基于主成分分析的两阶段最小二乘估计研究

Study on Two-stage Least Squares Estimation Based on Principal Component Analysis

研究目标:在许多工具变量尤其是弱工具变量的情况下,为了减少传统2SLS的有限样本偏差,本文基于主成分思想提出新的PC-2SLS参数估计方法,并探讨其适用性。研究方法:从理论上分析新方法满足一致性和渐近有效性的条件,并通过一系列的蒙特卡罗模拟揭示其有限样本性质。研究发现:新方法明显降低参数估计的偏差,但同时具有比传统2SLS法更大的方差;在许多弱工具变量情况下新方法表现稳健,且比Bai和Ng(2010)的因子分析法具有明显优势;能有效减少附带参数问题所带来的影响,更能获得拟合值的一致估计。研究创新:将主成分思想应用于工具变量集,减少了工具变量的维数,能降低参数估计的偏差。研究价值:通过主成分分析法构建了一个比传统2SLS估计具有明显优势的参数估计方法。

Research Objectives:This paper proposes a new PC-2SLS estimation method based on principal component analysis to reduce the bias of two-stage least squares estimation,and discusses the applicability of the new method in the presence of many instrumental variables,especially many weak instrumental variables.Research Methods:The consistency and asymptotic efficiency of the new estimation method are theoretically analyzed,and the finite sample properties of the method are revealed through some Monte Carlo simulations.Research Findings:It is found that the new method can significantly reduce the bias of parameter estimator,but it has a larger variance than the traditional two-stage least squares(2SLS)method.Under many weak instrumental variables,the new method performs robustly and has obvious advantages over the factor analysis method by Bai and Ng(2010),and alleviates the incidental parameter problem,and can easily obtain a consistent estimation of the fitted value.Research Innovations:Principal component method is applied to instrumental variables set,which reduces the dimension of instrumental variables and the bias of parameter estimation.Research Value:A new method with obvious advantages over traditional 2SLS estimation is constructed based on principal component analysis.