ESTIMATING PROBABILITIES,MARGINAL EFFECTS AND TREATMENT EFFECTS IN RECURSIVE BIVARIATE PROBIT MODELS

Abstract

This article addresses the interpreting results of recursive system of binary equations estimation in the case when the system does not satisfy exclusion restriction conditions. It means that the equation defining the endogenous variable does not contain a unique covariate. This article extends the analysis of previous studies on the identifiability of parameters of recursive binary systems by analyzing the conditions for the identifiability of probabilities, marginal effects and treatment effects. We provide a reasonable consideration suggesting that even if parameters of the model are unidentifiable, it is still possible to estimate accurately the conditional probabilities and marginal effects, but not the treatment effects. The problem of identifiability discussed in the paper is also considered on real data. We estimate the probability of purchasing medicine depending on individuals’ characteristics and the fact of visiting a doctor. An important practical contribution of the work is the recommendation for researchers to interpret the result recursive binary system estimation via marginal effects in the case when it is not possible to include at least one unique variable in the equation for the binary covariate.