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

Abstract

Performance 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 efficiency analysis that all input quantities are observed and develop a nonparametric methodology that is robust to endogeneity issues. Our methodology extends Cherchye et al. (2021) by introducing cost inefficiency in the nonparametric framework to recover unobserved heterogeneity of cost minimizing firms. Our main contribution is that we bridge the OR/MS literature and the economic literature by addressing the general critique of Stigler (1976) on the concept of inefficiency (Leibenstein, 1966), which argued that found inefficiencies reflect unobserved inputs rather than waste. As such, we are the first to differentiate 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 show the applicability of the approach by studying both cost efficiency and endogenous automation in a real-world and purpose-built dataset on Belgian railway traffic management control rooms. Our findings cast doubt on Stigler's argument showing instead 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.