A convenient test of functional form for pooled econometric models

Abstract

This paper demonstrates a parametric test of specification that can be used in validating econometric models employing pooled time series and cross-section data with fixed effects. This Lagrange multiplier test allows for the simultaneous testing of proper model functional form and the presence of nonspherical disturbances, using a combination of the Box-Cox transformation, the double-length regression of Davidson and MacKinnon, and the Bonferroni inducedt-test. Testing procedures are demonstrated using a model of long distance telephone demand in the United States. The illustrative model used is representative of models filed as direct testimony by telephone companies in administrative law proceedings, which usually require rigorous model validation and defenses of model results in a formal hearing room setting. The tests presented in this paper are useful to a wide variety of researchers who use pooled econometric models with fixed effects in their work.