VECTOR ERROR CORRECTION MODEL AN EVIEWS APPLICATION

Transcription

1 VECTOR ERROR CORRECTION MODEL AN EVIEWS APPLICATION DATA OBS CONS EX GDP Here, GDP = GDP CONS = Consumption EX= Export 1

2 UNIT ROOT TESTING USING AUGMENTED DICKEY FULLER CONSTANT AT LEVEL GDP DATA Null Hypothesis: GDP has a unit root Exogenous: Constant Lag Length: 4 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 04/28/09 Time: 17:57 Sample (adjusted): Included observations: 31 after adjustments Coefficient Std. Error t-statistic Prob. GDP(-1) D(GDP(-1)) D(GDP(-2)) D(GDP(-3)) D(GDP(-4)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Hannan-Quinn criter Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

3 CONSTANT LINEAR TREND Null Hypothesis: GDP has a unit root Exogenous: Constant, Linear Trend Lag Length: 4 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 04/28/09 Time: 18:01 Sample (adjusted): Included observations: 31 after adjustments Coefficient Std. Error t-statistic Prob. GDP(-1) D(GDP(-1)) D(GDP(-2)) D(GDP(-3)) D(GDP(-4)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Hannan-Quinn criter Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)

4 NONE Null Hypothesis: GDP has a unit root Exogenous: None Lag Length: 4 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 04/28/09 Time: 18:04 Sample (adjusted): Included observations: 31 after adjustments Coefficient Std. Error t-statistic Prob. GDP(-1) D(GDP(-1)) D(GDP(-2)) D(GDP(-3)) D(GDP(-4)) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat

5 FIRST DIFFERENCED GDP DATA CONSTANT Null Hypothesis: D(GDP) has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,2) Method: Least Squares Date: 04/28/09 Time: 18:11 Sample (adjusted): Included observations: 31 after adjustments Coefficient Std. Error t-statistic Prob. D(GDP(-1)) D(GDP(-1),2) D(GDP(-2),2) D(GDP(-3),2) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

6 CONSTANT LINEAR TREND Null Hypothesis: D(GDP) has a unit root Exogenous: Constant, Linear Trend Lag Length: 3 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,2) Method: Least Squares Date: 04/28/09 Time: 18:24 Sample (adjusted): Included observations: 31 after adjustments Coefficient Std. Error t-statistic Prob. D(GDP(-1)) D(GDP(-1),2) D(GDP(-2),2) D(GDP(-3),2) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

7 NONE Null Hypothesis: D(GDP) has a unit root Exogenous: None Lag Length: 4 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,2) Method: Least Squares Date: 04/28/09 Time: 18:25 Sample (adjusted): Included observations: 30 after adjustments Coefficien t Std. Error t-statistic Prob. D(GDP(-1)) D(GDP(-1),2) D(GDP(-2),2) D(GDP(-3),2) D(GDP(-4),2) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat

8 SECOND DIFFERENCED GDP DATA CONSTANT Null Hypothesis: D(GDP,2) has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,3) Method: Least Squares Date: 04/28/09 Time: 18:27 Sample (adjusted): Included observations: 30 after adjustments Coefficient Std. Error t-statistic Prob. D(GDP(-1),2) D(GDP(-1),3) D(GDP(-2),3) D(GDP(-3),3) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

9 CONSTANT LINEAR TREND Null Hypothesis: D(GDP,2) has a unit root Exogenous: Constant, Linear Trend Lag Length: 7 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,3) Method: Least Squares Date: 04/28/09 Time: 19:00 Sample (adjusted): Included observations: 26 after adjustments Coefficient Std. Error t-statistic Prob. D(GDP(-1),2) D(GDP(-1),3) D(GDP(-2),3) D(GDP(-3),3) D(GDP(-4),3) D(GDP(-5),3) D(GDP(-6),3) D(GDP(-7),3) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

10 NONE Null Hypothesis: D(GDP,2) has a unit root Exogenous: None Lag Length: 3 (Automatic based on SIC, MAXLAG=9) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP,3) Method: Least Squares Date: 04/28/09 Time: 19:01 Sample (adjusted): Included observations: 30 after adjustments Coefficient Std. Error t-statistic Prob. D(GDP(-1),2) D(GDP(-1),3) D(GDP(-2),3) D(GDP(-3),3) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Hannan-Quinn Log likelihood criter Durbin-Watson stat

