Econometrica: May, 1980, Volume 48, Issue 4

Formulation and Statistical Analysis of the Mixed, Continuous/Discrete Dependent Variable Model in Classical Production Theory

https://doi.org/0012-9682(198005)48:4<839:FASAOT>2.0.CO;2-I
p. 839-852

Gregory M. Duncan

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 OREG, 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 hole. Thus a test of the restriction based on the joint distribution of separate probit and regression estimates is proposed.