..the Fed does not engage in reflective equilibrium. It rejects the conclusions of what I regard as the standard Patinkin-style existing model of Krugman (1999). But it does not propose an alternative model. There seems to me to be no theoretical ground, no model even considered as a filing system, underpinning the "orthodox" modes of thought that the Fed believes. And it does not seem to feel this absence aaa a problem. I find that somewhat disturbing.It's unfortunate that Brad's post distracted me, as I was busily engaged in reflective equilibrum, but what the heck. I thought I would check out Krugman's 1999 article, to refresh my memory. As I thought, the meat of the thing isn't actually a "Patinkin" model, it's a simple Lucas cash-in-advance model. As far as I remember, this thing has not been rejected where I work, though some of my colleagues might object to the CIA constraint as being insufficiently grounded in theory. Further, out here in flyover country (or the pond, as it's come to be known in recent days), we take offense when people call our models "orthodox," and if someone suggested we think of our theories as "filing systems," we would likely scream and run away.

Oh, by the way, here's something interesting. Let's take Brad seriously and look at the implications of Krugman's (1999) model. There's a representative, infinitely lived agent, with discount factor

*B*and utility function

*u(c),*where

*c*is current consumption. There is a fixed endowment of perishable consumption goods each period, which must be purchased with money, which is supplied by the central bank. We can flesh out the details of transactions, for example there can be many households which sell their endowment and purchase output each period, or output could be grown on "Lucas fruit trees," with consumers owning shares in the trees. But those are details that are irrelevant for the equilibrium. As well, money could be injected by way of lump-sum transfers, or through open market operations. Again, the details don't matter for what we'll do here. Let

*R(t)*denote the nominal interest rate,

*i(t)*the inflation rate, and

*M(t)*the aggregate money stock.

Consider deterministic equilibria in which the central bank sets policy as a sequence of nominal interest rates

*R(0), R(1), R(2),*... . Then, intertemporal optimization implies

(1)

*i(t+1) = B - 1 + BR(t)*,

for

*t = 0, 1, 2, ... .*The central bank then supports the sequence of nominal interest rates in a rational expectations equilibrium through the appropriate series of money growth rates m(1), m(2), m(3), ..., where

(2)

*m(t) = M(t)/M(t-1) - 1*,

and the sequence of money growth rates required to support the interest rate policy is

(3)

*m(t+1) = B - 1 + BR(t).*

Basically, Krugman's model is a purely Fisherian model of inflation - there's no liquidity effect, only a Fisher effect, so the nominal interest rate always reflects only anticipated inflation. So if the central bank thinks inflation is too low and wants it to go up, what should it do? Equation (1) says it must

*raise the nominal interest rate.*

So, I'm pleased to report that Brad is a neo-Fisherian. Seemingly, so is Paul.

"In summary, the learning approach argues forcefully against the neo- Fisherian view."

ReplyDeleteGeorge and Bruce would probably be happy to engage a discussion on these issues:

http://economistsview.typepad.com/economistsview/2015/12/the-neo-fisherian-view-and-the-macro-learning-approach.html

Among people who do learning, you're not allowed to think about particular rational expectations equilibria unless you can construct "plausible" learning rules, under which convergence to the candidate equilibrium happens. Evans claims that, under plausible learning rules, nominal interest rate pegs can't happen because they are "unstable," and that equilibria under the Taylor principle that converge to the ZLB also can't happen. A robust result in rational expectations models is that you get Fisherian results with nominal interest rate pegs, and the Taylor principle leads to a lot of equilibria that go to the ZLB and ultimately produce low inflation. In reality, I see a 20-year history of a ZIRP (zero interest rate policy) in Japan, and a seven year experience in the U.S. with ZIRP. None of that experience appears to be associated with instability. But it is associated with low inflation. Further, central banks following Taylor rules have, around the world, ended up at the ZLB, or have shown us that zero actually isn't a bound, and gone lower. Universally, those central banks have produced low inflation. So, standard rational expectations reasoning helps me understand what is going on in the world. The learning literature doesn't help me at all.

DeleteA model in which the central bank increases the money growth rate in order to increase the inflation rate in order to increase the nominal interest rate is Fisherian.

ReplyDeleteA model in which the central bank increases the nominal interest rate in order to increase the inflation rate in order to increase the money growth rate is Neo-Fisherian.

It all hangs on that word "supports". What's exogenous and what's endogenous.

If you tell the Fed to raise the nominal interest rate tomorrow, it's going to interpret you to be telling it to cut the money growth rate and cut the inflation target.

If you tell the Fed to raise the nominal interest rate in a couple of years, it's going to interpret you to be telling it to increase the money growth rate and raise the inflation target.

"If you tell the Fed to raise the nominal interest rate tomorrow, it's going to interpret you to be telling it to cut the money growth rate and cut the inflation target."

DeleteWell, the Fed raised nominal interest rates a couple of weeks ago, and the New York Fed did it by just increasing the interest rates on some Fed liablities.

