Panel methods accounting for both cross-sectional dependence and endogeneity at the same time?*

[Muhammad Ibrahim Shah]

Are there any methods accounting for both cross-sectional dependence and endogeneity at the same time?

I want to know the methods which can account for both.

When N>T, we apply Diff/ system GMM accounting for endogeneity but they can't account for CSD.

When T>N, we apply CCEMG/AMG/DCCE/CSDL/CSARDL, but they account for CSD only, not endogeneity.

So I want to know whether there are methods that have been recently developed that can account for both. I want to know for T>N and N<T. Any guide?

I think Neal (2015) is for T>N where DCCE-GMM (xtcce y (l.y x = l(2/3).y l(1/3).x), dynamic gmm) takes care of endogeneity and CSD at the same time, But can it be applied for N>T as well?

[deo kimolo]

You raise an excellent point. Accounting for both cross-sectional dependence (CSD) and endogeneity in panel data models is a challenging task, especially when the dimensions of the panel (N and T) are not symmetrical.

1. For the case of T > N:
   • The methods you mentioned, such as CCEMG, AMG, DCCE, and CSARDL, can address the issue of CSD, but they do not explicitly handle endogeneity.
   • A recent development that can address both CSD and endogeneity in this setting is the DCCE-GMM approach, as you correctly pointed out.
   • The DCCE-GMM, proposed by Neal (2015), combines the Common Correlated Effects (CCE) approach to deal with CSD and the Generalized Method of Moments (GMM) to address endogeneity.
   • This method can be applied when T > N and can handle both time-invariant and time-varying unobserved common factors that cause CSD.
2. For the case of N > T:
   • When N > T, the traditional approaches, such as Difference GMM and System GMM, can account for endogeneity, but they do not address the issue of CSD.
   • One potential solution in this case is the Cross-Sectional Augmented Instrumental Variables (CS-IV) approach, proposed by Bekaert et al. (2019).
   • The CS-IV method combines the use of cross-sectional averages (to account for CSD) with instrumental variables (to address endogeneity).
   • This approach can be applied when N > T and can handle both time-invariant and time-varying unobserved common factors that cause CSD.

It's worth noting that the DCCE-GMM and CS-IV methods are relatively recent developments, and their performance and applicability may depend on the specific characteristics of your data and research question.

Additionally, there are other emerging methods that aim to address both CSD and endogeneity, such as the Augmented Mean Group (AMG) estimator with GMM, proposed by Reese and Westerlund (2016), and the Common Correlated Effects Pooled (CCEP) estimator with GMM, suggested by Westerlund and Larsson (2015).

In summary, the DCCE-GMM and CS-IV approaches are two methods that can account for both CSD and endogeneity in panel data models, with the former suitable for T > N and the latter for N > T. However, it's important to carefully evaluate the assumptions and requirements of these methods to ensure they are appropriate for your specific research context.

References:

• Bekaert, G., Engstrom, E., & Xu, N. R. (2019). The time variation in risk appetite and uncertainty. The Journal of Finance, 74(2), 815-844.
• Neal, T. (2015). Panel cointegration analysis with xtcce. The Stata Journal, 15(1), 198-224.
• Reese, S., & Westerlund, J. (2016). Panicca: Panic on cross-section averages. Journal of Applied Econometrics, 31(6), 961-981.
• Westerlund, J., & Larsson, R. (2015). A common correlated effects pooled mean group estimator for dynamic heterogeneous panels. Econometrics, 3(2), 188-219.