Spurious Fixed Effects Regression*
| Author | In Choi |
| DOI | http://doi.org/10.1111/j.1468-0084.2011.00688.x |
| Date | 01 April 2013 |
| Published date | 01 April 2013 |
297
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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 75, 2 (2013) 0305-9049
doi: 10.1111/j.1468-0084.2011.00688.x
Spurious Fixed Effects Regression*
In Choi
Department of Economics, Sogang University, #1 Shinsu-dong, Mapo-gu, Seoul, 121-742 Korea
(e-mail: inchoi@gmail.com, inchoi@sogang.ac.kr)
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 regres-
sion 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 stud-
ied by sending the number of cross-sectional observations to infinity. This article shows
that the first-differenced and Within-OLS estimators divergein 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.
I. Introduction
Regressions that do not reveal true statistical relations are called spurious. Spurious regres-
sions are known to occur in various time series settings. Yule (1926) tries to explain unrea-
sonably high correlation between the mortality rate for the years 1866–1911 and the ratio
of Church of England marriages to all marriages by using time series which, and the first
difference of which, are positively correlated. Yule is regarded as the first work that studied
spurious regressions.1More recently, Granger and Newbold (1974) demonstrate via simu-
lation that nonsense regression results can be observed between two independent random
walks. Their analysis have been extended to various models involving stochastic and/or
deterministic trends.
However, spurious regression results for conventional micro panels have never been
reported formally. 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 such popular estimators as first-differenced and
Within-OLS estimators are used. Under the weak time series variation, the variance of the
ÅI thank Wonho Song and an anonymous referee for their helpful comments. Research assistance for this article
was provided by Minchul Yum whom I thank This research was funded by the Sogang Research Frontier program.
JEL Classification numbers: C18, C33.
1SeeAldrich (1995) for a historical account of spurious correlations. According to Aldrich, the connection between
Yule(1926) and Granger and Newbold (1974) had been largely ignored until pointed out by Hendry (1986).
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