University of Southern California Dissertations and Theses

Monetary policy and the term structure of interest rates

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Monetary policy and the term structure of interest rates

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Content MONETARYPOLICYANDTHETERMSTRUCTUREOFINTEREST
RATES
by
Maria Eleni Athanasopoulou
|||||||||||||||||||||||||||||||{
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)
August 2008
Copyright 2008 Maria Eleni Athanasopoulou
Dedication
To my mother Evagelia, and my father Antonio
ii
Acknowledgments
I would like to express my gratitude to my advisors, Michael Magill and Roger Farmer
for their valuable guidance. I would also like to thank Robert Dekle for his support.
Chapter 2 is a result of a collaboration with Claus Brand (European Central Bank)
and Rasmus Pilegaard (European Central Bank): it re
ects the views of the authors
and does not necessarily re
ect the views of the European Central Bank. Claus
Brand, Rasmus Pilegaard and I would like to thank Juan Angel Garc a, Domenico Gi-
annone, Huw Pill, Diego Rodr guez Palenzuela, Oreste Tristani, Frank Smets, David
Vestin,Thomas Werner, and ECB seminar participants for their contribution.
Further appreciation goes to Claus Brandt and the seminar participants at the
Federal Reserve Bank of Cleveland, the European Central Bank, the University of
Southern California, and the European Economic Association 2007, for their insightful
comments on a previously published paper which resulted in the basis for Chapter 3.
iii
Table of Contents
Dedication ii
Acknowledgments iii
List of Figures xii
Abstract xii
Chapter 1: Introduction 1
1.1 Term Structure Models . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Monetary Policy Rule and the Ane Term Structure Models . 5
1.2 New Keynesian Monetary Models . . . . . . . . . . . . . . . . . . . . 7
1.2.1 New Keynesian Models and Central Bank Intervention . . . . 8
1.3 New Keynesian Monetary Models and the Term Structure of Interest
rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Chapter 2: Does real-time macroeconomic information aect the yield curve? 14
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Data releases and yield curve movements . . . . . . . . . . . . . . . . 18
2.2.1 A statistical analysis of the information content of high fre-
quency yield curve changes . . . . . . . . . . . . . . . . . . . 21
2.3 Capturing information used by nancial markets to update expectations 24
2.4 Analysis of impact on yield curve . . . . . . . . . . . . . . . . . . . . 27
2.4.1 Maturity response patterns: the cross-section perspective . . . 27
2.4.2 Maturity response patterns: cross-section regressions involving
forward rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.3 Interest rate responses from two term structure models with
macroeconomic and monetary policy news . . . . . . . . . . . 32
2.5 The likelihood function of the ane term structure model . . . . . . . 40
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Chapter 3: The European Central Bank's Monetary Policy Rule in an Ane
Term Structure Model 44
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
iv
3.1.1 Monetary Policy Rule . . . . . . . . . . . . . . . . . . . . . . 45
3.1.2 Yield Curve Model . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Statistical Description of the Data . . . . . . . . . . . . . . . . . . . . 50
3.3 Econometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 State Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.2 Jump diusion . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3.3 Yield Curve Model . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5.1 Estimated Parameters . . . . . . . . . . . . . . . . . . . . . . 69
3.5.2 Latent factor: The x-variable . . . . . . . . . . . . . . . . . . 73
3.5.3 Yield responses to the state variables shocks . . . . . . . . . . 74
3.5.4 Monetary Policy Rule . . . . . . . . . . . . . . . . . . . . . . 77
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Chapter 4: Periodic New Keynesian Monetary Models 83
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Periodic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3 Periodic New Keynesian Model . . . . . . . . . . . . . . . . . . . . . 90
4.3.1 Standard New Keynesian Model (NK) . . . . . . . . . . . . . 90
4.3.2 Periodic New Keynesian Model (PNK) . . . . . . . . . . . . . 92
4.3.3 Canonical Form . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.4 Exogenous Shocks . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.5 Season-Independent Canonical Form . . . . . . . . . . . . . . 96
4.3.6 Solving the Periodic New Keynesian Model (PNK) . . . . . . 99
4.3.7 Season-Independent State Space Representation . . . . . . . . 100
4.4 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4.1 Estimated PNK Models . . . . . . . . . . . . . . . . . . . . . 101
4.4.2 Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.3 Kalman Filter with Seasonal State-Space representation . . . 106
4.4.4 Univariate Optimal Filtering and Smoothing . . . . . . . . . . 107
4.4.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4.6 Prior Distributions . . . . . . . . . . . . . . . . . . . . . . . . 111
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.5.1 Quarterly versus Monthly Model Estimates . . . . . . . . . . . 115
4.5.2 Impulse Response Analysis . . . . . . . . . . . . . . . . . . . . 123
4.5.3 Robustness Check . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Chapter 5: Periodic New Keynesian Monetary Models and the Term Struc-
ture of Interest Rates 148
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
v
5.1.1 New Keynesian Models . . . . . . . . . . . . . . . . . . . . . . 149
5.1.2 Term Structure Models . . . . . . . . . . . . . . . . . . . . . 150
5.1.3 Overview of the Results . . . . . . . . . . . . . . . . . . . . . 153
5.2 Periodic New Keynesian model with Term structure information . . . 156
5.2.1 Periodic New Keynesian Model (PNK) . . . . . . . . . . . . . 156
5.2.2 Term Structure Model . . . . . . . . . . . . . . . . . . . . . . 159
5.2.3 Periodic New Keynesian Model and the Term Structure of In-
terest Rates (PNK-TS) . . . . . . . . . . . . . . . . . . . . . . 161
5.2.4 Season-Independent Canonical Form . . . . . . . . . . . . . . 163
5.2.5 Exogenous Shocks . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.3 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.3.1 Estimated PNK-TS models . . . . . . . . . . . . . . . . . . . 166
5.3.2 Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . 171
5.3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.3.4 Prior Distributions . . . . . . . . . . . . . . . . . . . . . . . . 175
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.4.1 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . 178
5.4.2 Impulse Response Analysis (IR) . . . . . . . . . . . . . . . . . 183
5.4.3 Yield Responses . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.4.4 Robustness Check . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Chapter 6: Conclusions 195
Bibliography 200
vi
List of Figures
2.1 Changes in zero-coupon yield curves 1/2 hour before and 1 hour after
an ECB policy decision and macroeconomic data releases . . . . . . . 19
2.2 Cross-section regressions of principal components of high and low fre-
quency euro-area yields . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Impact of news from recursive regression analysis on euro-area yields 29
2.4 Impact of news from recursive regression analysis on 10-day forward
rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Responses in yields to news in jump and path from a dynamic latent
factor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6 Yields responses to news in jump and path from an ane term struc-
ture model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1 Daily data on the ECB Minimum Bid Rate (policy rate) and the
1-month (zero-coupon) euro-area bond yields (short-term rate) from
November 2000 to July 2006. . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Daily data on the spread (s
t
) between the euro-area's short-term rate
(r
t
) and the ECB's policy rate (
t
) from November 2000 to July 2006. 52
3.3 Daily data on the euro-area yields at the 6-month, 2, 5 and 10 years
maturity from November 2000 to July 2006. . . . . . . . . . . . . . . 54
3.4 Monthly data on the euro area in
ation rate (
t
), (1961 - 2006). . . . 55
3.5 Normal Probability Plot for the euro-area spread (s
t
) between the
short-term rate and the policy rate. . . . . . . . . . . . . . . . . . . . 56
3.6 Yields responses for Model I and Model II to shocks in the state variables 75
vii
3.7 The estimated policy rule by Models I & II, the Taylor's rule, and the
data on the ECB's MBR for the sample period's meeting days. . . . . 80
4.1 Annual US output per capita (upper graph) & Annual US output
growth (lower graph) from 1960 to 2007. . . . . . . . . . . . . . . . . 110
4.2 US annual in
ation rate (1960-2007). . . . . . . . . . . . . . . . . . . 111
4.3 US FED Discount rate (1960-1979) & US FED Target rate (1980-2007).112
4.4 Monthly and Quarterly models prior & posterior distributions for the
policy coecients: pre-Volcker period . . . . . . . . . . . . . . . . . . 120
4.5 Monthly and Quarterly models prior & posterior distributions for the
policy coecients: Volcker-Greenspan period . . . . . . . . . . . . . . 121
4.6 Monthly and Quarterly models prior & posterior distributions for the
policy coecients: post-1993 period . . . . . . . . . . . . . . . . . . . 122
4.7 PNK Quarterly Model: Impulse responses (1960-1979) . . . . . . . . 124
4.8 PNK Quarterly Model: Impulse responses (1980-1992) . . . . . . . . 125
4.9 PNK Quarterly Model: Impulse responses (1993-2007) . . . . . . . . 126
4.10 PNK Monthly model: Impulse responses for the pre-Volcker period
(1960-1979) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.11 PNK Monthly model: Impulse Responses for the Volcker-Greenspan
period (1980-1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.12 PNK Monthly model: Impulse Responses for the Post-1993 period
(1993 - 2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.13 Priors 2: Monthly and Quarterly models prior & posterior distributions
for the policy coecients: pre-Volker period . . . . . . . . . . . . . . 134
4.14 Priors 2: Monthly and Quarterly models prior & posterior distributions
for the policy coecients: Volker-Greenspan period . . . . . . . . . . 135
4.15 Priors 2: Monthly and Quarterly models prior & posterior distributions
for the policy coecients: post-1993 period . . . . . . . . . . . . . . . 136
4.16 PNK Quarterly Model: Impulse responses (1960-1979)- Priors 2 . . . 140
viii
4.17 PNK Quarterly Model: Impulse responses (1980-1992)- Priors 2 . . . 141
4.18 PNK Quarterly Model: Impulse responses (1993-2007)- Priors 2 . . . 142
4.19 PNK Monthly Model: Impulse Responses for the Pre-Volcker period
(1960-1979)- Priors 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.20 PNK Monthly Model: Impulse Responses for the Volcker-Greenspan
period (1980-1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.21 PNK Monthly Model: Impulse Responses for the Post-1993 period
(1993 - 2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.1 Annual US output per capita (1980-2007). . . . . . . . . . . . . . . . 173
5.2 US monthly in
ation rate (1980-2007). . . . . . . . . . . . . . . . . . 174
5.3 Monthly series of the ocial Fed Funds rate (1980-2007). . . . . . . . 175
5.4 Monthly yields of the USA Government 90-day T-Bill, and the 1-year
and 2-year Bonds with Constant Maturity (1980-2007). . . . . . . . . 176
5.5 PNK-TS: Impulse responses for the Volcker-Greenspan period (1980-
1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.6 PNK-TS: Impulse responses for the Post-1993 period (1993 - 2007) . 185
5.7 Impulse responses of the 2-year yields . . . . . . . . . . . . . . . . . . 188
ix
List of Tables
2.1 Eect on Jump and Path indicators from individual news releases . . 26
2.2 Coecient estimates for the yield curve factors evolution . . . . . . . 34
2.3 Restricted coecient estimates for the yield curve factors evolution . 35
2.4 Maximum Likelihood estimates for the Ane Term Structure model . 40
3.1 Summary Statistics for the euro-area's data on in
ation (
t
) and the
spread (s
t
) between the policy rate
t
and the short-term rate from
November 2000 to July 2006. . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Summary Statistics of the euro-area's yields data from November 2000
to July 2006. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 Correlation coecients for the principal component of the euro-area
bond yields at the 6-month, 2 and 5 years maturities and the in
ation
and the spread. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Estimation Results for the Ane Tern Structure model . . . . . . . . 70
3.5 Correlation Coecients between the estimated state variables and the
yields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1 Prior Distributions: Priors 1 . . . . . . . . . . . . . . . . . . . . . . . 114
4.2 Estimation results for the PNK model: Pre-Volcker Sample (1960- 1979)116
4.3 Estimation Results for the PNK model: Volcker-Greenspan Sample(1980-
1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.4 Estimation Results for the PNK model: Post-1993 Sample (1993- 2007) 118
4.5 Prior Distributions: Priors 2 . . . . . . . . . . . . . . . . . . . . . . . 132
x
4.6 Log Marginal Density for the estimated models . . . . . . . . . . . . 133
4.7 Estimation results for Priors 2: Pre-Volcker sample(1960- 1979) . . . 137
4.8 Estimation results for Priors 2: Volcker-Greenspan sample (1980- 1992) 137
4.9 Estimation results for Priors 2: Post-1993 sample(1993- 2007) . . . . 138
5.1 Prior Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.2 Estimation results for the PNK & PNK-TS models: Volcker-Greenspan
period (1980-1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
5.3 Estimation results for the PNK & PNK-TS models: Post-1993 period
(1993-2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.4 Log Marginal density for the estimated models . . . . . . . . . . . . 189
5.5 PNK-TS: Estimation results for Priors 2 . . . . . . . . . . . . . . . . 190
xi
Abstract
There are two separate literatures studying the bidirectional relationship between
monetary policy and the term structure of interest rates: the New Keynesian Mone-
tary models and the Ane Term Structure models. This study presents four essays
that analyze the interaction between the yield curve and the monetary policy utilizing
and marrying both frameworks.
Chapter 2 utilizes an ane term structure model in order to answer a simple
but challenging question: can real time macroeconomic and policy information tell
us anything about the yield curve movements? The main nding is that indeed
macroeconomic data releases and policy announcements explain persistent jumps in
the euro area yield curve.
Chapter 3 develops an ane term structure model that the ECB's policy rate is
modeled as a jump diusion with a predetermined timing of the jumps that coincide
with the actual Governing Council meeting days. The message re
ected in the results
is that the policy rate is indeed an important driving factor of the term structure of
the yield curve, while the information contained in the yield curve vastly improves
the accuracy of the estimated policy rule.
Chapter 4 presents a novel extension of the New Keynesian Monetary model that
the central bank intervenes at regular points in time. Moreover, it presents an estima-
xii
tion technique which utilizes an information structure with more than one frequency.
The empirical results suggest that the presence of the non-intervention subperiods
force the central bank to over-respond to in
ation; the lack of information on output
during subperiods leads to lower estimates for the policy rule's response to output
which indicates that the CB gives less weight to the unobservable information.
Chapter's 5 main contribution is that it extends the periodic New Keynesian model
introduced in Chapter 4 in order to account for the information-rich environment
delivered by the yield curve and focuses on identifying the eects that the term
structure of interest rates and the seasonal central bank intervention have on the NK
model. The empirical results indicate the term structure information identies a more
conservative policy rule in terms of in
ation responses, and more aggressive, in terms
of output responses.
xiii
Chapter 1
Introduction
Central banks make policy decisions knowing that the success of their policy de-
pends heavily on how markets perceive their strategy and on how agents utilize their
announcements to update their expectations about the future. The term structure of
interest-rates captures the markets expectations about the future, and hence, yields
change in response to macroeconomic and policy information, and these changes re-

ect how nancial markets update their expectations due to incoming information.
Thus, there is a bidirectional relationship between monetary policy and the term
structure of interest rates. However, identifying either the magnitude or the trans-
mission mechanism of this relationship is rather dicult: what is the exact role of
monetary policy in explaining the yield curve? to what extent can the yield curve
improve our understanding of the eective monetary policy?
There are two separate literatures studying the monetary policy and the term
structure of interest rates: the New Keynesian Monetary models and the Ane
Term Structure models. This study presents four essays that analyze the interac-
tion between the yield curve and the monetary policy utilizing and marrying both
frameworks.
1
1.1 Term Structure Models
The term structure captures the market's expectations of future behavior of short
term interest rates. Agents revise their expectations due to new information (public
announcements) and make new investment decisions. Merton [33] presents a theoret-
ical characterization of the linkages between the yields and the optimal consumption
and portfolio decisions. He uses a partial equilibrium model that exogenously denes
real prices to follow a stochastic process. Although his model gives an economic in-
terpretation of the term structure model, it leaves out the monetary policy authority
and its role in the determination of the short term rate.
Next, Vasicek(1977) [52] presented a model where the short term rate is the only
factor that drives the market, and is taken to follow a stochastic mean reverting
process. Vasicek used the no-arbitrage condition to derive closed form formulas which
link the equilibrium yields to the factor (i.e., the short term rate) that drives the
market's expectations. His approach opened the way for the term structure's factor
analysis. Building on Vasicek's model, Cox, Ingersol and Ross(1985b) [11], analyze
a one factor term structure model in which the short term rate follows a square
root stochastic process. Extending this framework Dai and Singleton [12] analyze a
three-factor (i.e., level, slope ,curvature) term structure model.
Empirically, Due and Singleton(1997) [15], among others, make use of the no-
arbitrage conditions and estimate the parameters of a term structure model that
captures the relationship between the underlying factors and the equilibrium yields.
In their work, the factors (i.e., level, slope ,curvature) are latent and are backed out
from the yield curve as their main goal is to analyze the pricing of interest-rate related
securities. A number of extensions, both in terms of the number of state variables and
the data generating process for the state vector, have been introduced and analyzed.
2
All of the above models give a valuable insight into the relation between the term
structure and the underlying driving factors of the economy. However, they fail to
provide any economic interpretation of these factors as they neglect any interaction of
the factors with either the macroeconomy or the monetary policy decisions, although
there is an extensive literature that documents an increased volatility of interest rates
at all maturities before and after policy and macroeconomic announcements (Fleming
and Remolona (1998) [18], Fleming and Remolona (1999) [19]).
In addition, there is a rapidly growing macro-nance literature that was launched
in order to extend the term structure models by incorporating macro variables. Thus,
macro-nance models identify macroeconomic time series as the driving factors of the
yield curve. Ang and Piazzesi(2003) [1], estimated a term structure model with both
macroeconomic variables and latent factors as state variables. Their main conclusion
is that a large part of the variations in interest rates can be explained by macro
variables. H ordahl, Tristani and Vestin (2006) [51], and M onch (2005) [34] construct
dynamic ane term structure models using macroeconomic time series data as state
variables. Diebold, Rudebusch and Aruoba (2006) [44] add macroeconomic time se-
ries as state variables to a dynamic latent factor model (based on a Nelson-Siegel
representation of the yield curve) and conclude that the level factor is highly corre-
lated with in
ation, the slope factor is highly correlated with real activity while the
curvature factor is unrelated to any of the main macroeconomic variables. Their ap-
proach, although empirically relates the yield factors with macroeconomic variables,
fails to give any pure economic reasoning for these conclusions.
Indeed, the information rich environment provided by the term structure of in-
terest rates has been identied by the literature. However the Ane Term Structure
Models fail to introduce an economic interpretation of the yield curve's driving forces
and they neglect an explicit incorporation of the monetary policy; hence, they shed
3
no light on the interaction between the macroeconomy and the yield curve.
The present study utilizes the Ane Term Structure models to shed light on the
interaction between the yield curve and the monetary policy. In particular, Chapter
2 tries to answer a simple but challenging question: can real time macroeconomic and
policy information tell us anything about the yield curve movements? In principle,
there should be an very tight link between macroeconomic information and the yield
curve. On one hand, central banks set the short-term interest rate in response to
macroeconomic conditions. On the other hand, the term structure of interest rates,
besides term premia, re
ects expectations of the path of short-term interest rates.
Yet explaining changes in the yields on the basis of macroeconomic information is
challenging.
The approach presented in Chapter 2 bridges two important strands in the litera-
ture: event studies and macro-nance models. To capture the incoming information,
indicators on the basis of high-frequency money market forward rates changes re-
alized when macroeconomic data are released or news on monetary policy become
available are constructed. These indicators substitute for the survey data used in
related studies, and are used to estimate a dynamic ane term structure model to
investigate the link between macroeconomic information and the term structure of
interest rates. The closest studies are the ones by Fleming and Remolona (1999) [19]
and Piazzesi (2005) [38]. Yet both build on survey expectations. However, the anal-
ysis presented in Chapter 2, overcomes the limitations related to the use of surveys
by constructing indicators exclusively from nancial market data.
The main nding is that indeed macroeconomic data releases and policy announce-
ments explain persistent jumps in the euro area yield curve. Using exclusively nan-
cial market information, the constructed indicators have a sizable impact on the yield
curve. This impact is persistent across maturities and time. The response pattern to
4
the short-term related indicator is downward sloping across maturities. In contrast,
the response pattern to the long-term related indicator component is hump-shaped.
1.1.1 Monetary Policy Rule and the Ane Term Structure
Models
From a macro-policy perspective, the short-term rate is the instrument that cen-
tral banks use in order to make policy. Moreover, the eectiveness of monetary policy
depends heavily on how agents perceive the driving forces of policy decisions and
on how market participants use policy announcements to update their expectations
about the future state of the economy. Therefore the communication between mone-
tary authorities and market participants plays a fundamental role in monetary policy
analysis. To this end, in many countries, the central bank policy announcements (i.e.
European Central Bank, Federal Reserve Bank) are accompanied by explicit public
commitments related to the desired economic environment. This aims to guide better
the market participants and improve their understanding of monetary policy.
Although central banks make a general explanatory statement regarding their pol-
icy decisions, they do not reveal the actual numerical reasoning behind it. Empirical
research, however provides evidence that monetary policy authorities set the policy
rate according to a specic rule which assigns weights to current and/or past values
of the in
ation rate and the output growth. According to the simplest Taylor rule
(1993) [50], the Federal Funds rate is a linear function of in
ation (i.e. Consumer
Price Index) and deviations of output (i.e. GDP) from its trend.
Chapter 3 builds on the results presented in Chapter 2 in order to explicitly
analyze the relationship between the euro area yield curve and the European Central
Bank's monetary policy rule. To this end, Chapter 3 develops an ane term structure
5
model that takes advantage of the information rich environment provided by the term
structure of the yield curve in order to analyze the interaction between the European
Central Bank's (ECB) policy and the nancial markets. The state vector consists
of the policy rate, the spread between the short term rate and the policy rate, the
in
ation rate and a proxy for aggregate macroeconomic variables (e.g. real activity).
The ECB's policy rate is modeled as a jump diusion with a predetermined timing of
the jumps that coincide with the actual Governing Council meeting days, and jump
intensities that are driven by the state variables. The no-arbitrage condition allows for
closed form solutions for the bond yields, and therefore information is extracted from
the entire yield curve in order to identify a high-frequency policy rule. The estimated
models address questions related to the success of the ECB's communication with
the market and the interaction of the macroeconomy with the bond yields in an
environment consistent with the ECB's policy rule. The overall message re
ected in
the results is that the policy rate is indeed an important driving factor of the term
structure of the yield curve, while the information contained in the yield curve vastly
improves the accuracy of the estimated policy rule when compared to other estimated
policy rules that do not incorporate such information (e.g. Taylor's rule).
The primary contribution of the analysis presented in Chapter 3 is that it marries
a Taylor-type rule for the conditional probability of a policy rate move to an ane
term structure model while it explicitly incorporates into the policy rule, the price
stability denition provided by the European Central bank. However, there are two
main dierences between the policy rule implied by the model and the Taylor rule:
within the Taylor-type policy rules, the central bank does not take into consider-
ation information extracted from the yield curve while in the proposed framework
central banks conduct policy in an information-rich environment, based on both the
yield curve and the macroeconomy; within the Taylor-type policy rules the selected
6
macroeconomic variables (i.e. in
ation and output gap) determine the level of the
short term rate while in the model presented in Chapter 3, they drive the changes
of the policy rate. Additionally, the estimated policy rule explicitly incorporates the
ECB's public commitments of targeting to maintain in
ation rates below but close
to 2% over the medium term.
The empirical results indicate that policy rate shocks strongly aect the medium-
term maturities; shocks to the in
ation rate aect the whole yield curve, and shocks
to a proxy for macroeconomic variables aect mainly the short-term interest rates.
In addition, three policy implications are derived: market participants perceive the
ECB's policy rule to be an in
ation-targeting, due to the fact that the ECB has tied
its denition of price stability to a specic in
ation rate; changes in the policy rate
today aects the ECB decisions in the following meetings as well implying policy
inertia; last but not least, the ECB's monetary policy is substantially driven by
the macroeconomic information communicated by the 6-month rate, and its policy
decisions aect mainly the medium term maturities (i.e 2-years).
1.2 New Keynesian Monetary Models
The New Keynesian (NK) model builds on a dynamic general equilibrium model
that allows for a suitable use of frictions (i.e., nominal price and/or wage rigidities)
in order to set up an economic environment appropriate for policy evaluation. In
a very simple version agents in each period need to decide how much to spend and
how much to save in the form of money versus bonds; rms decide how much to
produce and what price to set given a deterministic price staggering environment. In
this setting, the short term interest rate becomes the instrument (Gali (1999) [27])
through which central banks exercise their policy. This simple New Keynesian model
7
is quite instructive for the analysis of the eects of supply and demand shocks and
the role of the monetary policy and models as in Yun [49], King [28] and Clarida et
al. (1999) [27] provide a powerful workhorse for monetary policy analysis. However,
there are two weaknesses of the New Keynesian framework addresses in the present
study: the rst refers to the model's assumption with respect to the central bank's
time of intervention and the second refers to the information set available to the
monetary policy authorities when they make decisions.
1.2.1 New Keynesian Models and Central Bank Intervention
The least intuitive and most unrealistic assumption of the NK model is that the
central bank sets the short-term rate at every period. There are two arguments that
can be raised against this restriction: rst, even those central banks, that participate
actively in the money market (e.g Federal Reserve Bank (FRB), European Central
Bank (ECB)), do not readjust the short term rate at every date; second, policy makers
and agents (and/or rms) do not decide simultaneously. There is a possible confusion:
are the agents and rms assumed to trade whenever the central bank has a scheduled
meeting or do central banks decide about their policy at every period that the agents
and rms trade? Both scenarios are highly restrictive and possibly misleading.
To this end, Chapter 4 presents a novel extension of the New Keynesian Monetary
model that relaxes this restricting assumption. In particular the underlying economy
is described by a periodic NK model, denoted as PNK, with the central bank inter-
vening at regular points in time. Between two successive central banks meetings, the
agents continue to make optimal decisions with respect to consumption and savings,
while the short-term rate remains unchanged. The PNK model is utilized to study
the consequences that seasonality has for the NK model's behavior, which is a special
case of the introduced family of models.
8
Moreover, Chapter 4 makes another basic contribution: in many cases the data
accompanying periodic economic phenomena come in dierent frequencies: for exam-
ple, the Gross Domestic Product data are usually updated every quarter, while the
nancial data, like the short-term interest rate, are available daily. Chapter 4 presents
an estimation technique, appropriate for forward looking models, which utilizes an
information structure with more than one frequency. The seasonal state equations
allow us to introduce seasonal measurement equations, and, thus, the period's state
space representation utilizes all the available information when it becomes available.
The absence of restrictive assumptions makes the estimation technique general, and,
thus, could be used to estimate any model that has incoming data with dierent
frequencies. The technique is implemented on the PNK model: data with dierent
frequencies are used, unlike similar studies (see for example Lubik and Schorfheide
(2004) [32] that use quarterly averages of the monthly series.
However There are two main conceptual dierences between the PNK and the
standard NK model, regarding the environment in which policy decisions are made.
In the NK model the CB has all the available information (i.e. output and in
ation)
in order to update the policy rule. Moreover, their intervention pattern gives them
the opportunity to immediately respond to any exogenous destabilizing deviation.
By contrast, the PNK framework creates two sources of uncertainty for the CB's
decision: the lack of information (i.e. output is not observable every subperiod) and
the non-intervention subperiod.
Our empirical results suggest that the presence of the non-intervention subperiods
force the CB to over-respond to in
ation in order to ensure the economy's stability for
the subperiods which they will not intervene. Furthermore, the lack of information
on output during subperiods leads to lower estimates for the policy rule's response to
output which indicates that the CB gives less weight to the unobservable information.
9
Thus, in a scenario where the CB does not intervene every subperiod and does not
have all the available information, then the policy rule would be more aggressive with
respect to the available information in order to ensure stability for the subperiods the
CB does not intervene.
Furthermore, the impulse response (IR) analysis indicates that the eects of a
contractionary demand shock results in an in
ation and interest rate decrease over
time; an in
ation increasing supply shock raises the interest rates, while it results
in a output decrease (below its steady state), and a contractionary monetary policy
shock causes output and in
ation to decrease. However, our framework's seasonality
introduces two types of impulse responses (IR): seasonal IRs that concentrate on the
structural responses to shocks occurred in a specic subperiod, and periodic IRs that
describe the economy's evolution over all the subperiods given the realization of a
structural shock at each initial subperiod.
The seasonal IRs distinguish between the responses corresponding to shocks oc-
curring during subperiods with and without CB intervention. There are three main
conclusions consistent over all the samples drawn by the analysis of the seasonal
the more a variable is weighted in the policy rule, the more sensitive the economy
becomes to this variable's deviations occurring at the non-intervention subperiods,
and the less sensitive to deviations occurring at the intervention subperiods; second,
the structural responses to the interest-rates exogenous shocks realized during either
the non-intervention or an intervention supberiod have similar magnitude. Thus, the
unanticipated policy rate's deviations from the rule (during the intervention subpe-
riods) and the unanticipated CB intervention (interest rate shocks realized during
the non-intervention periods capture unanticipated policy intervention) have similar
eects on the economy; nally, the interest rate responses to the structural shocks are
one subperiod lagged when the shocks realize during a non-intervention subperiod,
10
while the interest rate's adjustment back to its steady level is identical for both the
intervention and non-intervention subperiods. Thus, the absence of the monetary
policy intervention results only in the delay of the shocks eect on the interest rates
because during the non-intervention subperiods the interest rates are not aected by
either in
ation or output deviations.
The periodic IRs depict the economy's reversion back to its steady state and
indicate that the sample period's characteristics drive the model's seasonal behavior:
the more volatile the input series the longer the shocks remain in the economy and
the more volatile the structural responses are.
1.3 New Keynesian Monetary Models and the Term
Structure of Interest rates
The New Keynesian (NK) Monetary model, which is the current workhorse
for studying monetary policy, disregards any information contained in the yield
curve. However, there is an extended empirical literature that argues that the term
spreads are useful instruments for forecasting future real activity (Hamilton and Kim
(2002) [24], Harvey (1988) [26] and Ang, Piazzesi and Wei (2002) [36]); future in
a-
tion rate (Fama (1987) [17]), as well as monetary policy decisions (Piazzesi (2001) [37]
for the Federal Reserve Bank and Chapters 1 and 2 for the European Central bank).
Chapter's 5 main contribution is that extends the periodic New Keynesian model
introduced in Chapter 4 in order to account for the rich information environment
delivered by the yield curve and and focuses on identifying the eects that the term
structure of interest rates and the seasonal central bank intervention have on the NK
model. Hence, the present framework considers a model with periods divided into
subperiods with and without CB intervention; for the subperiods without intervention
11
the short-term rate remains unchanged. Moreover, the equations describing the yields
are derived by the periodic New Keynesian (PNK) model, and, thus explicitly dene
the economic linkage between the structural variables and the term structure.
The empirical results indicate the extended PNK model with term structure infor-
mation identies a more conservative policy rule than the PNK model (i.e. without
yield information), in terms of in
ation responses, and more aggressive, in terms of
output responses. Thus, the information set delivered by the term structure provides
the CB with enough insight into the current state of the economy that the CB needs
not to over-respond to in
ation deviations, or underweight the output. The high
estimates of the the price staggering coecient for the extended PNK imply a tighter
linkage between the structural variables, and the the small estimates of the coecient
of risk aversion suggest an improved hedging against risk environment.
One of Chapter 5 framework's most interesting applications is the computation of
the yields impulse responses to the structural shocks. In particular, an expansionary
demand shock results in an in
ation and interest rate increase over time and this
translates to a positive shift of the yield curve; an increasing supply shock (i.e. in
a-
tion increases) rises the interest rates and, hence, the yields, while a contractionary
monetary policy shock results in an immediate positive yields response. Moreover,
the magnitude of the yield responses to the economy's exogenous disturbances depend
on the policy coecients.
Additionally, the yields IRs to the period's rst subperiod structural shocks are
lower than the second's, although the CB intervenes during both subperiods. This
underlines that the anticipation of the non-intervention subperiod dampens the struc-
tural eects on the yields due to the zero structural eect when the CB does not in-
tervene. In addition, as expected, the demand and supply shocks realizing during the
non-intervention periods do not eect the yields as they do not aect the policy rate.
12
On the contrary, the lack of the CB intervention allows the full interest-rate shocks
pass through to the yields. So the yields responses to the interest-rates disturbances
maximize during the non-intervention periods.
13
Chapter 2
Does real-time macroeconomic
information aect the yield curve?
1
2.1 Introduction
Can real time macoeconomic and policy information tell us anything about the
yield curve movements? In principle, there should be an very tight link between
macroeconomic information and the yield curve. On one hand, central banks set
the short-term interest rate in response to macroeconomic conditions. On the other
hand, the term structure of interest rates, besides term premia, re
ects expectations
of the path of short-term interest rates. Yields should, therefore, change in response
to macroeconomic information, and these changes should re
ect how the nancial
markets perceive the central bank's policy rule. Yet explaining changes in the yields
1
This chapter is a result of a collaboration with Claus Brand (European Central Bank) and
Rasmus Pilegaard (European Central Bank) and it re
ects the views of the authors and not those
of the European Central Bank.
14
on the basis of macroeconomic information is challenging. For instance, yield curve
models that incorporate information from macroeconomic variables still require ad-
ditional latent variables to be able to explain most of the variation in yields.
The main conclusion of the present analysis is that macroeconomic data releases
and policy announcements explain persistent jumps in the euro area yield curve.
Indicators of high-frequency money market forward rates changes occurred when
macroeconomic data are released or news on monetary policy become available, are
constructed in order to capture the new information. These forward rate changes
are decomposed into two distinct components: changes re
ecting expectations about
monetary policy one month ahead and denoted as the `jump' component, and changes
in expectations about the path of monetary policy over longer horizons (half a year),
and denoted as `path' component. News related to monetary policy coincide with
relatively large readings of both components|up to 20 and 30 basis points for jump
and path. For the macroeconomic news these readings are smaller: around 1 and 8
basis points, respectively. Our indicators show that agents revise their expectations
of the the euro area's monetary policy in response to some key US macroeconomic
data.
The jump and path indicators have a sizable impact on the yield curve. This
impact is persistent across maturities and time. The response pattern to the jump
component is downward sloping across maturities. In contrast, the response pattern
to the path component is hump-shaped. Two dierent dynamic latent factor models
of daily yields which comprise the jump and path indicators conrm these ndings.
Our approach bridges two important strands in the literature: event studies and
macro-nance models. These approaches dier fundamentally in identifying informa-
tion moving the yield curve.
Event studies, based on cross-sectional regressions, explain yield curve movements
15
using a surprise indicator constructed from the dierence between data releases (or
policy decisions) and survey expectations (see Balduzzi, Elton and Green (2001) [16]
and the application by Andersson, Hansen and Sebesty en (2006) [25] to euro area
data).
However, event studies have a number of limitations. First of all, the news-
indicators constructed by the deviations of data releases from survey expectations,
are less informative than the actual data when they become available, and they re
ect
neither the data revisions nor the time-series break-down to their components. They
also neglect information about how nancial markets update their expectations of
monetary policy, in response to central bank communication, especially for longer
horizons. Furthermore, surveys may also be biased. Rigobon and Sack (2006) [42]
conrm these concerns. They show that high frequency changes in the principal
component of the US asset prices are a better measure of new information than the
data releases deviations from survey expectations. deviations of announced interest
rate decisions from survey expectations. Finally, the cross-section regressions used
within the event studies literature cannot provide evidence of the impact's persistence
at high frequency.
Macro-nance models identify macroeconomic time series as the driving factors of
the yield curve. Ang and Piazzesi (2003) [1], H ordahl, Tristani and Vestin (2006) [51],
and M onch (2005) [34] construct dynamic ane term structure models using macroe-
conomic time series data as state variables. Diebold, Rudebusch and Aruoba (2006) [44]
add macroeconomic time series as state variables to a dynamic latent factor model
(based on a Nelson-Siegel representation of the yield curve).
Using macroeconomic time series data as state variables in a dynamic yield curve
model, as recently adopted in the macro-nance literature, has weaknesses too. Typ-
ically, macro-nance models use ex-post macroeconomic time series in contrast with
16
the in real time information used by the market participants to update their expecta-
tions. In addition, in many cases the the information set delivered by the incorporated
time seres is rather limited, and, thus, additional latent factors are needed to explain
most of the observed variation in the yields. However, using a larger set of data (as
in Ang and Piazzesi (2003) [1] and M onch (2005) [34]) makes the statistical inference
on the parameters rather dicult.
Our study utilizes a dynamic modeling approach to study the yield curve responses
to macroeconomic and policy news. The closest studies are the ones by Fleming and
Remolona (1999) [19] and Piazzesi (2005) [38]. Yet both build on survey expectations.
Fleming and Remolona (1999) use data surprises to form expectations for labor
market conditions, prices and aggregate demand into a discrete-time ane term struc-
ture model. They show that the yields maturity response to surprises is similar to
the one resulting by cross-section regressions. Piazzesi (2005) models US-data and
policy-related news as jumps in a continuous time ane term structure model by
augmenting the state vector of latent variables with the surprise process. The model
does not, however, display the hump-shaped maturity response pattern of yields to
surprises obtained from cross{section regressions.
In our study, the limitations related to the use of surveys are overcomed by con-
structing indicators exclusively from nancial market data. This approach is close in
spirit to the one suggested by G urkaynak, Sack and Swanson (2005) [46], who also
construct indicators of changes in expectations relating to distinct maturity horizons,
but they rely on cross-sectional regressions in order to strengthen the yield curve
impact. Our analysis species a dynamic latent factor model to investigate the link
between macroeconomic information and the term structure of interest rates.
17
2.2 Data releases and yield curve movements
This section analyzes the high frequency changes in the yield curve, when macroeco-
nomic information or announcements of monetary policy become available. Financial
markets, indeed, react swiftly to such news, and this allows us to capture the infor-
mation used by the nancial markets in revising their expectations.
Figure 2.1 shows the adjustment in the euro-area zero-coupon yield curve in re-
sponse to two sets of news: the announcement of an ECB interest rate cut, which
apparently was not anticipated, on 10 May 2001 at 13:45, and the release of the Ger-
man Ifo business cycle indicator on 28 March 2007 at 10:00.
2
Figure 2.1 illustrates
that the yield curve's response to these news is completed within 5-10 minutes. After
that adjustment, no further movements are visible. Figure 2.1 also shows that the
yield curve responses can be of a quite dierent nature: the unanticipated interest
rate cut eects mainly the short-term interest rates, leaving the long end of the curve
unaected; conversely, the Ifo event has an impact exclusively on longer-term interest
rates.
A key objective of our study is to analyze the explanatory power of intraday re-
visions in expectations for the daily changes in interest rates; thus, indicators which
re
ect these revisions are constructed. For this purpose a dataset of time stamps for
days when news become available is built, consisting of the ECB Governing Coun-
cil's interest rate decisions and communication (in its press conference) and 15 key
macroeconomic data releases in the euro area, individual euro area countries and
the United States. In addition in the scheduled monetary policy announcements
2
The yield curve data presented here and used throughout this study are based on Reuters real
time quotes, ltered and interpolated as in Brousseau 2002 and 2006 [4].
18
Figure 2.1: Changes in zero-coupon yield curves 1/2 hour before and 1 hour after an ECB policy decision (a) and
macroeconomic data release (b).
(a) Changes in zero-coupon yield curves following announcement
of ECB policy decision on 10 May 2001
(b) Changes in zero-coupon yield curves following the German Ifo
business sentiment index release on 28 March 2006.
19
time stamps set, three unscheduled ECB announcements have been included: the
decision on 17 September 2001 to reduce ECB key interest rates and the monetary
policy announcements made by the ECB's president on 18 and 21 November 2005
(relating to interest rate decisions at subsequent Governing Council meetings). The
macroeconomic data releases include the: HICP, industrial producer prices, M3, GDP,
industrial production and retail sales, for the euro area; the industrial production and
the IFO business climate index for Germany; the Belgian NBB's business condence
indicator; and for the US: the GDP, the CPI, the non farm payroll employment, the
ISM manufacturing PMI and the conference board consumer condence. The FOMC
statement could not be included as it is released only after the closing time of the
european nancial markets.
Our goal is to measure the yields high frequency responses over a time window
that captures these time stamps. Thereby the width of the time window covering the
time stamps should be suciently small to exclude the impact of other information
becoming available. At the same time, it should be suciently large to allow yields to
fully adjust to news. Therefore, for data releases and policy news on non-interest-rate
setting days, we compare yields 5 minutes before and 10 minutes after the time of the
release. A wider time-window is set for the monetary policy announcements. On the
day of the interest-rate setting meeting, the interest rate decision is published at 13:45
and the considerations underlying that decision are explained in a press conference
starting at 14:30. Yield curve changes between 13:40 and 15:40 are taken to capture
these events. However, the size of this time window is rather large, and, hence, it may
capture other non-policy news too. In particular, weekly US unemployment claims are
released at 14:30 (i.e. within that time window). However, the high-frequency yield
curve responses (and indicators derived from it further below, as shown in Brand,
Buncic and Turunen (2006) [5] remain unaected if the variable's surprise component
20
is controlled.
The sample period covers from 30 November 2000 until 19 July 2006. This yields
947 time stamps for data releases and policy announcements. Daily data of the euro
area yield curve at 17:00, after all releases and policy announcements have become
available, are constructed. To tentatively gouge the explanatory power of intraday
changes in yields (in response to news) for daily interest rate changes, a single principal
component for the intraday and the daily yield curve data, is pursued. On calendar
days comprising more than one data releases, we add all the resulting principal com-
ponents. This leaves us with 681 out of the 947 intraday events. Concentrating on
news that trigger adjustments in interest rates higher than one quarter of a basis
point, yields a rather high correlation between the high-frequency and the daily prin-
cipal component, with a correlation coecient of 0.31 (see section 2.2.1 for the details
of this exercise). Considering that most of the intraday movements capture merely
1% of the time elapsing between daily yield curve observations, this suggests that
data releases and policy announcements capture vital information for daily changes
in yields.
2.2.1 A statistical analysis of the information content of high
frequency yield curve changes
Changes in the yield curve around news releases can account for a signicant part of
the daily variation in yields. The principal component factor of the intraday changes
is highly correlated with the corresponding factor of daily yield changes.
Our present analysis is focused on the changes in the 6-month yield, y
182
t
. The
observed variation in daily yields is greater than those in intraday yields. To measure
the intraday variation, yield changes are aggregated around news releases on days
21
when several news are released. The percentage of observations for which the change
in this yields exceed just one quarter of a basis point: y
182
t
0:0025, is taken as a
measure of the variations: on days with a news release, 93% of the daily changes in
yields satisfy this property, while only 48% of intraday changes do so.
To better account for the in
uence and cross-sectional correlation of the news
indicators on the daily changes in the overall yield curve, a principal components
analysis is pursued. One principal factor of the changes in the intraday yield curve
(F
news
) is derived; it is then aggregated for the days with several readings of F
news
,
and compared with the corresponding factor estimated from the daily changes in
yields, F
daily
. The factors are constructed as:
Y =F

