Update: since what I thought was my most controversial post ever has drawn precisely zero comments, let me re-title it: "A fiscal stimulus can more than pay for itself".

The English language is full of dead or dying technological metaphors. How many people have ever primed a pump or kick-started a motorcycle? (I'm old enough to have done both.) In both cases you give the machine (the pump or motorcycle) some temporary outside assistance (add water or kick down on the kick-start), and then it keeps on running by itself.

These metaphors are sometimes applied to fiscal policy. The idea is that a temporary increase in government spending or cut in taxes can get the economy running again under its own power, so that the fiscal stimulus can be withdrawn.

The simple Keynesian income-expenditure model often taught in first year macroeconomics is not a pump-priming model. The current level of output depends on the current level of the deficit. You need a permanent increase in the deficit to get a permanent increase in output. A temporary increase in the deficit will cause only a temporary increase in output. This has two important implications.

The first implication is that any benefits of higher output today come at a cost of lower output some time in the future, because you can't have a permanently increased deficit without eventually defaulting on the national debt. So you will need to run a surplus sometime in the future, which means (if the first-year model is correct) lower output in the future.

The second implication is that increased government spending, or tax cuts, can never be (fully) self-financing. It is true that an increase in output will cause increased tax revenue, but this could never be enough to eliminate the deficit, because if it did eliminate the deficit the model says you couldn't have that increased output in the first place.

In other words, there is no Keynesian equivalent of the Laffer curve, if the first-year model is correct. See Mark Thoma's post, and (H/T Mark) Andy Harless, Lane Kenworthy, and Paul Krugman.

There are two ways to escape these unpleasant implications of the first-year model.

The first way is to keep the first year model, but hope that there will be some future exogenous increase in demand, which will be more than enough to restore full employment, so you can run a surplus to pay off past deficits while keeping the economy at full employment. In other words, the fact that a temporary deficit will only cause a temporary increase in output is not a problem, because you only have a temporary shortage of demand.

The second way is to ditch the first year model, and replace it with a pump-priming model, where a temporary increase in the deficit can cause a permanent increase in output. With a pump-priming model, we don't have to worry about the long-run consequences for the debt; there can be a Keynesian Laffer curve, because permanently higher tax revenues can repay a temporary deficit.

Now any imaginative macroeconomist, given a free hand with the assumptions, can cook up a model to show almost anything. But in this case we don't need to do any imaginative cooking; we just take the second-year model off the shelf and stick it in a liquidity trap. We get a pump-priming model.

The standard second-year model has IS and LM curves, an expectations-augmented Phillips curve, and some sort of adaptive expectations of inflation. In normal times (outside of a liquidity trap), it eventually gets to full employment by itself, and can always be helped to get there with monetary policy, regardless of fiscal policy. But in abnormal times (a liquidity trap, when the nominal interest rate is stuck at zero) it reverts to the first-year model.

Starting in a liquidity trap, increase the deficit, and keep the deficit high enough for long enough to get inflation to increase, and expected inflation to increase, to get out of the liquidity trap. (Expected inflation creates a gap between the nominal and real interest rates, so a wedge between the IS and LM curves). Then the deficit can be slowly eliminated, and expansionary monetary policy, or the self-equilibrating forces of the model, can keep the economy at full employment indefinitely.

If we don't increase the deficit we stay permanently at low output (unless some deus ex machina exogenous increase in demand rescues the economy). If we do increase the deficit, even if only temporarily, we can get to full employment and stay there indefinitely. Compared to the counterfactual, a temporary deficit causes a permanent increase in output. It's a pump-priming model.

"Look Ma! I just built a pump-priming macroeconomic model with multiple equilibria and a Keynesian Laffer curve!" But all I really did was take the second-year model off the shelf. It's not rocket science (like the stuff they teach in grad skool).