Marginal effects in the probit model with a triple dummy variable interaction term

In non-linear regression models, such as the probit model, coefficients cannot be interpreted as marginal effects. The marginal effects are usually non-linear combinations of all regressors and regression coefficients of the model. This paper derives the marginal effects in a probit model with a triple dummy variable interaction term. A frequent application of this model is the regression-based difference-in-difference-in-differences estimator with a binary outcome variable. The formulae derived here are implemented in a Stata program called inteff3 which applies the delta method in order to compute also the standard errors of the marginal effects.