Thursday, May 28, 2015

Small shoes and headroom

I talked with Kathleen Hays and Michael McKee on Bloomberg Radio last week, and they asked (twice!) a question that comes up often in thinking about Fed policy: shouldn't the Fed raise rates now, so it has some "headroom" to lower them again if another recession should strike?

I could only answer with my standard joke: That's like the theory that you should wear shoes two sizes too small because it feels so good to take them off at the end of the day.

But the question comes up so often, it's worth thinking about a little more seriously. Under what views about the economy does this common idea make any sense?

One way to think about the question: is the effect of interest rates on the economy path-dependent, so that a given level of short-term interest rates has more "stimulative" effect if it comes from a previously high value than if short-term interest rates were zero all along?

The usual answer is no. The model is usually a linear system, in which lowering the rate from a high value has the same effect as raising to the same rate coming from a low value.  In fact, the usual model goes the other way:  If, say, a new recession hits in June 2017 and you want more stimulus then,  having had rates at zero all along is more "stimulative" than having raised them to 3% between now and then, and lowering rates all of a sudden.  In equations, if \(y_t = \sum \theta_j i_{t-j} + \varepsilon_{t} \) with \(\theta_j \ge0 \) then the partial derivative of any \(y_t\) with respect to any \(i_{t-j}\) is the same no matter what the path of interest rates before time \( t-j\), and raising \( i_t \) today lowers future \( y_{t+j} \) given any set of shocks \(\{\varepsilon_t\}\)  You need some sort of nonlinear system where a higher interest rate today \(i_t\)  makes \( y_{t+j}\) more sensitive to some future rate  \(i_{t+k} \).

Another way to think about this question is to think about what sort of state variables the interest rate affects. If the Fed raises rates now, the economy will be in a different state in June 2017. So in what view of things does raising rates now put the economy in state such that the economy can better weather a shock, or, more to the point, a state in which lowering rates back to zero will be more "stimulative" than if rates were zero all along? People usually think that raising rates between now and May 2017 would lower inflation, output and employment over what they would have been otherwise. Then, once rates go to zero again in June 2017, inflation, output, and employment will be lower than if interest rates had been zero all along.

If the economy were to boom on its own, with inflation, output and employment rising, and the Fed were to follow that good news by raising rates, then yes the Fed would have more "headroom." But that's not an argument that the Fed can get the "headroom" by acting now.

In fact, the opposite  story has been told by those who advocate forward guidance and raising the inflation target. They argue that the Fed should keep rates lower and for longer, in order to raise inflation (the "state variable"). Higher inflation then indeed gives the Fed "headroom" to lower real rates by lowering nominal rates in the next recession.

What does it take to turn this around, and to justify the idea that raising rates gives "headroom" to lower them in the future? The main answer I can think of is to turn the conventional stories around. Suppose that raising interest rates raises inflation, as I have speculated before (here). The desired "headroom" is the desire to raise inflation, so that when June 2017 comes around the same nominal rate (0) corresponds to a lower real rate. I doubt many people articulating the policy view want to travel to Fisher-land and reverse the effect of interest rates on inflation.

You still need a second belief: that despite the wrong sign on inflation the conventional theory has the right sign on output: That lowering rates in June 2017 will fight that recession, even as it will lower inflation again. My little model didn't deliver that. Maybe other models do.

Loud disclaimer: I'm not advocating any position here. I'm just thinking out loud about what kind of views, if any, lie behind this common idea that raising rates now gives the Fed some sort of "headroom" to stimulate the economy in the event of a future recession.

This is a good case for real economic models. There is a lot of cause and effect chat surrounding monetary policy and financial policy that is way ahead of (if you're being polite) or outside of (if you're being accurate) any well-understood or even well-articulated economic model. By tying ideas together, perhaps a policy belief ("headroom") can open one's mind to an interesting causal channel (Fisher equation), or perhaps seeing that channel needed can reverse a policy belief.


  1. John,

    A couple of other points to consider. If you look at total credit growth here:

    And Fed funds rate here:

    You will see no discernible correlation (positive or negative) between the two. Even if you swap out the short term Fed Funds rate for a longer term rate (for instance the 10 year Treasury), again there is no discernible correlation between an interest rate and credit growth.

    This begs the question, what if the central bank set an interest rate, and no one was willing to borrow at it? Surely for any Taylor type rule, the first order effect of an interest rate change must be the willingness of two parties to enter a debt agreement at that interest rate. Too low an interest rate and the lender may walk away. Too high an interest rate and the borrower may say no thanks.

    The standard theory is that low (negative) real rates encourage people to take on more debt.

    Two problems with that answer - first, someone else has to be willing to lend at a negative real rate. That is fine for a central bank that doesn't have shareholders to appease. Not so good for private banks that have profit considerations or fixed income investors that rely on the interest income for a portion of their disposable income.

