
Working Papers
"A Shadow Rate DSGE Model"
with Ji Zhang,
coming soon.
Abstract
Workhorse Gaussian affine term structure models (ATSMs) attribute timevarying bond risk premia entirely to changing prices of risk, while structural models with recursive preferences
credit it completely to stochastic volatility.
We reconcile these competing channels by introducing a novel form of external habit into an otherwise standard model with recursive preferences. The new model has an ATSM representation with analytical bond prices making it empirically tractable. We find that time variation in bond term premia is predominantly driven by the price of risk, especially, the price of expected inflation risk that comoves with expected inflation itself.
Abstract
We investigate the effectiveness of central bank communication when firms have heterogeneous inflation expectations that are updated through social dynamics. The bank's credibility evolves with these dynamics and determines how well its announcements anchor expectations. We find that trying to eliminate high inflation by abruptly introducing low inflation targets generates shortterm overshooting. Gradual targets, in contrast, achieve a smoother disinflation. We present empirical evidence to support these predictions. Gradualism is not equally effective in other situations though: our model predicts aggressive announcements are more powerful when combating deflation.
 In the news
Publications
Abstract
We investigate the relationship between uncertainty about monetary policy and its transmission mechanism, and economic fluctuations. We propose a new term structure model where the second moments of macroeconomic variables and yields can have a firstorder effect on their dynamics. The data favors a model with two unspanned volatility factors that capture uncertainty about monetary policy and the term premium. Uncertainty contributes negatively to economic activity. Two dimensions of uncertainty react in opposite directions to a shock to the real economy, and the response of inflation to uncertainty shocks vary across different historical episodes.
 In the news  Video
Abstract
This paper employs an approximation that makes a nonlinear term structure model
extremely tractable for analysis of an economy operating near the zero lower bound for interest rates. We show that such a model offers an excellent description of the data compared to the benchmark model and can be used to summarize the macroeconomic effects of unconventional monetary policy. Our estimates imply that the efforts by the Federal Reserve to stimulate the economy since July 2009 succeeded in making the unemployment rate in December 2013 1% lower, which is 0.13% more compared to the historical behavior of the Fed.
 Shadow rates  Code 
Online Table and Figures
 In the news
Abstract
We develop new procedures for maximum likelihood estimation of
affine term structure models with spanned or unspanned stochastic volatility. Our approach uses linear regression to reduce the dimension of the numerical optimization problem yet it produces the same estimator as maximizing the likelihood.
It improves the numerical behavior of estimation by eliminating parameters from the objective function that cause problems for
conventional methods. We find that spanned models capture the crosssection of yields well but not volatility while unspanned models fit volatility at the expense of fitting the crosssection.
 Data and code  Online
Appendix  In the news
Abstract
The last decade brought substantial increased participation in commodity markets by
index funds that maintain long positions in the near futures contracts. Policy makers
and academic studies have reached sharply different conclusions about the effects of
these funds on commodity futures prices. This paper proposes a unifying framework for
examining this question, noting that according to a simple model of futures arbitrage,
if indexfund buying influences prices by changing the risk premium, then the notional
positions of the index investors should help predict excess returns in these contracts.
We find no evidence that the positions of traders in agricultural contracts identified by
the CFTC as following an index strategy can help predict returns on the near futures
contracts. We review evidence that these positions might help predict changes in oil
futures prices, and find that while there is some support for this in the earlier data, this
appears to be driven by some of the dramatic features of the 20072009 recession, with
the relation breaking down out of sample.
 In the news
Abstract
If commercial producers or financial investors use futures contracts to hedge against
commodity price risk, the arbitrageurs who take the other side of the contracts may
receive compensation for their assumption of nondiversifiable risk in the form of positive
expected returns from their positions. We show that this interaction can produce an
affine factor structure to commodity futures prices, and develop new algorithms for
estimation of such models using unbalanced data sets in which the duration of observed
contracts changes with each observation. We document significant changes in oil futures
risk premia since 2005, with the compensation to the long position smaller on average
but more volatile in more recent data. This observation is consistent with the claim
that indexfund investing has become more important relative to commerical hedging in
determining the structure of crude oil futures risk premia over time.
