OPTIMAL IV ESTIMATION OF SYSTEMS WITH STOCHASTIC REGRESSORS AND VAR DISTURBANCES WITH APPLICATIONS TO DYNAMIC SYSTEMS
研究了可行广义最小二乘工具变量估计的最优条件，针对平稳动态系统推导出新矩条件，利用滞后内生变量构造工具变量，提高了估计的渐近和小样本效率。
This paper considers the general problem of Feasible Generalized Least Squares Instrumental Variables (FGLS IV) estimation using optimal instruments. First we summarize the sufficient conditions for the FGLS IV estimator to be asymptotically equivalent to an optimal GLS IV estimator. Then we specialize to stationary dynamic systems with stationary VAR errors, and use the sufficient conditions to derive new moment conditions for these models. These moment conditions produce useful IVs from the lagged endogenous variables, despite the correlation between errors and endogenous variables. This use of the information contained in the lagged endogenous variables expands the class of IV estimators under consideration and thereby potentially improves both asymptotic and small-sample efficiency of the optimal IV estimator in the class. Some Monte Carlo experiments compare the new methods with those of Hatanaka (1976). For the DGP used in the Monte Carlo experiments, asymptotic efficiency is strictly improved by the new IVs, and experimental small-sample efficiency is improved as well.