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.