To Pool or not to Pool: Revisited

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 fixed 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 coefficient, δ, which measures the degree of pervasiveness of the fixed effects in the panel. The use of exponent 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 which could be used in practice as a simple test of poolability. In the case where N and T → ∞, such that T = O (Nd), for some d > 0, the condition for poolability generalizes to δ < (1 - d)/2. Monte Carlo evidence supports the main theoretical findings and gives some indications of gains to be made from pooling when δ < (1 - d)/2.