Double Bootstrap Confidence Intervals in the Two-Stage DEA Approach

Contextual factors usually assume an important role in determining firms' productive efficiencies. Nevertheless, identifying them in a regression framework might be complicated. The problem arises from the efficiencies being correlated with each other when estimated by Data Envelopment Analysis (DEA), rendering standard inference methods invalid. Simar and Wilson (2007) suggest the use of bootstrap algorithms that allow for valid statistical inference in this context. This paper extends their work by proposing a double bootstrap algorithm for obtaining confidence intervals with improved coverage probabilities. It also offers an empirical application using bank-level data. Moreover, acknowledging the computational burden associated with iterated bootstrap procedures, we provide an algorithm based on deterministic stopping rules which is less computationally demanding. Monte Carlo evidence shows considerable improvement in the coverage probabilities after iterating the bootstrap procedure. The results also suggest that percentile confidence intervals perform better than their basic counterpart. The empirical application of the double bootstrap to a sample of European banks suggests that diversified financial conglomerates are more efficient than specialised institutions and the findings are robust to alternative double bootstrap confidence interval methods