# In Defense of Neo-Fisherism

The term neo-Fisherites has arisen to describe people like John Cochrane, who has suggested what New Keynesians believe to be a particularly weird policy conclusion. Namely, he has suggested that the Federal Reserve’s pegging of the interest rate on reserves at a rate very close to zero implies that we will experience deflation. A number of people I would identify as New Keynesians have privately communicated to me that they think this claim is preposterous and that Cochrane doesn’t understand how policy works. However, I would submit that John Cochrane understands the New Keynesian Model better than the New Keynesians and that if his prediction is wrong, then this has more to do with how little New Keynesian models teach us about monetary policy.

Let’s start with a basic premise that I think everyone would agree with. Let’s make three assumptions (1) the real interest rate is positive, (2) the Federal Reserve pegs the interest rate arbitrarily close to zero, and (3) the Federal Reserve pursues a policy of generating positive inflation. If (1), (2), and (3) are true, then the Federal Reserve is pursuing an unsustainable policy. This is the essence of neo-Fisherism. So what is wrong with this conclusion?

New Keynesians seem willing to admit the above policy is unsustainable. However, they think that it works in the opposite direction. In particular, New Keynesians have countered that if the Federal Reserve pegs the interest rate too long, then we should get more inflation and not less. This is certainly in keeping with the argument of Milton Friedman in his 1968 AEA Presidential Address. As Peter Howitt (2005) explains:

Friedman argued that at any given time there is a hypothetical (“natural”) real rate of interest that would generate a full employment level of demand. If the central bank set nominal interest rates too low, given the expected rate of inflation, then the real interest rate would be below this hypothetical natural rate, and this would generate excess aggregate demand, which would cause inflation to rise faster than expected… With inflation running faster than expected, people’s expectations of inflation would at some point start to rise, and if the nominal rate of interest were kept fixed that would just fuel the fire even more by reducing the real rate of interest still further below its natural rate.

I could have easily summarized Friedman’s position myself. However, the quote of Peter Howitt describing Friedman’s position is purposeful. The reason is because a number of observers have claimed that Cochrane and other neo-Fisherites should just read Howitt’s 1992 paper that seemingly shows how the New Keynesian model produces Friedman’s prediction. However, I would submit that this fails to understand Howitt’s paper.

For the interested reader, let me condense Howitt’s paper into a simplified New Keynesian framework. Suppose that there is an IS equation:

$y_t = -\sigma (i_t - E_t \pi_{t+1} - r^*)$

and a New Keynesian Phillips Curve:

$\pi_t = E_t \pi_{t+1} + \phi y_t$

where $y$ is the output gap, $\pi$ is inflation, $i$ is the nominal interest rate, $r$ is the natural real rate of interest, $E$ is the expectations operator, and $\sigma$ and $\phi$ are parameters. Suppose that the central bank decides to peg the interest rate and suppose that the Federal Reserve’s desired rate of inflation is $\pi^*$. In a rational expectations equilibrium, it will be true that $\pi_t = E_t \pi_{t+1} = \pi^*$. Using this result, we can now combine the two equations to get an equilibrium inflation rate. Doing so yields,

$\pi_t = i_t - r^* = \pi^*$

Thus, in this New Keynesian model, when the central bank pegs the interest rate, the equilibrium inflation rate is increasing in the nominal interest rate. This is precisely what Cochrane and others have argued!

New Keynesians, however, conveniently ignore this result.* Instead, they immediately jump to a different conclusion drawn by Howitt. In particular, the way in which Howitt argues that we can obtain Friedman’s result in this framework is by starting with a departure from rational expectations. He then shows that without rational expectations, individuals would make forecast errors and that this particular policy would reinforce the forecast errors thereby producing Friedman’s conclusion. Any learning rule would push us away from the unique equilibrium $\pi^*$.

But the New Keynesian model doesn’t assume a departure from rational expectations. Thus, our result that $\pi_t = i_t - r^*$ is not overturned by Howitt. Those who seek Howitt for support are abandoning the New Keynesian model.

