The unconditional distributions of the OLS, TSLS and LIML estimators in a simple structural equations model
研究了线性结构方程模型中OLS、TSLS和LIML估计量在不以外生变量为条件时的精确分布，探讨了条件化是否导致有限样本的异常特征。
The exact distributions of the standard estimators of the structural coefficients in a linear structural equations model conditional on the exogenous variables have been shown to have some unexpected and quirky features. Since the argument for conditioning on exogenous (ancillary) variables has been weakened over the past 20 years by the discovery of an “ancillarity paradox,” it is natural to wonder whether such finite sample properties are in fact due to conditioning on the exogenous variables. This article studies the exact distributions of the ordinary least squares (OLS), two-stage least squares (TSLS), and limited information maximum likelihood (LIML) estimators of the structural coefficients in a linear structural equation without conditioning on the exogenous variables.