Ana Luiza Abrão Roriz Soares de Carvalho
Monetary Policy Rules and Term Structure of
Interest Rates
PUC-Rio - Certificação Digital Nº 0713588/CA
A Factor-Augmented Approach
DISSERTAÇÃO DE MESTRADO
Thesis presented to the Postgraduate Program in Ciências Atuariais of the Instituto de Gestão de Riscos Financeiros e Atuariais
as partial fulfillment of the requirements for the degree of Mestre
em Ciências Atuariais
Adviser: Prof. Luciano Vereda Oliveira
Rio de Janeiro
March 2009
Ana Luiza Abrão Roriz Soares de Carvalho
Monetary Policy Rules and Term Structure of
Interest Rates
PUC-Rio - Certificação Digital Nº 0713588/CA
A Factor-Augmented Approach
Thesis presented to the Postgraduate Program in Ciências Atuariais of the Instituto de Gestão de Riscos Financeiros e Atuariais
as partial fulfillment of the requirements for the degree of Mestre
em Ciências Atuariais Approved by the following commission:
Prof. Luciano Vereda Oliveira
Adviser
Instituto de Gestão de Riscos Financeiros e Atuariais - PUC-Rio
Prof. Cristiano Coelho Augusto Fernandes
Departamento de Engenharia Elétrica - PUC-Rio
Prof. Hélio Côrtes Vieira Lopes
Departamento de Matemática - PUC-Rio
Prof. Nizar Messari
Coordinator of the Centro de Ciências Sociais — PUC–Rio
Rio de Janeiro , 27 de março de 2009
All rights reserved.
Ana Luiza Abrão Roriz Soares de Carvalho
PUC-Rio - Certificação Digital Nº 0713588/CA
Is an economist graduated by the Department of Economics at
the Pontifical Catholic University of Rio de Janeiro and is also
a MSc candidate in Financial Mathematics at the National
Institute of Pure and Applied Mathematics (IMPA).
Bibliographic data
Abrão Roriz, Ana Luiza
Monetary Policy Rules and Term Structure of Interest
Rates / Ana Luiza Abrão Roriz Soares de Carvalho ; adviser:
Luciano Vereda Oliveira. — 2009.
111 f. : il. ; 30 cm
Dissertação (Mestrado em Ciências Atuariais)-Pontifı́cia
Universidade Católica do Rio de Janeiro, Rio de Janeiro, 2009.
Inclui bibliografia
1. Instituto de Gestão de Riscos Financeiros e Atuariais
– Teses. 2. Modelos Estatı́sticos Aplicados a Finanças. 3.
Análise de fatores. 4. Análise de Componentes Principais. 5.
Regras de Polı́tica Monetária. 6. Variáveis Macroeconômicas.
7. Estrutura a Termo da Taxa de Juros. I. Oliveira, Luciano
Vereda. II. Pontifı́cia Universidade Católica do Rio de Janeiro.
Instituto de Gestão de Riscos Financeiros e Atuariais. III.
Tı́tulo.
CDD: 281
PUC-Rio - Certificação Digital Nº 0713588/CA
Acknowledgments
I would like to express my sincere acknowledgments to..
CAPES for the financial help and to IAPUC, in the person of Prof. Luiz
Roberto Cunha, for supporting research activities since the beginning of the
program.
Prof. Cristiano Fernandes, our coordinator and professor. I thank him
for the challenging courses, which made me give my best, and for the example
of academic conduct that I admire and will always try to follow.
My dear supervisor, Prof. Luciano Vereda. In spite of having “irreconcilable differences” with him regarding the order of integration of inflation and
interest rates, his dedication and availability were very important during the
whole program. Thank you for your patience and friendship.
Prof. Carlos Kubrusly, for the Measure Theory course. This course
changed the way I see Mathematics. Prof. Hélio Lopes who was very engaged
in the beginning of this work, and Prof. Adrian Pizzinga, who was always
available and willingful to help with my econometric doubts. I also thank
Luciene Pereira for helping with all the bureaucratic issues solved at IAPUC
and for the company during my studying afternoons.
I am (VERY!!) grateful to my mom. Thank you for your constant care
and friendship, for the endless prayers during the exam weeks, and for the
financial support that gave me tranquility to focus on my studies.
I also indebted to Ana Carla, my cousin and god-mother. Thank you for
your friendship, for the advice, and for never giving up on the task of making
me a more responsible and reasonable person.
To my great friends and master’s colleagues, Bruna Casotti, Eduardo
Bevilaqua and Tarso Madeira. The study was a lot more pleasant with you
around.
To my friends from IMPA Emilio Vital Brazil, Leonardo Muller and Julio
Daniel for the computational help, and Marcelo Hilario and Tertuliano Franco
for the probabilistic help.
