Like most people, economists love a mystery – especially if it involves not a missing person but a missing $2.9 trillion in United States debt.

That's $2.9 with 11 zeros after it.

Some words of explanation: Every quarter the Department of Commerce comes up with the US "International Investment Position." At the end of 2006, for instance, the US had a net negative position – by this measurement of international assets and liabilities – of $2.6 trillion. In other words, the country is by far the world's biggest debtor nation.

A quarter century ago, the US was the world's largest creditor nation.

The economists at Commerce count American-owned private assets in foreign nations (plants, equipment, retail outfits, property, corporate stocks and bonds, etc.), US official international reserves (gold, special drawing rights, foreign currencies), and other US assets abroad. The measurements get complicated. Then these economists count what foreigners own of American assets, looking at the same list of assets.

Subtracting the value of American international assets from what foreigners own of American assets, they come up with how much Americans are in debt to other nations and their peoples.

But if you look at the current account of the US balance of payments, which measures primarily the balance of trade, and also flows of interest and dividends, foreign aid, and other international transfers, the US should be far deeper in hock – $2.9 trillion more over the years from 1990 through 2006 than the official $2.6 trillion. Every month, the Commerce Department has reported huge deficits in trade and the broader current account. These deficits have to be financed somehow by foreigners, and so the US should be piling up its international debts in grand style.

Last year the US international deficit was running at a level equivalent to 6.5 percent of our gross domestic product, the nation's total output of goods and services. In a sense, Americans were living 6.5 percent better than they would if they weren't putting on the national tab, in effect, so many toys, shirts, computers, etc.

"Why aren't we more indebted?" asks Barry Bosworth, an economist at the Brookings Institution in Washington.

One related mystery is that American investments in foreign nations earn a much higher rate of return than do the investments by foreigners in the US.

"Why?" asks Mr. Bosworth in a working paper written with Susan Collins of the Gerald Ford School of Public Policy in Ann Arbor, Mich., and a graduate student, Gabriel Chodorow-Reich.

One-third of the gap in the return on investments can be attributed to US corporations reporting "extra" income in low tax jurisdictions of their foreign affiliates, the National Bureau of Economic Research paper finds. For example, Microsoft sells its software in foreign countries from an affiliate in Ireland – after making some changes in the software, says Bosworth. There, it pays only a 10 percent tax on its corporate profits, rather than the 38 percent corporate rate in the US. Other US firms set up affiliates in such tax havens as Barbados, the Bahamas, and Bermuda.

US firms are "quite aggres­sive" in taking advantage of such tax havens, notes Bosworth. It probably means that these companies avoid billions of dollars in taxes that otherwise would go to Uncle Sam. It also distorts the official balance-of-payments figures. "The data are very bad," says Bosworth.

Another economist intrigued by this international investment mystery is Pierre-Olivier Gourinchas of the University of California, Berkeley. He finds that the reason the US is earning so much more on its foreign assets than it is paying on its foreign liabilities is partly because US investors often take more risk and thus get a higher return. The American money goes into foreign direct investment (plant and equipment, etc.) and into foreign stock, for example. Many foreigners, especially central banks, tend to be more cautious in choosing American investments. They buy ultrasafe US Treasuries or relatively safe bonds issued by US corporations, for instance. "The US offers nice, liquid, safe investments," says Professor Gourinchas. The risk of default can be low.

The US is an entrepôt, says Jane D'Arista, of the Financial Markets Center, Philomont, Va. That is, it takes in savings from the world at relatively low cost and invests some of that money abroad at a higher return.

There's more to the mystery than that, however. One advantage for the US is that the dollar is the primary currency used in international reserves of other nations and for invoicing international trade and investment, such as for oil and other commodities.

So when the dollar loses value, foreign holders of dollar assets lose on their dollar investments. Almost all US foreign liabilities are in dollars and about 70 percent of US foreign assets are in foreign currencies.In what Gourinchas calls an "eye-catching, back-of-the-envelope calculation," a 10 percent depreciation of the dollar represents a transfer of 5.3 percent of US GDP from the rest of the world to the US. America's GDP is currently $13.7 trillion, and the dollar is down 20.6 percent since 2002. So foreigners have – in effect – given the US about $1.3 trillion.

It's not really that simple, emphasizes Gourinchas. Nonetheless, the US has had a free lunch.