半参数计量经济联立模型的变窗宽估计理论

Theory of variable bandwidth estimation for semi-parametric simultaneous equations econometric models

联立方程模型在经济政策制定、经济结构分析和经济预测方面起重要作用.文章将半参数单方程计量经济模型的局部线性估计方法与传统联立方程计量经济模型的工具变量估计方法相结合,在随机设计(模型中所有变量为随机变量)下,提出了半参数联立方程计量经济模型的局部线性工具变量变窗宽估计方法,并利用极限理论研究了估计的大样本性质.结果表明:参数分量的估计具有一致性和渐近正态性且收敛速度为n-1/2;非参数分量估计在内点处具有一致性和渐近正态性,其收敛速度达到了非参数函数估计的最优收敛速度.

Econometric simultaneous equation models play an important role in making economic policies, an- alyzing economic structure and economic forecasting. This paper presents an estimation method for semi-para- metric simultaneous equations econometric model. A local linear estimation with variable bandwidth was used with instrumental variables, when all variables were random. A local linear estimation method for semi-para- metric single equation model was combined with the traditional instrumental variable method for simultaneous equations model. The properties under large sample size were studied by using the asymptotic theory. The re- sults show that the estimators of the parameters have consistency and asymptotic normality, and their conver- gence rates are equal to n^-1/2. Further the estimator of the nonparametric function has the consistency and as- ymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.