### What is the return on fiscal stimulus?

Menzie Chinn attempts a valiant defence of fiscal stimulus against innumerate accusations from Richard Posner and others. Posner, to be fair, has corrected his arithmetic now and restated a few of his points in a more nuanced way.

However Chinn is now having to fight a battle against his own anonymous commenters, who say things like:
So explain to me still, how an 89B (regardless of interest expense) is a good investment if we only get a 39B return. It seems even if we got a multiplier of 2, we'd still only be at 80B and that is still a negative return. It seems like we're just delaying the pain.
This comment misunderstands the nature of stimulus and imposes a meaningless standard on the "return" on government spending. Here is what has actually happened:
1. The government borrows \$89 billion.

Savers have handed over an asset (\$89 billion in cash) in return for another asset (\$89 billion of government bonds). The government gains an asset (\$89 billion cash) and creates a new liability (\$89 billion of bonds). Net impact on both parties: zero.

There may be a small net impact due to the difference between the discount rate on foregone current private consumption and the interest rate on government bonds, but at present this is a minor effect. Depending on the discount rate we use, the effect could go in either direction. I have therefore ignored both discounts and interest payments in the remainder of this calculation to keep the calculations simple. Feel free to disagree with this in the comments.

2. The government spends \$89 billion.

Let's say it gives away A in transfers and spends B on goods and services, with A + B = \$89 billion.

Then the government's balance sheet is reduced by A, but the public's holdings are increased by A. Thus this is not an "investment" by the government which is meant to generate a return as if it were a private investment; it is simply a movement from one part of society to another. Society's total wealth does not change.

B is slightly more complex. Some government purchases are inefficient because they are being made on behalf of other people; on these, there is a loss in total economic value compared with the equivalent amount of private spending. Other government purchases are efficient because they are on public goods which bring a positive net benefit to society. Naturally there is an intense debate, broadly between right and left-leaning economists, about which effect predominates. But let's give the stimulus a harder challenge and assume that overall, there is a loss of 20% on B.

In the current quarter, B only represents around 25% of the total, so the economic loss overall is around 5% of the \$89 billion, or \$4.5 billion.

3. The money - or some of it - is spent again in the private sector: the Keynesian multiplier.

I'm going to take Menzie Chinn's figures as given, as this was our starting point for the debate: so \$39 billion of economic activity is created, compared to the counterfactual where no stimulus occurred. This is new activity created out of thin air (actually, out of otherwise unemployed resources) so it accrues on the positive side of the economy's balance sheet: new net wealth is created.

There is an argument that this \$39 billion of GDP, based on measurable economic transactions, is achieved at the expense of non-measured benefits such as leisure time. There is some truth in this, but looking realistically at involuntary unemployment it is hard to argue that the desire for leisure is anywhere near a straight trade-off for the alternative. Some would even argue that involuntary unemployment has negative utility and not positive; but again, if we impose high hurdles for the stimulus, we can accept that there is some positive utility. I would consider it credible that the opportunity cost is a third of the GDP-measured value of the alternative: thus, \$13 billion.

4. Finally, taxes must be collected to repay the \$89 billion.

Taxes generally create an economic loss because of both the effort required to collect them, and the incentives they create either to spend time on tax avoidance, or to reduce work effort since your income per hour worked is lower. It's not easy to agree on what that "deadweight loss" is, but Tyler Cowen suggests twenty percent or more. Unfortunately "or more" doesn't give us any guidance on the upper bound, so I'm going to use the figure of twenty percent (noting also that Tyler's views are on the libertarian side).

As Paul Krugman pointed out a few months ago, the stimulus partly pays for itself in new tax revenue. So of the \$39 billion of new economic activity, somewhere between 15-35% will come back in increased federal taxes. However, this doesn't count as net benefit because once again it is a transfer. It does mitigate the argument of the deadweight loss, however.

On the figure of 20%, the economic cost of collecting this \$89 billion will be just under \$18 billion.
Thus the correct figure on the "cost" side of the equation is not \$89 billion, but the total economic cost of executing all these transfers:
Cost = \$4.5 billion + \$13 billion + \$18 billion = \$35.5 billion
(Recall that I have tried to estimate the costs on the high side to give the stimulus a high bar to jump over.) The benefit, in this quarter alone, on Menzie Chinn's figures, is \$39 billion.

So, give or take a few billion, this quarter's stimulus has paid for itself by the end of the quarter. Any remaining impact in GDP in future periods - which is likely to be substantial, perhaps the same amount again - comes for free.

What's more, the utility of a \$39 billion gain in the middle of a recession far outweighs the impact of a \$35 billion cost in a future period of economic growth. This aside from the argument that redistribution from richer to poorer people in general (which to some extent is a feature of nearly any stimulus package) anyway improves total utility.

