More Thoughts on the Welfare Consequences of Stimulus Spending

Noah Smith has a short post questioning the reasoning of an earlier post of mine about stimulus spending. He includes a short numerical example which I reproduce below.  Here’s Noah:

Suppose [the] fiscal “multiplier” is substantial. Specifically, suppose … $100 of tax rebates will increase GDP by $110. In this case, stimulus spending is a “free lunch.”

Now suppose that instead of doing tax rebates, the government can build a bridge. The social benefit of the bridge is $90, and the bridge would cost $100. In the absence of stimulus effects, therefore, the bridge would not pass a cost-benefit analysis. For simplicity’s sake, suppose that spending money on the bridge would create exactly the same stimulus effect as doing a tax rebate – spend $100 on the bridge, and GDP goes up by $110 from the stimulus effect.

In this case, the net social benefit of spending $100 building the bridge is $90 + $110 – $100 = $100.
And the net social benefit of spending $100 on a tax rebate is $110 – $100 = $10.

Bridge wins!

Noah has a couple of subtle mistakes in his calculation. First, the increase in GDP from the stimulus isn’t completely a social benefit. Typically, every good produced is produced at some cost. If I go out to eat for lunch and buy $10 of Szechuan chicken, GDP goes up by $10. However, the net social benefit doesn’t go up by this amount. The gains to me (G) must be at least worth $10 otherwise I wouldn’t have willingly spent the money. The cost to the restaurant (C) can’t be more than $10 otherwise they wouldn’t have willingly provided that dish.  The social benefit (SB) is the difference between the gains and the cost.

SB = G – C

If markets are fairly competitive then at the margin both G and C will be “close” to $10 and so the social benefit will in all likelihood be less than $10. What this means for Noah’s calculation is that the $110 stimulus might not really be worth $110.  That’s ok however since this error is symmetric. It is worth pointing out however, that stimulus which is guided by the private sector typically passed cost/benefit tests of the kind I emphasize. In my example, G > 10 and C < 10 so SB = G – C must be positive. 

The second error is more important. In his calculation, Noah is counting the out-of-pocket revenue outlay for the tax cut as a cost. This isn’t correct. The tax cut is a transfer. There are no direct social costs associated with the tax cut.

Let me try to rephrase Noah’s example to make it clear. He is considering two options:

OPTION 1: tax cut (or transfer) of $100

OPTION 2: government spending of $100

(i) In both cases the Treasury is deprived of $100. 

(ii) In both cases the private sector gains $100 in after-tax income.

(iii) In both cases the private sector uses the additional income to spend or save (this is the source of the multiplier). 

(iv) In OPTION 1 a bridge is built. The social costs (C) of the bridge include the value of time, energy, materials, effort, etc. The social benefit (B) of the bridge is the value of having the bridge.

In comparing these two options, we can ignore (i) – (iii) since they are the same in both policies. The only difference is (iv). Whether government spending is preferable depends only on whether B is bigger than C.  Note that the magnitude of the multiplier doesn’t enter the comparison. It is symmetric in both cases. My argument is not “diametrically opposed to Econ 102 textbook Keynesianism” —  GDP will go up by more under OPTION 2.  The subtlety is that in Econ 102 we typically act as if maximizing GDP is the correct objective of public policy. This isn’t true though. GDP maximization can rationalize building pyramids, the Maginot Line, the bridge to nowhere, ethanol subsidies, … A social welfare criteria would skip these projects.

In the comments section to Noah’s post a number of readers make some points which are worth mentioning. One comment points out that many people don’t pay taxes and so wouldn’t benefit from a tax cut. Certainly, unemployed people won’t benefit from a tax cut. However, we could construct transfers that would reach these people. Rachel Maddow’s suggestion of sending people envelopes with money in them would work just fine. Also, many people and firms do pay taxes. Payroll tax cuts like those passed by the Obama administration are a particularly effective way of introducing stimulus.  These simultaneously put money in people’s pockets not to mention the beneficial incentive effects of the policy. 

