A structure for our value judgments

Earlier I mentioned that Paul Walker and myself had different ideas surrounding the need for a stimulus in the US. Fundamentally I think he is completely against while I see scope for some stimulus.

Over at Brad Delong’s blog he mentions a description of the stimulus by Kevin Murphy.

The structure he describes is below:

Evaluating the Fiscal Stimulus

Kevin M. 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

So the values of f, λ, α, and d define the different value judgments we may hold – which in turn determines what we think is the “best” solution. My impression is that:

α= government inefficiency,

λ=reservation value of unemployed resources (the opportunity cost from getting these people into work),

d=deadweight loss from taxation,

f=a “multiplier” on the net value created by the employment of idle resources.

As Brad says:

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

Interesting. So given that we need f(1-λ) > α+d, I would place my priors from a small targeted stimulus in the US at present at f=1, λ=0.2, α=0.2, d=0.5 which is a slight net gain. Feel free to provide evidence to make me change my priors 😉

Note:  Excellent post by Arnold Kling discussing what the value judgments are (ht Econlog).

  • Matt, the video that goes with this is here. Murphy is the second speaker.

  • MattYoung

    On the efficiency of government, their is an optimum limit. Assuming all sectors orthogonal, smooth, covering, etc; then the best distribution of resources is bell shaped. If government is the longest estimator in the economy, and the economy estimates itself with Hayek’s minimum of transactions, then efficiency is the difference between a bell shaped and its single pulse best estimate.

    Ok,ok, I will watch the video.

  • MattYoung

    I am still thinking on this.

    What I conjectured above would be the theoretical deadweight loss, the mis-pricing because he government has longer equilibrium times.

    Government inefficiency would be found in idleness, because the change in the surplus of government goods would be a change from our long or medium term expectations, and those expectations already include government inefficiency.

    f then becomes the distribution of government purchases, in fraction form, integrated over the distribution of the value of goods.

    That leaves us with, in normalized form, the possibility of lowering government purchases of goods that are over-utilized during a recession, government trying to twist the distribution of elasticities such that they are better formed after the government intrusion than before.

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  • “On the efficiency of government, their is an optimum limit. Assuming all sectors orthogonal, smooth, covering, etc; then the best distribution of resources is bell shaped. If government is the longest estimator in the economy, and the economy estimates itself with Hayek’s minimum of transactions, then efficiency is the difference between a bell shaped and its single pulse best estimate.”

    I think this stems from viewing government as a sector – rather than as a influence on sectors. I do not trust the government to appropriately alter sectors relative to the market price – but that is why we have deadweight loss 😉 .

    “That leaves us with, in normalized form, the possibility of lowering government purchases of goods that are over-utilized during a recession, government trying to twist the distribution of elasticities such that they are better formed after the government intrusion than before.”

    So are you stating that the government may keep spending in areas after a recession, rather than reverting to their previous spending/taxing plans. That is indeed a risk – something we would need political scientists to help us solve 😉

  • “Matt, the video that goes with this”

    Excellent, thanks Paul. I will update the post when my computer stops whining 😉