Stephen Williamson Gets Stuck at the Zero Lower Bound

Stephen Williamson started quite a ruckus on the econblogosphere with his recent posts arguing that, contrary to the express intentions of the FOMC, Quantitative Easing has actually caused inflation to go down. Whether Williamson’s discovery will have any practical effect remains to be seen, but in the meantime, there has been a lot head-scratching by Williamson’s readers trying to figure out how he reached such a counterintuitive conclusion. I apologize for getting to this discussion so late, but I have been trying off and on, amid a number of distractions, including travel to Switzerland where I am now visiting, to think my way through this discussion for the past several days. Let’s see if I have come up with anything enlightening to contribute.

The key ideas that Williamson relies on to derive his result are the standard ones of a real and a nominal interest rate that are related to each other by way of the expected rate of inflation (though Williamson does not distinguish between expected and annual inflation, that distinction perhaps not existing in his rational-expectations universe). The nominal rate must equal the real rate plus the expected rate of inflation. One way to think of the real rate is as the expected net pecuniary return (adjusted for inflation) from holding a real asset expressed as a percentage of the asset’s value, exclusive of any non-pecuniary benefits that it might provide (e.g., the aesthetic services provided by an art object to its owner). Insofar as an asset provides such services, the anticipated real return of the asset would be correspondingly reduced, and its current value enhanced compared to assets providing no non-pecuniary services. The value of assets providing additional non-pecuniary services includes a premium reflecting those services. The non-pecuniary benefit on which Williamson is focused is liquidity — the ease of buying or selling the asset at a price near its actual value — and the value enhancement accruing to assets providing such liquidity services is the liquidity premium.

Suppose that there are just two kinds of assets: real assets that generate (or are expected to do so) real pecuniary returns and money. Money provides liquidity services more effectively than any other asset. Now in any equilibrium in which both money and non-money assets are held, the expected net return from holding each asset must equal the expected net return from holding the other. If money, at the margin, is providing net liquidity services provided by no other asset, the expected pecuniary yield from holding money must be correspondingly less than the expected yield on the alternative real asset. Otherwise people would just hold money rather than the real asset (equivalently, the value of real assets would have to fall before people would be willing to hold those assets).

Here’s how I understand what Williamson is trying to do. I am not confident in my understanding, because Williamson’s first post was very difficult to follow. He started off with a series of propositions derived from Milton Friedman’s argument about the optimality of deflation at the real rate of interest, which implies a zero nominal interest rate, making it costless to hold money. Liquidity would be free, and the liquidity premium would be zero.

From this Friedmanian analysis of the optimality of expected deflation at a rate equal to the real rate of interest, Williamson transitions to a very different argument in which the zero lower bound does not eliminate the liquidity premium. Williamson posits a liquidity premium on bonds, the motivation for which being that bonds are useful by being readily acceptable as collateral. Williamson posits this liquidity premium as a fact, but without providing evidence, just an argument that the financial crisis destroyed or rendered unusable lots of assets that previously were, or could have been, used as collateral, thereby making Treasury bonds of short duration highly liquid and imparting to them a liquidity premium. If both bonds and money are held, and both offer the same zero nominal pecuniary return, then an equal liquidity premium must accrue to both bonds and money.

But something weird seems to have happened. We are supposed to be at the zero lower bound, and bonds and money are earning a liquidity premium, which means that the real pecuniary yield on bonds and money is negative, which contradicts Friedman’s proposition that a zero nominal interest rate implies that holding money is costless and that there is no liquidity premium. As best as I can figure this out, Williamson seems to be assuming that the real yield on real (illiquid) capital is positive, so that the zero lower bound is really an illusion, a mirage created by the atypical demand for government bonds for use as collateral.

As I suggested before, this is an empirical claim, and it should be possible to provide empirical support for the proposition that there is an unusual liquidity premium attaching to government debt of short duration in virtue of its superior acceptability as collateral. One test of the proposition would be to compare the yields on government debt of short duration versus non-government debt of short duration. A quick check here indicates that the yields on 90-day commercial paper issued by non-financial firms are very close to zero, suggesting to me that government debt of short duration is not providing any liquidity premium. If so, then the expected short-term yield on real capital may not be significantly greater than the yield on government debt, so that we really are at the zero lower bound rather than at a pseudo-zero lower bound as Williamson seems to be suggesting.

