New Keynesian Stimulus

One piece of interesting economics did come up while I was looking through the stimulus blogwars.

Paul Krugman pointed to New Keynesian stimulus models in a recent post, When Some Rigor Helps.

But take an NK [New-Keynesian] model like Mike Woodford’s (pdf) — a model in which everyone maximizes given a budget constraint, in which by construction all the accounting identities are honored, and in which it is assumed that everyone perfectly anticipates future taxes and all that— and you find immediately that a temporary rise in G produces a rise in Y"...

So I guess I’d urge all the people now engaging in contorted debates about what S=I does and does not imply to read Mike first, and see whether you have any point left. 

As it happens, I've spent a lot of time reading and teaching New Keynesian models.

I  wrote a paper about New Keynesian models, published in the Journal of Political Economy (appendix, html on JSTOR).  I haven't totally digested the NK stimulus literature --  In addition to Mike's paper, Christiano, Eichenbaum and Rebelo; Gauti Eggertsson; Leeper Traum and Walker; Cogan, Cwik, Taylor, and Wieland are on my reading list -- but I've gotten far enough to have some sharp questions worth passing on in a blog post.

Krugman continues,

That doesn’t mean that you have to use Mike’s model or something like it every time you think about policy; by and large, ad hoc models like IS-LM are actually more useful, in my judgment

One thing I know for sure: This is wrong. (It's an understandable mistake, and many people make it.) The New Keynesian models are radically different from Old-Keynesian ISLM models. They are not a magic wand that lets you silence Lucas and Sargent and go back to the good old days.

New-Keynesian models have multiple equilibria. The model's responses -- such as the response of output to government spending or to monetary policy shocks -- are not controlled by demand and  supply.  They occur by cajoling the economy to jump to a different one of many possible equilibria. If you're going to write an honest op-ed about New Keynesian models, you really have to say "government spending will make the economy jump from one equilibrium to another."  Good luck! 

New Keynesian models offer a fundamentally different mechanism from the IS-LM or standard stories that Krugman -- and Bernanke, and lots of sensible people who think about policy -- find "actually more useful."

For example, the common-sense story for inflation control via the Taylor rule is this:  Inflation rises 1%, the Fed raises rates 1.5% so real rates rise 0.5%, "demand" falls, and inflation subsides.  In a new-Keynesian model, by contrast, if inflation rises 1%, the Fed engineers a hyperinflation where inflation will rise more and more! Not liking this threat, the private sector jumps to an alternative equilibrium in which inflation doesn't rise in the first place. New Keynesian models try to attain "determinacy" -- choose one of many equilibria -- by supposing that the Fed deliberately introduces "instability" (eigenvalues greater than one in system dynamics). Good luck explaining that honestly!

In the context of the zero bound and multipliers, not even this mechanism can work, because the interest rate is stuck at zero. There are "multiple locally-bounded equilibria."  Some stimulus models select equilbria by supposing that for any but the chosen one, people expect that the Fed will l hyperinflate many years in the future once the zero bound is lifted. Hmmm.

These problems can be fixed, and my paper shows how. Alas, the fix completely changes the model dynamics and predictions for the economy's reaction to shocks. 

Or maybe not. I know the simple New Keynesian models suffer these problems. (That's what the JPE paper is about.)  Do they apply to the stimulus models? I don't know yet. I certainly have some sharp questions to ask, and I don't see anything in the models I've looked at with a hope of solving these problems.

Moreover, even taken at face value, the predictions of New Keynesian models are a lot different from Krugman's advertisement that more G gives more Y.

Every NK stimulus model that I have read is "Ricardian." Government spending has very large effects, even if it is financed by current taxes. Good luck writing an op-ed that says, "The government should grab a trillion of new taxes this year and spend it. We'll all be a trillion and a half better off by Christmas."  The popular appeal of stimulus comes from the idea that borrowed money doesn't transparently reduce demand as much as taxed money.  But that's the iron discipline of models -- you can't take one prediction without the other. If you don't believe in taxed stimulus, you can't use a Ricardian New Keynesian model to defend borrowed stimulus. (Or you have to construct one in which there is a big difference, which I have not found so far.)

More weird stuff, from Gauti Eggertsson's introduction

Cutting taxes on labor or capital is contractionary under the special circumstances the United States is experiencing today. Meanwhile, the effect of temporarily increasing government spending is large, much larger than under normal circumstances. Similarly, some other forms of tax cuts, such as a reduction in sales taxes and investment tax credits, as suggested, for example, by Feldstein (2002) in the context of Japan’s “Great Recession,” are extremely effective....

At positive interest rates, a labor tax cut is expansionary, as the literature has emphasized in the past. But at zero interest rates, it flips signs and tax cuts become contractionary. Similarly while capital tax cuts are almost irrelevant in the model at a positive interest rate (up to the second decimal point) they become strongly negative at zero. Meanwhile, the multiplier of government spending not only stays positive at zero interest rates but becomes almost five times larger.

Tax cuts are contractionary? The stimulus failed because the large tax cut component dragged output down? That's new, and I didn't hear Krugman complaining! Maybe it's right, but you can see we're a long long way from simple ISLM logic. Also, it's clear that these models make a sharp distinction between zero and nonzero rates, that stimulus advocates certainly do not make.

I also notice that "deflationary spirals" are a big part of the analysis. For example, in Christiano et al.,

But, in contrast to the textbook scenario, the zero-bound scenario studied in the modern literature involves a deflationary spiral which contributes to and accompanies the large fall in output.

OK, but we have near zero short-term government rates, a 3% positive rate of inflation and far from zero corporate and long term rates. Does the analysis apply?

Back to reading. I'll post again if I get more NK stimulus insights. It may take a while. I still think it's yesterday's news. Sovereign default seems more important for the future.