利用离散傅里叶变换检验含交互固定效应的面板数据模型中的结构变化

中文摘要

我们提出一种基于离散傅里叶变换 (DFT) 的检验方法, 用于检测含交互固定效应 (IFE) 的面板数据模型中的结构变化。当存在结构变化但被忽略时, Bai (2009) 的最小二乘 (LS) 估计量的常规渐近分布可能不再能提供可靠推断, 且所得残差包含参数不稳定性的信号。我们的检验正是利用这一特征, 通过将加权残差的 DFT 与无结构变化原假设下隐含的平坦 (零) 谱进行比较来构建。我们建立了该检验的理论性质, 包括其渐近原假设分布以及局部与全局功效, 并提出一种自助法 (bootstrap) 程序以保证有限样本下的有效推断。值得注意的是, 所提出的检验能够检测一类以 N − 1 / 2 T − 1 / 2 的速度收敛于原假设的局部备择假设, 与斜率估计量的收敛速度相一致, 其中 N 和 T 分别为截面维度和时间维度。蒙特卡洛模拟表明, 所提检验对因子载荷和斜率系数中各种类型的结构变化均表现出优良的性能。我们进一步将该方法应用于环境库兹涅茨曲线以及健康支出与收入之间的关系, 以说明其经验相关性。我们的研究结果凸显了在含 IFE 的面板数据模型中考虑结构变化的重要性。

Abstract

We propose a discrete Fourier transform (DFT)-based test for detecting structural changes in panel data models with interactive fixed effects (IFE). When structural changes are present but ignored, the conventional asymptotic distribution of the least squares (LS) estimator of Bai (2009) may no longer provide reliable inference, and the resulting residuals contain signals of parameter instability. Our test exploits this feature by comparing the DFT of weighted residuals to the flat (zero) spectrum implied under the null hypothesis of no structural change. We establish the theoretical properties of the test, including its asymptotic null distribution and its local and global power, and propose a bootstrap procedure for valid inference in finite samples. Notably, the proposed test can detect a class of local alternatives converging to the null at the rate of N − 1 / 2 T − 1 / 2 , matching the convergence rate of the slope estimators, where N and T are the cross-sectional and time dimensions, respectively. Monte Carlo simulations demonstrate the excellent performance of the proposed test across various types of structural changes in both factor loadings and slope coefficients. We further illustrate the empirical relevance of our method by applying it to the environmental Kuznets curve and the relationship between health expenditure and income. Our findings highlight the importance of accounting for structural changes in panel data models with IFE.