Formulation and Statistical Analysis of the Mixed, Continuous/Discrete Dependent Variable Model in Classical Production Theory - Duncan, Gregory M. (Econometrica, 1980)
Data sets which contain jointly endogenous discrete and continuous variables often occur in practice. This paper presents a model of the economic and stochastic processes generating such data as well as methods of estimation. A maximum likelihood estimator is examined and found to exhibit the usual optimality but it is computationally burdensome. A simpler estimator, the QREG, which is a simple weighted average of separate probit (or logit) and regression estimates is suggested as an attractive alternative. The QREG is also found to be optimal but only when a certain covariance restriction is found to hold. Thus a test of the restriction based on the joint distribution of separate probit and regression estimates is proposed.