A Dynamic “Fixed Effects” Model for Heterogeneous Panel Data

This paper introduces a dynamic panel data model in which the intercepts and the coefficients on the lagged endogenous variables are specific to the cross section units, while the coefficients on the exogenous variables are assumed to be normally distributed across the cross section. Thus the model includes mixture of fixed coefficients and random coefficients, which I call the “MFR” model. The paper shows that this model has several desirable characteristics. In particular, the model allows for a considerable degree of heterogeneity across the cross section both in the dynamics and in the relationship between the independent and dependent variables. Estimation of the MFR model produces an estimate of the variance of the coefficients across the cross section units which can be used as a diagnostic tool to judge how widespread a relationship is and whether pooling of the data is appropriate. In addition, unlike LSDV estimation of dynamic panel models, the MFR model does not produce severely biased estimates when T is small.