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 parameters in a regression model with fixed individual effects can be estimated consistently using the cohort approach proposed by Deaton (1985). 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 tends to infinity. Moreover, we propose an alternative estimator which does not suffer from a bias due to a small number of sampling periods and we introduce a new class of estimators, containing both estimators mentioned above. We discuss minimum mean squared error estimation within this class. Our results show that it may be optimal to eliminate only part of the measurement error in the cohort averages, since the implied bias is offset by a smaller variance.

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