Panel Regression of Arbitrarily Distributed Responses

Abstract

The primary advantage of panel over cross-sectional regression stems from its control for the effects of omitted variables or "unobserved heterogeneity". However, panel regression is based on the strong assumptions that measurement errors are independently identically (i.i.d.) and normal. These assumptions are evaded by design-based regression, which dispenses with measurement errors altogether by regarding the response as a fixed real number. The present paper establishes a middle ground between these extreme interpretations of longitudinal data. The individual is now represented as a panel of responses containing dependently non-identically distributed (d.n.d) measurement errors. Modeling the expectations of these responses preserves the Neyman randomization theory, rendering panel regression slopes approximately unbiased and normal in the presence of arbitrarily distributed measurement error. The generality of this reinterpretation is illustrated with German SocioEconomic Panel (GSOEP) responses that are discretely distributed on a 3-point scale.