Wednesday, January 11, 2012

Taylor Rules and the Fed

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.


  1. 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.


    1) Is there any model that shows that QE doesn't work? Or has a negative effect. You mention none, so my assumption is that you accurate position is that QE made no difference?

    2) What were the second and third order effects of QE, positive and negative>

    3) QE appears to be positively correlated with a rise in stock prices.

    What do the models show about this possible effect?

    1. 1. This is not a "model," it's just words, but I put what I think is a coherent arguement together in this post that says QE does nothing under the current circumstances:

      That's my position. If the Fed can't construct a coherent theory of why QE works, and for the better, they shouldn't be doing it. Also see this:

      2. No effect. So you don't have to worry about nth order, where n is any positive integer.

      3. So what?

    2. This comment has been removed by the author.

  2. You wrote, Inflation is not below target

    Who has ever done work on what rate of inflation should be targeted in light of a private debt bubble (300% of GDP) that lead to (and still prolongs) the Lesser Depression?

    Before recent events, did we ever have private debt at 300% of GDP from which to draw data to do such work?

    IOW, what justifies the current targets?

    1. What you seem to be saying is that it would be efficient at the current time to essentially forgive a large fraction of the existing private debt in the United States. I'm not sure that is true, but suppose it is. Why would it be efficient to forgive that debt via monetary policy, through an unanticipated inflation? Isn't that a fiscal policy matter? You understand that if you forgive nominal debt through inflation, that you're forgiving some debt that you might not want to forgive, and the cost of forgiving the debt is borne by a specific group of people. Maybe that's not the result you want.

  3. As you are clearly denying Fisher-style debt deflation respectively Koo#style balance sheet recessions and as you argue against against moderate inflation as a tool to reduce the overall debt level in the economy without even explaining why these theories are supposed to be bogus you are serving our oligarchal masters.

    "You understand that if you forgive nominal debt through inflation, that you're forgiving some debt that you might not want to forgive, and the cost of forgiving the debt is borne by a specific group of people. Maybe that's not the result you want." - This specific group of people are the rich. The poor don't own much property and virtually no property in the form of interest-bearing securities. You can talk all you want about being a left-winger, you showed your true colours.

    1. The purpose of this space is to exchange ideas about economics, not my place in the world power structure. I'll have to tell my family about the "oligarchal masters." That will get a good laugh at the dinner table.

    2. I love it when right-wingers cannot stand the truth: :D
      How often do you intend to delete my post? Cannot stand that I pointed out that you are for a certain form of wealth distribution that favours the rich?

  4. Are you saying this is not what happened with QE, QE2?

    Currently, short-term Treasury debt like T-bills are near-perfect substitutes for bank reserves because both earn close to zero percent and have similar liquidity. In order for the Fed to get investors to spend some of their money holdings it must first cause a meaningful change in their portfolio of assets. Swapping T-bills for bank reserves will not do it because they are practically the same now. In order to get traction, the Fed needs to swap assets that are not perfect substitutes. In this case, the Fed has decided to buy less-liquid, higher-yielding, longer-term Treasury securities. Doing so should lower the average maturity of publicly-held U.S. debt. It should also overweight investor's portfolios with highly-liquid, lower-yielding assets and force investors to rebalance them. In order to rebalance their portofolios, investors would start buying higher-yielding assets like stocks and capital. This would ultimately drive up consumption spending--through the wealth effect--and investment spending. The portfolio rebalancing, then, ultimately cause an increase in nominal spending. Given the excess economic capacity, this rise in nominal spending should in turn raise real economic activity

    1. I certainly agree with the first part of your argument. If the Fed swaps reserves for T-bills under the current conditions (a large stock of excess reserves in the system), this does nothing. Now, extend that logic to swaps of reserves for long-term Treasuries, say. What is the Fed doing when it makes such a swap? It is intermediating across maturities. It is issuing an overnight liability (reserves) in order to buy a long-maturity asset. But a private financial intermediary can do exactly the same thing, by acquiring long-maturity Treasuries and financing the purchase through overnight repos, collateralized with the long Treasuries. It then just rolls over the repos, just as the Fed essentially rolls over the reserves from day to day. Monetary policy only matters (just as any government policy will matter) only if it doing something that the private sector cannot. In this case, what the private sector can do is essentially identical to what the central bank can do. Therefore, when the central bank swaps reserves for long Treasuries, the private sector will undo it. It's just Modigliani-Miller.

