MANY INSTRUMENTS ASYMPTOTIC APPROXIMATIONS UNDER NONNORMAL ERROR DISTRIBUTIONS
推导了有限信息最大似然估计和偏差校正的两阶段最小二乘估计在非正态误差下的新渐近近似，允许工具变量数和集中参数随样本量同速增长，发现误差非正态时工具变量性质及误差三、四阶矩影响渐近方差。
In this paper we derive an alternative asymptotic approximation to the sampling distribution of the limited information maximum likelihood estimator and a bias-corrected version of the two-stage least squares estimator. The approximation is obtained by allowing the number of instruments and the concentration parameter to grow at the same rate as the sample size. More specifically, we allow for potentially nonnormal error distributions and obtain the conventional asymptotic distribution and the results of Bekker (1994, Econometrica 62, 657–681) and Bekker and Van der Ploeg (2005, Statistica Neerlandica 59, 139–267) as special cases. The results show that when the error distribution is not normal, in general both the properties of the instruments and the third and fourth moments of the errors affect the asymptotic variance. We compare our findings with those in the recent literature on many and weak instruments.