A Hypergeometric Test for Omitted Nonlinearity

A frequently used test for unspeciÞed nonlinear omissions is the parametric RESET, which is based upon a Þnite polynomial. We follow Abadir (1999), who suggests that the generalized hypergeometric function may provide a more ßexible proxy for the omission; and propose a new approach, semi-nonparametric in spirit, that is based upon estimation of the hypergeometric parameters, and which does not require large datasets. While minimal ex ante assumptions are made about the functional form, this is fully revealed following implementation. Using Monte Carlo simulation, we examine null distributions,and then show that the small-sample power of our test can be a considerable 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 numerical optimization) that arise in development of a workable procedure, and other practical solutions that should be especially useful whenever hypergeometrics are applied to problems of modelling nonlinearity.