Dynamics in the migration decision

As became clear in Section 1.3, network effects, proxied by including either the lagged migrant flow or the stock of migrants in the destination country, are usu-ally found to be very important in determining international migration flows and

location patterns. The coefficients on these dynamic factors are typically positive and statistically highly significant.

In fact, the first dynamic empirical studies of international migration, typically proxying for network effects using lagged migrant flows, found it to be the most significant variable in the regression (Gould, 1979). As outlined above, also more recent studies, such as Bertocchi and Strozzi (2008) and Mayda (2010), account for dynamics in the migration equation by adding lagged migrant flows to capture the family-friends effect. As opposed to early studies of international migration, the latter rely on bilateral panel data on migrant flows, which typically hold a small number of time series observations on a moderate number of cross-sections.

Estimating a dynamic model using such data is particularly challenging. The main problem is that the lagged dependent variable is by construction correlated with the individual effects. This renders the pooled ordinary least-squares (POLS) estimator, as used by Bertocchi and Strozzi (2008), biased and inconsistent. A within transformation wipes out the individual effects by taking deviations from individual sample means, but the resulting fixed effects estimator is biased and inconsistent for fixed T and N going to infinity (see Nickell, 1981). Given this inconsistency, the dynamic panel literature focuses mainly on a first-difference transformation to eliminate the individual effects while handling the remaining correlation with the (transformed) error term using instrumental variables (IV) and GMM estimators (see e.g. Mayda, 2010). Unfortunately, these GMM esti-mators are known to suffer from a weak instruments problem (see e.g. Bun and Windmeijer, 2010), which implies a small sample bias, large uncertainty around coefficient estimates and strong sensitivity to instruments choice. Alternatives to this approach are discussed in Chapter 2.

Nonetheless, as emphasized by (Dunlevy and Gemery, 1977), the network effect is better captured by the stock of all previous migrants, as opposed to those who

migrated only in the previous year. (Greenwood, 1969; Vedder and Gallaway, 1972; Levy and Wadycki, 1973) replaced the lagged dependent by the migrant stock and found positive and highly significant coefficients. As mentioned above, also more recent studies such as Hooghe et al. (2008), Lewer and Van den Berg (2008), Pedersen et al. (2008), Warin and Svaton (2008) and Vogler and Rotte (2000) follow this approach and predominantly find evidence for strong positive network effects.

It can however be argued that the migrant stock is the sum of all past migration flows less deaths and return migration, and that, consequently, it is itself a func-tion of all those factors that influenced the earlier migrafunc-tion flows (see Nelson, 1959; Greenwood, 1969; Laber, 1972). Therefore it will be correlated with all the explanatory variables and affect their parameter estimates. However, multi-collinearity is no reason to omit the migrant stock variable as this may result in a specification bias as well as in a loss of information regarding the network ef-fect. The interlinkage between migrant flows and stocks, however, forms another source of endogeneity which acquires an appropriate estimation method. As men-tioned above, the fixed effects estimator, used by e.g. Vogler and Rotte (2000), Hooghe et al. (2008) and Warin and Svaton (2008), is biased and inconsistent in the context of bilateral migration flows and stocks. Yet, the authors approximate the social network using lagged values of the migrant stock (at the beginning of the period or decade) and the first lag, respectively, in order to avoid endogeneity issues. The same procedure is followed in Lewer and Van den Berg (2008) and Pedersen et al. (2008), who turn to scaled OLS and a population averaged GEE procedure, respectively. Only the latter method is able to convincingly account for the dynamic panel bias but it requires that individual effects are uncorrelated with the explanatory variables, a strong assumption for which the authors do not test. Beine et al. (2011a) and Beine et al. (2011b), on the other hand, adopt an

IV approach through the use of a dummy variable for temporary guest-worker agreements and a variable capturing the unobserved diaspora in the 1960s as in-struments for the migrant stock.

A final point to raise concerns a longstanding discussion, dating back to e.g. Laber (1972) and Dunlevy and Gemery (1977), on whether these dynamic terms repre-sent network effects or rather capture a partial adjustment mechanism reflecting sluggishness in the response of migration to shifts in its underlying determinants.

The latter interpretation suggests a negative sign for the coefficient on the migrant stock to prevent migrant flows from being ever increasing in the future. This im-plies that migrant flows become smaller as we get closer to the equilibrium stock of migrants in the destination country. As such, network effects and the adjust-ment process cannot be separately identified from the parameter of migrant stocks.

Yet, in an attempt to disentangle the network effect from the partial adjustment mechanism, Dunlevy and Gemery (1977) argue that lagged migrant flows and mi-grant stocks should both be included as determinants. Only then it is possible to separately identify these two effects. If both are present, it is not possible to quantify the size of partial adjustment and network effects as their coefficients are a combination of both effects. Yet, even though nothing can be said about the size of these effects, it can be determined wether they are significantly different from zero. In Dunlevy and Gemery (1977) both appear significantly positive in the same regression, suggesting that two separate mechanisms are at work. This is not true in Fertig (2001) and Boeri et al. (2002) who find a negative impact of lagged migrant stocks, suggesting that they do not capture the network effects but rather decreasing returns to migration. Also the lagged migrant flow is found to be negatively significant in Fertig (2001), which is explained by the authors as an indication for German migration fluctuating around a stable level and as such pre-venting it from being ever increasing in the future. The positive impact of lagged

migrant flows in Boeri et al. (2002) is not discussed by the authors. Nonetheless, using a FE estimator and ML by iterated GLS, neither of these studies convinc-ingly correct for the dynamic panel bias distorting the coefficient for the dynamic variables.