A Low-Dimension Collinearity-Robust Test for Non-linearity

A new test for non-linearity is developed using weighted combinations of regressor powers based on the eigenvectors of the variance-covariance matrix. The test extends the ingenious test for heteroskedasticity proposed by White (1980), but both circumvents problems of high dimensionality and collinearity, and allows inclusion of cubic functions to ensure power against asymmetry or skewness. A Monte Carlo analysis compares the performance of the test to the optimal infeasible test and to a variant of White`s test. The relative performance of the test is encouraging: the test has the appropriate size and has high power in many situations. Furthermore, collinearity between regressors can increase the power of the test.