A Semiparametric Analysis of the Term Structure of the US Interest Rates*

Published date01 August 2009
Date01 August 2009
AuthorFabrizio Iacone
DOIhttp://doi.org/10.1111/j.1468-0084.2008.00546.x
475
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2009. Published by Blackwell Publishing Ltd,
9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 71, 4 (2009) 0305-9049
doi: 10.1111/j.1468-0084.2008.00546.x
A Semiparametric Analysis of the Term Structure
of the US Interest RatesÅ
Fabrizio Iacone
Department of Economics and Related Studies, University of York, Heslington, York,
YO10 5DD, UK (e-mail: fi501@york.ac.uk)
Abstract
The short end of the US$ term structure of interest rates is analysed allowing for the
possibility of fractional integration and cointegration. This approach permits mean-
reverting dynamics for the data and the existence of a common long run stochastic
trend to be maintained simultaneously. We estimate the model for the period 1963–
2006 and nd it compatible with this structure. The restriction that the data are I(1)
and the errors are I(0) is rejected, mainly because the latter still display long memory.
This result is consistent with a model of monetary policy in which the Central Bank
operates affecting contracts with short term maturity, and the impulses are trans-
mitted to contracts with longer maturities and then to the nal goals. However, the
transmission of the impulses along the term structure cannot be modelled using the
Expectations Hypothesis.
I. Introduction
In this study, we analyse the long term dynamics and interactions in a vector of
nominal interest rates of US$ interbank deposits with different maturities, allowing
for potential fractional integration and cointegration. In what follows, for brevity we
refer to the nominal interest rate simply as ‘interest rate’ or ‘rate’.
A model of the interactions in a vector of rates with different maturities is neces-
sary both to measure the effects of monetary policy and to price nancial assets.
*Financial support from the Economic and Social Research Council through grant R000239936, from the
Ente per gli Studi Luigi Einaudi and from the Dennis Sargan Memorial Fund is gratefully acknowledged. I
thank Peter M. Robinson, Javier Hualde, ValentinaCorradi, Roderick McCrorie, Les Godfrey, the Editor and
two anonymous referees for their helpful suggestions.
JEL Classication numbers: C22, E43.
476 Bulletin
Such a model is an important tool for policy evaluation because the Federal Reserve
operates by supplying liquidity on the Federal Funds market by open market oper-
ations and discount window loans, so that it is directly present in just one market,
and one that is characterized by contracts with very short maturity. It is therefore
necessary to model the conduction of the monetary policy impulses to the rates
of contracts with longer maturities and to other nancial activities, as a part of a
model of the transmission of monetary policy to the nal goals. If the Fisher equation
holds, central banks may also nd the information in the term structure of interest
rates valuable because long term rates include the market’s expectations of future
ination.
Modelling the interaction across rates is also important for the economic agents
who would like to forecast the effects of future monetary policy decisions on the price
of nancial assets. Apractical example of how to extract the market’s expectations on
future policy rates from a given term structure, and how to use them to price nancial
instruments, was discussed by S¨oderlind and Svensson (1997).
A theoretical model for the term structure of interest rates, i.e. the Expectations
Hypothesis, was discussed by Fisher (1896): given market efciency and rational
expectations, the interest rates of contracts which only differ in maturity, should be
linked by a no-arbitrage relation. Therefore, the return from investing in a contract
with maturity over multiple periods should be equivalent to the expected return from
investing in multiple consecutive contracts, provided that these span jointly the same
time.
Notable recent applications of the Expectations Hypothesis approach were pre-
sented by Ang and Piazzesi (2003), Favero (2006), where the hypothesis is combined
with a monetary policy rule and an impulse transmission mechanism, in order to
derive a dynamic macroeconometric model capable of successfully anticipating the
future movement of short and long term rates.
The empirical evidence, however, is usually not in favour of the Expectation
Hypothesis. Mankiw and Miron (1986), Campbell and Shiller (1987), Fama and
Bliss (1987), Campbell and Shiller (1991), Rudebusch (1995), Balduzzi, Bertola and
Foresi (1997), Dominguez and Novales (2000), Bekaert and Hodrick (2001), Della
Corte, Sarno and Thornton (2007) considered different models and tests, with various
datasets. All of these authors reported the rejection of the Expectations Hypothesis.
Longstaff (2000), on the other hand, did report evidence in support of the Expectations
Hypothesis.
The variety of models also indicates some uncertainty as to how to model the
interest rate. Drawing from the empirical perception that shocks to the interest rates
are highly persistent, and from the results of popular statistical procedures, such as the
Dickey–Fuller or the Phillips–Perron tests, many authors have described the interest
rates as a process with a unit root. This approach, pioneered by Nelson and Plosser
(1982) for univariate time series of interest rates, was developed into a cointegrated
model for vectors of interest rates with different maturities by Engle and Granger
(1987).
©Blackwell Publishing Ltd and the Department of Economics, University of Oxford 2009

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