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A brief outline of modern econometric modelling tools.

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- 1. Econometric Modelling using Eviews Edward Bahaw March19 th 2008 Natural Gas Institute of the Americas
- 2. Agenda <ul><li>Regression equations </li></ul><ul><li>Spurious regressions </li></ul><ul><li>Modern Econometric Modelling techniques </li></ul><ul><ul><li>Cointegration and error correction models (ECMs) </li></ul></ul><ul><ul><li>VAR – Vector Autoregressive Modelling </li></ul></ul>
- 3. The Regression Equation <ul><li>Multivariate </li></ul><ul><li>Linear regression </li></ul>
- 4. A Regression Equation X 2t X 1t u i
- 5. <ul><li>Residuals (u t ) arise as the regression line might not pass through all the points </li></ul><ul><li>Ordinary least squares – minimizes the square of such residuals </li></ul>Regression Equation
- 6. Non stationary data Time Non - Stationary Time Series Mean does not represent the value which the time series approaches Time Mean represents the value which the series approaches over time Stationary Time Series
- 7. Spurious Regression If the residual term u t is non-stationary about a mean of zero then t he regression equation would be spurious or unreliable <ul><li>If X 1t and X 2t are two variables </li></ul><ul><li>OLS regression would give: </li></ul><ul><li>X 1t = μ + β 2 X 2t + u t , </li></ul>
- 8. Spurious Regression Residuals Time u t is non-stationary u t corresponding to a spurious regression u t Mean
- 9. Spurious Regression Using X 1t = μ + β 2 X 2t + u t , Then u t = X 1t – β 2 X 2t – μ If X 1t and X 2t are non-stationary a spurious regression may be obtained
- 10. Cointegration and Non-Stationary Variables In the model: X 1t = μ + β 2 X 2t + u t , Or u t = X 1t – β 2 X 2t – μ If u t is stationary about a mean of zero then cointegration exists.
- 11. Cointegration and Equilbirum <ul><li>If cointegration exists then there is a long-run equilibrium relationship between X 1t and X 2t </li></ul><ul><li>If u t is non-stationary then there is no cointegration and the model does not represent a long run equilibrium </li></ul>
- 12. Error Correction Model <ul><li>If X 1t or X 2t are cointegrated then there must be a short-run relationship which specifies how the equilibrium is maintained. </li></ul><ul><li>This relationship is called the error correction model (ECM) </li></ul>
- 13. Error Correction Model <ul><li>This model expresses changes in the dependent variable as a function of: </li></ul><ul><li>current changes in the independent variables </li></ul><ul><li>the residual or ‘error’ term in the previous period </li></ul>
- 14. Long run and Short Run Models … (Long Run or Equilibrium Equation) … (Short run equation or ECM)
- 15. Error Correction Model <ul><li>If u t-1 is positive (an error exists) </li></ul><ul><li>In order to restore equilibrium X 1 has to decrease in the following period. </li></ul><ul><li>Thus Δ X 1t is negative </li></ul>
- 16. Error Correction Model <ul><li>A positive u t-1 is associated with a negative Δ X 1t </li></ul><ul><li>The coefficient must therefore be significantly negative </li></ul>
- 17. <ul><li>Autoregressive Models </li></ul>Such models express the current value of a variable as a function of past values <ul><li>K = lag length </li></ul><ul><li>Historical values of the variable help determine or forecast future values </li></ul>
- 18. <ul><li>Vector Autoregressive (VAR) Modeling </li></ul><ul><li>where X t is a p×1vector of p variables </li></ul><ul><li>All variables are endogenous </li></ul>
- 19. VAR Formulation <ul><li>In a two variable system (Y t and Z t ) a 2 lag order VAR can be expressed as follows. </li></ul>
- 20. VAR Formulation <ul><li>Using the following representations: </li></ul><ul><li>The system of equations can be expressed more compactly as: </li></ul>
- 21. VARs <ul><li>Applicable to time series data pertaining to economic data </li></ul><ul><li>Perform well at forecasting </li></ul><ul><li>Used widely in sensitivity analysis </li></ul>
- 22. VARs and Cointegration <ul><li>If u t is stationary then the variables are cointegrated. </li></ul><ul><li>That is there is a long run equilibrium relationship exists among the variables. </li></ul>
- 23. Vector Error Correction Model (VECM) <ul><li>The VECM is a VAR in first difference </li></ul>where β’ is the matrix of cointegration vectors α is the speed of adjustment parameter

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