**Summary:**

What should the Fed's long-run interest rate target be? The traditional view is that the glide path should aim at 4% -- 2% real plus 2% inflation.3%?One big question being debated right now is whether the "natural'' real rate of interest -- r* or "r-star" in econspeak -- has declined below 2%.Over the long run, the Fed cannot control the real rate of interest -- that comes from how much people want to save and what opportunities there are for investment, i.e. the marginal product of capital. So, if the real rate of interest is now permanently lower, say 1%, then one might argue that the glide path should aim for 3% long-run interest rate -- 1% real plus 2% inflation target -- not 4%. Janet Yellen recently came to Stanford and gave a very interesting speech that talked in part about a lower r-star, and seemed to be heading to something like this view. See the picture:Source: Federal Reserve. (She also talked a lot about Taylor Rules, seeming to move much closer to John Taylor's view of how to implement monetary policy. See interesting coverage on John Taylor's blog. On r*, see Measuring the Natural Rate of Interest Redux by Thomas Laubach and John C. Williams for a central paper on r*. Henrike Michaelis and Volker Wieland have an interesting post on r* and Taylor rules, also commenting on Ms. Yellen's speech.

**Topics:**

John H. Cochrane considers the following as important: growth, inflation, Monetary Policy, Thesis topics

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**3%?**

One big question being debated right now is whether the "natural'' real rate of interest -- r* or "r-star" in econspeak -- has declined below 2%.

Over the long run, the Fed cannot control the real rate of interest -- that comes from how much people want to save and what opportunities there are for investment, i.e. the marginal product of capital. So, if the real rate of interest is now permanently lower, say 1%, then one might argue that the glide path should aim for 3% long-run interest rate -- 1% real plus 2% inflation target -- not 4%.

Janet Yellen recently came to Stanford and gave a very interesting speech that talked in part about a lower r-star, and seemed to be heading to something like this view. See the picture:

Source: Federal Reserve. |

(She also talked a lot about Taylor Rules, seeming to move much closer to John Taylor's view of how to implement monetary policy. See interesting coverage on John Taylor's blog. On r*, see Measuring the Natural Rate of Interest Redux by Thomas Laubach and John C. Williams for a central paper on r*. Henrike Michaelis and Volker Wieland have an interesting post on r* and Taylor rules, also commenting on Ms. Yellen's speech.)

Of course, cynics will say that it's just the latest excuse not to raise rates. But these are serious arguments which should be considered on their merits.

**0%?**

Should the glidepath head to 3% interest rates? Maybe not. How about zero?

Long ago, Milton Friedman explained the "optimal quantity of money,'' which is really the optimal interest rate. It is zero. Peramazero in St. Louis Fed President Jim Bullard's colorful terminology. At interest rates above zero, people hold less cash, and spend time and effort collecting bills early, paying them late, and so on. This is all a waste of time. Also, taxes on rate of return are a bad idea. With all rates of return that much lower, the tax distortion is that much lower. With 0% interest rates, and correspondingly lower inflation, infaltion-induced capital gains taxes vanish.

So maybe the glidepath should be to 0% interest rate, not 3%. If the natural real rate is 1%, then inflation should be -1%.

In this line of thinking, the long-run interest rate is what counts directly. It is not a sum of a natural rate and an inflation target. Variation in the natural rate takes care of itself in variation in inflation.

Why not? The primary reason often given is that interest rates at zero cannot go substantially below zero, at least without banning cash and many other gyrations of our monetary and financial system. So, if the interest rate is near zero, the Fed does not have "headroom" to stimulate the economy in a recession. I don't necessarily agree with this, but let's go with it for a moment.

**4% ?**

Headroom logic however also implies a direct nominal interest rate target, not inflation plus real rate. If the Fed needs four percentage points of headroom (2% real + 2% inflation) then it needs four percentage points of headroom (1% real + 3% inflation), no?

So, from the optimal quantity vs. zero bound-headroom argument it does not follow obviously that the interest rate target should move up and down with the ``natural rate.''

**Permatwo?**

The question is, why is there a direct role for the inflation target? Why is that 2%, and then we add r* the long run real rate, to deduce the nominal rate glide point?

I think the answer is this: prices and wages are felt to be sticky, especially downward. That's the second argument against the Friedman rule: its steady deflation is said to require people to change prices and wages downward. That is said to cause disruption.

OK (maybe), no Friedman-optimal deflation. But why then 2% rather than 0% inflation?

**Quality and pi star**

One argument there is that inflation is overstated due to quality improvements. 2% is really 0%.

