The way to analyze whether, at the margin, it is raising or lowering government spending that is better for the economy right now is to do a benefit-cost analysis.

Following DeLong and Summers (2012), let the parameters for an economy at the zero lower bound of nominal interest rates and with anchored inflation expectations be:

μ, the multiplier—and a depressed-economy zero-lower-bound multiplier, not a monetary- offset multiplier;

η, the hysteresis coefficient: the shadow cast on potential output by today’s downturn;

τ, the marginal tax-and-transfer share: 1/3;

ξ, the deadweight loss from having to raise a dollar of extra tax revenue to service the debt;

r, the real government borrowing rate (and the social rate of time discount); and

g, the growth rate of potential GDP: 2.5%/year

Then for each extra dollar of government spending today the present value of total economic output now and in the future changes by:

μ(1+η(1+ξτ)/(r-g))-ξ(1-μτ)

Now:

Diamond and Saez and Romer and Romer have an estimate of the deadweight losses from having to raise taxes: ξ=0.25

Auerbach and Gorodnichenko have an estimate of the zero lower bound multiplier: μ=2.5

Oulton and Sebastiá-Barriel have an estimate of the hysteresis shadow: η=0.2

Make the short-sighted, biased, and in fact crazy assumption that Oulton and Sebastiá-Barriel are wrong--that the hysteresis shadow η is not 0.2 but zero--that no matter how deep the current downturn is there is no effect on the long-run growth of the economy’s productive potential. Then our benefit-cost expression becomes:

μ - ξ(1-μτ)

And each extra dollar of government spending now does not reduce but increases the present value of economic output now and in the future as long as:

ξ η=0 < 14.925

Having to raise a dollar of extra tax revenue to amortize debt must reduce economic output by $15--not the $0.25 of Diamond and Saez or Romer and Romer or even the $3 if we were at the top of the Laffer Curve, but by $15, in order for further fiscal expansion right now to be a bad deal.

Suppose we make the additional short-sighted, biased, and in fact crazy assumption that the multiplier μ at the zero lower bound is not 2.5 but rather 1. Then our cost benefit expression becomes:

1 - ξ(1-τ)

Then each extra dollar of government spending now does not reduce but increases the present value of economic output now and in the future as long as:

ξ η=0,μ=1 < 1.5

With these numbers, why are we in favor of expansionary fiscal policy only at the zero lower bound and not at all times? Because when the economy is away from the zero lower bound and when inflation expectations are potentially unanchored, the central bank is focused--for good reasons--on achieving its inflation target, which means that it acts to offset effects of changes in government spending on demand, which means that away from the zero lower bound μ=0.

And when μ=0 our cost-benefit expression is the very simple:

-ξ

There are then no special macroeconomic benefits to government spending, which should then be set at its optimal keel according to classical microeconomic principles.

And if you return from some imaginary planet in which a downturn does not cast a shadow on the growth of the economy’s productive potential, the case for more aggressive fiscal spending policy to hasten the return to full employment as long as the economy is at the zero lower bound on short-term nominal interest rates is even stronger.

Now you may not like Larry’s and my benefit-cost analysis. But, if you want to contribute constructively to the debate, I think you need to say why you do not like it and present an alternative benefit-cost analysis of your own that reaches a different conclusion.

Yes, I'm looking at you, Rudy Penner:

The Risks of Dumbing Down Fiscal Goals: In one of the more dangerous fiscal developments of recent months, some on the left are defining successful deficit reduction as merely stabilizing the federal debt [to GDP]…. While there is no magic target, this one is far too modest…. Richard Kogan… Martin Wolf… make the case…. [But] I would think the left would back more aggressive deficit reduction, if only to lower the risk of a sovereign debt crisis. It is, after all, the poor who are being most devastated by high unemployment in Ireland, Portugal, Spain and Greece…. Sovereign debt crises occur at all manner of debt-GDP ratios and are impossible to predict, but it is hard to believe that a higher ratio does not increase the risk to some degree. It is sobering to note that in 2008, just before their crises, the net debt to GDP ratio in Spain was less than 31 percent and in Ireland less than 25 percent.

Rudy Penner used to be better than this.

The Rudy Penner I used to know would say that the Irish, Portuguese, Spanish, and Greek crises were the result of their joining a currency union that was not an optimum currency area. He would say that countries in such a situation cannot afford to have even a small national debt. And he would say that the U.S. is not Greece, that claims that the U.S. is like Greece are at the least disingenuous, and that the Greek experience tells us nothing about risks for large countries that operate reserve currencies.

The Rudy Penner I used to know would, if he thought that fiscal policy needed to be more contractionary right now, present a benefit-cost analysis showing that the short-term benefits from boosting output in the near future were outweighed by the long-term risks of the effect of increasing short-term fiscal stimulus on the debt.

Where is that Rudy Penner?