### The Relationship Between Nominal Interest Rates and Inflation: Should Jaws be Dropping?

I'm getting some pushback on my post entitled "Jaws are Dropping," which is derived from a statement in one of the links I provided in the post. I think it must be either the title of the post or, when correcting a typo, the afterthought I added about the right answer to the question of whether a low federal funds rate *eventually* leads to a
fall in inflation that has some people so worked up (good to see that Williamson has taking a break from his exhibitions of
Krugman Derangement Syndrome, bashing Krugman seems to be the main point
of his blog lately). It can't be anything else I said since my main point was that I didn't have time to say much about the whole controversy due to an impending deadline.

The main issue revolves around this statement from Minnesota Fed President Narayana Kocherlakota:

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation

I think the assertion that it "must" lead to that outcome is unsupportable, there are models where that isn't true, but he means "must" in terms of a very specific model of how the economy works, including an assumption of the super neutrality of money (which is asserted as an uncontroversial assumption, but I'd quarrel with that). So, yes, it's possible to write down a very specific model that has this as an implication, but does that make it generally true? Not to me.

In any case, here's an email from a friend of Narayana defending his statements:

And, he sends along an update:Hi:

I rarely comment on posts on blogs, since most of the discussion seems to be most interested in scoring political points than in economic analysis. However today I will make an exception since Kocherlakota's words come directly from any standard treatment of monetary theory, and hence, they should have been anything except controversial.

In a large class of monetary models, the Euler equation of intertemporal maximization is:

FFR = (1/beta) *(u'(c

_{t})/u'(c_{t+1}))*inflationwhere u'(.) is the marginal utility of consumption, FFR is the federal funds rate, and beta is the discount factor (see, for instance, equation 1.21 in page 71 of Mike Woodford's Interest and Prices for a derivation in a simple context).

Let us take first the case where money is neutral, probably an implausible case but a good starting point. In this situation, the ratio of marginal utilities is unaffected by the change in inflation or the FFR. Thus, a lower FFR means lower inflation. Otherwise, there are arbitrage opportunities left on the table. What is more, in such a world, the Fed can control inflation by controlling the FFR, so the relation is causal in a well-defined sense.

Now, let's move to the much more empirically relevant case of a New Keynesian model (here I am thinking about the standard NK model people use these days to analyze policy in the style of Mike Woodford, Larry Christiano or Martin Eichenbaum, with a lot of nominal and real rigidities, so I will not discuss the assumptions in detail).

Imagine that the Fed is targeting the FFR and decides to lower the long run target from, let's say 4% to 2%. What happens? Well, in the very short run, nominal rigidities imply that we will have a transition where inflation might (but not necessarily, it depends on details of the model) be temporarily higher but, after the necessary adjustments in the economy had occurred (adjustments that can be quite painful, generate large unemployment, and might reduce welfare by a considerable amount), we settle down in the lower inflation path. Again, the reason is that in most New Keynesian models, the ratio of marginal utilities is independent of the FFR (this will happen even in many models with long-run non-neutralities) and the Euler equation will reassert itself: the only way we can have a real interest rate of 3% when the target FFR is 2% is with a 1% deflation.

Hence, in the long run, as Kocherlakota's speech explicitly says:

"To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation."

An alternative way to see this is to think about a Taylor rule of the form:

R

_{t}/R = (π_{t}/π)^{γ}where γ>1 (here I am eliminating extra terms in the rule for clarity) where R

_{t}is the FFR, R is the long run target for the FFR, π_{t}is inflation, and π is the long run target for inflation. In a general equilibrium model, the Fed can only pick either R or π but not both. If it decides to pick a lower R, the only way the rule can work is through a fall in π.While one may disagree with many aspects of modern monetary theory (and I have my own troubles with it), one must at least acknowledge that Kocherlakota's treatment of this issue or the relation between the FFR and inflation in the long run is what would appear in any standard macro model.

Thanks

Jesus Fernandez-Villaverde

One thing I forgot to mention: I guess that the intuition that most people have (and that reacts in a somewhat surprised way to Narayana's words) comes from a New Keynesian model, where lowering the FFR with respect to what the Taylor rule indicates (what we call a "monetary shock") increases inflation in the short run. But here we are not talking about the effects on inflation of a transitory monetary shock, but, as Narayana clearly says in his speech, about the long run effects of a change in the target of the FFR.

If you commit to a single class of models and the interpretation of the shocks within them, the kind of models and interpretations that Narayana Kocherlakota has questioned, at least in their standard forms, and if you buy all the embedded assumptions that are needed to obtain the result, not all of which are easy to defend (e.g. the assumption of long-run neutrality), then yes, "must" is correct. But "must" must be interpreted in a rather limited context, and in a more general setting it's not at all clear that this result will hold.

However, my real problem with this defense is that it doesn't deal with the assertion that if real rates normalize and the Fed doesn't raise its target rate in response, it will lead to deflation., i.e. it doesn't address Nick Rowe's point. If the target real rate is below the normal real rate, how does that cause deflation? That's the part that caused the objection in the first place, and the part that still leaves me puzzled. Here's Nick:

"

To sum up, over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation."That could be interpreted two ways: a wrong way, and maybe, just maybe, a right way.

"

When real returns are normalized, inflationary expectations could well be negative, and there may still be a considerable amount of structural unemployment. If the FOMC hews too closely to conventional thinking, it might be inclined to keep its target rate low. That kind of reaction would simply re-enforce the deflationary expectations and lead to many years of deflation."Nope. He definitely meant it the wrong way. If the economy returns to normal, and the natural rate of interest rises, the Fed must raise its target rate of interest. (So far so good). If it doesn't, the result would be....deflation. ("Inflation" would be the right answer).

I also wonder if a permanent shock is the right way to think about this type of a policy, but I'll leave that as a question since I don't want to distract from Nick's point.

**Update**: Here's more from Nick:

What standard monetary theory says about the relation between nominal interest rates and inflation, by Nick Rowe: This is what I understand "standard" monetary theory to say about the relation between inflation and nominal interest rates.

I want to distinguish two cases.

In the first case the central bank pegs the time-path of the money supply. The money supply is exogenous. The nominal interest rate is endogenous. Standard monetary theory says that a permanent 1 percentage point increase in the growth rate of the money supply will (in the long run) cause both the nominal interest rate and the rate of inflation to rise by 1 percentage point. The Fisher relation holds as a long-run equilibrium relationship. The real interest rate is unaffected by monetary policy in the long run.

In the second case the central bank pegs the time-path of the nominal rate of interest. The nominal interest rate is exogenous. The money supply is endogenous. Start in equilibrium (never mind how we got there). Standard monetary theory says that if the central bank pegs the time-path of the nominal interest rate permanently 1 percentage point higher, this will cause the price level, and the rate of inflation, and the stock of money, to fall without limit. The Fisher relation will not hold, because there is no process that will bring us to a new long run equilibrium. The real interest rate will rise without limit.

These two cases are very different, because a different variable is assumed exogenous in each case.

I am assuming super-neutrality of money, in long-run equilibrium. The Fisher relation is a long run equilibrium relationship. We never get to the new long-run equilibrium in the second case, and so the Fisher relation does not hold.

**Update**: Brad DeLong comments.

Posted by Mark Thoma on Thursday, August 26, 2010 at 12:33 AM in Economics, Inflation, Macroeconomics, Methodology, Monetary Policy |
Permalink
Comments (96)

You can follow this conversation by subscribing to the comment feed for this post.