Modelling Migration to the New World: Some Problems

An important drawback of single equation migration models is that in effect they assume wages and employment to be independent of the level of migration. Williamson has proposed instead a simple general equilibrium model with labour supply and demand equations for sending and receiving countries and a migration equation. The model yields a reduced form migration equation without current wage terms, casting doubt on the single-equation specifications which include such terms. Using data on migration flows from some European countries to the United States for 1870-1914, Williamson estimated the parameters of the structural model from the reduced form equation and extraneous information. The results are broadly as predicted by theory. However, when the structural model is estimated, this is no longer the case. This prompts a closer look at the model. It is argued that by assuming third country flows are exogenous, Williamson's estimation of his model is of a less general equilibrium nature than might appear. However, implementation of a full general equilibrium strategy is ruled out by data considerations. Instead, richer specifications of the model's equations are formulated and estimated. The results remain disappointing. The strategy recommended by Williamson seems potentially more applicable to modern migrations with better data.