Directional Distance Functions and Rate-of-Return Regulation

This paper is concerned with formulating directional distance functions assuming that firms operate subject to rate-of-return regulation. To this end, we consider two different contexts. First, we assume that input prices are known, which allows us to extend the rate of return regulated version of Farrell efficiency. Secondly, we assume that input prices are unknown, showing then that a specific reference direction arises as a natural choice for measuring efficiency with directional distance functions. 1. Introduction All over the world, most countries deal with the problem of monopoly by means of regulation. This type of solution is widespread in the case of natural monopolies: water, natural gas, and electric companies. These companies are not allowed to charge any price they want to. Instead, government agencies regulate their output prices. One form of regulation is that of rate-of-return regulation. After the firm subtracts its operating expenses from gross revenues, the remaining net revenue should be just sufficient to compensate the firm for its investment in plant and equipment. In particular, the regulator authorizes the output price which, if anticipated future market conditions are realized, results in the firm earning a rate of return equal to the predetermined allowed level upon which the output price has been estimated. At a subsequent stage, if the obtained firm rate of return is less than the allowed level, the firm can request an increase in the output price. It is well known that one disadvantage of rate-of-return regulation is that it may encourage inefficiency because the regulated firms have no incentive to decrease costs. For this reason, assessing the performance of regulated companies with respect to technical inefficiency is an important issue for government agencies. Measuring inefficiency of firms subject to rate-of-return regulation has been yet studied previously in the literature (see [1–4]). In particular, F？re and Logan [4] introduced and explored a regulated version of Farrell efficiency. Nevertheless, there are other alternatives to measure technical inefficiency in production theory. As Portela et al. [5] argue, on some markets it is not possible or is not desired to modify equiproportionately inputs or outputs. A well-known drawback of Farrell efficiency is the arbitrariness in imposing targets on the efficient frontier preserving the mix within inputs or within outputs, when really the firm’s very reason to change its input and output levels is often the desire to change the mix (see [6]). If so, an efficiency