How to Estimate Models with Indeterminacy

My coauthors, Vadim Khramov, Giovanni Nicolo and I, have recently completed a revision of our working paper, "Solving and Estimating Indeterminate DSGE Models".

Dynamic Stochastic General Equilibrium Models (DSGE) often have many equilibria. I have long argued that we should exploit that idea to explain real world phenomena. For example, multiple equilibrium models can help to explain why "animal spirits" drive real world markets (see my survey here).

In 2004, Thomas Lubik and Frank Schorfheide published an influential paper which applied that idea to US monetary policy.  A number of authors have taken up their method, but the technique they used is not very easy to apply in practice. Our paper shows how to solve and estimate models with indeterminate equilibria using readily available software packages such as Chris Sim's code Gensys, or the widely used Matlab based package Dynare.


TheTreasury and the Fed are at Loggerheads over QE

In my last post on QE, I quoted a paper by James Hamilton and Cynthia Wu that provides some empirical evidence for the importance of the asset composition of the Fed's balance sheet and its effect on the term structure of interest rates. They have posted their data online and it makes for interesting bedtime reading. 

Hamilton and Wu combined their data with evidence from the yield curve. They found that qualitative easing can be effective at the lower bound and that
... buying $400 billion in long-term maturities outright with newly created reserves, ... could reduce the 10-year rate by 13 basis points without raising short-term yields.
To construct these estimates, they used a theoretical model developed by Vayanos and Vila which assumes that there are investors who have a 'preferred habitat'.

The Hamilton Wu results are important. I ran some regressions of term premiums on bond supply by maturity, using their data, and I found the same orders of magnitude in the response of interest rates that they found. But there is an interesting sub-text to their analysis discussed in Section 8 of their paper. The Fed and the Treasury have been following conflicting policies. David Beckworth on his blog in 2012 makes the same point.

Quantitative Easing took place in three phases. QE1 from 11/08 to 03/10, QE2 from 11/10 to 06/11 and QE3 which is ongoing. Along with monetary expansion, the Fed attempted to refinance its portfolio by selling at the short end and buying at the long end of the yield curve. But at the same time, the Treasury was refinancing its own portfolio. The end result was that the Treasury restructuring completely swamped any effect of Fed operations at the long end of the yield curve.  

Figure 1
In Figure 1 I have broken down the System Open Market Account (SOMA) of Fed holdings of Treasuries by maturity as a percentage of all outstanding Treasuries, using the Hamilton Wu data set. The two vertical red lines are the beginning and end of the last recession and the vertical black line marks the collapse of Lehman Brothers.

There are two takeaways from Figure 1. First, the constancy of Fed holdings by maturity in the period leading up to the recession, and second, the dramatic change in this portfolio after the collapse of Lehmann Brothers. The big increase in Fed holdings at the long end is the result of 'operation twist'.

How big a player is the Fed in the Treasury markets? Leading up to the Great Recession, the Fed held 12% of all Treasuries with a maturity of two years or less, 3% of two to five year maturities, 1.5% of five to ten year maturities and 2% of maturities from ten to thirty years. Once the recession hit, Fed holdings of maturities shorter than two years plummeted, and longer maturities increased. 

But Figure 1 gives a misleading picture of Fed actions in response to the crisis since it divides SOMA holdings, chosen by the Fed, by total outstanding Treasury debt. There were two important changes going on during the recession. First, the Treasury dramatically changed the way it finances its deficit, substituting two to ten year bonds for shorter maturities. And second, the proportion of bonds held by the Fed fell dramatically.
Figure 2
In Figure 2, I illustrate the importance of the first point. This figure shows the percentage of all outstanding Treasuries, by maturity, as a percentage of total outstanding Treasury debt. After the collapse of Lehmann Brothers, the percentage of short denomination bonds plummeted. In their place, the Treasury sharply increased its issuance of two to ten year bonds. It is important to note that this Figure has nothing to do with any action by the Fed. It is a consequence of decisions by the Treasury to refinance its debt at longer maturities in the low interest rate environment that followed the collapse of Lehmann Brothers.

Figure 3

Figure 1 divides SOMA holdings by total Treasury debt outstanding. In contrast, in Figure 3 I divide Fed SOMA holdings by the Fed's holding of all maturities. This figure DOES reflect decisions made by the open market committee of the Fed. The Fed's holdings of short term bonds fell from 65% of its portfolio in 2007 to 25% in 2010. In contrast, holdings of two to five year bonds increased from 17% to 30%, five to ten year bonds increased from 6% to 26% and ten to thirty year bonds went from 12% to 19%. These are all percentages of the Fed's total Treasury holdings.
Figure 4
How successful was operation twist at changing the maturity structure of Treasury securities held by the public? In Figure 4, I break down Treasuries held by the public as a fraction of total debt outstanding. This figure shows that although the Fed switched its holdings from yields of three months to two years to yields in the two to ten year range (Figure 3) this operation was swamped, after November of 2008, by Treasury operations that increased the supply of maturities in the two to ten year range (Figure 4).  The end result was that the public ended up holding more of these two to ten year bonds in 2010 than before the recession hit.

