针对面板数据的半参数变系数可加模型的估计和推断

Estimation and Inference of a Semiparametric Varying-coefficient Additive Model for Panel Data

本文研究针对面板数据的半参数变系数可加模型的估计和推断问题,该模型将因变量与自变量之间的关系建模成未知函数的形式,并且假设它们之间的关系是随时间变化的.本文基于B样条方法估计未知的参数和函数.本文在允许(N,T)→∞的情况下建立各个估计量的渐近性质.通过大量的模拟评估所提出的估计方法的表现.最后,本文将所推荐的模型用于调查Fama-French三因子的时变行为.

This paper aims to study the estimation and inference of a semiparametric varying-coefficient additive model for panel data.The model assumes the relationship between a response variable and predictors as unknown functions and allows the relationship is time-varying,which can simultaneously capture time-variant and non-linear structure.We develop an estimation procedure to estimate unknown parameters and functions.We first average the response variable over cross-sections and,then our model becomes a varyingcoefficient additive model.We then provide initial estimates of functions by a spline smoothing method and those of parameters by a least square method.Once these initial estimates are obtained,we upgrade these estimates using the spline method and least square method based on our original model.Asymptotic properties of the resulting estimators are also derived under a setting of(N,T)→∞.Simulation studies are reported to evaluate the performance of our estimation procedure.We apply our model to investigate time-variant behaviours of Fama–French three factors and find that the size and value factors are significantly time-variant.