methods can be found in Guthrie and Rothstein, 1999; Duncombe and Yinger 1999; and Odden and Busch, 1998.) The first and second of these approaches usually depend on states' having sophisticated student achievement testing systems that provide standardized statewide measures of student performance, with data linking this performance to student background characteristics. In states where such testing systems do not exist, then the third and fourth approaches, based on professional judgment or whole-school designs, seem at present to be the only alternatives, where "getting to adequate" necessitates building instructional resource models to which costs can subsequently be assigned.

Each of these alternatives results in an estimate of the cost of an adequate education for a presumed or hypothetical typical student. Conceptually the next step must then be to adjust this cost (or perhaps redefine the goal of adequate outcomes) for students in different socioeconomic circumstances and locations. The statistical analysis approach accomplishes this second step simultaneously with the step of identifying costs for the typical student. It is important for explanatory purposes, however, to keep the two steps separate, and we address cost adjustments explicitly in the following section. Separating the steps permits us to give appropriate attention to the cost adjustment issue and also to make clear that methods of cost determination may have different strengths and weaknesses, depending on whether they are being used to find average costs or to adjust costs for student and district differences.

Inference from Outcomes by Statistical Analysis

This approach represents the efforts of econometricians to apply the tools of statistical modeling to the determination of educational costs. The approach originated in efforts to determine how intergovernmental aid formulas should be adjusted to take into account public service costs beyond the control of local jurisdictions. Researchers tried to develop cost indices that would measure how much higher (or lower) the costs of providing a given level of services were in each district compared with a statewide average. Thus, initially, the studies focused exclusively on the differences in costs, with little attention paid either to the particular service level or what it would cost a typical district to provide that level. More recent studies have extended the approach, so that a specific service level (defined, for example, in terms of the percentage of students achieving various educational goals) can be specified and the cost of providing that service estimated for the district with average characteristics. Ladd and Yinger (1994) and Downes and Pogue (1994) made important theoretical contributions on which have been constructed cost models applied to education data from New York (Duncombe and Yinger, 1999) and Wisconsin (Reschovsky and Imazeki, 1998).

Rather than attempting to determine the costs of an adequate education as the sum of the costs of individual instructional components, statistical models take a "black-box" approach, choosing an acceptable level of pupil performance or

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