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:

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}))*inflation

where 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

And, he sends along an update:

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.