Many papers have used a two-stage approach of first calculating DEA efficiency scores and then seeking to correlate these scores with various environmental variables. Most of the studies have not checked whether such a two-stage approach is statistically valid for identifying significant environmental variables. Recently Simar and Wilson (2007) (SW) introduce a sensible data generating process and bootstrap procedure based on truncated regression for the two-stage approach. Banker and Natarajan (2008) (BN) provide a statistical foundation for the two-stage approach comprising a DEA followed by an ordinary least squares or maximum likelihood estimation. Researchers have to identify an approach suitable for their research circumstances in terms of properties, merits, demerits, and robustness to plausible departures from its chosen data generating process. We summarize the foundations and properties of the two-stage procedures suggested by SW and BN. And we discuss merits and demerits of those procedures. Also using Monte Carlo simulation we assess their relative performance under several misspecified settings.