We provide a methodology for testing a polynomial model hypothesis by extending the approach and results of Baek, Cho, and Phillips (2015; Journal of Econometrics; BCP) that tests for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We examine and generalize the BCP quasi-likelihood ratio test dealing with the multifold identiﬁcation problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful in the application of sieve approximations. Simulations show good performance in the sequential test procedure in identifying and estimating unknown polynomial order. The approach, which can be used empirically to test for misspeciﬁcation, is applied to a Mincer (1958, 1974) equation using data from Card (1995). The results conﬁrm that Mincer’s log earnings equation is easily shown to be misspeciﬁed by including nonlinear eﬀects of experience and schooling on earnings, with some flexibility required in the respective polynomial degrees.
Cho, Jin Seo and Phillips, Peter C.B., "Sequentially Testing Polynomial Model Hypotheses Using Power Transforms of Regressors" (2016). Cowles Foundation Discussion Papers. 2522.