Federal Reserve Bank of Chicago
Core and ‘Crust’: Consumer Prices and
the Term Structure of Interest Rates
Andrea Ajello, Luca Benzoni, and Olena Chyruk
November 2014
WP 2014-11
Core and ‘Crust’: Consumer Prices and
the Term Structure of Interest Rates
∗
Andrea Ajello,
†
Luca Benzoni,
‡
and Olena Chyruk
§
First version: January 27, 2011
This version: December 19, 2012
Abstract
We propose a no-arbitrage model that jointly explains the dynamics of consumer
prices as well as the nominal and real term structures of risk-free rates. In our frame-
work, distinct core, food, and energy price series combine into a measure of total
inflation to price nominal Treasuries. This approach captures different frequencies in
inflation fluctuations: Shocks to core are more persistent and less volatile than shocks
to food and, especially, energy (the ‘crust’). We find that a common structure of latent
factors determines and predicts the term structure of yields and inflation. The model
outperforms popular benchmarks and is at par with the Survey of Professional Fore-
casters in forecasting inflation. Real rates implied by our model uncover the presence
of a time-varying component in TIPS yields that we attribute to disruptions in the
inflation-indexed bond market. Finally, we find a pronounced declining pattern in the
inflation risk premium that illustrates the changing nature of inflation risk in nominal
Treasuries.
∗
We are grateful to Torben Andersen, Andrew Ang, Jeff Campbell, Anna Cieslak, Larry Christiano,
Charlie Evans, Spence Krane, Michael McCracken, Marcel Priebsch, Alejandro Justiniano, Giorgio Primiceri,
and seminar participants at the Kellogg School of Management, the University of British Columbia, Essex
University, the University of Lugano, the Board of Governors of the Federal Reserve System, the European
Central Bank, the Bank of England, the 2013 Asset Pricing meeting at the NBER SI, the 2012 Western
Finance Association conference, the 2012 Society for Financial Econometrics annual meeting, the 2012 Society
for Economic Dynamics conference, the 2012 European Meeting of the Econometric Society, the 2012 Federal
Reserve System conference on Business and Financial Analysis, the 2012 Midwest Macroeconomics Meetings,
the 2014 HEC Applied Financial Time Series Workshop, the 2013 Computational and Financial Econometrics
Conference, and the 2013 Symposium on Control and Modeling of Social and Economic Behavior at UIUC
for helpful comments and suggestions. All errors remain our sole responsibility. Part of this work was
completed while Benzoni was a visiting scholar at the Federal Reserve Board. The views expressed herein
are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal
Reserve System. The most recent version of this paper is at http://ssrn.com/abstract=1851906.
†
Board of Governors of the Federal Reserve System, andrea.ajello@frb.gov.
‡
Corresponding author. Federal Reserve Bank of Chicago, lbenzoni@frbchi.org.
§
Federal Reserve Bank of Chicago, ochyruk@frbchi.org.
Core and ‘Crust’: Consumer Prices and
the Term Structure of Interest Rates
Abstract
We propose a no-arbitrage model that jointly explains the dynamics of consumer
prices as well as the nominal and real term structures of risk-free rates. In our frame-
work, distinct core, food, and energy price series combine into a measure of total
inflation to price nominal Treasuries. This approach captures different frequencies in
inflation fluctuations: Shocks to core are more persistent and less volatile than shocks
to food and, especially, energy (the ‘crust’). We find that a common structure of latent
factors determines and predicts the term structure of yields and inflation. The model
outperforms popular benchmarks and is at par with the Survey of Professional Fore-
casters in forecasting inflation. Real rates implied by our model uncover the presence
of a time-varying component in TIPS yields that we attribute to disruptions in the
inflation-indexed bond market. Finally, we find a pronounced declining pattern in the
inflation risk premium that illustrates the changing nature of inflation risk in nominal
Treasuries.
1
1 Introduction
A general view in the empirical macro-finance literature is that financial variables do little to
help forecast consumer prices. In particular, most empirical studies find that there is limited
or no marginal information content in the nominal interest rate term structure for future
inflation (Stock and Watson (2003)). The challenge to reconcile yield curve dynamics with
inflation has become even harder during the recent financial crisis due to the wild fluctuations
in consumer prices, largely driven by short-lived shocks to food and, especially, energy prices
(Figure 1). There is hardly any trace of these fluctuations in the term structure of interest
rates. Core price indices, which exclude the volatile food and energy components, have been
more stable. Nonetheless, attempts to forecast core inflation using Treasury yields data have
also had limited success.
