CONSISTENT SPECIFICATION TESTING VIA NONPARAMETRIC SERIES REGRESSION

This paper proposes two consistent one-sided specification tests for p arametric regression models, one based on the sample covariance betwee n the residual from the parametric model and the discrepancy between t he parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and non parametric models. We estimate the nonparametric model by series regre ssion. The new test statistics converge in distribution to a unit norm al under correct specification and grow to infinity faster than the pa rametric rate (n(-1/2)) under misspecification, while avoiding weighti ng, sample splitting, and non-nested testing procedures used elsewhere in the literature. Asymptotically, our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regressio n model are zero, where the dependent variable is the residual from th e parametric model, and the series terms are functions of the explanat ory variables, chosen so as to support nonparametric estimation of a c onditional expectation. We specifically consider Fourier series and re gression splines, and present a Monte Carlo study of the finite sample performance of the new tests in comparison to consistent tests of Bie rens (1990), Eubank and Spiegelman (1990), Jayasuriya (1990), Wooldrid ge (1992), and Yatchew (1992); the results show the new tests have goo d power, performing quite well in some situations. We suggest a joint Bonferroni procedure that combines a new test with those of Bierens an d Wooldridge to capture the best features of the three approaches.