Estimating output substitutability of hospital services: A distance function approach

The purpose of this paper is to provide hospital specific estimates of the relative marginal costs and elasticity of transformation of hospital services (acute inpatient days, intensive care inpatient days, number of surgeries, and number of ambulatory care plus emergency room visits) using recently developed empirical techniques. One of the major goals of this paper is to provide an illustration of these empirical techniques to estimate multiple output technology, which we feel is particularly useful for the case of the hospital sector. Following Färe and Grosskopf, we estimate a multiple output distance function (a generalization of scalar-valued production functions) which is dual to the more familiar revenue function, and employ a dual Shephard's lemma to retrieve revenue-deflated shadow prices of hospital services. These shadow prices reflect the real resource use (opportunity or marginal cost) of producing an additional unit of some output. These can then be used to calculate marginal rates of transformation and Morishima elasticities of substitution among hospital services as well. The output distance function is extremely flexible and readily models multiple output technology without requiring input price data. This allows us to finesse the problem that salary information is not available for doctor services. We apply this technique to a sample of private not-for-profit and public hospitals operating in California and New York.