Standard errors of marginal effects in the heteroskedastic probit model

In non-linear regression models, such as the heteroskedastic probit model, coefficients cannot be interpreted as marginal effects. Marginal effects can be computed as a non-linear combination of the regression coefficients. Standard errors of the marginal effects needed for inference and hypothesis testing have to be derived by approximation using methods such as the delta method. This paper applies the delta method to derive analytically the standard errors of marginal effects in a heteroskedastic probit model. The computation is implemented as a Stata ado-file called mehetprob which can be downloaded from the internet. This allows to compute marginal effects at means and their standard errors in a heteroskedastic probit model faster than by numerical calculation which is implemented in the mfx routine currently available in Stata for that purposes.