Spurious Fixed Effects Regression*

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 R2s 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.