Bootstrap Testing in Nonlinear Models

When a model is nonlinear bootstrap testing can be expensive because of the need to perform at least one nonlinear estimation for every bootstrap sample We show that it may be possible to reduce computational costs by performing only a xed small number of articial regressions or Newton steps for each bootstrap sample The number of iterations needed is smaller for likelihood ratio tests than for other types of classical tests The suggested procedures are applied to tests of slope coe cients in the tobit model where asymptotic procedures often work surprisingly poorly In contrast bootstrap tests work remarkably well and very few iterations are needed to compute the