Last week, the Congressional Budget Office released a report claiming that the $814 billion "stimulus" has added 3.4 million net jobs. This surely comes as a surprise to the 3.5 million Americans who have lost their jobs and remained unemployed since the stimulus was enacted in February 2009.

Such implausible analysis does not come from actually observing the post-stimulus economy. Rather, it comes from Keynesian economic models that have been programmed to conclude that government spending injects new dollars into the economy, thereby increasing demand and spurring economic growth. In other words, these models are programmed to conclude that stimulus spending always creates jobs and growth, no matter how the economy actually performs.

But there is one problem with the government stimulus theory: No one asks where Congress got the money it spends.

Congress does not have a vault of money waiting to be distributed. Every dollar Congress injects into the economy must first be taxed or borrowed out of the economy. No new spending power is created. It is merely redistributed from one group of people to another.

It is intuitive that government spending financed by taxes merely redistributes existing dollars. Yet spending financed by borrowing also redistributes existing dollars today. The fact that borrowed dollars (unlike taxes) will be repaid some years later does not change that.

Some believe stimulus spending is the mechanism by which the Federal Reserve injects new dollars into the economy. Yet the Fed could run the printing press and then inject those dollars into the economy by buying existing bonds (with mostly inflationary results). It doesn't need an expensive stimulus bill to conduct monetary policy.

Before spending $814 billion on the stimulus, Congress had to borrow it from some combination of the following three sources:

• Foreign countries. Government spending funded from foreign borrowing is no free lunch. Before China can lend America dollars, it must acquire them by running a trade surplus (which is a trade deficit for America). For example, American consumers spend dollars on Chinese imports (reducing Americas gross domestic product), and then China lends those dollars to the U.S. government to spend (increasing Americas GDP). The increased trade deficit exactly offsets the stimulus spending, leaving a net GDP impact of zero.

• Savers/investors. Much government spending is financed by borrowing from banks, businesses and individuals seeking a safe place to park their savings. Keynesian economics downplays savings — as if they fall out of the economy — and believes government can increase demand by borrowing and spending those savings.

In reality, savings do not fall out of the economy. They are invested, or deposited in banks that quickly lend them to others to spend. The financial markets exist to convert one persons savings into another persons spending. So when investors lend their savings to Washington to spend, it displaces private consumption and investment spending dollar-for-dollar.

• Idle savings. The only government spending that truly increases current purchasing is the amount that would have otherwise sat idle in safes and mattresses. Those are the only dollars not already circulating through the economy as consumption, or through the financial markets as investment spending.

Idle savings are rare. People and businesses generally invest or bank their savings, where the financial markets transfer them to other spenders. Banks that receive savings either lend them out to a spender, or (when afraid to loan) invest them conservatively to earn some interest. They are not hoarding customer deposits in massive vaults (beyond the required cash reserves).

And even if all these idle savings did exist, how would Washington acquire them for stimulus spending? After all, any idle savings would result from people not trusting the financial system or government with their money. So how could Washington acquire them to finance a stimulus?

To recap: All government stimulus spending requires first borrowing dollars that would have otherwise been applied elsewhere in the economy. The only exception is money borrowed from "idle savings," which for reasons described above likely constitute a minuscule portion of the $814 billion stimulus.

Yet Washington relies on Keynesian economic models that essentially assume that (in a recession) every dollar of government purchases raises GDP dollar-for-dollar — which could be true only if 100 percent of government spending was borrowed from idle savings to create new demand. That is implausible.

Once it becomes clear that government spending only redistributes existing demand, the case for "stimulus" spending collapses.

Yes, government spending can recirculate through the economy via the multiplier effect. But the same dollars would have recirculated through the private economy had they not been lent to Washington.

Yes, in a recession, Washington can spend $814 billion putting idle factories and people to work. But that requires first borrowing $814 billion of spending power out of the private sector, which — by the same logic — will result in idle factories and workers in the locations that financed the stimulus.

In that sense, government spending is the equivalent of removing water from one end of a swimming pool, dumping it in the other end, and then claiming to have raised the water level.

Economic growth requires raising worker productivity to create more goods and services. Government stimulus spending represents a naive "magic wand" attempt to create purchasing power and wealth out of thin air.

No wonder the unemployment rate remains high.

• Brian Riedl is Grover M. Hermann fellow in federal budgetary affairs at the Heritage Foundation.