1. An Introduction to Macroeconometrics: VEC and VAR Models Prepared by Vera Tabakova, East Carolina University

2.  13.1 VEC and VAR Models  13.2 Estimating a Vector Error Correction model  13.3 Estimating a VAR Model  13.4 Impulse Responses and Variance Decompositions

8. Figure 13.1 Real Gross Domestic Products (GDP)

11. Figure 13.2 Real GDP and the Consumer Price Index (CPI)

14.  13.4.1 Impulse Response Functions  13.4.1a The Univariate Case The series is subject it to a shock of size ν in period 1.

15. Figure 13.3 Impulse Responses for an AR(1) model (y =.9y(–1)+e) following a unit shock

19. Figure 13.4 Impulse Responses to Standard Deviation Shock

20.  13.4.2a The Univariate Case

21.  13.4.2b The Bivariate Case

25.  13.4.2c The General Case  The example above assumes that x and y are not contemporaneously related and that the shocks are uncorrelated. There is no identification problem and the generation and interpretation of the impulse response functions and decomposition of the forecast error variance are straightforward. In general, this is unlikely to be the case. Contemporaneous interactions and correlated errors complicate the identification of the nature of shocks and hence the interpretation of the impulses and decomposition of the causes of the forecast error variance.

26. Slide 13-26 Principles of Econometrics, 3rd Edition  Dynamic relationships  Error Correction  Forecast Error Variance Decomposition  Identification problem  Impulse Response Functions  VAR model  VEC Model

27. Slide 13-27 Principles of Econometrics, 3rd Edition

28. Slide 13-28 (13A.1)

29. Principles of Econometrics, 3rd Edition Slide 13-29 (13A.2)