On the use of the f ratio in a mis-specified model with an interval restriction

The size and power of the F test for testing the joint significance of regression coefficients is considered in the context of an omitted variable model with an interval constraint. It is assumed that the F test is based on the interval constrained least squares (INCLS) estimator, and exact power of the test is computed by numerical integrations. Our results show that when the model is correctly specified, the test based on the INCLS estimator is not necessarily more powerful than the test by the OLS estimator even if the constraint is valid. On the contrary, over a large region in the parameter space, the test based on the OLS estimator has considerably higher power than the test based on the INCLS estimator. When the model is sufficiently mis-specified, we find that both tests, by the OLS as well as the INCLS estimators, always reject the null hypothesis even if it is true. © 1995, Taylor & Francis Group, LLC. All rights reserved.