Duncombe and Yinger (1999). Using data from 631 school districts in New York, they estimated the average effects on district spending of the following "cost factors," that is, characteristics of each district that are outside the immediate control of school officials that affect the costs of educating students: input prices, district size, percentage of children in poverty, percentage of female-headed households, percentage of students with severe disabilities, and the percent of students with limited English proficiency. This work is more sophisticated than other efforts to develop cost estimates in that the authors use a creative (but somewhat controversial) method to control for the relative efficiency or inefficiency of each district and in that they explicitly account for the fact that educational outcomes, spending on education, and production are all simultaneously determined.

Emerging from their analyses are estimates of cost indices for each district. A district's cost index is 100 if it has average values of all the cost factors, exceeds 100 to the extent the district faces a harsher than average environment for educating students (as measured by its cost factors), and is less than 100 to the extent that the district faces a less harsh environment for educating students. For example, based on their most complete model, the authors estimate that the cost indices for the state's upstate large cities (which include Buffalo, Rochester, and Syracuse) average 189. This figure implies that the cost of providing an adequate education in those districts would exceed the cost of adequacy for the average district by 89 percent. In contrast, costs in 47 small upstate cities are estimated to exceed the average by only 9 percent, while those in upstate suburbs fall short of the average by about 9 percent. The most striking cost indices are for Yonkers (with a cost index of 192) and New York City, with a cost index of 397. (All figures are in Duncombe and Yinger, 1999: Table 8-2, column 2). Taken literally, the New York City estimate would imply that the city would need almost four times as much revenue per pupil as the typical district to educate its students to an adequate level. However the estimates for New York City are quite dependent on the particular specification of the equation and range from 112 to 397. These very large differences underscore the challenges of specifying the model correctly.

This econometric approach to estimating cost differentials highlights the important observation that education costs may well vary quite dramatically across districts depending on the characteristics of the district. As Duncombeand Yinger document, their estimated cost indices exhibit much greater variation across districts than those based on the weighted pupils method currently used by New York State, which weights secondary, disabled, and other-at-risk students more heavily than the typical student, or those based on average teacher salaries. The implication is that relative to the district with average cost factors, the state is currently providing inadequate assistance to some districts (those with high cost indices) and is giving relatively too much state assistance to other districts (those with low cost indices).

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