Revisiting Heterogeneity and Dependence in Panel Data Modeling

The primary objective of the paper is to revisit the statistical foundations of panel data modeling with a view to render their probabilistic assumptions testable vis-a-vis the data. This involves (a) recasting the error assumptions in terms of the probabilistic structure of the observable processes underlying the data, (b) specifying panel data models in terms of a complete and internally consistent set of testable probabilistic assumptions, and (c) proposing general misspecification testing procedures for evaluating the validity of the model assumptions. An important dimension of this recasting, is to put forward pertinent interpretations for the individual-specific fixed and random effects are proposed, by relating such effects to the probabilistic structure of the observable process underlying the data. The suggested interpretations call into question the Munlak (1978) reformulation of the random effects model, as well as the conventional wisdom on the fixed vs. random effects issue.