My main point is that the debate concerning choice in education has seriously neglected one important variable in the form of special costs that are unique to the public system. These relate to the deadweight losses (welfare costs) associated with the tax collection necessary to finance government schools. From recent estimates they amount to between 50 and 80 cents per marginal dollar of revenue raised. This point is of enormous consequence for the whole discussion and is particularly pertinent, for instance, to the "Coleman debate" on the relative efficiency of private and public schools. The severest critics of Coleman's results claim that his evidence shows no appreciable difference in efficiency between the two types of institutions. Once we correct for the omitted variable (the welfare costs of taxation) the balance is swung unambiguously in favor of Coleman's private schools. The market system that Levin focusses upon, meanwhile, refers to a narrow version of it, namely the voucher system. Since this system also requires tax revenues to finance it, it also suffers the extra welfare costs of taxation in comparison with the completely free market in education. Because, however, the voucher system will bring increased choice, and therefore introduce some meaningful competition, it too is predictably relatively more efficient than the conventional public school system.

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Journal Economics of Education Review
West, E.G. (1991). Public schools and excess burdens. Economics of Education Review, 10(2), 159–169. doi:10.1016/0272-7757(91)90006-B