Testing for Non-Normality in the Presence of One-Sided Slope Parameters

In a recent paper, Hughes (1999) showed that the power of tests of linear regression parameters could be improved by utilizing one-sided information regarding the nuisance parameters in the testing problem. In this paper, we extend this principle to the problem of diagnosing departures from the assumption of normality in linear regression residuals. We show that the asymptotic theory of the popular normality test developed by Jarque and Bera (1987) is also applicable when inequality constraints are imposed on the slope parameters. Monte Carlo evidence is then presented which suggests that the size of tests based on inequality constrained residuals is roughly equivalent to the size of tests based on unconstrained residuals using both asymptotic and bootstrap critical values. We then demonstrate that significant improvements in the power of the Jarque-Bera test can be made via the application of one-sided information concerning the slope parameters in the model.