In his NYT column today Ross Douthat picked up on a line of attack initiated by Tyler Cowen last week: that the push for stimulus is asking politicians to take big risks based on a theory. To paraphrase a former president, this depends on what your definition of "theory" is.

We always take actions based on our expectation of how the world will respond. This expectation can be called a theory, since we have a whole set of postulates about how the universe behaves. If fire fighters hook up a hose to a fire hydrant, it is because they have the expectation that when the hose is connected, that water will run through it and that the water will quench the fire. We can follow Tyler Cowen and Ross Douthat and call the belief that motivates the fire fighters' actions a theory, but it is a theory that is grounded in considerable evidence.

Presumably Douthat and Cowen don't object to the fire fighters hooking up hoses to fire hydrants to put out fires; their concern is that the evidence for stimulus is weaker than the evidence that hoses connected to hydrants put out fires. To my mind, the evidence for the effectiveness of stimulus is roughly comparable to the evidence for the effectiveness of fire hoses hooked up to hydrants in putting out fires, but this would be a very long story.

It might be more interesting to note what passes for contradicting evidence in current debates. A few weeks ago, the NYT published a short piece by Edward Glaeser that showed no correlation between the amount of stimulus spending awarded by state and the change in the unemployment rate from January of 2009 and March of 2010. This piece of evidence against stimulus was promptly cited by David Brooks in his column the following week.

Should Glaeser's finding have left supporters of stimulus disappointed? Well, if we look to Glaeser's source, we would see that he was looking only at the $61.4 billion in stimulus spending on infrastructure projects that had been received by the states by the end of March of 2010, not the entire stimulus package.

There are several reasons why we would not have expected to find much of an effect in this analysis, first and foremost, its size. This money was awarded over a 13 month period over which GDP would have been almost $16 trillion. This means that Glaeser was looking for differences in the change in unemployment rates by state based on spending that was less than 0.4 percent of GDP over this period.

We would expect spending equal to 0.4 percent of GDP to increase GDP by roughly 0.6 percent of GDP, once the full multipler effects are felt (although not all within one state -- more later). According to the assumptions used by the Obama administration in laying out its stimulus plan, this would be expected to increase total employment by roughly 600,000 workers (some demand is met by increased hours per worker), or by just over 0.4 percentage points. Of course, this is the average gain in employment due to this spending, Glaeser was looking for differences in the change in unemployment based on differences in spending.

This would be difficult to detect even in a very stable economy. Picking up the impact of such a relatively small amount of spending over a period in which the unemployment rate rose from 7.7 percent to 9.9 percent would be virtually impossible even if the data were perfect, but they are not.

First, the measure of spending is money received by state, not money actually spent. Some states may spend money as soon as they get it from the federal government or possibly even beforehand, if they know it is coming. Other states may still be in the process of taking bids on contracts for some of this money even after they have received it. This means that there would be no close relationship between money received and the jobs created by the stimulus.

Second, we would not expect there to be a one to one relationship between stimulus per state and declines in the unemployment rate for two reasons. First, much of the money will support jobs that go outside of the state. Suppose New York City spends lots of money improving its infrastructure, thereby creating a large number of jobs. Many of the people hired will no doubt live in New Jersey and Connecticut. Glaeser's methodology would find little evidence that this spending lowered unemployment since the effect would be diffused throughout the three states. This would be the case with many states with metropolitan areas that overlap state boundaries.

This problem would be even more important with the indirect employment created by the respending of income. While some of this money may be spent on services provided in the local economy (e.g. hair cuts and restaurants), much of it will be spent on goods that were manufactured all over the world, making it even harder to detect any relationship between stimulus spending per state and changes in the unemployment rate.

A second reason why there could be little relationship between changes in unemployment rate by state and stimulus spending is that the unemployment rate measures people who are looking for work, not jobs. This number may actually rise when there are more jobs created. People often drop out of the labor force in a period of high unemployment because they feel it is futile to look for work. This means that they are not counted as being unemployed. When they start to see jobs being created, they begin to look for work again, raising the unemployment rate.

This effect is well-known. That is why economists who are seriously looking for a relationship between employment and stimulus spending would look at jobs created by state rather than changes in the unemployment rate. This would also help to get around the state spillover effect since we would look at which state the employer is in, as opposed to the state where the worker lives.

Finally, Glaeser's time periods do not coincide. He looking at spending that was allocated from mid-February 2009 until the end of March 2010. He compared this to the change in the unemployment rate from January 2009 to March of 2010. While the endpoints are reasonably close (the March data is compiled based on a survey conducted in the middle of the month), the start points do not match and it matters.

The unemployment rate rose from 7.7 percent to 8.2 percent between January 2009 and February 2009, an increase of 0.5 percentage points. Presumably we would not expect the state by state distribution of this rise in unemployment to be affected by a stimulus package that was not even approved until the following month. This one-month increase in the unemployment rate was larger than the expected effect of the stimulus.

In short, it would have been astounding if Glaeser's methodology had found a relationship between stimulus spending and changes in the unemployment rate by state, even if the stimulus was working exactly as predicted. Yet, this little exercise is taken as serious evidence against the effectiveness of the stimulus.

Getting back to the Douthat/Cowen complaint that the belief in stimulus is only a theory, it would not be difficult to create equally flimsy evidence showing the ineffectiveness of fire hoses in putting out fires. Fortunately, this evidence would not be taken seriously by anyone with fire fighting responsibility. The main difference between the theories of fighting unemployment with stimulus and fighting fires with water pumped through fire hoses is what is accepted as evidence against the theory. This takes us to the sociology of the economics profession, which is a very bad neighborhood.

What is a mild-mannered politician concerned about getting re-elected supposed to do? Well, there are theories about this as well. Most of them show that politicians do very badly in their quest for re-election in periods of high unemployment. So, it is not clear that the proponents of stimulus are asking politicians to take too great a risk when they suggest hooking up the fire hose and trying more stimulus.

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