Further Stimulus?

Obama is pushing for further stimulus. It might be good to trot out the arguments we saw on this back in January.

Princeton Economist Paul Krugman has laid out the numbers for his pro-stimulus analysis here. He relies on Okun's Law, which details the relationship between unemployment and GDP. It suggests we need a much larger stimulus than is in play (probably much larger than is politically feasible) to truly correct the economy. Krugman has suggested we need something close to a 2 trillion dollar stimulus.

Also from months ago, Kevin Murphy put forth the best anti-stimulus argument in the field. Freakonomics mentions here. Here's his argument from his slides:

A Framework for Thinking about the Stimulus Package

• Let G = increase in government spending
• 1-α= value of a dollar of government spending (α measures the inefficiency of government)
• Let f equal the fraction of the output produced using “idle” resources
• Let λ be the relative value of “idle” resources
• Let d be the deadweight cost per dollar of revenue from the taxation required to pay for the spending

When Will the Stimulus Add Value?

• The net gain is the value of the output produced less the costs of the inputs and the deadweight loss
• In terms of the previous notation we have: Net Gain = (1-α)G –[(1-f)G + λfG] –dG
• Net gain = (f(1-λ) –α–d)G
• A positive net gain requires that: f(1-λ) > α+d
• Difference of opinion comes from different assumptions about f, λ, α, and d

[Murphy's] View:

• α likely to be large
• Government in general is inefficient
• The need to act quickly will make it more inefficient
• The desire to spend a lot in a short period of time will make it more inefficient
• Trying to be both stimulus and investment will make it even more inefficient
• 1-f likely to be positive and may be large
• With a large fraction of resources employed (roughly 93%) much will be drawn from other activities rather than “idle” resources
• Ricardian equivalence implies that people will save to pay for future taxes reducing private spending
• λ is non-zero and likely to be substantial
• People place positive value on their time
• Unemployed resources produce value through relocation (e.g. mobility & job search)
• d is likely to be significant
• Wide range of estimates of d
• Estimates based on the analysis of taxable income imply d≈0.8
• With these parameters the stimulus package is likely to be a bad idea.

Both of these arguments seem persuasive, and both are somewhat technical, so I'm not really sure how to dig in and rectify them. I'll try.

Krugman believes that α is likely to be -.5, that for each dollar of spending, you get one and a half dollars of economic productivity. This assumption may seem strange based on Murphy's very common sense suggestions for why α should be positive and high, but Krugman relies on the "widely cited estimates of Mark Zandi." He suggests that d from payroll tax cuts can be close to .3, but that the value of business tax cuts are uncertain, suggesting maybe 0 deadweight loss from business taxes. He thinks that a high d on payroll taxes pushes for him though, because he's hoping to cut payroll taxes as part of his stimulus. Here's a key difference. It's implied from this reasoning that Krugman believes that you can't just crunch the numbers and follow the best dollar for dollar option, but that there's some value to spreading out the pain. If we can pay a little more in taxes when we're well off in a few years than we would have paid right now, then we'll be better off because we smoothed out the costs of this recession. That seems intuitive and reasonable. We should probably add some variable, s, to Murphy's equation to measure the value of smoothing costs over time. But we can just leave s out for now, as Murphy appears to believe s is 0, and realizing that Krugman's case might look slightly better to Krugman than this analysis implies, due to a high rating of s.

It's not clear what Krugman thinks about f, how much of the stimulus would target idle resources. But you could address f directly, if it was a major concern. You could provide tax rebates or subsidies to businesses who hire employees that are registered with the government as unemployed. The longer they have been on the rolls, the greater the stimulus. The risk here is greater overhead to police cheating, but you could lightly police the program, knowing that even if 75% of those stimulated were complying (much lower than tax compliance rates), you'd be on the right track of focusing your stimulus towards f.

Of course, you wouldn't want to target f if you believed λ was more substantial. But it's a hard sell that this high level of unemployment is a great boon.

So, plugging some numbers into f(1-λ) > α+d, the condition under which we get positive net gain, we have:
.75(1-λ) > -.5+0 (or replace the 0 with .3, if you use payroll taxes to finance it on the back end)

We weren't sure what λ was in Krugman's estimation, but I believe he thinks it is very low. With so many unemployed, that seems reasonable. Of course, it looks like Krugman would support the stimulus whenever λ < 1.66, a figure which seems unlikely (or we would pay large groups of people to never work).

My intuitions lie with Murphy on the right side of the equation, but with Krugman on the left, making the question of stimulus much closer than I originally thought, certainly much closer than the voices from the right and left make it sound.

Notably, these arguments are pretty much unchanged from before. Krugman's analysis kicks in whenever there's high unemployment, and Murphy's analysis applies in all conditions. It'd be interesting to see Krugman and Murphy debate the particulars of alpha, lambda, f or d. Or it'd be nice if anyone has revised their opinions about alpha, lambda, f or d by measuring the effects of the last stimulus.

I feel obliged to link to some articles against the stimulus by Forbes and Penn Jilette which were fun to read, even though they avoid the heavy lifting above. More than anything, I'd really like to see Murphy and Krugman debate the particulars of the variables above.