0
+ (2.1)
whereY is at14 matrix witht = 1;:::;T observations of changes in 14 yields of
maturity (days), y

t
, with T = 947 for high frequency observations and T = 1470
for the daily ones, and =31, 91, 182, 273, 365, 731, 1096, 1461, 1826, 2192, 2557,
2922, 3287, 3653. F and
are of dimension t 1 and 1, respectively.
Figure 2.2 shows that there is a visible correlation (

R
2
=0.22) between F
news
and
F
daily
, although the rst is obviously relatively smaller. Using a subset of F
news
,
however, selected on the days when the change in the 6-month yield exceeds just
one quarter of a percentage point, the correlation coecient rises to

R
2
=0.31 (see
Figure 2.2). This suggests that the modest impact stemming from news indicators
contributes signicantly to the daily variation.
22
Figure 2.2: F
news
vs. F
daily
for 681 observations: Cross-section regressions of principal components of high and low
frequency yields of maturities =31, 91, 182, 273, 365, 731, 1096, 1461, 1826, 2192, 2557, 2922, 3287, 3653 days.
y = 1.1464x - 0.0011
R
2
= 0.2159
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.4 -0.2 0 0.2 0.4
intraday principal factor
daily principal factor
y = 1.1343x - 0.0016
R
2
= 0.3179
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.4 -0.2 0 0.2 0.4
intraday principal factor
daily principal factor
(b) F
news
vs. F
daily
where y
182
t
0:25, 326 observations
23
2.3 Capturing information used by nancial mar-
kets to update expectations
This section constructs the indicators that re
ect the market's expectations of
monetary policy over dierent horizons by identifying changes in 10-day money mar-
ket forward rates with changes in expectations, taking that that, at this frequency,
term premia remain constant.
Two time horizons are considered: a horizon of one month, capturing the next
policy rate setting meeting of the ECB, and a half-year horizon, re
ecting the path of
monetary policy. A simple, but statistically robust, procedure is used to decompose
the expectations revisions at these two time horizons.
Let f

t
denote the high-frequency changes in forward rates periods ahead. The
changes in the 10-day forward rates, 30 days ahead, are labeled as `jump':
f
30
t
jump
t
(2.2)
`Jump' re
ects revisions in expectations of the next ECB meeting's policy decision,
given the incoming data or any central bank communication.
Furthermore, all revisions in expectations of the money market rate 5 months
ahead (f
150
t
), which are not accounted for by the as `jump' are denoted as `path'.
Thus the `path' is taken to be the residual of the following regression:
f
150
t
=
0
+
1
jump
t
+ path
t
: (2.3)
Given the high correlation of forward rates across maturities, path
t
re
ects revi-
24
sions in expectations of the future evolution of short-term rates as set by the central
bank. As an illustration of how jump and path may be related to yield curve move-
ments, one may simply reconsider Figure 2.1 above. The unanticipated cut in key
ECB interest rates of 10 May 2001 represents information that should be captured by
the jump indicator, as it leaves the long end of the yield curve unaected. Conversely,
the increase in longer-term yields triggered by the release of the Ifo on 28 March 2007,
as depicted in the same gure, is most likely accompanied by an adjustment in the
path dimension.
The indicators suggested here bear resemblance with the slope and the curvature
factors, as dened within the Finance literature. However, they do not exactly rep-
resent these yield curve factors, as they are constructed by just two forward rates;
neither can they be associated with a level component: jump loads exclusively into
the short end of the yield curve. and path does not load at all into the short end.
An alternative to our recursive approach presented here is suggested by G urkaynak,
Sack and Swanson (2005) [46]. It is based on conformably rotating two principal com-
ponent factors of the forward rate curve. Their approach yields no major qualitative
dierences with the recursive one. Yet the scale of the resulting indicators based on
the recursive approach is less prone to be aected by potential outliers|such as the
one associated with the unexpected interest rate cut on 17 September 2001. Con-
structing indicators exclusively for monetary policy announcements, Brand, Buncic
and Turunen (2006) [5] also nd congruent results on the basis of both methods.
Overall, jump and path indicators are constructed by 947 events and policy an-
nouncements observed over the sample. The comparison of the indicators size across
data releases yields the following features (see Table 2.1): First, by far the largest
revisions in expectations are associated with the ECB Governing Council's decisions
and communication. Jump and path responses to these announcements are almost
25
Table 2.1: Eect on Jump and Path indicators (in basis points) from individual news releases
Jump Path
25% quantile Median 75% quantile Max 25% quantile Median 75% quantile Max
ECB Governing Council
decisions and communica-
tion
0.21 0.78 2.33 30.73 0.34 1.48 3.30 20.77
Euro area
HICP (
ash estimate) 0.03 0.10 0.29 6.24 0.06 0.16 0.40 2.38
HICP (including HICP
excluding energy and un-
processed food)
0.04 0.11 0.23 2.20 0.10 0.24 0.54 3.90
Industrial producer prices 0.03 0.09 0.39 2.07 0.09 0.26 0.61 7.95
M3 0.07 0.21 0.39 2.13 0.11 0.31 0.81 4.38
GDP 0.02 0.05 0.20 1.14 0.11 0.29 0.65 2.79
Industrial production 0.04 0.09 0.21 2.86 0.11 0.22 0.45 4.84
Retail sales 0.02 0.07 0.23 1.59 0.06 0.17 0.37 2.67
Germany
Industrial production 0.02 0.07 0.20 2.70 0.09 0.21 0.42 2.96
IFO business climate in-
dex
0.06 0.17 0.80 3.19 0.20 0.54 1.28 6.38
Belgian NBB's business
condence indicator
0.03 0.07 0.14 4.72 0.07 0.17 0.45 4.95
United States
GDP 0.07 0.20 0.38 1.98 0.25 0.55 0.97 2.73
CPI 0.04 0.11 0.24 3.84 0.23 0.38 0.69 6.25
Nonfarm payroll employ-
ment
0.07 0.22 0.51 2.76 0.37 0.95 1.59 7.93
ISM manufacturing PMI 0.04 0.09 0.18 4.22 0.17 0.36 1.08 5.28
Conference board con-
sumer condence
0.03 0.06 0.21 1.81 0.16 0.34 0.84 5.94
Full set of events 0.04 0.12 0.35 30.73 0.12 0.33 0.815 20.77
26
of the same size. Central banks can aect yields of longer maturities through com-
munication, leaving the short-end of the yield curve unaected, while unanticipated
interest rate decisions in
uence the yield curve through their impact on the short-
term rates. Second, the strongest impact seems to be associated with data on euro
area industrial production, industrial producer prices and the German Ifo business
sentiment index,, among the euro area macroeconomic data releases. Third, US data
releases during market opening hours in Europe have an impact of similar size, with
the US CPI and non-farm payroll data triggering the strongest adjustments. Finally,
across macroeconomic indicators, data releases tend to be associated with relatively
higher readings in the path dimension than in the jump dimension.
It is striking that some key euro area data releases do not lead to stronger adjust-
ments in expectations of monetary policy. Specically, the HICP release has turned
out to have only a marginal impact. A plausible explanation is that given information
contained in national and regional indicators, released prior to the euro-area indica-
tors, nancial markets are in a very good position to predict the latter ones and are
therefore hardly ever surprised.
2.4 Analysis of impact on yield curve
2.4.1 Maturity response patterns: the cross-section perspec-
tive
This section analyzes the the jump and path indicators impact on the yield curve.
For this purpose we run cross{section regressions of yield changes on the jump and
path indicators. The changes in yields are measured over the same time windows as
the ones used for the construction of our indicators. Previous studies such as Fleming
27
and Remolona (1999) [19] and Piazzesi (2001) [37] have documented a hump-shaped
maturity response pattern in relation to macroeconomic news and a downward-sloping
pattern in relation to monetary policy announcements. our analysis indicates that
this pattern depends on whether expectations are revised in terms of the path or the
jump component and not on the source of the new information.
The following regressions assess the impact of monetary policy on yields:
y

t
= [
1

2
]
2
6
4
jump
t
path
t
3
7
5
+"
t
(2.4)
where y

t
is the change in the days ahead yield,8 = 1; 10; 20;:::; 3650.
Figure 2.3 plots the sequential estimates of [
1

2
] in (2.4), respectively. As a
result, the time horizon over which expectations of monetary policy change is cru-
cial in distinguishing how monetary policy and macroeconomic announcements aect
the yield curve. In particular, jump news tend to have an impact predominantly on
the short and the medium-term maturities, and exhibit a downward-sloping maturity
response pattern. Conversely, the path news are accompanied by changes in yields
of medium-term maturities, and, thereby, display a hump-shaped maturity response
pattern. These results are also in line with earlier ndings in G urkaynak, Sack and
Swanson (2005) [46] for the U.S., and Brand, Buncic and Turunen (2006) [5] for the
euro area|although these studies focus exclusively on monetary policy announce-
ments.
Given the high correlation of yields across maturities, it is certainly not surprising
that the jump turns out to be highly correlated with the short end of the yield curve,
and the path with higher maturity yields. It is therefore important to look at how
much of this correlation is preserved in lower-frequency changes in yields. The yield
regressions presented here constitute independent regressions. But they may blur the
28
Figure 2.3: Impact of news from recursive regression analysis on yields of maturities = 1; 10; 20;:::; 3650 days.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1
500
1000
1500
2000
2500
3000
3500
95% confid. band
bt ˙1t
(a) Impact of jump news on changes in yields with corrected
asymptotic 95% condence bounds
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1
500
1000
1500
2000
2500
3000
3500
95% confid. band
b(2 t)
(b) Impact of path news on changes in yields with corrected
asymptotic 95% condence bounds
29
impact of the indicators on yields of longer maturity with that on yields of shorter
maturity. Yet using instead forward rates on the left-hand side of equation (2.4), to
avoid this problem, leads to congruent results. The following section elaborates on
this issue.
2.4.2 Maturity response patterns: cross-section regressions
involving forward rates
The yield regressions (2.4) constitute independent regressions, but they may blur
the impact of the indicators on yields of longer maturity with that on yields of shorter
maturity: to the extent that an impact of the indicator on the change in yield y

i
can be found, it will automatically have an impact on y

8 >
i
. In order to
assess the impact on each maturity horizon independently, one can replace yields y

t
by forward rates f

t
:
f

t
= [
1

2
]
2
6
4
jump
t
path
t
3
7
5
+"
t
= 1; 10; 20;:::; 3650 (2.5)
Figure 2.4 shows plots of the sequential estimates of [
1

2
] in (2.5), respectively.
The results are congruent with what could be expected on the basis of taking deriva-
tives of the yield curve impact shown in Figure 2.3: In response to jump, forward
rate only at short-term maturities are aected. At long-term maturities they may
even decline slightly. This conrms the downward-sloping maturity pattern in terms
of yields. In response to path, forward rates at medium-term maturities, up until 5
years ahead are signicantly revised upwards. This conrms a hump-shaped maturity
response pattern in terms of yields.
30
Figure 2.4: Impact of news from recursive regression analysis on 10-day forward rate = 1; 10; 20;:::; 3650 days ahead.
-1
-0.5
0
0.5
1
1.5
2
1
500
1000
1500
2000
2500
3000
3500
95% confid. band
b(1 t)
(a) Impact of jump news on changes in forward rates with
corrected asymptotic 95% condence bounds
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1
500
1000
1500
2000
2500
3000
3500
95% confid. band
b(2 t)
(b) Impact of path news on changes in forward rates with
corrected asymptotic 95% condence bounds
31
2.4.3 Interest rate responses from two term structure models
with macroeconomic and monetary policy news
The cross-section evidence provided by the event studies remain silent about
the magnitude of the measured impact which is left after a day, a week, or even a
month. To address this issue, the jump
t
and path
t
are incorporated into two dierent
period-by-period term structure models. If on one calendar day several data releases
are available, the resulting indicators are summed up, and they are loaded as shocks
to the dynamic latent factors of two yield curve models: the rst model adapts
the framework proposed by Diebold and Li (2006) [14], and the second, specied a
discrete-time ane term-structure model in the spirit of Dai and Singleton (2002) [13].
The two approaches are complementary in identifying the impact of our indicators
on yields. Diebold and Li (2006) pre-impose the loading coecients of the latent
factors into the yields, and thus, the latent factors are given. However, the impact
of the indicators on these latent factors can be estimated freely. Conversely, in the
ane term structure model, the loading coecients of the latent factors can only be
identied and estimated by pre-imposing the way which our indicators aect them.
So, the way that the latent factors load into yields is engineered by using the indicators
as shocks in the latent factor equations.
Our approach diers from the discrete-time ane term-structure models for the
US developed by Piazzesi (2001) and Fleming and Remolona (1999). As key US data
are published weekly, on a Friday, at 8:30 (Eastern time), these models can be set
up with weekly frequency. Conversely, euro area data releases are less regular and
distributed over the whole week. This requires setting up a model of daily frequency.
However, estimating a discrete time ane term structure model at this frequency is a
major challenge. Thus, the ane term structure model is treated as a complementary
32
exercise that cross-checks the results between our two models.
A dynamic latent factor model
Adapting the Diebold and Li (2006) framework to daily observations of the euro area
yield curve at 17:00 on every business day, a daily time series of yield curve factors is
constructed on the basis of the Nelson and Siegel approximation of the yield curve:
y
()
t
=
t
; (2.6)
with
=

1
1exp(
t
)

t
1exp(
t
)

t
exp(
t
)

;

t
= [
0t

1t

2t
]
0
:
wherey
()
t
is a ( 1) vector of yields to maturity with = 1;:::; 120 months; is
a ( 3) matrix of loading coecients used to extract the factors
t
(of conformable
dimension) which approximate level, slope and curvature factors, respectively. These
yield curve factors evolve according to

t
= +
t1
+ s
t
+"
t
; (2.7)
with s
t
= [jump
t
path
t
]
0
, E(s
t
) = 0, E("
t
) = 0 and E("
t
"
t1
) = 08 t = 1;:::; 1479
observations at daily frequency.
To achieve stability in the estimation and to contain the time variability of the
factors ,
t
is set equal to 0.0609 , 8 t. This choice maximises the loading
of curvature at the 2.5 year horizon. The choice of the Nelson-Siegel coecients in
(2.6) pre-imposes the loadings of the latent factors into yields; thus, the latent factors
33
are given. However in (2.7) the impact of the indicators on these latent factors is
estimated freely (through estimates of ).
The coecient estimates for (2.7) are presented in Table 2.2. The estimates for
suggest that the degree of persistence is very high, as expected, given the high
frequency of the data. Also without explicitly using unit root tests it seems fair to
say that the eigenvalues of are statistically indistinguishable from unit eigenvalues.
There is very little cross-factor interaction among the three yield curve factors. As
regards the impact of the news indicators, jump
t
has a rather strong and positive
impact on the slope, and path
t
has a relatively strong, positive, impact on the cur-
vature factor (plus a statistically signicant, but minor, positive impact on the level
and a negative impact on the slope). This suggests that a rather large amount of
high-frequency changes of the yield curve in response to news is preserved over daily
time intervals.
Table 2.2: Coecient estimates for the yield curve factors evolution (equation (2.7)),
with Newey-West standard errors in parenthesis (corrected for autocorrelation and
heteroskedasticity up to lag 3).
0.0001 -0.0000 0.0004 0.9990 0.0001 -0.0128

0
(0.0001) (0.0001) (0.0002) (0.0015) (0.0018) (0.0044)
-0.0354 0.8530 -0.2462 0.0016 0.9953 -0.0047
(0.0014) (0.0017) (0.0050)

(0.1069) (0.1068) (0.3108)

0
0.0974 -0.0860 0.6108 0.0003 0.0030 0.9945
(0.0232) (0.0256) (0.0788) (0.0009) (0.0012) (0.0027)
Our analysis restricts all the statistically insignicant parameters in and to
be zero. The resulting coecient estimates are presented in Table 2.3 and conrm
the ndings from the unrestricted estimates.
To obtain a comprehensive picture of how announcements aect the yield curve
over time and maturity, we calculate impulse responses
(i)
:
34
Table 2.3: Restricted coecient estimates for the yield curve factors evolution (
equation (2.7)), with Newey-West standard errors in parenthesis (corrected for auto-
correlation and heteroskedasticity up to lag 3).
0.0001 -0.0001 -0.0001 0.9984 0.0000 0.0000

0
(0.0001) (0.0000) (0.0001) (0.0013) | |
0.0000 0.8443 0.0000 0.0000 0.9974 0.0000
| (0.1108) |

| (0.0015) |

0
0.0983 -0.0871 0.6070 0.0000 0.0000 0.9970
(0.0234) (0.0258) (0.0812) | | (0.0022)

(i)
=
(i1)
8 i = 1;:::; 1050 (days):
The resulting impulse response functions over time and maturities are presented in
Figure 2.5. They conrm a downward sloping maturity response pattern to jump
and a hump-shaped maturity response pattern to path. At the same time, given the
persistence in shocks, as determined by the unrestricted diagonal elements of , it is
evident that the impact has all but vanished after 1050 days (i.e. three years). Still
the impact persists even at a time horizon of up to 6 months. (Of course, if one
were to impose unit roots on , the impact would persist across all time horizons.)
Overall, the intraday shocks to the yield curve factors around data release times can
account for signicant movements in the yield curve at lower frequency.
Ane term Structure Model
To complement our analysis of the yield curve impact over time, a discrete-time ane
term structure model with two latent factors is also presented. As before, the jump
t
and path
t
are loaded as shocks into the latent factor equations.
Let X
t
denote the state vector and r
t
the short-term nominal interest rate. Fol-
lowing the canonical class of ane term structure models introduced by Dai and
35
Figure 2.5: Responses in yields to news in jump (a) and path (b) from a dynamic latent factor model.
(a) Yields responses to jump. (b) Yields responses to path.
36
Singleton (2000) [12], the state dynamics take the form:
Short Rate : r
t
=
0
+
0
1
X
t
(2.8)
Factors: X
t
= + X
t1
+
t
+"
t
(2.9)
where and
0
represent intercepts of the factors and the short term rate, respectively.
The transition matrix () describes the evolution of the states over time.
1
contains
the factor loadings into the short term interest rate equation. "
t
and
t
are distributed
N(0,1), with

t
(jump
t
path
t
)
0
In contrast to the dynamic latent factor model presented in the previous section,
we need to impose unit loadings of
t
to identify the latent factors. This means that
by using the indicators as shocks in the latent factor equations, we engineer how
latent factors load into yields.
Ane term structure models require that the log of the underlying pricing kernel,
denoted by m
t
=log(M
t
), is linear with conditionally normal shocks. Let
t
denote
the market prices of risk:
Pricing Kernel : m
t+1
=r
t

1
2

0
t

t

0
t

t+1
(2.10)
Market Prices of Risk :
t
=
0
+
1
X
t
(2.11)
with
0
and
1
of conformable dimension. The dynamics of the pricing kernel charac-
terize a Gaussian price-of-risk model that, in turn, results in an ane term structure
with time-varying term premia.
Our model imposes a no arbitrage condition (i.e. the existence of a risk neutral
measure) through a set of cross-equation restrictions on the bond prices. Let P

t
37
denote the nominal price at time t of a zero-coupon bond of maturity. P
()
t
satises:
P
()
t
=E
t
[M
t+1
P
()
t+1
]: (2.12)
Through
P
()
t
= exp(A

+B

X
t
): (2.13)
the zero coupon bond yields (y
()
t
) become linear functions of the state variables:
y
()
t
=
logP
()
t
t
:
Finally the yields are given by:
Yields: y
()
t
=a

+b
0

X
t
(2.14)
where a

=
1

A

; b

=
1
t
B

(2.15)
Given that (2.13) should satisfy a system of dierence equations dened by (2.12),
the coecients A

; B

, and a

; b

are fully characterized recursively by:
A

= A
1
+B
0
1
(
0
) +
1
2
B
0
1

0
B
1

0
(2.16)
B
0

= B
0
1
(
1
)
0
1
(2.17)
whereby is the variance-covariance matrix of the state dynamics.
This model is very close in spirit to Fleming and Remolona (1999) [19] and Pi-
azzesi (2005) [38], apart from the fact that both use survey data in order to back
out the surprise element from macroeconomic news. Fleming and Remolona (1999)
38
incorporate data surprises into expectations formation processes for labor market
conditions, prices and aggregate demand which form the state variables of a discrete-
time ane term structure model. In their specication they x the market prices of
risk. Piazzesi (2005) uses macroeconomic data surprises directly as state variables.
She introduces a jump diusion for the monetary policy announcements and sets the
market prices of risk proportional to the volatilities of the state variables.
The estimation of this model is challenging due to the high persistence in yields at
daily frequency. A number of restrictions is used to facilitate estimation. Considering
the high degree of persistence the eigenvalues of cannot be numerically pinned down.
Therefore, given the estimates of the dynamic latent factor presented in the previous
subsection, the diagonal elements of the transition matrix to 0.995. Furthermore, as
in Chen and Scott (1993) [7], some yields are taken to be ex ante measured correctly,
while the rest of the yield curve is considered to be measured with error.
3
This
allows us to back out the latent factors from the yield curve by simply inverting
(2.14). Finally, to capture the whole yield curve with a daily ane term structure
model requires modeling 3650 yields. Thereby, the bond pricing recursions (2.16)
yield extreme parameter values. To avoid this, the model is estimated using only the
short-end of the yield curve (i.e. 3-month, 6-month, 9-month and 1-year maturity).
Table 2.4 presents the maximum-likelihood estimates of the parameters (see Section
2.5 for a presentation of the likelihood function).
Figure 2.6 plots the maturity responses to a shock of the latent factors that are
driven by the jump and path component, respectively.
4
The responses of yields across
3
In our analysis the yields at 3 and 9 months are perfectly observable.
4
Impulse-response functions are calculated as in (2.4.3), stackinga

andb

from 2.14 accordingly
to retrieve and setting I
2
.
39
Table 2.4: Maximum Likelihood estimates for the Ane Term Structure model
Estimates Standard Errors

11
0.9950

22
0.9950

1
-0.0347 0.0229

2
-0.0194 0.0105

2
0
-3.4682 0.0190

2
0
0.7060 0.0105

11
1
0.2047 0.1906

12
1
-0.0049 3.1007

22
1
0.0155 1.4767

1
1.0013 0.0470

2
0.0193 0.6739
maturities are downward sloping to jump and hump-shaped to path, respectively.
Therefore, using the jump and path indicators as shocks, the rst and the second
latent factor are identied as slope and curvature factors. These results are fully in
line with the ones obtained in the context of the dynamic latent factor approach.
2.5 The likelihood function of the ane term struc-
ture model
LetN be the number of dierent maturities used for the estimation andk
u
is the
number of maturities of yields that are observed with an error. Additionally, let u
i
t
and
i
, fori = 1;::;k
u
, denote the measurement errors and their standard deviations,
respectively. We assume that these errors are uncorrelated. Then, if is the vector
40
Figure 2.6: Yields responses to news in jump (a) and path (b) from an ane term structure model.
0
20
40
60
80
100
120
0
200
400
600
800
1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Maturity in months
Yield responses to shock in jump
Time in days
Response
(a) Responses of yields to jump.
0
20
40
60
80
100
120
0
200
400
600
800
1000
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Maturity in months
Yield responses to shock in path
Time in days
Response
(b) Responses of yields to path.
41
of parameters to be estimated, the likelihood function takes the form:
L() =(T 1)
(
lnkJk +
1
2
ln(
0
) +
k
u
2
i=ku
X
i=1
ln(
i
)
2
)