Given his assumption that there is a significant liquidity premium attaching to money and short-term government debt, I understand Williamson to be making the following argument about Quantitative Easing. There is a shortage of government debt in the sense that the public would like to hold more government debt than is being supplied. Since the federal budget deficit is rapidly shrinking, leaving the demand for short-term government debt unsatisfied, quantitative easing at least provides the public with the opportunity to exchange their relatively illiquid long-term government debt for highly liquid bank reserves created by the Fed. By so doing, the Fed is reducing the liquidity premium. But at the pseudo-zero-lower bound, a reduction in the liquidity premium implies a reduced rate of inflation, because it is the expected rate of inflation that reduces the expected return on holding money to offset the liquidity yield provided by money.

Williamson argues that by reducing the liquidity premium on holding money, QE has been the cause of the steadily declining rate of inflation over the past three years. This is a very tricky claim, because, even if we accept Williamson’s premises, he is leaving something important out of the analysis. Williamson’s argument is really about the effect of QE on expected inflation in equilibrium. But he pays no attention to the immediate effect of a change in the liquidity premium. If people reduce their valuation of money, because it is providing a reduced level of liquidity services, that change must be reflected in an immediate reduction in the demand to hold money, which would imply an immediate shift out of money into other assets. In other words, the value of money must fall. Conceptually, this would be an instantaneous, once and for all change, but if Williamson’s analysis is correct, the immediate once and for all changes should have been reflected in increased measured rates of inflation even though inflation expectations were falling. So it seems to me that the empirical fact of observed declines in the rate of inflation that motivates Williamson’s analysis turns out to be inconsistent with the implications of his analysis.

13 Responses to “Stephen Williamson Gets Stuck at the Zero Lower Bound”

  1. 1 Rob Rawlings December 6, 2013 at 6:54 am

    I think this is the best analysis of the Williamson debate I have read. Most of the discussion has focused on Williams’s claim that reduced liquidity premia on money will drive deflation As you point out conventional analysis indicates that (other things equal) it would rather drive increased inflation as people reduce their real money balances to keep them in line with the (unchanged) expected return (itself based on expected rates of inflation).

    However in Williamson’s model other things are not equal, He sees QE, by reducing liquidity premia, as also driving increased economic activity. Is it possible that he sees something in this that will cause expected returns to adjust inline with desired returns, prevent the fall in the value of money that one would expect, and lead to the reduction in the rate of inflation that he describes ?

    (Perhaps the actors in his model, having rational expectations, see that QE will increase RGDP which (other things equal) would be deflationary. They then simultaneously adjust their expected and desired returns on money to drive the deflationary outcome)

  2. 2 Philippe December 7, 2013 at 3:42 am

    “If people reduce their valuation of money, because it is providing a reduced level of liquidity services, that change must be reflected in an immediate reduction in the demand to hold money, which would imply an immediate shift out of money into other assets. In other words, the value of money must fall. Conceptually, this would be an instantaneous, once and for all change, but if Williamson’s analysis is correct, the immediate once and for all changes should have been reflected in increased measured rates of inflation even though inflation expectations were falling.”

    If people shift out of money into other assets, this will presumably raise the prices of other assets, but why should this then lead to an increased rate of inflation, i.e. higher prices for goods and services?

  3. 3 Benjamin Cole December 8, 2013 at 11:59 am

    Something tells me economics is getting off track with these (fragile, btw) models.
    Also, sellers of bonds (to the Fed) do have another option: they can spend the money. Consumption! Demand!
    Where does this fit in?

  4. 4 Mike Sax December 9, 2013 at 3:11 am

    Wow! Nobody even wants to take a swing here? I think this is in part that no one feels like they know for sure what SW is getting at.

    At least David has a novel way of looking at it. Here is my attempt-partly inspired by his post to make some sense of it.

    Later on SW and Nick Rowe were having a pretty good discussion.

  5. 5 tommy December 9, 2013 at 3:06 pm

    (6) p(t+1)/p(t) = B/(1-L)
    does not mean if L goes up then p(t+1) goes up. It means if L goes up then p(t) goes down. For tomorrow’s inflation, the economy becomes deflation today.

