Improved Errors-in-Variables Estimators for Grouped Data

Grouping models are widely used in economics but are subject to finite sample bias. I show that the standard errors-in-variables estimator is exactly equivalent to the jackknife instrumental variables estimator and use this relationship to develop an estimator which, unlike the standard errors-in-variables estimator, is unbiased in finite samples. The theoretical results are demonstrated using Monte Carlo experiments. Finally, I implement a model of intertemporal male labor supply using microdata from the U.S. Census. There are sizable differences in the wage elasticity across estimators, showing the practical importance of the theoretical issues even when the sample size is quite large.