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Spurious Fixed Effects Regression *
Author(s) -
Choi In
Publication year - 2013
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/j.1468-0084.2011.00688.x
Subject(s) - spurious relationship , estimator , mathematics , statistics , series (stratigraphy) , econometrics , regression , fixed effects model , regression analysis , jump , ordinary least squares , model selection , panel data , physics , paleontology , quantum mechanics , biology
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.