**Summary:**

According to my friend and former colleague Steve Williamson, inflation is low in Japan because of the Bank of Japan's policy of keeping its policy rate low. Accordingly, if the BOJ wants to hit its 2% inflation target, it should raise its policy rate and keep it persistently higher. This is what I've called the NeoFisherian proposition. It's a provocative idea because it flies in the face of conventional wisdom. But is it correct? Does it serve as a practical guide for monetary policy? My feeling is that the answers to these questions are "no" and "no." In what follows, I explain why.At some point in their undergraduate career, students of macroeconomics are introduced to the Fisher equation. The Fisher equation usually stated as R = r + π or, in words: Nominal Rate of Interest = Real

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*raise*its policy rate and keep it persistently higher. This is what I've called the

*NeoFisherian proposition*. It's a provocative idea because it flies in the face of conventional wisdom. But is it correct? Does it serve as a practical guide for monetary policy? My feeling is that the answers to these questions are "no" and "no." In what follows, I explain why.

At some point in their undergraduate career, students of macroeconomics are introduced to the Fisher equation. The Fisher equation usually stated as R = r + π or, in words:

For simplicity, think of the real rate of interest as the rate of return an investor can achieve by storing goods across time. For squirrels storing nuts, the real rate of interest is negative. For humans planting corn, it is positive. Whatever its value, let's just fix it at some number and assume it remains invariant over time (this is not a critical assumption for the arguments I want to develop below). Then, the

*Fisher hypothesis*is that the nominal rate of interest should move one-for-one with the expected rate of inflation.

How does the Fisher equation hold up in the data? Let's just say that the evidence is mixed. Fisher himself famously rejected it as being empirically relevant. But over long periods of time, and also across countries, various nominal interest rates do appear positively correlated with the measured inflation rate (taken as a proxy for expected inflation).

Well, correlation is one thing, explanation is another. What is the theoretical underpinning of the Fisher equation? One way to view it is as a no-arbitrage-condition. Suppose that planting a bushel of corn yields 1.02 bushels at harvest (2% real rate of interest). Suppose that the nominal price of corn (its price measured in dollars) is expected to rise 10% by harvest time. What rate of return would an investor demand of a bond promising to deliver money at harvest time? The Fisher equation says that the investor should demand a rate of return of at least 12%. The bond would then deliver 12% more dollars that, if spent on corn at harvest, would leave an inflation-adjusted return of 2%. In this case, the investor would be just indifferent between investing in a corn planting venture and the nominal security.

Viewed in this light, the Fisher equation can be interpreted as the interest rate bond-holders demand, given their outlook on inflation. And, indeed, the standard textbook explanation for why nominal interest rates tend to rise with inflation provides a clear causal link, starting with monetary policy in the form of base-money growth rate:

[1] increase in money supply growth (spent on goods or delivered as tax cuts or transfers);

[2] causes increase in demand, which causes prices to rise;

[3] inflation expectations adjust upwards accordingly;

[4] bondholders demand higher interest rate to compensate for higher expected inflation.

The interpretation above assumes that monetary policy does not target the interest rate on bonds. Instead, it grows the money supply and lets the market determine the nominal interest rate. But note that monetary policy *is* targeting an interest rate in this explanation. In particular, the nominal interest rate on central bank money (reserves and currency) is set to zero. This policy goes by the acronym ZIRP (zero-interest-rate-policy). Moreover, there is a Fisher equation that holds for money. It looks like this R_m + LP = r + π, or in words:

If the nominal interest rate on money is zero, then money must be held for its non-pecuniary benefits (liquidity). The liquidity premium on money is in this case equal to the nominal interest rate on an

*illiquid*bond; i.e., LP = R = r + π.

Now, if the nominal security yielding a positive interest rate in the story above consists of government bonds (denominated in the domestic currency), then the only way to explain the apparent discount on government bonds is by appealing to an explicit government policy that renders these bonds illiquid relative to central bank money. And indeed, we see restrictions like this in place throughout history. For example, convenient low-denomination zero-interest notes (cash) versus inconvenient large-denomination notes (bonds) trading at discount. Or consider today, where interest-bearing accounts at the U.S. Treasury are deliberately rendered useless for making payments. Or the Fed's apparent aversion to setting up a repo facility for U.S. Treasury debt in order to enforce a ceiling on its interest rate target path (such a facility would serve to reduce the demand for reserves).

Monetary theorists like Neil Wallace have puzzled forever over the phenomenon of why government bonds should trade at a discount (the so-called, coexistence puzzle). Others, like former Minneapolis Fed president Narayana Kocherlakota, have attempted to rationalize policies that render government bonds illiquid; see here. At the end of the day what is true is the following: *the nominal interest rate on government bonds is, one way or another, a deliberate policy choice *(for governments that issue debt denominated in the money they issue). This goes for default risk as well. There is no reason to default on debt that constitutes a promise to deliver money that one can costlessly produce. If default takes place in such circumstances, it is a policy choice, not an economic necessity.

Alright, what does all this have to do with Neo-Fisherism and the Neo-Fisherian proposition? I hope everything will fall together in due course. In the meantime, let's assume that the Fisher equation is sound theoretically and holds approximately well in the data. Would this support the proposition? It's clearly not enough because the proposition has to do with causality. The conventional view outlined above is also consistent with theory and evidence. Moreover, the conventional view as expressed through [1]-[4] provides a *simple, coherent, easy-to-understand* story for why we'd expect to see a positive correlation between interest rates and inflation in the data. It may not be correct, but at least it's understandable. Can the Neo-Fisherian proposition be explained in a similarly simple and compelling way? I think it's important for ideas to expressed in clear and simple terms. If policymakers are going to take the proposition seriously, the underlying economic mechanisms will have to be explained in a simple and straightforward manner. It will have to resonate with listeners at some level.