    Second, a lot of things that are bought with borrowed money are not included in the consumer price index or in any generalized measure of inflation (GDP deflator for instance). This is particularly true for government expenditures (guns, planes, and aircraft carriers) and for leveraged players in the financial markets (buying equity / derivatives on margin).

  2. John, Good analogy with shoe sizes. But do you think the Fed has much control over interest rates other than by changing expected inflation, in which case the Fed is affecting mainly nominal interest rates?

    1. You know how to ask the tough question! Actually with some price-stickiness, the Fed can raise real rates by raising nominal rates. ("Monetary policy with interest on reserves" is a recent model of mine with this feature.) So, that leaves us with the deeper question of just what is this apparent price stickiness, can the fed exploit it, shouldn't we then have anti-stickiness policies rather than monetary policies and so forth, all topics for another day.

    2. John,

      But how does the Fed (or any other bank) get an individual to borrow at a positive real rate if that person knows that prices are sticky? The Fed (administratively through the discount window) can set any interest rate they want to lend at.

      I think you are missing the implications of the tax deductibility of interest. This helps to offset the real cost of borrowing. In fact, the higher the nominal interest rate, the larger the benefit.

      If I know that prices are sticky, and I know that the Fed is going to exploit that stickiness by trying to maintain a positive real interest rate, I may still borrow at that positive real rate if I can offset the real cost through reduced taxation.

    3. To expand on David's question (apologies David if I'm putting words in your mouth): Do you think the Fed has much control over interest rates other than by changing expected inflation, in which case the Fed is affecting mainly nominal interest rates, by changing the money supply rather than the fed funds and IOR rates?

  3. Interesting post--- but looking at the Bank of Japan and the current situation that the Fed faces, I think the story going forward is all about QE.
    It may be the situation seen in Japan will be the new normal, and that QE must become a part of conventional monetary policy.

  4. This reminds me of people not putting on coats when they're cold because they say it keeps getting colder and they want to put on their coat only when it's really cold, to not waste their "ammunition" against the cold to early. (observable at BBQs during spring or fall)

    That makes no sense at all. Obviously you should stop, or at least delay, losing to much energy as soon as possible. No matter if you model the coat as an one time increase in warmth or as a steady reduction of the rate of getting colder, maybe even turning the rate of getting colder into a rate of getting warmer if you brought a really thick coat. (in case of finite periods -> getting in the car and drive home)

    The only explanation I have for this is that people put such a high value on the option that their lost utility from being cold is compensated for. Most people change their behavior once explained to them though. I told it to my girlfriend and she's putting her coat right on as soon as she gets cold now :D.

    Maybe that's also the explanation why the question you mentioned is so common: "Let us suffer now (a bit) but spare our option to lower rates again for later (when the situation may be really bad)." The fallacy in it is just less obvious.

  5. To sustain inflation, wages or income must rise, especially for those on the low end of the scale who spend all they earn (and then some). Commodity price inflation is not sustainable in the absence of wage inflation. Inflation-deflation is a continuum. Inflation that is too low is marginally less worse than deflation. Wages are sticky they do not easily deflate. Inflation needs to be high enough to allow relative wages to reset upward relative to price. If inflation is too low, the result is unemployment. The 2% inflation target was too low to absorb the economic shock of 2008. Massive unemployment resulted as millions of workers were laid off or worked fewer hours instead of nominal decline in wages.

    Our economy is in Catch-22. Wages will not rise until demand increases. Demand will not rise until the unemployed are back to work and wages rise. Monetary policy is ineffective because unemployed and creditmaxxed are poor risk for loans and the Monetary Institutions cannot give money away. There is no useful monetary channel. How to break the Catch-22? Wages at the lowest end can be raised by regulatory policy, raise the MinWage. Demand can be increased by moving government purchases of goods and services forward, spend more today cut back tomorrow. There is plenty of useful work to be done. Government is positioned to capture returns on investments that business is not able to capture.

    As Bernanke indicated many times, monetary policy needs help from regulatory and fiscal policy to increase demand. Once demand increases, monetary policy will become more effective.

  6. Maybe you're confusing the term "linear" with "memoryless". A system output can depend on past as well as current inputs and still be linear. For your example, you would not need a nonlinear model, but rather a model with memory.

    1. Anonymous,

      I agree.

      Many times a single interest rate is used in economic models, and all debt (past and present) pays that interest rate. Obviously this isn't true. Most debt is fixed term / fixed interest rate. Refinancing / competition sometimes allows a borrower to reach a lower interest rate on the same loan, but that isn't always an option.

      And so, modeling a credit economy correctly requires you to incorporate all prior credit decisions by both borrowers and lenders (central bank included) - hence your model needs "memory".


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