Chapter 47 VECTOR AUTOREGRESSIONS COINTEGRATION Introductory An example A useful lemma Continuing A general Applications Implications for econometric practice with the example framework comments regressors | chapter 47 VECTOR AUTOREGRESSIONS AND COINTEGRATION MARK w. WATSON Northwestern University and Federal Reserve Bank of Chicago Contents Abstract 2844 1. Introduction 2844 2. Inference in VARs with integrated regressors 2848 . Introductory comments 2848 . An example 2848 . A useful lemma 2850 . Continuing with the example 2852 . A general framework 2854 . Applications 2860 . Implications for econometric practice 2866 3. Cointegrated systems 2870 . Introductory comments 2870 . Representations for the 1 1 cointegrated model 2870 . Testing for cointegration in 1 1 systems 2876 . Estimating cointegrating vectors 2887 . The role of constants and trends 2894 4. Structural vector autoregressions 2898 . Introductory comments 2898 . The structural moving average model impulse response functions and variance decompositions 2899 . The structural VAR representation 2900 . Identification of the structural VAR 2902 . Estimating structural VAR models 2906 References 2910 The paper has benefited from comments by Edwin Denson Rob Engle Neil Ericsson Michael Horvath Soren Johansen Peter Phillips Greg Reinsei James Stock and students at Northwestern University and Studienzentrum Gerzensee. Support was provided by the National Science Foundation through grants SES -89 10601 and 91- 22463. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2844 . Watson Abstract This paper surveys three topics vector autoregressive VAR models with integrated regressors cointegration and structural VAR modeling. The paper begins by developing methods to study potential unit root problems in multivariate models and then presents a simple set of rules designed to help applied researchers conduct inference in VARs. A large number of examples are studied including tests for Granger causality tests for VAR lag length spurious regressions and OLS estimators of cointegrating vectors.