Paul Krugman's simple model assumes that holding money pays 0% nominal interest. His M is like currency. So the only monetary instrument the Fed would have in that world is reducing the growth rate of the money supply M to reduce inflation. But some of the Fed's monetary liabilities do pay interest, and if the Fed raises the nominal interest rate it pays on those liabilities, holding the stock of monetary liabilities constant, that increases the demand for those monetary liabilities and causes a one-time fall in the equilibrium price level.

DeleteYou confused me. If you say "the Fed," I'll interpret it as the real Fed, not the people in Krugman's CIA model that print money. So, back to your previous comment:

Delete"If you tell the Fed to raise the nominal interest rate tomorrow, it's going to interpret you to be telling it to cut the money growth rate and cut the inflation target."

No. The central bank in Krugman's model has to promise to increase the future money growth rate to bring about an increase in the current nominal interest rate. It's a pure-Fisher-effect model. The nominal interest rate is determined by anticipated inflation (equal to future money growth with perfect foresight) and the rate of time preference.

"But some of the Fed's monetary liabilities do pay interest, and if the Fed raises the nominal interest rate it pays on those liabilities, holding the stock of monetary liabilities constant, that increases the demand for those monetary liabilities and causes a one-time fall in the equilibrium price level."

Now, I'm assuming that you're talking about a different model that has interest-bearing central bank liabilities in it. I would have thought that increasing the interest rate on interest-bearing central bank liabilities would reduce the demand for the non-interest-bearing central bank liabilities (currency), producing a one-time increase in the price level.

"The central bank in Krugman's model has to promise to increase the future money growth rate to bring about an increase in the current nominal interest rate. It's a pure-Fisher-effect model. The nominal interest rate is determined by anticipated inflation (equal to future money growth with perfect foresight) and the rate of time preference."

DeleteAgreed.

"Now, I'm assuming that you're talking about a different model that has interest-bearing central bank liabilities in it."

Yes.

"I would have thought that increasing the interest rate on interest-bearing central bank liabilities would reduce the demand for the non-interest-bearing central bank liabilities (currency), producing a one-time increase in the price level."

If there were flexible exchange rates between non-interest-bearing liabilities (currency) and interest-bearing liabilities (reserves), then (holding the stock of currency fixed) we would see the value of currency fall against both reserves and goods (a rise in the price level).

But if instead the Fed fixes the exchange rate between currency and reserves, we would see the stock of currency fall, as the Fed buys it back (with sterilisation to prevent the stock of reserves rising), and the equilibrium price level will fall.

Let's go back to Krugman's model. You can put some reserves in that model, pay interest on them, and they will be just like Treasury bills. Another detail that doesn't matter. Then, the M in the model is currency, and we can have monetary policy that is purely changes in the nominal interest rate - no open market operations. But currency and reserves are convertible one-for-one.

DeleteThen, think about an experiment where the nominal interest rate increases sometime in the future - a one-time increase that's permanent. Then, M grows at a constant rate until the nominal interest rate goes up in period T. Then in period T+1, the money growth rate is higher forever. There's no price level effect, as the price level is always P(t) = M(t)/y, so in this model we're both wrong.

Let's take Brad seriously.....

ReplyDeleteWhy, Steve, in God's name why ?

from an adjunct community college lecturer

You know I'm just having fun.

DeleteSteve:

ReplyDeleteI'm glad you read Krugman's paper (really just an html -- did he publish it somewhere?). If you're willing to go along with Krugman's model, I think we can use it to clarify the difference of opinion between Keynesians and Neo-Fisherians.

Let's be clear what I'm talking about here: I mean the version of Krugman's model where the current price P(t) is fixed, and all future prices are flexible. So we're talking about one-period sticky prices. And we can ignore the liquidity trap stuff, because that isn't relevant here.

Now consider two monetary policies that the Fed could take:

Policy 1: The Fed increases M(t), but leaves all future M unchanged. Since future M are unchanged, all future prices are unchanged, and since P(t) is fixed inflation is constant. From the CIA constraint, lower M(t) (with fixed P(t)) means that c(t) must fall. Then from the Euler equation, i(t) must rise. Thus we get higher interest rates and a real contraction.

Policy 2: The Fed increases all future M. Then all future P are increased. c(t) remains unchanged, but higher P(t+1) implies higher i(t). Thus we get higher interest rates and inflation.

Now the question: which of these policies (in the model) best corresponds to the policy "The Fed raises interest rates" in the real world? Keynesians say policy 1, while Neo-Fisherians say policy 2.

Sorry, there may have been a typo in my previously submitted comment. I meant:

ReplyDeletePolicy 1: Fed *decreases* M(t). c(t) falls and i(t) rises.

Policy 2: Fed *increases* all future M. i(t) rises and all future P rise, so inflation rises.