  6. 6 Mike sax December 9, 2013 at 4:23 pm

    David I left a comment earlier that hasn’t shown up. I know you usually allow comments so maybe it’s just a technical issue.

    Again, I find this a very interesting debate but there seem to be few takers-I think this may be because not too many even now have much confidence they know exactly what SW is getting at.

    Here is my attempt to make some sense of it-partly inspired by your post here.

  7. 7 David Glasner December 10, 2013 at 12:19 pm

    Rob, I think that there are many possible stories that one could tell and each one seems to be contingent on a different assumption about how people adjust their expectations in response to Fed policy. That’s partly why I think that it would be helpful if the Fed were more explicit about its goals for a higher price level and higher nominal GDP. It’s certainly possible that there could be a surprise burst of real GDP growth that would keep the price level below target and the Fed would not necessarily be obligated to meet the price level target under those circumstances. That’s certainly an advantage of the nominal GDP target.

    Phillipe, Asset prices reflect the prices of the services they embody, and a discount rate. So if asset prices rise at a given discount rate and an unchanged physical yield, the higher asset price must reflect higher prices for services. Otherwise you would have to say that shift out of money into assets is causing real interest rates to fall. But Williamson says that QE is reducing inflation and increasing the real interest rate.

    Benjamin, Maybe so, but sometimes we learn from following ideas into the blind alleys that they lead us into. But we do have to be able to recognize that we have gone down a blind alley, at least eventually. Let’s hope.

    Mike, Sorry that I was late in approving your post from the queue awaiting moderation. Is this your first time commenting here? First timers get put into the queue first. I claim no insight into what Williamson is trying to accomplish. He’s obviously a very smart guy, but I don’t care for his way of doing economics.

    Tommy, Good point. But the inflation rate has been falling for three years. What does that say about his the empirical status of his model? I notice that your comment elicited no response from Williamson or anyone else on his blog.

  8. 8 Roman P. December 11, 2013 at 1:27 am

    I once constructed a chart that graphed US Fed rates vs seasonally rate of inflation and to my surprise they were really well-correlated. It looked almost like when Fed tried to combat inflation it was causing it instead. No idea of how valid my amateurish results were, though.

    But consider this: banks will factor inflation into their retail interest rates. But inflation itself must be a function of interest rate, because increases in price (including the price of credit) will manifest as cost-push inflation to some degree. There must be some complicated dynamics going on here.

  9. 9 JP Koning December 15, 2013 at 8:09 am

    Hi David, I’m a bit late on this one.

    First, I find it quite interesting how both you and Williamson use the Fisher equation at the ZLB, yet arrive at very different results. I’m referring here to your Fisher Effect Under Deflationary Expectations paper.

    “Conceptually, this would be an instantaneous, once and for all change, but if Williamson’s analysis is correct, the immediate once and for all changes should have been reflected in increased measured rates of inflation even though inflation expectations were falling. ”

    I agree. Just to paraphrase to make sure that we’re on the same page… when the liquidity premium falls, money needs to provide investors with a compensating return in the form of lower expected inflation (higher expected deflation)… or put differently, it needs to provide a sweetened capital gain. However, in order to promise this deflation/capital gain, a sudden fall in money’s purchasing power, or inflation, is necessary. So QE announcements should cause quick jumps in inflation, these jumps being the mechanism that bring the purchasing power of money low enough to engender investor expectations of deflation, or sweetened capital gains on money holdings.

    Also, if you have the time, can you critique this post? I wrote it over a year ago and it seems to be on the same subject. It’s very short:

  1. 1 What is the evidence on quantitative easing? Trackback on December 7, 2013 at 11:42 pm
  2. 2 Stephen Williamson Gets Stuck at the Zero Lower Bound | Fifth Estate Trackback on December 11, 2013 at 8:21 am
  3. 3 Does Macroeconomics Need Financial Foundations? | Uneasy Money Trackback on December 13, 2013 at 8:16 am
  4. 4 Monetary Theory on the Neo-Fisherite Edge | Uneasy Money Trackback on May 6, 2014 at 8:05 pm

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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