1
2
t=T
X
t=2
(X
t
X
t1
)
0
(
0
)
1
(X
t
X
t1
)
1
2
t=T
X
t=1
i=T
X
i=1
(u
i
t
)
2
(
i
)
2
(2.18)
where T is the number of available observations and the Jacobian is:
J =
2
6
4
I
(Kku)(Kku)
0
(Kku)N
B B
u
3
7
5
where K denotes the number of the state variables (i.e. K = 2) and B is the NK
matrix of the yield coecients. Finally,B
m
is theN(Nk
u
) matrix of the loadings
of the measurement errors which we set equal to unity.
2.6 Conclusions
Our analysis indicates that responses in money market rates to macroeconomic
data releases and monetary policy announcements can explain sizable and persistent
jumps in the euro area yield curve. This impact depends on the maturity horizon
over which nancial market participants revise their expectation of monetary policy
given incoming data. News related to monetary policy are found to coincide with
relatively large revisions in expectations of short-term interest rates, if compared
with macroeconomic news.
Our approach diers from existing event studies and macro-nance models, which
identify survey expectations or macroeconomic time series as the driving factors of
yields. These factors are likely to neglect important information used by nancial
markets in revising expectations of the path of short-term interest rates. Indicators
42
constructed exclusively by changes in the money-market forward rate curve in re-
sponse to news are identied as important factors explaining changes in yields at
lower frequency.
43
Chapter 3
The European Central Bank's
Monetary Policy Rule in an Ane
Term Structure Model
3.1 Introduction
There is a bidirectional relationship between monetary policy and the term struc-
ture of interest rates, but identifying either the exact magnitude or the transmission
mechanism of this relationship is rather dicult. On one hand, monetary authori-
ties monitor the economy and make policy decision which are based on information
extracted from both the yield curve and aggregate macroeconomic variables. On the
other hand, market participants react to monetary policy announcements, and form
expectations about the future state of the economy based on monetary policy. But
what is the exact role of monetary policy in explaining the yield curve? Or, to what
extent can the yield curve improve our understanding of the eective monetary policy?
44
Can they be studied separately, or is it wiser to consider them simultaneously?
This chapter develops an ane term structure (ATS) model that takes advantage
of the information rich environment provided by the term structure of the yield curve
in order to analyze the interaction between the European Central Bank's (ECB)
policy and the nancial markets. The state vector consists of the policy rate, the
spread between the short term rate and the policy rate, the in
ation rate and a
proxy for aggregate macroeconomic variables (e.g. real activity). The ECB's policy
rate is modeled as a jump diusion with a predetermined timing of the jumps that
coincide with the actual Governing Council meeting days, and jump intensities that
are driven by the state variables. The no-arbitrage condition allows for closed form
solutions for the bond yields, and therefore information is extracted from the entire
yield curve in order to identify a high-frequency policy rule. The estimated models
address questions related to the success of the ECB's communication with the market
and the interaction of the macroeconomy with the bond yields in an environment
consistent with the ECB's policy rule. The overall message re
ected in the results
is that the policy rate is indeed an important driving factor of the term structure of
interest rate, while the information contained in the yield curve vastly improves the
accuracy of the estimated policy rule when compared to other estimated policy rules
that do not incorporate such information (e.g. Taylor's rule).
3.1.1 Monetary Policy Rule
From a macro-policy perspective, the short-term rate is the instrument that cen-
tral banks use in order to make policy. Moreover, the eectiveness of monetary policy
depends heavily on how agents perceive the driving forces of policy decisions and on
how market participants use policy announcements to update their expectations about
the future state of the economy. Therefore the communication between monetary au-
45
thorities and market participants plays a fundamental role in monetary policy design.
To this end, in many countries, the central bank's policy announcements (e.g. ECB,
Federal Reserve Bank) are accompanied by explicit public commitments related to
the desired economic environment. This aims to guide better the market participants
and improve their understanding of monetary policy.
Although central banks (i.e. ECB, FRB) make a general explanatory statement
regarding their policy decisions, they do not reveal the actual numerical reasoning
behind it. Empirical research, however provides evidence that monetary policy au-
thorities set the policy rate according to a specic rule which assigns weights to
current and/or past values of the in
ation rate and the output growth. According to
the simplest Taylor rule (see Taylor (1993) [50]), the policy rate is a linear function of
the deviations of in
ation (i.e. Consumer Price Index) and output (i.e. GDP) from
their trend. There are two main dierences between the policy rule implied by the
model presented in this paper and the Taylor rule.
The rst and most important dierence relates to the information that is available
to monetary policy authorities. Within the Taylor-type policy rules, the central
bank does not take into consideration information extracted from the yield curve.
In this setting, the short-term interest rate and, in some cases, its lagged values is
the instrument through which central banks exercise their policy (see Gali, Clarida
and Gertler (1999) [27] and (2000) [39]). This simple policy rule is quite instructive;
however, the fact that this framework neglects the interaction between the yield
curve and policy decisions can lead to suboptimal or even misleading results. In the
framework presented in this paper, central banks conduct policy in an information-
rich environment, based on both the yield curve and the macroeconomy.
The second dierence is that in the Taylor-type policy rules the selected macroe-
conomic variables (i.e. in
ation and output gap) determine the level of the short term
46
rate while in the model presented in this study, they drive the changes of the policy
rate. More specically, the conditional probability of a policy rate jump is dened
as a weighted average of the deviations of the current state vector from a vector of
target values. Therefore, deviations between the current state of the economy and
the target values directly drive the conditional probability of a change in the policy
rate; through this mechanism, they indirectly aect the actual level of the policy
rate. Thus, the estimated intensities of the policy rate's jump diusion fully dene
the weights that the model's high frequency policy rule assigns to each state variable.
Additionally, the policy rule estimated in this paper explicitly incorporates the
ECB's public commitments. In particular, the European Central Bank (ECB), in
the Treaty
1
, has set the maintenance of price stability within the euro area as the
primary objective of its monetary policy. In 1998 price stability was explicitly dened
as a year-on-year increase of below 2% in the Harmonised Index of Consumer Prices
(HICP) for the euro area, and in 2003 the Governing Council further claried that
" it aims to maintain in
ation rates below but close to 2% over the medium term".
Therefore, the policy rate jumps are determined by the deviations of the current
in
ation from 2% .
3.1.2 Yield Curve Model
In nance, the term structure captures the market's expectations of the future
behavior of the short-term interest rates. Agents revise their expectations when they
receive new information (public announcements), and they make new investment
decisions based on these revised expectations. From a theoretical point of view, Va-
sicek(1977) [52] and Cox, Ingersol and Ross(C.I.R 1985b) [11] manage to concretely
1
Treaty establishing the European Community, Article 105 (1)
47
dene the linkages between the equilibrium yields and the factors that drive the mar-
ket's expectations. Additionally, Cox, Ingersol and Ross (1985a) [10] present a char-
acterization of these linkages through a partial equilibrium model that gives a purely
economic interpretation of the existing literature of the term structure framework.
However they remain silent about monetary policy eects.
From an empirical point of view, Due and Singleton (1997) [15], among others,
make use of the no-arbitrage conditions and estimate the parameters of an ane term
structure model (ATS) that captures the relationship between the underlying factors
and the equilibrium yields. In their work, the factors are latent and are determined
from the yield curve since their main goal is to analyze the pricing of interest-rate-
related securities. However, they neglect any interaction of the factors with both
the macroeconomy and the monetary policy, although there is an extensive literature
that documents an increased volatility of interest rates at all maturities before and
after policy and macroeconomic announcements (Fleming and Remolona (1998) [18],
Fleming and Remolona (1999) [19]).
The model presented in this chapter has the same spirit as the work of Ang and
Piazzesi (2003) [1] and Hordahl et al (2004) [51] who incorporate macroeconomic
variables within a term structure model, but this paper mainly builds on the work of
Piazzesi(2001) [37], who models the FRB's target rate as a jump diusion. The pri-
mary contribution of this paper is that it marries a Taylor-type rule for the conditional
probability of a policy rate move to an ane term structure model. In addition, when
the ECB's desired level of in
ation (2%) is explicitly incorporated into the model, em-
pirical analysis allows for an economic interpretation of the estimated state dynamics
and the policy rate's jump intensities.
In particular, two models are estimated using the Simulated Maximum Likelihood
(SML) method, introduced by Pedersen(1995) [35] and Santa Clara(1995) [9]. Both
48
estimations incorporate data on the in
ation rate and the policy rate. The rst
estimation (Model I) considers all the state variables, except for the policy rate and
the in
ation rate, to be latent factors, while the second (Model II) treats only the
last state variable (i.e. the proxy for macroeconomic information) as an unobservable
variable. Model's II estimation is completed in two steps. In the rst step the
dynamics of the in
ation rate and the spread (between the policy rate and the short-
term rate) are estimated from the available data; in the second step the remaining
parameters are estimated through the term structure model, taking as given the values
of the parameters estimated in the rst step. Therefore, Model I estimates the ATS
dynamics from the perspective of a pure term structure model, while Model II sheds
light on the policy rule, using information from both the yield curve and the available
macro and policy rate data.
There are three main estimation results presented later in the paper. First, in
a-
tion rate data drastically improves the power of the model to predict changes in the
policy rate. Second, the model-implied values for the proxy of the macroeconomic
variables are highly correlated with the 6-month rate. Third, a shock to the pol-
icy rate strongly aects the medium-term maturities, similar to the curvature factor
of the term structure of interest rates; whereas shocks to the in
ation rate aect
the whole yield curve (i.e. level factor), and shocks to the proxy of macroeconomic
variables aect mainly the short-term interest rates (i.e. slope factor) similar to the
ndings of Diebold et all. (2006) [44].
In addition, there are three policy implications derived from the empirical analysis.
First, comparison of the models indicates that market participants perceive the ECB's
policy rule to be an in
ation-targeting. One immediate explanation is the fact that
the ECB has tied its denition of price stability to a specic in
ation rate, although
it ocially denies that it means an in
ation-targeting policy. Second, both models
49
suggest that changes in the policy rate today aects the ECB decisions in the following
meetings as well (i.e. policy inertia). Last but not least, we conclude that the
ECB's monetary policy is substantially driven by the macroeconomic information
communicated by the 6-month rate, and its policy decisions aect mainly the medium
term maturities (i.e 2-years).
The rest of the paper is organized as follows: Section 3.2 presents the statistical
analysis of the data; Sections 3.3 and 3.4 present the econometric model and the
estimation method; Section 3.5 presents the results and Section 3.6 concludes.
3.2 Statistical Description of the Data
This section describes the data used in the empirical analysis and their statistical
properties. Specically, daily data on the ECB's announcements on the Minimum
Bid Rate (MBR) are used for the policy rate (
t
) for the period between November,
2000 and July, 2006. Decisions regarding the key interest rates for the euro area
have been announced in a press release issued at 2:00 p.m. C.E.T. on the day of the
Governing Council's monthly meeting. For the days between the ECB meetings, the
value of the policy rate remains constant. Therefore, the MBR has the shape of a
step function with the step size proportional to 25bp and co-moves with the 1-month
yield, as shown in Figure 3.1.
Furthermore, daily data, extracted by the Global Financial Database, on the 1-
month rate are used for the short-rate (r
t
) for the same sample period. Figure 3.2
graphs the spread (s
t
) between the short-term rate (r
t
) and the policy rate (
t
) for
the sample period, where s
t
=r
t

t
. The spread appears to be quite stabilized on
average (std 0.0638) around 0.09, except for a few periods. In particular, up to 2003
the spread is much more volatile and negative during several short periods. Between
50
Figure 3.1: Daily data on the ECB Minimum Bid Rate (policy rate) and the 1-month
(zero-coupon) euro-area bond yields (short-term rate) from November 2000 to July
2006.
2000 2001 2002 2003 2004 2005 2006
1.5
2
2.5
3
3.5
4
4.5
5
5.5

Policy Rate
1−month
Table 3.1: Summary Statistics for the euro-area's data on in
ation (
t
) and the spread
(s
t
) between the policy rate
t
and the short-term rate from November 2000 to July
2006.
Mean St. Dev. 1-Lag 2-Lags 3-Lags

t
0.0224 0.0029 0.7421 0.4558 0.2550
s
t
0.0913 0.0638 0.8035 0.6757 0.5835
2003 and 2005, the spread's volatility drops and the policy rate is always lower than
the short-term rate (i.e. the spread is positive). Thereafter, the spread remains
positive but with higher volatility. Additionally, both the spread and the short-term
rate are autocorrelated with coecients 0.8035 and 0.7421 respectively, as shown by
the sample statistics presented by Table 3.1.
51
Figure 3.2: Daily data on the spread (s
t
) between the euro-area's short-term rate (r
t
)
and the ECB's policy rate (
t
) from November 2000 to July 2006.
2000 2001 2002 2003 2004 2005 2006
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5

Spread
Daily data on the euro-zone zero-coupon bond yields of 6-month, 2-year and 5-year
maturities (available at the Global Financial Database) for the same sample period
are used for the estimation. The euro-area yield curve has similar characteristics as
the US yield curve (Ang and Piazzesi (2003) [1]), as it is shown by the sample statistics
of the yield data reported in Table 3.2. In particular, yield volatility decreases with
maturity, and this decrease has a signicant magnitude even between subsequent
maturities. For example, there is a 4% decrease in the standard deviation between
the 1-month rate (std 0.9077) and the 3-month rate (std 0.8741), while it jumps
to a 30% when you compare the standard deviations of the 1-month rate and the
10-year. In addition, yields of all maturities are highly autocorrelated, while the
(autocorrelation) coecients decrease slightly with maturity.
Furthermore, up to the rst half of 2002, the euro area yield curve has a reversed
52
Table 3.2: Summary Statistics of the euro-area's yields data from November 2000 to
July 2006.
Yields Mean St. Dev. 1-Lag 2-Lags 3-Lags
1-month 2.8490 0.9077 0.9981 0.9963 0.9945
3-month 2.8322 0.8741 0.9981 0.9962 0.9944
6-month 2.8246 0.8374 0.9978 0.9955 0.9934
9-month 2.8405 0.8111 0.9974 0.9948 0.9923
1-year 2.8776 0.7943 0.9970 0.9941 0.9913
2-year 3.1133 0.7568 0.9962 0.9926 0.9891
3-year 3.3573 0.7363 0.9966 0.9929 0.9892
4-year 3.5613 0.7132 0.9966 0.9931 0.9896
5-year 3.7404 0.6996 0.9967 0.9934 0.9901
6-year 3.8999 0.6923 0.9969 0.9938 0.9908
7-year 4.0418 0.6879 0.9971 0.9942 0.9914
8-year 4.1659 0.6823 0.9972 0.9945 0.9918
9-year 4.2728 0.6760 0.9973 0.9947 0.9921
10-year 4.3640 0.6701 0.9974 0.9949 0.9923
shape (i.e. downward sloping) for limited periods. In Figure 3.3, which graphs the
6-month, 2, 5 and 10-year maturities of (zero-coupon) bond yields, the 6-month yields
appear to exceed the 2-year for specic periods between 2000 and 2002. It is worth
noting that for this same period the spread (s
t
) volatility is high. Afterward, the
yield curve slopes upward and the spread volatility drops.
The annual in
ation rate is the last observable variable considered in the analysis,
and it is computed as the log ratio of the current value of the euro-zone Harmonized
Consumer Price Index (HCPI) and its 12
th
-lag (i.e. i
t
= log
HCPIt
HCPI
t12
). The data
for the euro-area HCPI have monthly frequency and are available at EUROSTAT.
Figure 3.4 graphs the in
ation rate data for the period between January, 1960 and
September, 2006. However, the sample period for in
ation, used for the estimation,
remains the same as the rest of the variables (i.e. November, 2000 and July, 2006).
For this period, the euro-zone in
ation rate has mean close to 2.23%, low volatility
53
Figure 3.3: Daily data on the euro-area yields at the 6-month, 2, 5 and 10 years
maturity from November 2000 to July 2006.
11/2000 2001 2002 2003 2004 2005 07/2006
1
2
3
4
5
6

6−months
2−years
2000 2001 2002 2003 2004 2005 2006
2.5
3
3.5
4
4.5
5
5.5
6

5−years
10−years
(std is 0.0028), and, interestingly, small autocorrelation coecients that decrease for
the lagged values.
The rest of the statistical analysis aims to shed light on the compatibility of the
data and the dynamics of the model (presented in Section 3.3). In particular there
are three issues that need to be checked. First the level of independence between the
in
ation rate and the spread needs to be low as we assume that they are independent.
The fact that their correlation coecients are not statistically signicant, makes the
assumption of their independence less restrictive. Second, the existence of gaussian
dynamics in the in
ation rate's dynamics are checked: the Kolmogorov-Smirno (K-S)
test does not the reject the Gaussian hypothesis for the in
ation rate (with p-value
0.3923 at the 5% signicance level). Finally, the spread's t to a mean-reverting
square root process is evaluated: the normality hypothesis is strongly rejected for
54
Figure 3.4: Monthly data on the euro area in
ation rate (
t
), (1961 - 2006).
1961 1970 1980 1990 2000 2006
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16

HCPI EuroZone
the spread (p-value = 3:59 10
18
) at 5% signicance level. The main reason for this
rejection is the fat tails that appear in the spread's distribution. This feature of the
spread data is clearly illustrated in Figure 3.5 which plots the spread's distribution
against the normal distribution. This implies that modeling the spread as a mean
reverting square root process imposes a strong restriction and needs to be taken into
consideration.
Finally, it is essential to have a picture of the relationship between the state
variables (i.e. the policy rate, the in
ation rate, the spread and the proxy for macroe-
conomic information) and the yield data. To this end, a principal component analysis
of the euro-area bond yields at the 6-month, 2 and 5 years maturities is pursued. Ta-
ble 3.3 presents the correlation coecients between the representation of the yields in
the principal component space and the two state variables (i.e. the in
ation rate and
the spread). In
ation is signicantly, negatively correlated with the rst principal
55
Figure 3.5: Normal Probability Plot for the euro-area spread (s
t
) between the short-
term rate and the policy rate.
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5
0.0001
0.0005
0.001
0.005
0.01
0.05
0.1
0.25
0.5
0.75
0.9
0.95
0.99
0.995
0.999
0.9995
0.9999
Data
Probability
Probability plot for Normal distribution
component; the spread is negatively correlated with the third principal component,
while the two coecients have similar magnitude. This implies that the two state
variables will try to capture dierent orthogonal driving forces of the yields, with the
in
ation rate playing a fundamental role in explaining the yield curve.
Table 3.3: Correlation coecients for the principal component of the euro-area bond
yields at the 6-month, 2 and 5 years maturities and the in
ation and the spread.
1st Component 2nd Component 3rd Component
In
ation -0.5652

0.2029 -0.1634
Spread -0.0303 0.0624 -0.4060

=signicant at a 0.05 level
56
3.3 Econometric Model
3.3.1 State Dynamics
Let
t
denote the ECB's policy rate;
t
the expected in
ation; s
t
the spread
between the short-term rate and the target rate, and x
t
the latent factor that is
considered be a proxy for the macro variables that drive the economy's real activity.
Then the vector of state variables (Y
t
) is given by:
Y
t
= [
t

t
s
t
x
t
]
0
The state dynamics considered in our analysis are fully described by the following
assumption.
Assumption 1: The state vector that drives the dynamics of the economy evolves
under:
dY
t
=
Y
dt +
Y
dW
t
+dJ
t
(3.1)
where W
t
= [0 w

t
w
s
t
w
x
t
]
0
is a 4x1 vector of independent Brownian motions, J
t
is a
4x1 vector of jump process with deterministic timing for the jumps, and (
Y
;
Y
) are
the mean and variance of the multivariate diusion. More specically, the evolution
of each state variable can be described by:
d
t
= dJ
t
(3.2)
d
t
=

(
t
)dt +

p

t
dw

t
(3.3)
ds
t
=
s
(s
t
s)dt +
s
p
s
t
dw
s
t
(3.4)
dx
t
=
x
x
t
+dw
x
t
(3.5)
57
where V=[

s
s
s

x
] is a vector of constants.
The statistical analysis of the data, presented in Section 3.2, justies the state
dynamics described by Assumption 1.
3.3.2 Jump diusion
Modeling the policy rate (
t
) as a jump diusion is fully motivated by the shape
of the ECB's announcements on the Minimum Bid rate (MBR) graph (see Figure
3.1) which is identical to a step function. In particular, the MBR remains constant
for the period between the Council meetings, and it moves only after them.
Let N
U
and N
D
be an upward and downward Poisson process with probability
distribution
U
t
and
D
t
respectively. The jump size for both processes is set to 25bp in
order to keep it consistent with the actual ECB's announcements magnitude. Then:
dJ
t
=
J
[(dN
U
dN
U
) 0
1x3
]
0
where
J
= [0:0025 0
1x3
] is the matrix dening the one-jump size.
In order to keep the model ane, the corresponding intensities are assumed to
be ane functions of the state variables. Furthermore, the timing of the jumps is
deterministic and coincides with the exact dates of the policy announcements made
by the ECB Governing council during the press conference. Therefore, the jump
intensities for the up and the down processes are considered to be constant and equal
to the the empirical frequency of a move for the ECB's policy rate ( 0.143) for
the periods without an ECB meeting, and symmetrically time-varying and state-
dependent for the periods during an ECB meeting.
58
Let
e
Y be the vector ot the ECB's target values. Then
e
Y = [

s x]
0
where

(z) denotes the mean value of a variable z and

is the in
ation rate that
ECB has tied to price stability (i.e

= 2%).
In addition, if M is the set that contains all the meeting-time points, then
I
meeting
= fh :h2 [t
i
;t
i+1
];i2Mg. Finally, let
Y
be the vector of the parame-
ters describing the force that each state variable applies on the evolution of the (up
and down) Poisson probabilities, or:

Y
= [

s

x
]
0
Therefore the jump intensities have the form:

U
h
=
8
>
<
>
:
0:143 if h= 2I
meeting
+
Y
(Y
h

e
Y ) if h2I
meeting
(3.6)

D
h
=
8
>
<
>
:
0:143 if h= 2I
meeting

Y
(Y
h

e
Y ) if h2I
meeting
(3.7)
By the above specication of the intensities, the policy rate reacts to the state
of the economy at a rate
Y
. An interesting feature of this specication is that the
conditional probability of a policy rate's jump during an ECB meeting depends on
the dierence between the level of each state variable and its mean, for all the state
variables, except for the expected in
ation. The role of in
ation in a change in the
policy rate is determined by the distance of the current in
ation rate from the one
that the ECB uses to dene price stability (i.e.

= 2%).
59
The available data correspond to the dierence of the two processes (N
U
- N
D
)
with conditional probability P
data
given by:
P
data
=
i
t
(1
j
t
) ;i;j = 2U;D and i6=j
3.3.3 Yield Curve Model
The following assumption is essential for the solution of the ane term structure
curve model:
Assumption 2: A risk neutral measure
e
Q exists within the economy.
Assumption's 2 direct result is that the no arbitrage condition holds, and, hence, a
set of cross-equation restrictions hold for the bond-price processes. More specically,
if P (Y
t
;t;t +) denotes the nominal price at time t of a zero-coupon bond, with
maturity date at t +, and r(Y
t
) is the nominal short rate, then the nominal bond
prices should satisfy:
P (Y
t
;t;t +) =
e
E
t
[exp(
Z
t+
t
r(Y
s
)ds)] (3.8)
where
e
E is the expectations under
e
Q.
The state dynamics captured by equation (3.1) are related to the data-generating
measure Q while the bond pricing equation (3.8) refers to the expectations under
the risk-neutral measure
e
Q. Therefore, in order to proceed with solving equation
(3.8), the transition link, mostly referred to as risk-adjustment, from the risk neutral
measure to the data-generating one needs to be dened:
Assumption 3: Market prices of risk are proportional to the variances of the state
variables. Therefore, a strictly positive martingale
t
and a function

Yt
:A
Y
! R
n
60
exist and satisfy:

0
= 0

Yt
= [0 q

p

t
q
s

s
p
s
t
q
x
]
d
t

t
=

Yt
dW
t
such that for every random variable X:
E
t
[X

t+

t
] =
e
E
t
[X]; 8 >t
Therefore, the state dynamics under the risk neutral measure solve:
dY
t
=e
Y
dt +
e

Y
d
f
W
t
+dJ
t
with
e
Y
=
Y

Y
(

Y
)
0
e

Y
=
Y
where
f
W
t
is a 4x1 vector of standard Brownian motions under
e
Q.
Nominal Bond Prices and Yields
Given Assumption 3, the solution to equation (3.8) satises a system of partial
dierential integral equations (PDIE). Due to the time dependent specication of the
jump intensities, the PDIE dierentiates between the time during the ECB meetings
and between them, and takes the form:
61
P (t +;t +) = 1
P (t;t +) = P
Y
(t;t +)[
Yt

Yt

0
(
Y
t
) +
1
2
tr[P
YY
(t;t +)
Yt

0
Yt
]r

U
t
[P (Y
t+
+J
Y
t+
;t;t +)P (Y
t+
;t;t +)]
+
D
t
[P (Y
t+
J
Y
t+
;t;t +)P (Y
t+
;t;t +)]
where P
Y
;P
YY
;P
t
denote the partial derivatives with respect to the state variables
and time respectively, and tr is the trace of the matrix.
The solution to the PDIE is characterized by the method of undetermined coe-
cients. First, a guess is made on the functional relationship between the bond prices
and the state vector. In particular, let the solution have the form:
P (Y
t
;t;t +) =e
A(t;t+)+B(t;t+)Yt
(3.9)
where both coecient functionsA(t;t+) andB(t;t+) are taken to to be integrable;
due to the time-varying jump intensities they depend on both the current time t and
the maturity time t +:
B(t;t +) =
0
B
B
B
B
B
B
B
@
B

(t;t +)
B

(t;t +)
B
s
(t;t +)
B
x
(t;t +)
1
C
C
C
C
C
C
C
A
; A(t;t +) =
0
B
B
B
B
B
B
B
@
A

(t;t +)
A

(t;t +)
A
s
(t;t +)
A
x
(t;t +)
1
C
C
C
C
C
C
C
A
The nominal bond prices,P (Y
t
;t;t+), should satisfy the system of PDIE and the
equation (3.8). Therefore, a system of time-dependent ordinary dierential equations
(ODE's) fully characterize the solution's coecients. Specically, A(t;t +) and
62
B(t;t +) satisfy the following system of ODE's:
For t2I
meeting
dA
dt
= B

B
s

s
s +B
x
q
x
+
B
2
x
2
+ 2 ( +
Y
e
Y )e
0:0025B

(
Y
e
Y )e
0:0025B

dB

dt
= 1

(e
0:0025B

e
0:0025B

)
dB

dt
= B

(

+q

2

) +
B

2

2

(e
0:0025B

e
0:0025B

)
dB
s
dt
= 1 +B
s
(
s
+q
s

2
s
) +
B
s
2

2
s

s
(e
0:0025B

e
0:0025B

)
dB
x
dt
= B
x

x

x
(e
0:0025B

e
0:0025B

)
For t = 2I
meeting
dA
dt
= B

B
s

s
s +B
x
q
x
+
B
2
x
2
+ 0:286 0:143(e
0:0025B

+e
0:0025B

)
dB

dt
= 1
dB

dt
= B

(

+q

2

) +
B

2

2

dB
s
dt
= 1 +B
s
(
s
+q
s

2
s
) +
B
s
2

2
s
dB
x
dt
= B
x

x
where A
i
and B
i
denote the partial derivatives with respect to the variable i,
for i= ; ; s; x.
Finally, let y(t, t+) denote the zero-coupon bond yield at time t and maturity date
63
at t +:
y(t;t +) =
ln(P (t;t +))

Then the nominal yields are given by:
y(t;t +) =
e
A(t;t +) +
e
B(t;t +)Y
t
(3.10)
where
e
A(t;t +) =
A(t;t+)

and
e
B(t;t +) =
B(t;t+)

.
Overall, equations (3.1) and (3.10) describe the evolution of the state dynamics
and the resulting yield curve, and thus, they dene the ane term structure (ATS)
model used in our empirical analysis.
3.4 Empirical Analysis
Our empirical analysis uses the 6-month, denoted by y(t;t + 0:5), the 2-year
(y(t;t + 2)) and the 5-year zero-coupon bond yields (y(t;t + 5)) for the sample period
between November 2000 and July 2006. Hence, for the ATS model, the vector of
observables can be summarized as:
O
t
= [
t

t
y(t;t + 0:5) y(t;t + 2) y(t;t + 5)]
0
The vector of parameters that needs to be estimated is:
= [

s

x

s

x
s

s
q

q
s
q
x
]
where ,

,

,
s
,
x
are the jump intensities;

,
s
,
x
are the speeds of mean
reversion;q

,q
s
,q
x
are the market prices for risk, and,,s and

,
s
are the state
vector's means and volatilities.
64
3.4.1 Estimation Method
The model assumes that equation (3.1) describes the dynamics of the state vector
under the data generating measure Q. As the there is no closed form for the density
of the state vector (f(Y
t+1
)jY
t
;t; )), following Pedersen(1995) [35] and Santa Clara
(1995) [9], the density f(Y
t+1
jY
t
;t; ) is approximated by the simulated density of
the discretized state constructed by the Euler discretization of the state dynamics:

^
Y
t+;h
=
^
Y
t;h
+
^
Y
t;h
!
t+
p
+
Y

t;h
(3.11)
where
^
Y
t;h
denotes the simulated state vector; !
t
= [0 N
1x4
(0; 1)]
0 2
; h is the number
of approximated paths (h = 1;::;H);
t;h
captures the state's random component,
and is given by:

t;h
= [
t;h
0
1
x3]
0
where
t;h
denotes a Markov chain with three possible outcomes: up, down and
constant (j =fU;D;Cg) and probabilities of success p
u;h
, p
d;h
, p
c;h
, given by:
p
u;h
=
U
t;h
(1
D
t;h
)
p
d;h
=
D
t;h
(1
U
t;h
)
p
c;h
= (1
U
t;h
)(1
D
t;h
)
Furthermore, for days without an ECB meeting, the discretization's time incre-
ment is set equal to
1
300
; for the meeting days, is set to
1
600
in order to increase the
accuracy of the time-dependent jump intensities (
j
t;h
; j =fU;D;Cg).
2
N
1x4
(0; 1) is a four dimensional standard normal distribution.
65
Hence, each simulated path's density function (
e
f
h
(Y
t
j
^
Y
t;h
;t; )) is computed
numerically, using Monte Carlo approximation. Specically:
For t= 2I
meeting
:
e
f
h
(Y
t
j
^
Y
t;h
;t; ) =(Y

t
;tj
^
Y
t;h
;t))1

t;h
t
1

t;h
t
For t2I
meeting
:
e
f
h
(Y
t
j
^
Y
t;h
;t; ) =(Y

t
;tj
^
Y
t;h
;t)1

t;h
t
I

t;h
t
^ p
j;h
t
where Y

t
= [
t
s
t
x
t
]
0
, and (:) is the conditional density of a three dimensional
normal distribution. Moreover, 1

t;h
t
and 1

t;h
t
are the indicator functions of the correct
simulated paths. in particular, they assign zero probability to the paths for which the
simulated values of the policy rate (
t
) and the in
ation rate (
t
), respectively, do not
coincide with the actual data. One critical issue is that the available data for the euro
area's in
ation rate have monthly frequency. Therefore, the in
ation rate process is
simulated conditional upon the observations at the points with observations, and the
indicator function (1

t;h
t
) is set to 1 for the days without data. Hence, with respect
to the in
ation rate the likelihood function assigns zero probability to the paths that
do not lead to values of in
ation equal to the actual data.
For the time during an ECB meeting, I

t;h
t
indicates whether the simulated value
(
^

t;h
) can lead to the observed policy rate (
t
) in one jump. Finally, d
j;h
t
indicates
the simulated Markov chain's outcome (i.e. up, down or constant)l, and is given by:
^ p
j;h
t
=
X
j=U;D;C
p
j;h
t
d
j;h
t
The state is simulated by 5000 paths (i.e. H=5,000), and the density function
of the state vector is approximated by the weighted conditional density of the h
t
h
discretization, or
e
f
Y
(Y
t
jY
t
;t; ) =
1
H
N
X
h=1
e
f
h
(Y
t
jY
t
;t; ) (3.12)
66
where
e
f
h
(Y
t
jY
t
;t; ) is the appropriate conditional density of the h
th
simulated
path.
Using the Bayes Rule and the Markov property of the state vector, the density
between t and t + 1 is approximated by Monte Carlo integration:
f
Y
(Y
t+1
jY
t
;t; ) =
Z
2
e
f
Y
(Y
t+1
jY
t+1
;t; )
e
f
Y
(Y
t+1
jY
t
;t; )dY
t+1
(3.13)
where is a the set of time grids chosen for the Euler's discretization.
Finally, given equation (3.13), the likelihood function of the vector of observables
(f(O
t+1
;t+1jO
t
;t; )) can be derived from the conditional density of the state vector
after a change of variable, or:
f(O
t+1
;t + 1jO
t
;t; ) =f
Y
(u(O
t+1
; )ju(O
t
; );t; )j r
Y
u(O
t
; )j (3.14)
where u(O
t
; ) = Y
t
denotes the function that maps the observable variables to the
state vector by inverting equation 3.10). Therefore, the vector of parameters will be
estimated by maximizing the product of the log-likelihood, given by (3.14), across
time, or:
^
=argmax
Q
t2T
f(O
t+1
;t + 1jO
t
;t; )

where T is the set consisting of all the working days during the sample period.
3.5 Results
The ane term structure model presented in Section 3.3 is estimated twice.
In both cases the same estimation method is used, namely the Simulated Maximum
Likelihood (SML), the same set of observable variables (O
t
) and the target rate's mean
67
is set equal to its sample mean. Moreover, the key conceptual similarity between the
two models is that the yield curve and the policy rate are driven by the same factors,
or in other words, they both estimate the same ATS model. Their main dierence,
however, can be summarized by the set of information utilized while estimating the
ATS model.
More specically, in the rst estimation, denoted by Model I, the observable vari-
ables (O
1
t
) are the yields, the policy rate and the in
ation rate, while the rest of the
state variables are treated as a latent factors, or:
^

1
=argmax
(
Y
t2T
f(O
t+1
;t + 1jO
t
;t; )
)
In the second estimation, denoted by Model II, the main goal is to match the
state dynamics with the available data. This is done in two steps. In the rst step
the diusion parameters for the evolution of the in
ation rate and the spread are
estimated by maximizing the log likelihood function (MLE). In particular, rst the
MLE estimators for a subset

2
of the parameters () are derived:

2
consists of the
speed of mean reversion (

,
s
), the mean (, s) and the volatility (

,
s
) of the
in
ation rate and the spread:
~
= [

s
s

s
]
In the second step, the rest of the model's parameters (
2
) are estimated by the SML
method, taking as given the MLE estimates for the dynamics of the in
ation rate and
the spread, estimated in the rst step, or:
^

2
=argmax
(
Y
t2T
f(O
t+1
;t + 1jO
t
;
~
;t;
2
)
)
68
where
2
consists of the remaining parameters to be estimated which are the inten-
sities, the market prices of risk and the evolution dynamics of the x-variable.
This two-step procedure ensures that the SML estimators for the rest of the pa-
rameters derived in the second step, maximize the likelihood function of the model in
order to t the yield curve, while utilizing information available in the in
ation rate
and the spread data.
3.5.1 Estimated Parameters
Table 3.4 presents the estimates and their standard errors for the two ATS models.
These estimates help address issues related to the economics of the driving factors
of the yield curve and the ECB's monetary policy. Both models identify the same
driving forces for the yield curve and the policy rate changes, namely the policy rate
itself (), two independent, mean-reverting square root processes (the in
ation rate
() and the spread (s)), and a zero-mean process (the proxy for macro information
(x)). The next sections describe the statistical and economical characteristics of these
estimated driving forces.
State Dynamics - Mean Reversion
The estimated state dynamics for Models I and II are quantitatively dierent. In
particular, the mean reversion parameter for the in
ation rate (

= 0:5154 for Model
I and

= 0:7025 for Model II) suggests a half life of almost 1.5 years (
ln2

)=1.345)
for Model I and less than one year (
ln2

=0.98675) for Model II. The corresponding
daily autoregressive coecient (exp(

365
)) is 0.9926 for Model I and 0.9982 for Model
II. Additionally, the half life for a shock to the spread is less than 20 days (=0.048)
for Model I and more than one month (0.0914) for Model II, with autoregressive
coecients of 0.9612 and 0.9794, respectively. For the x-variable both models estimate
69
Table 3.4: Estimation Results for the Ane Tern Structure model
Model I t-ratios Model II t-ratios

0.5410 0.2343 0.1264 1.9034

-0.4290 0.0128 -0.3725 -5.8960

0.2940 7.9234 0.9102 12.9070

s
0.3120 4.9237 0.6321 1.8945

x
0.2120 2.9012 0.6473 10.9782

0.5154 11.2782 0.7025 17.3562

s
7.5970 5.7892 14.4406 0.5627

x
0.3510 3.8294 0.2962 2.3674

2.7576 2.7576
0.0319 0.8943 0.0246 8.9023
s 0.2200 0.9102 0.1210 4.1672

0.0055 0.0013 0.0012 0.0109

s
0.0123 0.0057 0.0026 0.0420
q

-5.4721 0.0042 0.7025 17.3562
q
s
-2.1711 -3.0962 14.4406 0.5627
q
x
3.1203 -1.9254 0.2962 2.3674
a relatively high half life for the respective shock, specically, almost 2 years (1.975)
for Model I and 2.3 years for Model II.
Interestingly, both models send the same message regarding the characteristics of
the three factors that drive the yield curve and the policy rate. Specically, the rst
factor (in
ation) is characterized by a low mean and volatility, and its shock stays
in the system for an average period of 1-1.5 years; the second (spread) has a very
high mean and quite high volatility (relatively to in
ation), while its shock stays in
the model for a very short period of time (1-2 months). Finally, a shock to the third
factor (proxy for macro variables) aects the evolution of the system for an extended
period that ranges between 2-2.3 years.
70
From a policy perspective, the high values of the half lives for the in
ation rate
and the x-variable shocks imply policy inertia. Specically, a shock to either of them
aects not only the ECB's decision during the immediate meeting but the decisions
during the following meetings, as the shocks remain in the system for a period that
overlaps with several ECB meetings.
Intensities
In our sample period, the ECB has announced ve policy rate increases and six
decreases which result to an unconditional probability of a policy rate change equal
to 0.143. Model I gives a rather high estimation for the unconditional probability
of a change (

=0.54) while Model II estimates it more accurately (0.1264). This
signicant dierence implies that either the yield curve contains information that
would require more changes in the policy rate over the sample period or that the
estimated dynamics of the driving forces for the policy rate are less informative in
Model I than in Model II. Looking at the rest of the intensities, the second implication
seems more realistic. The estimated intensities for the in
ation rate and the spread
are smaller for Model I than Model II. Given that the evolution dynamics of these
variables are estimated by the data in Model II, this feature indicates that Model I
estimates state dynamics that fail to t the policy rate's jump diusion as well as
Model II and hence both

and

seem to be over-estimated in Model I. Therefore,
we further concentrate our economic interpretation on Model's II estimates.
Note that the jump intensity magnitude indicates the role played by the corre-
sponding state variable in the policy rate change. In Model II the in
ation rate jump
intensity (

)is the highest implying that the policy jump's main driving force is the
in
ation rate. The way, however, that

aects the conditional probability of a
policy rate's move is proportional to the distance between the current in
ation rate
71
and the pre-announced in
ation rate that is tied to price stability (i.e. 2%). This
indicates that the market, represented by the yield curve, weights heavily the devia-
tion of the current in
ation rate from 2% in order to update its expectations about
a possible policy change. Therefore, ECB's announcement of a desired in
ation level
(i.e. 2%) improves the communication between the policy strategy and the market.
Specically, if the ECB had not announced the desired in
ation rate of 2%, then the
target value for in
ation would have been equal to its mean (i.e. 2.46% for Model II).
Thus, since the distance between the in
ation rate during the sample period and it's
mean would have been less than its distance from 2%, the conditional probability of
a policy rate change at the next ECB meeting would have been underestimated by
the market. In other words, the ECB would not have communicated its policy to the
market if it hasn't tied its price stability denition to a prespecied level of in
ation
(2%). Moreover, the fact that the highest intensity is assigned to the in
ation factor
indicates that the ECB's policy rule is considered in
ation-targeting by the market.
The second highest intensity coecient is assigned to the state variable that prox-
ies for the macroeconomic information (i.e. x-variable). Additionally, this x-variable
intensity is positive and signicant implying that if the x-factor grows the market
expects a policy rate increase, during the next ECB meeting, with higher probability.
Finally, the policy rate's intensity (