    2. Prof. Williamson, while I agree with many of your points I am afraid you are approaching policy from an overly academic perspective. Policy-makers, especially in the midst of such a severe crisis, do not have the luxury to tell people that they are going to do nothing until economists have developed models that are adequate enough to evaluate the effectiveness of their actions. Policy usually works through trial and error. Of course there are a few things most economists agrees should not be done, and a few things most economists agree should be done. For everything in-between policy-makers need to take chances!

    3. "...from an overly academic perspective."

      No way. I'm not addressing this in any more an academic way than people who sit on the FOMC.

      "For everything in-between policy-makers need to take chances!"

      Wrong. You have a policy here that has never been used before. Not only that, but there is no good theory to tell you what happens when you implement it. Thus, you're completely in the dark about what it does. Further, I can offer you what I think is a good reason why it does absolutely nothing. You then say we should go ahead and do it anyway. I'm glad you're not on the FOMC.

    4. "I'm glad you're not on the FOMC."

      That makes two of us. In any case, I do not agree that we are completely in the dark. There are some crude arguments why it might work. But, to use a baseball analogy, just because you may not be able to predict where the ball will go once you hit it does not necessarily mean that you should not swing at all. The cost of not swinging should also be taken into account.

    5. That's not a good argument. There's a tornado coming. It's going to be really bad. We're all in the basement and you tell me we should do something. You're trying to convince me that we should all run outside and scream at the tornado, as that's better than sitting in the basement and doing nothing.

    6. Prof. Williamson, is what Evans is proposing equivalent to screaming at a tornado? Is the the FED, when it finances a purchase of long maturities, really operating under the same constraints and facing the same risk as a financial intermediary doing the same by issuing repos, as you stated above? Is the yield to TIPS the appropriate interest rate to look at? And how about looking at the PPI jointly with the CPI (


    How come nobody in power seems to care about what Chicago has to offer?

    1. Actually, they do.

      Narayana Kocherlakota, President Minneapolis Fed, PhD Chicago
      Charles Plosser, President Philadelphia Fed, PhD Chicago

      MIT hardly dominates. Here are some other ones:

      UW-Madison - Lacker (Richmond Fed President) and Rosengren (Boston Fed President)
      Minnesota - Zvi Eckstein, Deputy Governor, Bank of Israel.
      Indiana U. - Bullard (St. Louis Fed President)

      Krugman, for example, likes to characterize "fresh water" types as out of touch, but they have their hands in policy as much as anyone does.

  6. Says John Williams: "Of course, it’s not possible for the federal funds rate to go below zero".

    Steve, why do you think Williams and so many other people say this? Is it because of 1. legal restrictions in the Federal Reserve Act 2. infrastructure limitations (here's an example... until recently German debt could not be auctioned off at negative interest rates because their computers didn't allow negative numbers, see, kind of like the Y2k problem) or 3. they think negative interest rates are simply impossible, like ghosts or vampires? Maybe another reason?

    1. 1. The relevant interest rate is the interest rate on reserves, which in principle could be negative, but the Federal Reserve Act does not seem to allow it.

      2. In spite of the fact that the short-term nominal interest rate cannot be negative, there are tax schemes that can make it effectively so:

    2. I realize that you think the relevant interest rate can go negative in principle, but why do those like Williams think it can't go negative? Do they think it can't in principle become negative, or it cannot legally do so? It is a pretty widely held view, in any case.