has a lower dimension than the nominal term structure. In this paper, we let the data decide the
dimensionality of the real term structure.
Overall, compared with previous studies, two main features of this model help us better
distinguish the inﬂation risk premium and the liquidity premium components of the TIPS BEI. On
the one hand, the use of price level data Q
in the estimation and the unrestricted correlation
structure between factor innovations help us better pin down expected inﬂation and the inﬂation
risk premium. On the other hand, the higher-dimensionality of the real term structure, the
estimation of which is assisted by the additional information from TIPS yields, allows us to better
identify the parameters governing the real yield dynamics. As a result, the spread between TIPS
and indexation lag-adjusted real yields is pinned down, and can be estimated separately from the
inﬂation risk premium. These features can only be fully appreciated when considered within the
context of the empirical methodology used to estimate the model, to which we now turn.
IV. Data and Empirical Methodology
We use 3- and 6-month, 1-, 2-, 4-, 7-, and 10-year nominal yields and CPI-U data from
January 1990 to March 2013. In contrast, our TIPS yields are restricted by data availability and
cover a shorter period from January 1999 to March 2013, with the earlier period without TIPS
data (1990-1998) treated as missing observations.
We sample yields at the weekly frequency
and assume that the monthly CPI-U data is observed in the last week of the current month.
3-and 6-month T-bill yields are fromthe Federal Reserve Board’s H.15 release and converted to continuously
compounded basis. Longer-term nominal yieldsand TIPS yieldsare based on zero-coupon yield curvesﬁtted at the
Federal Reserve Board. In particular,nominal yieldsare based on the Svensson (1995) curve speciﬁcation forthe
entire sample; TIPS yields are based on the Nelson and Siegel (1987) curve speciﬁcation prior to January 2004 and
the Svensson (1995) curve speciﬁcation thereafter. See G¨urkaynak,Sack, and Wright (2007, 2010)for details.
Here we abstract from the real-time data issue by assuming that investors correctly infer the current inﬂation
rate in a timely fashion.