Lag length selection in panel autoregression

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.

KEYWORDS:

• BIC
• dynamic panel
• lag selection
• sequential testing
• X-differencing

JEL CLASSIFICATION:

• C33

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

holds for all fixed k which is so by virtue of independence over i and the existence of fourth moments of ϵ_it.

³Note that when k_max → ∞ 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.