Revisiting the Statistical Foundations of Panel Data Modeling

Despite the impressive developments in panel data modeling, the statistical foundations of such models are rather weak in so far that they are inadequate for securing the reliability and precision of inference. In statistical induction we learn from data about phenomena of interest when we employ reliable and incisive inference procedures. When one invokes either untested probabilistic assumptions, or/and broad (including nonparametric) premises, one has to rely on crude approximations (asymptotic) for evaluating the relevant error probabilities. This invariably leads to imprecise inference of unknown reliability because one does not know how closely the actual error probabilities approximate the assumed nominal ones, or how effective the inference procedures are! The primary objective of the paper is to revisit these probabilistic foundations with a view to: (a) recast the error assumptions in terms of the probabilistic structure of the observable processes underlying the data, (b) provide a complete and internally consistent set of testable probabilistic assumptions for several statistical models for panel data, and (c) propose pertinent interpretations for the individual-specific (fixed or random) and time-specific effects. It is shown that the current interpretations of the individual-specific effects (fixed or random) need to be reconsidered in light of the implicit statistical parameterizations in terms of the observable stochastic processes involved. This provides a more appropriate framework for securing learning from panel data by bringing out the neglected facets of empirical modeling which include specification, misspecification testing and respecification.