) is negative for both models indicating that
if the policy rate is higher than its mean (

) the market expects (assigns higher
probability) a decrease in the policy rate during the next meeting. Hence, there is
a mean reverting nature suggested for the policy rate which implies that the market
identies an interest-rate smoothing feature in the ECB's rule.
72
3.5.2 Latent factor: The x-variable
Given the estimated parameters presented in the previous section, a time-series
corresponding to the latent factors can be computed by inverting equation (3.10). The
statistical analysis of the time-series corresponding to the x-factor provides further
insight into the underlying interactions and it's economic interpretation.
Both models remain silent about the economic interpretation of the zero-mean
reverting latent factor denoted by x. In other words, although the x-variable is con-
sidered to be a proxy for the macroeconomic variables, there is no mathematical or
economical link between the variable and the underlying European macroeconomy.
Hence both models treat it as a latent factor. However, there is a consensus (see
Taylor (1993) [50]) that the policy rate is mainly driven by the in
ation rate and
the output gap. Hence, in our model, the x-factor should bring in information con-
tained in the euro-area's aggregate macroeconomy (i.e. real activity) given that the
two other state variables deliver information from the in
ation rate and the spread
respectively. Therefore, it is important to pin down the information set for which the
x-variable proxies. To this end, the correlation coecients of x with the yield data
presented are reported in Table 3.5.
The x-factor is highly and signicantly correlated with short term maturities,
especially with the 6-month maturity, while the correlation coecients drop with
maturity. It is quite interesting that both models suggest similar results about both
the magnitude and the pattern of the correlation coecients. This consensus makes
clear that the latent factor (x) shares a common information set with the short end
of the yield curve.
Hence, all the state variables (i.e. in
ation, spread and the x-factor) are highly
and positively correlated with the short end of the yield curve. This fact, combined
73
Table 3.5: Correlation Coecients between the estimated state variables and the
yields.
In
ation Factor Spread Factor X-Factor
Model I Model II Model I Model II Model I Model II
1-month 0.7164 0.7913 0.4079 0.6423 0.5331 0.9225
3-month 0.7207 0.7768 0.4113 0.6480 0.5345 0.9229
6-month 0.8267 0.7498 0.5134 0.6501 0.5398 0.9223
9-month 0.7311 0.7241 0.4151 0.6485 0.4430 0.9207
1-year 0.6340 0.7028 0.4163 0.5426 0.4431 0.8188
2-year 0.5343 0.6708 0.1176 0.5219 0.3342 0.8108
3-year 0.5307 0.6647 0.2189 0.4062 0.3306 0.8056
4-year 0.4269 0.6646 0.1178 0.3962 0.2286 0.8016
5-year 0.3225 0.6657 0.1161 0.2872 0.2275 0.7007
6-year 0.3182 0.6682 0.1141 0.2793 0.2268 0.7027
7-year 0.1142 0.6700 0.1123 0.2737 0.2267 0.6041
8-year 0.0109 0.6711 0.1106 0.2706 0.1274 0.6054
9-year 0.0083 0.6707 0.1089 0.2681 0.1280 0.6063
10-year 0.0059 0.6695 0.1079 0.2668 0.1284 0.6070
with their positive estimated jump intensities, implies that ECB policy rule is mainly
aected by information contained in the short end of the yield curve (especially the
6-month). The medium term maturities do aect monetary policy decisions, but at
a lower level, while the longer maturities are less important.
3.5.3 Yield responses to the state variables shocks
In order to understand better the estimated model dynamics each state variable's
eect on the yield curve needs to be identied. Therefore, this section addresses the
question of how shocks in the state variables are translated into the yield curve.
As depicted by equation (3.10), the yields' reaction to the state variables (Y
t
) are
driven by the coecients
~
A(t;t +) and
~
B(t;t +). In particular,
~
B
i
(t;t +); i =
fx; ;s; g denes the magnitude of the i-state variable's direct eect on the yields
74
with maturity , at time t, denoted by
~
B
i

. Therefore, the mean of
~
B
i
(t;t +) over
time is an indicator of the yields', with maturity , response to an i state variable's
shock. Formally:
~
B
i

=
t=T
X
t=0
~
B
i
(t;t +)
As expected
~
B
i

depends only on the yield's maturity () and the state variable i.
Figure 3.6 graphs
~
B
i

; for i =fx; ;s; g; and = 1;:::; 120 over the sample
period for each model, and, therefore, depicts the yield curve's response to the state
variables shock for each model. A comparison of the two graphs indicates that the
two models share the same shape of the yield curve response while they dier in the
magnitude of the response.
Figure 3.6: Yields responses for Model I (upper graph) and Model II (lower graph)
to shocks in the state variables.
1 3 6 9 12 24 36 48 60 72 84 96 108 120
0
0.2
0.4
0.6
0.8
1
Model II

B
x
B
π
B
s
B
θ
1 3 6 9 12 24 36 48 60 72 84 96 108 120
0
0.2
0.4
0.6
0.8
1
Model I

B
x
B
π
B
s
B
θ
Moreover,
~
B

; = 1;:::; 120 has a hump shape for both models. This feature
argues that the monetary policy shocks eect on the yield curve reach its maximum
75
at the 2-year maturity, however it is quite limited for both the short and the long end
of the yield curve. In other words, shocks to the policy rate play the role of the "cur-
vature" factor (as dened within the nance literature) in both models. Therefore,
the ECB's policy rule mostly aects the medium term maturity yields (i.e. 2-year)
with a non-negligible eect on both ends of the yield curve.
Furthermore,
~
B

; = 1;:::; 120 is a line parallel to the x-axis for both models
indicating that the magnitude of the in
ation shock eect on the yield curve is the
same over the whole yield curve. So, the in
ation rate acts as a level-eect on the
yield curve in both models. In addition,
~
B
x

; = 1;:::; 120 is a decreasing line
indicating that the x-factor shocks mainly aect the short end of the yield curve with
the magnitude of their eect dying out with maturity. Consequently, the x-variable
appears to be the slope-factor of the term structure models. Overall, the yield curve
response pattern to the in
ation and the x-variable shocks estimated by the models
is similar to those suggested by Diebold, Rudebusch and Aruoba (2006) [44].
Finally, as expected,
~
B
s

; = 1;:::; 120 has a shape similar to
~
B
x

; = 1;:::; 120
but with a much sharper decrease to its slope. Indeed, the spread shock mainly aects
the very short end of the yield curve while there is a negligible eect on the medium
and longer term maturities, as measured by both models.
On the other hand, the main dierence between the two models, as depicted in
Figure 3.6, is the magnitude of the yield curve response to the state variables shocks.
In particular, the magnitude of the policy shocks declines with the yield maturities
much faster in Model I than Model II. Consequently, Model II estimates a higher
policy eect on the long term maturities, than Model I. Similarly, Model II indicates
a much higher yield curve response to the in
ation rate. More specically, a one-
standard-deviation in
ation shock is translated to an average (over maturities) eect
of 25bp for Model I and 40bp for Model II. On the contrary, Model I estimates a
76
lower eect (92bp) of an one-standard-deviation x-factor shock to the short end of
the yield curve than Model II (62bp).
Another signicant dierence between the two models is the eect of the state
variable shocks on the long-term maturities. More specically, in Model I, the magni-
tude of the 10-year yield response to the policy rate, the in
ation rate and the x-factor
shocks is almost the same. This is not the case for Model II, where the long end of the
yield curve is vastly more aected by shocks to the policy rate. This results from the
fact that in Model II the dynamics of the in
ation rate and the spread are estimated
independently of the yield curve model. Hence, Model II addresses the ECB's mone-
tary policy rule by taking as given the underlying forces. The estimation of the rest of
the parameters simply reveals the optimal policy rule from the perspective of a yield
curve model. Therefore, Model II mainly uses the policy rate's and the x-factor's
dynamics in order to t the euro area yield curve, and, thus, it underestimates the
in
ation rate's eect on the yield relatively to Model I.
3.5.4 Monetary Policy Rule
In general, the estimation of the term-structure models sheds light on the way
the state variables interact with the yield curve. However, the specic innovative
modeling of the policy rate as a jump diusion, as presented in this analysis, has the
advantage of addressing issues regarding both the direction and the magnitude of the
expected changes in the policy rate from the nancial market's perspective.
To this end, our analysis proceeds with presenting a high-frequency monetary
policy rule, which results from the ane term structure model, and comparing the
estimated high-frequency rule with a simple Taylor rule.
77
High frequency Policy Rule
The way to derive a the high-frequency policy rule (HFPR) from the Ane Term
Structure model (ATS) is to treat the expected changes in the policy rate (E[d
t
]) as
the policy rule and the deviations from this expectation (dJ
t
E[d
t
]) as the monetary
policy shocks. Thus, if the policy shocks are taken to have a zero mean distribution,
the HFPR has the form:
E
t
[d
t
] =2
Y
(Y
t

e
Y )
where Y
t
is the state vector;
e
Y is the target vector, and t corresponds only to the
meeting days.
The ATS considered in this analysis includes four state variables, and consequently
identies four dierent driving forces for the policy rule, namely the policy rate (
t
),
the in
ation rate (
t
), the spread (s
t
) and a proxy for macro information (x
t
). More-
over, the magnitude of each of these driving forces eect on the policy rule is dened
by the distance from its target value (Y
t

e
Y ). The target vales are the mean for all
the state variables, and 2% for the in
ation rate. Therefore, the ECB policy rule, for
the meeting days, is fully dened by the variable's jump intensities (
Y
) and their
eects (Y
t

e
Y ).
The policy rule implied by each model (i.e. Model I and II) is derived by the
estimated values for
Y
;
e
Y , applying the law of iterated expectation:
Model I :
E
t
[
t+1
] = 3:014 0:1515
t
+ 1:4290
t
+ 0:3056s
t
+ 0:2128x
t
(3.15)
Model II :
E
t
[
t+1
] = 2:3650 0:1275
t
+ 1:6394
t
+ 0:4222s
t
+ 0:6316x
t
(3.16)
78
Equations (3.15) and (3.16) describe the HFPR that corresponds to each of the
estimated models.
Furthermore, equations (3.15) and (3.16) allow us to compute the policy rates that
correspond to the estimated ATS models. This can be done by using the estimated
parameters together with the data on the state variables and the euro-area yields.
The values for the latent factor (i.e. the x-variable) are computed by invertingu(:; )
(equation 3.10).
Comparison of the Policy Rules
Taylor Rule
The simplest Taylor rule (TR) uses the in
ation rate (
t
) and the output gap (y
t
) as
explanatory variables for the policy rate (
TR
t
). Note thaty
t
is dened as the output's
percent deviation from its trend. Hence the TR takes the form:

TR
t
= +
t
+
y
t
The estimated TR for the ECB, uses the quarterly average of the euro-zone's
annual in
ation rate, and the (quarterly) Minimum Bid rate for the same sample
period
3
; he percent deviation of the euro-zone's quarterly real GDP (data available
in Eurostat) from its Hodrick-Prescott ltered series is used for the output gap.
Moreover, in order to improve the accuracy of the regressions, the reweighed least
squares regression is used which lowers the regression's weight to points that do
not t well. The estimated parameters are quite close to those proposed by Taylor
3
Regressions on the quarterly euro-area money market rate over the sample period gave similar
results.
79
(1993) [50] for the US target rate (i.e. US: target rate= 3 + 1:5
t
+ 0:5y
t
), or:

t
= 0:4067 + 1:1380
t
+ 0:3607y
t
(3.17)
Figure 3.7 presents the policy rates implied by the two ATS models, the Taylor
rule, and the data on the ECB's Minimum Bid rate. The comparison of the accuracy
of the three estimated policy rules results in three main conclusions.
Figure 3.7: The estimated policy rule by Models I & II, the Taylor's rule, and the
data on the ECB's MBR for the sample period's meeting days.
0 10 20 30 40 50 60 70 80 90
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6

Actual Policy Rate
Model I
Model II
Taylor Rule
First, Model II succeeds in following the actual policy rates particularly well. Its
estimates are quite accurate in terms of both the direction and the magnitude of the
changes in the policy rate, over the whole sample period.
Second, Model I fails to capture the meetings where the policy rate remained
constant. This failure stems from the more volatile state dynamics, and the higher
80
in
ation rate's mean estimated in Model I than those in Model II. These large esti-
mates result in an increased policy rate's change probability for Model I relatively to
Model II. This Model's I discrepancy is more obvious during the periods where there
was no actual policy rate change.
Finally, the policy rate implied by the Taylor rule is, on average, quite close to
the data, but does not possess any high-frequency accuracy, and it is not informative
about either the direction or the magnitude of the policy decisions. This result is
quite intuitive as the original Taylor rule leaves out any high-frequency information
from the yield curve, and this is re
ected in the limited accuracy of the policy rate
changes estimated by a Taylor-type rule.
3.6 Conclusion
In this chapter, two term structure models are estimated in order to analyze the
interaction between the ECB's monetary policy rule and the euro-area yield curve.
The ECB's policy rate enters the state vector as a jump diusion, with jumps at
determined points in time and jump intensities proportional to the state vector (i.e.
the in
ation rate, the spread between the policy rate and the short term rate and a
proxy for aggregate macroeconomic variables ). Furthermore, the fact that the yield
curve is driven by the same factors with the ones included in the policy rule, results
in intuitive economic interpretations for the latent factor; hence, the x-variable is
considered to be a proxy for the macroeconomic variables (i.e. real activity).
The estimation of the models clearly indicates that the policy rate plays a key
role in explaining the forces driving the yield curve. In particular, as monetary policy
shocks mainly aect the medium-term maturities, the policy rate appears to play the
role of the "curvature factor" in the term structure of the yield curve. Moreover, the
81
in
ation shocks shift the whole yield curve (i.e. level factor), and the shocks to the
proxy for the macro variables mainly aect the short-term yields with the magnitude
of the eect decreasing with maturity (i.e. slope factor).
From a policy perspective, the results presented in this chapter, indicate that
the ECB appears to primarily value information that is communicated through the
short end of the yield curve (6-month rate) and mostly aects the medium-term
maturity yields (i.e. 2-year) with a non-negligible eect to both ends of the yield
curve. Furthermore, although announcing the desired level of in
ation rate (i.e. 2%)
vastly improves the communication between the ECB and the market, it also leads
the market to heavily weight the deviation of the current in
ation from 2%; this leads
to the market's perception of the ECB policy rule as in
ation-targeting.
The comparison of the estimated policy rules accuracy clearly implies that the
nancial markets play a fundamental role in optimal policy design. The policy rule
that uses information from the yield curve and allows for interaction between the
policy rate and the yields, can practically pin down the actual ECB policy decisions
with a striking accuracy with regard to the timing, the direction and the magnitude
of the changes in the policy rate. Hence, the main conclusion of this analysis is that
monetary policy estimates that neglect the information available in the yield curve
will perform poorly and consequently will lead to suboptimal policy design.
82
Chapter 4
Periodic New Keynesian Monetary
Models
4.1 Introduction
Many economic phenomena exhibit seasonal behavior. However, in many of the
economic models of these phenomena the seasonal nature is disregarded. Moreover,
in many cases the data accompanying these phenomena come in dierent frequencies:
for example, the Gross Domestic Product data are usually updated every quarter,
while the nancial data, like the short-term interest rate, are available daily.
This analysis presents a class of models which is able to capture the seasonal be-
havior of the economic phenomena. The model's empirical strength and theoretical
validity is illustrated through an example: the central bank intervention. To this
end, a novel extension of a widely studied economic framework: the New Keynesian
Monetary model, is studied. The New Keynesian (NK) Monetary models have been
the standard framework for studying monetary policy, see Clarida,Gali and Gertler
83
(1999) [21] and Lubik and Schorfheid (2004) [32]. Within this literature, the cen-
tral bank (CB) uses simple rules for conducting policy, while the short term rate is
the policy instrument, see Woodford (2003) [53]. However, the standard NK model
builds on a quite unrealistic assumption: the central bank sets the short-term rate
at every period. Our extension of the NK model, which ts the proposed class of
models, relaxes this assumption. Thus, a New Keynesian model where the central
bank intervenes periodically is introduced and utilized to study the consequences that
seasonality has for the model's behavior. The current workhorse is a special case of
the introduced family of models.
Furthermore, the present analysis introduces an estimation technique, appropri-
ate for forward looking models, which utilizes an information structure with more
than one frequency. The seasonal state equations allow us to introduce seasonal
measurement equations, and, thus, the period's state space representation utilizes
all the available information when it becomes available. The absence of restrictive
assumptions makes the estimation technique general, and, thus, could be used to es-
timate any model that has incoming data with dierent frequencies. The technique
is implemented on the NK model: data with dierent frequencies are used, unlike
similar studies (see Lubik and Schorfheide (2004) [32] that use quarterly averages of
the monthly series.
Our choice of the NK model as the most appropriate example of the proposed
seasonal class of models has a valid theoretical motivation. In particular, in a the-
oretical model that incorporates monetary policy intervention there are four time
intervals that must be dened: First, the representative agent's lifetime, which in
the standard NK model is innite; second, the transaction period, which is the time
between two successive agent transactions, and is xed from the structure of the mar-
kets; third, the decision period, which is the time between two successive decisions
84
made by the rms or/and the agents about their future consumption and allocation
of wealth, and he has to remain consistent with them throughout the decision period,
and nally the policy maker's decision period, which is the time between the central
bank's scheduled meetings.
In the standard NK model, similar to the traditional macroeconomic models, there
are two time restrictions. First, the transaction and the decision period are assumed
to coincide, and all the decisions by agents (rms) are made simultaneously. In par-
ticular, at each datet, the agents (rms) plan for the current and the future periods,
while they remain inactive until t + 1. In reality, decisions are made continuously;
they overlap in time, while neither agents nor the private sector coordinate their de-
cisions or remain inactive for any xed period. Although this restriction's eects on
the NK model's are of great importance, this idea is not pursued here.
However, the least intuitive and most unrealistic assumption of the NK model
is that the the policy makers and the agents (rms) decision periods are the same.
There are two arguments that can be raised against this restriction, while taking
for granted that the monetary policy instrument is the short-term rate. First, even
those central banks, that participate actively in the money market (e.g Federal Re-
serve Bank (FRB), European Central Bank (ECB)), do not readjust the short term
rate at every date. Second, policy makers and agents (and/or rms) do not decide
simultaneously. There is a possible confusion: Are the agents and rms assumed to
trade whenever the central bank has a scheduled meeting or do central banks decide
about their policy at every period that the agents and rms trade? Both scenarios
are highly restrictive and possibly misleading.
In order to allow for a more realistic time-setting, one has to consider a model
with dierent timing. Therefore, in the present setting, the underlying economy is de-
scribed by a periodic NK model, denoted as PNK, with the central bank intervening
85
at regular points in time. Between two successive central banks meetings, the agents
continue to make optimal decisions with respect to consumption and savings, while
the short-term rate remains unchanged. There are two main conceptual dierences
between the PNK and the standard NK model, regarding the environment in which
policy decisions are made. In the NK model the CB has all the available information
(i.e. output and in
ation) in order to update the policy rule. Moreover, their inter-
vention pattern gives them the opportunity to immediately respond to any exogenous
destabilizing deviation. By contrast, the PNK framework creates two sources of un-
certainty for the CB's decision: the lack of information (i.e. output is not observable
every subperiod) and the non-intervention subperiod.
Our empirical results suggest that the non-intervention subperiods force the CB
to set a policy rule that over-responds to in
ation and has a limited interest-rate
smoothing coecient and the seasonal lack of output information leads to lower policy
responses indicating that the CB gives less weight to the unobservable information.
Thus, in a scenario where the CB does not intervene every subperiod and does not
have all the available information, the policy rule would be more aggressive with
respect to the available information in order to ensure the economy's stability for the
subperiods that the CB does not intervene.
The impulse response (IR) analysis indicate that the direction of the structural
shocks eects on the state variables remain unchanged: a contractionary demand
shock results in an in
ation and interest rate decrease over time; an in
ation in-
creasing supply shock raises the interest rates, while it results in a output decrease
(below its steady state), and a contractionary monetary policy shock causes output
and in
ation to decrease.
Our framework's seasonality introduces two types of impulse responses (IR): sea-
sonal IRs that concentrate on the structural responses to shocks occurred in a specic
86
subperiod, and periodic IRs that describe the economy's evolution over all the sub-
periods given the realization of a structural shock at each initial subperiod.
The seasonal IRs distinguish between the responses corresponding to shocks oc-
curring during subperiods with and without CB intervention. There are three main
conclusions consistent over all the samples drawn by the analysis of the seasonal
the more a variable is weighted in the policy rule, the more sensitive the economy
becomes to this variable's deviations occurring at the non-intervention subperiods,
and the less sensitive to deviations occurring at the intervention subperiods; second,
the structural responses to the interest-rates exogenous shocks realized during either
the non-interevtion or an intervention supberiod have similar magnitude. Thus, the
unanticipated policy rate's deviations from the rule (during the intervention subperi-
ods) and the unanticipated CB intervention (interest rate shocks realized during the
non-intervention periods capture unananticipated policy intervention) have similar
eects on the economy; nally, the interest rate responses to the structural shocks
are one subperiod lagged when the shocks realize during a non-intervention subpe-
riod, while the interest rate's adjustment back to its steady level is identical for both
the intervention and non-intervention subperiods. Thus, the absence of the monetary
policy intervention results only in the delay of the shocks eect on the interest rates
because during the non-intervention subperiods the interest rates are not aected by
either in
ation or output deviations.
The periodic IRs depict the economy's reversion back to its steady state and
indicate that the sample period's characteristics drive the model's seasonal behavior:
the more volatile the input series the longer the shocks remain in the economy and
the more volatile the structural responses are.
The chapter proceeds as follows: Section 4.2 presents the theoretical model; Sec-
tion 4.3 describes the Periodic New Keynesian (PNK) model and its transformation
87
to its seasonal-independent equivalent; Section 4.4 explains the estimation method
and the estimated models. The estimation results are presented in Section 4.5.
4.2 Periodic Model
Consider an economy with time-varying inter-dependence among the state vari-
ables captured by a time-dependent state equation's transition matrix. In other
words, let the economic environment change regularly over time and call these dier-
ent environments states. Assume that there are N dierent states, n = 0;:::;N 1,
which follow one another and repeat themselves at regular intervals. The time needed
for staten to be completed is named as subperiod (or season), while the corresponding
time for all subperiods to realize is called period.
Hence, our economy can be modeled as a periodic system where time is dened by
the occurring subperiod and the number of periods that have already been completed:
t =n +Nt; t2@
+
with t corresponds to the already realized number of periods.
Furthermore, let X
n+Nt
denote the economy's state vector, and A
n
the seasonal
transition matrix. Note that A
n
represents the n
th
subperiod which repeats itself
every period and, hence A
n
is a periodic matrix:
A
n+Nt
=A
n
;8n = 0;:::;N 1; t2@
+
Therefore the economy's evolution over time takes the form:
X
n+Nt
= A
n
X
(n1)+Nt
+R

n
e
n+Nt
; n = 0;:::;N 1 and t2@
+
(4.1)
88
whereX
n+Nt
2<
Kx1
,A
n
2<
KxK
;8n, ifK is the number of state variables, and
t+Nt
is the vector of independent exogenous disturbances with
n+Nt
N(0;H
n
)
It is important to underline that in this setting the state vector's current values
depend on the previous subperiod's values. However it is possible to write the seasonal
state equations in a form that the state vector depends only on its own lags. That
would require iterating backward equation (4.1) for N subperiods, and would take
the form:
X
n+Nt
=

A
n
X
n+N(t1)
+
N1
X
i=0
R
e
ni
e
ni+Nt
; for n = 0;:::;N 1 (4.2)
where

A
n
=
N1
Y
i=0
A
ni
Furthermore, the seasonal nature of the underlying economy yields a very in-
teresting and helpful result. In particular, we are able to dene a set of seasonal
measurement equations matching the seasonal state equations. This allows us to use
dierent sets of observable variables for the dierent subperiods.
Specically, letY
n+Nt
denote the observable variables at the n
th
subperiod. Then
the seasonal measurement equations take the following form:
Y
n+Nt
=
0
+
n
X
n+Nt
+
n+Nt
; for n = 0;:::;N 1 (4.3)
where
n+Nt
are the measurement errors with
n+Nt
N(0;
y
n+Nt
).
Note that the matrices
n
can dier across the subperiods, and hence, they can
deliver all the season-specic information in order to update the state vector in the
most ecient way. Hence, we can use all the observable variables in order to estimate
the model, regardless their possible seasonal unavailability. Therefore, the system's
89
seasonal state-space representation consists of equations (4.1) and (4.23).
The following section describes how seasonality can be explicitly introduced within
the New Keynesian Monetary models: Sections 4.3.1 and 4.3.2 describe the standard
and the seasonal version of the NK model, and Sections 4.3.3 to 4.3.7 construct the
model's season-independent state-space representation.
4.3 Periodic New Keynesian Model
4.3.1 Standard New Keynesian Model (NK)
The baseline model is in the same spirit as the dynamic general equilibrium
(DSGE) New Keynesian (NK) framework. The common practice is to use the linear
rational expectations model (LRE) as a local approximation for the DSGE's solu-
tion (see Woodford (2003) [53], Lubik and Schorfheide (2003) [32] , Clarida et al.
(2000) [27]). The resulting LRE model is represented by two equations: an inter
temporal (IS) equation capturing the representative agent's (RA) decision problem
and a Philips curve (PC) resulting from a Calvo price staggering environment (for
more details see Calvo (1993) [6]).
In particular, lety
t
be the percent deviation of the current output from the poten-
tial one
1
, and named as the output gap;
t
be the in
ation rate at timet, and dened
as the percent change in the price level (P
t
) between t and t 1 (
t
= log
Pt
P
t1
),
and, nally, let i
t
be the short-term nominal interest rate (i.e. the risk less bond
with 1-period ahead maturity date) controlled by the central bank (CB). Moreover,
the variable's x conditional expectations at time t are denoted as in Woodford and
1
The potential or natural rate of output corresponds to a perfectly
exible pricing framework.
90
Svensoon (2000) [54]:
E
t
[x
t+1
jI
t
] =x
t+1jt
where I
t
is the information set available at time t.
The standard NK model is represented by the log-linearized state equations around
the non-stochastic steady state which are given by:
IS: y
t
= y
t+1jt

1

(i
t

t+1jt
) (4.4)
PC:
t
=
t+1jt
+y
t
(4.5)
where (0< < 1) is the discount factor;
1
(> 0) is the inter-temporal elasticity
of substitution and ( > 0) is the price staggering coecient. Detailed derivation
of the above system of equations can be found in King (2000) [28], or Woodford [53].
Equation (4.4) is the log-linearized approximation of the representative agent's
(consumption) Euler equation around the non-stochastic steady state. Interestingly,
the (IS) equation relates the current output gap directly to its expected future values
and inversely to the current real interest rate which is given by the Fisher equation as:
r
t
=i
t

t+1jt
, where r
t
is the real interest rate. Within the model, monetary policy
(i.e. i
t
), which is conducted through the short-term interest rate, has short-term real
eects.
Similar, equation (4.5) is the log-linearized approximation of the aggregate opti-
mal pricing decision, and represents an expectational Philips curve with slope. The
key simplifying assumption (due to Calvo) is that at every period t, each (monopo-
listically competitive) rm charges the same price with a common and time-invariant
probability , or it optimally adjusts the price with probability 1.
In order to close the model a policy rule (PR), which describes how the short-
term interest rate evolves over time, is dened. To this end, a simple Taylor rule (see
91
Taylor (1993) [50]) is considered, according to which the short-term interest rate, set
by the CB, responds to the current percent deviations of the in
ation rate and the
output gap from their steady state values, while it exhibits an interest rate smoothing
nature, and is given by:
PR: i
t
=i
t1
+ (1)(
t
+
y
t
) (4.6)
where ( < 1) is the smoothing coecient and ;, with ; > 0, dene the
magnitude of the interest rate's response to the in
ation rate and the output gap
respectively.
Equations (4.4), (4.5) and (4.6) describe the simplest version of the standard NK
model, where the central bank intervenes at each datet, which in most models counts
quarters. The following section presents the periodic version of this model according
to which the CB intervenes at regular points in time and not at every date.
4.3.2 Periodic New Keynesian Model (PNK)
Consider an economy identical to the one presented in Section (4.3.1) except of
the central bank's time of intervention: the CB intervenes regularly every N sub-
periods. In order to capture the central bank's behavior pattern a Periodic New
Keynesian model (PNK), falling into the class of models presented in Section (4.2),
is introduced. The PNK's period consists ofn
1
subperiods with CB intervention and
Nn
1
subperiods without. LetI
in
andI
non
denote the subperiods with and without
CB's intervention respectively:
I
in
=fnj subperiods that the CB intervenesg
92
and
I
non
=fnj subperiods that the CB does not interveneg
with #I
in
+ #I
non
=N.
Thus, if n denotes the current subperiod the policy rule has the form:
i
n+Nt
=
8
>
<
>
:
i
n1+Nt
+ (1)(
n+Nt
+
y
n+Nt
) , if n2I
in
i
n1+Nt
, if n2I
non
(4.7)
Moreover, the structural relationships described by equations (4.4) and (4.5) are
independent of the central bank's seasonal behavior, and, hence, they remain un-
changed across all subperiods. So their seasonal form is given by:
y
n+Nt
= y
(n+1)+Ntjn+Nt

1

(i
n+Nt

(n+1)+Ntjn+Nt
) (4.8)

n+Nt
=
(n+1)+Ntjn+Nt
+y
n+Nt
(4.9)
Equations (4.7), (4.8) and (4.9) describe the periodic version of the NK model,
denoted as PNK, which introduces a more realistic intervention pattern for the CB.
The standard model used in the literature, is a special case, with N = 1, #I
in
= 1,
and #I
non
= 0.
The sections that follow describe the PNK's canonical from (Section 4.3.3), its
solution (Section 4.3.6) and its season-independent state-space representation (Section
4.3.7).
4.3.3 Canonical Form
LetX
n+Nt
denote the expanded state vector which consists of the current values of
the structural variables that dene the underlying economy: the output gap (y
n+Nt
),
93
the in
ation rate (
n+Nt
), the short-term interest rate (i
n+Nt
)) and the conditional
expectations of the forward looking variables y
n+1+Ntjn+Nt
and
n+1+Ntjn+Nt
. Thus
for the PNK model X
n+Nt
is a 5x1 vector:
X
n+Nt
= [y
n+Nt

n+Nt
i
n+Nt
y
(n+1)+Ntjn+Nt

(n+1)+Ntjn+Nt
]
0
and the equations (4.7), (4.8), and (4.9) become:
A
n
X
n+Nt
=B
n
X
(n1)+Nt
+R

n+Nt
; n = 0;::;N 1; t2@ (4.10)
where
n+Nt
is the 2x1 matrix of the expectational errors. R

is a season-independent
matrix due to the season-independent structural equations referring to the forward
looking variables:
R

=
0
B
@
0 0 0 1 0
0 0 0 0 1
1
C
A
0
8n (4.11)
For each n2I
in
A
n
and B
n
are the periodic (5x5) structural matrices:
A
n
=
0
B
B
B
B
B
B
B
B
B
B
@
1 0 1= 1 1=
1 0 0
^
(1) 1 0 0
1 0 0 0 0
0 1 0 0 0
1
C
C
C
C
C
C
C
C
C
C
A
; B
n
=
0
B
B
B
B
B
B
B
B
B
B
@
0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0 1 0
0 0 0 0 1
1
C
C
C
C
C
C
C
C
C
C
A
(4.12)
94
For n2I
non
:
A
n
=
0
B
B
B
B
B
B
B
B
B
B
@
1 0 1= 1 1=
1 0 0
0 0 1 0 0
1 0 0 0 0
0 1 0 0 0
1
C
C
C
C
C
C
C
C
C
C
A
; B
n
=
0
B
B
B
B
B
B
B
B
B
B
@
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
1
C
C
C
C
C
C
C
C
C
C
A
(4.13)
where ^
=(1)
and ^ =(1)
4.3.4 Exogenous Shocks
This section introduces three sets of periodic exogenous disturbances: one set of
demand shocksfu
y
n+Nt
g
n=0;:::;N1
); one of cost-push shocksfu

n+Nt
g
n=0;:::;N1
, and one
set of interest-rate shocksfu
i
n+Nt
g
n=0;:::;N1
N(0,
2
i
). Thefu
i
n+Nt
g
n=0;:::;N1
shocks
capture any unanticipated deviations from the policy rule realizing during the inter-
vention periods; for the non-intervention periods u
i
n+Nt
represent any unanticipated
central bank intervention.
The exogenous disturbances are periodic and season-specic, and thus, occur once
every period. Following the literature the structural demand and cost-push distur-
bances, u
y
n+Nt
and u

n+Nt
, are considered persistent, and are given by:
u
y
n+Nt
=
y
u
y
n+N(t1)
+v
y
n+Nt
(4.14)
u

n+Nt
=

u

n+N(t1)
+v

n+Nt
and (4.15)
u
i
n+Nt
N(0,
2
i;n
) (4.16)
wherev
y
n+N(t1)
andv

n+N(t1)
are iid with mean zero and variances
2
y;n
; n = 0;::;N
and
2
;n
; n = 0;::;N, while the autoregressive coecients

and

satisfy :
y
;

2
95
(0; 1).
Let e
n+Nt
be the 3x1 matrix of the seasonal exogenous disturbances:
e
n+Nt
= [v
y
n+Nt
v

n+Nt
v
i
n+Nt
]
0
where e
n+Nt
N(0,H
n
) with H
n
=
0
B
B
B
B
@

2
y;n
0 0
0
2
;n
0
0 0
2
i;n
1
C
C
C
C
A
In the present analysis, the seasonal exogenous disturbances are taken to be inde-
pendent, although this assumption can be easily relaxed.
4.3.5 Season-Independent Canonical Form
This section presents a simple and ecient way to covert the PNK model to its
time-invariant version. To this end, the model period's state equation is constructed.
In this form the model is solvable by standard methods because it has eliminated the
matrices periodicity.
For every period t, the PNK consists of system of N seasonal linear rational
expectations (LRE) equations:
A
n
X
n+Nt
=B
n
X
(n1)+Nt
+R

n+Nt
; 8n = 0;:::;N 1 (4.17)
The rst objective is to write each seasonal LRE with a lag interval equal to
the number of subperiods. Therefore equation (4.17) is iterated backwards for N
subperiods. A key challenge it to keep truck of the expectational errors because the
expectational errors which realize during past subperiods are zero.
To keep the model tractable the seasonal matrices A
n
are take to be invertible,
similar to Sims (2002) [48]. In case of invertibility, the QZ decomposition for matrix
96
An allows to continue with the solution. Using backward iteration, equation (4.17)
leads to:
A
n
X
n+Nt
=
^
B
n
X
n+N(t1)
+R

n+Nt
; 8n = 0;:::;N 1 (4.18)
where
^
B
n
=B
n
N1
Y
i=1
(A
ni
)
1
B
ni
Let
~
X
n+Nt
denote the extended state vector which accounts for the persistent
structural shocks: u
y
n+Nt
and u

n+Nt
:
~
X
n+Nt
=

X
n+Nt
u
y
n+Nt
u

n+Nt

0
=

y
n+Nt

n+Nt
i
n+Nt
y
(n+1)+Ntjn+Nt

(n+1)+Ntjn+Nt
u
y
n+Nt
u

n+Nt

0
By denition the exogenous shock are subperiod-specic and realize once every
period. Hence, taking this into account the extended seasonal state-equations that
include the exogenous disturbances have the form:
~
A
n
~
X
n+Nt
=
~
B
n
~
X
n+N(t1)
+
~
R
e
e
n+Nt
+
~
R

n+Nt
; 8n = 0;:::;N 1 (4.19)
where
~
R
e
=
0
B
B
B
B
@
0 0 1 0 0 0 0
0 0 0 0 0 0 1
0 0 0 0 0 1 0
1
C
C
C
C
A
0
;
~
R

