MINIMUM MSE ESTIMATION OF A REGRESSION-MODEL WITH FIXED EFFECTS FROM A SERIES OF CROSS-SECTIONS

If panel data are not available but repeated cross-sections are. the p arameters in a regression model with fixed individual effects can be e stimated consistently using the cohort approach proposed by Deaton (19 85). In this paper we show that Deaton's estimator is inconsistent if the number of time periods is small, even if the number of cohorts ten ds to infinity. Moreover, we propose an alternative estimator which do es not suffer from a bias due to a small number of sampling periods an d we introduce a new class of estimators, containing both estimators m entioned above. We discuss minimum mean squared error estimation withi n this class. Our results show that it may be optimal to eliminate onl y part of the measurement error in the cohort averages, since the impl ied bias is offset by a smaller variance.