Monetary Policy Rules and Term Structure of Interest Rates

Transcription

1 Ana Luiza Abrão Roriz Soares de Carvalho Monetary Policy Rules and Term Structure of Interest Rates 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

2 Ana Luiza Abrão Roriz Soares de Carvalho Monetary Policy Rules and Term Structure of Interest Rates 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

3 All rights reserved. Ana Luiza Abrão Roriz Soares de Carvalho 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). Abrão Roriz, Ana Luiza Bibliographic data Monetary Policy Rules and Term Structure of Interest Rates / Ana Luiza Abrão Roriz Soares de Carvalho ; adviser: Luciano Vereda Oliveira f. : il. ; 30 cm Dissertação (Mestrado em Ciências Atuariais)-Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Inclui bibliografia 1. Instituto de Gestão de Riscos Financeiros e Atuariais Teses. 2. Modelos Estatísticos Aplicados a Finanças. 3. Análise de fatores. 4. Análise de Componentes Principais. 5. Regras de Poĺıtica Monetária. 6. Variáveis Macroeconômicas. 7. Estrutura a Termo da Taxa de Juros. I. Oliveira, Luciano Vereda. II. Pontifícia Universidade Católica do Rio de Janeiro. Instituto de Gestão de Riscos Financeiros e Atuariais. III. Título. CDD: 281

4 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.

5 Abstract Abrão Roriz, Ana Luiza; Oliveira, Luciano Vereda. Monetary Policy Rules and Term Structure of Interest Rates. Rio de Janeiro, p. MScThesis Departamento de Instituto de Gestão de Riscos Financeiros e Atuariais, Pontifícia 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.

6 Resumo Abrão Roriz, Ana Luiza; Oliveira, Luciano Vereda. Regras de Política Monetária e Estrutura a Termo da Taxa de Juros: Uma Abordagem com Fatores. Rio de Janeiro, p. Dissertação de Mestrado Departamento de Instituto de Gestão de Riscos Financeiros e Atuariais, Pontifícia 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 política 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 Estatísticos Aplicados a Finanças. Análise de fatores. Análise de Componentes Principais. Regras de Política Monetária. Variáveis Macroeconômicas. Estrutura a Termo da Taxa de Juros.

7 Contents 1 Introduction 12 2 Theoretical Framework Factor Analysis Monetary Policy Rules 21 3 Results from Factor Analysis Overall Strategy Data Analysis Method 1 - Benchmark method Method 2 - I(0) assumption Method 3 - EM Algorithm Testing the Factor Decomposition Throughout Time 49 4 Monetary Policy Rules Reaction Functions in a Data Rich Ambient Testing the efficiency of extracted factors Does the Central Bank really care about everything? 67 5 Term Structure of Interest Rates Continuous Time Bond Pricing A Factor-Augmented Model in Discrete Time Term Structure Estimation 85 6 Conclusions 94 Bibliography 97 A Data Appendix - USA 100 B Data Appendix - Brazil 106

8 List of Figures 3.1 Interest rates and prices - USA Interest rates and prices - Brazil Estimated Factor Scores - USA, Method Correlation between Factors and Series - USA, Method Industrial Production and Factor 1 - USA, Method New Private Housing Units and Factor 2 - USA, Method Personal Expenditures Index and Factor 3 - USA, Method Total Consumer Credit Outstanding and Factor 4 - USA, Method Estimated Factor Scores - Brazil, Method Correlation between Factors and Series - Brazil, Method Installed Capacity Utilization and Factor 1 - Brazil, Method Spot Exchange Rate: USD-BRL and Factor 2 - Brazil, Method Investment: Construction and Factor 3- Brazil, Method Investment: Construction and Factor 4- Brazil, Method Estimated Factor Scores - USA, Method Correlation between Factors and Series - USA, Method Year Treasury Bill and Factor 1 - USA, Method All Employees: Total Private Industries and Factor 2 - USA, Method Installed Capacity Utilization and Factor 3 - USA, Method Installed Capacity Utilization and Factor 4 - USA, Method Estimated Factor Scores - Brazil, Method Correlation between Factors and Series - Brazil, Method Swap Preset Di-Rate Term Rate 2 and Factor 1 - Brazil, Method Emerging Markets Bond Index (EMBI) and Factor 2 - Brazil, Method Industrial Production and Factor 3- Brazil, Method Ibovespa Stock Index and Factor 4- Brazil, Method Estimated Factor Scores - USA, Method Correlation between Factors and Series - USA, Method Industrial Production and Factor 1 - USA, Method Civilians Unemployed and Factor 2 - USA, Method Producer Price Index: Finished Goods and Factor 3 - USA, Method Installed Capacity Utilization and Factor 4 - USA, Method Estimated Factor Scores - Brazil, Method Correlation between Factors and Series - Brazil, Method Time Deposits Rate (CDB) and Factor 1 - Brazil, Method Spread: Selic Rate - 12-month Term Rate and Factor 2- Brazil, Method Industrial Production Index and Factor 4- Brazil, Method Estimated Factor Scores - Sub-sample ( ), USA Estimated Factor Scores - Sub-sample ( ), USA Correlation between Factors and Series - Sub-sample ( ), USA 55

9 3.41 Correlation between Factors and Series - Sub-sample ( ), USA Estimated Factor Scores - Sub-sample ( ), Brazil Estimated Factor Scores - Sub-sample ( ), Brazil Correlation between Factors and Series - Sub-sample ( ), Brazil Correlation between Factors and Series - Sub-sample ( ), Brazil Iterative Estimations of Reaction Functions - USA - Balanced Panel Iterative Estimations of Reaction Functions - USA - Unbalanced Panel Iterative Estimations of Reaction Functions - Brazil - Balanced Panel Iterative Estimations of Reaction Functions - Brazil - Unbalanced Panel Term structure estimates, 3 month yields - USA Term structure estimates, 6 month yields - USA Term structure estimates, 1 year yields - USA Term structure estimates, 3 month yields - BRAZIL Term structure estimates, 6 month yields - BRAZIL Term structure estimates, 1 year yields - BRAZIL 92

10 List of Tables 3.1 Methods used for comparing extracted factors Extracted Factors and Explained Variance - USA Extracted Factors and Explained Variance - BRAZIL Factor-Augmented Reaction Function - USA - Method Factor-Augmented Reaction Function - USA - Method Factor-Augmented Reaction Function - USA - Method Factor-Augmented Reaction Function - Brazil - Method Factor-Augmented Reaction Function - Brazil - Method Factor-Augmented Reaction Function - Brazil - Method Taylor rule estimates - USA Taylor rule estimates - Brazil Correlation of factors, lagged factors and yields - USA Correlation of factors, lagged factors and yields - Brazil Estimate results - Term structure model 93

11 ...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,.