11 DECISION: Above ADF operation reveals that GDP is staionary at second difference. So we will use second differenced data of GDP as VAR or VECM model requires stationary data. HYPOTHESIS SETTING ABOUT DATA ADF TEST Null: There is Unit Root in the Data Alternative: Data is stationary CORRELOGRAM Q STATISTICS Null: Dats is stationary Alternative: It is unit root 11

12 CORRELOGRAM GDP AT LEVEL Date: 04/28/09 Time: 19:03 Sample: Included observations: 36 Autocorrelation Partial Correlation AC PAC Q-Stat Prob. *******. ******* ****** *****.* ***** **** ***.* *** ** **.* * * Date: 04/28/09 Time: 19:04 Sample: Included observations: 35 GDP AT FIRST DIFFERENCED Autocorrelation Partial Correlation AC PAC Q-Stat Prob **. ** **. ** **..* * *.. * * ** *.. * * *

13 DECISION GDP is stationary at First differenced as per Correlogram Q statistics result. Here I have taken Lag number one third of data size. FINAL DECISION We have taken ADF testing as benchmark so GDP is stationary at second difference, that is DD(GDP). In this similar fashion I have come to decision that EX data is stationary at first difference while CONS is at second difference. 13

14 COINTEGRATION TEST Now perform cointegration analysis using Johansen Cointegration Test GDP, EX and CONS are found cointegrated. There exists 1 cointegrated vector or 1 error term as per Trace and Maximum Eigenvalue shown below. It implies that there exists a long run relationship among three variables. If we get one or more than one cointegrated vector (error terms) in the model, we say that there exists a long run relationship among the variables. Cointegration is tested in non-stationary data only We choose option no. 3 in the EVIEWS screen as each data has some sort of trend from plotting We adopted 2 lag length or we can select from lag selection All variables are endogenous. No exogenous variables in the model. 14

15 JOHANSEN CO-INTEGRATION TEST Date: 04/28/09 Time: 19:15 Sample (adjusted): Included observations: 33 after adjustments Trend assumption: Linear deterministic trend Series: GDP EX CONS Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * At most At most Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * At most At most Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegrating Coefficients (normalized by b'*s11*b=i): GDP EX CONS Unrestricted Adjustment Coefficients (alpha): D(GDP) D(EX) D(CONS)

16 1 Cointegrating Equation(s): Log likelihood Normalized cointegrating coefficients (standard error in parentheses) GDP EX CONS ( ) ( ) Adjustment coefficients (standard error in parentheses) D(GDP) ( ) D(EX) ( ) D(CONS) ( ) 2 Cointegrating Equation(s): Log likelihood Normalized cointegrating coefficients (standard error in parentheses) GDP EX CONS ( ) ( ) Adjustment coefficients (standard error in parentheses) D(GDP) ( ) ( ) D(EX) ( ) ( ) D(CONS) ( ) ( ) Null Hypothesis: Number of cointegartion equation or error term(s) 16

17 VECTOR AUTOREGRESSION MODEL Since our target is to find out how and in what ways GDP is affected by other variables, we must put GDP variable first in EVIEWS screen followed by EX and CONS while going for estimating VECM model. We need to set variables such as GDP, EX and CONS in the EVIEWS program in such a way so that these variables become stationary. For your information, Eviews automatically do one difference in case of VECM (restricted Var) operation. So we put the variable in the following manner in EVIEWS that is DGDP,EX and DCONS. As we have already noticed that the variables are cointegrated, we go for VECM model (restricted Var). If variables are not cointegrated, we should go for unrestricted Var. We select one cointegrated vector and choose 2 leg length We choose option 3 as data appears to have trend from plotting. VECM (restrcited Var) is tested using stationary data. No exogenous variable.. All variables are endogenous. As per Nasiruddin Ahmed (2001), the main feature of the ECM (Error Correction Model) is its capability to correct for any disequilibrium that may shock the system from time to time. The error correction term picks up such disequilibrium and guides the variables of the system back to equilibrium. ECM is true in case of single equation while in case of VECM there is a system of equations. 17

18 VECTOR ERROR CORRECTION MODEL OUTCOME Vector Error Correction Estimates Date: 04/28/09 Time: 19:34 Sample (adjusted): Included observations: 32 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 DGDP(-1) EX(-1) ( ) [ ] DCONS(-1) ( ) [ ] C Error Correction: D(DGDP) D(EX) D(DCONS) CointEq ( ) ( ) ( ) [ ] [ ] [ ] D(DGDP(-1)) ( ) ( ) ( ) [ ] [ ] [ ] D(DGDP(-2)) ( ) ( ) ( ) [ ] [ ] [ ] D(EX(-1)) ( ) ( ) ( ) [ ] [ ] [ ] D(EX(-2)) ( ) ( ) ( ) [ ] [ ] [ ] D(DCONS(-1))

