This working paper comments on Monika Piazzesi and Martin Schneider's "Bond Positions, Expectations, and the Yield Curve," delivered at the Fiscal Policy and Monetary/Fiscal Policy Interactions conference held at the Atlanta Fed on April 19–20, 2007.Bonds - Prices ; Consumer behavior

Jon Faust

English

Research Papers in Economics

 
WORKING PAPER SERIES
F
E
D
E
R
A
L
 
R
E
S
E
R
V
E
 
B
A
N
K
  o
f
 
A
T
L
A
N
T
A
 
Comments on Piazzesi and Schneider’s  
“Bond Positions, Expectations, and the Yield Curve” 
 
Jon Faust 
 
Working Paper 2008-4 
February 2008  
 
 
The views expressed here are the author’s and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal 
Reserve System. Any remaining errors are the author’s responsibility. 
 
Please address questions regarding content to Jon Faust, Director, Center for Financial Economics and Economics Department, 
Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, 410-516-7614, faustj@jhu.edu. 
 
Federal Reserve Bank of Atlanta working papers, including revised versions, are available on the Atlanta Fed’s Web site at 
www.frbatlanta.org. Click “Publications” and then “Working Papers.” Use the WebScriber Service (at www.frbatlanta.org) to 
receive e-mail notifications about new papers. 
FEDERAL RESERVE BANK of ATLANTA       WORKING PAPER SERIES 
Comments on Piazzesi and Schneider’s  
“Bond Positions, Expectations, and the Yield Curve” 
 
Jon Faust 
 
Working Paper 2008-4 
January 2008 
 
Abstract: This working paper comments on Monika Piazzesi and Martin Schneider’s “Bond Positions, 
Expectations, and the Yield Curve,” delivered at the Fiscal Policy and Monetary/Fiscal Policy Interactions 
conference held at the Atlanta Fed on April 19–20, 2007. 
 
Key words: expectations, surveys, interest rates, portfolio choice, asset positions, term structure, yield 
curve   1
The allocation of research resources in the profession between fiscal and monetary policy 
has long been quite skewed toward monetary policy.  This conference on monetary and 
fiscal interactions reminds us once again that the overemphasis of monetary policy may 
not make sense even from the narrow standpoint of understanding monetary policy.  It is 
very fitting that the Federal Reserve Bank of Atlanta is promoting a more integrated view 
of policy analysis. 
  Another area would also benefit from a more integrated approach:  
macroeconomics and finance.  There is an immense macroeconomic literature on how 
monetary policy is transmitted through the yield curve and a similarly immense finance 
literature on the yield-curve.  Only recently have we begun to integrate these literatures.  
A proper integrated treatment of monetary and fiscal interactions cries out for an 
integrated view of finance and macro.  Understanding policy interactions requires 
resolving important questions about yield curve dynamics, their relation to policy 
expectations, and to the magnitude and composition of outstanding debt.     
Given this background, I was very pleased to be asked to discuss a paper entitled 
“Bond Supply, Expectations, and the Yield Curve,” authored by Monika Piazzesi and 
Martin Schneider, two of the pioneers in the fledgling enterprise of integrating modern 
finance and macro.  This is an excellent piece of research and I learned a great deal in 
reading it. 
  In these comments, I’ll try to provide some perspective on key choices faced in 
producing this ambitious work.  In doing so, I’ll highlight some ways in which I like the 
paper more, perhaps, than the authors do.  I’ll also discuss some directions for further 
progress.   2
Dynamic, Stochastic Models in Finance and Macro 
One central project in finance is to answer the question: Can we rationalize observed data 
on asset prices and portfolio shares?  It turns out that this question is too challenging, and 
so we often simplify by ignoring quantities, except to assume that the representative, or  
marginal, agent holds a bit of all assets.  That is, we assume the portfolio choice problem 
is at an interior solution.  This allows us to examine many questions regarding asset 
prices by studying Euler equations arising in optimization problems, and we can get a 
very long way without understanding, or even specifying, most of the model.  The 
ultimate goal remains to understand prices and quantities, but this generally requires a 
more complete model.   
Until recently, there were very few results on the difficult problem of solving a 
dynamic, stochastic, general equilibrium (DSGE) model of portfolio choice in the 
realistic setting in which agents face a rich array of assets.  The last 10 years, however, 
have seen an explosion of finance work in dynamic, stochastic models.  We see brute-
force numerical solution of models, complete solutions of special cases, and clever 
approximations around the special solved cases.  Monika and Martin’s paper falls in this 
latter category, building on the important work of Campbell, Chan, and Viceira (2003), 
who derive an approximate solution to a simple dynamic, stochastic portfolio problem.   
Of course, since the work of Kydland and Prescott, macroeconomics has also 
made great strides in analyzing DSGE models.  The macro models present agents with a 
rich set of choices about real stuff--labor supply, consumption, physical investment, etc--
while including a trivial set of intertemporal claims (assets).  For example, there may be   3
only direct ownership of capital and one-period bonds.  Alternatively, there may be 
complete contingent claims markets, and this trivializes the problem in another way.   
In contrast, in the finance DSGE work, agents face a rich portfolio problem, but the 
macroeconomic side of the model is trivial: the real outcomes on which agents write 
claims might, for example, be simply a random endowment stream. 
Of course, we would like to see DSGE models with both rich macroeconomics 
and rich portfolio choice problems.  Ultimate resolution of many problems including 
those regarding monetary and fiscal interactions will almost certainly require a model that 
is rich in both dimensions.   
One main roadblock we face on the pathway to integration is that it is very hard to 
reconcile asset price dynamics with economic fundamentals.  Thus, an important aspect 
of current integration work involves documenting puzzles and anomalies in asset price 
behavior from the standpoint of existing models.  Where do we stand on the project of 
resolving these anomalies?  I believe we are not at the end of this process, or even at the 
beginning of the end.  Perhaps work such as the current paper brings us to the end of the 
beginning. 
  Given the current state of understanding, anyone building an integrated model 
faces a challenging problem of how in the face of all the anomalies to use data to improve 
our current models.  In both macro and finance, there are four important challenges we 
face in bringing DSGE models to data:    4
 
