Tag Archive for 'Cynthia Wu'

More on Woodford and QE

Continuing on from my previous post, I note that James Hamilton has also written a piece on Woodford’s paper [pdf here].  He expands on another way in which QE in the form of long-dated asset purchases could have an effect on the real economy:  the pricing kernel is almost certainly not constant.  Before I get to him, though, recall Woodford’s argument:

But it is important to note that such “portfolio-balance effects” do not exist in a modern, general-equilibrium theory of asset prices — in which assets are assumed to be valued for their state-contingent payoffs in different states of the world, and investors are assumed to correctly anticipate the consequences of their portfolio choices for their wealth in different future states — at least to the extent that financial markets are modeled as frictionless. It is clearly inconsistent with a representative-household asset pricing theory (even though the argument sketched above, and many classic expositions of portfolio-balance theory, make no reference to any heterogeneity on the part of private investors). In the representative-household theory, the market price of any asset should be determined by the present value of the random returns to which it is a claim, where the present value is calculated using an asset pricing kernel (stochastic discount factor) derived from the representative household’s marginal utility of income in different future states of the world. 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.

Given that context, here’s Hamilton:

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.

Hamilton goes on to point out that a similar risk-aversion story may be at play at the Federal Reserve:

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.

Which is funny, if only for a specialised sub-set of humanity, because it translates into the Fed being worried that by engaging in stimulus whose effect ranges from weak to uncertain, they may be forced to engage in stimulus that will absolutely work.