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2018 | OriginalPaper | Chapter

Term Structure, Market Expectations of the Short Rate, and Expected Inflation

Authors : Jian Luo, Xiaoxia Ye

Published in: New Methods in Fixed Income Modeling

Publisher: Springer International Publishing

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Abstract

Based on the classic Gaussian dynamic term structure model \( {\mathbb{A}}_{0} \left( 3 \right) \), we rotate the model to a special representation, the so called “Companion Form Realization”, in which the state variables comprise the short rate and its related expectations. This unique feature makes the representation very useful in analyzing the response of the yield curve to the shocks in the short rate and its related expectations, and monitoring market expectations. Using the estimated model, we quantify a variety of yield responses to the changes in these important state variables; and also give an “unsurprising” pattern in which changes in state variables have little impact on the long end of the yield curve. Estimated state variables have strong explanatory power for expected inflation. Three case studies of the unconventional monetary policies are presented.

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The expected inflation mentioned here is in the sense Haubrich et al. (2012) and Potter (2012). The data is publicly available at http://www.clevelandfed.org/research/data/inflation_expectations/index.cfm.

\( mV \) is chosen to be \( \left[ {\begin{array}{*{20}c} {3\,{\text{month}}} & {2\,{\text{year}}} & {10\,{\text{year}}} \\ \end{array} } \right]^{{ \intercal }} \) in the empirical analysis.

Here is the link: https://www.federalreserve.gov/releases/h15/data.htm.

There are some noticeable exceptions after 2009. These discrepancies might be due to the distortion at the short end of the yield curve which has been artificially set to “zero” since 2009. This distorted nominal short rate can barely reflect the real economic fluctuation. By fitting to the whole yield curve, the model implied short end of the yield curve could be more consistent with the real economy, therefore, gives a better description of the actually nominal short rate.

Here we assume the easing is conducted via a conventional monetary policy, e.g., setting the Fed funds rate’s targets.

The downward impact on the short end would be bounded by the zero lower bound.

Since the data used to estimate the expected inflation provided by the Federal Reserve Bank of Cleveland includes the TIPS data, and the 10-year TIPS are most liquid, the 10-year expected inflation is relatively free of estimation errors.

Notice that \( \Delta X_{2,t}^{1} \) and \( \Delta X_{3,t}^{1} \) are not directly included in the regressions, instead residual \( \xi_{t} \) is used in the regressions to avoid the multicollinearity issue and have meaningful interpretations for coefficients.

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Title: Term Structure, Market Expectations of the Short Rate, and Expected Inflation
Authors: Jian Luo
Xiaoxia Ye
Publisher: Springer International Publishing
Book: New Methods in Fixed Income Modeling
Print ISBN: 978-3-319-95284-0

Electronic ISBN: 978-3-319-95285-7

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-95285-7_1