The pairwise pseudo-likelihood estimator (PPLE) is introduced for estimating the parameters of pair-tractable copulas, so copulas with analytically or numerically tractable pairwise margins, such as Archimedean, hierarchical Archimedean, Archimax and hierarchical Archimax copulas. In cases where feasible, the PPLE is compared, by simulation, to the standard maximum pseudo-likelihood estimator (MPLE) in terms of bias, root mean squared error (RMSE) and run time. The PPLE is also compared to the aggregated MPLE (AMPLE) for hierarchical Archimedean copulas. The simulation results indicate that the PPLE has a bias and RMSE comparable to the MPLE for those Archimedean copulas where the latter is available. For hierarchical Archimedean and hierarchical Archimax copulas for which the MPLE is not easily available, the PPLE mostly outperforms the AMPLE in bias and RMSE, with a clear advantage in terms of run time.