Convenient specification tests for logit and probit models

We propose several Lagrange multiplier tests of logit and probit models, which may be inexpen- sively computed by means of artificial linear regressions. These maybe used to test for various forms of model inadequacy, including the omission of specified variables and heteroskedasticity of known form. We perform a number of sampling experiments, in which we compare the small-sam- ple properties of these tests and of likelihood ratio tests. One of the LM tests turns out to have better small-sample properties than any of the others. We then investigate the power of the tests against local alternatives, and conduct a further series of sampling experiments to compare the power of various tests.