of Table 8-4, helps large cities but still leaves them at an performance level well below the 25th percentile of the current distribution!

Related simulations in Duncombe and Yinger (1998b) make the key point here in a different way. Consider, the notion of a "performance gap," defined as the sum across districts of the amount by which actual district performance falls below the performance standard, weighted by the number of students in the district. Duncombe and Yinger show that with the foundation level (and implicit performance standard) set at the 25th percentile of the 1991 performance distribution and a required minimum tax rate, an expenditure-based foundation plan would close only 36 percent of the current performance gap in New York. In contrast, a comparable, and equal-cost performance-based foundation plan would close 84 percent of performance gap (and would close 100 percent of the gap if all districts met the baseline efficiency standard). The point should be clear: expenditure-based foundation plans, which are used in most states, leave many high-cost districts short of even a minimal performance standard.

A state cannot implement a performance-based aid program without estimating a cost index. As noted earlier, an aid program for municipal services, including education, based on an estimated cost index was implemented in Massachusetts (Bradbury et al., 1984), and school aid programs based on estimated cost indexes are presented in Ratcliffe et al. (1990) and Downes and Pogue (1994). However, the cost indexes estimated in these cases do not control for efficiency. Thus, we now examine performance-based foundation programs that incorporate a cost index estimated without controlling for efficiency and that implicitly assume, following Equation 2, that all districts are efficient. A cost index estimated in this way is biased, because the omission of an efficiency variable biases the coefficients of the included cost variables, but it takes a large step toward recognizing the role of input and environmental cost factors.

Results for these programs, presented in the third column of Table 8-4, reveal that in most cases adding a cost index closes a large share of the gap between the expenditure-based foundation in the fifth column and the complete performance-based foundation in the second column. Under the most generous plan (75th percentile), for example, adding a biased cost index raises performance in upstate large cities from 64.2 (column 5) to 100 (column 3), compared to the complete-information performance (column 2) of 104.7.

In contrast, the foundation plan based on a biased cost index leads to higher aid and higher performance for downstate small cities and suburbs than either the expenditure-based foundation or the complete-information foundation in the second column. As explained earlier, this result mainly reflects the large, negative correlation between efficiency and wage rates; because of this correlation, leaving efficiency out of the cost equation biases upward the coefficient of the wage variable and hence biases upward the cost index in places, like downstate districts, with high labor costs.18 In effect, therefore, an aid program based on a



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