Identifying Distributional Characteristics in Random Coefficients Panel Data Models

We study the identification of linear panel data models with strictly exogenous regressors and individual-specific coefficients, when the time length of the panel T is fixed. In addition to common parameters and averages of individual effects, we show the identification of the variance of the effects under conditional uncorrelatedness assumptions on error variables. Identification requires the dependence structure of errors to be restricted, reflecting a trade-off between the number of individual-specific parameters and error dynamics. Assuming that effects and errors are independent conditional on regressors, we show the identification of the density of individual effects in cases where errors follow moving averages or ARMA structures with independent innovations. We propose method-of moments estimators of the moments of individual effects and errors, and introduce a simple estimator of the density of the effect of a binary regressor in a special case. We apply the method to estimate the effect that a mother smokes during pregnancy on the weight of her child at birth.

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