Interesting how everyone in jumping on Christiano and Eichenbaum while Krugman, of all people, is getting away with murder.
To log-linearize or not to log-linearize? | EL
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Braun et al's paper is a disaster. Have any of you actually read it? By their own admission, the dramatic results are all coming from the Rotemberg costs of price adjustment, which (in the parameter range they consider) can go up to nearly 100% of output (!!!) once you get to 20% deflation or inflation.
Any intelligent person should read this paper as an argument for why we should log-linearize: if we take the nonlinear properties of a modeling hack like Rotemberg pricing too seriously, we get completely absurd results. Do you seriously think that the costs of price adjustment were taking up 20-30% of output during the Great Depression? Wtf? What does that even mean?
In certain cases they have the same silly "reverse comparative statics" as in the Mertens and Ravn paper. Basically the story is this: people in other fields have long understood that when an equilibrium is unstable, all the comparative statics are reversed, in a way that doesn't really make any sense if you tell it as a causal story. (This dates back to Paul Samuelson, for the love of God. Here is a more recent take by Echenique. Here is a piece by Dixit on the oligopoly literature.) Unfortunately, certain macroeconomists do not have any of this intellectual background and go off trumpeting their new comparative statics as if they've made some great discovery, when in fact they're just repeating old errors.
In the Mertens and Ravn paper (and implicitly in the Braun one too, though there's less of a focus on this), the government spending multiplier is less than one during a liquidity trap for the following reason. The expectations-driven liquidity trap is indexed by the Poisson exit rate of the sunspot process. For this to be a liquidity trap (in their parameter range), deflation has to be high enough that it substantially depresses demand and is self-fulfilling. So if you do anything at all to increase demand, including a government spending increase, the only way you can stay in a liquidity trap with this particular exit rate is that deflation becomes even worse. Inversely, if you do anything at all to decrease demand, a liquidity trap with that particular exit rate is only possible if deflation becomes better.
This means that if the central bank raises interest rates during the liquidity trap in the Mertens and Ravn model, it will actually increase output and make deflation less severe. So there you have it: these geniuses have come up with a model of liquidity traps where optimal monetary policy involves raising interest rates when you're in the trap. Of course, they don't realize this. But it's true, and it happens for exactly the same reason they get a fiscal multiplier of less than 1.
Episodes like this weaken my (already very weak) confidence in the economics profession. Basically, everyone has some general idea that log-linearization in macro models has some severe limitations. (And this is true.) But everyone is so eager to hear more about how log-linearization is flawed that they'll lap up preposterous, incredibly shoddy papers as long as they're singing the right song.
Excuse me while I kill myself. Or stop reading macro papers. One of the two will happen soon.
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Nice analysis, but consider this: Braun et al. show that with log-linearization all sorts of weird stuff happens, but that weird stuff has some similarities with the situation where the ZLB does not bind. Now take the same model, linearize it (the Rothenberg pricing is then equivalent to Calvo pricing), and even weirder stuff happens at the ZLB.
Would you still have confidence about these much touted linear results? Exactly.
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I'm confused. Christiano, Eichenbaum and Rebelo use a deterministic model which doesn't need to be linearized. Plus Fernandez Villa-verde and co-authors have a paper where they nonlinearly solve a DSGE model and fine multipliers > 1 when ZLB binds, and they also have a paper where they solve a NK model in continuous time that has the same finding. Also, multipliers > 1 also show up in Gurrieri and Lorenzoni's incomplete markets model.
What are these guys on about?
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to 38ee: Nice analysis. You could also put it this way:
In the liquidity trap, the large spending multiplier has a weird property - the government spends more, tells all households they will have to pay higher taxes, but still households consume more. This is really weird if you think about it. This is what Krugman is arguing that actual policy should pursue but it can occur in new keynesian models at the liquidity trap.
In the equilibrium that Mertens and Ravn look at, the multiplier is smaller than one but there are other weird things going on. One may not like those weird things but they can happen.
So essentially, you would need to be god to know which equilibrium you're in before you could state absolutely surely what is the impact of policy.
