Multilateral resistance to migration
Introduction
The responsiveness of the scale of migration flows to varying economic conditions — both in sending and recipient countries — and to changing immigration policies at destination represents a central topic in the international migration literature. While some recent contributions have provided econometric analysis of aggregate data where the identification strategy is consistent with the proposed underlying individual-level migration decision model (Beine et al., 2011, Grogger and Hanson, 2011, Ortega and Peri, 2013),1 others have relied on econometric specifications that have not been fully micro-founded (Clark et al., 2007, Mayda, 2010, McKenzie et al., 2012, Pedersen et al., 2008).
This methodological difference notwithstanding, these papers share a crucial feature, as Hanson (2010) observes that the literature is characterized by a long-standing tradition of “estimating bilateral migration flows as a function of characteristics in the source and destination countries only” (p. 4373). Still, would-be migrants sort themselves across alternative destinations, so that it is important to understand whether this econometric approach allows to control for the possible dependence of the migration rate between any pair of countries upon the time-varying attractiveness of other migrants' destinations. Hanson (2010) argues that “failing to control other migration opportunities could […] produce biased estimates” (p. 4375), and this issue resembles the one raised by Anderson and van Wincoop (2004) with respect to the estimation of the determinants of bilateral trade flows.
Trade between two countries does not depend on bilateral trade costs only, but rather on the relationship between these costs and the costs with the other trading partners; Anderson and van Wincoop (2004) refer to the attractiveness of trading with other partners as multilateral resistance to trade.2 Similarly, migration rates between a dyad represented by an origin and a destination country do not depend solely on the attractiveness of both, but also on how this relates to the opportunities to move to other destinations. Following the terminology introduced by Anderson and van Wincoop (2004), we refer to the influence exerted by the attractiveness of other destinations as multilateral resistance to migration.3
Why can multilateral resistance to migration introduce a bias in the estimates of the determinants of bilateral migration flows? Consider, for instance, the case of migration policies, which can be coordinated at a supranational level. An instance of such a policy coordination was represented by the visa waiver granted in 2001 by the European Council to the citizens of the countries which would have eventually joined the EU three years later. If one is interested in estimating, say, the impact of the change in the Spanish visa policy toward Polish citizens on the migration flows from Poland to Spain, a key analytical challenge is represented by the need to control for the influence exerted by the simultaneous policy changes implemented by other countries following the EC Regulation. These changes can increase the attractiveness of alternative European destinations for Polish would-be migrants, confounding the identification of the effect of interest.
This paper directly tackles this challenge, thus addressing the concern raised by Hanson (2010). First, it relates the stochastic properties of the underlying individual migration decision model to the need to control for multilateral resistance to migration when estimating the determinants of bilateral migration rates. Second, it shows which type of data usually employed in the literature suffices to obtain consistent estimates even when multilateral resistance to migration matters. Third, it applies the proposed econometric approach — which draws on Pesaran (2006) — to analyze the determinants of migration flows to Spain over 1997–2009 using high-frequency administrative data.
The paper presents a general random utility maximization (RUM) model that describes the migration decision problem that individuals face. The theoretical model shows that multilateral resistance to migration represents an issue for the analysis of aggregate data whenever the stochastic component of location-specific utility is such that the independence of irrelevant alternatives assumption fails.4 The derivation of the econometric specification from the RUM model reveals that multilateral resistance to migration, which is unobservable for the econometrician, gives rise to an endogeneity problem, as the regressors are correlated with the error term, which also exhibits serial and spatial correlation.
We show that the multilateral resistance to migration term entering the error of the equation that describes the determinants of aggregate migration rates on the basis of the RUM model can be expressed as the inner product of a vector of dyad-specific factor loadings and a vector of time-specific common effects. This entails that the structure of the error term coincides with the multifactor error model presented in Pesaran (2006). Pesaran (2006) proposed an estimator, the Common Correlated Effects (CCE) estimator, which allows to derive consistent estimates from panel data when the error follows this structure, i.e. it is serially and spatially correlated, and the regressors are endogenous.5 The CCE estimator requires to estimate a regression where the cross-sectional averages of the dependent and of all the independent variables are included as auxiliary regressors: consistency of the estimates follows from the fact that the multilateral resistance to migration term can be approximated by a dyad-specific linear combination of the cross-sectional averages (Pesaran, 2006).
The adoption of the CCE estimator allows us to address the challenge posed by multilateral resistance to migration using the same type of data that are traditionally employed in the literature. This approach is more general than the one proposed in Mayda (2010), who includes a weighted average of income per capita in the other destinations as a control for their time-varying attractiveness,6 and the one in Ortega and Peri (2013), which is valid only under a more restrictive specification of the underlying RUM model and which assumes that would-be migrants from different origin countries have identical preferences over the set of possible destinations. For instance, in our earlier example on migration from Poland to Spain, Ortega and Peri (2013) restrict the effect of a change in French migration policies on the Polish migration rate to Spain to be the same as the effect of a change in Greek migration policies, while the CCE estimator is much more flexible and it allows for a differentiated responsiveness to variations in the attractiveness of alternative destinations.
The proposed econometric approach is applied to the analysis of the determinants of bilateral migration rates to Spain between 1997 and 2009, when this country experienced an unprecedented boom in immigration. In fact, Spain recorded “the highest rate of growth of the foreign-born population over a short period observed in any OECD country since the Second World War” (OECD, 2010): the immigrant share went from 3% of the population in 1998 to 14% in 2009 (INE, 2010b).7 Migration data come from the Estadística de Variaciones Residenciales, EVR (INE, 2010a), an administrative dataset collected by the Instituto Nacional de Estadística. A key feature of the EVR is that it provides us with high-frequency data, which give to the dataset the longitudinal dimension that is required to be confident about the application of the CCE estimator (Pesaran, 2006).
