Interpreting logit regressions with interaction terms: an application to the management turnover literature

Logit and probit models of turnover=f(performance, firm type, firm type*performance, controls) are often used when testing whether turnover is “more sensitive to performance” for different types of firms. Researchers using this specification typically focus on the significance of the interaction term coefficient. If the intent is to show that the likelihood (rather than the odds) of turnover changes by more for one type of firm as performance varies, then this is an inappropriate test. Simulations are used to demonstrate how focusing on this particular coefficient can generate incorrect inferences. I then show how analyzing marginal effects eliminates this inference problem.