Analytical power comparisons of nested and nonnested tests for linear and loglinear regression models

This paper compares several tests for linear and loglinear regression model s where both the dependent and independent variables are transformed. It is shown that the Lagrange multiplier test proposed by Godfrey and Wickens (1 981, Review of Economic Studies 48, 487-496) in the framework of the Box-Co x regression model has the highest asymptotic power of the compared tests. The extended projection test of MacKinnon, White, and Davidson (1983, Journ al of Econometrics 11, 53-70), the test of Bera and McAleer (1983, paper pr esented to the SSRC Econometric Study Group Conference on Model Specificati on and Testing, Warwick; 1989, Sankhya B 51, 212-224), and the test of Andr ews (1971, Biometrika 58, 249-254) are shown to have asymptotically equival ent powers and to have lower powers than the nonnested test of Cox (1961, P roceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 105-123, Berkeley: University of California Press; 196 2, Journal of the Royal Statistical Society B 24, 406-424).