The data from the EVR, which have been aggregated by quarter, have been combined with data from IMF (2010a) and World Bank (2010) on real GDP and population at origin for 61 countries,8 which represent 87% of the total flows to Spain over our period of analysis. Furthermore, we have compiled information about the various facets of Spanish immigration policies — such as bilateral visa waivers and agreements on the portability of pension rights — which have been shown to be relevant determinants of recent immigration to Spain (Bertoli et al., 2011). The quality of the data is thus notably higher than it is typical in the literature: it includes both legal and illegal migration, gross rather than net flows and a vast array of migration policy variables not usually available.9
Our results show that ignoring the multilateral resistance to migration term biases the estimation of the determinants of migration rates to Spain. In addition, the direction of the bias is the one we could expect. The effect of GDP at origin on migration rates to Spain is two thirds of that found in a specification that does not control for multilateral resistance to migration, although it is still negative and significant: a 1% drop in GDP per capita in a country increases its emigration rate to Spain by 3.1%. This bias is in the opposite direction of that found on the impact of migration policies. The only migration policy that is found to have a significant effect on migration rates to Spain is the adoption of a visa waiver. This effect only turns significant when multilateral resistance to migration is accounted for: establishing a visa waiver for a country multiplies its emigration rate to Spain by a factor of 4,10 while the estimated effect when multilateral resistance to migration is not controlled for is not significantly different from zero.
The paper is related to four strands of the literature. First, the papers that analyze the determinants of bilateral migration flows using panel data in a multi-origin multi-destination framework (Clark et al., 2007, Lewer and den Berg, 2008, Grogger and Hanson, 2011, Mayda, 2010, Ortega and Peri, 2013, Simpson and Sparber, 2012, Pedersen et al., 2008, Beine et al., 2011). Our theoretical model can also be applied to that framework but, in terms of the structure of the data, our paper is more closely related to Clark et al. (2007) and McKenzie et al. (2012), which estimate the determinants of bilateral flows to one destination, the United States, and from one origin, the Philippines, respectively.11
Second, we draw on the papers that have analyzed high-frequency migration data. Specifically: Hanson and Spilimbergo (1999) and Orrenius and Zavodny (2003), who analyze monthly migration flows from Mexico to the United States.
Third, the theoretical and empirical analysis presented here is related to the papers in the trade literature that discuss the relevance of multilateral resistance to trade (Anderson and van Wincoop, 2003, Anderson and van Wincoop, 2004, Baldwin, 2006).
Fourth, the paper is related to the contributions in the econometric literature that present estimators which allow to deal with violations on the classical assumption about the variance structure of the error term (Coakley et al., 2002, Driscoll and Kraay, 1998, Hoechle, 2007), and with the endogeneity of the regressors (Bai, 2009, Pesaran, 2006, Pesaran and Tosetti, 2011).12
The paper is structured as follows: Section 2 presents the RUM model that represents the individual migration decision problem; Section 3 analyzes the relationship between the stochastic properties of the RUM model and the need to control for multilateral resistance to migration in the econometric analysis through the CCE estimator proposed by Pesaran (2006). Section 4 presents the sources of the data used in the econometric analysis and the descriptive statistics. Section 5 discusses the estimates, and the empirical relevance of multilateral resistance to migration for the case that we have analyzed. Finally, Section 6 draws the main conclusions.
Section snippets
From individual decisions to aggregate rates
We present here a random utility maximization model that describes the location choice problem that would-be migrants face, which gives us the basis for deriving the determinants of bilateral aggregate migration rates. To keep it as general as possible, we do not specify the factors that influence location-specific utility.
Estimation strategy
The distribution of the stochastic term ϵijk in Eq. (1), which depends upon the specific assumptions about the GEV generating function, is closely related to the shape of the multilateral resistance to migration term rjkt in Eq. (7). This section analyzes which are the specifications about the GEV generating function in Eq. (2) justifying the alternative econometric approaches that have been adopted in the literature, and it then introduces the more general specification adopted in this paper,
Data and descriptive statistics
Our dataset has three main components: migration flows to Spain in the 1997–2009 period; migration policies in Spain during the same period; and quarterly real GDP series for the countries of origin of migrants to Spain. Here, we focus on providing the relevant descriptive statistics for the three series while we leave a more detailed description for the appendix.
Setup
The econometric analysis of the determinants of bilateral migration rates to Spain over 1997–2009 follows the steps entailed by the estimation strategy outlined in Section 3. We report here the equation to be estimated, derived on the basis of the RUM model presented in Section 2:
Consistently with the model, the dependent variable yjkt is represented by the log of the quarterly migration rate to Spain (the only k in our empirical application) for each of
Concluding remarks
The possible dependence of bilateral migration rates upon the time-varying attractiveness of other destinations represents a source of concern for the econometric analysis of the determinants of migration (Hanson, 2010), as it can generate an endogeneity problem due to the correlation between observed determinants of migration and the error term that stems from omitted variable bias. This paper has explored the relationship between the stochastic properties of the individual migration decision
Acknowledgements
The authors are grateful to Kaivan Munshi, Hillel Rapoport and to two anonymous referees for the comments they provided us with; they also wish to thank Herbert Brücker, Christian Dustmann, Francesc Ortega, Giovanni Peri, Kenneth Train and the participants at the Fourth World Bank-AFD Migration and Development Conference at Harvard, the Second TEMPO Conference on International Migration in Vienna, the CEPR Workshop in Turin and to seminar presentations at CERDI, EUI, IAE, the University of
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