Braun et al instead claims that the large multiplier is just because of the log-linearization. Christiano's note seems to kills this argument.
Of course a physicist would laugh because they would quickly run an experiment to see which equilibrium had occurred but we economists cannot easily do this.
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A question I'd like to see asked is the following. Forget the output multiplier. What is the welfare multiplier?
The only way to get higher output following an increase in government spending is for people to work more. So I think what's going on in the model is that the government is increasing spending, which impoverishes people and makes them want to work harder. Output goes up, which has to be consumed in equilibrium. Are people better or worse off? I don't know.
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ea14, I don't think the intuitive explanation Krugman's recommendation is that weird. The point is that the natural rate of interest is negative, and the only way to push the real rate to be negative is to induce inflation (and government spending induces inflation, and increases household consumption by reducing the real rate).
There's also the other stuff about some households being hand-to-mouth consumers who will spend whatever money they get.
Now can someone explain to me what is going on in this other equilibrium?
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cbdf: It is still a bit weird - the natural real interest rate is negative and we need inflation so .... ok the government goes around saying: "you guys are saving too much, so I will confiscate some of your goods, tax you more, and therefore you better spend more on the goods that I am confiscating. For every dollar that I promise to spend more in the future, these households spend an extra 60 cents or even more."
I think this is weird despite the natural interest rate being negative.
What would perhaps be less weird would be to tax the high savers and give to the high propensity to consume guys but that (a) wouldn't have to involve any government purchases of goods and (b) be unfortunate in terms of incentives.
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ea14, have a look at the paper by Farhi and Werning on fiscal multipliers. When the government starts spending, there are two effects:
1) Households now have lower permanent incomes, so they cut back on consumption. But because they smooth consumption, the fall in consumption is lower than the sudden burst of spending, so this gives a government multiplier > 0 but < 1.
2) On the other hand, the spending increases inflation and expected via the Phillips curve (because the central bank isn't responding). This pushes down the real interest in the household's Euler equation. So households consumer more.
(1) + (2) = multiplier > 1. This is not that strange a story... at least it's no more strange than anything else you can get out of these models.
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cbdf, the Farhi and Werning story is nicer, that's right (these guys are geniuses so it's not a total surprise that they can cut it out). But still when you combine (1) + (2), it is a bit weird.
Maybe the weirdness is even clearer if you think about a tax cut. In the liquidity trap the tax cut actually leads to a drop in activity. The reason is again weird if you think about it. Suppose it's a flat rate income tax. I cut it which lowers distortions and increases you current income but you save like mad. What happens here is that the tax cut actually leads to even less inflation.
So it then follows that one should hike taxes in a liquidity trap. Now that's weird squared.
So now return to the other equilibrium that Mertens and Ravn look at. If I am right, they have a positive but low spending multiplier and a moderate but positive tax multiplier. Now, as pointed out earlier there may be weird things that can happen if you increased the nominal interest rate, but it still doesn't sound that much weirder than the new keynesian prescriptions above.
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Wow, an EJMR thread I can actually learn from! 38ee good.
I've personally been skeptical of the Christiano-Eichenbaum research agenda for a while, but not because of some nuance of log-linearization. There are a lot of meaningful questions to be raised about the new-keynesian framework that deal directly with the macroeconomics we are supposed to be using them to learn about. For instance, wtf IS any particular shock representing? When we "identify" the parameters associated with these shocks, are we identifying something meaningful, or just picking up information from some other important economic phenomenon that we should have in the model? And, to the heart of the problems in the DSGE framework, is aggregation covering up any meaningful economic behavior that will make a representative agent model give a false impression of what equilibrium should look like?
Many of the questions for macro right now have a lot more to do with empirics than log-linearization or some other math related distraction, but it seems they have been ignored by the current crop of top-ranked macroeconomists because answering these empirical questions both difficult and requires skills they didn't spend time developing. Fortunately, I think most younger macroeconomists I meet are interested, or at least concerned with these sort of issues, and are far more focused on empirics. The work is just overshadowed by a number of established macroeconomists like Christiano that have worked to develop a theory that is now in serious need of testing to meaningfully expand.