Improving a linear regression through joint estimation with a probit model

This paper considers joint estimation of a linear equation and a probit model when the explanatory variables are common, but extra observations are available for the binary variable. The practical significance of the problem is outlined and it is shown that the standard single-equation estimator of the linear model can be improved on. An efficient estimator, in the usual sense of minimum asymptotic variance, is derived and discussed. Finite sample variance properties are investigated via Monte Carlo simulation.