Greg Mankiw has a

post on Taylor rule predictions and liquidity traps. Mankiw points out that, if you fit a Taylor rule to the data, that rule should soon give a prediction in positive territory. A common argument in the Fed system that has been used for a long time now (see for example

this 2009 piece by Glenn Rudebusch) is that, since fitted Taylor rules predict a negative fed funds rate, the Fed should be taking some kind of unusual accommodative action, since of course the Fed is constrained by the zero lower bound on the fed funds rate.

Here's how John Williams, President of the San Francisco Fed,

explains it: We at the Fed have guidelines that allow us to set interest rate targets based on the levels of unemployment, inflation, and other economic indicators. So what do those guidelines tell us now? With inflation under control and unemployment so high, those guidelines tell us something most unusual: the federal funds rate should actually be in negative territory.

Of course, it’s not possible for the federal funds rate to go below zero, which is about where we’ve put it for the past three years. But that doesn’t mean that we are out of ammunition. We’ve created new ways to stimulate the economy. For example, we’ve purchased over one-and-a-half trillion dollars of longer-term securities issued by the U.S. government and mortgage agencies.

So, when our Taylor rule predicts a negative fed funds rate, apparently this tells us that quantitative easing (QE) is appropriate. Never mind that the model we are using (a New Keynesian model for Williams) does not tell us how QE works or how much of it we should be doing. Actually, no one has a serious model that can justify quantitative easing, though Williams wants to convince us that it's just Econ 101:

This policy works through the law of supply and demand. When we buy large quantities of securities, we increase demand for those securities. Higher demand equals lower interest rates. As the yields on longer-term Treasury securities come down, other longer-term interest rates also tend to fall. That reduces the cost of borrowing on everything from mortgages to corporate debt. Our securities purchases are an important reason why longer-term interest rates are at or near post-World War II lows.

It's simple! It's easy! It works!

What if we take the San Francisco Fed approach seriously. Mankiw's Taylor rule looks like this:

R = 8.5 + 1.4(i - u),

where R is the fed funds rate, i is the year-over-year inflation rate, and u is the unemployment rate, all in percentages. Of course the predicted value for R that we get given current data depends critically on the inflation measure that we use. Provided my arithmetic is correct, I get 1.4%, -0.3%, 0.1%, and -1.0%, if I use headline CPI, core CPI, PCE deflator, or core PCE deflator, respectively. So if I'm Mankiw, and I follow Williams's logic, it would be hard to make a case for QE3, for example, and I might want to start to think about raising the interest rate on reserves (IROR).

Alternatively, I could use a Taylor rule like

Glenn Rudebusch's, which is:

R = 2.1 + 1.3i - 2.0G,

where G is the gap between the actual unemployment rate and the "natural rate." Here of course, the predicted value for R depends not just on the inflation measure we choose, but on what the natural rate is. For the contribution to R from the constant and inflation, if we use the four alternative inflation measures above we get numbers between 4.3 and 6.5. What is the natural rate? In New Keynesian parlance, that would be the unemployment rate in a world with flexible wages and prices. Hardliners at one extreme might think that in the flexible-wage-and-price world the unemployment rate would be what it was before the recession started, i.e. about 4.5%. In that case, the contribution from the gap would be -8.0. Hardliners at the other extreme might say that the outcome we are looking at is efficient, in which case the gap is zero, and there is no contribution from unemployment. Thus, our predictions could run anywhere from -3.7% to 6.5%. Maybe we should tighten. Maybe we should not. In any case, if we buy into this way of looking at things, it really does not tell us much. I think I could be a regular New-Keynesian Phillips-curve Taylor-rule kind of guy, and still be arguing for raising the IROR and arguing against QE3.

But there seem to be some people on the FOMC who want more accommodation. Not happy with a Fed balance sheet that has more than tripled in size, a policy rate at 0.25% until mid-2013, and

new forward guidance about the Fed's intentions, Charles Evans is

yelling for more. Recall that Evans has now been the sole dissenter on the FOMC in the last two meetings. The language in the

FOMC press release has been:

Voting against the action was Charles L. Evans, who supported additional policy accommodation at this time.

What does Evans want and why?

The traditional course of action when inflation is below target and real output is expected to be below potential is to run an accommodative monetary policy. I support such accommodation today. And I believe the degree of accommodation should be substantial.

Note that this in not quite Taylor-rule language. He's saying that the forecast for real output matters - "real output is expected to be below potential." Two comments here:

1. Inflation is not below target, unless you cherry pick and take the core PCE deflator, which is running at 1.7% year-over-year. At the high end, headline CPI inflation is running at 3.4% - well above the Fed's implicit 2% target.

2. If you are recommending "accommodative" policy, you should have an idea what that means in the current context.

Evans and Williams are speaking more-or-less the same language on liquidity traps:

I believe that the disappointingly slow growth and continued high unemployment that we confront today reflects the fact that we are in what economists call a “liquidity trap.” Let me explain. In normal times, real interest rates—that is, nominal interest rates adjusted for expected inflation—rise and fall to bring desired savings into line with investment and to keep productive resources near full employment.

This market dynamic is thwarted in the case of a liquidity trap. That is, when desired savings increase a great deal, nominal interest rates may fall to zero and then can go no lower. Real interest rates become “trapped” and may not be able to become negative enough to equilibrate savings and investment. That is where we seem to be now—short-term, risk-free nominal interest rates are close to zero and actual real rates are modestly negative, but they are still not low enough to return economic activity to its potential.

That last sentence is very unconvincing. The zero lower bound is a problem in New Keynesian economics because it implies that you cannot reduce the real rate to the "Wicksellian natural rate." The real rate is thus inefficiently high in a liquidity trap. But it seems real rates are actually pretty low. Indeed, the five-year TIPS yield is down to -1.0%, and even the 10-year TIPS yield is negative. Evans seem pretty certain about what "low enough" real interest rates are, and what "potential" output is. I wish he would explain these things to us, so that we all know.

Finally, there are some arguments about why we should tolerate an inflation rate of as much as 3%, so as to escape from our liquidity trap. These arguments seem based on Ivan Werning's paper, which you can find on

this conference program. The model in Werning's paper is essentially the 1970s version of New Keynesian economics - the stripped-down linearized two-equation version. There's an "IS curve" and a "Phillips curve," describing the trajectories for the inflation rate and the output gap, given the nominal interest rate, which is set by the central bank, subject to the zero lower bound. Then, evaluate how policy rules perform according to a quadratic loss function. But what's the optimal inflation rate? What's potential output? Werning's paper does not answer those questions, and those are the ones we need to have answers to.

For someone who is holding out on the FOMC for something more "accommodative," Evans is not telling us a lot about how he wants to do the accommodation. There's some stuff in there about how Fed policy should be much more explicit about addressing its dual mandate by setting numerical objectives for the unemployment rate, for example. However, it's unclear whether that is the key point of disagreement with the rest of the FOMC.