ONLY 21 states require students to attend high school until they graduate or turn 18. The proposal President Obama announced on Tuesday night in his State of the Union address — to make such attendance compulsory in every state — is a step in the right direction, but it would not go far enough to reduce a dropout rate that imposes a heavy cost on the entire economy, not just on those who fail to obtain a diploma.

In 1970, the United States had the world’s highest rate of high school and college graduation. Today, according to the Organization for Economic Cooperation and Development, we’ve slipped to No. 21 in high school completion and No. 15 in college completion, as other countries surpassed us in the quality of their primary and secondary education.

Only 7 of 10 ninth graders today will get high school diplomas. A decade after the No Child Left Behind law mandated efforts to reduce the racial gap, about 80 percent of white and Asian students graduate from high school, compared with only 55 percent of blacks and Hispanics.

Like President Obama, many reformers focus their dropout prevention efforts on high schoolers; replacing large high schools with smaller learning communities where poor students can get individualized instruction from dedicated teachers has been shown to be effective. Rigorous evidence gathered over decades suggests that some of the most promising approaches need to start even earlier: preschool for 3- and 4-year-olds, who are fed and taught in small groups, followed up with home visits by teachers and with group meetings of parents; reducing class size in the early grades; and increasing teacher salaries from kindergarten through 12th grade.

These programs sound expensive — some Americans probably think that preventing 1.3 million students from dropping out of high school each year can’t be done — but in fact the costs of inaction are far greater.

High school completion is, of course, the most significant requirement for entering college. While our economic competitors are rapidly increasing graduation rates at both levels, we continue to fall behind. Educated workers are the basis of economic growth — they are especially critical as sources of innovation and productivity given the pace and nature of technological progress.

If we could reduce the current number of dropouts by just half, we would yield almost 700,000 new graduates a year, and it would more than pay for itself. Studies show that the typical high school graduate will obtain higher employment and earnings — an astonishing 50 percent to 100 percent increase in lifetime income — and will be less likely to draw on public money for health care and welfare and less likely to be involved in the criminal justice system. Further, because of the increased income, the typical graduate will contribute more in tax revenues over his lifetime than if he’d dropped out.

When the costs of investment to produce a new graduate are taken into account, there is a return of $1.45 to $3.55 for every dollar of investment, depending upon the educational intervention strategy. Under this estimate, each new graduate confers a net benefit to taxpayers of about $127,000 over the graduate’s lifetime. This is a benefit to the public of nearly $90 billion for each year of success in reducing the number of high school dropouts by 700,000 — or something close to $1 trillion after 11 years. That’s real money — and a reason both liberals and conservatives should rally behind dropout prevention as an element of economic recovery, leaving aside the ethical dimensions of educating our young people.

Some might argue that these estimates are too large, that the relationships among the time-tested interventions, high school graduation rates and adult outcomes have not been proved yet on a large scale. Those are important considerations, but the evidence cannot be denied: increased education does, indeed, improve skill levels and help individuals to lead healthier and more productive lives. And despite the high unemployment rate today, we have every reason to believe that many of these new graduates would find work — our history is filled with sustained periods of economic growth when increasing numbers of young people obtained more schooling and received large economic benefits as a result.

Of course, there are other strategies for improving educational attainment — researchers learn more every day about which are effective and which are not. But even with what we know, a failure to substantially reduce the numbers of high school dropouts is demonstrably penny-wise and pound-foolish.

Proven educational strategies to increase high school completion, like high-quality preschool, provide returns to the taxpayer that are as much as three and a half times their cost. Investing our public dollars wisely to reduce the number of high school dropouts must be a central part of any strategy to raise long-run economic growth, reduce inequality and return fiscal health to our federal, state and local governments.