A Note on a Random Coefficients Model

In this note I will consider a random coefficients model in which the regression coefficients are assumed to be the dependent variables of another regression equation. Such a model is likely to arise in econometric applications when one wants to pool time series and cross-section data. See, for example, Wachter 1970. First, I will prove the equivalence of certain two estimators in the general model, and then show how a special case of the general model arises when time series and cross-section data are pooled. The model in its most general form can be defined by