(FORTUNE Magazine) – Long the pet of free-market theorists, the idea of using vouchers to make schools compete has gone mainstream. In New York City, Mayor Rudolph Giuliani is advocating the use of public funds for vouchers to private schools (and started a brawl with his schools chief by doing so). In Florida, Governor Jeb Bush is pushing a plan to give them to students from public schools with subpar performance records. Milwaukee's voucher program boasts 15,000 students. And when billionaire investor Ted Forstmann and friends recently offered 40,000 private-school scholarships to students from low-income families, more than a million families entered the lottery, including about a third of those eligible from New York City.

Would increased competition among schools improve the quality of education? That's the bottom line--and American experience, however unwittingly, constitutes a spontaneous test of exactly this question. At the elementary and secondary levels, our educational system is largely a collection of local monopolies, and the outcomes are often disappointing. But higher education is extremely competitive, and U.S. colleges and universities are the best in the world.

Critics of the voucher concept argue that what works for higher education would not work lower down the education ladder. Vouchers, they say, would strip the public schools of their better students while robbing them of the money needed to educate the rest. In fact, the outcome could be considerably more cheerful. Look at the evidence of Harvard economist Caroline Minter Hoxby in her study "Do Private Schools Provide Competition for Public Schools?" (National Bureau of Economic Research Working Paper No. 4978).

School competition varies substantially across U.S. counties, Hoxby notes, largely because of differences in religious affiliation. Nationwide, about 80% of private schools are run by the Catholic church. It should come as no surprise, therefore, that counties with more Catholics typically have more private schools. The result? Rather than eviscerating the public schools, Hoxby reports that in those counties "greater private-school competitiveness significantly raises the quality of public schools, as measured by the educational attainment, wages, and high school graduation rates of public school students." Competition achieves these results not just for Catholics but for students of all denominations--without significantly changing spending per pupil in the public schools.

Teachers' unions have long opposed voucher plans. Monopolists, after all, rarely give up that status, even if they have their own doubts about quality of service: In Chicago, a pro-voucher city official involved with education reform says that most of the city's teachers send their own children to private schools. Yet vouchers could serve teachers well, Hoxby finds, because the evidence is that "public schools react to greater competitiveness of private schools by paying higher teacher salaries."

The reason that competition can raise both student performance and teacher salaries without costing much more might lie in keeping a lid on school bureaucracies. New York's public schools have more than ten times as many administrators per student as the city's Catholic schools. This drains financial resources from teaching; it may also erode school performance. "Excessive regulation undermines the professionalism and vitality of teachers and principals, leading many good people to leave the profession," argues John Chubb of the Brookings Institution, a center-left think tank, in a 1990 study. "Political conflict increases, and despite lots of good intentions the system grows more bureaucratic, less manageable, and less successful."

If the economic history of the 20th century teaches us anything, it is that an economy based on free and competitive markets serves consumers better than one based on central planning by the government. Schoolchildren, too, should enjoy the benefits of that lesson.

N. GREGORY MANKIW is a Harvard economics professor and author of Principles of Economics.