Some people are claiming that Obama's job package will cost $280,000 per job. The actual cost is not trivial, but I don't think that figure is correct (it simply divides a proposed stimulus amount, $700 billion, by the stated job goal of 2.5 million). I've also seen the claim that the $700 billion number is simply pulled out of a hat, but that's not right either, it's based upon transparent calculations.

(The calculations follow along the lines of Krugman). GDP last year was around $14 trillion dollars, and the labor force is in the neighborhood of 155 million people.

Suppose we expect a 3.5% unemployment gap (that is, we expect a shortfall of 3.5% of 155 million, or 5.425 million jobs).

By Okun's law - which states that a 1% change in unemployment translates into a 2% change in output - this means we expect a 7% shortfall in output. Now, 7% of $14 trillion is, with rounding, a trillion dollars (actually $980 billion, but close enough for government stabilization work).

The government expenditure multiplier is approximately 2.0, so that means a $500 billion dollar stimulus package is needed. [That is, (change in GDP) = (multiplier)*(change in government spending, i.e. ($1 trillion) = (2.0)*($500 billion).]

If we actually get the 5 million jobs the estimates say we will get, what is the cost per job? It is $490 billion divided by 5,425,000, or $90,323. (Note that by targeting spending to places that have a high employment rate per dollar spent, we may be able to do even better than this.)

But this is GDP per job, it includes wages, rent, interest, and profit, it's not the amount labor takes home. About 70 percent of income goes to labor (though the figure may be even smaller over the last few years given the change in the income distribution - I haven't checked recently - so I'll use 70% ; Update: I missed that Greg Mankiw used .67 plus a bit more to account for supervisors, see below, so .70 seems okay). If we take 70% of $90,323, we get about $63,000 (actually, $63,226). That's less than a quarter of the $280,000 figure.

Now, the actual stimulus package numbers are larger than $500 billion, proposals for $600 or $700 billion are heard frequently. That's because extra has been added in to be sure the stimulus is large enough. But this extra spending will also add to job creation, so this won't change the cost per job.

Greg Mankiw, who first reported the $280,000 figure, wonders why the figure is so high. He says, looking at the multiplier formula, the answer must be that either the change in government spending is smaller than $500 billion, his first reason below, or the multiplier is smaller than the value of 2.0 used above, the third reason he gives. The other possibility, the "low bar" in his second reason, is that the 2% change in output to 1% change in unemployment based upon Okun's law overstates the actual employment change, and a lower value was used to arrive at the 2.5 million figure:

Logically, it must be one of three possibilities:



1. The fiscal stimulus is going to be much smaller than is being reported.

2. The new administration is setting a low bar for itself when it comes to job creation.

3. The Obama team believes in very small fiscal policy multipliers. Let me amplify the last point with a rough back-of-the-envelope calculation. The average weekly earnings of production and nonsupervisory workers is about $600, or about $60,000 over a two-year period. Granted, labor income is only about two-thirds of national income, and we have to add a few supervisors into the mix. So let's say each job created means $100,000 of extra national income. If we are generating $100,000 of income with $280,000 of government spending, the multiplier is only 100/280, or 0.36. By contrast, traditional Keynesian models suggest a multiplier closer to 2.0.

Notice the average annual salary of $60,000, that's pretty close to the cost calculation of $63,000 above.

As to why the estimates differ, I don't think the expenditure multiplier will change much - an increase in the savings rate would lower it, but there are reasons to increase saving and to decrease saving in a recession (some people save for the rainy days ahead, others have no choice but to consume out of saving), and the multiplier would increase with a fall in the responsiveness of investment to changes in the interest rate as we enter a recession, and the latter change likely dominates (to say this another way, crowding out is less of a worry). So I doubt the multiplier has fallen, it's more likely that it increased.

The remaining uncertainties are the size of the stimulus, and the coefficient characterizing Okun's law. I don't think the coefficient of Okun's law is 1.0, that seems way too low given the estimates I've seen, so the 2.5 million figure for job creation is likely just a safe, conservative statement of what they expect to accomplish. That's understandable since the estimates above are pretty rosy, and they still have to get a stimulus package through congress - the ultimate size of the package is unknown and not entirely their call - and overestimates of what they can do on the job front are not a good idea in any case. That's a lot of jobs to create, and it's better to under promise and over deliver than to do the reverse.

Update: Ezra Klein:

What Will the Stimulus Buy?:Over at the Motherblog, my colleague Tim Fernholz neatly dispenses with a bit of economics spin from Greg Mankiw. My hunch is you're going to hear Mankiw's point a lot in the coming weeks, so it's worth knocking it down. He begins by looking at Obama's intention to pursue a $700 billion stimulus measure and create 2.5 million new jobs. Using an ellipsis that cuts through four paragraphs in the original article, he manages to make it seem as if the stimulus is a policy meant to simply create jobs. He then does some back-of-the-envelope math and notes that this works out to approximately $280,000 per job. Not a very good deal. Fernholz responds:

Not all of the stimulus package is focused directly on job creation...most economists I've spoken to and many reports I've read predict that a big chunk of the stimulus -- tens of billions of dollars -- will include increased funding for things like food stamps, TANF, and unemployment insurance. It will likely also include federal aid to states, much of which will be used to make up massive budget shortfalls on programs like medicare. While that aid doesn't directly create jobs, without it, states would have been firing public employees to balance their budgets, especially with the bond market as tight as it is. None of those facets of the stimulus program directly create jobs, but they ease the pain for the millions of people losing jobs, preventing them from falling into deep poverty while the economy returns to course, and stimulate the economy in the aggregate. Subtracting the cost of these kinds of aid from the total cost of the stimulus will probably make the cost-per-job figure seem more reasonable. ...

Actually, programs like food stamps and unemployment insurance do provide jobs (or stop job losses which is the same thing) by increasing aggregate demand. So these types of effects are included in estimates of the job benefits from public spending. I can see how jobs that are simply maintained may not be counted in as a new jobs in a job creation tally, but they should be and such effects are part of the estimates of how many jobs will be created due to a particular level of government spending.