Could we have a little coordination here guys?
__________________
Footnote: The Hamilton Wu data have since been updated through January of 2011 but I haven't had time yet to update my figures using their revisions.


The Greenspan Put and the Yellen Call

In today's Guardian, I make the case for a more aggressive financial stabilization policy,  "No more boom and bust? The financial policy committee has time on its side". I argue that the Bank of England's FPC should buy shares in the stock market when the PE ratio is low, and sell them when it is high.

Kimdriver makes the following comment.
The Greenspan put with real teeth ?
My worry is that, while CAPE has historically been a good predictor of future returns, the level that the FPC should be ready to intervene would have to be set so low that it might be fairly useless. Otherwise the safety net would just encourage increased irrational exuberance.
My response ...
I am not arguing just for a Greenspan Put: but also for a Yellen Call. It is just as dangerous to allow market bubbles as it is to allow them to crash.
Read more here...

Why Death Matters for Central Bank Policy

Noah Smith raises the question: can the Fed influence the interest rate? Although the answer may seem obvious, the question itself reflects a conundrum for neoclassical theory. It is representative of a related but more comprehensive question: does the asset composition of the central bank balance sheet matter?

Let me set aside, for now, the deep question: what is money? I will take for granted the fact that the liabilities of the central bank are special. Perhaps this is due to legal restrictions, as Neil Wallace has suggested, or perhaps it is a matter of social convention. My focus here is not on central bank liabilities; but on their assets.

Figure 1
Figure 1 is a stylized representation of the balance sheet  of the Fed. Like King Midas who turned everything he touched to gold, so the Fed turns everything it purchases into money. Commercial banks hold accounts at the Fed, and when the Fed purchases an asset, any asset, those accounts are credited with the creation of new money.

Historically, the asset composition of the Fed has consisted almost exclusively of short term Federal government bonds, the item in red on Figure 1. In September of 2008 two things happened. First, the size of the balance sheet increased. The RHS of the table in Figure 1 went from $800b to $2,000b overnight. Second, the composition of the asset portfolio changed dramatically.
Figure 2
Figure 2 is a highly stylized representation of what happened following the collapse of Lehman Brothers in the fall of 2008.  The Fed purchased a whole boatload of long-term government debt: And for the first time in its history, it bought mortgage backed securities (MBS). 

The fact that the asset side of the balance sheet went from $800b to $2,000b is referred to as quantitative easing. The fact that the fraction of liabilities held as short term treasury securities went from 94% (750/800) to 38% (750/2000) is referred to as qualitative easing.

Here's the puzzle for neoclassical theory. According to received wisdom (Michael Woodford's Jackson Hole paper is an excellent exposition of this idea) the asset composition of the Fed's balance sheet is irrelevant. If the Fed had bought more short-term government debt instead of intervening in the riskier MBS market; it would not have made one whit of difference to the economy.

Why is that? According to standard neoclassical models, all transactions are carried out by infinitely lived families who take into account the welfare of their descendants. The far sighted paternalistic patriarchs of these families trade assets with each other that are contingent on every possible future event.  

Because the price of long bonds reflects all known facts about the probabilities of future outcomes, central bank asset positions do not influence the market price of risk. When the government takes a new position in the asset markets, the private sector unwinds that position through its own open-market trades.

But that is not what happened. A wealth of evidence shows not just that quantitative easing matters, but also that qualitative easing matters. (see for example Krishnamurthy and Vissing-Jorgensen, Hamilton and Wu, Gagnon et al). In other words, QE works in practice but not in theory. Perhaps its time to jettison the theory.

Replacing all of neoclassical theory with an operational alternative is a daunting task. There is no lack of contenders. Perhaps people are irrational as the behaviorists have claimed. Perhaps the market is segmented and institutional constraints cause pension funds to favor safe assets. Perhaps there are borrowing constraints that prevent some trades from taking place. These are all possibilities and I do not want to suggest that they do not have merit. But there is a much simpler explanation for the failure of the irrelevance result. Human beings do not live forever.

The fact that our lives are finite has consequences for the efficiency of asset markets. Davis Cass and Karl Shell called this idea sunspots. Asset markets are volatile because we all, eventually, meet the grim reaper. And although governments are sometimes overturned, they have much longer horizons than individuals. That simple fact explains why the asset composition of the central bank matters.