 Data and code  In the news
Abstract
Term premia implied by maximum likelihood estimates of affine term structure models
are misleading because of smallsample bias. We show that accounting for this bias
alters the conclusions about the trend, cycle, and macroeconomic determinants of the
term premia estimated in Wright (2011). His term premium estimates are essentially
acyclical, and often just parallel the secular trend in longterm interest rates. In contrast,
biascorrected term premia show pronounced countercyclical behavior, consistent with
theoretical and empirical arguments about movements in risk premia.
 Data and code  In the news
Abstract
Affine term structure models have been used to address a wide range of questions in macroeconomics and finance. This paper investigates a number of their testable implications which have not previously been explored. We show that the assumption that certain specified yields are priced without error is testable, and find that the implied measurement or specification error exhibits serial correlation in all of the possible formulations investigated here. We further find that the predictions of these models for the average levels of different interest rates are inconsistent with the observed data, and propose a more general specification that is not rejected by the data.
Abstract
The affine dynamic term structure model (DTSM) is the canonical empirical finance
representation of the yield curve. However, the possibility that DTSM estimates may be
distorted by smallsample bias has been largely ignored. We show that conventional estimates
of DTSM coefficients are indeed severely biased, and this bias results in misleading
estimates of expected future shortterm interest rates and of longmaturity term premia.
We provide a variety of biascorrected estimates of affine DTSMs, both for maximallyflexible
and overidentified specifications. Our estimates imply short rate expectations
and term premia that are more plausible from a macrofinance perspective.
 Data and Code
 Online
Appendix  In the news
The affine dynamic term structure model (DTSM) is the canonical empirical finance representation of the yield curve. However, the possibility that DTSM estimates may be distorted by smallsample bias has been largely ignored. We show that conventional estimates of DTSM coefficients are indeed severely biased, and this bias results in misleading estimates of expected future shortterm interest rates and of longmaturity term premia. We provide a variety of biascorrected estimates of affine DTSMs, both for maximallyflexible and overidentified specifications. Our estimates imply short rate expectations and term premia that are more plausible from a macrofinance perspective.
Abstract
This paper develops new results for identification and estimation of Gaussian
affine term structure models. We establish that three popular
canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate
contribution of the paper is the proposal of minimumchisquare estimation as an
alternative to MLE. We show that, although it is asymptotically
equivalent to MLE, it can be much easier to compute.
In some cases, MCSE allows researchers to recognize with certainty whether a given
estimate represents a global maximum of the likelihood function and makes feasible the
computation of smallsample standard errors.
 Data and Code  In the news
Abstract
This paper reviews alternative options for monetary policy when the shortterm interest rate is at the zero lower bound and develops new empirical estimates of the effects of the maturity structure of publicly held debt on the term structure of interest rates. We use a model of riskaverse arbitrageurs to develop measures of how the maturity structure of debt held by the public might affect the pricing of level, slope and curvature termstructure risk. We find these Treasury factors historically were quite helpful for predicting both yields and excess returns over 19902007. The historical correlations are consistent with the claim that if in December of 2006, the Fed were to have sold off all its Treasury holdings of less than oneyear maturity (about $400 billion) and use the proceeds to retire Treasury debt from the long end, this might have resulted in a 14basispoint drop in the 10year rate and an 11basispoint increase in the 6month rate. We also develop a description of how the dynamic behavior of the term structure of interest rates changed after hitting the zero lower bound in 2009. Our estimates imply that at the zero lower bound, such a maturity swap would have the same effects as buying $400 billion in longterm maturities outright with newly created reserves, and could reduce the 10year rate by 13 basis points without raising shortterm yields.
 Data  In the news
