Individuals are commonly surveyed about their perception or assessment of risk and these variables are often used to explain individuals’ actions to protect themselves against these risks. Perceptions appear as endogenous variables in traditional theoretical averting-decision models but, quite surprisingly, endogeneity of perceived risk is not always controlled for in empirical studies. In this article, we present different models that can be useful to the practitioner when estimating binary averting-decision models featuring an endogenous discrete variable (such as risk perception). In particular we compare the traditional bivariate probit model with the special regressor model, which is less well known and relies on a different set of assumptions. In the empirical illustration using household data from Australia, Canada, and France, we study how the perceived health impacts of tap water affect a household’s decision to drink water from the tap. Individuals’ perceptions are found to be endogenous and significant for all models, but the estimated marginal effect is sensitive to the model and underlying assumptions. The special regressor appears to be a valuable alternative to the more common bivariate probit model
