基于局部线性工具变量的半参数模型估计方法研究
Research on Semiparametric Model Estimation Method Based on Local Linear Instrumental Variables
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摘要: 本文针对半参数模型中工具变量的求解方法,考虑到传统工具变量需要特定假设的狭隘性,提出一种不需要假定特定的误差模型或者已知误差的估计方法,并将其命名为SEMI-LWLR-IV估计.首先通过局部线性回归对工具变量拟合矫正,之后使用得到的矫正估计值对半参数模型进行估计,给出无偏性与渐近正态性的定理及其证明.随后,本文通过蒙特卡洛数值模拟,使用新估计方法对生成数据进行拟合,拟合结果表明,在工具变量与内生变量呈线性关系时,新的估计方法与传统2SLS估计结果基本一致;在工具变量与内生变量呈非线性关系时,新方法具有比已有方法更优良的有限样本性质.Abstract: Considering the weak instrumental variables, aiming at the solution method of instrumental variables in the semiparametric model, the paper creatively introduces the local linear estimation in the nonparametric estimation into the two-stage instrumental variable estimation, and names it SEMI-LWLR-IV estimation. After which, the paper gives the unbiased and asymptotic normality theorems and their proofs. Then, this paper uses the Monte Carlo method to generate data, and uses a new estimation method to fit the generated data. The fitting results show that when the relation between instrumental variables and endogenous variables is linear, the new estimation method is basically consistent with the traditional 2SLS estimation results; when the relation between instrumental variables and endogenous variables is nonlinear, the new method has better properties than the existing methods.
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