of free movement is hard to obtain from our es-timates. The free movement dummy is identified onlyby the integration of relatively rich countries into theEU. As a consequence, very low coefficients havebeen obtained for the free movement dummy in allregressions. This might be traced back to the fact thatmigration stocks of the countries in the sample havebeen already very close to their equilibrium levelswhen free movement was granted, such that the liber-alisation has not much affected migration behaviour.


Thus, without a major change in the institutional mi-gration conditions, the migration potential from theEuropean source countries seem to be already largelyexhausted for Germany according to our estimates.Eastern Enlargement of the EU is such a major insti-tutional change. As discussed before, the Central andEastern European countries have not been includedin the sample due to the iron curtain, which effect-ively prevented emigration for most of the time pe-riod under consideration. Thus, on basis of our esti-mates, we have to rely on an out-of-country projec-tion. This involves further problems, especially incase of the fixed effects estimators. Fixed effects areby definition country-specific variables and coverboth observable and non-observable factors. We fol-low here the procedure by Fertig (2001) and Boeri/Brücker (2001) and explain the fixed effects by time-invariant variables. More specifically, we use distanceand distance squared, a dummy variable for geo-graphic proximity (ADJACENT), a dummy variablefor a location in the eastern part of Europe (EAST),and a dummy variable for common language as ex-planatory variables. The adjusted R2 statistics suggest

ZAF 1/2006 49

that almost 90 percent of the variance in the fixed ef-fects is explained by these variables (see Annex TableA4).

Moreover, the migration scenario is based on the fol-lowing assumptions for the explanatory variables: theper capita GDP in Germany grows at an annual rateof 2%; the per capita GDP of the accession countriesconverges to that of Germany and the EU-15 at anannual rate of 2%; the (un-)employment rates inGermany and the accession countries remain con-stant. Note that the convergence rate of 2% p.a. forthe per capita GDP corresponds to that found byBarro/Sala-i-Martin (1991, 1995) and in many otherstudies for the EU and other European market econ-omies. The growth rates of the accession countries fitpretty well into this picture since the end of the transi-tion recession.

Under these assumptions, the FE(HET+COR) esti-mator predicts an initial immigration of around225,000 persons from all ten accession countries fromCentral and Eastern Europe (the eight new Member


States and Bulgaria and Romania) if the free move-ment would have been hypothetically introduced forall countries in 2004. The long-run migration poten-tial is achieved at around 2.4 million persons around25 years later (Table 7). According to the FE(HET)estimator, which is not reported here, the initial im-migration would be at around 185,000 persons andthe long-run migration potential at around 2.2 millionpersons.

5 Conclusion and policy-implica-tions

Forecasts of the migration potential from Central andEastern Europe differ largely. In this paper, severalmethodological and empirical problems in estimatingmacro migrations models and forecasting migrationpotentials have been analysed. The methodologicalaspects of our analysis can be summarised as follows:first, our results suggest that the standard migrationmodel, which explains migration flows by income andemployment variables and (lagged) migration stocks,is at least in case of our data set not properly speci-fied, since the migration flow variable seem to be sta-tionary, while the explanatory variables seem to beI(1). As a consequence, the conditions for a long-runequilibrium relationship are violated. Instead ourdata set suggests that there seem to be cointegrationrelationship between migration stocks and the ex-planatory variables of the standard migration model.However, one caveat applies to our findings: we canreject the null hypothesis of no cointegration only atthe 10%-significance level. Probably, this can betraced back to the rather short time dimension of thepanel.

50 ZAF 1/2006

Second, by testing a large set of panel and heteroge-neous estimators, we find that the forecasting accu-racy of standard fixed effects estimators outperforms(i) pooled OLS estimators and random effects esti-mators, which are widely applied in the migrationcontext, (ii) GMM-system estimators, which try toavoid the simultaneous equation bias of dynamicpanel models with finite time dimension, (iii) hetero-geneous estimators, which relax by one way or an-other the fundamental homogeneity assumption ofpanel estimation procedures.

These technical findings have a number of policy con-sequences. First, the flow model suggests that migra-tion ceases not before (expected) income levels be-tween the host and the source country have con-verged to a certain threshold level, which is deter-mined by the costs of migration. In case of persistentdifferences in (expected) income levels, either the to-tal population will eventually migrate or migrationwill not happen at all from the beginning. In contrast,the stock model predicts that migration ceases whenthe benefits from migration equals its costs for themarginal migrant, such that a long-run equilibriumbetween migration stocks and the income variablesemerges. This helps to explain why the introductionof the free movement in case of the EU’s Southernenlargement has not involved any significant increasein migration: in this case, the equilibrium stock of mi-grants has been already achieved before the freemovement was introduced, such that introducing thefree movement had no effect.

Second, the comparison of different panel and heter-ogeneous estimators has some policy consequencesas well. The pooled OLS estimators implicitly assumethat all factors which have a persistent impact on mi-


gration, that is inter alia distance, language and cul-ture, are the same for all source countries. Statisticaltests clearly reject this assumption, and, not surpris-ingly, the forecasting performance of these estimatorsis weak. More surprising is our finding that the heter-ogeneous estimators are dominated by fixed effectsestimators, since it is reasonable to assume that slopeparameters differ between countries as well. How-ever, the individual regression results have turned outto be rather unstable. Thus, at least in our sample ofEuropean source countries, the restriction that theslope parameters are identical increases the forecast-ing accuracy. Note that similar results have been ob-tained also in other contexts.

These findings have implications for the scale of themigration potential from the accession countries: Ex-tremely high estimates of the migration potential,which predict on basis of the pooled OLS estimatora long-run migration potential for Germany alone of7.2% of the population in the source countries (Flaig2001; Sinn et al. 2001), can be laid to rest, since theforecasting performance of these estimators hasproved to be poor and the assumption of a commonintercept is clearly rejected by the specification tests.On basis of the fixed effects estimators, which havethe best forecasting performance in our sample, thelong-run migration stock from the accession coun-tries amounts to 2.2Ð2.4 million persons for Ger-many, which implies a net immigration of another 1.6to 1.8 million persons at a present population of600,000 from this region. The long-run migration po-tential will be realised in a period of around 20 years.

Moreover, our quantitative findings suggest that mi-gration stocks within the EU-15 are already at or veryclose to their equilibrium levels. This finding is con-firmed by the fact that international migration withinthe EU-15 is low. Thus, we do not have to expect thatmigration will accelerate in this area in the future.Even in the case of Turkey, fears of a mass-migrationwave seem to be ill-founded. Most estimators suggestthat the migration potential is already relatively closeto its equilibrium. The major exception is the individ-ual OLS estimator, which predicts that the long-runequilibrium stock amounts to 4.5% of the Turkishpopulation, while at present 2.8% of the Turkish pop-ulation reside in Germany.

Needless to say, all these estimates are based on anumber of artificial assumptions and can provide nomore than a hint to the actual magnitudes involved.The heterogeneity in the migration behaviour acrosscountries increases in particular the uncertainty onthe migration potential from countries which are notincluded in the estimation sample such as the acces-sion countries from Central and Eastern Europe.

ZAF 1/2006 51

Moreover, the different application of transitionalperiods across the EU members might result in thediversion of migration flows, which in turn mightyield a reduced migration potential when the transi-tional periods expire in Germany. Thus, all forecastsof future migration flows and stocks from the acces-sion countries have to be treated with great caution.

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