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# Econometric modelling

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A brief outline of modern econometric modelling tools.

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• The mean of a time series is suppose to give a measurement of a typical value (average) of the data over the time horizon. In a stationary time series the mean is a value around which the time series fluctuates over and above as it continuously approaches this value. In fact one would expect that the value of this time series would remain around this typical value. In a non stationary time series there is no constant mean. The data does not revolve around a particular value and although the mean can be calculated it does no give an idea of the typical value which the time series is approaching.
• This is just one possibility as shown in the figure.
• Since in the model it is implied that u t is a linear combination of two non-stationary time series then this term would also be non-stationary
• The variables might be related as suggested by the underlying theory to be investigate but since the data is non-stationary a spurious regression might be obtained.
• If cointegration is established then this implies a long run equilibrium (non spurious) relationship exist among the set of variables as expressed by the OLS equation.
• where: Γi are known as short run parameters, α is the speed of adjustment parameter, ν t is a random disturbance term
• Univariate analysis
• The Ai matrices contains all the coefficients to be estimated
• ### Econometric modelling

1. 1. Econometric Modelling using Eviews Edward Bahaw March19 th 2008 Natural Gas Institute of the Americas
2. 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. 3. The Regression Equation <ul><li>Multivariate </li></ul><ul><li>Linear regression </li></ul>
4. 4. A Regression Equation X 2t X 1t u i
5. 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. 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. 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. 8. Spurious Regression Residuals Time u t is non-stationary u t corresponding to a spurious regression u t Mean
9. 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. 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. 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. 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. 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. 14. Long run and Short Run Models … (Long Run or Equilibrium Equation) … (Short run equation or ECM)
15. 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. 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. 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. 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. 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. 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. 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. 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. 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