One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A “one-step” model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a “two-step” procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z. In this paper we propose a class of one-step models based on the “scaling property” that u equals a function of z times a one-sided error u∗ whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for onestep models whenever one is interested in the effects of firm characteristics on efficiency levels. JEL classification: C51, C52, D24