One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels
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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 one-step models whenever one is interested in the effects of firm characteristics on efficiency levels.
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