=
0
B
@
0 0 0 1 0 0 0
0 0 0 0 1 0 0
1
C
A
0
(4.20)
The augmented periodic transition matrices,
~
A
n
2 <
7x7
;
~

n
2 <
7x7
, are given
97
by:
~
A
n
=
0
B
@
A
n

1
0
5x2
I
2x2
1
C
A
; with
1
=
0
B
B
B
B
B
B
B
@
1 0
0 1
0 0
.
.
.
.
.
.
1
C
C
C
C
C
C
C
A
;
~
B
n
=
0
B
@
^
B
n
0
5x2
0
5x2

2
1
C
A
; with
2
=
0
B
@

y
0
0

1
C
A
where I
2x2
is the 2x2 identity matrix, and 0
5x2
is the 5x2 matrix of zeros.
The period's state vector (S
t
) consists of all the seasonal extended state vectors:
S
t
= [
~
X
Nt
~
X
1+Nt
:::
~
X
N1+Nt
]
0
Similarly, the period's exogenous disturbances (~ e
t
) and expectational errors (~
t
) are
given by:
~ e
t
= [e
Nt
e
1+Nt
::: e
N1+Nt
]
0
and ~
t
= [
Nt

1+Nt
:::
N1+Nt
]
0
Thus the season-independent canonical form of the model is given by:

0
S
t
=
1
S
t1
+
e
~ e
t
+

~
t
(4.21)
where
0
;
1
; are time-independent block diagonal matrices with their diagonal
98
formed by
~
A
n
;
~

n
respectively, or:

0
=
0
B
B
B
B
B
B
B
@
~
A
0
0 :::
0
~
A
1
:::
.
.
.
.
.
.
.
.
.
0 :::
~
A
N1
1
C
C
C
C
C
C
C
A
2<
(NK)x(NK)
;
1
=
0
B
B
B
B
B
B
B
@
~
B
0
0 :::
0
~
B
1
:::
.
.
.
.
.
.
.
.
.
0 :::
~
B
N1
1
C
C
C
C
C
C
C
A
2<
(NK)x(NK)
Similarly
e
;

are given by:

e
=
0
B
B
B
B
B
B
B
@
~
R
e
0 :::
0
~
R
e
:::
.
.
.
.
.
.
.
.
.
0 :::
~
R
e
1
C
C
C
C
C
C
C
A
2<
(NK)x(3N)
;

=
0
B
B
B
B
B
B
B
@
~
R

0 :::
0
~
R

:::
.
.
.
.
.
.
.
.
.
0 :::
~
R

1
C
C
C
C
C
C
C
A
2<
(NK)x(2N)
where K=7 for the PNK model.
4.3.6 Solving the Periodic New Keynesian Model (PNK)
The PNK model, presented in the previous section, is an extended but standard
linear rational expectations (LRE) model. The solution to these models was rst pre-
sented by Blanchard and Kahn (1980) [3], and was generalized by Sims (2002) [48].
It is widely known that the LRE models may have multiple equilibria (i.e. indetermi-
nacy). Although the conditions determining the solution's existence and uniqueness,
is of great interest and importance, this analysis is not pursued here. However, it
is worth mentioning that the stability conditions of the PNK model depend on the
model's season-independent canonical form, captured by equation (4.21), and not on
the seasonal PNK. In other words, the PNK may have a unique and stable solu-
tion even when there is an explosive seasonal system given that it is followed by a
99
subsequent damping subperiod.
The present analysis is restricted within the model's determinant region, and thus,
the model's solution, similar to Sims (2002), is given by:
S
t
=

1
S
t1
+

e
~ e
t
(4.22)
4.3.7 Season-Independent State Space Representation
Let Y
n+Nt
denote the observable variables at the n
th
subperiod. Thus, the seasonal
measurement equations have the following form:
Y
n+Nt
=
0
n
+
1
n
X
n+Nt
+

n

n+Nt
; for n = 0;:::;N 1 (4.23)
where
n+Nt
are the seasonal measurement errors with
n+Nt
N(0;
n+Nt
).
Similar to the construction of the period's state equation, the period's measure-
ment equation is given by:
Z
t
=
~

0
+
~

1
S
t
+
~

~
t
whereZ
t
is the period's vector of observables: Z
t
= [Y
Nt
::: Y
N1+Nt
]
0
; ~
n+Nt
is the
period's vector of measurement errors: ~
n+Nt
= [
Nt
:::
N1+Nt
]
0
, and
~

0
,
~

1
and
~

are the season-independent block diagonal matrices with their diagonal formed by

0
n
;
1
n
;

n
; for n = 0;:::;N 1 respectively.
Thus the period's season-independent state-space representation is given by:
S
t
=

1
S
t1
+

e
~ e
t
(4.24)
Z
t
=
~

0
+
~

1
S
t
+
~

~
t
(4.25)
100
where t counts periods.
This state-space representation distinguishes between the subperiods with, and
without CB interventions, and hence, utilizes observable variables with dierent fre-
quencies. The following Section elaborates further on this basic advantage of the
presented framework through an example.
4.4 Empirical Analysis
4.4.1 Estimated PNK Models
Our empirical analysis studies the consequences that seasonality has for the NK
model's behavior. To this end, two PNK models with dierent seasonal patterns, are
estimated: the rst has quarterly period with three monthly subperiods (i.e. N = 3)
and is referred to as the Monthly Model (MM); the second one has also quarterly
period but it has one subperiod during which the CB intervenes, and is called the
Quarterly Model (QM).
Since the Federal Reserve Bank's (FRB) regular meetings are scheduled every six
weeks (1.5 months), without loss of generality, the Monthly model (MM) takes the
rst two subperiods of each period to be the policy intervention ones:
I
n
= [0; 1]; I
non
= 2
The MM's seasonal state equations are given by equation (4.24) for N=3:
S
t
=

1
S
t1
+

e
~ e
t
101
where
S
t
= [
~
X
Nt
~
X
1+Nt
~
X
2+Nt
]
0
; ~ e
t
= [e
Nt
e
1+Nt
e
2+Nt
]
0
with e
n+Nt
N(0,H
n
) and H
n
=
0
B
B
B
B
@

2
y
0 0
0
2
;n
0
0 0
2
i;n
1
C
C
C
C
A
The demand shocks distribution is period-specic: v
y
Nt
; v
y
1+Nt
; v
y
2+Nt
N(0,
2
y
),
and the supply and the interest-rate shocks distributions are season-specic. In this
way the number of observable variables coincide with the number of exogenous shocks.
The seasonal vector of observables (Y
n+Nt
) is composed by the in
ation and the
interest rate series (Section 4.4.5 describes the construction of the time series):
Y
n+Nt
= [
n+Nt
i
n+Nt
]
0
; for n = 0; 1; 2
and, thus, the seasonal measurement equations take the form:
Y
n+Nt
=
1
X
n+Nt
; n = 0; 1; 2
with

1
=
0
B
B
B
B
@
0 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
1
C
C
C
C
A
The output data, denoted by ay
t
, are taken to be released the period's rst sub-
period and to correspond to the overall periods output:
ay
t
=y
Nt
+y
1+Nt
+y
2+Nt
102
Thus, the period's state vector consists of the quarter output and the seasonal
state vectors:
Z
t
= [ay
t
Y
Nt
Y
1+Nt
Y
2+Nt
]
0
and the period's measurement equation is given by:
Z
t
=
~

1
S
t
and
~

1
is a season-independent matrix :
~

1
=
0
B
B
B
B
B
B
B
@
1=3 0 ::: 1=3 0 ::: 1=3 0 :::

1
0 :::
0 :::
1
0 :::
0 :::
1
1
C
C
C
C
C
C
C
A
Thus the state-space representation precisely captures the data's information set.
In particular, we match the quarterly output data to the period's average output as
the rst row of
~

1
reads:
The Quarterly model (QM) considers only one sub-period with CB intervention :
N=1, I
Q;in
= 1; I
Q;non
= 0, and thus the seasonal and the period's state equations
coincide:
S
Q
t
=
;Q
1
S
Q
t1
+
;Q
e
~ e
Q
t
where
S
Q
t
=

y
t

t
i
t
y
t+1jNt

t+jt
u
y
t
u

t

0
; ~ e
t
= [v
y
t
v

t
u
i
t
]
0
with v
j
t
N(0,
2
j
); for j=fy; ; ig
103
The vector of observables (Z
Q;t
) is composed by the quarterly averages of the out-
put, the in
ation and the interest rate series, and the period's measurement equations
have the following form:
Z
Q
t
=
~

1;Q
S
t
with

1;Q
=
0
B
B
B
B
@
1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
1
C
C
C
C
A
;
In principle the QM is a standard NK model, and thus its estimates are comparable
to those reported within the literature.
4.4.2 Estimation Method
The Bayesian approach is used for our empirical analysis, as in Smets and Woot-
ers (2004) [20]. The Bayesian method utilizes an information set broader than the
one delivered by the data: information coming from other related studies, like mi-
croeconomic empirical estimates, or even personal beliefs based on economic theory,
is used in order to form a set of prior distributions for the parameters. These prior
distributions play a basic role in determining the parameters posterior distribution
as they used to weight the likelihood function.
In particular, if denotes the vector of parameters to be estimated, then the
posterior density (p(jY )) is proportional to the model's likelihood function (L(jY ))
and the prior density p().
p(jY )/L(jY )p()
104
where / denotes proportionality. For a detailed description of the Bayesian
method see Robert and Casella (1999) [43].
The model's likelihood function (L(jY )) needs to be computed. In principle, a
seasonal model like the one presented in Section 4.2 could be estimated by a periodic
Kalman Filter (KF), as the KF can deal with seasonal state-space representation: if
the seasonal systems are independent, the seasonal log-likelihood (L(jY
n+Nt
)) can
be sequentially calculated by feeding the seasonal state-space representation in the
KF (for details see Hamilton (1994) [23]). Section 4.4.3 describes the KF update
equations which take into account the model's seasonality.
However, using the seasonal state-space representation is not the appropriate ap-
proach when the model includes forward-looking components, like the New Keynesian
Monetary model. The forward looking models include expectational errors conditional
on the current subperiod which forbid either to treat each subperiod independently,
or to iterate backward the state equations similar to equation (4.2). The way to
proceed is to construct the model's time invariant state-space representation, as in
Section 4.3.7.
Thus, for the estimation of the PNK models the period's likelihood function
(L(jY
t
)) is computed by the Kalman Filter (KF). The period's measurement equa-
tions capture the seasonal information availability, and pass this information to the
Kalman Filter's update equations. Therefore, the KF, at every subperiod, uses only
the available data to update the hidden state's estimates and compute the period's
likelihood function.
In general the standard Kalman Filter, induce the inversion of large matrices. This
problem is augmented for thee PNK models, as there are subperiods with a reduced
number of observable variables, and, thus, entire rows of the measurement equation's
matrix become zero. The univariate approach introduced by Koopman and Durbin
105
(1998) [29],and described in Section 4.4.4, is used in order to overcome the problematic
matrix inversion. The basic idea of this algorithm is to convert the multivariate state
space model into a univariate model of series and apply the univariate ltering and
smoothing to avoid matrix inversion.
4.4.3 Kalman Filter with Seasonal State-Space representa-
tion
The seasonal state-space representation has the form
X
n+Nt
= A
n
X
(n1)+Nt
+R

n
e
n+Nt
; n = 0;:::;N 1 and t2@
+
Y
n+Nt
=
n
X
n+Nt
+W
n+Nt
(4.26)
where X
n+Nt
is the state vector, and Y
n+Nt
is the vector of observables. Moreover,

t+Nt
is the vector of independent exogenous disturbances and W
n+Nt
are the mea-
surement errors with W
n+Nt
N(0;
y
n+Nt
).
Hence, following the standard Kalman Filter, the one-step ahead prediction error
(e
n
N
t
) takes the form:
e
n+Nt
= Y
n+Nt
E[Y
t
n +NtjY
n+Nt1
]
= Y
n+Nt

n1
X
n+Nt1
with variance matrix:
V
y
n+Nt
= var(Y
n+Nt
jY
n+Nt1
) =var(e
n+Nt
)
=
n
V
x
n+Nt

0
n+Nt
+
y
n+Nt
106
where V
x
n+Nt
=var(X
n+Nt
jY
n+Nt1
) and covariance matrix:
C
n+Nt
= cov(X
n+Nt
;Y
n+Nt
jY
n+Nt1
)
= V
x
n+Nt

0
n
Then, given the initial conditions (i.e. X
1
; V
x
1
) the update equations become:
X
(n+1)+Nt
= A
n+1
(X
n+Nt
+C
n+Nt
(V
y
n+Nt
)
1
e
n+Nt
)
V
x
(n+1)+Nt
= A
n+1
(V
x
n+Nt
C
n+Nt
(V
y
n+Nt
)
1
C
0
n+Nt
)A
0
n+1
+R
n+1

x
n+Nt
R
0
n+1
In general the PKF, similar to the standard Kalman Filter, induce the inversion
of large matrices. In our case this problem is augmented as there are seasons that
the number of the observable variables reduce, and, therefore, entire rows of the G
n
matrix become zero. In order to overcome the problematic matrix inversion we build
on the univariate approach of Koopman and Durbin (2000) for ecient estimation.
The basic idea of this algorithm is to convert the multivariate state space model into
a univariate model of series and apply univariate ltering to avoid matrix inversion.
In the next section we describe the main steps need to be taken for the periodic model
presented in this chapter.
4.4.4 Univariate Optimal Filtering and Smoothing
Let I be the number of observable seasonable variables, and T be the total
number of observable periods. The key transformation for the Koopman and Durbin
procedure is to decompose the observable variables (Y
n+Nt
) and into their scalar
107
components:
Y
n+Nt
= [y
1
n+Nt
::: y
I
n+Nt
]
0
; 8 n = 0;:::;N 1; and N = 1;:::T
Moreover, the same univariate decomposition applies to the measurement errors:
W
n+Nt
= [w
1
n+Nt
::: w
I
n+Nt
]
0
; 8 n = 0;:::;N 1; and N = 1;:::T
while the corresponding observation system matrices become:

y
n+Nt
=
0
B
B
B
B
@
(
y;1
n+Nt
)
2
0 :::
0
.
.
. 0
0 ::: (
y;I
n+Nt
)
2
1
C
C
C
C
A
and

n
= [
1
n
:::
I
n
]
0
; 8 N = 1;::T
wheref
i
n
g
i=1;::;I
are 1xK row matrices.
Similarly, the state vector (X
n+Nt
) and
X
n+Nt
= [x
1
n+Nt
::: x
K
n+Nt
]
0
; 8n = 0;::;N 1; N = 1;::T
Y
n+Nt
= [fy
i
n+Nt
g
i=1;::;I
n=0;::;N1; N=1;::T
)
Following the standard KF the one-step ahead prediction error for thei
th
variable
108
(e
n
+Nt;i) takes the form:
e
i
n+Nt
= y
i
n+Nt;i
E[y
t
n +Nt;ijY
n+Nt1;i
]
= Y
n+Nt
G
n+Nt1
X
n+Nt1
with variance matrix:
V
y
n+Nt
= var(Y
n+Nt
jY
n+Nt1
) =var(e
n+Nt
)
= G
n+Nt
V
x
n+Nt
G
0
n+Nt
+
y
n+Nt
where V
x
n+Nt
=var(X
n+Nt
jY
n+Nt1
) and covariance matrix:
C
n+Nt
= cov(X
n+Nt
;Y
n+Nt
jY
n+Nt1
)
= V
x
n+Nt
G
0
n+Nt
4.4.5 Data
The empirical analysis uses data on the US output, the US in
ation rate and the
Fed Funds target rate (FFT). Similar to the monetary policy literature, three sample
periods are considered: a pre-Volcker period, from January 1960 to December 1979;
a Volcker - Greenspan, period from January 1980 to December 1992, and a post-1993
sample, from January 1993 to December 2007. The present section describes the
construction of the time series used for the Monthly model (MM); for the estimation
of the Quarterly model (QM) are used the quarterly averages of the constructed
in
ation and policy rate series, together with the quarterly output series are.
The demeaned quarterly per capita US output growth series is used in the esti-
109
mation, and is constructed by:
g
t
= 100 (log
RGDP
t
Pop
t
log
RGDP
t4
Pop
t4
)
where RGDP
t
is the seasonally adjusted quarterly data on the annual real US GDP
(in chained 2000 dollars) extracted from the Bureau of Economic Analysis, and Pop
t
is the annual data on the US population (available by the United States Census
Bureau) taken to remain constant throughout a given year.
Figure 4.1 graphs the quarterly data on the annual US output per capita (upper
graph) and US output growth (lower graph) from 1960 to 2007.
Figure 4.1: Annual US output per capita (upper graph) & Annual US output growth
(lower graph) from 1960 to 2007.
1960 1970 1980 1990 2000 2007
0
5
10
15
x 10
12
US OUTPUT per capita (1960−2007)
1960 1970 1980 1990 2000 2007
−4
−2
0
2
4
US OUTPUT GROWTH (1960−2007)
The in
ation time series correspond to the demeaned series of the monthly US
in
ation rate :

n+Nt
=
1
12
(log
CPI
n+Nt
CPI
n+N(t4)
) 100
110
Figure 4.2: US annual in
ation rate (1960-2007).
1960 1970 1980 1990 2000 2007
0
1
2
3
4
5
6
US INFLATION RATE (1960−2007)
whereCPI
n+Nt
is the monthly series on the US Consumer Price Index (CPI)extracted
by the Global Financial Database (www.globalnancialdata.com). Figure 4.2 depicts
the monthly series of the annual US in
ation rate.
For the nominal interest rate are used monthly data on the US Fed Ocial Dis-
count rate for the pre-Volcker period (1960 - 1979), and the Fed Funds Ocial Target
rate thereafter (i.e. 1980 - 2007). Both time series are available on the Global Finan-
cial Database and graphed in Figure 4.3. The extracted data correspond to the annual
interest rates, and hence for consistency purposes they are converted to monthly rates
(i.e. divided by 12).
4.4.6 Prior Distributions
In general, the choice of the parameters prior distributions is based on the re-
searcher's beliefs combined with economic theory's principals. In the present empirical
111
Figure 4.3: US FED Discount rate (1960-1979) & US FED Target rate (1980-2007).
1960 1965 1970 1975 1979
0
5
10
15
US FED DISCOUNT RATE (1960−1979)
1980 1985 1990 1995 2000 2007
0
5
10
15
20
US FED TARGET RATE (1980−2007)
analysis the choice of the priors is motivated by either values widely accepted by the
literature, or by an empirical analysis of the data. All parameters are considered to
be a priori independent, and the priors are truncated only within the determinacy
region. Moreover, the discount factor is not estimated but is taken to be equal to
0.9. Table 4.1 reports the means and the standard deviations for the set of priors
used in our empirical analysis, denoted by Priors 1.
The prior mean for the Philips curve slope () is set to 0.5, following the micro-
study by Bils and Klenow (2004) [2], which reports that an average 26% of US prices
are changed every 3.3 months. For the coecient of risk aversion () the prior mean
and standard deviation are set to one: the prior standard deviation is taken to be
large in order to allow for increased changes, due to lack of widely accepted values
regarding .
The in
ation rate for the rst sample period (i.e. 1960 - 1979) is characterized
by a high mean and volatility. A plausible explanation, presented by Clarida, Gali
112
and Getler (1999) [21], is that the monetary policy authorities followed a passive
monetary policy (i.e. < 1) indicating indeterminacy for the NK model. However,
our estimation is conditioned within the determinacy region even for the pre-Volcker
period. Thus, the prior means and the standard deviations for is set to 1.5 for the
Volcker-Greenspan and the post-1993 periods and 1.1 for the pre-Volcker period; for

the prior mean is set to 0.25 for all the sample periods. The priors for the interest
rate smoothing coecient () and the variance of the monetary policy exogenous
shock (v
i
) are derived from the following Ordinary Least Squares (OLS) regression,
conducted for each sample:
i
t
=
1
i
t1
+
2

t
+
3
y
t
+v
i
t
Moreover, using equations (4.8) and (4.9), an indicator time series for the struc-
tural exogenous shocks u
y
, u

is constructed for each sample. These indicator series
are used to t an AR(1) model: the variances of the tted AR(1) models are used as
the prior means for the variances of the exogenous disturbances v
y
, v

.
However, a second set of priors, denoted by Priors 2, intends to check the NK
model's sensitivity to the policy rule's specication. To this end, Priors 2 restrict the
interest-rate smoothing coecient () to be zero. The comparison of the resulting
QM and MM estimates evaluates the eect of the seasonal CB non-intervention on
the NK model's sensitivity to the policy rule's specication. Section 4.5.3 elaborates
further on the comparison over the estimation results regarding the dierent prior
distributions.
113
Table 4.1: Prior Distributions: Priors 1
Density Mean Std.
Structural Parameters
Gamma 1.50
1
0.10

Gamma 0.25 0.10
Gamma 0.50 0.10
Beta 0.75 0.20
Gamma 1.00 1.00

y
Beta 0.50 0.10

p
Beta 0.50 0.10
Standard Deviation of Shocks
u
y
Inv. Gamma 0.41 0.26
u

n
, n=0,1,2 Inv. Gamma 0.31 0.22
u
i
n
, n=0,1,2 Inv. Gamma 0.18 0.09
1
= 1.1 for the pre-Volcker period
4.5 Results
The empirical results refer to the estimates of the Monthly model (MM) and the Quar-
terly model (QM) for all the three sample periods: the pre-Volcker period (1960-1979),
the Volcker-Greenspan period (1980-1992) and the post-1993 period (1993-2007). The
main goal of the present analysis is to empirically evaluate the consequences that both
the seasonality and the central bank's non-intervention have for the NK model's be-
havior. To this end, Section 4.5.1 compares the estimates over the two models: QM
versus MM; Section 4.5.2 studies the model's sensitivity to the exogenous distur-
bances in terms of an impulse response analysis. The validity and robustness of the
basic conclusions are checked by the re-estimation the QM and MM models using a
non interest-rate smoothing policy rule. Section 4.5.3 elaborates on the results of the
estimation.
114
4.5.1 Quarterly versus Monthly Model Estimates
The QM model is identical to the standard NK model, and thus, the parameters
estimates for the QM are comparable to the ones reported within the literature. For
the Pre-Volcker period, the 90% condence intervals of the estimated policy param-
eters (i.e. ^ 2 [0:9231; 1:2912], ^
2 [0:2386; 0:5141], ^ 2 [0:8925; 0:9535]) overlap
with those reported by Lubik and Schorfheide (2003) [30], ^ 2 [0:81; 0:99]; ^
2
0:03; 0:27]; ^ 2 [0:43; 0:65] for almost the same sample period (1960:I - 1979:II). The
dierences between the estimates yield by the demeaning of the data used in our em-
pirical analysis ; for the Volcker-Greenspan and the post-1993 periods, our estimates,
^ = 1:5798; ^
= 0:4194; ^ = 0:7404 and ^ = 1:6076; ^
= 0:4916; ^ = 0:7584, indi-
cates analogous dynamics with those reported by Lubik and Schorfheide (2005) [31],
^ = 1:51; ^
= 0:69; ^ = 0:76, for a sample period between 1983:I and 2002:IV.
Tables 4.2, 4.3 and 4.4 report the parameters posterior means and the 90% con-
dence intervals for all the models and samples, based on draws from the estimated
posterior distributions generated by Markov Chain Monte Carlo methods. The com-
parison of the estimates, across the QM and MM models, yields the same qualitative
results for all the samples: the policy rule's responses to in
ation and the stuctural
shocks persistence are higher for the MM than the QM; in contrast, the policy re-
sponses to the output gap, the interest-rates smoothing coecient (
1
), the Phillips
curve's slope and the risk aversion coecient are smaller for the MM than the QM.
In particular, for the pre-Volcker period the estimates for the policy response to
in
ation (i.e parameter ) increases from 1.0879 for the QM to 1.7168 for the MM;
for the Volcker-Greenspan period grows from 1.5798 (QM) to 2.1155 (MM), and
for the post-1993 period from 1.6076 to 2.1848. This persistent increase in the
estimates over all the samples indicates that the non-intervention subperiod forces
115
Table 4.2: Estimation results for the PNK model: Pre-Volcker Sample (1960- 1979)
Quarterly Model (QM) Monthly Model (MM)
Mean 90% Interval Mean 90% Interval
1.0879 0.9231 1.2912 1.7169 1.6190 1.8167

0.3724 0.2386 0.5141 0.0247 0.0155 0.0348
0.4564 0.4555 0.4572 0.2326 0.1807 0.2878
0.9222 0.8925 0.9535 0.2223 0.1462 0.2844
0.2528 0.4206 2.0358 0.3939 0.3079 0.4668

y
0.4616 0.3149 0.6093 0.9483 0.9277 0.9677

p
0.3299 0.2645 0.4142 0.6901 0.6143 0.7400
u
y
0.6031 0.5046 0.7190 0.1487 0.1179 0.1788
u

0
0.1001 0.0890 0.1102 0.1079 0.0914 0.1225
u

1
0.4234 0.3218 0.5164
u

2
0.0944 0.0810 0.1072
u
i
0
0.0556 0.0462 0.0642 0.0670 0.0571 0.0760
u
i
1
0.0639 0.0557 0.0721
u
i
2
0.0498 0.0420 0.0594
the CB to over-respond to in
ation during the subperiods that it intervenes.
The dierence between the QM and the MM estimates of the policy responses to
output is much sharper: for the pre-Volcker period
decreases from 0.3724 for the
QM to 0.0247 for the MM; for the Volcker-Greenspan drops from 0.4194 to .0235, and
from 0.4619 (QM) to 0.0708 (MM) for the post-1993. This sharp decrease is justied
by the seasonal lack of output data, and underlines that the CB gives less weight to
the variable that is not observable when the policy decisions are made.
The seasonal lack of CB intervention fully justies the sharp decrease is the esti-
mates for the interest-rate smoothing coecient: drop from 0.9222 (QM) to 0.2223
(MM) for the pre-Volcker period; from 0.7404 to 0.2310 for the Volcker-Greenspan pe-
riod and from 0.7584 to 0.3589 for the Post-1993 period. During the non-intervention
subperiods the interest rate remains unchanged within the Monthly model (MM)
116
Table 4.3: Estimation Results for the PNK model: Volcker-Greenspan Sample(1980-
1992)
Quarterly Model Monthly Model
Mean 90% Interval Mean 90% Interval
1.5798 1.4039 1.7510 2.1155 1.9328 2.2473

0.4194 0.2692 0.5347 0.0235 0.0099 0.0392
0.4887 0.3626 0.6271 0.2053 0.1434 0.2641
0.7404 0.6488 0.8112 0.2310 0.1519 0.3257
1.0442 0.4176 1.6321 1.3744 1.0983 1.6711

y
0.5081 0.3965 0.6343 0.8827 0.8363 0.9284

p
0.3665 0.2660 0.4680 0.9302 0.9044 0.9595
u
y
0.5904 0.4517 0.7786 0.1361 0.1115 0.1638
u

0
0.1208 0.0931 0.1467 0.1320 0.1067 0.1566
u

1
0.4572 0.3154 0.5754
u

2
0.1222 0.1042 0.1469
u
i
0
0.1316 0.1081 0.1563 0.1587 0.1252 0.1976
u
i
1
0.1841 0.1494 0.2131
u
i
2
0.1449 0.1181 0.1728
resulting in fully smoothed interest rates by construction. Hence, during the inter-
vention subperiods the CB need to assign a smaller interest-rate smoothing coecient.
There are mainly two conceptual dierences between the QM and the MM, re-
garding the environment in which the policy decisions are made, which justify these
consistent dierences in their estimates. In the QM the CB has all the available
information in order to update the policy rule while the intervention pattern gives
them the opportunity to immediately respond to any exogenous destabilizing devia-
tion. On the contrary, the MM accounts for two sources of uncertainty for the CB's
decision: the lack of information due to the quarterly observable output and the non-
intervention subperiods. The estimation results shed light on the consequences of
these conceptual dierences.
117
Table 4.4: Estimation Results for the PNK model: Post-1993 Sample (1993- 2007)
Quarterly Model Monthly Model
Mean 90% Interval Mean 90% Interval
1.6076 1.4435 1.7638 2.1848 1.9968 2.3531

0.4619 0.3255 0.5829 0.0708 0.0354 0.1087
0.4599 0.4982 0.6137 0.3361 0.2624 0.4122
0.7584 0.6868 0.8259 0.3589 0.2575 0.4806
0.0963 0.0439 0.1477 0.4601 0.3663 0.5518

y
0.8004 0.7374 0.8755 0.9072 0.8683 0.9432

p
0.6070 0.4940 0.7112 0.7693 0.6685 0.8823
u
y
0.5728 0.3765 0.7587 0.1525 0.1220 0.1800
u

