To Pool or Not to Pool: Revisited
研究了面板数据中，当时间维度固定而截面维度增大时，合并最小二乘与固定效应估计量的比较，提出基于指数系数δ的合并条件及检验方法。
Abstract This paper provides a new comparative analysis of pooled least squares and fixed effects (FE) 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 FE 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 FE 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.