"To Pool or not to Pool: Revisited", by M. Hashem Pesaran and Qiankun Zhou, forthcoming in Oxford Bulletin of Economics and Statistics, October 2017.

Abstract: This paper provides a new comparative analysis of pooled least squares and fixed effects estimators of the slope coefficients in the case of panel data models when the time dimension (T) is …xed while the cross section dimension (N) is allowed to increase without bounds. The individual effects are allowed to be correlated with the regressors, and the comparison is carried out in terms of an exponent coefficients, δ, which measures the degree of pervasiveness of the fixed effects in the panel. The use of δ allows us to distinguish between poolability of small N dimensional panels with large T from large N dimensional panels with small T. It is shown that the pooled estimator remains consistent so long as δ < 1, and is asymptotically normally distributed if δ < 1/2, for a fixed T and as N → ∞. It is further shown that when δ < 1/2, the pooled estimator is more efficient than the fixed effects estimator. We also propose a Hausman type diagnostic test of δ < 1/2 as a simple test of poolability, and propose a pretest estimator that could be used in practice. Monte Carlo evidence supports the main theoretical …findings and gives some indications of gains to be made from pooling when δ < 1/2.
JEL Classifications: C01, C23, C33
Key Words: Short panel, Fixed effects estimator, Pooled estimator, Efficiency.
Full Text: http://www.econ.cam.ac.uk/people-files/emeritus/mhp1/fp17/Pesaran-ZhouTo-pool-or-not-to-pool-Oct-2017.pdf

"Estimation of Time-invariant Effects in Static Panel Data Models", by M. Hashem Pesaran and Qiankun Zhou, forthcoming in Econometrics Reviews, June 2016.

Abstract: This paper proposes the Fixed Effects Filtered (FEF) and Fixed Effects Filtered instrumental variable (FEF-IV) estimators for estimation and inference in the case of time-invariant effects in static panel data models when N is large and T is fixed. The FEF-IV allows for endogenous time-invariant regressors but assumes that there exists a suficient number of instruments for such regressors. It is shown that the FEF and FEF-IV estimators are [code]-consistent, and asymptotically normally distributed. The FEF estimator is compared with the Fixed Effects Vector Decomposition (FEVD) estimator proposed by Plumper and Troeger (2007) and conditions under which the two estimators are equivalent are established. It is also shown that the variance estimator proposed for FEVD estimator is inconsistent and its use could lead to misleading inference. Alternative variance estimators are proposed for both FEF and FEF-IV estimators which are shown to be consistent under fairly general conditions. The small sample properties of the FEF and FEF-IV estimators are investigated by Monte Carlo experiments, and it is shown that FEF has smaller bias and RMSE, unless an intercept is included in the second stage of the FEVD procedure which renders the FEF and FEVD estimators identical. The FEVD procedure, however, results in substantial size distortions since it uses incorrect standard errors. In the case where some of the time-invariant regressors are endogenous, the FEF-IV procedure is compared with a modified version of Hausman and Taylor (1981) (HT) estimator. It is shown that both estimators perform well and have similar small sample properties. But the application of standard HT procedure, that incorrectly assumes a sub-set of time-varying regressors are uncorrelated with the individual effects, will yield biased estimates and significant size distortions.
JEL Classifications: C01, C23, C33.
Key Words: Static panel data models, time-invariant effects, endogenous time-invariant regressors, Monte Carlo experiments, fixed effects filtered estimators.
Full Text: http://www.econ.cam.ac.uk/emeritus/mhp1/fp16/PesaranZhou_Time-invariant-estimation_June-11-2016.pdf
Supplementary Data: http://www.econ.cam.ac.uk/emeritus/mhp1/fp16/PesaranZhou_Time-invariant-estimation_May-27-2016_supplement.pdf
Stata Code and Instructions: http://qiankunzhou.weebly.com/research.html