The Exact Sampling Distribution of Ordinary Least Squares and Two-Stage Least Squares Estimators
The Exact Sampling Distribution of Ordinary Least Squares and Two-Stage Least Squares Estimators
复制标题
普通最小二乘和两阶段最小二乘估计器的精确采样分布
DOI：
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
T. Sawa
中科院分区：
文献类型：
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作者：
T. Sawa
本文给出了一个完备随机方程组中具有两个内生变量的结构方程中结构参数的普通估计和两阶段最小二乘估计的精确抽样分布。结果表明，这两种估计量的分布基本相似。还可以看出，这两种分布都依赖于两个内生变量的干扰项的回归系数与结构参数的偏差，第一种估计量的矩达到N-2阶，而第二种估计量的矩达到K-1阶，其中N是样本量，K是从待估计的方程中排除的外生变量的数量。估计的小样本性质的密度函数的数值计算进行了研究。
Abstract This paper presents the exact sampling distributions of the ordinary and the two-stage least squares estimators of a structural parameter in a structural equation with two endogenous variables in a complete system of stochastic equations. The results show that the distributions of the two estimators are essentially similar to each other. It can also be seen that both distributions depend crucially upon the deviation of a regression coefficient of disturbance terms of two endogenous variables from a structural parameter, and that the first estimator possesses moments up to the order N-2, while the second possesses them up to the order K-1, where N is the sample size and K is the number of exogenous variables excluded from the equation to be estimated. The small sample properties of the estimators are investigated by numerical evaluations of the density functions.