It's one thing to put a price tag on something. It's another to figure out its cost.

Consider education. Every year, taxpayers invest $14,400 per student in the District of Columbia school system. That's a lot, considering that fourth- and eighth-graders there scored dead last in the nation on the 2007 National Assessment of Educational Progress.

Those raw numbers don't include the hidden costs, especially the lives damaged or ruined when children get a subpar education or drop out altogether. Yet few attempt to quantify the total cost of our nation's failing education program. Most politicians and education activists are content simply to call for more spending, even if it's throwing good money after bad.

Oddly, though, many are eager to lay out the cost of our supposedly failing military operation in Iraq.

The latest attempt is by Joseph Stiglitz, a Nobel Prize-winning economist from Columbia University, and Linda Bilmes of Harvard University. Their new book says the war will cost at least $3 trillion. Including the cost of the war in Afghanistan, they write, the total could approach $5 trillion.

Now, it's usually pointless to argue dollar figures with an economist. As the old joke says, if an economist were trapped in a well, to get out he'd "assume he had a ladder." So we should focus on the assumptions an economist is making.

To reach their figures, Mr. Stiglitz and Ms. Bilmes assume that "expenditures on the Iraq war have no benefits [for America]." That's simply not true.

For one thing, the war has allowed thousands of terrorists to meet their Maker. Last year the Pentagon estimated 19,000 enemy militants had been killed since 2003. That number has certainly risen since. Another 25,000 militants are in military custody. That's quite a few dangerous individuals no longer around to attack Americans.

Our military intervention also has allowed Iraqis to experience freedom, something they were systematically denied during the decades Saddam Hussein ruled their country.

Iraq is the first Middle Eastern country with a constitution written by its citizens. Iraq's government may be imperfect, but at least it has democratic legitimacy - unlike neighboring Iran, Saudi Arabia or Syria.

In addition, the wars have given millions of women basic human rights they were denied by their oppressors. Under the Taliban, for example, Afghan women weren't allowed to go to school, let alone work or vote. Today women serve in Afghanistan's elected legislature.

Meanwhile, the Iraqi government is expanding its authority. Recently, Iraqi troops - without help from Americans - pushed into Baghdad's troubled Sadr City. They took control of the area without facing any significant resistance. That follows a similarly successful mission in Basra.

Mr. Stiglitz and Miss Bilmes have based their analysis on a patently false assumption. Why? Because they are making a political argument, not a serious economic study. They seem to want a complete pullout as quickly as possible. As Ms. Bilmes put it in an interview, even the withdrawal plans being discussed on the presidential campaign trail are "not as rapid as one might hope."

A precipitous pull-out would pretty much guarantee failure on the Iraqi front in the war on terrorism. It makes sense only if you assume, as do Mr. Stiglitz and Ms. Bilmes, that the war in Iraq is lost. But that's another false assumption.

The United States hasn't lost. Not by a long shot. The "surge" strategy has made major gains, opening the path to victory. And that's helping us make gains elsewhere.

Researchers from Simon Fraser University in Canada find global terrorism is declining. Their Human Security Report Project found fatalities from terrorist attacks have decreased 40 percent since 2001. That's a very tangible benefit - for America and the world.

Yes, winning a war is expensive. But losing would be even costlier. And you can't put a price tag on true victory.