RECENTERED AND RESCALED INSTRUMENTAL VARIABLE ESTIMATION OF TOBIT AND PROBIT MODELS WITH ERRORS IN VARIABLES
针对含测量误差的非线性Tobit和Probit模型，提出对观测因变量进行重新中心化和重新缩放，使标准工具变量估计量保持一致性，蒙特卡洛实验表明该方法对偏离正态性较为稳健。
Since Durbin (1954) and Sargan (1958), instrumental variable (IV) method has long been one of the most popular procedures among economists and other social scientists to handle linear models with errors-in-variables. A direct application of this method to nonlinear errors-in-variables models, however, fails to yield consistent estimators. This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality.