Imposing moment restrictions from auxiliary data by weighting

In this paper we analyze the estimation of coefficients in regression model s under moment restrictions in which the moment restrictions are derived fr om auxiliary data. The moment restrictions yield weights for each observati on that can subsequently be used in weighted regression analysis. We discus s the interpretation of these weights under two assumptions: that the targe t population (from which the moments are constructed) and the sampled popul ation (from which the sample is drawn) are the same, and that these populat ions differ. We present an application based on omitted ability bias in est imation of wage regressions. The National Longitudinal Survey Young Men's C ohort (NLS)- in addition to containing information for each observation on wages, education, and experience - records data on two test scores that may be considered proxies for ability. The NLS is a small dataset, however, wi th a high attrition rate. We investigate how to mitigate these problems in the NLS by forming moments from the joint distribution of education, experi ence, and log wages in the 1% sample of the 1980 U.S. Census and using thes e moments to construct weights for weighted regression analysis of the NLS. We analyze the impacts of our weighted regression techniques on the estima ted coefficients and standard errors of returns to education and experience in the NLS controlling for ability, with and without the assumption that t he NLS and the Census samples are random samples from the same population.