Another commenter points out that calculating the social costs and benefits of a given project are quite difficult.  This is absolutely true but it is a calculation that should be carefully considered none the less.  In Noah’s example, the cost of bridge is probably closely approximated by $100.  The benefit of the bridge is more difficult to assess.  Such difficulties probably come up often.  What is the benefit of protecting or cleaning up a wetland?  What is the benefit of political stabilization in the Middle East? Tricky questions but questions that should be considered nonetheless. 


15 thoughts on “More Thoughts on the Welfare Consequences of Stimulus Spending

  1. Another way of putting the point is that a check mailed by the government is just one kind of government spending–it purchases an activity that has zero cost and zero benefit (namely, having a mailbox). To make the case for government spending on other things, then, you have to argue that the net benefit is positive for it to dominate a check in the mail.

  2. But if you’re agreeing that GDP goes up more in the bridge case than the rebate case, should it at least be noted that the omitted social “cost” of the bridge would presumably be very different from what the cost would be in a zero output gap economy? These $100 of resources (simplicity: labor) would as a first order approximation have laid idle by assumption but for the bridge. The opportunity cost of these resources is a version of leisure, perhaps involuntary leisure. The social value of leisure in a depressed economy with presumably some kind of externality distortion preventing full employment is likely to be much lower than in an typical opportunity cost environment. It might even be negative. Maybe people are actually digging ditches in their backyards for free just to feel productive — BLS doesn’t have that question in its surveys.

    • True. The cost-benefit calculations are not constant. In recessions, costs will likely go down so there is a neoclassical argument for expanding government spending during such periods.

  3. Isn’t the problem that you can transfer $100 to the private sector and get less that $100 spending, since people use the case to pay off debts etc.

    Whereas if you spend the money on wages, bridges, whatever, you get something for it even if wages are subsequently used to pay off debts.

    Also, comparing the costs and benefits of building a bridge in a depressed or booming economy will be different. If there are idle resources, costs properly measured will be lower than where there is full employment (no idle resources).

  4. Lump-sum subsidies are government purchases–specifically, they are purchases of nothing. The cost of producing nothing is zero, and the benefit of purchasing nothing is zero. Thus, any government purchase has to have SOME net benefits to dominate lump-sum subsidies.

    Some government purchases have next to no benefits (e.g., bridges to nowhere). The only reason to prefer such purchases to lump-sum subsidies of equal amount is if the cost of production is zero. This is, to put it lightly, a heroic assumption, even when there are plenty of unemployed resources (surely SOME employed resources will be reallocated to less productive uses in the process).

    Additionally, the costs and benefits of lump-sum subsidies are certain, while the costs and benefits of most government purchases are uncertain. Risk aversion favors government purchases only if the benefits clearly exceed the costs, in which case the purchase was probably warranted regardless of the macroeconomic situation.

    Obviously, we should purchase those things which we should purchase. The question is whether we should purchase things we wouldn’t normally purchase to stimulate the economy. Professor House is correct that the answer here is plainly ‘no’.

  5. Pingback: Further reading | FT Alphaville

  6. When you trace the cost of the bridge through the input-output matrix, the bulk will be labor, a chunk will be capital depreciation, and a small bit will be things like imports and resource depletion. Of the depreciation chunk, most of that will be either depreciation that would have happened anyhow (wearing out of capital that would otherwise have been idle) or depreciation of new capital, the real cost of which is mostly the current labor used to produce it. For purposes of argument, it’s a reasonable simplification to ignore the non-labor costs of the bridge.

    Now, there is evidence that unemployment has severe adverse psychological effects. So it’s not obvious to me there is a net welfare cost to the labor that goes into the bridge, let alone one that is nearly as high as the total social benefit of the bridge. Weighing the adverse psychological effects of unemployment against foregone leisure, it seems like a reasonable guess that the net welfare cost of the labor is near zero. (In principle it could be either positive or negative.) If we use zero as a approximation, I think Noah’s argument goes through.

    • Hi Andy,

      This is correct but you are really just saying that you think the costs have dropped sufficiently to justify the project on the cost-benefit basis that I’m suggesting. (Though I highly doubt that the social costs of something like a brigde would ever be close to zero in reality.) The question you should consider is this: if there is a project that doesn’t meet the cost-benefit test, are there circumstances where we should fund it in the name of stimulus? My answer is that in virtually every case, the answer is ‘no’.


