1. Economics 5310
Lecture 26
Causality, VAR

2. Causality
Question: Can one statistically determine the direction of causality when temporally there is a lead-lag relationship between two variables.
Granger test
Sims test

3. Granger Test

4. Granger Test

5. Example Granger Causality
Interest Rates cause housing starts
housing starts cause interest rates

6. Interest causes housing
|_ols hgrth hgrth1 hgrth2 hgrth3 rate1 rate2 rate3
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
HGRTH
HGRTH
HGRTH
RATE E E
RATE E E
RATE E E
CONSTANT E E E
|_test
|_test rate1
|_test rate2
|_test rate3
|_end
F STATISTIC = WITH 3 AND 29 D.F. P-VALUE=
WALD CHI-SQUARE STATISTIC = WITH 3 D.F. P-VALUE=
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY =

7. Housing Causes Interest Rate
|_ols rate rate1 rate2 rate3 hgrth1 hgrth2 hgrth3
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
RATE
RATE E
RATE E
HGRTH
HGRTH
HGRTH
CONSTANT
|_test
|_test hgrth1
|_test hgrth2
|_test hgrth3
|_end
F STATISTIC = WITH 3 AND 29 D.F. P-VALUE=
WALD CHI-SQUARE STATISTIC = WITH 3 D.F. P-VALUE=
UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY =
|_stop

8. Logic of Vector Autoregressive Models
SIM’s criticism of traditional simultaneous equation models.
Seed for VAR lies with Granger causality testing.
Term autoregressive comes from fact that lagged values of dependent variable appear on RHS.
Term vector comes from fact that we are discussing at least two variables.

9. Basic VAR model

10. Example VAR-Exchange Rate lag 6
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEX E
TWEX E E
TWEX E E E
TWEX E E E
TWEX E E
TWEX E E
BA6M
BA6M
BA6M E
BA6M E
BA6M
BA6M
CONSTANT

11. Example VAR – Banker’s Acceptance Rate–lag 6 month
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEX E E
TWEX E E
TWEX E E
TWEX E E
TWEX E E
TWEX E E
BA6M E
BA6M
BA6M
BA6M
BA6M
BA6M E
CONSTANT

12. Problems VAR VAR model is a-theoretic.
Less suited for policy analysis since emphasis is forecasting.
Problem of selecting lag length.
In theory variables should be stationary, but many use levels for interpretation.
Quite often look at impulse response function (IRF).

13. Selecting the lag length
AIC-Ex
Scwartz-Ex
AIC-Int
Scwartz-Int 1
2.900
3.013
0.395
0.411 2
2.915
3.108
0.353
0.376 3
2.924
3.198
0.342
0.374 4
2.920
3.277
0.346
0.388 5
2.951
3.398
0.347
0.400 6
2.977
3.517
0.343
0.406

14. Exchange rate – lag 2
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEX E
TWEX E E
BA6M
BA6M
CONSTANT

15. Interest Rate – lag 2
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEX E E
TWEX E E
BA6M E
BA6M E
CONSTANT

16. 1st Difference exchange rate
SCHWARZ (1978) CRITERION - SC =
AKAIKE (1974) INFORMATION CRITERION - AIC =
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEXDIF E
BA6MDIF
CONSTANT E E

17. 1st difference interest rate
SCHWARZ (1978) CRITERION - SC =
AKAIKE (1974) INFORMATION CRITERION - AIC =
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEXDIF E E
BA6MDIF E
CONSTANT E E E

18. 1st difference exchange rate – 2 lags
SCHWARZ (1978) CRITERION - SC =
AKAIKE (1974) INFORMATION CRITERION - AIC =
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEXDIF E
TWEXDIF E E
BA6MDIF
BA6MDIF
CONSTANT E E

19. 1st difference interest rate – 2 lags
SCHWARZ (1978) CRITERION - SC =
AKAIKE (1974) INFORMATION CRITERION - AIC =
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR DF P-VALUE CORR. COEFFICIENT AT MEANS
TWEXDIF E E
TWEXDIF E E
BA6MDIF E
BA6MDIF E
CONSTANT E E E