Spurious Fixed Effects Regression*
发现当解释变量时间序列变化弱或误差项时间序列变化强时，固定效应模型的一阶差分和组内OLS估计会产生虚假回归，并分析了估计量、t检验和模型选择准则的渐近性质。
Abstract This article shows that spurious regression results can occur for a fixed effects model with weak time series variation in the regressor and/or strong time series variation in the regression errors when the first‐differenced and Within‐OLS estimators are used. Asymptotic properties of these estimators and the related t ‐tests and model selection criteria are studied by sending the number of cross‐sectional observations to infinity. This article shows that the first‐differenced and Within‐OLS estimators diverge in probability, that the related t ‐tests are inconsistent, that R 2 s converge to zero in probability and that AIC and BIC diverge to −∞ in probability. The results of the article warn that one should not jump to the use of fixed effects regressions without considering the degree of time series variations in the data.