Econometrica: Mar, 1980, Volume 48, Issue 2

Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage Tobit Methods for Simultaneous Equations Models with Selectivity

https://doi.org/0012-9682(198003)48:2<491:ACMOTP>2.0.CO;2-R
p. 491-504

G. S. Maddala, Lung-Fei Lee, R. P. Trost

The paper discusses the two-stage estimation method for switching simultaneous equations models where the criterion function determining the switching is of the probit type and the tobit type. It derives the asymptotic covariance matrices of these estimators and shows that when the criterion function is of the probit type the correct covariance matrix is underestimated when the heteroscedasticity introduced in the first step is ignored, whereas the same is not necessarily the case for one of the regimes when the criterion function is of the tobit type.