Productive efficiency analysis with unobserved inputs: An application to endogenous automation in railway traffic management

Productive efficiency analytics are commonly used in managerial decision making, but are vulnerable to an omitted variable bias issue when there is incomplete information on the used production factors. In this paper, we relax the standard assumption in productive efficiency analysis that all input quantities are observed, and we propose a nonparametric methodology for cost inefficiency measurement that accounts for the presence of unobserved inputs. Our main contribution is that we bridge the nonparametric OR/MS and the economic Industrial Organization literature by addressing the general critique of Stigler (1976) on the concept of inefficiency (Leibenstein, 1966), which states that found inefficiencies reflect unobserved inputs rather than waste. Our methodology explicitly differentiates between cost inefficiency (i.e., waste; deviations from optimizing behavior) and unobserved input usage (i.e., optimally chosen input factors that are unobserved to the empirical analyst). We apply our novel method to a purpose-built dataset on Belgian railway traffic management control rooms. Our findings show the existence of meaningful inefficiencies that cannot be attributed to use of unobserved inputs or environmental factors. In addition, we document how the omitted variable bias impacts cost efficiencies of individual observations in a dissimilar way in case the use of unobserved inputs is not controlled for.