Two-Stage DEA: Caveat Emptor L ´ eopold Simar Paul W. Wilson ∗ May 2011 Abstract This paper examines the wide-spread practice where data envelopment analysis (DEA) efficiency estimates are regressed on some environmental variables in a second- stage analysis. In the literature, only two statistical models have been proposed in which second-stage regressions are well-defined and meaningful. In the model consid- ered by Simar and Wilson (2007), truncated regression provides consistent estimation in the second stage, where as in the model proposed by Banker and Natarajan (2008a), ordinary least squares (OLS) provides consistent estimation. This paper examines, compares, and contrasts the very different assumptions underlying these two models, and makes clear that second-stage OLS estimation is consistent only under very pecu- liar and unusual assumptions on the data-generating process that limit its applicability. In addition, we show that in either case, bootstrap methods provide the only feasible means for inference in the second stage. We also comment on ad hoc specifications of second-stage regression equations that ignore the part of the data-generating process that yields data used to obtain the initial DEA estimates. Keywords: technical efficiency, two-stage estimation, bootstrap, data envelopment analysis (DEA). Forthcoming, Journal of Productivity Analysis ∗ Simar: Institut de Statistique, Universit´ e Catholique de Louvain, Voie du Roman Pays 20, B 1348 Louvain-la-Neuve, Belgium; email leopold.simar@uclouvain.be. Wilson: The John E. Walker Depart- ment of Economics, 222 Sirrine Hall, Clemson University, Clemson, South Carolina 29634–1309, USA; email pww@clemson.edu. Financial support from the “Inter-university Attraction Pole”, Phase VI (No. P6/03) from the Belgian Government (Belgian Science Policy) and from l’Institut National de la Recherche Agronomique (INRA) and Le Groupe de Recherche en Economie Math´ ematique et Quantitative (GRE- MAQ), Toulouse School of Economics, Toulouse, France are gratefully acknowledged. Part of this research was done while Wilson was a visiting professor professor at the Institut de Statistique Biostatistique et Sci- ences Actuarielles, Universit´ e Catholique de Louvain, Louvain-la-Neuve, Belgium. We have benefited from discussions with Valentin Zelenyuk; of course, any remaining errors are solely our responsibility.