ABSTRACT
Model selection by BIC is well known to be inconsistent in the presence of incidental parameters. This article shows that, somewhat surprisingly, even without fixed effects in dynamic panels BIC is inconsistent and overestimates the true lag length with considerable probability. The reason for the inconsistency is explained, and the probability of overestimation is found to be 50% asymptotically. Three alternative consistent lag selection methods are considered. Two of these modify BIC, and the third involves sequential testing. Simulations evaluate the performance of these alternative lag selection methods in finite samples.
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Acknowledgement
We thank two referees, an associate editor, and the editor for helpful comments. Chengcheng Jia provided excellent research assistance.
Notes
1These terms also arise in conventional time series applications of BIC, but produce no overfitting tendency because there are only a finite number of these terms. In a panel context, this finite number is scaled by the number of cross-section observations, thereby disturbing the asymptotic properties of BIC.
2It is sufficient for our main result that the CLT
3Note that when kmax → ∞ the number of such terms potentially becomes large in a time series setting.
A referee suggested the Hannan–Quinn (1979, HQ hereafter) penalty function instead of IC1. The HQ penalty is much weaker than IC1. We examined their respective finite sample performance and found that the HQ criteria performs better than IC1 only when n is large. Moreover, as discussed shortly, IC2 outperforms IC1 and the HQ criteria. Hence, the finite sample performance of the HQ criterion is not reported here.