efficiency in the public sector is often fraught with methodological difficulties.<sup>6</sup> 1 In consequence, many studies of efficiency in this context restrict attention to technical efficiency.<sup>6 2</sup> Much of the recent literature on efficiency of health care providers in the industrialized world has employed a statistical frontier model (see Dor 1994; F0rsund, Lovell, and Schmidt 1980; Li and Rosenman 2001; L6pez Casanovas and Wagstaff 1996; Rosko 1999; 2001; Vitaliano and Toren 1994; Wagstaff 1989b; Zuckerman, Hadley, and lezzoni 1994). The traditional cost function links costs to outputs, input prices, and-in the shortrun-capital stock. The cost frontier model extends this by introducing a term that represents the excess above the minimized cost, given the facility's outputs, input prices, and so on. Kutzin and Barnum use a frontier model to test for inefficiency in their sample of Chinese hospitals, but find none. Dor (1987), in his study of Peruvian hospitals, does not use a frontier model, but includes in his cost function a dummy variable to indicate whether the hospital is operated by the Ministry of Health (MoH) or the Social Security Institute (SSI). His findings suggest that the MoH hospitals are more efficient than those operated by the SSI. Inefficiency in a cost frontier model can be due to technical inefficiency, or input-mix inefficiency, or both. Wouters (1993), in her study of Nigerian facilities, explores the issue of input-mix inefficiency. She finds evidence in her sample of under-employment of health workers relative to non-health workers, and that inefficiency is greater in the private sector.

Another important issue confronting policy-makers is whether hospitals should be encouraged to specialize or to provide a broad range of services. Should hospitals, for example, provide both inpatient and outpatient care? Should hospitals providing inpatient services aim to treat most case types, or should they specialize? This is the issue of economies of scope-whether costs can be reduced by producing two or more products jointly. In many studies of health facilities, the functional form used in the regression analysis is too restrictive to explore this issue. Of the four studies surveyed by Wagstaff and Barnum (1992) only one employ a specification that is sufficiently general not to prejudge the issue of economies of scope. Both Anderson's study of Keynan hospitals and Wouters' study of Nigerian facilities employ a multiproduct Cobb-Douglas production, which, as Baumol, Panzar, and Willig (1982) note, implicitly assumes cost anti-complementarities and hence assumes diseconomies of scope unless there are sufficiently strong offsetting fixed costs. Dor's (1987) specification, in his study of Peruvian hospitals, is less rigid but is consistent with economies of scope only in the implausible case where the marginal cost of an outpatient visit is negative. Only in the Bitran-Dunlop study of Ethiopian hospitals is the model specification sufficiently general not to prejudge the issue of economies of scope. The results imply mild economies of scope-a result that is similar to that reported by Kutzin and Barnum in their analysis of Chinese hospitals.

> 61 First, the choice of inputs is often beyond the control of the individual facility individual facility (at least m the public sector). where there is discretion, price signals may be weak. Second, cost minimization may not be an appropnate behavioral assumption. For example, staff allocation may be driven by a policy to ensure minimum service standards. As a result, we should not necessarily expect to observe allocative efficiency.

> 62 In cases where the allocative efficiency in the health sector has been addressed, this has typically been done by comparing the ratio of marginal products to the ratio of staff remuneration for the respective categories. Marginal products are calculated on the basis of an estimated production function with, _inter alia,_ different categones of staff as its arguments (Goldman and Grossman 1983).

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