Model selection for panel data models with fixed effects: a simulation study

ABSTRACT

This study considers model selection criteria, such as the Akaike’s Information Criterion (AIC), the corrected Akaike’s Information Criterion (AIC${ }_C$) and the Bayesian Information Criterion (BIC), for panel data models with fixed effects. Applying these information criteria to fixed effects panel models is not a trivial matter due to the incidental parameter problem that might adversely affect their practical performance, especially when it comes to short panel data. Monte Carlo experiments suggest that the information criteria are quite successful in selecting the true model. In particular, the AIC${ }_C$ and the AIC operate successfully unless a time dimension is extremely small.

KEYWORDS:

• Panel data
• fixed effects
• model selection criteria

JEL CLASSIFICATION:

• C23
• C53

Acknowledgements

This note is based on my master’s thesis submitted to Sogang University. I am indebted to the thesis supervisor, In Choi, for his guidance and support. I am also grateful to the anonymous referee for the insightful and constructive comments and to Seung C. Ahn, Hanbat Jeong, and participants at the 2010 Korean Economic Association Joint Conference at Seoul National University for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ The model selection approach has led to significant advances in statistics and has been applied to economics as well (see Chao and Phillips 1999; Bai and Ng 2002; Baltagi and Wang 2007; Choi and Kurozumi 2012; Choi and Jeong 2019, for some recent examples). The exercise presented herein is another attempt to apply model selection to an important empirical model in economics.

² Table 8 reports the relative likelihood of model $i$ (Burnham and Anderson 2002):

$exp\left(\frac{AI{C}_{min}-AI{C}_i}{2}\right)$

for each different true model under consideration, with largest sample number ($N=500$ and $T=6$). This statistic could be helpful to evaluate prediction accuracy losses from model selection. The reported numbers are the averages across replications for ${\sigma }_{\alpha }^2={\sigma }_{\lambda }^2=1$. The results with other values of ${\sigma }_{\alpha }^2$ and ${\sigma }_{\lambda }^2$ are essentially the same.