A Generalized Hyperbolic Distance Function for Benchmarking Performance: Estimation and Inference

This paper describes a new multiplicative, generalized hyperbolic distance function (GHDF) that allows the researcher to measure technical efficiency while holding a subset of inputs or outputs fixed. This is useful when dealing with “bad” or undesirable outputs, or in applications where some inputs or outputs are regarded as quasi-fixed. The paper provides computational methods for both free-disposal hull and data envelopment analysis estimators of the GHDF. In addition, statistical properties of the estimators are derived, enabling researchers to make inference and test hypotheses. An empirical illustration using data on U.S. credit unions is provided, as well as Monte Carlo evidence on the performance of the estimators. As illustrated in the empirical example, estimates of the GHDF are easier to interpret than estimates of additive, directional distance functions that until know have been the only non-parametric estimator of efficiency allowing subsets of input our outputs to be held constant.