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A plethora of papers have used multi-stage estimation procedures where nonparametric estimates of productive efficiency are obtained in the first stage and then regressed on environmental variables in a subsequent stage in attempts to account for exogenous factors that might affect firms’ performance. None of these papers have described a coherent data-generating process (DGP). Moreover, conventional approaches to inference employed in these papers are invalid due to complicated, unknown serial correlation among the estimated efficiencies. We first describe a DGP wherein firms’ efficiencies are influenced by environmental variables. We then propose a single and a double bootstrap procedure; both permit valid inference, and the double bootstrap procedure improves statistical efficiency in the second-stage regression. We examine the statistical performance of our estimators using Monte Carlo experiments.