Local Stimulus: Some Quick Unemployment Math

In the same spirit as Paul Krugman, who in his New York Times Blog did a quick back-of-the-envelope calculation on the expected effects of the Obama federal stimulus plan on unemployment, let's take a look at Mayor Adams's plan to stimulate the local economy.  My question is: is the claim that 5000 new jobs will be created by this spending reasonable?

Estimates of the Okun's law coefficient, or the relationship between real GDP growth and declines in the unemployment rate are generally between 2 and 3 for the national economy.  Let's take the best-case scenario, 2, which stipulates that a 2% increase in GDP will lead to a 1 percentage point decrease in unemployment.  I think this is reasonable, though I am not sure how to think about leakages: presumably leakages are greater the more localized is the stimulus spending so perhaps 2 is too high, but I'll stick with it for the time being.  

The Adams administration proposes to spend $500 million on local stimulus.  The latest Bureau of Economic Analysis estimate of Portland metro area GDP is around $100 billion.  Thus the proposed stimulus amount represents about a half a percent of local GDP.  

How much will this increase local GDP?  For this we have to think about the multiplier effect we expect from the spending.  The multiplier refers to the fact that money that becomes income for one person is spent, at least in part, on other things and becomes income for someone else, and so on.  How big is this multiplier in reality?  Mark Zandi suggests slightly more than 1.5 is a reasonable estimate.  Let's be conservative and use 1.5, which means that a $500 million injection of government money would represent about a $750 million boost to local GDP, or about 0.75 percent.  

Using the Okun's Law coefficient of 2, this suggests about a 0.375 percentage point decrease in unemployment from what it otherwise would have been.  

Finally, the latest local jobs report from the Bureau of Labor Statistics shows the Portland metro area labor force at about 1.19 million, of which 85,700 are currently unemployed (for a rate of 7.2%).  Using the current rate as a baseline, the proposed stimulus could be expected to reduce unemployment to 6.825%.  This represents about 4,460 new jobs.  Slightly lower than the Mayor's claim, but well in the ballpark.  

However, if you use the more pessimistic Okun's Law coefficient of 3, you get a .25 percentage point decrease in the unemployment rate which would yield about 3,000 new jobs, which is considerably under the Mayor's projections.

So the conclusion seems to be that they are being optimistic, but not wildly so.  

What is interesting to think about now is the interaction between federal stimulus, state stimulus and local stimulus: will they be complements or will there be some type of crowding out?  Perhaps public finance-types have some insight...