To all my friends from the financial market who helped me with collecting
time series to my data sets. Without their goodwill with my countless demands
this thesis would not have been completed. I am extremely grateful to Beatriz
Aiex, Eduardo Lourenço, Julia Ladeira, Livio Ribeiro, Roberto Padovani and
Túlio Barbosa.
Last but not least to my friend Guilherme Maia, who besides belonging
to the previous paragraph, was also a great consultant to econometric and
monetary policy issues.
Abstract
PUC-Rio - Certificação Digital Nº 0713588/CA
Abrão Roriz, Ana Luiza; Oliveira, Luciano Vereda. Monetary Policy
Rules and Term Structure of Interest Rates . Rio de Janeiro,
2009. 111p. MScThesis — Departamento de Instituto de Gestão de
Riscos Financeiros e Atuariais, Pontifı́cia Universidade Católica do Rio
de Janeiro.
The Central Bank collects and analyzes hundreds of economic time
series. Therefore, if it bears the costs of monitoring all this information, it
is expected that the monetary authority considers it when taking monetary
policy decisions. In this thesis, we apply an idea by Bernanke and Boivin to
test whether the Central Bank truly reacts to an informational set that goes
beyond the traditional measures of inflation and output gap, when deciding
the base interest rate. We use Factor Analysis to extract latent factors of a
large set of macroeconomic variables e we test whether these factors lead to
better specified reaction functions. Besides, we test the factors’ efficacy in a
“Factor-Augmented Affine Model” to the term structure of interest rates.
Keywords
Statistical Models Applied to Finance. Factor Analysis. Principal
Component Analysis. Monetary Policy Rules. Macroeconomic Variables.
Term Structure of Interest Rates.
Resumo
PUC-Rio - Certificação Digital Nº 0713588/CA
Abrão Roriz, Ana Luiza; Oliveira, Luciano Vereda. Regras de Polı́tica
Monetária e Estrutura a Termo da Taxa de Juros: Uma Abordagem com Fatores. Rio de Janeiro, 2009. 111p. Dissertação de Mestrado — Departamento de Instituto de Gestão de Riscos Financeiros e
Atuariais, Pontifı́cia Universidade Católica do Rio de Janeiro.
O Banco Central coleta e acompanha centenas de séries temporais. Logo
se este arca com os custos de monitorar toda essa informação, é de se esperar
que ele a leve em conta ao tomar suas decisões de polı́tica monetária. Neste
trabalho aplicamos uma idéia de Bernanke e Boivin para testar se de fato o
Banco Central reage a um conjunto informacional que vai além das medidas
tradicionais de inflação e hiato do produto ao decidir a taxa básica de juros.
Usamos Análise de Fatores para extrair fatores latentes de um grande conjunto
de variáveis macroeconômicas e testamos se estes fatores levam a funções
de reação melhor especificadas. Além disso, testamos também a eficácia dos
fatores em um “Factor-Augmented Affine Model” para a estrutura a termo da
taxa de juros.
Palavras–chave
Modelos Estatı́sticos Aplicados a Finanças. Análise de fatores. Análise
de Componentes Principais. Regras de Polı́tica Monetária. Variáveis Macroeconômicas. Estrutura a Termo da Taxa de Juros.
