Bootstrap testing in nonlinear models

Bootstrap testing of nonlinear models normally requires at least one nonlin ear estimation for every bootstrap sample. We show how to reduce computatio nal costs by performing only a fixed, small number of Newton or quasi-Newto n steps for each bootstrap sample. The number of steps is smaller for likel ihood ratio tests than for other types of classical tests and smaller for N ewton's method than for quasi-Newton methods. The suggested procedures are applied to tests of slope coefficients in the tobit model and to tests of c ommon factor restrictions. In both cases, bootstrap tests work well, and ve ry few steps are needed.