A hypergeometric test for omitted nonlinearity

Abstract

A frequently used test for unspeciÞed nonlinear omissions is the parametric RESET, which is based upon a Þnite polynomial. We fol- low Abadir (1999), who suggests that the generalized hypergeometric function may provide a more ßexible proxy for the omission; and pro- pose a new approach, semi-nonparametric in spirit, that is based upon estimation of the hypergeometric parameters, and which does not re- quire large datasets. While minimal ex ante assumptions are made about the functional form, this is fully revealed following implemen- tation. Using Monte Carlo simulation, we examine null distributions, and then show that the small-sample power of our test can be a con- siderable improvement over that of the RESET, when the correct class of functional forms of the omission is known. We investigate a variety of theoretical and numerical issues (including rapid and stable numer- ical optimization) that arise in development of a workable procedure, and offer practical solutions that should be especially useful whenever hypergeometrics are applied to problems of modelling nonlinearity.