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This book discusses the econometric foundations of structural vector autoregressive modeling, as used in empirical macroeconomics, finance, and related fields.
Time series econometrics is a rapidly evolving field. Particularly, the cointegration revolution has had a substantial impact on applied analysis. Hence, no textbook has managed to cover the full range of methods in current use and explain how to proceed in applied domains. This gap in the literature motivates the present volume. The methods are sketched out, reminding the reader of the ideas underlying them and giving sufficient background for empirical work. The treatment can also be used as a textbook for a course on applied time series econometrics. Topics include: unit root and cointegration analysis, structural vector autoregressions, conditional heteroskedasticity and nonlinear and nonparametric time series models. Crucial to empirical work is the software that is available for analysis. New methodology is typically only gradually incorporated into existing software packages. Therefore a flexible Java interface has been created, allowing readers to replicate the applications and conduct their own analyses.
1. Introduction 1 2. Identification Analysis and F.I.M.L. Estimation for the K-Mode1 10 3. Identification Analysis and F.I.ML. Estimation for the C-Model 23 4. Identification Analysis and F.I.M.L. Estimation for the AB-Model 32 5. Impulse Response Analysis and Forecast Error Variance Decomposition in SVAR Modeling 44 5 .a Impulse Response Analysis 44 5.b Variance Decomposition (by Antonio Lanzarotti) 51 6. Long-run A-priori Information. Deterministic Components. Cointegration 58 6.a Long-run A-priori Information 58 6.b Deterministic Components 62 6.c Cointegration 65 7. The Working of an AB-Model 71 Annex 1: The Notions ofReduced Form and Structure in Structural VAR Modeling 83 Annex 2: Some Considerations on the Semantics, Choice and Management of the K, C and AB-Models 87 Appendix A 93 Appendix B 96 Appendix C (by Antonio Lanzarotti and Mario Seghelini) 99 Appendix D (by Antonio Lanzarotti and Mario Seghelini) 109 References 128 Foreword In recent years a growing interest in the structural VAR approach (SVAR) has followed the path-breaking works by Blanchard and Watson (1986), Bemanke (1986) and Sims (1986), especially in U.S. applied macroeconometric literature. The approach can be used in two different, partially overlapping directions: the interpretation ofbusiness cycle fluctuations of a small number of significantmacroeconomic variables and the identification of the effects of different policies.
This handbook presents emerging research exploring the theoretical and practical aspects of econometric techniques for the financial sector and their applications in economics. By doing so, it offers invaluable tools for predicting and weighing the risks of multiple investments by incorporating data analysis. Throughout the book the authors address a broad range of topics such as predictive analysis, monetary policy, economic growth, systemic risk and investment behavior. This book is a must-read for researchers, scholars and practitioners in the field of economics who are interested in a better understanding of current research on the application of econometric methods to financial sector data.
In this book leading German econometricians in different fields present survey articles of the most important new methods in econometrics. The book gives an overview of the field and it shows progress made in recent years and remaining problems.
"Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Many analyses of time series data involve multiple, related variables. Modeling Multiple Time Series presents many specification choices and special challenges. This book reviews the main competing approaches to modeling multiple time series: simultaneous equations, ARIMA, error correction models, and vector autoregression. The text focuses on vector autoregression (VAR) models as a generalization of the other approaches mentioned. Specification, estimation, and inference using these models is discussed. The authors also review arguments for and against using multi-equation time series models. Two complete, worked examples show how VAR models can be employed. An appendix discusses software that can be used for multiple time series models and software code for replicating the examples is available. Key Features: * Offers a detailed comparison of different time series methods and approaches. * Includes a self-contained introduction to vector autoregression modeling. * Situates multiple time series modeling as a natural extension of commonly taught statistical models.
1. 1 Objective of the Study Vector autoregressive (VAR) models have become one of the dominant research tools in the analysis of macroeconomic time series during the last two decades. The great success of this modeling class started with Sims' (1980) critique of the traditional simultaneous equation models (SEM). Sims criticized the use of 'too many incredible restrictions' based on 'supposed a priori knowledge' in large scale macroeconometric models which were popular at that time. Therefore, he advo cated largely unrestricted reduced form multivariate time series models, unrestricted VAR models in particular. Ever since his influential paper these models have been employed extensively to characterize the underlying dynamics in systems of time series. In particular, tools to summarize the dynamic interaction between the system variables, such as impulse response analysis or forecast error variance decompo sitions, have been developed over the years. The econometrics of VAR models and related quantities is now well established and has found its way into various textbooks including inter alia Llitkepohl (1991), Hamilton (1994), Enders (1995), Hendry (1995) and Greene (2002). The unrestricted VAR model provides a general and very flexible framework that proved to be useful to summarize the data characteristics of economic time series. Unfortunately, the flexibility of these models causes severe problems: In an unrestricted VAR model, each variable is expressed as a linear function of lagged values of itself and all other variables in the system.
This comprehensive Handbook presents the current state of art in the theory and methodology of macroeconomic data analysis. It is intended as a reference for graduate students and researchers interested in exploring new methodologies, but can also be employed as a graduate text. The Handbook concentrates on the most important issues, models and techniques for research in macroeconomics, and highlights the core methodologies and their empirical application in an accessible manner. Each chapter is largely self-contained, whilst the comprehensive introduction provides an overview of the key statistical concepts and methods. All of the chapters include the essential references for each topic and provide a sound guide for further reading. Topics covered include unit roots, non-linearities and structural breaks, time aggregation, forecasting, the Kalman filter, generalised method of moments, maximum likelihood and Bayesian estimation, vector autoregressive, dynamic stochastic general equilibrium and dynamic panel models. Presenting the most important models and techniques for empirical research, this Handbook will appeal to students, researchers and academics working in empirical macro and econometrics.