Two-stage estimation of the impact of contextual variables in stochastic frontier production function models using Data Envelopment Analysis: Second stage OLS versus bootstrap approaches

Banker and Natarajan (2008) identified sufficient conditions in a stochastic framework to justify the popular two-stage approach of Data Envelopment Analysis followed by Ordinary Least Squares (DEA + OLS) to estimate the impact of contextual variables on productivity. Simar and Wilson (2007) suggested an alternative approach involving a second-stage truncated regression model and bootstrap method to estimate confidence intervals. We show that the effectiveness of the Simar–Wilson approach critically depends on the assumption that the actual data generating process (DGP) exactly matches their assumed DGP and their approach does not yield correct inferences in environments characterized by stochastic noise. Extensive simulations from a stochastic frontier data generating process document that the simple two-stage DEA + OLS model significantly outperforms the more complex Simar–Wilson model with lower mean absolute deviation (MAD), lower median absolute deviation (MEAD) as well as higher coverage rates when the contextual variables significantly impact productivity.