We propose a dynamic term structure model (DTSM) that fits inflation and nominal
yields data well, both in and out of sample. We price both the real and nominal Treasury
yield curves using no-arbitrage restrictions. In the tradition of the affine DTSM literature
(e.g., Duffie and Kan (1996), Piazzesi (2010), Duffie, Pan, and Singleton (2000)), we assume
that the real spot rate is a linear combination of latent and observable macroeconomic
factors. The macroeconomic factors are the three main determinants of consumer prices
growth: core, food, and energy inflation. We model them jointly with the latent factors in
a vector autoregression (VAR). Nominal and real bond prices are linked by a price deflator
that grows at the total inflation rate, given by the weighted average of the individual core,
food, and energy measures.
This framework easily accommodates the properties of the different inflation components.
Shocks to core inflation are much more persistent and less volatile compared to shocks to food
and, especially, energy inflation (the ‘crust’ in the total consumer price index). The model
fits these features by allowing for different degrees of persistence and volatility of the shocks
to each of the three inflation measures, and for contemporaneous and lagged dependence
among the factors. The three individual components combine into a single measure of total
inflation that we then use to price the nominal yield curve.
When we estimate the model on a panel of nominal Treasury yields and the three infla-
tion series, we find a considerable improvement in the fit compared to DTSM specifications
that rely on a single inflation factor (either total or core). In particular, we see a significant
improvement in the out-of-sample performance of the model when forecasting inflation. This
is most evident in core consumer price index (CPI) forecasts, which we find to systematically
outperform the forecasts of various univariate time series models, including the ARMA(1,1)
benchmark favored by Ang, Bekaert, and Wei (2007) and Stock and Watson (1999). Our
model does well on total CPI too, often improving on the ARMA and other benchmarks. Re-
markably, it is at par with the Survey of Professional Forecasters (SPF) on total inflation and
it outperforms the University of Michigan survey forecasts. Finally, total inflation forecasts
from our preferred no-arbitrage DTSM are more precise than forecasts from unconstrained
VAR models estimated on interest rate and inflation data, including specifications that use
2
core, food, and energy inflation series.
These results underscore the advantages of modeling the dynamics of the individual in-
flation components. A DTSM that prices bonds out of a single measure of inflation delivers
forecasts for the specific proxy of inflation used for estimation (e.g., total, core, or a prin-
cipal component of several price series). In contrast, jointly modeling the three inflation
factors (core, food, and energy) produces forecasts for total inflation as well as each of its
components. Moreover, this approach proves to be more robust to the extreme fluctuations
observed in some price indices. In particular, the estimation finds shocks to energy infla-
tion to be short-lived and to have limited impact on the yield curve and long-run inflation
expectations.
Our inflation forecasts not only reflect information from past price realizations, but also
from yield curve dynamics. In fact, we find that the latent factors explain a large fraction
of the variation in both nominal yields and core inflation. In particular, we allow the latent
factors to shape the conditional mean of core inflation, and model estimation supports such
dependence. When we decompose the variance of the forecasting error for core inflation, we
find that the latent factors explain approximately 60% of it at the five-year horizon. This
fraction remains sizeable even at the short one-year horizon (>18%), and it increases even
further when we perform an unconditional variance decomposition.
A related analysis shows that the latent factors are the main drivers in bond yields’
variation and crowd out inflation variables in explaining the term structure of interest rates.
This is consistent with the model of Joslin, Priebsch, and Singleton (2010), who impose
restrictions on the model coefficients such that the loadings of the yields (or their linear
combinations) on macroeconomic variables are zero. In contrast, we do not impose such
conditions a priori. We estimate an unconstrained model and find factor loadings on the
inflation series that are nearly zero. We then demonstrate using simulated yields and infla-
tion series that our model replicates the empirical linkage between yields and inflation data
extremely well.
The model produces estimates for the real term structure of interest rates. We find a
real spot rate pattern that is tightly linked to the history of monetary policy intervention.
Longer maturity real yields show a much smoother behavior. At all maturities, real rates
exhibit a declining pattern since the 1980s.
While we do not use data on Treasury Inflation Protected Securities (TIPS), we compare
our real rates estimates to TIPS yields during the sub-sample for which those data are
available. In the early years of TIPS trading, TIPS rates are systematically higher than
model-implied real rates, with a spread of approximately 150bps at the ten-year maturity in
the first quarter of 1999. The spread progressively shrinks to near zero by 2004. This evidence
points to the presence of a time-varying liquidity premium in the TIPS market as documented
by D’Amico, Kim, and Wei (2010), Fleckenstein, Longstaff, and Lustig (2010), Haubrich,
Pennacchi, and Ritchken (2009), and Pflueger and Viceira (2012). More interestingly, the
TIPS-real-rate spread widens again during the financial crisis, with a peak immediately after
the collapse of Lehman Brothers. This is related to disruptions in the TIPS market, where
