Grasping Reality on TypePad, by Brad DeLong

The Best Anti-Stimulus Argument: Kevin Murphy, January 16, 2009:

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: [Kevin'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

As I read it, Kevin thinks α = 1/2, f = 1/2, λ = 1/2, d = 0.8, and gets 0.25 < 1.3.

UPDATED: I would say that:

• α = 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 = 5 (there are multipliers out there, markets work if there is sufficient demand--and so as long as there are idle resources people will use them first as long as demand is available--and there is substantial hysteresis in employment)
• λ = -1/5 (the cyclically unemployed are not having much fun, and are losing their skills and workforce attachment)
• d = 0 (at the moment, there is no first order cost to financing government spending via borrowing)

So I get 6 > 0.