An Introduction to Macroeconometrics: VEC and VAR Models

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Chapter 13

• An Introduction to Macroeconometrics VEC and VAR
  Models

Prepared by Vera Tabakova, East Carolina
University
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Chapter 13 An Introduction to Macroeconometrics
VEC and VAR Models

• 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

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Chapter 13 An Introduction to Macroeconometrics
VEC and VAR Models

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13.1 VEC and VAR Models

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13.1 VEC and VAR Models

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13.1 VEC and VAR Models

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13.2 Estimating a Vector Error Correction Model

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13.2.1 Example

• Figure 13.1 Real Gross Domestic Products (GDP)

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13.2.1 Example

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13.2.1 Example

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13.3 Estimating a VAR Model

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

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13.3 Estimating a VAR Model

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13.3 Estimating a VAR Model

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13.4 Impulse Responses and Variance
Decompositions

• 13.4.1 Impulse Response Functions
• 13.4.1a The Univariate Case
• The series is subject it to a shock of size
  ? in period 1.

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13.4.1a The Univariate Case

• Figure 13.3 Impulse Responses for an AR(1) model
  (y .9y(1)e) following a unit shock

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13.4.1b The Bivariate Case

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13.4.1b The Bivariate Case

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13.4.1b The Bivariate Case

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13.4.1b The Bivariate Case

• Figure 13.4 Impulse Responses to Standard
  Deviation Shock

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13.4.2 Forecast Error Variance Decompositions

• 13.4.2a The Univariate Case

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13.4.2 Forecast Error Variance Decompositions

• 13.4.2b The Bivariate Case

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13.4.2 Forecast Error Variance Decompositions

• 13.4.2b The Bivariate Case

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13.4.2 Forecast Error Variance Decompositions

• 13.4.2b The Bivariate Case

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13.4.2 Forecast Error Variance Decompositions

• 13.4.2b The Bivariate Case

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13.4.2 Forecast Error Variance Decompositions

• 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.

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Keywords

• Dynamic relationships
• Error Correction
• Forecast Error Variance Decomposition
• Identification problem
• Impulse Response Functions
• VAR model
• VEC Model

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Chapter 13 Appendix

• Appendix 13A The Identification Problem

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Appendix 13A The Identification Problem

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Appendix 13A The Identification Problem