This research presents two-stage panel data envelopment analysis (DEA) models for the estimation of efficiency measures. In the first stage, the variances of normal errors, v used in the transformation of the variables are recovered from pooled (Wallace-Hussain in 1969); within (Amemiya in 1971); or within, cross-sectional and time-series (Swamy-Arora in 1972) stochastic frontier analysis (SFA) models. The second stage involves estimating panel DEA efficiency measures using transformed data based on alternative two-way random effect econometric estimators in the first stage. The alternative panel DEA models might over- or under-estimate the pooled DEA model estimated efficiency measure due to the non-existence or existence of the spatial and temporal variations. An empirical application to 48 U.S. states from 1960 to 2004 suggests differences in the efficiency measure estimated by the pooled and panel DEA models. In addition, the efficiency measure estimated by the Swamy-Arora panel estimator is statistically different compared to the Wallace-Hussain and Amemiya panel estimator.