The formally equal representation of the structural migration gravity model and the structural trade gravity model allows me to borrow several insights from the trade gravity literature for a structural estimation of Equation (2.4). With a stochastic error term, Equation (2.4) can be written as
Mod= exp (lnLd+ lnNo−lnNw+ ln(1/δod)−ln Ωd−lnWo) +εod. (2.6) Multilateral resistance to migration terms, ln Ωd and lnWo, are accounted for in the estimation with origin and destination xed eects as do Orece (2015) and Figueiredo et al. (2016). Anderson and van Wincoop (2003) and Feenstra (2004) are usually credited for the inclusion of importer and exporter xed eects to capture multilateral resistance to trade. I follow Santos Silva and Tenreyro (2006) who show a bias from estimating a log-linearized gravity equation via OLS if data are heteroskedastic. Standard het-eroskedasticity tests reject the Null hypotheses of a constant variance of residuals after an estimation of a correctly specied gravity also for migration data. The argument for the bias from estimating a log-linearized gravity via OLS then holds true. Therefore, I estimate Equation (2.6) via Poisson Pseudo Maximum Likelihood (PPML). I control for lnLd and lnNo via the inclusion of the correct set of xed eects to capture the multilateral resistance terms. Note also that with included origin and destination xed
10The same is true for any structural trade gravity model.
eects, all unilaterally varying determinants of migration ows and many classical push and pull factors of migration are accounted for. World population,lnNw, is captured by a constant.
PPML allows me to include migration ows in levels instead of logged migration ows in a log-linearized version of the model for a linear estimation via OLS. Thus, zero migration ow observations do not drop out during the estimation.11 Also following Santos Silva and Tenreyro (2006), PPML estimates Equation (2.6) consistently for a sample which includes many zero observations. Remember that the theoretical model only predicts zero migration ows between a pair of countries if their migration barriers are innite.
Zero observations in the data thus are assumed to occur randomly or due to measurement errors in form of rounding errors.12
For the purpose of this paper, I stick to a fairly simple specication of δod. I specify bilateral migration barriers as
δ−1od = exp(γ1lnDISTod+γ2CON T IGod+γ3COLON Yod+γ4LAN God+γ5EUod), (2.7) where lnDISTod is the log of distance between country o and d. CON T IGod and COLON Yodindicate contiguity and a common colonial history of country-pairs. LAN God is equal to one if a country-pair shares at least one common ocial language and EUod is one if a country-pair belongs to the European Union.
As usual I have to assume regressors to be exogenous to collect consistent estimates of the γ coecients and consistent estimated migration barriers for the comparative static analysis. This assumption might not be plausibly fullled for theEUod indicator variable due to a selection bias. One might argue that the inclusion of distance and origin and destination xed eects already captures a lot of the selection process of becoming a European Union member. However, to overcome a potentially left selection bias, as Figueiredo et al. (2016), I follow Baier and Bergstrand (2007) and include directional bilateral xed eects in an auxiliary estimation. Augmenting data by the time dimension allows me to infer γ5 less prone to a bias from selection. I then estimate Equation (2.7) with the constrained coecient from the auxiliary estimation to infer δod.
There are further observations one might make with respect to the specication. As
11Ortega and Peri (2013) add a small value to all observations to circumvent the problem of zero observations. In general, this leads to biased estimates. See Santos Silva and Tenreyro (2006).
12This is also true for structural trade gravity estimations. Egger et al. (2011) use a two part model to allow for a dierent data generating process for zero observations of bilateral trade ows. See also Helpman et al. (2008) and Chapter 4 of this thesis on zero observations in trade gravity estimations.
previously mentioned, wages are substituted out by the labor market clearance condi-tion, and therefore bilaterally varying wage dierentials do not show up in the empirical specication. Note also that the classical distinction between push and pull factors of mi-gration is perfectly in line with a correct specication of mimi-gration barriers in a structural gravity estimation. Most of these factors are already captured by the origin and destina-tion xed eects. An obviously missing determinant of bilateral migradestina-tion barriers is the restrictiveness of migration policies. A bilaterally varying measure for migration policy is simply not yet available. An already launched data project, the IMPALA database, might solve this missing data problem for future research.13 With the free movement of labor within the European Union, the EU-pair dummy variable captures at least a part of this potential variation.
To sum up, my preferred estimation includes origin and destination xed eects, species migration costs according to (2.7) with a constrained coecient forγ5and employs PPML.
I present the results of the auxiliary regression and the outlined estimation in Section 2.6.
2.5. Data
As a measure for Mod I use the yearly inow of foreign population by nationality. The meta source for this information here is the International Migration Database (IMD) compiled and freely provided by the OECD.14 To my knowledge the IMD oers the most extensive coverage in terms of origin and destination country combinations of aggregate and dyadic migration ow data. The IMD collects data which are initially gathered at the national level, mainly by statistical oces and ocial registers who try to maintain consistent denitions of immigrants over time. I use the inows of foreign population by nationality from the IMD. National information are either derived from population registers and residence and/or work permits or by special surveys for some countries.15 Countries rarely use specic methods to collect data on migration, especially when it comes to migrant outows. Even if there might be a legal obligation to report out migration in a specic country, there is no obvious incentive for individuals to indicate emigration. Therefore, I only use migrant inows and follow the literature to construct
13See http://www.impaladatabase.org/.
14See https://stats.oecd.org/Index.aspx?DataSetCode=MIG.
15The countries which use dierent special survey approaches are Ireland, United Kingdom, Australia and New Zealand. Detailed Information on methods and sources by country can be found at the website given in Footnote 14.
a dyadic data set on migration ows.16 Standard geographical information stem from the GeoDist data set provided by CEPII.17 I extracted population data from World Development Indicators provided by the World Bank.18 For the auxiliary estimation I compile data over the period from 2000 to 2012. For the main regressions I keep the cross section of 2010 because coverage in this year is most extensive. Potentially the IMD oers a set of 210 origin regions and 34 destination countries. For some specications in 2.6 I employ the largest possible sample, excluding duplicates due to regional aggregations.
The main sample is dened by the countries which belong to the OECD and/or to the European Union. Due to missing migration data, I provide the comparative static results on a subsample of 33 countries of these.19