引用本文: 杨宜平, 覃少红, 赵培信. 基于辅助回归的面板数据固定效应变系数模型的估计[J]. 应用概率统计, 2024, 40(4): 608-624.
YANG Y P, QIN S H, ZHAO P X. Estimation of varying coefficient fixed effects models in panel data based on auxiliary regression [J]. Chinese J Appl Probab Statist, 2024, 40(4): 608−624.
 Citation: YANG Y P, QIN S H, ZHAO P X. Estimation of varying coefficient fixed effects models in panel data based on auxiliary regression [J]. Chinese J Appl Probab Statist, 2024, 40(4): 608−624.

## Estimation of Varying Coefficient Fixed Effects Models in Panel Data Based on Auxiliary Regression

• 摘要: 本文针对面板数据固定效应变系数模型引入辅助回归来解释个体效应与协变量之间的关系, 以此来处理固定效应, 将模型转化为部分线性变系数模型. 为了获得系数函数的估计, 采用正交投影的方法消除固定效应, 进一步基于局部线性估计对系数函数进行估计. 在一些正则条件下, 给出了系数函数估计的渐近性质. 随后, 模拟研究了所提出的估计方法的有限样本性质. 模拟结果表明无论个体效应是随机的还是固定的, 本文方法优于已有的方法. 最后, 对艾滋病人的CD4数据进行了实证分析.

Abstract: In this paper, the auxiliary regression is introduced for the varying coefficient fixed effect models in panel data to explain the relationship between individual effects and covariates. We transform the varying coefficient models into partial linear varying coefficient models based on the auxiliary regression. In order to obtain the estimation of the function coefficient, the orthogonal projection and the local linear estimation method are used to eliminate the fixed effect, and estimate the function coefficient. Under some regular conditions, the asymptotic properties of the function coefficient estimation are given. Then, the finite sample property of the proposed estimation method is studied by the simulation. The simulation results show that no matter whether the individual effect is random or fixed, the proposed method is superior to the existing methods. Finally, the CD4 data of AIDS patients are analyzed.

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