0
0.1059 0.0885 0.1201 0.1193 0.0997 0.1393
u

1
0.2937 0.2216 0.3539
u

2
0.1100 0.0928 0.1280
u
i
0
0.0678 0.0515 0.0833 0.1285 0.1028 0.1598
u
i
1
0.0842 0.0497 0.1091
u
i
2
0.0696 0.0481 0.0905
The non intervention subperiods have two basic results: force the CB to over-
respond to in
ation in order to ensure the economy's stability for the seasons which
they do not intervene, and lead the CB to care less about smoothing the interest
rates. On the other hand, the output's seasonal lack of information leads to lower
estimates for the policy rule's response to output indicating that the CB counts more
on the available information in order to stabilize the economy.
Thus, within the MM where the CB does not intervene every subperiod and does
not have all the available information, the policy rule is more aggressive with respect
to the available information in order to ensure stability for the subperiods that the
CB does not intervene; within the QM that the monetary authorities intervene every
period and make decisions in an information rich environment, the policy rule is more
conservative with respect to in
ation, and weight more the output gap, as the CB
118
can correct their policy next period, if needed.
The striking example for the dierences between the two models is the policy rule's
estimates for the Pre-Volcker period: the QM, in line with the literature, estimates a
marginally passive policy rule; a feature that many researchers used as an excuse for
the overall economically problematic period. However, within the MM perspective
the policy rule was active suggesting that explaining the period's problems as a result
of a passive rule, if not wrong, is certainly doubtful.
Figures 4.4, 4.5 and 4.6 graph the posterior distributions for the policy coecients
(;
; ) estimates for all the samples and models, and indicate that the QM and
the MM estimates are indeed statistically dierent.
Moreover, the QM estimates for the Philips curve slope are comparable to the
values reported in other similar studies: for the pre-Volcker period (1960 - 1979)
the mean estimate for is 0.4564; for the Volcker-Greenspan period (1980 - 1992)
is 0.4887, and for the post-1993 period (1993 - 2007) is 0.4599. Similarly, Gali and
Rabanal (2004) [22] report a mean estimate of 0.53 for the period 1948 to 2002;
Schorfheide (2005) [47] estimate to be 0.55 for the period 1960 to 1997, while
Rabanal and Rubio-Ramirez (2003) [40] , (2005) [41] estimate to be 0.77 for a
sample period from 1960 to 2001. However, the corresponding MM estimates are
much smaller: for the pre-Volcker period (1960 - 1979) drops from 0.4564 (QM) to
0.2326 (MM) ; for the Volcker-Greenspan period (1980 - 1992) from 0.4887 to 0.2053,
and for the post-1993 period (1993 - 2007) from 0.4599 to 0.3361.
In contrast, the estimates of the coecient of risk aversion () is rather increased
in the MM than in the QM: for the pre-Volcker period (1960 - 1979) from 0.2528
(QM) raises to 0.3939 (MM) ; for the Volcker-Greenspan period (1980 - 1992) from
1.0442 to 1.3744, and for the post-1993 period (1993 - 2007) from 0.0963 to 0.4601.
119
Figure 4.4: Prior & Posterior Distributions for the policy coecients (;
; ), for
the MM (a) and the QM (b) model, over the pre-Volcker period
1 1.5 2
0
1
2
3
4
5
6
alpha
0 0.2 0.4 0.6
0
10
20
30
40
50
60
gamma
0.2 0.4 0.6 0.8
0
1
2
3
4
5
6
7
8
9
rho
(a) Monthly Model: 1960-1979
0.6 0.8 1 1.2 1.4 1.6
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0.2 0.4 0.6 0.8
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
gamma
0.4 0.6 0.8
0
5
10
15
20
rho
(b) Quarterly Model: 1960-1979
120
Figure 4.5: Prior & Posterior Distributions for the policy coecients (;
; ), for
the MM (a) and the QM (b) model, over the Volcker-Greenspan period
1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
alpha
0 0.2 0.4 0.6
0
5
10
15
20
25
30
35
40
45
gamma
0 0.2 0.4 0.6 0.8
0
1
2
3
4
5
6
7
rho
(a) Monthly Model: 1980-1992
1.2 1.4 1.6 1.8 2
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0.2 0.4 0.6 0.8
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
gamma
0.4 0.6 0.8
0
1
2
3
4
5
6
7
8
rho
(b) Quarterly Model: 1980-1992
121
Figure 4.6: Prior & Posterior Distributions for the policy coecients (;
; ), for
the MM (a) and the QM (b) model, over the post-1993 period
1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0 0.2 0.4 0.6
0
2
4
6
8
10
12
14
16
18
gamma
0.2 0.4 0.6 0.8
0
1
2
3
4
5
rho
(a) Monthly Model: 1993-2007
1.2 1.4 1.6 1.8 2
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0.2 0.4 0.6 0.8
0
1
2
3
4
5
gamma
0.4 0.6 0.8
0
1
2
3
4
5
6
7
8
9
10
rho
(b) Quarterly Model: 1993-2007
122
Comparison of the estimated policy rules over the sample periods
This section presents the qualitative comparison of the policy rule's estimates
over the sample periods. In particular, other similar studies have estimated a passive
policy rule for the pre-Volcker period. The QM estimates are indeed in line with this
result, as the 90% condence interval for parameter overlaps with values less than
one. However, the MM estimates for the same sample indicate that an active policy
rule would have been applied if the CB did not intervene for some subperiods.
Furthermore, both the QM and the MM estimates assign to the post-1993 the
highest estimated for the policy responses to in
ation and output. Thus, the post-
1993 period is characterized by the most aggressive rule through the samples. The
MM estimates for the interest-rate smoothing coecient are also the highest for the
Post-1993 in line with the smoother interest rate data during this period.
The Volcker-Greenspan period, similarly to the post-1993 sample, has also an
active policy rule, with high responses to in
ation but quite limited interest rates
smoothing coecient mainly due to the sample's volatile policy rate data.
4.5.2 Impulse Response Analysis
The impulse response (IR) analysis presented here focuses mainly on investigating
how the model's seasonality and the CB non-intervention subperiod aect the NK
model's sensitivity to exogenous disturbances.
Both the QM's and the MM's impulse responses, depicted in Figures 4.7 to 4.12,
exhibit the expected responses: a contractionary demand shock results in an in
ation
and interest rate decrease over time; an in
ation-increasing supply shock raises the
interest rates, and results in an output decrease, and a contractionary monetary policy
shock causes output and in
ation to decrease.
123
Figure 4.7: Quarterly Model: Impulse Responses for the Pre-Volcker period (1960-
1979). Figure depicts the Quarterly model's posterior means for the output (y),
the in
ation (p) and the interest rate (i) impulse responses to a standard deviation
demand, supply and policy shock respectively. Figures (a) and (b) depict also the
evolution of the persistent demand (e
y
) and supply shocks (e
p
).
10 20 30 40
0
0.2
0.4
0.6
0.8
e_y
10 20 30 40
0
0.02
0.04
0.06
i
10 20 30 40
−0.01
0
0.01
0.02
p
10 20 30 40
−0.5
0
0.5
1
y
(a) Impulse responses to demand shocks
10 20 30 40
0
0.05
0.1
0.15
0.2
e_p
10 20 30 40
0
0.005
0.01
0.015
0.02
i
10 20 30 40
−0.1
0
0.1
0.2
0.3
p
10 20 30 40
−0.1
−0.08
−0.06
−0.04
−0.02
0
y
(b) Impulse responses to supply shocks
5 10 15 20 25 30 35 40
0
0.05
0.1
i
5 10 15 20 25 30 35 40
−0.02
−0.01
0
p
5 10 15 20 25 30 35 40
−0.4
−0.2
0
y
(c) Impulse responses to policy shocks
124
Figure 4.8: Quarterly Model: Impulse Responses for the Volcker-Greenspan period
(1980-1992). Figure depicts the Quarterly model's posterior means for the output (y),
the in
ation (p) and the interest rate (i) impulse responses to a standard deviation
demand, supply and policy shock respectively. Figures (a) and (b) depict also the
evolution of the persistent demand (e
y
) and supply shocks (e
p
).
10 20 30 40
0
0.2
0.4
0.6
0.8
e_y
10 20 30 40
0
0.05
0.1
0.15
0.2
i
10 20 30 40
−0.05
0
0.05
0.1
0.15
p
10 20 30 40
−0.5
0
0.5
1
y
(a) Impulse responses to demand shocks
10 20 30 40
0
0.05
0.1
0.15
0.2
e_p
10 20 30 40
0
0.02
0.04
0.06
0.08
i
10 20 30 40
−0.1
0
0.1
0.2
0.3
p
10 20 30 40
−0.2
−0.15
−0.1
−0.05
0
y
(b) Impulse responses to supply shocks
5 10 15 20 25 30 35 40
0
0.1
0.2
i
5 10 15 20 25 30 35 40
−0.04
−0.02
0
p
5 10 15 20 25 30 35 40
−0.4
−0.2
0
y
(c) Impulse responses to policy shocks
125
Figure 4.9: Quarterly model: Impulse Responses for the Post-1993 period (1992
- 2007). Figure depicts the Quarterly model's posterior means for the output (y),
the in
ation (p) and the interest rate (i) impulse responses to a standard deviation
demand, supply and policy shock respectively. Figures (a) and (b) depict also the
evolution of the persistent demand (e
y
) and supply shocks (e
p
).
10 20 30 40
0
0.2
0.4
0.6
0.8
e_y
10 20 30 40
0
0.02
0.04
0.06
i
10 20 30 40
−0.02
0
0.02
0.04
0.06
p
10 20 30 40
−0.2
0
0.2
0.4
0.6
y
(a) Impulse responses to demand shocks
10 20 30 40
0
0.05
0.1
0.15
0.2
e_p
10 20 30 40
−0.01
0
0.01
0.02
0.03
i
10 20 30 40
−0.05
0
0.05
0.1
0.15
p
10 20 30 40
−0.3
−0.2
−0.1
0
0.1
y
(b) Impulse responses to supply shocks
5 10 15 20 25 30 35 40
0
0.02
0.04
i
5 10 15 20 25 30 35 40
−0.1
0
0.1
p
5 10 15 20 25 30 35 40
−0.5
0
0.5
y
(c) Impulse responses to policy shocks
126
The QM's responses, indicate that the Volcker - Greenspan IRs to supply shocks
are the highest among the samples, due to the sample period's high volatility of the
in
ation data and the large policy rule's response to in
ation. For the post-1993
period the IRs to policy shocks are the highest due to the large estimated policy
rule's coecients. Moreover, the large output growth during the Volcker-Greenspan
period results in high IRs with respect to demand shocks.
The MM's IRs exhibit the same response pattern with the QM. However, the MM's
seasonality introduces two types of impulse responses, both of whom are depicted in
Figures 4.10 - 4.12: the seasonal IRs concentrate on the seasonal structural responses
to shocks occurred in a specic subperiod; the periodic IRs describe the economy's
evolution over all the subsequent subperiods given the realization of a structural shock
at each initial subperiod. Each of the Figures 4.10 - 4.12 consist of two panels: the
upper and the lower panel exhibit the seasonal and the periodic IRs respectively.
The seasonal IRs distinguish between the responses corresponding to shocks oc-
curring during subperiods with and without CB intervention. There are three main
conclusions consistent over all the samples drawn by the analysis of the seasonal IRs.
First, the in
ation responses to the non-intervention demand shocks are much sharper
than the responses to the intervention ones. Thus, the monetary policy dampens the
eect of the demand shocks. In contrast, the output responses to the to the non-
intervention supply shocks are much smaller than the responses to the intervention
ones, indicating that the CB amplies the eects of the supply shocks. Both results
yield from the policy rule's estimates: for all the samples the policy rate's responses
to in
ation is much higher than to the output. Hence, the more a variable is weighted
in the policy rule, the more sensitive the economy becomes to this variable's devia-
tions occurring at the non-intervention subperiods, and the less sensitive to deviations
occurring at the intervention subperiods.
127
Figure 4.10: Monthly Model: Impulse responses for the pre-Volcker period (1960-
1979). Figure depicts the Monthly model's seasonal (upper panel) and periodic (lower
panel) impulse responses of the output, in
ation and interest rate to a 100*standard
deviation demand, supply and policy shock, for the intervention (dashed line) and
the non-intervention (solid line) subperiods.
0 5 10
0
1
2
3
4
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
0
0.2
0.4
0.6
0.8
INTEREST RATE
0 50
0
1
2
3
4
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
0
0.2
0.4
0.6
0.8
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−60
−40
−20
0
Monthly Model
OUTPUT
0 5 10
0
0.2
0.4
0.6
0.8
1
INFLATION
0 5 10
−0.5
0
0.5
1
INTEREST RATE
0 50
−60
−40
−20
0
OUTPUT
0 50
0
0.2
0.4
0.6
0.8
1
INFLATION
0 50
−0.5
0
0.5
1
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−1
−0.5
0
0.5
Monthly Model
OUTPUT
0 5 10
−0.3
−0.2
−0.1
0
0.1
INFLATION
0 5 10
−0.1
0
0.1
0.2
0.3
INTEREST RATE
0 50
−1
−0.5
0
0.5
OUTPUT
0 50
−0.3
−0.2
−0.1
0
0.1
INFLATION
0 50
−0.1
0
0.1
0.2
0.3
INTEREST RATE
(c) Impulse responses to policy shocks
128
Figure 4.11: Monthly Model: Impulse Responses for the Volcker-Greenspan period
(1980-1992). Figure depicts the Monthly model's seasonal (upper panel) and peri-
odic (lower panel) impulse responses of the output, in
ation and interest rate to a
100*standard deviation demand, supply and policy shock, for the intervention (dashed
line) and the non-intervention (solid line) subperiods.
0 5 10
0
1
2
3
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
−0.5
0
0.5
1
1.5
INTEREST RATE
0 50
0
1
2
3
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
−0.5
0
0.5
1
1.5
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−60
−40
−20
0
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
−2
−1
0
1
2
INTEREST RATE
0 50
−60
−40
−20
0
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
−2
−1
0
1
2
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−4
−2
0
2
Monthly Model
OUTPUT
0 5 10
−1.5
−1
−0.5
0
0.5
INFLATION
0 5 10
−1
0
1
2
3
INTEREST RATE
0 50
−4
−2
0
2
OUTPUT
0 50
−1.5
−1
−0.5
0
0.5
INFLATION
0 50
−1
0
1
2
3
INTEREST RATE
(c) Impulse responses to policy shocks
129
Figure 4.12: Monthly model: Impulse Responses for the Post-1993 period (1993 -
2007). Figure depicts the Monthly model's seasonal (upper panel) and periodic (lower
panel) impulse responses of the output, in
ation and interest rate to a 100*standard
deviation demand, supply and policy shock, for the intervention (dashed line) and
the non-intervention (solid line) subperiods.
0 5 10
0
1
2
3
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
0
0.2
0.4
0.6
0.8
1
INTEREST RATE
0 50
0
1
2
3
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
0
0.2
0.4
0.6
0.8
1
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−15
−10
−5
0
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
−0.5
0
0.5
1
INTEREST RATE
0 50
−15
−10
−5
0
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
−0.5
0
0.5
1
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−2
−1
0
1
Monthly Model
OUTPUT
0 5 10
−1
−0.5
0
0.5
INFLATION
0 5 10
−0.2
0
0.2
0.4
0.6
INTEREST RATE
0 50
−2
−1
0
1
OUTPUT
0 50
−1
−0.5
0
0.5
INFLATION
0 50
−0.2
0
0.2
0.4
0.6
INTEREST RATE
(c) Impulse responses to policy shocks
130
The structural responses to the interest-rates exogenous shocks realized during ei-
ther the non-interevtion or an intervention supberiod have similar magnitude. Thus,
the unanticipated policy rate's deviations from the rule (during the intervention sub-
periods) and the unanticipated CB intervention (interest rate shocks realized during
the non-intervention periods capture unananticipated policy intervention) have simi-
lar eects on the economy.
Additionally, the interest rate responses to the structural shocks are one-subperiod
lagged when the shocks realize during a non-intervention subperiod. However, the
over time interest rate's adjustment back to its steady level is identical for both the
intervention and non-intervention subperiods. This fact implies that the absence of
the monetary policy intervention results only in the delay of the shocks eect on the
interest rates as during the non-intervention subperiods the interest rates are not
aected by either in
ation or output deviations. The monetary authorities respond
to these deviations one subperiod after the shocks realization, when their size has
already been reduced, and thus the CB's initial, but one-subperiod lagged, response
is smaller.
Furthermore, the periodic IRs depict the model's reversion back to its steady
state, and are depicted by the lower panels of Figures 4.10 to 4.12. The analysis
of the periodic responses indicates that the sample period's characteristics drive the
model's seasonal behavior. In particular for the Pre-Volcker period which has the most
volatile output series among the samples, demand shocks remain in the system for
more subperiods and cause the most volatile structural responses among the samples.
For the Volcker-Greenspan period the eects of the sample's high and volatile in
ation
are more clear: the seasonal responses to the supply shocks are far more volatile than
in any other sample. The fact that the interest rate shocks remain in the system for
a few subperiods is an immediate result of the model's non-persistent specication
131
of the shocks, and thus could be relaxed. Hence, the model is capable of replicating
richer dynamics, in terms of the system's evolution over time, than the standard NK
model.
4.5.3 Robustness Check
The validity and the robustness of our conclusions are tested by changing the
policy rule's specication: the interest rate smoothing coecient is set to zero. In
this way a dierent set of priors, called Priors 2, is dened and reported in Table
4.5. The optimality of the estimation results for each prior is dened by the log
marginal density. Table 4.6 reports the log marginal densities for each sample and
set of priors, and indicate that the estimates using Priors 1 are optimal. However the
estimates using Priors 2 shed light on the validity of the model's specication and
the robustness of our results.
Table 4.5: Prior Distributions: Priors 2
Density Mean Std.
Structural Parameters
Gamma 1.50
1
0.10

Gamma 0.25 0.10
Gamma 0.50 0.10
Gamma 1.00 1.00

y
Beta 0.50 0.10

p
Beta 0.50 0.10
Standard Deviation of Shocks
u
y
Inv. Gamma 0.41 0.26
u

n
, n=0,1,2 Inv. Gamma 0.31 0.22
u
i
n
, n=0,1,2 Inv. Gamma 0.18 0.09
1
= 1.1 for the pre-Volcker period
132
Table 4.6: Log Marginal Density for the estimated models
Pre Volcker Volcker-Greenspan Post 1992
(1960-1979) (1980-1992) (1992-2007)
Quarterly Monthly Quarterly Monthly Quarterly Monthly
Priors 1 -259.75 -318.77 -251.14 -221.37 -153.15 -178.56
Priors 2 -397.51 -388.43 -260.43 -251.86 -171.84 -277.15
Tables 4.7, 4.8 and 4.9 report the parameters posterior means and the 90% con-
dence intervals for all the models and samples corresponding to Priors 2. Similar to
the conclusions drawn by the estimates using Priors 1, the policy rule's responses to
in
ation and the stuctural shocks persistence are higher for the MM than the QM;
in contrast, the policy responses to the output gap are smaller for the MM than the
QM. The dierences of the policy coecients estimates between the QM and the MM
are statistically dierent, as depicted by Figures 4.13, 4.14 and 4.15 that graphs the
prior and posterior distributions of the estimates.
Furthermore, the estimates form Priors 2 verify the conclusions drawn from the
previous analysis: the non-intervention subperiod forces the CB to over-respond to
in
ation during the subperiods that it intervenes, as the MM estimates for the policy
rule's responses to in
ation are higher than the QM ones; the seasonal lack of output
data result in a quite limited output's weight in the policy rule. The estimates for the
Volcker-Greenspan and the post-1993 periods yield analogous results with those from
Priors 1: active policy rule with very small policy responses to output for the MMs.
However, the policy rule for the pre-Volcker period is also active, unlike the Priors 1
estimates, indicating that indeterminacy doubtfully explains the periods problems.
The impulse response (IR) analysis of the estimates from Priors 2, depicted in
133
Figure 4.13: Priors 2: Prior & Posterior Distributions for the policy coecients
(;
; ), for the MM (a) and the QM (b) model, over the pre-Volker period
0.8 1 1.2 1.4 1.6 1.8
0
1
2
3
4
5
6
7
alpha
0 0.2 0.4 0.6
0
10
20
30
40
50
60
70
gamma
1 2 3
0
1
2
3
4
5
6
7
8
sigma
(a) Monthly Model: 1960-1979
0.8 1 1.2 1.4 1.6 1.8
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0.2 0.4 0.6 0.8
0
100
200
300
400
500
600
700
gamma
(b) Quarterly Model: 1960-1979
134
Figure 4.14: Priors 2: Prior & Posterior Distributions for the policy coecients
(;
; ), for the MM (a) and the QM (b) model, over the Volker-Greenspan period
1.41.61.8 2 2.22.4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
alpha
0 0.2 0.4 0.6
0
5
10
15
20
25
30
35
40
45
gamma
1 2 3
0
0.5
1
1.5
2
sigma
(a) Monthly Model: 1980-1992
1.4 1.6 1.8 2 2.2 2.4
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0 0.2 0.4 0.6 0.8
0
1
2
3
4
5
6
7
8
gamma
(b) Quarterly Model: 1980-1992
135
Figure 4.15: Priors 2: Prior & Posterior Distributions for the policy coecients
(;
; ), for the MM (a) and the QM (b) model, over the post-1993 period
1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0 0.2 0.4 0.6
0
2
4
6
8
10
12
14
16
18
20
gamma
1 2 3
0
1
2
3
4
5
6
7
8
sigma
(a) Monthly Model: 1993-2007
1.4 1.6 1.8 2 2.2 2.4
0
0.5
1
1.5
2
2.5
3
3.5
4
alpha
0.2 0.4 0.6 0.8
0
1
2
3
4
5
6
7
gamma
(b) Quarterly Model: 1993-2007
136
Table 4.7: Estimation results for Priors 2: Pre-Volcker sample(1960- 1979)
Quarterly Model Monthly Model
Mean 90% Interval Mean 90% Interval
1.4071 1.2836 1.5259 1.5767 1.4995 1.6615

0.0984 0.0977 0.0988 0.0258 0.0164 0.0341
0.0654 0.0486 0.0778 0.2272 0.1680 0.2860
0.0315 0.0185 0.0575 0.3223 0.2450 0.3867

y
0.8495 0.7029 0.9280 0.9506 0.9339 0.9674

p
0.2305 0.1344 0.3052 0.6472 0.5870 0.7028
u
y
0.8711 0.6794 1.0193 0.1611 0.1280 0.1935
u

0
0.1129 0.0951 0.1259 0.1012 0.0894 0.1144
u

1
0.3919 0.2788 0.4947
u

2
0.0973 0.0839 0.1083
u
i
0
0.1133 0.0922 0.1249 0.0776 0.0670 0.0865
u
i
1
0.0686 0.0590 0.0765
u
i
2
0.0481 0.0401 0.0555
Table 4.8: Estimation results for Priors 2: Volcker-Greenspan sample(1980- 1992)
Quarterly Model Monthly Model
Mean 90% Interval Mean 90% Interval
1.8164 1.5876 1.9941 2.0620 1.9350 2.2048

0.2338 0.1522 0.3261 0.0235 0.0094 0.0366
0.1293 0.0656 0.1857 0.2186 0.1462 0.2995
0.1156 0.0565 0.1771 1.2380 0.9593 1.5099

y
0.6096 0.5025 0.7175 0.8836 0.8436 0.9261

p
0.3802 0.2551 0.4968 0.9169 0.8847 0.9505
u
y
1.3487 0.7924 1.8424 0.1403 0.1130 0.1701
u

0
0.1441 0.1050 0.1779 0.1260 0.1084 0.1497
u

1
0.4882 0.3317 0.6445
u

2
0.1262 0.1048 0.1480
u
i
0
0.1800 0.2580 0.1903 0.1841 0.1558 0.2174
u
i
1
0.1940 0.1643 0.2267
u
i
2
0.1348 0.1110 0.1630
137
Table 4.9: Estimation results for Priors 2: Post-1993 sample(1993- 2007)
Quarterly Model Monthly Model
Mean 90% Interval Mean 90% Interval
1.8092 1.6100 1.9775 2.2113 2.0096 2.3929

0.2926 0.1873 0.3948 0.0604 0.0320 0.1020
0.2159 0.1027 0.3287 0.4381 0.3300 0.5484
0.0248 0.0135 0.0346 0.4503 0.3644 0.5554

y
0.8371 0.7818 0.8934 0.9078 0.8757 0.9348

p
0.1922 0.1028 0.2765 0.7104 0.6380 0.7831
u
y
1.1786 0.7975 1.6700 0.1635 0.1325 0.2000
u

0
0.1392 0.0959 0.1786 0.1204 0.0990 0.1388
u

1
0.3515 0.2603 0.4423
u

2
0.1175 0.0984 0.1354
u
i
0
0.1779 0.1417 0.2234 0.1483 0.1246 0.1727
u
i
1
0.1403 0.1176 0.1636
u
i
2
0.0553 0.0449 0.0655
Figures 4.16 to 4.21, are also in line with the IRs from Priors 1. First, with re-
spect to the QM: the pre-Volcker period exhibits the highest IRs to demand shocks;
the Volcker - Greenspan to supply shocks, and the post-1993 IRs to policy shocks.
With respect to the MM, both the seasonal and the periodic IRs from the Priors 2
are in line with those from Priors 2: the in
ation responses to the non-intervention
demand shocks are much sharper than those to the intervention ones; the output
responses to the non-intervention supply shocks are much smaller than the responses
to the intervention ones, and the the interest rate responses to the structural non-
intervention shocks are one-subperiod lagged. Thus the results from Priors 2 verify
the rest of the empirical analysis: the more a variable is weighted in the policy rule,
the more sensitive the economy becomes to this variable's deviations occurring at
the non-intervention subperiods, and the less sensitive to deviations occurring at the
intervention subperiods; the unanticipated policy rate's deviations from the rule real-
138
ized during the intervention subperiods and the unanticipated CB intervention have
similar eects on the economy; the non-intervention subperiods results only in the
seasonal delay of the shocks eect on the interest rates.
Furthermore, the periodic IRs depicted by the lower panels of Figures 4.19 to 4.21
comply with the conclusions drawn from the previous analysis: the sample period's
characteristics drive the model's seasonal behavior: for the Pre-Volcker period the
highly volatile output series causes the long life of the demand shocks and results in
the most volatile structural responses among the samples; for the Volcker-Greenspan
period the seasonal responses to the supply shocks are far more volatile than in any
other sample due to the sample's high and volatile in
ation.
The present analysis indicates that our conclusions with respect to the eects of
either the model's seasonality or the CB's non-intervention, are robust and consistent
even with a dierent policy rule specication.
4.6 Conclusion
This chapter presented a class of models which is appropriate to capture any seasonal
behavior of the economic phenomenon. Additionally, it introduces a novel estimation
technique which allows us to use an information structure with higher (than one)
dimension for a forward looking model. Moreover, it presents the model's empiri-
cal strength and theoretical validity through an example: a novel extension of the
New Keynesian Monetary model where the central bank intervenes periodically. Fur-
thermore, the periodic NK (PNK) model is estimated by the proposed estimation
technique, and, thus, data with dierent frequencies are used, unlike similar studies
(Lubik and and Schorfheide (2006) [31]) that are forced to used quarterly averages of
the monthly series.
139
Figure 4.16: Quarterly Model - Priors 2: Impulse Responses for the Pre-Volcker
period (1960-1979). Figure depicts the Quarterly model's posterior means for the
output (y), the in
ation (p) and the interest rate (i) impulse responses to a standard
deviation demand, supply and policy shock respectively. Figures (a) and (b) depict
also the evolution of the persistent demand (e
y
) and supply shocks (e
p
).
10 20 30 40
0
0.5
1
1.5
e_y
10 20 30 40
0
0.02
0.04
0.06
0.08
i
10 20 30 40
0
0.01
0.02
0.03
0.04
p
10 20 30 40
0
0.1
0.2
0.3
0.4
y
(a) Impulse responses to demand shocks
10 20 30 40
0
0.05
0.1
0.15
0.2
e_p
10 20 30 40
0
0.02
0.04
0.06
0.08
0.1
i
10 20 30 40
−0.05
0
0.05
0.1
0.15
p
10 20 30 40
−1
−0.5
0
0.5
y
(b) Impulse responses to supply shocks
5 10 15 20 25 30 35 40
0
0.02
0.04
i
5 10 15 20 25 30 35 40
−0.05
0
0.05
p
5 10 15 20 25 30 35 40
−1
0
1
y
(c) Impulse responses to policy shocks
140
Figure 4.17: Quarterly model - Priors 2: Impulse Responses for the Volcker-Greenspan
period (1980-1992). Figure depicts the Quarterly model's posterior means for the
output (y), the in
ation (p) and the interest rate (i) impulse responses to a standard
deviation demand, supply and policy shock respectively. Figures (a) and (b) depict
also the evolution of the persistent demand (e
y
) and supply shocks (e
p
).
10 20 30 40
0
1
2
3
e_y
10 20 30 40
0
0.05
0.1
0.15
0.2
i
10 20 30 40
0
0.02
0.04
0.06
0.08
0.1
p
10 20 30 40
0
0.1
0.2
0.3
0.4
y
(a) Impulse responses to demand shocks
10 20 30 40
0
0.05
0.1
0.15
0.2
e_p
10 20 30 40
0
0.05
0.1
0.15
0.2
i
10 20 30 40
0
0.05
0.1
0.15
0.2
p
10 20 30 40
−0.8
−0.6
−0.4
−0.2
0
y
(b) Impulse responses to supply shocks
5 10 15 20 25 30 35 40
−0.1
0
0.1
i
5 10 15 20 25 30 35 40
−0.1
0
0.1
p
5 10 15 20 25 30 35 40
−1
0
1
y
(c) Impulse responses to policy shocks
141
Figure 4.18: Quarterly model - Priors 2: Impulse Responses for the Post-1993 period
(1992 - 2007). Figure depicts the Quarterly model's posterior means for the output
(y), the in
ation (p) and the interest rate (i) impulse responses to a standard deviation
demand, supply and policy shock respectively. Figures (a) and (b) depict also the
evolution of the persistent demand (e
y
) and supply shocks (e
p
).
10 20 30 40
0
0.5
1
1.5
2
e_y
10 20 30 40
0
0.02
0.04
0.06
i
10 20 30 40
0
0.01
0.02
0.03
p
10 20 30 40
0
0.01
0.02
0.03
0.04
y
(a) Impulse responses to demand shocks
10 20 30 40
0
0.05
0.1
0.15
0.2
e_p
10 20 30 40
−0.01
0
0.01
0.02
0.03
i
10 20 30 40
0
0.02
0.04
0.06
0.08
0.1
p
10 20 30 40
−0.6
−0.4
−0.2
0
0.2
y
(b) Impulse responses to supply shocks
5 10 15 20 25 30 35 40
0
0.01
0.02
i
5 10 15 20 25 30 35 40
−0.1
0
0.1
p
5 10 15 20 25 30 35 40
−0.5
0
0.5
y
(c) Impulse responses to policy shocks
142
Figure 4.19: Monthly model - Priors 2: Impulse Responses for the pre- Volcker pe-
riod (1960-1979). Figure depicts the Monthly model's seasonal (upper panel) and
periodic (lower panel) impulse responses of the output, in
ation and interest rate
to a 100*standard deviation demand, supply and policy shock, for the intervention
(dashed line) and the non-intervention (solid line) subperiods.
0 5 10
0
1
2
3
4
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
0
0.5
1
1.5
INTEREST RATE
0 50
0
1
2
3
4
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
0
0.5
1
1.5
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−40
−30
−20
−10
0
Monthly Model
OUTPUT
0 5 10
0
0.2
0.4
0.6
0.8
1
INFLATION
0 5 10
−0.5
0
0.5
1
INTEREST RATE
0 50
−40
−30
−20
−10
0
OUTPUT
0 50
0
0.2
0.4
0.6
0.8
1
INFLATION
0 50
−0.5
0
0.5
1
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−1
−0.5
0
0.5
Monthly Model
OUTPUT
0 5 10
−0.3
−0.2
−0.1
0
0.1
INFLATION
0 5 10
−0.1
0
0.1
0.2
0.3
INTEREST RATE
0 50
−1
−0.5
0
0.5
OUTPUT
0 50
−0.3
−0.2
−0.1
0
0.1
INFLATION
0 50
−0.1
0
0.1
0.2
0.3
INTEREST RATE
(c) Impulse responses to policy shocks
143
Figure 4.20: Monthly model - Priors 2: Impulse Responses for the Volcker-Greenspan
period (1980-1992). Figure depicts the Monthly model's seasonal (upper panel) and
periodic (lower panel) impulse responses of the output, in
ation and interest rate
to a 100*standard deviation demand, supply and policy shock, for the intervention
(dashed line) and the non-intervention (solid line) subperiods.
0 5 10
0
1
2
3
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
0
0.5
1
1.5
2
INTEREST RATE
0 50
0
1
2
3
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
0
0.5
1
1.5
2
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−60
−40
−20
0
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
−1
0
1
2
INTEREST RATE
0 50
−60
−40
−20
0
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
−1
0
1
2
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−4
−2
0
2
Monthly Model
OUTPUT
0 5 10
−1
−0.5
0
0.5
INFLATION
0 5 10
−1
0
1
2
3
INTEREST RATE
0 50
−4
−2
0
2
OUTPUT
0 50
−1
−0.5
0
0.5
INFLATION
0 50
−1
0
1
2
3
INTEREST RATE
(c) Impulse responses to policy shocks
144
Figure 4.21: Monthly model - Priors 2: Impulse Responses for the post-1993 pe-
riod (1993 - 2007). Figure depicts the Monthly model's seasonal (upper panel) and
periodic (lower panel) impulse responses of the output, in
ation and interest rate
to a 100*standard deviation demand, supply and policy shock, for the intervention
(dashed line) and the non-intervention (solid line) subperiods.
0 5 10
0
1
2
3
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
−0.5
0
0.5
1
1.5
INTEREST RATE
0 50
0
1
2
3
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
−0.5
0
0.5
1
1.5
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−20
−15
−10
−5
0
Monthly Model
OUTPUT
0 5 10
0
0.5
1
1.5
INFLATION
0 5 10
0
0.2
0.4
0.6
0.8
1
INTEREST RATE
0 50
−20
−15
−10
−5
0
OUTPUT
0 50
0
0.5
1
1.5
INFLATION
0 50
0
0.2
0.4
0.6
0.8
1
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−1.5
−1
−0.5
0
0.5
Monthly Model
OUTPUT
0 5 10
−1
−0.5
0
0.5
INFLATION
0 5 10
0
0.2
0.4
0.6
0.8
1
INTEREST RATE
0 50
−1.5
−1
−0.5
0
0.5
OUTPUT
0 50
−1
−0.5
0
0.5
INFLATION
0 50
0
0.2
0.4
0.6
0.8
1
INTEREST RATE
(c) Impulse responses to policy shocks
145
There are mainly two conceptual dierences between the PNK and the standard
NK model, regarding the environment in which the policy decisions are made. In the
NK model the CB has all the available information in order to update the policy rule,
while the intervention pattern gives them the opportunity to immediately respond to
any exogenous destabilizing deviation. On the contrary, the PNK model introduces
two sources of uncertainty for the CB's decision: the seasonal lack of information and
a non-intervention subperiod.
Our empirical results suggest that the non-intervention subperiods force the CB
to set a policy rule that over-responds to in
ation and has a limited interest-rate
smoothing coecient and the seasonal lack of output information leads to lower policy
responses indicating that the CB gives less weight to the unobservable information.
Thus, in a scenario where the CB does not intervene every subperiod and does not
have all the available information, the policy rule would be more aggressive with
respect to the available information in order to ensure the economy's stability for the
subperiods that the CB does not intervene.
The impulse response (IR) analysis indicate that the direction of the structural
shocks eects on the state variables remain unchanged: a contractionary demand
shock results in an in
ation and interest rate decrease over time; an in
ation in-
creasing supply shock raises the interest rates, while it results in a output decrease
(below its steady state), and a contractionary monetary policy shock causes output
and in
ation to decrease.
Our framework's seasonality introduces two types of impulse responses (IR): sea-
sonal IRs that concentrate on the structural responses to shocks occurred in a specic
subperiod, and periodic IRs that describe the economy's evolution over all the sub-
periods given the realization of a structural shock at each initial subperiod.
The seasonal IRs distinguish between the responses corresponding to shocks oc-
146
curring during subperiods with and without CB intervention. There are three main
conclusions consistent over all the samples drawn by the analysis of the seasonal
the more a variable is weighted in the policy rule, the more sensitive the economy
becomes to this variable's deviations occurring at the non-intervention subperiods,
and the less sensitive to deviations occurring at the intervention subperiods; second,
the structural responses to the interest-rates exogenous shocks realized during either
the non-interevtion or an intervention subperiod have similar magnitude. Thus, the
unanticipated policy rate's deviations from the rule (during the intervention subperi-
ods) and the unanticipated CB intervention (interest rate shocks realized during the
non-intervention periods capture unananticipated policy intervention) have similar
eects on the economy; nally, the interest rate responses to the structural shocks
are one subperiod lagged when the shocks realize during a non-intervention subpe-
riod, while the interest rate's adjustment back to its steady level is identical for both
the intervention and non-intervention subperiods. Thus, the absence of the monetary
policy intervention results only in the delay of the shocks eect on the interest rates
because during the non-intervention subperiods the interest rates are not aected by
either in
ation or output deviations.
The periodic IRs depict the economy's reversion back to its steady state and
indicate that the sample period's characteristics drive the model's seasonal behavior:
the more volatile the input series the longer the shocks remain in the economy and
the more volatile the structural responses are.
Overall, the proposed theoretical class of models and the estimation technique
yields interesting results. Its main advantage is the lack of restrictive assumptions
which make the methodology general and appropriate for a wide range of economic
models. Further research in that direction seems fruitful and capable of shed light in
many seasonal economic phenomena.
147
Chapter 5
Periodic New Keynesian Monetary
Models and the Term Structure of
Interest Rates
5.1 Introduction
The central banks make policy decisions knowing that the success of their policy
depends heavily on how markets perceive their strategy and on how agents utilize their
announcements to update their expectations about the future. The term structure
of interest-rates captures the markets expectations about the future, and therefore,
is a basic tool for the monetary policy authorities. However, the New Keynesian
(NK) Monetary model, which is the current workhorse for studying monetary policy,
disregards any information contained in the yield curve. This study extends the
standard model in order to account for the rich information environment delivered
by the yield curve.
148
In addition, the NK framework is based on an unrealistic assumption that the
central bank intervenes at each date. However, the present framework considers a
seasonal central bank's intervention pattern similar to the one presented in Chap-
ter 4: the model's period is divided into subperiods with and without central bank
intervention.
Moreover, in many cases the data accompanying the monetary policy analysis
come in dierent frequencies: for example, the Gross Domestic Product data are
usually updated every quarter, while the nancial data, like the short-term interest
rate, are available daily. Our framework provides an estimation technique which
utilizes a higher than one dimension of data frequency.
Thus, this analysis overcomes both weaknesses of the NK model and focuses on
identifying the eects that the term structure of interest rates and the seasonal central
bank intervention have on the NK model.
5.1.1 New Keynesian Models
The New Keynesian (NK) model builds on a dynamic general equilibrium model
that allows for a suitable use of frictions (i.e., nominal price and/or wage rigidities) in
order to set up an economic environment appropriate for policy evaluation. In a very
simple version agents in each period need to decide how much to spend and how much
to save in the form of money versus bonds; rms decide how much to produce and
what price to set given a deterministic price staggering environment. In this setting,
the short term interest rate becomes the instrument (Gali et al. (1999) [27]) through
which central banks exercise their policy. This simple New Keynesian model is quite
instructive for the analysis of the eects of supply and demand shocks and the role
of the monetary policy and models as in Yun [49] and King [28], provide a power-
ful workhorse for monetary policy analysis. However, the fact that this framework
149
neglects the interaction between the yield curve and the policy decisions can lead to
suboptimal or even misleading results. To this end, this study presents a framework
where the equilibrium dynamics are consistently ltered through the term structure,
and hence, the hidden state space dynamics are revealed by a broad information set
which contains the yield curve.
Our study is motivated by an extended empirical literature that argues that the
term spreads are useful instruments for forecasting future real activity (Hamilton
and Kim (2002) [24], Harvey (1988) [26] and Ang, Piazzesi and Wei (2002) [36]);
future in
ation rate (Fama (1987) [17]), as well as monetary policy decisions (Piazzesi
(2001) [37] for the Federal Reserve Bank and Chapters 1 and 2 of the present study,
for the European Central bank).
Moreover, our framework deals with one more unrealistic restriction imposed by
the NK model regarding the policy makers and the agents decision time. In partic-
ular, even those central banks, that participate actively in the money market (e.g
Federal Reserve Bank (FRB), European Central Bank (ECB)), do not readjust the
short term rate at every date,unlike the NK assumption. The present framework
considers a dierent central bank (CB) intervention pattern: the model's period con-
sist of subperiods with and without CB intervention; for those subperiods without
intervention the short-term rate remains unchanged.
5.1.2 Term Structure Models
The term structure captures the market's expectations of future behavior of short
term interest rates. Agents revise their expectations due to new information (public
announcements) and make new investment decisions. Merton [33] presents a theoretic
characterization of the linkages between the yields and the optimal consumption and
portfolio decisions. He uses a partial equilibrium model that exogenously denes
150
real prices to follow a stochastic process. Although his model gives an economic
interpretation of the term structure model, it leaves out the monetary policy authority
and its role in the determination of the short term rate.
Next, Vasicek(1977) [52] presented a model where the short term rate is the only
factor that drives the market, and is taken to follow a stochastic mean reverting
process. Vasicek used the no-arbitrage condition to derive closed form formulas which
link the equilibrium yields to the factor (i.e., the short term rate) that drives the
market's expectations. His approach opened the way for the term structure's factor
analysis. Building on Vasicek's model, Cox, Ingersol and Ross(1985b) [11], analyze
a one factor term structure model in which the short term rate follows a square
root stochastic process. Extending this framework Dai and Singleton [12] analyze a
three-factor (i.e., level, slope ,curvature) term structure model. Empirically, Due
and Singleton(1997) [15], among others, make use of the no-arbitrage conditions and
estimate the parameters of a term structure model that captures the relationship
between the underlying factors and the equilibrium yields. In their work, the factors
(i.e., level, slope ,curvature) are latent and are backed out from the yield curve as
their main goal is to analyze the pricing of interest-rate related securities. A number
of extensions, both in terms of the number of state variables and the data generating
process for the state vector, have been introduced and analyzed. All of the above
models give a valuable insight into the relation between the term structure and the
underlying driving factors of the economy, but they fail to provide any economic
interpretation of these factors as they neglect any interaction of the factors with
either the macroeconomy or the monetary policy decisions.
However, there is a rapidly growing macro-nance literature that was launched in
order to extend the term structure models by incorporating macro variables. First,
Ang and Piazzesi(2003) [1], estimated a term structure model with both macroeco-
151
nomic variables and latent factors as state variables. Their main conclusion is that
a large part of the variations in interest rates can be explained by macro variables.
From this point the literature started to analyze the relationship between the latent
factors that drive the yield curve and the macroeconomy. For example Diebold et al.
(2006) [44] empirically conclude that the level factor is highly correlated with in
a-
tion, the slope factor is highly correlated with real activity while the curvature factor
is unrelated to any of the main macroeconomic variables. These models include both
macroeconomic and latent factors but the evolution of the state is abstract and is not
based on any structural interaction. Their approach, although empirically relates the
yield factors with macroeconomic variables, fails to give any pure economic reasoning
for these conclusions. Rudebusch and Wu (2004) [45] and Hordahl et al.(2003) [51]
impose on the state vector a structure similar to the NK model but add an arbi-
trary number of lags in the aggregate demand and supply equations. Additionally,
Bekaert et all. (2006) [8] incorporate a standard sticky pricing model with endoge-
nous persistence into a term structure model with a risk adjustment consistent with
the intertemporal substitution equation; however, they do not actually incorporate
the yield curve into the equilibrium dynamics.
Indeed, the power and the signicance of the term structure of interest rates has
been identied by the literature. However the Term Structure Models (TS) fail to
introduce an economic interpretation of the yield curve's driving forces, and hence,
they shed no light on the interaction between the macroeconomy and the yield curve.
The present framework derives the equations describing the yields by the periodic New
Keynesian (PNK) model, and, thus explicitly denes the economic linkage between
the structural variables and the term structure.
152
5.1.3 Overview of the Results
The present analysis focuses on studying the consequences that the term struc-
ture information and the seasonal CB intervention have on the NK model, and, in
particular, on the monetary policy analysis in particular. To this end our empirical
analysis consist of three parts: rst, the extended PNK is estimated using informa-
tion from the yield curve; second, the estimates are compared to the ones derived by
estimating the PNK model without the term structure information; nally a set of
empirical exercises is provided in order to ensure the validity of our results.
The PNK model introduces two sources of uncertainty for the CB's decision: one
due to the seasonal lack of information as the output is quarterly observable, and
one due to the non-intervention subperiods. The non-intervention subperiod forces
the CB to over-respond to in
ation in order to ensure the economy's stability for
the subperiods which they will not intervene, and the lack of information leads the
CB to give less weight to the output in the policy rule (for more details see Chapter
4). However, the extended PNK model with term structure information identies a
more conservative policy rule, in terms of in
ation responses, and more aggressive,
in terns of the output responses than the PNK model without information from the
yields. Thus, the information set delivered by the term structure provides the CB
with enough insight into the current state of the economy that the CB needs not to
over-respond to in
ation deviations, or underweight the output. The high estimates
of the the price staggering coecient for the extended PNK imply a tighter linkage
between the structural variables, and the the small estimates of the coecient of risk
aversion suggest an improved hedging against risk environment.
Moreover, similar to the PNK impulse responses (IR), the extended PNK's IR
analysis suggest that a contractionary demand shock results in an in
ation and in-
153
terest rate decrease over time; an in
ation-increasing supply shock raises the interest
rates, while it results in a long run output decrease, and a contractionary monetary
policy shock causes output and in
ation to decrease. Furthermore, the framework's
seasonality allows us to distinguish between the responses corresponding to shocks
occurring during subperiods with and without CB intervention. There are three
main conclusions consistent over all the samples: the in
ation responses to the non-
intervention demand shocks are much sharper than the responses to the intervention
ones; the output responses to the non-intervention supply shocks are much smaller
than the responses to the intervention ones, and the non-intervention interest-rate
shocks have a much sharper eect on in
ation and output than the intervention ones.
Thus, similar to the results presented in Chapter 4, the monetary policy dampens
the eect of the demand shocks and amplies the eects of the supply shocks. Both
results yield from the policy rule's estimates: for all the samples the policy rate's
responses to in
ation are much higher than those to output. Thus, the higher weight
is given to a variable in the policy rule, the more sensitive the economy becomes to
this variable's deviations occurring at the non-intervention subperiods, and the less
sensitive to deviations occurring at the intervention subperiods.
The intervention interest rate shocks capture the unanticipated policy rate's de-
viations from the rule, while the non-intervention ones capture the unananticipated
policy interventions. The PNK estimation results presented in Chapter 4 indicated
that the unanticipated policy rate's deviations from the rule and the unanticipated
CB intervention have similar eects on the economy. In contrast, the PNK-TS esti-
mation results imply that the unanticipated CB intervention has a much sharer eect
on the economy that policy rate's deviations from the rule because the structural
responses to the non-intervention interest-rate shocks are much higher than those to
the intervention ones.
154
Additionally, the interest rate responses to the structural shocks are one-subperiod
lagged when the shocks realize during a non-intervention subperiod. However, the
over time interest rate's adjustment back to its steady level is identical for both the
intervention and non-intervention subperiods. This fact implies that the absence of
the monetary policy intervention results only in the delay of the shocks eect on the
interest rates as during the non-intervention subperiods the interest rates are not
aected by either in
ation or output deviations. The monetary authorities respond
to these deviations one subperiod after the shocks realization, when their size has
already been reduced, and thus the CB's initial, but one-subperiod lagged, response
is smaller.
One of our framework's most interesting applications is the computation of the
yields impulse responses to the structural shocks. In particular, an expansionary
demand shock results in an in
ation and interest rate increase over time and this
translates to a positive shift of the yield curve; an in
ation-increasing supply shock
raises the interest rates and, hence, the yields, while a contractionary monetary policy
shock results in an immediate positive yields response. Moreover, the magnitude of
the yield responses to the economy's exogenous disturbances depend on the policy
coecients. Additionally, the yields IRs to the period's rst subperiod structural
shocks are lower than the second's, although the CB intervenes during both subperi-
ods. This underlines that the anticipation of the non-intervention subperiod dampens
the structural eects on the yields due to the zero structural eect when the CB does
not intervene. In addition, as expected, the demand and supply shocks realizing dur-
ing the non-intervention periods do not eect the yields as they do not aect the
policy rate. On the contrary, the lack of the CB intervention allows the full interest-
rate shocks pass through to the yields. So the yields responses to the interest-rates
disturbances maximize during the non-intervention periods; this implies that the
155
unanticipated central bank interventions have sharper eects on the yield curve than
the unanticipated deviations of the policy rate during the intervention subperiods.
The rest of the study is organized as following: Section 5.2, presents the Periodic
New Keynesian model which accounts for the term-structure (PNK-TS); Section 5.3
describes the models used for the estimation, the estimation method and the available
data; Section 5.4 reports the empirical results, and Section 5.5 concludes.
5.2 Periodic New Keynesian model with Term struc-
ture information
5.2.1 Periodic New Keynesian Model (PNK)
The Periodic New Keynesian Model (PNK) is in the same spirit as the dynamic gen-
eral equilibrium (DSGE) New Keynesian (NK) model. The main dierence between
the PNK and the standard NK model is the central bank's (CB) intervention pattern:
within the PNK framework the model's period is divided into subperiods with and
without CB intervention. In the present analysis, a specic case of the class of models
introduced in Chapter 4 is used: the model's period consist of three subperiods, while
the CB intervenes for the two rst successive subperiods, and remains inactive during
the third one.
The model's seasonal evolution is represented by the local approximation of the
DSGE's solution, which constitute a seasonal linear rational expectations model
156
(LRE) (see Woodford 2003 [53], LS (2003) [30]), and in our setting has the form
1
:
IS: y
n+Nt
= y
(n+1)+Ntjn+Nt