The issue: Suppose the iphone 6 turns in to the iphone 7, and costs $100 more. How much of that is inflation, and how much of that is that the iphone 7 is $100 better? Or maybe $200 better, so we are actually seeing iphone deflation? The Bureau of Labor Statistics makes heroic efforts to adjust for this sort of thing, but the consensus seems to be that inflation is still overstated by something like 1-2%.

Some reading on this: The Boskin Commission Report suggested the CPI is overstated by about 1%, as of 1996. Mark Bils, Do Higher Prices for New Goods Reflect Quality Growth or Inflation? argued that it's a good deal more. Mark measured that sales move quickly to new models, which they would not do if it were a price increase after controlling for quality. But Mark's analysis was limited to consumer durables, where quality has been increasing quickly. Many other CPI categories, especially services, are likely less affected. Philippe Aghion, Antonin Bergeaud, Timo Boppart, Pete Klenow and Huiyu Li's Missing Growth from Creative Destruction suggest there is another 0.5%-1% overall because of goods that just disappear from the CPI. (This post all started with discussion following Pete's presentation of the paper recently.)

This is good news. Nominal GDP growth = real GDP growth + inflation. Nominal GDP growth is relatively well measured. If inflation is 1% overstated, then real growth is 1% understated.

It also means our real interest rates are mismeasured. If 2% inflation is really 0% inflation, then 1% interest rates are really +1% real rates, not -1% real rates.

But back to monetary policy. Suppose that 2% inflation is really 0% inflation due to quality effects. Does that mean we should have a 2% long run inflation rate target?

I don't think so. Again, the motivation for a positive inflation target is that there is some economic damage to having to lower prices. But during quality improvements of new goods, nobody has to lower any prices. They are new goods! No existing good has to have lower prices. In fact, actual sticker prices rise.

There is a deeper point here. Not all inflations are equal. One purpose of the CPI is to compare living standards over time. For that purpose, quality adjustments are really important. Another purpose of the CPI is to determine if people have to undergo whatever the pain is associated with lowering prices. For that purpose, quality adjustments are irrelevant.

(On both prices and wages, we also should remember the huge churn. Lots of prices and wages go up, lots go down. The individual is not the average. Changing the average one or two percentage points doesn't change that many individual prices.)

In sum, the argument that quality improvements mean 2% inflation is really 0% inflation does not argue that therefore the inflation target should be 2% because otherwise people have to lower prices. They don't. Standard-of-living inflation is not the right measure for costs-of-price-stickiness inflation. In price stickiness logic, the Fed should be looking at a CPI measure with no quality adjustments at all! (At least in this simplistic analysis. This is an invitation to academic papers. If new and old goods are Dixit-Stiglitz substitutes, what are the costs of price stickiness with quality improvements?)

So the argument for a separate inflation target much above zero seems to be weak to me. We're back to Friedman rule vs. headroom, which argues for a direct nominal interest rate target. Since I'm not much of a fan of headroom, I lean to lower values.

Leaving aside price-stickiness, I'm still sympathetic to a price level target on expectations grounds. If the quality adjusted CPI is the same forever, then we have a CPI standard, the value of a dollar is always constant, and long-run uncertainty decreases. We don't shortern the meter 2% every year. For this purpose, we do want the quality-adjusted CPI, and for this purpose the inflation target is primary. An interest rate target would have to rise and fall with r*.

**Real rate variation**

**r* is the real rate. There really is no reason that the "natural" real rate only varies slowly over time. Interest rates crashed in a month 2008 because**

**real**rates crashed -- everyone wanted save, and nobody wanted to invest. The Fed couldn't have kept rates at 6% if it wanted to.

So, the procedures used to measure r*, like those used to measure potential output, are a bit suspect. They amount to taking long moving averages, and assuming that "supply" shocks only act slowly over time. More deeply, typical optimal monetary policy discussions use a Taylor rule

funds rate = r* + 1.5 ( inflation - target) + 0.5 (output gap)

and recommend active short run deviations from the Taylor rule if there are "supply shocks" i.e. r* shocks. Just how the Fed is supposed to distinguish "supply" from "demand" shocks is less clear in reality than the models, which presume shocks are directly visible. A "secular stagnation" fan might say that the moving averages used to measure r* are instead picking up eternally deficient "demand," like a driver with his foot on the brake complaining of headwinds.

**Bottom line**

As often in policy, we argue too much about the external causes and not enough about the logic tying causes to policy. r* may or may not have declined. But it does not follow that the glidepath nominal rate should be r* plus 2% inflation target. Maybe the glidepath should be 0% nominal rate or 4% nominal rate independent of r*. You see lots of mechanisms and tradeoffs worthy of modeling.