19 ( ) ( ) ( ) [ ] [ ] [ ] D(DCONS(-2)) ( ) ( ) ( ) [ ] [ ] [ ] 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

20 SYSTEM EQUATIONS D(DGDP) = C(1)*( DGDP(-1) *EX(-1) *DCONS(- 1) ) + C(2)*D(DGDP(-1)) + C(3)*D(DGDP(-2)) + C(4)*D(EX(-1)) + C(5)*D(EX(-2)) + C(6)*D(DCONS(-1)) + C(7)*D(DCONS(-2)) + C(8) D(EX) = C(9)*( DGDP(-1) *EX(-1) *DCONS(-1) ) + C(10)*D(DGDP(-1)) + C(11)*D(DGDP(-2)) + C(12)*D(EX(-1)) + C(13)*D(EX(-2)) + C(14)*D(DCONS(-1)) + C(15)*D(DCONS(-2)) + C(16) D(DCONS) = C(17)*( DGDP(-1) *EX(-1) *DCONS(-1) ) + C(18)*D(DGDP(-1)) + C(19)*D(DGDP(-2)) + C(20)*D(EX(-1)) + C(21)*D(EX(-2)) + C(22)*D(DCONS(-1)) + C(23)*D(DCONS(-2)) + C(24) System: UNTITLED Estimation Method: Least Squares Date: 04/28/09 Time: 19:35 Sample: Included observations: 32 Total system (balanced) observations 96 Coefficient Std. Error t-statistic Prob. C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14) C(15) C(16) C(17) C(18) C(19)

21 C(20) C(21) C(22) C(23) C(24) Determinant residual covariance Equation: D(DGDP) = C(1)*( DGDP(-1) *EX(-1) *DCONS(-1) ) + C(2)*D(DGDP(- 1)) + C(3)*D(DGDP(-2)) + C(4)*D(EX(-1)) + C(5)*D(EX(-2)) + C(6) *D(DCONS(-1)) + C(7)*D(DCONS(-2)) + C(8) Observations: 32 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Prob(F-statistic) Equation: D(EX) = C(9)*( DGDP(-1) *EX(-1) *DCONS(-1) ) + C(10)*D(DGDP( -1)) + C(11)*D(DGDP(-2)) + C(12)*D(EX(-1)) + C(13)*D(EX(-2)) + C(14) *D(DCONS(-1)) + C(15)*D(DCONS(-2)) + C(16) Observations: 32 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Prob(F-statistic) Equation: D(DCONS) = C(17)*( DGDP(-1) *EX(-1) *DCONS(-1) ) + C(18)*D(DGDP( -1)) + C(19)*D(DGDP(-2)) + C(20)*D(EX(-1)) + C(21)*D(EX(-2)) + C(22) *D(DCONS(-1)) + C(23)*D(DCONS(-2)) + C(24) Observations: 32 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Prob(F-statistic)

22 GRANGER CAUSALITY: WALD STATISTICS Granger causality test can be performed using Wald statistics. Hypothesis: Null Ho. Lagged values of coefficients in each equation are zero Alt H1: Not zero Granger causality is done to see the short run causality running from independent variable to dependent variable. It is found that test statistics for granger test should follow chi-sqaure distribution instead of F distribution. So we would follow Chi-square result. DEPENDENT VARIABLES INDEPANDENT VARIABLES DD(GDP) p-value D(EX) p-value D(DCONS) p-value DD(GDP) c(2)=c(3)= c(10)=c(11)= c(18)=c(19)=0 D(EX) c(4)=c(5)= c(12)=c(13)= c(20)=c(21)=0 D(DCONS) c(6)=c(7)= c(14)=c(15)= c(22)=c(23)=0 The figure in the table are the p-values of chi-square for Wald statistics. The Granger causality in above figure shows that there is no short run causality running from lag of independent variables to dependent variables. DECISION: Since all values are not significant ( as p values are more than 0.05) in the above table so we can not reject null meaning that there is no short causality running from independent variables to dependent variables. 22

23 LECTURE NOTE IS PREPARED BY: Sayed Hossain Lecturer of Economics Multimedia University Cyberjaya, Malaysia Personal homepage: for comments: April NOTE Please use the information of this website on your own risk. The website shall not be responsible for any loss or expenses suffered in connection with the use of this website. Acknowledgement is required only. No written permission is required to use this website. 23