A detailed decomposition for nonlinear econometric models

Abstract

This paper proposes a detailed decomposition for nonlinear econometric models, covering well-known limited dependent variable models such as the logit, probit and Tobit models. The purpose of the proposed method is to relate between-group differences in an outcome variable to differences in observable characteristics. The method overcomes disadvantages of existing decompositions for nonlinear models discussed in the literature. In particular, it leads to a unique decomposition and absorbs the present nonlinearities in a natural way. In this paper, the proposed decomposition is theoretically identified and it is shown how it can be estimated and how inference can be conducted. It is then compared to existing decomposition methods. An empirical application is presented where the results from the proposed decomposition method are compared with results from existing methods. It is demonstrated that linear methods such as the Oaxaca-Blinder decomposition may not be appropriate in the presence of substantial nonlinearities, and that the decomposition approach proposed in this paper leads to a theoretically sensible decomposition of the outcome differential.