In this paper we analyze the estimation of coefficients in regression models under moment restrictions in which the moment restrictions are derived from auxiliary data. The moment restrictions yield weights for each observation that can subsequently be used in weighted regression analysis. We discuss the interpretation of these weights under two assumptions: that the target population (from which the moments are constructed) and the sampled population (from which the sample is drawn) are the same, and that these populations differ.
Imposing Moment Restrictions from Auxiliary Data by WeightingJudith K. Hellerstein and Guido Imbens ,
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The Review of Economics and Statistics