Now this is an unashamedly utilitarian argument; I accept there is a libertarian case against redistribution, no matter if it does increase total welfare. But the question here is about the "return" on stimulus, and that is a utilitarian question.

All in all, Chinn's calculations (and by extension, Christina Romer's) are a pretty convincing argument for the success - on its own terms at least - of the fiscal stimulus so far.

Donald Pretari said…
"I'm going to take Menzie Chinn's figures as given, as this was our starting point for the debate: so \$39 billion of economic activity is created, compared to the counterfactual where no stimulus occurred."

A good post. This is my only quibble with Chinn. The assumptions. To me, they fall into the category of reasonable, but not provable. I consider Posner's disentangling point to be fair. I also agree that the stimulus could have been better spent. Nevertheless, it was a wise move.

Posner's main point seems to be that academics loosen their criteria of proof when they enter the govt. Of course, if, as Posner says, it can't be proven, then what's a policy maker to do? I suppose that he wants them say that I've no idea. But saying that you can't prove something isn't the same as saying that it's groundless.

The bottom line is that Posner believes that Romer used to be a Multiplier Skeptic, but that now she isn't. Unfortunately for him, he didn't come anywhere near proving his point.

Don the libertarian Democrat
Leigh Caldwell said…
I heard somewhere that you are the "least agreed with commenter on economics blogs on the planet" so I am wary of agreeing with you for fear of spoiling your record. But you're right.

Most of the pro- and anti-stimulus people are talking past each other. Anti-stimulators say "but multipliers have been shown in recent decades to be low - even by Christina Romer - so stimulus isn't worth it". Stimulators say "but none of those studies were done with a 6% output gap and 10% unemployment - as Christina Romer has pointed out".

Anti-stimulators say "monetary policy is much more effective than fiscal - as Krugman said in 1995". Stimulators say "not when interest rates are zero - as Krugman said in 2008". Anti-stimulators say "interest rates are not the only fruit - monetary policy can still work".

Both groups end up in a reasonably defensible position, each based on different subtle and hard-to-test assumptions about effectiveness of certain policy actions in this specific environment.

Nobody really wants to work out analytically the best combination of policies because they are busy proving that their original prescription was right.
Donald Pretari said…
Leigh,

Thanks for agreeing with me.

Take care,

Don
PunditusMaximus said…
The anti-stimulators would not make the same arguments if the guy in office had an "R" after his name, so I'm uneasy with treating them as capable of the intellectual honesty necessary to accept when they're wrong.
Anonymous said…
One of your assumptions was that since the govt got cash and the investors got bonds, society as a whole's balance sheet broke even. What happens when you factor in, say 40% of the government bonds are sold to foreigners, foreigners who we are competing the the global economy. I'm not saying it does or doesn't matter, I just want you to explain your thoughts on this.

"This is new activity created out of thin air (actually, out of otherwise unemployed resources) so it accrues on the positive side of the economy's balance sheet: new net wealth is created."

I was with you up until this point. Those bonds were invested with the Govt because those investors felt like that was the best thing to do with that money at the time. However, your calculations assume that the money would have been put in a shoebox under the bed if it had not been invested in the bonds (unemployed resources). This is an incorrect assumption.

It is true that the investor for whatever reason found that the Govt bond provided the best risk/reward at the time, but that doesn't mean they would have done nothing with it otherwise. The Govt bond at the time was only marginally better than the next best investment. So you didn't add 89B to the economy that wouldn't have already been there in the first place.
Leigh Caldwell said…
Fair points, Anonymous.

First the foreign investment question: if the money comes from overseas, and is repaid overseas, the net effect is still zero. There is still a question of interest payments but in my argument I am taking those as approximately equal to the discount rate.

In general however, I would see the overall argument applying to the world as a whole. So foreign borrowing is just borrowing from people in a specific part of the economy. Recall that most other developed countries also have a stimulus package (or automatic stabilisers) of roughly similar magnitude to that in the US.

Second, your point about investment being diverted from other uses (the crowding-out argument). The counter to this is that large-scale involuntary unemployment implies that there are no attractive investment opportunities for private funds.

Of course this is a simplification, and in reality there are some opportunities to invest. So you're correct that there is some marginal cost to the government borrowing funds. I don't know how to estimate what that cost would be, but I'd point out two things:

One, the Federal Reserve has printed a ton of money which is essentially, in the short term, financing the stimulus. It has created about \$1 trillion, give or take, which covers the \$787 billion of the stimulus. This takes the place of any required private investment. However, you could argue that the Fed would have done this anyway, and if not soaked up by government borrowing the money would have gone into private investment.

Two, the 'paradox of thrift' argument. Krugman is quite good on this - essentially if the public's desired level of savings rises in aggregate, economic activity must reduce in order for this demand to be satisfied - unless government borrowing fills the gap. It's a subtle argument but I think it's a convincing one.