      • Obviously the answer is “no” if you fully include the welfare benefit of the stimulus in the cost-benefit test — which is what I’m trying to make a stab at in the response above. But it can get complicated to figure out what that benefit is, particularly if there are hysteresis issues.

        Occurs to me that the counterargument to my point above would be something like, “Fine, maybe employing people is a benefit in itself, but can’t you employ the same number of otherwise unemployed people without building a bridge? Just do the tax rebate, but do more of it, until it has the same employment effect as the bridge.”

        The tax rebate might have to be quite large, though, which brings up another question: if the government has a long-term budget constraint, then the tax rebate is not a pure transfer, because it has to be funded by future distortionary taxes.

  7. Great points, but I have one problem. You said: “In Noah’s example, the cost of bridge is probably closely approximated by $100.”

    Yet, if we are in a Keynesian world with suboptimal “aggregate demand”, then the cost of the bridge is probably not close to $100. Just like the benefits of the bridge, in this Keynesian world, the costs of the bridge are hard to assess. Suppose the only cost is labor. A firm may charge $100 to build the bridge, but workers won’t necessarily get $100 more disutility. There may be an unemployed worker hired to build the bridge and paid the wage of $100 even though she actually would work for $10, but isn’t allowed to (due to some sticky wage explanation that keeps unemployment high). In that case, the social cost of building the bridge is just $10.

  8. I don’t want to get into a whose smarter than who kind of discussion… but, Noah is more right than you are on this one. This is for two related reasons:

    1) The first issue is related to the balanced budget multiplier and it is what Noah, I think, has in mind (although I agree that he didn’t express his objection to make this entirely clear).

    If you didn’t deny treasury of funds and instead used a rise in taxes to pay for the bridge, than GDP rises by the cost, because the cost includes paying the suppliers who now have extra income. An unfunded bridge is a funded bridge plus a tax cut.

    I don’t think you’ll disagree with this point, instead you’re probably thinking “you still have to calculate SB”! or something to that effect… which brings me to point 2.

    2) The opportunity cost of the bridge is a function of the economic slack. In this case, opportunity cost of a bridge is that resources devoted to building the bridge are not available for building other projects. So, the cost is in employing people and material to build it, and those people and materials are by definition not doing anything else during a slump.

    But by extension price rigidities mean that the actual budget cost overstates, perhaps by quite a bit, the opportunity cost of the bridge. There are simply fewer opportunities for erstwhile bridge builders to find gainful employment elsewhere as long as the slump lasts.

    On the other hand, the benefits of the bridge, since they are spread over many years, are not effected by the downturn, at least not to first approximation.

    Noah may have deployed argument (1) incorrectly, but putting (1) together with (2) means that bridges which in normal times would not be socially profitable, on the margin will be so in a recession. So Noah’s right for the wrong reason, and you’re wrong for kinda the right reason.

    • On 1, you are considering another transfer, which again doesn’t enter the calculation. Any string of taxes / transfers to and from the government can be appended to either policy without changing the final calculation.

      On 2, you are right (see above). You are just saying that the cost / benefit test is more likely to be passed in a recession — this is true. Your point about price rigidity is also well taken. You can also add the presence of markups in the price quotes that the government gets. Ultimately though these are just problems for making an accurate cost / benefit assessment. It doesn’t change the conclusion.

  9. “Subtle mistakes”, hah! I’ll bet that you got a good laugh out of Smith criticizing your cost/benefit analysis, and then giving such a bogus analysis himself.

    I commented on his blog before finding your response here. I made points similar to yours, but much more laboriously, about his two errors.

    Smith may indeed have a case that the bridge should be built, because of the underutilized resources. I gave, as an example in another comment, that the social cost of a bridge with $90 social value might be only $70, so that there was a social benefit of $20. I also agreed with another commenter, who said that, in this situation, “I believe that Chris House would have no problem” with building the bridge – which seems to be born out in your reply to Andy Harless above.

    But Smith’s argument is a joke. As I put it, ” … your disagreement with Chris House seems to come down to: House does not realize that bridges are free.”

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