ECON 366: ECONOMETRICS II SPRING TERM 2005: LAB EXERCISE #12 VAR Brief suggested solution

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1 DEPARTMENT OF ECONOMICS UNIVERSITY OF VICTORIA ECON 366: ECONOMETRICS II SPRING TERM 2005: LAB EXERCISE #12 VAR Brief suggested solution Location: BEC Computing LAB 1) See the relevant parts in lab 11 solution. 2) a) Estimate the VAR(1) model given as: t1 t 2 = δ + θ = δ + θ 21 t 1,1 t 1,1 + γ 11 + γ 21 t 1,2 t 1,2 + v t1 + v Report the asmptotic standard errors in parenthesis. Answer: To specif a VAR in EViews, ou must first create a var object. Select Quick/Estimate VAR The Basics tab of the VAR Specification dialog box will prompt ou to define the structure of our VAR. You should fill out the dialog box with the appropriate information: Select the VAR tpe: Unrestricted VAR. Set the estimation sample (For this question, the default is fine). Enter the lag specification in the appropriate edit box. This information is entered in pairs: each pair of numbers defines a range of lags. For example, the lag pair here will be: 1 1 which tells EViews to use the first lag of all the endogenous variables in the sstem as right-hand side variables. You can add an number of lag intervals, all entered in pairs. The lag specification for part (c) will be: 1 2 uses lags 1-2 of all the endogenous variables in the sstem as right hand side variables. Enter the names of endogenous and exogenous series in the appropriate edit boxes. Here ou will list 1, 2 as endogenous series, and will use the special series c as the constant exogenous term. t 2

2 The output: Vector Autoregression Estimates Date: 04/01/05 Time: 14:23 Sample (adjusted): 1951Q3 1969Q4 Included observations: 74 after adjustments Standard errors in ( ) & t-statistics in [ ] Y1 Y2 Y1(-1) ( ) ( ) [ ] [ ] Y2(-1) ( ) ( ) [ ] [ ] C ( ) ( ) [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion Each column in the table corresponds to an equation in the VAR. For each right-hand side variable, EViews reports the estimated coefficient, its standard error, and the t-statistic. ˆt1 ˆ t 2 = t-1, t-1,2 (2.4178) (0.1034) (0.0979) = t-1, t-1,2 (2.9343) (0.1255) (0.1189)

3 b) Use the results from part (a) to test for Granger causalit. Answer: We support the notion that 2 Granger causes 1 if we reject the null hpothesis: H 0 : γ 11 = 0 (1 restriction) vs H a : γ 11 0 From the output, the value of the test statistic is and the associated asmptotic p- value is So we reject H 0, which means the sample supports the notion that 2 Granger causes 1. We support the notion that 1 Granger causes 2 if we reject the null hpothesis: H 0 : θ 21 = 0 (1 restriction) vs H a : θ 21 0 From the output, the value of the test statistic is and the associated asmptotic p- value is So we fail to reject H 0 at 5% level of significance, which means the sample does not support the notion that 2 Granger causes 1. VAR Granger Causalit/Block Exogeneit Wald Tests Date: 04/01/05 Time: 16:17 Sample: 1951Q2 1969Q4 Included observations: 74 Dependent variable: Y1 Y All Dependent variable: Y2 Y All (To obtain the Granger causalit test results in EViews, click on View/Lag Structure in the VAR window. Then choose Granger Causalit Test. It carries out pairwise Granger causalit tests and tests whether an endogenous variable can be treated as exogenous. For each equation in the VAR, the output displas chi-

4 squared (Wald) statistics for the joint significance of each of the other lagged endogenous variables in that equation. The statistic in the last row (All) is the chi-squared statistic for joint significance of all other lagged endogenous variables in the equation. Note that here we have no other lagged endogenous variables besides those associated with 1 and 2.) c) Instead of a VAR(1) as in part (a), estimate a VAR(2) model now. Report the asmptotic standard errors in parenthesis. Answer: Report the results as we did in part (a). Vector Autoregression Estimates Date: 04/01/05 Time: 14:28 Sample (adjusted): 1951Q4 1969Q4 Included observations: 73 after adjustments Standard errors in ( ) & t-statistics in [ ] Y1 Y2 Y1(-1) ( ) ( ) [ ] [ ] Y1(-2) ( ) ( ) [ ] [ ] Y2(-1) ( ) ( ) [ ] [ ] Y2(-2) ( ) ( ) [ ] [ ] C ( ) ( ) [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC

5 Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion d) Use the results from part (c) to test for Granger causalit. Answer: We support the notion that 2 Granger causes 1 if we reject the null hpothesis: H 0 : γ 11 = γ 12 = 0 (2 restrictions) vs H a : at least one of them 0 From the output, the value of the test statistic is and the associated asmptotic p- value is So we reject H 0, which means the sample supports the notion that 2 Granger causes 1. We support the notion that 1 Granger causes 2 if we reject the null hpothesis: H 0 : θ 21 = θ 22 = 0 (2 restrictions) vs H a : at least one of them is not equal to 0. From the output, the value of the test statistic is and the associated asmptotic p- value is So we fail to reject H 0 at 5% level of significance, which means the sample does not support the notion that 2 Granger causes 1. VAR Granger Causalit/Block Exogeneit Wald Tests Date: 04/01/05 Time: 16:29 Sample: 1951Q2 1969Q4 Included observations: 73 Dependent variable: Y1 Y All

6 Dependent variable: Y2 Y All