Here's a published version (actually 1998):

Deletehttp://www.brookings.edu/~/media/projects/bpea/1998%202/1998b_bpea_krugman_dominquez_rogoff.pdf

This model is pretty crude for working through sticky price results. I think you want some dynamics. Cochrane has actually worked out neo-Fisherian results in a standard Woodford-type New Keynesian model with sticky prices:

http://faculty.chicagobooth.edu/john.cochrane/research/papers/fisher.pdf

What Krugman's model does not have, with flexible prices, is liquidity effects. To not get Fisherian results, i.e. to have inflation go down on impact when the nominal interest rate goes up, you have to have a very large liquidity effect. That is, absent uncertainty, the real rate has to go up by more than the nominal rate.

You say crude, I say simple and potentially clarifying.

Delete"What Krugman's model does not have, with flexible prices, is liquidity effects."

Sure, but if you fix P(t) then you get the required liquidity effect: reducing M(t) (through an open market operation, say) lowers c(t) and raises i(t). And since inflation is constant, the real interest rate rises.

With policy #1, nothing happens to the inflation rate when the nominal interest rate goes up. But of course that's extreme, as you've fixed the prices, and the experiment, so that inflation is going to be invariant to the monetary intervention. This is all liquidity effect and no Fisher effect. The nominal rate and real rate increase by the same amount. See if you can give me an example where the nominal interest rate goes up and the inflation rate goes down. That seems to be the standard logic.

Delete"See if you can give me an example where the nominal interest rate goes up and the inflation rate goes down. That seems to be the standard logic."

DeleteTake the standard log-linearized NK model, e.g. equations (1) and (2) from the Cochrane paper. Suppose the economy is initially at (0,0) (inflation and output gap). Consider an unanticipated one-period increase in the interest rate, with a return thereafter to (0,0). The result will be a one-period decrease in output and inflation.

If we added money (as Cochrane does in section 3), we see that this experiment involves an unanticipated decrease in the money supply for one period. So this is really just the same as experiment 1 in Krugman's model, with a few extra bells and whistles (that, among other things, let us model inflation dynamics).

By contrast, the Neo-Fisherian policy that Cochrane analyzes is a *permanent* increase in the nominal interest rate. In his model with money, though he doesn't plot the path of money, we can figure out that this must involve a *permanent* increase in the growth rate of the money supply in the future. Thus this amounts to experiment 2 (with a little experiment 1 thrown in, since the money supply decreases initially before rising later -- which is why he gets an initial negative effect on output).

By the way, although I have great respect for Woodford and understand the convenience of avoiding explicitly modelling money, for some conversations (such as this one) I think it's very useful to think about money.

I was actually interested in the experiment where the nominal interest rate goes up permanently - an example where it's obvious the inflation rate goes down on impact.

DeleteHere's another thought on policy experiments in Krugman's model with the first period price level fixed. Increasing M in the first period does nothing - that's Krugman's liquidity trap result. But that's an experiment where M goes up temporarily, and then the central bank takes it back the next period. People are content to hold the money for one period and then it's taxed away. But suppose the money injection is permanent in the first period. Then, if the central bank injects enough money, the inefficiency goes away, with the future price level rising enough that all goods are consumed in the first period. But what happens if more money than that is injected? That depends on what you assume about the fixed prices. Does the price level stay fixed, with some buyers showing up to buy goods the sellers will not sell? A convenient fix is to assume that the price level is only sticky downward. Then if more money is injected than needed to remove the inefficiency, the nominal interest rate starts to go up in the first period. So liftoff is a good thing in that case.

Steve:

DeleteExactly. This is why Krugman has always qualified his claim that monetary policy is ineffective in a liquidity trap. He thinks that monetary stimulus is ineffective *if* everyone expects it to be temporary. If the Fed could credibly promise to allow future inflation, what he calls "credibly promising to be irresponsible", then the economy could escape the trap. However, he doesn't think they can do this, which is why he supports fiscal stimulus as a second-best policy.

So one interpretation here is that Neo-Fisherians think the Fed can commit to future inflation, while Keynesians don't. Thus under the Neo-Fisherian view, if the Fed raises the nominal interest rate permanently (which would involve reducing the money supply in the short run, but promising future money growth), inflation would rise because of the expected future inflation. Keynesians think the promise of future inflation would not be credible, and so current inflation would fall (because of the current decrease in the money supply).

In other words, Keynesians think that the Fed raising interest rates is policy 1 (regardless of what they promise to do in the future). Neo-Fisherians think it would be policy 2 (plus a little 1).

A Keynesian thinks that, if the central bank keeps the nominal interest rate at zero for a long time, then eventually the Phillips curve will assert itself and inflation will go up. A neo-Fisherian knows that, when the central bank keeps the nominal interest rate at zero for a long time, the inflation rate will be low. So the only way that inflation can go up is if the central bank increases the nominal interest rate.

DeleteSorry Stephen, but IMHO a Keynesian thinks that if the nominal interest rate is zero, then the Liquidity preference is infinite and there is no monetary traction.

DeleteA Keynesian thinks the only way to get out of a Liquidity trap is trough a combination of fiscal (trough government spending) and monetary policy.

"...the only way to get out of a Liquidity trap is trough a combination of fiscal (trough government spending) and monetary policy."

DeleteI think most everyone would agree with that. That's not particular to Keynesians.