The new $787 billion stimulus bill has tax cuts to encourage households and businesses to spend more. It’s got a lot of new government spending, too. We hope that all this new spending will give businesses a reason to produce more goods and services and hire more employees. The policy analysts in Washington use huge computer models to estimate the impact of the stimulus. But we can make a guess on the back of an envelope.

To do this, we need to answer three questions. First, how low is the unemployment rate when the economy is doing well? This is sometimes called the “natural rate of unemployment.” It’s the unemployment rate when inflation is neither rising nor falling.
The natural rate is a little hard to pin down. During the mid-1990s, we thought it was about 6 percent. Later in the decade, though, the unemployment rate got lower and the inflation rate didn’t go up. The Congressional Budget Office uses a natural rate of 4.8 percent in their calculations. Let’s use 5 percent to make the arithmetic easier.

Suppose the unemployment rate hits 9 percent this year and stays there through 2010. Those would be the worst unemployment rates since 1982-83. A 9 percent unemployment rate is 4 percent higher than the natural rate. People are without jobs, and the goods and services they would have produced don’t get produced. Gross domestic product (GDP) is less than it could be.

To know how much less, we need to answer a second question. How much does gross domestic product change when the unemployment rate changes? This is a relationship called “Okun’s Law,” after Arthur Okun, an economist in the Kennedy administration. Okun found that each 1 percent drop in the unemployment rate resulted in a 3 percent addition to GDP growth. I get a number closer to two, using Okun’s method with data since 1960.

So, if the unemployment rate is 4 percent higher than it should be, by Okun’s Law, GDP must be 8 percent lower than it ought to be. GDP is running around $14.3 trillion. That would mean it could have been about $15.5 trillion if unemployment was at the natural rate. At 9 percent unemployment, GDP would be about $1.2 trillion too low.

So, if the unemployment rate is 4 percent higher than it should be, by Okun’s Law, GDP must be 8 percent lower than it ought to be. GDP is running around $14.3 trillion. That would mean it could have been about $15.5 trillion if unemployment was at the natural rate. At 9 percent unemployment, GDP would be about $1.2 trillion too low.

That’s the gap in the economy that the stimulus spending is meant to fill. But there’s more to stimulus spending than meets the eye. If a household spends a dollar, or the government spends a dollar, it becomes income for someone else. That person will spend a part of that dollar, which will become income for another person, who will spend part of it, too. That’s the famous “multiplier effect.” The effect of a dollar spent on total GDP is greater than one dollar.

The multiplier is the answer to the third question: How much does each dollar of spending contribute to GDP? Not all of each extra dollar can be spent. Some must be paid in taxes. Some is saved. Some is spent on imports, which stimulate another country’s economy.

Add up all those “leaks” from spending, and I get about 57 cents on the dollar. If that’s right, when the government spends a dollar, the employee who earns it spends 43 cents.

The business that receives that income spends 43 percent of 43 cents, which is 18 cents, and so forth. Eventually, you’ll get about $1.75 in total spending, for the first dollar and all the added amounts. Our multiplier is 1.75.

We expect a $1.2 trillion gap in GDP. If each one dollar in stimulus gives us added GDP of $1.75, then we need about $700 billion to fill that gap, for each year that unemployment is 9 percent. If it stays at 9 percent for two years, we need $1.4 trillion in stimulus. The $787 billion stimulus bill is huge, but - I’m amazed to type — it’s too small.

The stimulus is not the only thing we’re trying. The Federal Reserve has cut its interest rates to near zero. The Treasury is trying to figure out how to buy up bad assets in banks. There’s a new program to help homeowners avoid foreclosure. We’ve got a really big GDP gap, but taking all of this together, maybe we can fill it.

The views and opinions expressed in this column are those of the author and not necessarily those of Farm World. Readers with questions or comments for Larry DeBoer may write to him in care of this publication.