I've only heard of one mechanism that I find semi-plausible: the idea that a higher policy rate increases the interest expense of government debt which, if not met with a tax increase, must be met by an acceleration in money/bond printing (some empirical evidence here). Alternatively, could it be that an increase in the policy rate serves as a type of cost-push shock that propagates itself forward through some adaptive inflation expectations mechanism? I don't know, but it seems worth exploring.

But this is not how Neo-Fisherians explain the mechanism. You can listen to Steve explaining the mechanism in this David Beckworth podcast beginning at the 21 minute mark. There is also this piece published in the St. Louis Fed's Regional Economist: Neo-Fisherism: A Radical Idea or the Most Obvious Solution to the Low-Inflation Problem? Here is how he explains it (boldfont text representing my emphasis):

But, what if we turn this idea on its head, and wethink of the causation running from the nominal interest rate targeted by the central bank to inflation?This, basically, is what Neo-Fisherism is all about[...] But how would this work? [...] To simplify, think of a world in which there is perfect certainty and where everyone knows what future inflation will be. Then, the nominal interest rate R can be expressed as R = r + π, where r is the real (inflation-adjusted) rate of interest and π is future inflation.

Then, suppose that the central bank increases the nominal interest rate R by raising its nominal interest rate target by 1 percentand uses its tools (intervention in financial markets)to sustain this forever. What happens? [...] after a long period of time, the increase in the nominal interest rate will have no effect on r and will be reflected only in a one-for-one increase in the inflation rate, π. In other words, in the long run,the only effect of the nominal interest rate on inflation comes through the Fisher effect; so, if the nominal interest rate went up by 1 percent, so should the inflation rate—in the long run.

But I think he means something else. As I explained above, the "Fisher effect" is a statement about how expected inflation affects the interest rate, not the other way around. The interest rate in Steve's thought experiment is fixed. Therefore, the "Fisher effect" here *must relate to the economic force that causes inflation expectations to rise.* What is this force? He doesn't say. One is left with the feeling that, well, since the Fisher equation holds in theory (and to Steve, in the data as well), inflation expectations somehow *must* adjust to make this true. Ergo, raising the interest rate will eventually lead to an increase in inflation. Central bankers need more than this to go on. In any case, I think that the logic is flawed. Let me explain.

### How Neo-Fisherism Leads to Bad Monetary Policy Advice

(i) How does the CB keep R=0 "along the yield curve." How could you have a flat yield curve at zero with positive inflation? (ii) If you're eliminating all taxes and the fiscal authority is financing everything by issuing debt, and the CB is trying to sustain R=0, then something has to give. For example, people start anticipating that fiscal authority can't roll over the debt, default premia rise on the government debt, and CB is forced to increase R to generate the CB profits required to keep the government afloat.To answer (i), I think the BOJ has shown how it can be done. If the market is discounting JGBs, the BOJ can just buy (or threaten to buy) them up at par. To answer (ii), there is no nominal default risk to consider for Japan--at least, there's no economic reason to default: Japan can print the money it's promising its bond holders. (And if one is worried about the real default implicit in inflation, remember that increasing the inflation rate is exactly the policy goal here.)

Steve has also pointed out that Japan's nominal debt has already grown substantially, so where's the inflation? The answer is that one cannot just look at supply--one must also consider demand. Evidently, the demand for JGBs has been increasing rapidly as well. If the supply had not accommodated this growing demand, Japan may very well have experienced the mother of all deflations (that demand is not observed and has to be inferred from price and quantity is a key weakness in this story).

Alright, so Steve does not like my way of increasing inflation. What does he recommend as an alternative? The BOJ should raise its policy rate, say from 0 to 400bp, and keep it there. There may be a short-run "liquidity effect," but the inflation will eventually come. How do we know? The Fisher equation. Can you elaborate? The Fisher effect will mean that inflation expectations will rise and inflation will follow. Why should inflation expectations rise? Because ... well, rational expectations ... and the Fisher equation. Can you elaborate? (Rinse and repeat.)

In any case, even if one accepts "rational expectations," the argument is not correct. As I explained above, there are really two Fisher equations:

[Fisher 1]: R = r + π

[Fisher 2]: R_m + LP = r + π

where, in case you forgot, r is real interest rate, π is expected inflation, R is nominal rate on illiquid bond, R_m is nominal rate on liquid bond (including reserves) and LP is a liquidity premium.

The interest rate controlled directly by the central bank is R_m. The central bank can easily set R_m = 0 and then monetize all the tax-cuts that are necessary to increase π. As π increases, so will R, in accordance with the Fisher equation. Could it be that Neo-Fisherians are confusing R with R_m? (This seems unlikely as I know that Steve knows the difference.)

What then is the effect of raising R_m? Well, it's complicated. Much depends on the structure of fiscal policy (Ricardian vs. Non-Ricardian); see here. In some models, raising R_m leaves r and π unchanged, which implies that the liquidity premium on government money LP falls. Eliminating the liquidity premium on government money/bonds is the famous Friedman rule prescription (convention version sets R_m = 0 and π = -r, but R_m = r + π for any π > 0 also works). But in other models, increasing R_m puts upward pressure on the real rate of interest, reducing the demand for investment, leading to economic contraction with no change in long-run inflation; see here.

The point of all this is, IF higher inflation is desired (and I am by no means advocating any such policy), THEN why not keep the policy rate low and use "free lunch" fiscal policies as long as inflation remains below target? Why bother experimenting with the Neo-Fisherian prescription of raising the policy rate that's somehow supposed to make people magically expect higher inflation?