Empirical researchers may wonder whether or not a two-way fixed effects estimator (with individual and period fixed effects) is sufficiently sophisticated to isolate the influence of common shocks on the estimation of slope coefficients. If it is not, practitioners need to run the so-called panel factor augmented regression instead. There are two pretesting procedures available in the literature: the use of the estimated number of factors and the direct test of estimated factor loading coefficients. This article compares the two pretesting methods asymptotically. Under the presence of the heterogeneous factor loadings, both pretesting procedures suggest using the common correlated effects (CCE) estimator. Meanwhile, when factor loadings are homogeneous, the pretesting method utilizing the estimated number of factors always suggests more efficient estimation methods. By comparing asymptotic variances, this article finds that when the slope coefficients are homogeneous with homogeneous factor loadings, the two-way fixed effects estimation is more efficient than the CCE estimation. However, when the slope coefficients are heterogeneous with homogeneous factor loadings, the CCE estimation is, surprisingly, more efficient than the two-way fixed effects estimation. By means of Monte Carlo simulations, we verify the asymptotic claims. We demonstrate how to use the two pretesting methods through the use of an empirical example.