Asymptotic Variance–Covariance Matrices of Two-Stage Estimators in the Presence of Continuous and Binary Dependent Variables with an Empirical Application

Abstract

We develop a general procedure to derive the asymptotic variance–covariance matrices of several two-stage estimators that can be used to estimate simultaneous equation systems with a mixture of any number of binary and continuous dependent variables. To demonstrate the usefulness of our procedure, we estimate a familiar simultaneous equations model that includes one continuous and two binary dependent variables, and derive their covariance matrices directly from our general formula. Our results are expected to be of tremendous help to numerous practitioners of econometrics using two-stage procedures to estimate their simultaneous equations models with different numbers of continuous and binary dependent variables.