1.  Pick a subset of all possible implications of the model to take seriously.   
We cannot solve all problems at once, so every current DSGE will have problem areas.  
We ignore these in order to focus on certain focal implications.  For example, we might 
emphasize the consumption or investment Euler equations. 
2. Pick a small subset of all potentially relevant data to use in drawing inferences about 
the model.  Our models simply cannot account for the joint dynamics of a very large set 
of variables.  Thus, in macro, we may focus on aggregate GDP, consumption, and 
inflation, along with, say, a single rate of return.  In finance, we may leave out most, if 
not all, macro variables and focus on a larger (but still smallish) set of returns. 
3. Pick a treatment of expectations.  Here there are many choices, but the problems begin 
to multiply.  We may use “rational” expectations, expectations that are derived to be 
consistent with the full set of implications of the model.  Of course, in steps 1 and 2 we 
admitted that we are not really comfortable with the full set of implications of the model.  
Thus, the case for rational expectations, which to many economists might otherwise be 
compelling, is substantially weakened.  An alternative is to do inference on the model 
using instrumental variables (IV), which leaves the treatment of expectations largely 
implicit.  This allows the researcher to sweep under the rug some troubling questions 
about expectations, but in my view this is not a virtue of the approach.   
A little-used approach is to estimate expectations using an ad hoc time series 
model (ad hoc in the sense of not imposing any model-based restrictions).  Of course, this 
approach is a close cousin of the IV approach; in both approaches expectations are 
inferred from reduced-form time series correlations in the data.  The principle difference   5
between the IV and ad hoc time series approaches, in my view, is that the ad hoc time 
series approach is more explicit and open to discussion and criticism.  I see this as a 
virtue.  
4.  Choose a metric for success of the model. Here, of course, we have formal methods, 
Bayesian (e.g., posterior odds ratios) and classical (e.g., J-tests in the GMM case).  Given 
the fact, however, that we know our current models have gross deficiencies, formal 
inference is sometimes argued to be uninteresting:  it is fairly straightforward to make 
current models look about as bad as we like using formal inference.  In light of this, we 
often find ourselves using informal methods, which amount to discussing whether or not 
the model “looks pretty good” in certain dimensions.  This is surely an intermediate step 
on the path of research, but has proven a useful technique.   
The Four Choices in the Current Paper 
The basic plan in the paper starts with measuring at each point in time the portfolio 
allocation of U.S. households.  For this purpose, assets are gathered into broad categories 
to form a small number of synthetic assets and measures are created of the evolution of 
portfolio shares through time.  Next, the authors build a time series model of returns on 
those synthetic assets.  We take the predicted values from this model as a proxy for the 
expectations of households.  Given asset holdings, price expectations, and a model of 
optimal behavior, we then invert the decision process of the agents to infer what asset 
prices would are implied.  These model-deduced prices are compared to actual prices to 
determine if the model is “pretty good.”   Let me make some comments organized around 
the four choices discussed above.   6
Choice 1.  This paper begins with a Campbell, Chan, Viceira-style (CCV) solution of a 
dynamic asset allocation problem.  Using a clever approximation around a solved case, 
CCV derive fairly simple expressions for the joint behavior of three items:  asset prices, 
portfolio allocations, and expectations.  Given any two of these items, we can make 
inferences about the third.  CCV derive implications for asset allocations based on a price 
data and a model for expectations.  The current paper also takes seriously CCV-style 
implications for the joint behavior of asset prices, portfolio allocations, and expectations.  
  As a small aside, CCV and the current paper perform two of the three natural 
permutations with the framework.  The final exercise is to take price and quantity data 
and to derive implications for expectations:  given the price and quantity data, what must 
people have been expecting?  (Or as my Mother used to say when faced with my choices, 
“What in God’s name were you thinking!?”)   In many ways, this third exercise is the 
most natural.  We have excellent data on prices, decent data on quantities, but essentially 
no data on expectations.  It probably makes sense to use the better-measured items to 
learn about the less well measured. 
Choice 2. Regarding data, the current paper is nearly unique in focusing on 
portfolio allocations.  The authors construct a good deal of the portfolio share data 
required for the paper.  Constructing these data required a great deal of work and I think 
this alone is a major contribution of the research project.  Consistent with most work 
coming from the finance side, macroeconomics is treated in a fairly trivial way; for 