Contents
PUC-Rio - Certificação Digital Nº 0713588/CA
1
Introduction
12
2 Theoretical Framework
2.1 Factor Analysis
2.2 Monetary Policy Rules
14
14
21
3 Results from Factor Analysis
3.1 Overall Strategy
3.2 Data Analysis
3.3 Method 1 - Benchmark method
3.4 Method 2 - I(0) assumption
3.5 Method 3 - EM Algorithm
3.6 Testing the Factor Decomposition Throughout Time
23
23
26
28
37
43
49
4 Monetary Policy Rules
4.1 Reaction Functions in a Data Rich Ambient
4.2 Testing the efficiency of extracted factors
4.3 Does the Central Bank really care about everything?
61
61
65
67
5 Term Structure of Interest Rates
5.1 Continuous Time Bond Pricing
5.2 A Factor-Augmented Model in Discrete Time
5.3 Term Structure Estimation
72
73
78
85
6
94
Conclusions
Bibliography
97
A
Data Appendix - USA
100
B
Data Appendix - Brazil
106
PUC-Rio - Certificação Digital Nº 0713588/CA
List of Figures
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
3.29
3.30
3.31
3.32
3.33
3.34
3.35
3.36
3.37
3.38
3.39
3.40
Interest rates and prices - USA
Interest rates and prices - Brazil
Estimated Factor Scores - USA, Method 1
Correlation between Factors and Series - USA, Method 1
Industrial Production and Factor 1 - USA, Method 1
New Private Housing Units and Factor 2 - USA, Method 1
Personal Expenditures Index and Factor 3 - USA, Method 1
Total Consumer Credit Outstanding and Factor 4 - USA, Method 1
Estimated Factor Scores - Brazil, Method 1
Correlation between Factors and Series - Brazil, Method 1
Installed Capacity Utilization and Factor 1 - Brazil, Method 1
Spot Exchange Rate: USD-BRL and Factor 2 - Brazil, Method 1
Investment: Construction and Factor 3- Brazil, Method 1
Investment: Construction and Factor 4- Brazil, Method 1
Estimated Factor Scores - USA, Method 2
Correlation between Factors and Series - USA, Method 2
10 Year Treasury Bill and Factor 1 - USA, Method 2
All Employees: Total Private Industries and Factor 2 - USA, Method 2
Installed Capacity Utilization and Factor 3 - USA, Method 2
Installed Capacity Utilization and Factor 4 - USA, Method 2
Estimated Factor Scores - Brazil, Method 2
Correlation between Factors and Series - Brazil, Method 2
Swap Preset Di-Rate - 360 Term Rate 2 and Factor 1 - Brazil,
Method 2
Emerging Markets Bond Index (EMBI) and Factor 2 - Brazil,
Method 2
Industrial Production and Factor 3- Brazil, Method 2
Ibovespa Stock Index and Factor 4- Brazil, Method 2
Estimated Factor Scores - USA, Method 3
Correlation between Factors and Series - USA, Method 3
Industrial Production and Factor 1 - USA, Method 3
Civilians Unemployed and Factor 2 - USA, Method 3
Producer Price Index: Finished Goods and Factor 3 - USA, Method 3
Installed Capacity Utilization and Factor 4 - USA, Method 3
Estimated Factor Scores - Brazil, Method 3
Correlation between Factors and Series - Brazil, Method 3
Time Deposits Rate (CDB) and Factor 1 - Brazil, Method 3
Spread: Selic Rate - 12-month Term Rate and Factor 2- Brazil,
Method 3
Industrial Production Index and Factor 4- Brazil, Method 3
Estimated Factor Scores - Sub-sample (1983-1995), USA
Estimated Factor Scores - Sub-sample (1995-2008), USA
Correlation between Factors and Series - Sub-sample (1983-1995),
USA
27
27
30
31
32
32
33
33
34
35
36
36
36
37
38
39
40
40
40
41
42
43
44
44
45
45
46
47
48
48
49
49
50
51
52
52
53
53
54
55
3.41 Correlation between Factors and Series - Sub-sample (1995-2008),
USA
3.42 Estimated Factor Scores - Sub-sample (1999-2003), Brazil
3.43 Estimated Factor Scores - Sub-sample (2003-2008), Brazil
3.44 Correlation between Factors and Series - Sub-sample (1999-2003),
Brazil
3.45 Correlation between Factors and Series - Sub-sample (2003-2008),
Brazil
4.1
4.2
PUC-Rio - Certificação Digital Nº 0713588/CA
4.3
4.4
5.1
5.2
5.3
5.4
5.5
5.6
Iterative
Iterative
Panel
Iterative
Iterative
Panel
Term
Term
Term
Term
Term
Term
56
57
58
59
60
Estimations of Reaction Functions - USA - Balanced Panel 69
Estimations of Reaction Functions - USA - Unbalanced
69
Estimations of Reaction Functions - Brazil - Balanced Panel 70
Estimations of Reaction Functions - Brazil - Unbalanced
70
structure
structure
structure
structure
structure
structure
estimates,
estimates,
estimates,
estimates,
estimates,
estimates,
3
6
1
3
6
1
month yields - USA
month yields - USA
year yields - USA
month yields - BRAZIL
month yields - BRAZIL
year yields - BRAZIL
90
91
91
91
92
92
PUC-Rio - Certificação Digital Nº 0713588/CA
List of Tables
3.1
3.2
3.3
Methods used for comparing extracted factors
Extracted Factors and Explained Variance - USA.
Extracted Factors and Explained Variance - BRAZIL
25
28
29
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Factor-Augmented Reaction Function
Factor-Augmented Reaction Function
Factor-Augmented Reaction Function
Factor-Augmented Reaction Function
Factor-Augmented Reaction Function
Factor-Augmented Reaction Function
Taylor rule estimates - USA
Taylor rule estimates - Brazil
62
62
62
64
64
64
66
66
5.1
5.2
5.3
Correlation of factors, lagged factors and yields - USA
Correlation of factors, lagged factors and yields - Brazil
Estimate results - Term structure model
-
USA - Method 1
USA - Method 2
USA - Method 3
Brazil - Method 1
Brazil - Method 2
Brazil - Method 3
88
89
93
PUC-Rio - Certificação Digital Nº 0713588/CA
...the program of understanding the real, macroeconomic risks that drive asset prices (or the
proof that they do not do so at all) is not some
weird branch of finance; it is the trunk of the
tree.
John Cochrane, .