A flexible parametric approach to the binary outcome model

Abstract

One of the major difficulties associated with econometric models for binary dependent variables is the fact that erroneous distributional assumptions regarding the error term are bound to result in inconsistent parameter estimates. This paper introduces a family of fully parametric, univariate density functions designed for use in connection with binary outcome models,which is capable of providing an arbitraly close approximation to the standard logistic and Burr II densities but can also represent a wealth of skewed and multi-modal distributions. The applicability of the approach under discussion is demonstrated by means of an application to an econometric model of self-employment. A simple, residual –based specification test applied in this context clearly rejects the standard logit, probit and Burr II specifications used as reference models. Moreover, most of the flexible parametric specifications under consideration clearly outperform the reference models if measured by the number of correct predictions.