A Detailed Decomposition for Limited Dependent Variable Models

In this paper, we consider a detailed decomposition method for limited dependent variable models. That means, we propose a method to decompose the differential in the (limited dependent) outcome variable between two groups into the contributions of the explanatory variables. We provide a theoretical derivation of the detailed decomposition and show how this decomposition can be estimated consistently. In contrast to decomposition approaches already presented in the literature, our method leads to a unique decomposition and accounts for the nonlinearity of the underlying econometric model in a rather intuitive way. Our results can be applied to the most common limited dependent variable models such as probit, logit and tobit models.