A Tale of Two New Keynesian Models, or Noah Smith v. Paul Krugman
Matthew Martin 7/16/2013 11:08:00 AM
Background: In New Keynesian models, prices are "sticky," and because of this aggregate supply is upward-slopping with respect to inflation: higher inflation means higher output and higher employment in the short run. Normally, the central bank can raise and lower the inflation rate by adjusting the nominal interest rate--a lower nominal rate means higher inflation and more output. A situation where the nominal interest rate is 0%, meaning that the central bank cannot lower the rate and increase inflation, is called a "liquidity trap."
Noah Smith's point is this: in the New Keynesian model, individual prices adjust slowly, which is why inflation has real effects on short-run output. But in the long run, prices adjust so that inflation is just that: inflation, with no impact on long-run output. Japan has been in the liquidity trap--where the nominal interest rate is stuck at 0%--for two decades, which surely must be enough time for all prices to fall commensurate with whatever fall in aggregate demand started this episode. Thus, by this logic, Japan should be pretty close to full employment and long-run output, despite their long-running liquidity trap.
Paul Krugman's response leans heavily on Keynes, who commented that an aggregate price decline does not restore demand. Krugman quotes a passage of Keynes that, logically, is completely incoherent to me. Is Keynes suggesting that it is not possible to find a price system in which aggregate demand equals potential output? That means that an equilibrium doesn't even exist, which is certainly not what the typical New Keynesian model says about liquidity traps.
Here is a graph of a stereotypical New Keynesian liquidity trap scenario, as you'll find in the works of Christiano, Eggertson, Woodford, and even some of Krugman's papers.
Why is there a kink? You can think about this in terms of real interest rates. The real interest rate is what people use to decide how much to consume or save--at higher real rates, they consume less and save more. The real interest rate, however, is the difference between the nominal interest rate and inflation, according to the fisher equation: $$real~interest~rate=nominal~interest~rate-inflation~rate$$ Thus, if the nominal interest rate is zero, the only way to lower the real interest rate is to raise inflation. Supply-side measures, which lower inflation, are actually contractionary because they increase the real interest rate, reducing consumption.
Anyway, Smith points out that Japanese prices actually aren't that sticky, and Krugman's rebuttal is essentially 'nevermind, what matters is that the length of the liquidity trap is long.' I do not share Krugman's certainty in that declaration. Here is what a standard New Keynesian model looks like, except with parameters adjusted so that prices are more flexible and the liquidity trap is longer:
Ok. Krugman seems to be working off of a more unique and unusual New Keynesian model, in particular his own paper on debt deleveraging. I certainly haven't worked through the mathematics, but its Krugman so I'm pretty sure there are no excel errors. I will skip right to figure 3 from the paper:
In conclusion, I think Krugman's derision toward's Smith's post is a bit unwarranted. Krugman never "killed" the price flexibility "zombie idea," but rather he merely presented an alternative internally logically consistent model in which price flexibility doesn't help in a liquidity trap. Anecdotal evidence from Japan, and the Great Depression seem to support this theory, but it isn't the only theory that fits the facts. And, for the record, I don't see any empirics in Krugman's paper.
However, part of what Krugman has said on the topic of price flexibility, I think, rings true regardless of which New Keynesian model is right. In both Krugman's paper and the standard New Keynesian framework above, policy efforts to decrease prices are likely to backfire, because the government doesn't literally set all the prices in the economy. Instead the policy instruments available to the government can only put downward pressure on the market clearing levels of prices, thus increasing the gap between the current and the market-clearing prices, and decreasing output and employment. This, as far as I can tell, is true of all imputations of the New Keynesian model at the zero-lower-bound. Yes, even this one.