07/17/2009

# More multipliers (double super wonkish)

I’ve been thinking a bit more about contrasting results about fiscal multipliers in different New Keynesian models. Here are some further thoughts:

The simplest NK model is one in which there’s only consumption, no investment, and in which there’s a one-period “short run” in which prices are fixed, followed by an infinite-horizon long run of flexible prices. That’s the kind of model I used in my original analysis of Japan’s liquidity trap, and in my more recent stab at analyzing optimal fiscal policy.

In this kind of model, the key thing tying down consumption is an Euler condition:

MU1/DMU2 = (1+i)(P1/P2)

where MU1, MU2 are the marginal utilities of consumption in periods 1 and 2, D<1 is a subjective discount factor, i is the nominal interest rate, and P1, P2 are price levels in the two periods. Future consumption and prices are tied down by full employment and the future money supply; that leaves i and the initial price level to play with. Even if i is up against zero, short-run price flexibility can ensure full employment — but not in the usual way: a lower current price level increases expected inflation (by reducing current prices compared with expected future prices), and thereby reduces the real interest rate. If prices aren’t flexible, and i=0, the marginal utility of period 1 consumption, and hence its level, must move in lockstep with long-run consumption.

What does this say about fiscal multipliers?

If the fiscal expansion is temporary, consumption does not change; so the multiplier is exactly 1. If the fiscal expansion is permanent, it must crowd out an equal amount of consumption in the long run, and hence do the same in the short run. So the multiplier on a permanent expansion is zero.

Now, how does that fit with the results in Eichenbaum et al and Cogan et al?

I understand Eichenbaum et al pretty well, I think. They have a multi-period model in which the liquidity trap can extend for some time, and lead to disinflation or even deflation. Expected deflation, in the equation above, raises the real interest rate and depresses current consumption. Fiscal expansion reduces the expected rate of deflation, and therefore has a positive effect on consumption — but not through the conventional Keynesian channel.

Cogan et al is harder to puzzle out. In their initial policy exercise they assume that the fiscal expansion is permanent, which should imply a zero multiplier; I’m not sure why that doesn’t happen exactly. In their attempt to reproduce the actual stimulus plan, some of the spending comes after the zero bound has lifted, so there’s some crowding out there. But I don’t think that’s the whole story.

My guess — but it’s really hard to decipher — is that in Cogan et al the zero lower bound isn’t really binding; they think the Fed is being too expansionary. So imposing a zero rate is, in their view, inflationary — and forces a period of tight money and depressed spending later on. Fiscal expansion adds to this inflationary problem. And through the Euler equation this feeds back to current consumption.

So, how seriously should we take any of this?

Bear in mind that all these models assume perfectly rational, perfectly informed consumers engaged in optimal forward-lookin behavior. Economists are in vast disagreement about the right model to use — but consumers are assumed to know the true model, and base their spending decisions on that knowledge. Um, I think we have a problem here.

And for what it’s worth, my sense is that the empirical literature on consumption behavior casts doubt on the underlying model of long-run intertemporal maximization: consumer spending is much more responsive to short-term fluctuations in income than it “should” be. If so, a bigger multiplier would be appropriate.

What I really think is that consumers rely on rough rules of thumb, which leads in the short run to something much more like a Keynesian consumption function than is currently fashionable to admit.

But the true bottom line is that New Keynesian models, while they can help you clarify your thought, aren’t a literal description of how things work, and they certainly shouldn’t be taken as “proof” of anything.

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