Assume the worst case scenario. Your economy is stuck in a permanent liquidity trap. It will stay there forever, unless you do something.
Do you have to do something big, measured in the trillions of dollars?
Suppose you do something, something very small, that has a direct effect of increasing Aggregate Demand by $1 per year. It could be monetary policy, fiscal policy, or sacrificing a goat. And you promise to keep on doing the same thing every year forever.
Now the multiplier kicks in. The direct effect of sacrificing a goat every year is to increase current and expected future AD by (say) $1. Which causes current and expected future income to rise, which causes a further rise in current and expected future AD. And so on, ad infinitum. The paleo-Keynesian multiplier is a positive feedback mechanism. It's a deviation-amplifying process. Why isn't this multiplier infinite? Why should each round of the multiplier be smaller than the last, so that the sum of all the rounds is finite?
If the multiplier is infinite, we won't need to sacrifice a lot of goats. One goat should be enough to do the job of getting us out of the liquidity trap, no matter how deep we are in it currently. Why do economists suffer from multiplier pessimism? Why do they say we need to sacrifice trillions of goats?
I can understand why the multiplier would be very small, maybe zero, if the economy is operating normally. Rising interest rates, capacity constraints, would create negative feedback to offset the positive feedback of the multiplier process. And if the economy is already operating where the central bank wants it to be operating, the multiplier would be approximately zero, because the central bank wants it to be zero. Anything - fiscal policy, goat policy - that increased AD, would be offset 100% by monetary policy (unless the central bank miscalculates and makes it 90% or 110%). But if the central bank, and those in charge of fiscal policy and goat policy, all agree that more AD is needed, and if more AD really is needed, that's not an issue.
If the marginal propensity to spend is less than one, as it is assumed to be in simple old Keynesian models, each successive round is smaller than the last, and the multiplier will be finite. And modellers need a marginal propensity to spend of less than one, otherwise the equilibrium will be unstable. Modellers don't like unstable equilibria.
But why should we assume the liquidity trap equilibrium is stable? Is there anything in theory that tells us the marginal propensity to spend must be less than one?
Theory tells us that the marginal propensity to consume out of a temporary increase in income will be less than one, except for borrowing-constrained or "hand-to-mouth" households, where it will be one. If some households are, and others are not, borrowing-constrained, the marginal propensity to consume on average will be less than one.
But theory also tells us that the marginal propensity to consume out of a permanent increase in income will be much closer to one. And I am talking about a permanent policy -- sacrificing one goat per year forever.
Then there's the marginal propensity to invest. If the desired capital/output ratio is independent of output, everything should just scale up. If output doubles, the desired capital stock should double, and so should desired investment, in the long run. And it would more than double in the short run, as firms tried to adjust the actual capital stock to the diesired.
To a first-order approximation, economies that are twice as big will have twice the consumption and twice the investment. Everything just scales up. The marginal propensity to spend -- consume plus invest -- is roughly one.
So if the marginal propensity to spend out of a permanent increase in income is around one, the multiplier effect of any permanent policy (monetary, fiscal, goats) should be roughly infinite. We don't need trillions of dollars of stimulus. $1 should do the job. If it's permanent.
Can we make it permanent? No problem with goats; they breed, so we can sacrifice one a year forever if we want to. No problem with money either; we can print more. But there's a bit of a problem with fiscal policy, if the long-run government budget constraint is binding, so that bigger deficits today imply bigger surpluses sometime in future. So let's stick to goats, or money.
Would people believe it would be permanent? Is a permanent policy credible? Bit of a problem with goats. Future generations might be unwilling to keep on sacrificing goats just because we promised to. But I don't see a problem with money. If we succeed in raising nominal income over the next few years, I really don't see future monetary policymakers deliberately trying to reduce it again, just because it used to be lower in 2010. I think they will just treat the higher level of nominal income as the new normal. They will validate whatever we do today.
So, a very small monetary policy stimulus should be enough to do the trick, just as long as it's permanent. The multiplier will take care of the rest.
I've been thinking of writing this for some time. Mark Thoma's post about George Evans' model triggered my decision to write it now. Here's George:
"In the stagnation regime, inflation is trapped at a low steady deflation level, consistent with zero net interest rates, and there is a continuum of consumption and output levels that may emerge."
A model with a marginal propensity to spend of one, and an infinite multiplier, has a continuum of equilibria. A marginal propensity to spend out of permanent income equal to one is what drops out of the New Keynesian Consumption-Euler equation, if you make the standard assumption about homogenous preferences.
Addendum: in an open economy, there will be leakage through extra imports, of course, so the marginal propensity to spend on domestic output will be less than one. So, you need every country to do the same policy. It might be hard if the policy is fiscal, or goats. But there shouldn't be a problem if it's monetary policy. It shouldn't be too hard to start a small global currency war, if you make the right inflammatory noises. And if the other countries fail to retaliate when their exchange rates appreciate, it doesn't matter to you anyway.
And I should credit Megan McArdle for the goat metaphor, from a couple of years back (I searched, but couldn't find the actual post).