多项分布内生回归元计数模型的两阶段估计方法研究

Two-stage Estimation for Count Data Models with Endogenous Explanatory Variable of Multinomial Distribution

两阶段估计方法是解决计量模型变量内生性问题的重要方法,而现代社会科学领域的研究文献在选择两阶段估计方法时存在较多误区,缺乏比较系统的研究。基于多项分布内生回归元的计数模型,采用蒙特卡洛模拟比较2SLS、2SPS、2SRI三种两阶段估计方法的优劣,并从检验水平和功效角度评价Wald、LR、LM三种内生性检验方法的有效性,结果发现:当忽略模型非线性、内生性或错误设定计数数据分布时,2SLS和2SPS均会存在较大的估计偏差,但2SRI估计量具有良好的有限样本特征;基于2SRI的三种内生性检验方法,在计数数据分布设定正确时都有合理的实际检验水平和功效,但在忽略计数数据过度分散特征时,Wald和LR检验统计量会发生严重的水平扭曲,而LM检验则更有效。

Two-stage estimation method is important to solve the endogenous problem of models. However, there are many misunderstandings and lacking of systematic comparative study in selecting the two stage estimations when scholars carry out empirical analysis in the field of modern social science. Based on the count data models with endogenous explanatory variable of multinomial distribution, this paper analyzes and compares three types of two stage estimation methods, such as 2SLS, 2SPS and 2SRI. Moreover,it evaluates the relevance of Wad, LR and LM test methods in finite sample properties. Extensive Monte Carlo simulations indicate that 2SLS and 2SPS with ignoring the nonlinearity and endogeneity of model, or mis specified data distribution cause large bias. But 2SRI could have the good performance. These test methods have the reasonable test sizes and powers when correctly setting the data distribution. Wald and LR test statistics have the serious test size distortions when the over dispersion of count data is neglected. However, LM test statistic shows the advantage. Furthermore, the estimation results and LM test statistics perform better by using the standardized residual in 2SRI.