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Mathematics - Probability Theory and Stochastic Processes | Model Reduction Methods for Vector Autoregressive Processes

Model Reduction Methods for Vector Autoregressive Processes

Brüggemann, Ralf

Softcover reprint of the original 1st ed. 2004, X, 218 p. 105 illus.

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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.

Content Level » Professional/practitioner

Keywords » Cointegration - Model Reduction - Structural VAR Models - Time Series Econometrics - Time series - Vector Autogressive (VAR) Modeling - calculus - modeling

Related subjects » Business, Economics & Finance - Econometrics / Statistics - Probability Theory and Stochastic Processes

Table of contents 

1 Introduction.- 1.1 Objective of the Study.- 1.2 Outline of the Study.- 2 Model Reduction in VAR Models.- 2.1 The VAR Modeling Framework.- 2.2 Specification of Subset VAR Models.- 2.2.1 System Versus Single Equation Strategies.- 2.2.2 System Strategies.- 2.2.3 Single Equation Strategies for Subset Modeling.- 2.2.4 Multiple Search Paths Strategies.- 2.2.5 Summarizing Remarks.- 2.3 Monte Carlo Comparison.- 2.3.1 Evaluation of Subset Methods.- 2.3.2 The Monte Carlo Design.- 2.3.3 Monte Carlo Results.- 2.4 Summary.- 3 Model Reduction in Cointegrated VAR Models.- 3.1 The Cointegrated VAR Modeling Framework.- 3.2 Modeling Cointegrated VAR Processes.- 3.3 Data Based Model Reduction.- 3.3.1 Specification of Subset VECMs.- 3.3.2 Testing for Weak Exogeneity.- 3.4 Evaluation of Model Reduction Method.- 3.4.1 Monte Carlo Comparison of Subset Methods.- 3.4.2 Small Sample Properties of Weak Exogeneity Tests.- 3.5 Summary.- 3.A DOP Parameters and Properties.- 4 Model Reduction and Structural Analysis.- 4.1 The Structural VAR Modeling Framework.- 4.2 Estimation of Structural VAR Models.- 4.2.1 Estimation with Unrestricted Reduced Form Parameters.- 4.2.2 Estimation with Restricted Reduced Form Parameters.- 4.2.3 Estimation of Just-identified Models.- 4.2.4 Estimation at Work - An Illustrative Example.- 4.3 Monte Carlo Experiments.- 4.3.1 Model Reduction and the Properties of SVAR Estimates.- 4.3.2 Model Reduction and Impulse Response Point Estimates.- 4.3.3 Model Reduction and Interval Estimates of Impulse Responses.- 4.4 Summary.- 4.A Time Series Plots.- 4.B DGP Parameters.- 5 Empirical Applications.- 5.1 The Effects of Monetary Policy Shocks.- 5.1.1 Introduction.- 5.1.2 Identification of Monetary Policy Shocks.- 5.1.3 The Empirical Model Specification.- 5.1.4 Specifying Subset VAR Models.- 5.1.5 Impulse Response Analysis.- 5.1.6 Conclusion.- 5.2 Sources of German Unemployment.- 5.2.1 Introduction.- 5.2.2 Econometric Methodology.- 5.2.3 A Small Labor Market Model.- 5.2.4 Cointegration Analysis of the German Labor Market.- 5.2.5 Structural Analysis.- 5.2.6 Conclusion.- 5.3 Summary.- 5.A Data Sources.- 5.B Two Cointegrating Vectors.- 5.C VECM Estimates.- 6 Concluding Remarks and Outlook.- 6.1 Summary.- 6.2 Extensions.- Index of Notation.- List of Figures.- List of Tables.

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