Thus, we are left with an unfortunate conclusion. The New Keynesian discussion of policy doesn’t fit with the New Keynesian model of policy. Thus, either the model is wrong and the discussion is correct or the discussion is wrong and the model is correct. But consider the implications. Much of policy advice that is given today is informed by this New Keynesian discussion. If the model is correct, then this advice is actually wrong. However, if the model is wrong and the discussion is correct, then the New Keynesians are correct in spite of themselves. In other words, they still have no idea how policy is working because their model is wrong. Either way we are left with the conclusion that New Keynesians have no idea how policy works.

* – A subsequent argument is that pegging $i_t$ causing a multiplicity of equilibria even under the assumption of rational expectations. Thus, the equilibrium I describe above might not be unique in more general models in which the expectation of the output gap appear in the IS equation. New Keynesians have argued that you can generate a unique equilibrium by having the central bank increase the interest rate adjust more than one-for-one with changes in the inflation rate. However, Benhabib, et al. have shown that this isn’t sufficient for global uniqueness and that there is a multiplicity of stable equilibria near the zero lower bound on interest rates.

### 8 responses to “In Defense of Neo-Fisherism”

1. PJ

Great post. This is a great sentence:

“However, I would submit that John Cochrane understands the New Keynesian Model better than the New Keynesians and that if his prediction is wrong, then this has more to do with how little New Keynesian models teach us about monetary policy.”

2. Good post Josh. But I would say it a little differently. The New Keynesians have an equilibrium model, but a disequilibrium story of what keeps us on that equilibrium path.

3. That no one has given an English translation of “neo-fisherian” ideas (ie. non mathematical) immediately renders it suspect to me. Well, Stephen Williamson has tried several times on his blog but failed miserably each time. I’ve tried to put the idea into writing, but failed too–which only makes me more skeptical.

4. Frank Restly

Josh,

In many cases, interest expense paid by private borrowers is tax deductible. It seems to me that this would reduce the Fisher effect at higher nominal interest rates.

For instance, company ABC, has D amount of debt that they pay an N nominal interest rate on. They also have net income INC that is taxed at rate TR.

The amount of taxes paid (without deductible interest would be):
Taxes = INC * TR

The amount of taxes paid (with deductible interest would be):
Taxes = (INC – D*N) * TR

The tax savings is simply:
D * N * TR

The after tax interest rate is:
NAT = ( D * N – D * N * TR ) / D = N * (1 – TR)

Assuming a 25% tax rate, the nominal and after tax interest rates go as follows:

N = 3%, NAT = 2.25% (tax savings = 0.75%)
N = 5%, NAT = 3.75% (tax savings = 1.25%)
N = 7%, NAT = 5.25% (tax savings = 1.75%)
N = 12%, NAT = 9% (tax savings = 3%)

And so the inflation rate would track the NAT (after tax interest expense), not the N (nominal interest expense).

5. Nick,

The issue at stake is of first-order importance, so shouldn’t be waved away by appealing to “out of equilibrium stories.” If it is important, then it should be included in the logic of the model.

David

6. Ole Smidth

I disagree with you when you write:
“Thus, either the model is wrong and the discussion is correct or the discussion is wrong and the model is correct.”
Both could be wrong.

7. David J Roach

In the article you present a system of two linear equations. These are:
1./ y(t) = -σ∙{i(t) – r*-E(π(t+1)}
2./ π(t) = E(π(t+1))+φ∙y(t)
The term E(π(t+1)) common to both equations can be eliminated to yield a single equation relating y(t), π(t), r*, and i(t):
3./ – (φ + 1/σ) ∙y(t) = i(t) – r* – π(t)

The right-hand side of equation (3) is, in the neo-Fisherism hypothesis, equal to zero. Since y(t) is seldom zero, the only other way in which the hypothesis can hold is if (φ + 1/σ) = 0 for all time periods, t. If (φ + 1/σ) ≠ 0, then the neo-Fisherism hypothesis is invalid in an economy for which equations (1) and (2) hold true.

There is then no need to bring into the discussion any other hypotheses (e.g., “rational expectations). We can conclude that i(t) – r* – π(t) ≠ 0 except in the special circumstance when y(t) = 0, i.e., when the output gap is nil.