1

(i
n+Nt

(n+1)+Ntjn+Nt
); n = 0; 1; 2 (5.1)
PC:
n+Nt
=
(n+1)+Ntjn+Nt
+y
n+Nt
; n = 0; 1; 2 (5.2)
PR: i
n+Nt
=
8
>
<
>
:
i
n1+Nt
+ (1)(
n+Nt
+
y
n+Nt
), if n = 0; 1
i
n1+Nt
, if n = 2
(5.3)
where y
n+Nt
is the seasonal output's percent deviation from the one corresponding
to a perfectly
exible pricing framework;
n+Nt
is the in
ation rate dened as the
seasonal percent change in the price level, and i
n+Nt
is the short-term nominal in-
terest rate (i.e. the riskless bond with 1-subperiod ahead maturity date) controlled
by the central bank (CB) for the two rst subperiods. Moreover, for simplicity, we
utilize the notation presented in Woodford and Svensson (2000) [54] for the condi-
tional expectations at time n +Nt. In particular, if I
n+Nt
is the currently available
information set then a variable's x conditional expectation is denoted by:
E
n+Nt
[x
(n+1)+Nt
jI
n+Nt
] =x
(n+1)+Ntjn+Nt
Moreover, (0 < < 1) is the discount factor;
1
( > 0) is the inter temporal
elasticity of substitution; ( > 0) is the price staggering coecient; ( < 1) is
the smoothing coecient, and;, with; > 0, dene the magnitude of the policy
rate's response to the in
ation rate and the output gap respectively.
Equation (5.1) is the log-linearized approximation of the representative agent's
(consumption) euler equation around the non-stochastic steady state. Similar to
the NK framework, the (IS) equation relates the current output gap directly to its
1
Detailed derivation of the non-periodic system can be found in King (2000) [28], or Woodford [53]
157
expected future values and inversely to the current real interest rate which is given
by : r
t
=i
1
t

t+1jt
, where r
t
is the real interest rate (Fisher equation).
Analogously, equation (5.2) is the log-linearized approximation of the aggregate
optimal pricing decision resulted by a Calvo price staggering environment. In partic-
ular, at every subperiod n +Nt each (monopolistically competitive) rm receives a
signal to adjust its price with probability 1, while charges the same price other-
wise. Thus, equation (5.2) is an expectational Philips curve with slope, as it relates
the current in
ation with its future values and the current output.
Equation (5.3) describes the short-term interest rate's seasonal behavior: for the
non intervention subperiods (n=2) it remains unchanged; for the intervention subpe-
riods (n=0,1) the CB follows a simple Taylor rule (Taylor 1993 [50]) with an interest
rate smoothing nature, according to which the CB responds to the current in
ation
rate and the output gap.
Seasonal State Equations
Let X
n+Nt
denote the seasonal state vector consisting of the current values of the
structural variables that dene the underlying economy and the conditional expecta-
tions of the forward looking variables:
X
n+Nt
= [y
n+Nt

n+Nt
i
n+Nt
y
(n+1)+Ntjn+Nt

(n+1)+Ntjn+Nt
]
0
; for n = 0; 1; 2
The PNK can be written in matrix form as:
A
n
X
n+Nt
=B
n
X
(n1)+Nt
+R

n+Nt
; n = 0;::;N 1; t2@ (5.4)
158
where
n+Nt
is the 2x1 matrix of the expectational errors and
R

=
0
B
@
0 0 0 1 0
0 0 0 0 1
1
C
A
0
(5.5)
Moreover, A
n
; B
n
are the seasonal transition matrices which, if ^
=(1)
and ^ =(1), have the form:
For n=0,1:
A
n
=
0
B
B
B
B
B
B
B
B
B
B
@
1 0 1= 1 1=
1 0 0
^
^ 1 0 0
1 0 0 0 0
0 1 0 0 0
1
C
C
C
C
C
C
C
C
C
C
A
; B
n
=
0
B
B
B
B
B
B
B
B
B
B
@
0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0 1 0
0 0 0 0 1
1
C
C
C
C
C
C
C
C
C
C
A
(5.6)
For n=2:
A
2
=
0
B
B
B
B
B
B
B
B
B
B
@
1 0 1= 1 1=
1 0 0
0 0 1 0 0
1 0 0 0 0
0 1 0 0 0
1
C
C
C
C
C
C
C
C
C
C
A
; B
2
=
0
B
B
B
B
B
B
B
B
B
B
@
0 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
1
C
C
C
C
C
C
C
C
C
C
A
(5.7)
5.2.2 Term Structure Model
In principal the NK framework, and, thus, the PNK model, presented in Section
5.2.1, assumes complete nancial markets. Thus the existence of risk-free bonds with
159
dierent maturities can be utilized. For simplicity leti
T
n+Nt
denote the nominal bond
yield with maturity T periods ahead, at time n +Nt. The log-linearized rst order
condition (FOC) around the non-stochastic steady state which corresponds to the
representative agent's bond holdings for the rst subperiod (i.e. n=0) takes the form:
y
Nt
=y
NTjNt

1

i
T
Nt
+
1

(
1+NtjNt
+
2+NtjNt
+
T
X
k=1
(
2
X
m=0

m+N(t+k)jNt
)) (5.8)
For the short-term interest rate (i
n+Nt
), which is the CB instrument, the analogous
FOC is given by equation (5.3). Iterating forward equation (5.3) for T periods we
have:
y
Nt
= y
1+NtjNt

1

i
Nt
+
1

1+NtjNt
(5.9)
y
1+Nt
= y
2+Ntj1+Nt

1

i
1+Nt
+
1

2+Ntj1+Nt
(5.10)
y
2+Nt
= y
1+N(t+1)j2+Nt

1

i
2+Nt
+
1

1+N(t+1)j2+Nt
(5.11)
.
.
.
y
2+N(T1)
= y
NTj2+N(T1)

1

i
2+N(T1)

1

NTj2+N(T1)
) (5.12)
Taking expectations of equations (5.9) to (5.12) at Nt and adding them up:
y
Nt
= y
NTjNt

1

k=T1
X
k=0
(
m=2
X
m=0
(i
m+N(t+k)
))
+
1

(
1+NtjNt
+
2+NtjNt
+
T
X
k=1
(
2
X
m=0

m+N(t+k)jNt
)) (5.13)
Substituting equation (5.13) into equation (5.8) results in an intuitive relationship
between the short-term interest rate and the nominal bond yield with maturity T
160
periods ahead.
i
T
Nt
=i
Nt
+i
1+NtjNt
+i
1+NtjNt
+
k=T1
X
k=1
(
m=2
X
m=0
(i
m+N(t+k)
)) (5.14)
Analogously, for the rest of the period's subperiods:
i
T
1+Nt
= i
1+Nt
+i
2+Ntj1+Nt
+
k=T1
X
k=1
(
m=2
X
m=0
(i
m+N(t+k)
)) +i
N(t+T )j1+Nt
(5.15)
i
T
2+Nt
= i
2+Nt
+
k=T1
X
k=1
(
m=2
X
m=0
(i
m+N(t+k)
)) +i
N(t+T )j2+Nt
+ +i
1+N(t+T )j2+Nt
(5.16)
Equations (5.14), (5.15) and (5.16) capture the simplest linkage between the term
structure of interest rates and the structural economy represented by the short-term
rate, and hold8 T . They underline that he PNK's seasonal state vector needs to
be extended in order for the model to account for the bond yields. In particular,
the short-term interest rate's conditional expectations should be included as state
variables. In the next Section the PNK is extended in order to account for the term-
structure of interest rates.
5.2.3 Periodic New Keynesian Model and the Term Struc-
ture of Interest Rates (PNK-TS)
Let
~
X
n+Nt
denote the extended state vector of the n
th
subperiod including the
short-term interest rate's conditional expectations. Then, for the 3-subperiod model
161
used in the present analysis,
~
X
n+Nt
has the form:
~
X
Nt
= [ X
Nt
i
T
Nt
i
1+NtjNt
i
2+N(t+1)jNt
I
N(t+1)jNt
:::I
N(t+T1)jNt
]
0
~
X
1+Nt
= [ X
1+Nt
i
T
1+Nt
i
2+Ntj1+Nt
I
N(t+1)j1+Nt
:::I
N(t+T1)j1+Nt
i
N(t+T )j1+Nt
]
0
~
X
2+Nt
= [ X
2+Nt
i
T
2+Nt
I
N(t+1)j2+Nt
:::I
N(t+T1)jNt
i
(Nt+T )j2+Nt
i
1+N(t+T )j2+Nt
]
0
where
I
N(t+k)jNs
= [i
N(t+k)jS
i
1+N(t+k)jS
i
1+N(t+k)jS
]
0
; k = 1;:::; S =Nt; 1+Nt; 2+Nt
Hence, in order to include the bond yield with maturity in T periods into the PNK,
the seasonal state vector need to be extended with 2 +N(T 1) short-term rate's
conditional expectations.
Thus the PNK model that accounts for the term structure, denoted thereafter as
PNK-TS, is given by:
~
A
n
~
X
n+Nt
=
^
B
n
~
X
2+N(t1)
+
^
R

^
n+Nt
(5.17)
where
^
R

=
0
B
@
R

0
0 I
2+N(T1)
1
C
A
162
~
A
n
=
0
B
B
B
B
B
B
B
@
A
n
O
5;2+N(T1)
:::
I

1 I
1;2+N(T1)
I

O
1;2+N(T1)
:::
O
1+N(T1);5
I
1+N(T1)
O
1+N(T1);1
1
C
C
C
C
C
C
C
A
;
^
B
n
=
0
B
B
B
B
B
B
B
@
B
n
O
5;2+N(T1)
:::
O
1;2+N(T1)
::: :::
O
2+N(T1)
I
2+N(T1)
:::
.
.
.
.
.
. :::
1
C
C
C
C
C
C
C
A
; for n = 0; 1; 2
with I
k;l
; O
k;l
denoting the kxl identity and zero matrix respectively, and
I

=

0 0 1 0 0

5.2.4 Season-Independent Canonical Form
The PNK-TS needs to be converted into its time-invariant version in order to be
solvable with standard methods. Therefore, each seasonal system of equations (
i.e. equation 5.17) is iterated backwards for N = 3 subperiods. For simplicity, the
seasonal matrices
~
A
n
are taken to be invertible; otherwise, a QZ decomposition of
the matrix overcomes the problematic inversion. The overall procedure results in the
intra-period seasonal model which takes the following form:
~
A
n
~
X
n+Nt
=
~
B
n
~
X
n+N(t1)
+
^
R

~
n+Nt
; 8n = 0; 1; 2 (5.18)
163
where
~
B
n
=
^
B
n
N1
Y
i=1
(
~
A
ni
)
1
^
B
ni
The model's time-invariant state-equation is based on the period's state vector
which is constructed by stacking up all the seasonal state vectors (
~
X
n+Nt
):
S
t
= [
~
X
Nt
~
X
1+Nt
~
X
2+Nt
]
0
; 8t
Similarly, the period's expectational errors are given by:
~
t
= [^
Nt
^
1+Nt
^
2+Nt
] 8t
Therefore S
t
, where t counts periods, evolves according to:

0
S
t
=
1
S
t1
+

~
t
(5.19)
where
0
;
1
;

are time-independent block diagonal matrices with their diagonal
formed by
~
A
n
;
~
B
n
;
^
R

respectively, or:

0
=
0
B
B
B
B
@
~
A
0
0 :::
0
~
A
1
:::
0 :::
~
A
2
1
C
C
C
C
A
;
1
=
0
B
B
B
B
@
~
B
0
0 :::
0
~
B
1
:::
0 :::
~
B
2
1
C
C
C
C
A
;

=
0
B
B
B
B
@
~
R

0 :::
0
~
R

:::
0 :::
~
R

1
C
C
C
C
A
(5.20)
5.2.5 Exogenous Shocks
This section introduces three sets of exogenous disturbances into the PNK-TS: a
demand shock (u
y
), a cost-push shock(u

) and an interest rate shock (u
i
). The u
i
shocks capture any unanticipated deviations from the policy rule for the intervention
164
periods, and any unanticipated central bank intervention for the non-intervention
periods. The shocks distributions are taken to be season-specic even for those ex-
ogenous disturbances that hit the same structural variables. Moreover, the shocks are
periodic and, therefore, they realize once every period. Hence, let e
n+Nt
denote the
exogenous shocks hitting the seasonal structural model during the n
th
subperiod: ny
unanticipated central bank intervention for the non-intervention periods. The shocks
distributions are taken to be season-specic even for those exogenous disturbances
that hit the same structural variables. Moreover, the shocks are periodic and, there-
fore, they realize once every period. Hence, let e
n+Nt
denote the exogenous shocks
hitting the seasonal structural model during the n
th
subperiod:
u
n+Nt
= [u
y
n+Nt
u

n+Nt
u
i
n+Nt
]
0
where u
n+Nt
N(0, H
n
), and H
n
=
0
B
B
B
B
@

2
y;n
0 0
0
2
;n
0
0 0
2
i;n
1
C
C
C
C
A
The intra-period matrix of exogenous shocks (i.e. U
t
) consist of all the seasonal
shocks (i.e. u
n+Nt
):
U
t
= [u
Nt
u
1+Nt
u
2+Nt
];
Therefore equation (5.19) takes the form:

0
S
t
=
1
S
t1
+
u
U
t
+

~
t
(5.21)
165
with

u
=
0
B
B
B
B
@
R 0 :::
0 R 0
0 ::: R
1
C
C
C
C
A
; and R =
0
B
@
I
3;3
0
0 :::
1
C
A
(5.22)
In the present analysis, the seasonal exogenous disturbances are taken to be in-
dependent, although this assumption can be easily relaxed. Moreover, the system
of equations described by equation (5.21) falls into the class of the standard linear
rational expectation models (LRE). Although the LRE models may have multiple
equilibria (i.e. indeterminacy), our analysis considers only the determinant region. It
is worth mentioning that the stability conditions of the extended model depend on the
overall period's LRE captured by equation (5.21) and not on the seasonal LREs. In
other words, the PNK-TS has a unique and stable solution even when there is an ex-
plosive seasonal system, given that it is followed by subsequent damping subperiods.
The model's solution, similar to Sims (2002) [48], satises:
S
t
=

1
S
t1
+

u
U
t
(5.23)
5.3 Empirical Analysis
5.3.1 Estimated PNK-TS models
The present section describes the state-space representation if the PNK-TS model
used in our empirical analysis: the model's period is set equal to a (year's) quarter,
and is divided into three subperiods (i.e. months); the Federal Reserve Bank's (FRB)
regular meetings schedule (i.e. every six weeks (1.5 months)) is translated into a
166
policy intervention for the rst two subperiods (of each period) in our model; the
in
ation rate, the policy rate and the 3-month (i.e. T =1 period), 1-year (i.e. T =4
period) and 2-year (i.e. T =8 period) nominal bond yields are seasonally observable,
while the output is observed on a quarterly basis. In the present section the exact
state-space representation of the estimated models is described
The seasonal state-vectors take the form:
~
X
Nt
= [ X
Nt
i
1
Nt
i
4
Nt
i
8
Nt
i
1+NtjNt
i
2+N(t+1)jNt
I
N(t+1)jNt
:::I
N(t+7)jNt
]
0
~
X
1+Nt
= [ X
1+Nt
i
1
1+Nt
i
4
1+Nt
i
8
1+Nt
i
2+Ntj1+Nt
I
N(t+1)j1+Nt
:::I
N(t+7)j1+Nt
i
N(t+8)j1+Nt
]
0
~
X
2+Nt
= [ X
2+Nt
i
1
2+Nt
i
4
2+Nt
i
8
2+Nt
I
N(t+1)j2+Nt
:::I
N(t+7)j2+Nt
i
N(t+8)j2+Nt
i
1+N(t+8)j2+Nt
]
0
wherei
1
n+Nt
; i
4
n+Nt
; i
8
n+Nt
denote the the 3-month, 1-year and 2-year nominal bond
yields and I
N(t+k)jNs
is the vector of the period's N(t +k) interest-rate's conditional
expectations:
I
N(t+k)jNs
= [i
N(t+k)jS
i
1+N(t+k)jS
i
1+N(t+k)jS
]
0
; k = 1;:::; S =Nt; 1+Nt; 2+Nt
The seasonal state equations of the PNK-TS are given by:
~
A
n
~
X
n+Nt
=
^
B
n
~
X
2+N(t1)
+
^
R

^
n+Nt
(5.24)
167
where
~
A
n
=
0
B
B
B
B
B
B
B
@
A
n
O
5;2+N(T1)
:::
I

I(3; 3) M
I

O
1;2+7N
:::
O
1+N7;5
I
1+7N)
O
1+7N;1
1
C
C
C
C
C
C
C
A
with
M =
0
B
B
B
B
@
I
2x1
O
1;2+N7
:::
I
2x1
I(N 3x1) O
N4x1
I
2x1
I(N 3x1) I
N4x1
1
C
C
C
C
A
;
I

=
0
B
B
B
B
@
I

O
1;2+N7
:::
O
1;2+N7
I(N 3x1)
.
.
.
.
.
. ::: I

1
C
C
C
C
A
; I

=

0 0 1 0 0

;
^
B
n
=
0
B
B
B
B
B
B
B
@
B
n
O
5;2+7N
:::
O
1;2+7N7
::: :::
O
2+7N)
I
2+7N
:::
.
.
.
.
.
. :::
1
C
C
C
C
C
C
C
A
; for n = 0; 1; 2
^
R

=
0
B
B
B
B
@
R

0
0 I
2+7N
1
C
C
C
C
A
with R

, A
n
, and B
n
dened by equations (5.5), (5.6), and (5.7) respectively.
Moreover the seasonal exogenous demand shocks are taken to have the same vari-
168
ance:
u
y
n+Nt
N(0;
2
y;n
) 8n
Thus, the period's state equation satises:

0
S
t
=
1
S
t1
+
u
U
t
+

~
t
(5.25)
with
0
;
1
given by equation (5.20);
u
;

is given by equation (5.22), andS
t
, ~
t
,
U
t
are the period's state vector, expectational errors and exogenous disturbances:
S
t
= [
~
X
Nt
~
X
1+Nt
~
X
2+Nt
]
0
~
t
= [^
Nt
^
1+Nt
^
2+Nt
]
U
t
= [u
Nt
u
1+Nt
u
2+Nt
]
where u
n+Nt
= [u
y
n+Nt
u

n+Nt
u
i
n+Nt
]
0
8n with u
n+Nt
N(0, H
n
), and
H
n
=
0
B
B
B
B
@

2
y
0 0
0
2
;n
0
0 0
2
i;n
1
C
C
C
C
A
The vector of seasonal observables (Y
n+Nt
) consist of the monthly in
ation and
policy rate, the 3-month, 1-year and 2-year yields nominal bond yields:
Y
n+Nt
= [
n+Nt
i
n+Nt
i
1
n+Nt
i
4
n+Nt
i
8
n+Nt
]
0
where (
Nt
;
1+Nt
;
2+Nt
), (i
Nt
; i
1+Nt
; i
2+Nt
) and (i
j
Nt
; i
j
1+Nt
; i
j
2+Nt
)
j=1;4;8
corre-
spond to the values of the rst, the second and the third month of the t
th
quarter.
The yields are taken to be measured with error in order to deal with the added
169
uncertainty due to the term structure information. Hence, seasonal measurement
errors are introduced:

n+Nt
= [
1
n+Nt

4
n+Nt

8
n+Nt
]
0
for n = 0; 1; 2
with
i
n+Nt
N(0;
2
i;n
); i = 1; 4; 8; n = 0; 1; 2. Therefore,
The seasonal measurement equations take the form:
Y
n+Nt
=
1
n+Nt
~
X
n+Nt
+R

n+Nt
(5.26)
where

1
n
=

O
5;1
I
5;5
O
5;2+7N

; R

=

O
2;2
I
3;3

0
For simplicity, the output data are taken to be released the period's rst subperiod,
and correspond to the quarters average, denoted byay
t
. Hence the period's vector of
observables and measurement errors are given by:
~
Y
t
= [ay
t
Y
Nt
Y
1+Nt
Y
2+Nt
]
~
t
= [
Nt

1+Nt

2+Nt
]
Thus, the period's measurement equations take the form:
~
Y
t
=
~

1
S
t
+
~
R

~
t
(5.27)
170
where
~

1
=
0
B
B
B
B
B
B
B
@
1 ::: 1 ::: 1 :::

1
1
0 :::
0 :::
1
2
0 :::
0 :::
1
3
1
C
C
C
C
C
C
C
A
;
~
R

=
0
B
B
B
B
B
B
B
@
0 :::
R

0 :::
0 R

0
0 ::: R

1
C
C
C
C
C
C
C
A
Therefore, equations (5.25) and (5.27) constitute the model's season-independent
state-space representation.
5.3.2 Estimation Method
The Bayesian approach is used for our empirical analysis, as in Smets and Wooters
(2004) [20] because it utilizes an information set broader than the one delivered by
the data. In particular, a set of prior distributions for the parameters is formed
by any information coming from other related studies, like microeconomic empirical
estimates, or even personal beliefs based on economic theory. These prior distributions
play a basic role in determining the parameters posterior distribution as they used to
weight the likelihood function:
p(jY )/L(jY )p()
where denotes the vector of parameters to be estimated; p(jY ) is the posterior
density; L(jY ) is the model's likelihood function; p() is the prior density and/
denotes proportionality
2
.
Hence, rst the model's likelihood function (L(jY )) needs to be computed. How-
2
For a detailed description of the Bayesian method see Robert (1999) [43]
171
ever, the model's forward looking component include expectational errors conditional
on the current subperiod which forbid either to treat each subperiod independently, or
to iterate backward the state equations. Thus, the model's time invariant state-space
representation is used, and the period's likelihood function (L(jY
t
)) is computed by
the Kalman Filter (KF). The period's measurement equations capture the seasonal
information availability, and pass this information to the Kalman Filter's update
equations. Therefore, the KF, at every subperiod, uses only the available data to
update the hidden state's estimates and compute the period's likelihood function.
In general the standard Kalman Filter, induce the inversion of large matrices.
This problem is augmented for the PNK-TS models, as there are subperiods with a
reduced number of observable variables, and, thus, entire rows of the measurement
equation's matrix become zero. The univariate approach introduced by Koopman and
Durbin (1998) [29],and described in the Appendix C, is used in order to overcome
the problematic matrix inversion. The basic idea of this algorithm is to convert
the multivariate state space model into a univariate model of series and apply the
univariate ltering and smoothing to avoid matrix inversion.
5.3.3 Data
Our empirical analysis is focused on the US economy for two periods: from
January 1980 to December 1992, denoted as the Volcker-Greenspan period, and from
January 1993 to December 2007, denoted as the post-1993 sample. sed on the US
economy for two periods: from January 1980 to December 1992, denoted as the
Volcker-Greenspan period, and from January 1993 to December 2007, denoted as the
post-1993 sample.
The series of the demeaned annual (per capita) US output growth (g
t
) is used as
input for the output;g
t
is constructed by the US output seasonally adjusted quarterly
172
Figure 5.1: Annual US output per capita (1980-2007).
1980 1985 1990 1995 2000 2005 2007
5
6
7
8
9
10
11
12
x 10
12
data of the annual real US GDP (in chained 2000 dollars) extracted from the Bureau
of Economic Analysis:
g
t
= 100 (log
RGDP
t
Pop
t
log
RGDP
t4
Pop
t4
)
where Pop
t
is the annual US population (available by the United States Census
Bureau) taken to remain constant throughout the year;t counts the number of periods
(i.e. quarters) in the sample. Figure 5.1 depicts the annual US output per capita for
the period from January 1980 to December 2007.
Moreover, monthly data of the US Consumer Price Index (CPI) extracted from the
Global Financial Database are used to construct the demeaned series of the monthly
US in
ation rate:

n+Nt
=
100
12
(log
CPI
n+Nt
CPI
n+N(t4)
)
Figure 5.2 depicts the monthly US in
ation rate from January 1980 to December
173
Figure 5.2: US monthly in
ation rate (1980-2007).
1980 1985 1990 1995 2000 2005 2007
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
2007.
For the nominal interest rate monthly data on the US Fed Funds Ocial Target
Rate are used; for the bond yields are used data from the monthly series of the 1, and
2 year US Bond Constant Maturity Yield, and the US Government 90-day T-Bills
Yields. All the time series are extracted from the Global Financial Database and
correspond to the annual rates. For consistency purposes the series are converted to
monthly rates (dividing them by 12). Figure 5.3 depicts the monthly series of the
ocial Fed Funds rate from January 1980 to December 2007; Figure 5.4 graphs the
monthly yields of the USA Government 90-day T-Bill, the 1-year and 2-year Bonds
with Constant Maturity (1980-2007) for the same period.
174
Figure 5.3: Monthly series of the ocial Fed Funds rate (1980-2007).
1980 1985 1990 1995 2000 2005 2007
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
5.3.4 Prior Distributions
For comparison and sensitivity check purposes, two sets of estimations, corresponding
to two dierent sets of prior distributions are pursued. The two sets of priors are
reported in Table 5.1 and are labeled as Priors 1 and 2. Each estimated model uses
the same set of priors for both samples (i.e. the Volcker-Greenspan and the post-1993
period). All the parameters are considered to be a priori independent, and the priors
are truncated only in the model's determinacy region; the discount factor () is not
estimated but is set to 0.9, while led as Priors 1 and 2. Each estimated model uses
the same set of priors for both samples (i.e. the Volcker-Greenspan and the post-1993
period). All the parameters are considered to be a priori independent, and the priors
are truncated only in the model's determinacy region; the discount factor () is not
estimated but is set to 0.9, while
The priors of the structural parameters, which are motivated from other related
175
Figure 5.4: Monthly yields of the USA Government 90-day T-Bill, and the 1-year and
2-year Bonds with Constant Maturity (1980-2007).
1980 1985 1990 1995 2000 2005 2007
0
0.5
1
1.5

3−month
1−year
2−year
studies, remain the same over all the chosen sets of priors used in our analysis. In
particular, the prior mean for the Philips curve slope is set to 0.65, following the
micro-study by Bils and Klenow (2004) [2], which reports that an average 26% of
US prices are changed every 3.3 months. In addition, the prior means for the policy
rule's coecients and
are set to 1.5 and 0.5 respectively, similar to the values
used and reported within the monetary policy literature (LS (2003) [30], Taylor(
1993) [50]). Additionally, due to the lack of academic consensus, the prior mean
for the coecient of intertemporal substitution () is set to 1.5, while we assign a
relatively large variance of 0.5 in order to allow for large changes.
However, the dierence across Priors 1 and 2 are limited to standard deviation
(std) of the measurement errors and the structural shocks: Priors 2 consider set the
std of all the shocks equal to 1; very high relatively to Priors 2. The results underline
that the dierent priors do not alter the basic conclusions. Section 5.4.4 elaborates
176
Table 5.1: Prior Distributions
Priors 1 & 2
Density Mean Std.
Structural Parameters
Gamma 1.50 0.50

