Alpha = 0?

Josh Wright —  26 January 2009

Geoff’s post about Kevin Murphy’s recent slides and analytical framework for thinking about the stimulus are worth reading and if you haven’t yet. Here’s a link to the video. Here’s Murphy’s analysis in a nutshell for those who haven’t:

A Framework for Thinking about the Stimulus Package

  • Let G = increase in government spending
  • 1-a= value of a dollar of government spending (? measures the inefficiency of government)
  • Let f equal the fraction of the output produced using “idle” resources
  • Let L 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-a)G –[(1-f)G + ?fG] –dG
  • Net gain = (f(1-L) –a–d)G
  • A positive net gain requires that: f(1-L) > a+d
  • Difference of opinion comes from different assumptions about f, a, L, and d

My View * a 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 * L 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

Brad DeLong calls this the best anti-stimulus argument he’s seen and suggests that perhaps the evidence would switch Murphy’s ideological priors:

As I read it, Kevin thinks ? = 1/2, f = 1/2, ? = 1/2, d = 0.8, and gets 0.25 > 1.3. I would say that a = 0 (increasing income inequality and starvation of the non-health non-military public sector over the past generation have left a bunch of low hanging fruit), f = 1.5 (there are multipliers out there, and markets work if there is sufficient demand: as long as there are idle resources people will use them first as long as demand is available), L = 1/5 (the cyclically unemployed are not having much fun), and d = 1/3. So I get 1.2 > 0.33.

More interesting, I think, is that there is an unemployment rate at which Kevin Murphy’s priors would switch and he would become a stimulus advocate. What is it?

Alpha = 0!? Huh? I just noticed that Geoff picks up on this in the update to his post. Oh well, I’m too bothered by this to delete the post now (Tom Smith thinks Alpha > 1). Is it even possible for Alpha to be zero unless we assume away not only government inefficiency but also public choice problems? Perhaps the interesting question here is not so much about Murphy’s priors’ sensitivity to the unemployment rate but DeLong’s sensitivity to evidence on Alpha? I’d like to see evidence suggesting that Alpha is anywhere close to zero. Like Murphy, my prior is that Alpha is likely to be non-trivial and certainly greater than zero. But let me join Geoff in appreciating the fact that DeLong is acknowledging that there may well be some logical economic arguments to be made against the stimulus and discussing priors as to parameters rather than just name-calling. A discussion of the economics and evidence certainly beats this. Or this. What Nobel Laureate Paul Krugman has done with his epithets and attacks is both intellectually dishonest and bad for the profession. But at least he’s consistent, sparing no highly respected economists whom dares to publicly express skepticism about the stimulus, ranging from Robert Barro and Greg Mankiw to John Cochrane, Eugene Fama and Gary Becker. As Tyler suggests, a far more productive path to proceed under the presumption that “there aren’t any boneheads in the room.”