An Investigation of Tests for Linearity and the Accuracy of Flexible Nonlinear Inference

A new approach recently suggested by Hamilton for flexible parametric inference in nonlinear models is examined through simulation studies. Hamilton suggests a new test for neglected nonlinearity and we compare it with the neural network test, Tsay's test, White's dynamic misspecification test, Ramsey's Reset test, the so-called V23 test, and the nonparametric BDS test. With respect to size and power properties, the results on the relative performance of Hamilton's test are very encouraging. In particular, we find that against almost all the nonlinear alternatives where the size and power properties of the popular neural network test are good the size and power properties of Hamilton's new test are even better. Secondly, we examine the convergence properties of Hamilton's estimator of the conditional mean function. Our finding suggest that in the case of a true linear relationship, the costs of using the flexible nonlinear approach in terms of efficiency and speed of convergence are minor. We also show that for many nonlinear models the percentage improvement in fit relative to the linear least squared estimator can be substantial. Finally, we present evidence showing that in finite samples the flexible regression approach suggested by Hamilton clearly outperforms the neural network regression approach in terms of accuracy