Bootstrapping the Information Matrix Test

In this paper we provide considerable Monte Carlo evidence on the finite sample performance of several alternative forms of White’s [1982] IM test. Using linear regression and probit models, we extend the range of previous analysis in a manner that reveals new patterns in the behavior of the asymptotic version of the IM test – particularly with respect to curse of dimensionality effects. We also explore the potential of parametric and nonparametric bootstrap methods for reducing the size bias that characterizes the asymptotic IM test. The nonparametric bootstrap is of particular interest because of the weak conditions it imposes, but the results of our Monte Carlo experiments suggest that this technique is not without limitations. The parametric bootstrap demonstrates good size and power in reasonably small samples, but requires assumptions that may be auxiliary from the standpoint of a QMLE. We observe that the effects of violating one of these auxiliary assumptions has a non-trivial impact on the size of IM tests that employ this technique.