example, the only macro variable involved in the forecasting model is inflation.    
Choice 3.  When it comes to expectations, the authors sound an apologetic note in 
taking the ad hoc time series approach.  I do not think such apologies are needed.  As   7
noted above, the rational expectations approach is questionable in the current context and 
the IV approach has little to recommend it over the ad hoc time series approach.   
Choice 4.  The authors take the informal approach to evaluating the merits of the 
model.  For example, the paper presents plots of actual asset prices and prices inferred 
using the model; the authors then discuss whether the model-based prices “look pretty 
good.”  We would ultimately prefer more formal criteria, but I think this paper is another 
excellent demonstration of the fact that these informal comparisons may be quite 
informative, especially at this early stage in the work synthesizing macro and finance. 
On the whole then, I think the authors have dealt with the four choices in ways 
that are astute at best, and natural at worst. Let me raise two other issues. 
First, I would like to see better motivation for the auxiliary time series model used 
to generate expectations.  The main point of this exercise may be boiled down to asking 
whether observed dynamics of portfolio shares are associated in the proper way with 
agent’s predictions regarding returns.  From this standpoint, it is essential that the time 
series model reflect the predictions agents may have made.  Is a low-dimensional VAR 
likely to do this?  We know that VARs generally produce very poor predictions, and they 
are essentially never used in practical forecasting.  At minimum, I would like to see 
documentation that the predictions from the model are somewhere near the frontier of 
best practice in forecasting excess returns. 
Further, the authors impose the restrictions of a particular arbitrage-free term 
structure model on the time series model.  It is becoming common to do this, but I have 
yet to see an argument as to why it is coherent to do so.  Informally, I put the issue this 
way. If the restrictions hold with probability one in the data, then there is zero (precisely   8
zero) benefit from imposing them.  If they do not hold in the data, then we need a theory 
of why and how they do not hold before we know whether it is coherent to impose the 
restrictions.  Greg Duffee (2007) has made this point much more thoroughly in a recent 
paper. 
 Thus, while I have no difficulty with using an auxiliary time series model for 
expectations, I would like to see a much stronger case made that the model used here is 
appropriate. 
  Second, as the authors are aware, the treatment of the residual asset is currently 
very unsatisfactory.  The assets in the economy essentially divide into a set of bonds and 
the residual asset, which as the name implies is everything else:  equities, real estate, 
human capital, etc.  From the standpoint of integrating finance and macro, I think it is fair 
to say that the vast majority of macro is residing in the residual asset.   In the current 
version of the paper, the return on this asset is taken to be independent and identically 
distributed and independent of the return on all other assets.   
From the standpoint of integrating realistic macro and finance models, this model 
is squarely in the tradition of treating fundamentals as an exogenous process with no 
interesting dynamics.  Further, there is no sensible view of economics or finance in which 
the returns on a firm’s bonds and equities are related in this way.  Indeed, this surely 
violates accounting identities.  
  The authors call this assumption about the return on the residual asset a 
benchmark.  Because it cannot be made consistent with any reasonable view of 
economics or finance, I think that this is a highly problematic benchmark and the results   9
under this benchmark are of little interest. 
Bottom line   
Work integrating finance and macro is at an early stage and the initial forays into it will 
have readily apparent areas for future improvement.  I see these not as problems, but as 
opportunities.  This is an outstanding paper pointing out a direction in which we should 
be moving.  From the standpoint of the issue in the title of this conference, I think this 
paper shows we have a long way to go.  Understanding monetary and fiscal interactions 
will require a model with a rich finance side, perhaps like that in this paper, but also a 
much richer treatment of the economic fundamentals. 
 
References 
 
Campbell, J.,  Y. Chan, and Viceira, L, 2003. “A mulitvariate model of strategic asset 
allocation.” Journal of Financial Economics, 67, 41-80. 
 
Duffee, Gregory, 2007. “Forecasting with the term structure:  the role of no-arbitrage.” 
manuscript, Berkeley. 

A mulitvariate model of strategic asset allocation.”

Forecasting with the term structure: the role of no-arbitrage.” manuscript,

Comments on Piazzesi and Schneider's "Bond positions, expectations, and the yield curve"

http://www.frbatlanta.org/filelegacydocs/wp0804.pdf

Comments on Piazzesi and Schneider's "Bond positions, expectations, and the yield curve"

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics