Explainer: Understanding fiscal multipliers

It has been five years this month that President Obama signed an $816.3 billion fiscal stimulus package, known as the American Recovery and Reinvestment Act, into law. Has it worked?

To answer this question, economists look at something known as the expenditure multiplier. It tells us how a change in consumption, investment, net exports or, in this case, government spending and tax changes, impacts GDP. For example, if the expenditure multiplier is 1.5, then every dollar of new government spending generates $1.50 of new GDP.

How is it possible for a $1 change in government spending to translate into more than $1 in economic growth? In traditional Keynesian models, the key to understanding the multiplier is first to recognize that money spent purchasing goods and services translates into income for the store owner and the people who provided the raw materials used to produce the product. Second, income generated from that initial sale is used to purchase even more goods and services.

For example, if the government spends $1,000 on a new desk - which increases GDP by $1,000 - the $1,000 covers the wages of the people who made the desk, the cost of the raw materials and the profit that goes to the owner of the furniture store. In other words, $1,000 of income is created from selling the desk.

Part of that income will be saved and part will go to taxes -- say, $400 for both, leaving $600 in income to be used to purchase new goods and services. When those goods and services are purchased, GDP goes up by another $600, and $600 in additional income is created at the same time. Notice that the total increase in GDP at this point -- $1,000 plus $600 - is greater than the initial change in government spending of $1,000.

This process then continues, part of the $600 will be saved, part will go to pay taxes, and the rest will be used to purchase goods and services, and so on.

In this particular example, if we add up the total change in GDP arising from the initial $1,000 in GDP, it would amount to $2,500, implying a multiplier of 2.5. Actual multipliers are smaller than that, probably closer to 1.5 in severe recessions (when multipliers are the largest). That means a $1,000 increase in government spending leads to approximately a $1,500 change in GDP, which should also increase employment.

In modern "New Keynesian" models, the mechanism producing the multiplier is a bit different. It arises from how the change in spending alters expectations about the future course of the economy. But the bottom line is the same -- the government spending multiplier in deep recessions is greater than one, and likely around 1.5 (there is a large range of estimates in the economics literature, but a value of 1.5 seems like a reasonable estimate of what most economists believe based upon this econometric work).

Returning to our initial question, it's important to note that the 2009 stimulus wasn't just government spending: 36 percent of the package - $290.7 billion dollars - came in the form of tax cuts, and the multiplier is smaller for tax cuts than for government spending. The reason is that while government spending impacts GDP one for one on the initial sale of goods and services, tax changes have a smaller impact.

An increase in taxes, for example, will be paid partly by reducing consumption which has multiplier effects, and partly by reducing saving, which does not. Conversely, a tax cut will be used partly for consumption, and partly to increase saving. Thus, for example, if 25 percent of the tax cut is saved, the initial impact of a $1,000 tax cut will only be $750, and the subsequent multiplier effects described above will be smaller as well (the total effect would be 2.5 x $750 = $1,875, instead of 2.5 x $1.000 = $2,500).

Since there is evidence that in recovering from the financial crisis U.S. households used tax cuts to rebuild the loss of retirement and education saving, and to offset losses of home equity, there is reason to believe that the tax cuts were not as effective as government spending at stimulating the economy.

It's clear in retrospect that the stimulus package was too small and ended too soon, and thus did not have as large of an impact as hoped. But it still mattered. As economist Paul Krugman says, "everything we have seen since 2009 confirms that expansionary fiscal policy is expansionary... There is every reason to believe that the Recovery Act boosted GDP and employment while it was in effect relative to what would have happened without it."

To quantify precisely how much fiscal policy mattered, fiscal policy multipliers are an essential tool.