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.
So let’s do the 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.