Computing numerical distribution functions in econometrics

Many test statistics in econometrics have asymptotic distributions that cannot be evaluated analytically. In order to conduct asymptotic inference, it is therefore necessary to resort to simulation. Techniques that have commonly been used yield only a small number of critical values, which can be seriously inaccurate. In contrast, the techniques discussed in this paper yield enough information to plot the distributions of the test statistics or to calculate P values, and they can yield highly accurate results. These techniques are used to obtain asymptotic critical values for a test recently proposed by Kiefer, Vogelsang, and Bunzel (2000) for testing linear restrictions in linear regression models. A program to compute P values for this test is available from the author's web site.