costs, that voters are rational and well informed about educational quality. If not, we can't utilize voting behavior to define adequacy.

Because assumptions of this kind are so necessary before modeling can be interpreted, the seemingly precise results of the models reflect the imprecision of the assumptions. Unless we can become more satisfied with the precision of the assumptions, we cannot conclude that statistical modeling is a more precise means of estimating the cost of adequacy than is the informed judgment of policymakers and professionals. This should not be surprising. While econometric modeling of the costs of education is relatively new, this aid to policymaking has long been used in other social policy fields. And while econometricians plausibly defend the validity of their conclusions, they have not been able to persuade policymakers that particular models can effectively predict, for example, whether a minimum wage increase will cause unemployment, whether trade agreements cause job relocation, whether higher welfare benefits reduce poverty, or whether interest rate reductions are inflationary. In each of these cases, conclusions from modeling may challenge commonsense misconceptions and may help to inform debates, but cannot resolve them.

We do not mean to suggest that these modeling exercises in education are not important or useful. Quite the contrary. They hold great academic and theoretical interest, and may suggest insights that would stimulate productive further research into the relationship between spending and student achievement. We consider, for example, the Duncombe and Yinger findings of widely different costs for New York City using direct and indirect methods of estimating achievement to be a particularly provocative call for further investigation.

Because the technology of calculating "adequacy" is so primitive, it can be very useful to compare, for a given state, the costs of adequacy determined by these statistical methods with the costs determined by alternative approaches described below (empirical observation and professional judgment). If the results of the three approaches differ significantly, this should cause policymakers to reexamine the assumptions in each of the models to determine, if possible, which variations in assumption are driving the differences. There is no state, however, where such an exercise has been conducted.

At the most practical level, because of its technical complexity, there is little chance that statistical modeling can be proposed to any state as the primary means of calculating the cost of an adequate education or as the primary way of estimating how the costs of education may vary from place to place or from student to student. Ultimately, when courts demand or legislatures determine that an adequate education be funded, they will require a calculation of this adequacy that seems intuitively reasonable, that is understandable to reasonably well-educated policymakers, and that can be explained to constituents. For such calculations, other methods are required. These other methods must rely upon assumptions about educational productivity that are no less intuitive than the assumptions made by modelers, but in these other methods, the assumptions are more explicit,



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