Gamma 0.50 0.10
Gamma 0.65 0.10
Gamma 1.50 0.50
Beta 0.80 0.20
Priors 1 Priors 2
Density Mean Std. Density Mean Std.
Standard Deviation of Measurement Errors

T
, T=1,. . . Inv. Gamma 0.50 0.20 Inv. Gamma 0.50 1
Standard Deviation of Structural Shocks
u
y
Inv. Gamma 0.5 0.20 Inv. Gamma 0.5 1
u

n
;n = 0; 1; 2 Inv. Gamma 0.5 0.20 Inv. Gamma 0.5 1
u
i
n
;n = 0; 1; 2 Inv. Gamma 0.5 0.20 Inv. Gamma 0.5 1
on the sensitivity of our estimates with respect to the dierent prior distributions.
5.4 Results
The present study focuses on understanding the bidirectional relationship between
the structural variables and the term structure revealed by eh estimated PNK-TS
models. Thus, rst, the nature and the extend of the term structure information's
eect on the estimates is explored. To this end, the PNK-TS estimates are compared
to the estimates of the PNK models estimated without the yields information. Section
5.4.1 presents the comparison of the two sets of estimates and analyzes the in
uence
177
of the information delivered by the TS on the PNK estimates.
Our second goal focuses on understanding how the the state vector aects the
term-structure. The PNK-TS model denes an one-away interaction between the
yields and the structural variables: through the policy rate. The present study takes
advantage of the model's seasonality in order to pursue a separate analysis for sub-
periods with and without CB intervention. Section 5.4.3 elaborates on this issue.
5.4.1 Estimation Results
Tables 5.2 and 5.3 report the parameters posterior means and the 90% conrdence
interval for the PNK-TS model for both sample periods. The posterior means are
based on draws from the posterior distributions generated by Markov Chain Monte
Carlo methods. For comparison purposes Tables 5.2 and 5.3 also report the estimation
results referring to the PNK model, estimated without the term structure information,
for the same sample periods. The main dierence between the PNK and the PNK-TS
models is that within the PNK model the term-structure information is not included
in the vector of observables.
The magnitude of our estimations are comparable to the ones reported in the liter-
ature for both periods, although the time unit in the models is dierent that the mod-
els used in related studies. In particular, for the monetary policy coecients our esti-
mates for the Volcker-Greenspan sample (i.e. ^ = 1:8843; ^
= 0:4492; ^ = 0:4875)
are similar to those presented by LS (2003) [30] (i.e. ^ = 2:19; ^
= 0:30; ^ = 0:84),
although they use a larger sample period (1979:III and 1997:IV). Furthermore, for the
Post-1993 period, our policy parameters estimates (i.e. ^ = 1:3313; ^
= 0:4760; ^ =
0:4580) are quite close to those reported by LS (2005) [31] who estimate the model
for a shorter sample period (1983:I - 2002:IV) (i.e. ^ = 1:51; ^
= 0:69; ^ = 0:76).
The discrepancies between the policy responses stem from the smoother in
ation data
178
Table 5.2: Estimation results for the PNK & PNK-TS models: Volcker-Greenspan
period (1980-1992)
PNK model PNK-TS model
Mean 90% Interval Mean 90% Interval
Structural Parameters
2.5871 1.9413 2.6476 1.8843 1.1007 1.6708

0.4661 0.4413 0.4902 0.6492 0.3794 0.5051
0.4301 0.3544 0.5178 0.6692 0.6547 0.6869
0.3177 0.2645 0.3696 1.5570 1.3182 1.8115
0.3095 0.2684 0.3599 0.4875 0.4335 0.5637
Standard Deviation of Structural Shocks
u
y
0.1139 0.1036 0.1254 0.2495 0.2224 0.2793
u

0
0.3423 0.2631 0.4191 0.9724 0.7958 1.1606
u

1
0.6297 0.5258 0.7814 0.5976 0.4935 0.6778
u

2
0.1257 0.1073 0.1396 0.2285 0.1920 0.2715
u
i
0
0.1986 0.1606 0.2351 0.2887 0.1999 0.3764
u
i
1
0.1449 0.1214 0.1656 0.2063 0.1461 0.2576
u
i
2
0.1179 0.1017 0.1322 0.3182 0.2693 0.3659
Standard Deviation of Measurement Errors

1
0
0.1400 0.1199 0.1656

1
1
0.1629 0.1379 0.1787

1
2
0.1413 0.1192 0.162

4
0
0.0913 0.0781 0.1048

4
1
0.1333 0.1118 0.1531

4
2
0.1595 0.1376 0.1796

8
0
0.1509 0.1289 0.1733

8
1
0.1809 0.1558 0.2074

8
2
0.1615 0.1410 0.1880
179
Table 5.3: Estimation results for the PNK & PNK-TS models: Post-1993 period
(1993-2007)
PNK model PNK-TS Model
Mean 90% Interval Mean 90% Interval
Structural Parameters
2.2127 2.0009 2.4089 1.3132 1.9946 2.2818

0.1486 0.0915 0.2108 0.4760 0.4019 0.5381
0.3744 0.2842 0.4577 0.6728 0.6591 0.6899
0.2933 0.2356 0.3466 1.1316 0.9512 1.3006
0.3715 0.3084 0.4248 0.4580 0.3878 0.5277
Standard Deviation of Structural Shocks
u
y
0.1396 0.1256 0.1541 0.1675 0.1484 0.1883
u

0
0.4381 0.3073 0.5819 0.6557 0.5267 0.7620
u

1
0.3378 0.2643 0.4169 0.2914 0.2425 0.3378
u

2
0.1506 0.1291 0.1803 0.1742 0.1469 0.1997
u
i
0
0.2104 0.1729 0.2487 0.1669 0.1258 0.2084
u
i
1
0.1727 0.1427 0.2005 0.1213 0.0965 0.1446
u
i
2
0.1356 0.1151 0.1540 0.1819 0.1517 0.2064
Standard Deviation of Measurement Errors

1
0
0.1271 0.1072 0.1519

1
1
0.1249 0.1100 0.1439

1
2
0.1055 0.0921 0.1190

4
0
0.0822 0.0707 0.0934

4
1
0.0778 0.0683 0.0930

4
2
0.1306 0.1107 0.1482

8
0
0.1364 0.1181 0.1529

8
1
0.1357 0.1133 0.1554

8
2
0.1231 0.1074 0.1382
180
for the period 2002-2007 included in our analysis. The interest-rate smoothing coef-
cients () is the parameter in
uenced most by the CB's seasonal non-intervention
pattern. Moreover, for the Philips curve slope, our estimates are 0.6692 for the
Volcker-Greenspan period and 0.6728 for the Post-1993. Similar Gali and Rabanal
(2004) [22] report a mean estimate of 0.53 for the period 1948 to 2002; Schorfheide
(2005) [47] estimate to be 0.55 for the period 1960 to 1997, while Rabanal and
Rubio-Ramirez (2003) [40] , (2005) [41] estimate to be 0.77 (sample period 1960-
2001).
Comparing the results over the two sample periods we see that the policy coef-
cients for the Volcker-Greenspan period are higher than those for the Post - 1993
period. Therefore, the Volcker-Greenspan period is characterized by the most active
policy rule mainly due to the high and volatile in
ation rate during the sample period.
On the other hand, the smoother interest-rates during the Post-1993 period justify
the period's higher (interest-rate) smoothing coecients.
Estimates With and Without the Term-Structure Information
This section describes and explains the dierences between the estimated PNK-
TS and PNK models reported in Tables (5.2) and (5.3) for the Volcker-Greenspan
and the Post - 1993 periods respectively; columns 1-3 refer to the PNK model, and
columns 4-6 refer to the PNK-TS model.
In principle, the PNK model with seasonal CB intervention creates two sources
of uncertainty for the CB's decision: the lack of information (i.e. output is quarterly
observable) and the non-intervention subperiod. The estimates without the term-
structure information, report higher policy responses to in
ation and lower policy
responses to output than the PNK-TS model. These dierences indicate that on
one-hand the non-intervention subperiod forces the CB to over-respond to in
ation
181
in order to ensure the economy's stability for the subperiods which they will not have
the chance to intervene. On the other hand, the lack of information leads the CB to
weight less the output in the policy rule.
Interestingly, the PNK-TS model's estimates for both samples indicate that the
information delivered by the term structure helps the CB re-evaluate the policy rule.
In particular, the policy rule's responses to in
ation are much less, especially for the
Post-1993 sample ( drops from 2.2127 for the PNK model to 1.3132 for the PNK-TS
model), while in contrast the responses to output increase (from 0.1486 to 0.4760 for
the Post-1993 sample and from 0.4661 to 0.6492 for the Volcker-Greenspan period).
This consistent dierence between the two models indicate that the PNK-TS
model oers a much richer information environment. In particular, the CB assigns a
much higher weight to the output gap because the observable variables (i.e. the term
structure) deliver enough information about the economy to do so. Furthermore,
the CB does not over-react to in
ation due to the available information structure.
Hence, a more conservative policy rule, in terms of in
ation responses, and more ag-
gressive, in terns of the output responses, is estimated for both samples due to the
term structure information.
Furthermore, the interest-rate smoothing coecient's estimates () are also higher
for the PNK-TS model. Hence the eects of the seasonal lack of CB intervention on
the policy rule's smoothing nature, is limited due to the term structure information.
On the contrary, the linkage between the current in
ation and output, represented
by the Philip's curve slope () is augmented within the PNK-TS framework. In
particular, ^ increases from 0.4301 for the PNK models to 0.6692, while for the
Post -1993 sample the increase is even bigger: from 0.3741 to 0.6728. Moreover,
the coecient of risk aversion (
1
) decreases drastically in the PNK-TS framework
suggesting a much less risk avert agent. This is fully in line with our initial intuition
182
as the term-structure (data) helps the agents to hedge against the risk, which in our
framework is translated into a reduced risk aversion coecient.
5.4.2 Impulse Response Analysis (IR)
Figures 5.5 and 5.6 depict the state variables' impulse responses (IR) to the structural
shocks which realize during either an intervention or a non-intervention subperiod,
for the Volcker-Greenspan and the Post-1993 period.
The eects of the structural shocks on the state variables are similar for both
samples. In particular, a contractionary demand shock results in an in
ation and
interest rate decrease over time; an in
ation-increasing supply shock raises the in-
terest rates, while it results in a long run output decrease (below its steady state),
and a contractionary monetary policy shock causes output and in
ation to decrease.
However, the magnitude of the shocks eect dier among the dierent samples. The
model does not consider persistent structural shocks, and, thus, the shocks half-life
is rather limited.
The Post-1993 responses to policy shocks are lower than those referring to the
Volcker-Greenspan period, due to the smaller estimated monetary policy coecients.
Similar the lower risk-aversion coecient estimates for the Post-1993 period, results
in a smaller interaction between in
ation and output, and hence justify the lower
in
ation responses to demand shocks for the Post-1993 period.
The seasonal IRs distinguish between the responses corresponding to shocks occur-
ring during subperiods with and without CB intervention. There are three main con-
clusions consistent over all the samples: the in
ation responses to the non-intervention
demand shocks are much sharper than the responses to the intervention ones; the
output responses to the non-intervention supply shocks are much smaller than the
responses to the intervention ones, and the non-intervention interest-rate shocks have
183
Figure 5.5: PNK-TS: Impulse responses for the Volcker-Greenspan period (1980-
1992). Figure depicts posterior means for the output, the in
ation and the interest rate
impulse responses to a standard deviation demand, supply and policy shock realizing during
an intervention period (upper panel) and a non-intervention period (lower panel) respec-
tively. In the upper panels the dotted line corresponds to the IRs referring to the second
intervention subperiod, while the solid line corresponds to the rst intervention subperiod
0 5 10
−0.05
0
0.05
0.1
0.15
Intervention
OUTPUT
0 5 10
−0.05
0
0.05
0.1
0.15
INFLATION
0 5 10
−0.05
0
0.05
0.1
0.15
INTEREST RATE
0 5 10
−0.1
0
0.1
0.2
0.3
OUTPUT
Non−Intervention
0 5 10
−0.1
0
0.1
0.2
INFLATION
0 5 10
0
0.5
1
1.5
2
x 10
−16
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−0.8
−0.6
−0.4
−0.2
0
Intervention
OUTPUT
0 5 10
−1
−0.5
0
0.5
INFLATION
0 5 10
−0.2
0
0.2
0.4
0.6
INTEREST RATE
0 5 10
−2
0
2
4
x 10
−16
OUTPUT
Non−Intervention
0 5 10
−0.1
0
0.1
0.2
0.3
INFLATION
0 5 10
0
0.5
1
1.5
2
x 10
−16
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−0.06
−0.04
−0.02
0
Intervention
OUTPUT
0 5 10
−0.08
−0.06
−0.04
−0.02
0
INFLATION
0 5 10
0
0.02
0.04
0.06
0.08
INTEREST RATE
0 5 10
−0.4
−0.3
−0.2
−0.1
0
OUTPUT
Non−Intervention
0 5 10
−0.4
−0.3
−0.2
−0.1
0
INFLATION
0 5 10
0
0.1
0.2
0.3
0.4
INTEREST RATE
(c) Impulse responses to policy shocks
184
Figure 5.6: PNK-TS: Impulse responses for the Post-1993 period (1993 - 2007). Figure
depicts posterior means for the output, the in
ation and the interest rate impulse responses
to a standard deviation demand, supply and policy shock realizing during an intervention
period (upper panel) and a non-intervention period (lower panel) respectively. In the upper
panels the dotted line corresponds to the IRs referring to the second intervention subperiod,
while the solid line corresponds to the rst intervention subperiod
0 5 10
−0.02
0
0.02
0.04
0.06
Intervention
OUTPUT
0 5 10
−0.02
0
0.02
0.04
0.06
INFLATION
0 5 10
−0.02
0
0.02
0.04
0.06
INTEREST RATE
0 5 10
0
0.05
0.1
0.15
0.2
OUTPUT
Non−Intervention
0 5 10
−0.05
0
0.05
0.1
0.15
INFLATION
0 5 10
−5
0
5
10
x 10
−17
INTEREST RATE
(a) Impulse responses to demand shocks
0 5 10
−0.4
−0.3
−0.2
−0.1
0
Intervention
OUTPUT
0 5 10
−1
−0.5
0
0.5
INFLATION
0 5 10
−0.1
0
0.1
0.2
0.3
INTEREST RATE
0 5 10
−3
−2
−1
0
x 10
−16
OUTPUT
Non−Intervention
0 5 10
−0.1
0
0.1
0.2
INFLATION
0 5 10
0
2
4
6
8
x 10
−17
INTEREST RATE
(b) Impulse responses to supply shocks
0 5 10
−0.03
−0.02
−0.01
0
Intervention
OUTPUT
0 5 10
−0.04
−0.03
−0.02
−0.01
0
INFLATION
0 5 10
0
0.01
0.02
0.03
INTEREST RATE
0 5 10
−0.2
−0.15
−0.1
−0.05
0
OUTPUT
Non−Intervention
0 5 10
−0.2
−0.15
−0.1
−0.05
0
INFLATION
0 5 10
0
0.05
0.1
0.15
0.2
INTEREST RATE
(c) Impulse responses to policy shocks
185
a much sharper eect on in
ation and output than the intervention ones.
Thus, similar to the results presented in Chapter 4, the monetary policy dampens
the eect of the demand shocks and amplies the eects of the supply shocks. Both
results yield from the policy rule's estimates: for all the samples the policy rate's
responses to in
ation are much higher than those to output. Thus, the higher weight
is given to a variable in the policy rule, the more sensitive the economy becomes to
this variable's deviations occurring at the non-intervention subperiods, and the less
sensitive to deviations occurring at the intervention subperiods.
The intervention interest rate shocks capture the unanticipated policy rate's de-
viations from the rule, while the non-intervention ones capture the unananticipated
policy interventions. The PNK estimation results presented in Chapter 4 indicated
that the unanticipated policy rate's deviations from the rule and the unanticipated
CB intervention have similar eects on the economy. In contrast the PNK-TS esti-
mation results imply that the unanticipated CB intervention has a much sharer eect
on the economy that policy rate's deviations from the rule because the structural
responses to the non-intervention interest-rate shocks are much higher than those to
the intervention ones.
Additionally, the interest rate responses to the structural shocks are one-subperiod
lagged when the shocks realize during a non-intervention subperiod. However, the
over time interest rate's adjustment back to its steady level is identical for both the
intervention and non-intervention subperiods. This fact implies that the absence of
the monetary policy intervention results only in the delay of the shocks eect on the
interest rates as during the non-intervention subperiods the interest rates are not
aected by either in
ation or output deviations. The monetary authorities respond
to these deviations one subperiod after the shocks realization, when their size has
already been reduced, and thus the CB's initial, but one-subperiod lagged, response
186
is smaller.
5.4.3 Yield Responses
Yield Responses to the Structural Shocks
Our framework allows us to compute the yields impulse response functions to the
structural shocks. Figure 5.4.3 plots the 2-year yields IRs to the demand, supply and
interest-rate shocks for both samples.
Within our framework, the policy rule is the link between the exogenous shocks
and the yields. Furthermore, this link is one-dimensional, with the state vector af-
fecting the yields and the policy rule's coecients dene the magnitude of this ef-
fect. Therefore, an expansionary demand shock results in an in
ation and interest
rate increase over time and this translates to a positive shift of the yield curve; an
in
ation-increasing supply shock raises the interest rates and, hence, the yields, and
a contractionary monetary policy shock results in an immediate positive yields re-
sponse. The non-persistent structural shocks cause the short yield responses.
Moreover, the yield responses to the economy's exogenous disturbances during the
Volcker-Greenspan period are higher than those during the Post-1993 period. This
stems from the less aggressive policy rule implemented during the Post-1993 sample.
However, the magnitude of the yields responses to shocks dier across the dier-
ent subperiods. In particular, the yields IRs to the period's rst subperiod structural
shocks are lower than the second's, although the CB intervenes during both subperi-
ods. This underlines that the anticipation of the non-intervention subperiod dampens
the structural eects on the yields due to the zero structural eect when the CB does
not intervene.
In addition, as expected, the demand and supply shocks realizing during the non-
187
Figure 5.7: Impulse responses of the 2-year yields. Figure depicts the posterior means
for the 2-year yield's impulse responses to a standard deviation demand (rst panel),
supply (second panel) and policy shock (third panel) realizing during an intervention
period (panel's rst two graphs ) and a non-intervention period (panel's last graph)
respectively.
0 5 10
0
0.1
0.2
Intervention
OUTPUT
0 5 10
0
0.05
0.1
0 5 10
0
1
2
x 10
−16
Non − Intervention
0 5 10
0
0.5
1
Intervention
INFLATION
0 5 10
0
0.2
0.4
0 5 10
0
1
2
x 10
−16
Non − Intervention
0 5 10
0
0.05
0.1
Intervention
POLICY
0 5 10
0
0.02
0.04
0 5 10
0
0.2
0.4
Non − Intervention
(a) Volcker-Greenspan period (1980 - 1992)
0 5 10
0
0.1
0.2
Intervention
OUTPUT
0 5 10
0
0.05
0 5 10
−1
0
1
x 10
−16
Non − Intervention
0 5 10
0
0.5
1
Intervention
INFLATION
0 5 10
0
0.1
0.2
0 5 10
0
0.5
1
x 10
−16
Non − Intervention
0 5 10
0
0.02
0.04
Intervention
POLICY
0 5 10
0
0.005
0.01
0 5 10
0
0.1
0.2
Non − Intervention
(b) Post-1993 period (1993 - 2007)
188
Table 5.4: Log Marginal density for the estimated models
Volcker-Greenspan Post - 1993
(1980-1993) (1993-2007)
PRIORS (1) -324.75 -308.13
PRIORS (2) -473.38 -368.13
intervention periods do not eect the yields as they do not aect the policy rate. On
the contrary, the lack of the CB intervention allows the full interest-rate shocks pass
through to the yields. So the yields responses to the interest-rates disturbances max-
imize during the non-intervention periods indicating that the short-term deviations
coming from an unanticipated CB intervention have sharper eects on yields than
the unanticipated short-term deviations during the intervention subperiods.
5.4.4 Robustness Check
In order to check the validity of our results we pursued a number of estimation us-
ing dierent sets of priors. Table 5.1 presents the priors used for the results presented
in this present study, and Table 5.4 reports the estimation's log-marginal densities.
The second set of prior distributions (Priors 2) focus mainly on the the standard
deviation of the structural shocks and the measurement errors. In general, there is
a great uncertainty about the correct priors for these parameters given the model's
novel time unit and information set. Hence, Priors 2 consider prior means similar to
Priors 1 but much higher volatilities. Table 5.5 reports the estimation results for the
second set of prior distributions.
The estimates referring to the dierent sets of priors are statistically similar in-
dicating that the presented results are stable. Indeed the estimates 90% condence
189
Table 5.5: PNK-TS: Estimation results for Priors 2
Volcker-Greenspan Period Post-1993 periosd
Mean 90% Interval Mean 90% Interval
Structural Parameters
1.8481 1.4499 2.2143 1.2202 1.1933 2.2587

0.4553 0.3733 0.5170 0.4747 0.3904 0.5542
0.6526 0.5682 0.7184 0.7840 0.7242 0.8349
1.3643 0.9791 1.6656 1.7988 1.5917 1.9495
0.4410 0.4000 0.48108 0.4247 0.4082 0.4351
Standard Deviation of Structural Shocks
u
y
0.1909 0.1647 0.2126 0.2021 0.1527 0.2766
u

0
1.0009 0.7630 1.2860 0.7788 0.4583 1.0229
u

1
0.2616 0.2035 0.3291 0.2242 0.0624 0.3619
u

2
0.2059 0.1673 0.2415 0.1602 0.1235 0.2418
u
i
0
0.2104 0.2869 0.1452 0.3269 0.1641 0.5450
u
i
1
0.1182 0.0950 0.1460 0.1235 0.0965 0.1446
u
i
2
0.3013 0.2582 0.3544 0.2830 0.2567 0.3181
Standard Deviation of Measurement Errors

1
0
0.0792 0.0671 0.0889 0.1456 0.0943 0.1903

1
1
0.1198 0.1007 0.1396 0.1001 0.0567 0.1351

1
2
0.1047 0.0897 0.1193 0.1507 0.0479 0.5009

4
0
0.0813 0.0664 0.0948 0.0792 0.0581 0.0896

4
1
0.1215 0.1049 0.1371 0.1251 0.0585 0.2234

4
2
0.1103 0.0934 0.1255 0.0778 0.0474 0.1039

8
0
0.1008 0.0863 0.1153 0.0952 0.0599 0.1253

8
1
0.1473 0.1232 0.1673 0.0790 0.0694 0.0913

8
2
0.1324 0.1132 0.1506 0.2267 0.0766 0.5871
190
intervals reported for Priors 1 and 2 overlap suggesting the valdity of the estimates.
5.5 Conclusion
In this chapter the periodic class of models introduced in Chapter 4 is extended
in order to account for the term structure of interest rates. Furthermore, the estima-
tion technique proposed within the same chapter is applied in order to use a richer
information environment. In particular, the extended PNK model is estimated using
information from the yield curve, and is compared to the PNK estimates without the
term structure information.
The non-intervention subperiod forces the CB to over-respond to in
ation in order
to ensure the economy's stability for the subperiods that they do not intervene; on
the other hand, the seasonal lack of information leads the a lower output weight in the
policy rule. However, the PNK-TS models estimate a more conservative policy rule,
in terms of in
ation responses, and more aggressive, in terns of the output responses,
which indicates that the term-structure of interest rates provide enough information
for the current space of the economy that the CB assigns a higher weight to the
output gap.
The PNK model introduces two sources of uncertainty for the CB's decision: one
due to the seasonal lack of information as the output is quarterly observable, and
one due to the non-intervention subperiods. The non-intervention subperiod forces
the CB to over-respond to in
ation in order to ensure the economy's stability for
the subperiods which they will not intervene, and the lack of information leads the
CB to give less weight to the output in the policy rule (for more details see Chapter
4). However, the extended PNK model with term structure information identies a
more conservative policy rule, in terms of in
ation responses, and more aggressive,
191
in terns of the output responses than the PNK model without information from the
yields. Thus, the information set delivered by the term structure provides the CB
with enough insight into the current state of the economy that the CB needs not to
over-respond to in
ation deviations, or underweight the output. The high estimates
of the the price staggering coecient for the extended PNK imply a tighter linkage
between the structural variables, and the the small estimates of the coecient of risk
aversion suggest an improved hedging against risk environment.
Moreover, similar to the PNK impulse responses (IR), the extended PNK's IR
analysis suggest that a contractionary demand shock results in an in
ation and in-
terest rate decrease over time; an in
ation-increasing supply shock raises the interest
rates, while it results in a long run output decrease, and a contractionary monetary
policy shock causes output and in
ation to decrease. Furthermore, the framework's
seasonality allows us to distinguish between the responses corresponding to shocks
occurring during subperiods with and without CB intervention. There are three
main conclusions consistent over all the samples: the in
ation responses to the non-
intervention demand shocks are much sharper than the responses to the intervention
ones; the output responses to the non-intervention supply shocks are much smaller
than the responses to the intervention ones, and the non-intervention interest-rate
shocks have a much sharper eect on in
ation and output than the intervention ones.
Thus, similar to the results presented in Chapter 4, the monetary policy dampens
the eect of the demand shocks and amplies the eects of the supply shocks. Both
results yield from the policy rule's estimates: for all the samples the policy rate's
responses to in
ation are much higher than those to output. Thus, the higher weight
is given to a variable in the policy rule, the more sensitive the economy becomes to
this variable's deviations occurring at the non-intervention subperiods, and the less
sensitive to deviations occurring at the intervention subperiods.
192
The intervention interest rate shocks capture the unanticipated policy rate's de-
viations from the rule, while the non-intervention ones capture the unananticipated
policy interventions. The PNK estimation results presented in Chapter 4 indicated
that the unanticipated policy rate's deviations from the rule and the unanticipated
CB intervention have similar eects on the economy. In contrast, the PNK-TS esti-
mation results imply that the unanticipated CB intervention has a much sharer eect
on the economy that policy rate's deviations from the rule because the structural
responses to the non-intervention interest-rate shocks are much higher than those to
the intervention ones.
Additionally, the interest rate responses to the structural shocks are one-subperiod
lagged when the shocks realize during a non-intervention subperiod. However, the
over time interest rate's adjustment back to its steady level is identical for both the
intervention and non-intervention subperiods. This fact implies that the absence of
the monetary policy intervention results only in the delay of the shocks eect on the
interest rates as during the non-intervention subperiods the interest rates are not
aected by either in
ation or output deviations. The monetary authorities respond
to these deviations one subperiod after the shocks realization, when their size has
already been reduced, and thus the CB's initial, but one-subperiod lagged, response
is smaller.
One of our framework's most interesting applications is the computation of the
yields impulse response functions to the structural shocks. In particular, our models
identies the policy rule to be the only linkage between the exogenous shocks and the
yields. Therefore, an expansionary demand shock results in an in
ation and interest
rate increase over time and this translates to a positive shift of the yield curve; an in-
creasing supply shock (i.e. in
ation increases) rises the interest rates and, hence, the
yields, while a contractionary monetary policy shock results in an immediate positive
193
yields response. Moreover, the magnitude of the yield responses to the economy's
exogenous disturbances depend on the policy coecients. For example, the yield re-
sponses to the structural shocks during the Volcker-Greenspan period are higher than
those during the Post-1993 period due to the more aggressive policy rule. Addition-
ally, the yields IRs to the period's rst subperiod structural shocks are lower than the
second's, although the CB intervenes during both subperiods. This underlines that
the anticipation of the non-intervention subperiod dampens the structural eects on
the yields due to the zero structural eect when the CB does not intervene. In addi-
tion, as expected, the demand and supply shocks realizing during the non-intervention
periods do not eect the yields as they do not aect the policy rate. On the contrary,
the lack of the CB intervention allows the full interest-rate shocks pass through to the
yields. So the yields responses to the interest-rates disturbances maximize during the
non-intervention periods indicating that the short-term deviations coming from an
unanticipated CB intervention have sharper eects on yields than the unanticipated
short-term deviations during the intervention subperiods. This indicates that the
short-term deviations stemming from an unanticipated CB intervention have sharper
eects on the economy than the unanticipated short-term deviations during the in-
tervention subperiods.
Overall, the proposed extension yields interesting results. Its main advantage is
that combines the seasonal central bank intervention with a information rich environ-
ment due to the term-structure. However, the model identies an one-way relationship
between the state vector and the yields which results is a rather un-informative term-
structure. Yet the results shed light on the underlying linkages but underline the
need of a higher-dimension interaction. Hence, it seems fruitful to enrich the model
with a two-dimensional relationship between the state variables and the yields, which
translates into a policy rule reacting to the term-structure of interest rates.
194
Chapter 6
Conclusions
The present study focused on analyzing the interaction between the term structure
of interest rates and the monetary policy. To this end two dierent strands in the
literature are used: the Ane Term Structure (ATS) models and the New Keynesian
Monetary (NK) models.
From the ATS perspective, our analysis indicates that responses in the money
market rates to macroeconomic data releases and monetary policy announcements
can explain sizable and persistent jumps in the euro area yield curve. This impact
depends on the maturity horizon over which nancial market participants revise their
expectation of monetary policy given incoming data. News related to monetary policy
are found to coincide with relatively large revisions in expectations of short-term
interest rates, if compared with macroeconomic news.
Furthermore, Chapter 3 indicates that the policy rate plays a key role in explaining
the yield curve. In particular, monetary policy shocks mainly aect the medium-
term maturities, while in
ation shocks shift the whole yield curve. From a policy
perspective, our analysis imply that the ECB appears to primarily value information
that is communicated through the short end of the yield curve (6-month rate) and
195
mostly aects the medium-term maturity yields (i.e. 2-year) with a non-negligible
eect to both ends of the yield curve. Furthermore, although announcing the desired
level of in
ation rate (i.e. 2%) vastly improves the communication between the ECB
and the market, it also leads the market to heavily weight the deviation of the current
in
ation from 2%; this leads to the market's perception of the ECB policy rule as
in
ation-targeting. The policy rule that uses information from the yield curve and
allows for interaction between the policy rate and the yields, can practically pin down
the actual ECB policy decisions with a striking accuracy regarding the timing, the
direction and the magnitude of the changes in the policy rate; monetary policy rules
that neglect the information available in the yield curve perform poorly in comparison.
From a periodic NK perspective, without information from the term structure of
interest rates, in a scenario where the CB does not intervene every subperiod and does
not have all the available information, the policy rule would be more aggressive with
respect to the available information in order to ensure stability for the subperiods
that the CB does not intervene. The non-intervention subperiods force the CB to set
a policy rule that over-responds to in
ation and has a limited interest-rate smoothing
coecient and the seasonal lack of output information leads to lower policy responses
to output. However, our study indicates that by introducing information from the
yield curve the periodic NK policy rule becomes more conservative with respect to
the in
ation responses, and more aggressive, with respect to output responses; this
implies that the term structure delivers enough information about the economy's
current state that the CB considers safe to give output a higher weight.
Moreover, the impulse response (IR) analysis indicates that the direction of the
structural shocks eects on the state variables remain unchanged: a contractionary
demand shock results in an in
ation and interest rate decrease over time; an in
ation
increasing supply shock raises the interest rates, while it results in a output decrease
196
(below its steady state), and a contractionary monetary policy shock causes output
and in
ation to decrease. However, the more volatile the input series the longer the
corresponding structural shocks remain in the economy and the more volatile the
structural responses are.
In addition, the seasonal IRs distinguish between the responses corresponding to
shocks occurring during subperiods with and without CB intervention, and indicate
that the in
ation responses to the non-intervention demand shocks are much sharper
than the responses to the intervention ones, while the output responses to the non-
intervention supply shocks are much smaller than the responses to the intervention
ones. Thus, for both the PNK and the PNK-TS models, the monetary policy dampens
the eect of the demand shocks and amplies the eects of the supply shocks due to
the much higher policy rate's responses to in
ation than those to output. Hence, the
higher weight is given to a variable in the policy rule, the more sensitive the economy
becomes to this variable's deviations occurring at the non-intervention subperiods,
and the less sensitive to deviations occurring at the intervention subperiods.
The intervention interest rate shocks capture the unanticipated policy rate's de-
viations from the rule, while the non-intervention ones capture the unananticipated
policy interventions. The PNK estimation results presented in Chapter 4 indicated
that the unanticipated policy rate's deviations from the rule and the unanticipated
CB intervention have similar eects on the economy. In contrast, the PNK-TS esti-
mation results imply that the unanticipated CB intervention has a much sharer eect
on the economy that policy rate's deviations from the rule because the structural
responses to the non-intervention interest-rate shocks are much higher than those to
the intervention ones.
Additionally, the interest rate responses to the structural shocks are one-subperiod
lagged when the shocks realize during a non-intervention subperiod. However, the
197
over time interest rate's adjustment back to its steady level is identical for both the
intervention and non-intervention subperiods. This fact implies that the absence of
the monetary policy intervention results only in the delay of the shocks eect on the
interest rates as during the non-intervention subperiods the interest rates are not
aected by either in
ation or output deviations. The monetary authorities respond
to these deviations one subperiod after the shocks realization, when their size has
already been reduced, and thus the CB's initial, but one-subperiod lagged, response
is smaller.
The framework presented in Chapter 5 has one more interesting application: the
computation of the yields impulse response functions to the structural shocks: an
expansionary demand shock results in an in
ation and interest rate increase over
time and this translates to a positive shift of the yield curve; an in
ation increasing
supply shock raises the interest rates and, hence, the yields, while a contractionary
monetary policy shock results in an immediate positive yields response. Moreover,
the magnitude of the yield responses to the economy's exogenous disturbances depend
on the policy coecients. The lack of the CB intervention allows the full interest-
rate shocks pass through to the yields. So the yields responses to the interest-rates
disturbances maximize during the non-intervention periods indicating that the short-
term deviations stemming from an unanticipated CB intervention have sharper eects
on the economy than the unanticipated short-term deviations during the intervention
subperiods.
Overall, the proposed extensions yield interesting results. Its main advantage is
that combines the seasonal central bank intervention with a information rich envi-
ronment due to the term-structure. However, the model identies only an one-way
relationship between the state vector and the yields which results in a rather un-
informative term-structure. Yet, the results shed light on the underlying linkages but
198
underline the need of higher-dimension interaction. Hence, it seems fruitful to enrich
the model with a two-dimensional relationship between the state variables and the
yields, which translates into a policy rule reacting to the term-s1tructure of interest
rates.
199
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Abstract (if available)

Abstract There are two separate literatures studying the bidirectional relationship between monetary policy and the term structure of interest rates: the New Keynesian Monetary models and the Affine Term Structure models. This study presents four essays that analyze the interaction between the yield curve and the monetary policy utilizing and marrying both frameworks.

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Asset Metadata

Creator Athanasopoulou, Maria Eleni (author)

Core Title Monetary policy and the term structure of interest rates

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 08/07/2008

Defense Date 05/21/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag interest rates,monetary policy,OAI-PMH Harvest,term structure

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Magill, Michael J.P. (committee chair), Dekle, Robert (committee member), Farmer, Roger (committee member)

Creator Email athanaso@usc.edu,m.athanaso@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1555

Unique identifier UC1126417

Identifier etd-Athanasopoulou-2107 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-110540 (legacy record id),usctheses-m1555 (legacy record id)

Legacy Identifier etd-Athanasopoulou-2107.pdf

Dmrecord 110540

Document Type Dissertation

Rights Athanasopoulou, Maria Eleni

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu