Woodford and QE3

Woodford and QE3:
Columbia University Professor Michael Woodford's paper at the Fed's Jackson Hole conference last week made the case that more large-scale asset purchases by the Fed would by themselves do nothing, and suggested that instead what really matters is the Fed's communication of its future intentions. There's a fair bit in Woodford's analysis that I agree with. But unlike Woodford, I think that asset purchases can be an important part of what the Fed could do in the here and now. Here I explain why.

Let me begin with Woodford's theoretical analysis of why large-scale asset purchases by the Fed wouldn't be expected to have any effects. The foundation of modern finance theory is the belief in what is called a pricing kernel, which one can think of as the value that the market places on getting $1 if some specified relevant future event were to occur. If investors were risk-neutral, that value would just be the probability of the event times a risk-free discount rate. With risk aversion, the value might be higher or lower than that based on how important it is to investors to have funds in that particular state of the world. Standard theory further teaches that this value ultimately is determined by the real resources that investors end up having available in that state of the world. Hence Woodford's conclusion:

Insofar as a mere re-shuffling
of assets between the central bank and the private sector should not change the real
quantity of resources available for consumption in each state of the world, the representative
household's marginal utility of income in different states of the world should
not change. Hence the pricing kernel should not change, and the market price of one
unit of a given asset should not change, either, assuming that the risky returns to
which the asset represents a claim have not changed....
All that
one needs for the argument are the assumptions that (i) the assets in question are
valued only for their pecuniary returns-- they may not be perfect substitutes from
the standpoint of investors, owing to different risk characteristics, but not for any
other reason-- and that (ii) all investors can purchase arbitrary quantities of the
same assets at the same (market) prices, with no binding constraints on the positions
that any investor can take, other than her overall budget constraint.

Under these assumptions, the irrelevance of central-bank open-market operations
is essentially a Modigliani-Miller result, as noted by Wallace (1981). If the central
bank buys more of asset x by selling shares of asset y, private investors should wish
purchase more of asset y and divest themselves of asset x, by exactly the amounts
that undo the effects of the central bank's trades.

Another implication of this view is that it should not matter what maturity of debt the Treasury chooses to issue. If one takes the future path of spending and taxes as given, whether the Treasury chooses to finance its current deficit with short- or long-term debt should be completely irrelevant. In a recent paper with University of Chicago Professor Cynthia Wu, I discussed this theory. We noted that 3-month and 10-year Treasury securities are treated by the private market as very different investments. Based on a very long historical record we can say with some confidence that, if the U.S. Treasury were to borrow $10 B in the form of 3-month T-bills and roll these over each quarter for a decade, it would end up on average paying a substantially lower total borrowing cost than if it were to issue $10 B in 10-year bonds. If it's really true that nothing in the world would change if the Treasury did more of its borrowing short-term, the natural question is why does the Treasury issue any 10-year bonds at all?

I think if you ask that question at a practical, institutional level, the answer is pretty obvious-- the Treasury believes that if all of its debt were in the form of 3-month T-bills, then in some states of the world it would end up being exposed to a risk that it would rather not face. And what is the nature of that risk? I think again the obvious answer is that, with exclusive reliance on short-term debt, there would be some circumstances in which the government would be forced to raise taxes or cut spending at a time when it would rather not, and at a time that it would not be forced to act if it instead owed long-term debt with a known coupon payment due.

The implication of that answer is that the assumption underlying Woodford's analysis-- that changing the maturity structure would not change the real quantity of resources available for private consumption in any state of the world-- is not correct.

Now, I presume that Woodford's response to this argument would be to say, well, yes there might be some effects, but the effects arise not from changing the maturity structure of the debt per se, but instead from changes in the timing of future spending and distortionary taxes that the changed maturity structure would lead to. But if the question we're asking is, would changing the maturity structure of Treasury debt cause anything else to change, I feel the correct answer is, yes, it surely would.

If the Fed buys 10-year Treasury bonds with newly created reserves, my view is that it is performing a similar operation to that just described, replacing long-term government debt with what is in effect the shortest-term government debt, namely Fed deposits that the holders could ask for in the form of cash immediately. I think the Fed's reluctance to do more has to do with the same kind of risk aversion exhibited by the Treasury, namely, large-scale asset purchases tie the Fed into a situation in which, under some possible future scenarios, the Fed would be forced to allow a larger amount of cash in circulation than it would otherwise have chosen.

Apart from the theory, Woodford separately discusses the empirical evidence of whether the Fed's large-scale purchases so far have had any effect. He raises a number of doubts about the event-study methodology that has been employed by many researchers in this area, doubts by the way with which I am sympathetic. But there is a second way to look for evidence about these questions using historical data, and that is to examine the relation between the maturity structure of publicly-held Treasury debt and the interest rates that investors earn on different Treasury securities. What one finds in the data is that periods in which there was a larger proportion of long-term debt are also periods in which long-term bonds paid a higher yield relative to short-term. This finding was reported by Gagnon, et. al. (2011). Woodford's paper discussed the event-study evidence from the Gagnon paper at length, but I did not see any mention of this important alternative form of evidence. Gagnon, et. al.'s finding has also been confirmed by a number of other researchers using very different data sets and methods, including Kuttner (2006), Greenwood and Vayanos (2010), Doh (2010), and Hamilton and Wu (2012), none of which are cited in Woodford's paper.

Having said all this, I should clarify that my position is not really that far from Woodford's. Cynthia and my estimates of the size of the effects are pretty modest. As I have said on a number of occasions, I believe that the primary significance of large-scale asset purchases is not their direct effects, but rather their usefulness as a supplementary signaling device, adding an exclamation point, if you will, to the Fed's communication of its future intentions. Woodford would like the Fed to say something such as it will restore nominal GDP to trend, but that begs the question of exactly how. The public could easily respond to the Fed, ok, so you don't like the current situation, but what are you going to do about it? And if the Fed's answer is, well, nothing right now, but trust us, we're going to do something a few years down the road, then the theorists may be surprised to find that the Fed's announcement doesn't change all that much, either.


The financial press writes with a perspective that is deeply rooted in American culture-- actions speak louder than words. I think it's necessary for the Fed to accompany its forward communication strategy with a specific plan of action in the here and now. And even if, as Woodford and I both believe, the effects of those immediate actions are of necessity limited, I think including those immediate actions in the Fed's overall plan can be helpful.

DIGITAL JUICE