Using Weights to Adjust for Sample Selection When Auxiliary Information is Available

In this paper I analyze GMM estimation when the sample is not a random draw from the population of interest. I exploit auxiliary information, in the form of moments from the population of interest, in order to compute weights that are proportional to the inverse probability of selection. The essential idea is to construct weights, for each observation in the primary data, such that the moments of the weighted data are set equal to the additional moments. The estimator is applied to the Dutch Transportation Panel, in which refreshment draws were taken from the population of interest in order to deal with heavy attrition of the original panel. I show how these additional samples can be used to adjust for sample selection.