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Two economists on opposite sides of the stimulus debate recently expressed their opinions in terms of algebra. The opponent, Kevin Murphy of the University of Chicago, laid out the basic framework at a panel where he was the second speaker.  The proponent, Brad DeLong of Berkeley, reacted by reprinting Murphy's framework and using it to articulate his disagreement with Murphy.

My goal here is to translate their thoughts into English and then add my comments.

Murphy and DeLong decompose the analysis of the stimulus into four effects:

--a Keynes Effect
--a Housework Effect
--a Galbraith Effect
--a Feldstein Effect

The Keynes Effect is the use of unemployed resources to produce useful output.  DeLong says that for every $100 of spending on stimulus, we will get $150 in output from otherwise unemployed resources.  The estimate of more than one dollar of new output per dollar of stimuls reflects Keynes' famous multiplier effect--when newly hired workers earn more income, they spend more money, creating more demand, leading firms to hire more workers, etc.

Murphy thinks that for every $100 spent on stimulus, only $50 will go toward hiring unemployed resources.  After all, he points out, over 90 percent of the labor force is currently employed, so it will be difficult for government to target unemployed resources.  Moreover, as I like to say, it is hard to imagine unemployed investment bankers driving bulldozers on highway projects.

The Housework Effect reflects the fact that we count the output people produce in the market but not the value of leisure or unpaid work that they can produce when not on a paying job.  Murphy evidently thinks that for every $100 of market output produced by the stimulus, we will lose about $50 of housework.  DeLong says that we will lose only $20 of housework.

The Galbraith Effect is the additional value of government output over private output.  John Kenneth Galbraith famously argued that the public sector in the United States was starved, and that we needed fewer private goods and more public goods.    DeLong channels Galbraith when he writes,

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

Murphy, on the other hand, thinks that the government is inherently unwise and inefficient, so he treats the Galbraith effect as negative.  For Murphy, every $100 of government output is worth only $50.  DeLong thinks that the net Galbraith effect is zero, so that $100 of government output is truly worth $100.

Finally, there is the fact that government output eventually must be paid for with taxes, and most taxes cause supply-side distortions to the economy.  Taxes tend to penalize work, thrift, and investment, which are the sources of prosperity.  I call this the Feldstein effect, because Martin Feldstein has provided the most well-known quantitative estimates.  As Murphy points out, these estimates are rather high, so that Murphy assumes that for every $100 of government output, the distortions caused by the taxes that ultimately will pay for that output will cost the economy $80.  DeLong only thinks that the Feldstein effect is $33.

Putting it all together, DeLong says that the Keynes effect means that $100 of government spending gives us $150 of output from previously unemployed resources.  We subtract only one-fifth of this ($30) for the Housework effect and nothing for the Galbraith effect, for a net of $120.  Subtract from this a Feldstein effect of $33, so the net gain is $87.

Murphy says that the Keynes effect is much less, so that we get only $50 from unemployed resources.  Adjusting for the Housework effect, this leaves a $25 net gain.  Murphy sees the other $50 as shifting spending from the private sector to the public sector, and he sees the Galbraith effect as negative, so that this shift costs the economy $25.  That cancels out the net gain.  In addition, he sees the Feldstein effect as $80, which means that Murphy sees each $100 of stimulus producing a loss of $80 in output.

I have a few comments on this framework:

First, it assumes that the four parameters are constants.  That is, they assume that what is true of $100 of government spending is proportionately true for $800 billion of government spending or for $100 trillion of government spending.  However, the more the government spends, the less likely it is that the additional dollars will soak up unemployed resources and the more likely it is that instead additional dollars will draw resources away from private output.  Furthermore, there probably are diminishing returns to the Galbraith effect--as you get beyond the "low-hanging fruit," the usefulness of additional government projects will decline.

Second, I think that the spending plan will pass because politicians, particularly Democrats, assume a huge Galbraith effect.  They value government output much more highly than private output.  Larry Summers famously said that in order to be effective, fiscal stimulus must be "timely, targeted, and temporary."  The Democrats' plan is none of those things.  Instead, it is an enormous Galbraithian transfer from the private sector to the public sector.  While I can understand their enthusiasm for this transfer, I cannot share in their glee.