CAUSAL.RPF

CAUSAL.RPF is an example of various forms of Granger causality tests. This does a test for FM1 (log of nominal money) Granger causing GDPH (log of real GDP).

Note that the significance level of the Granger test in this is questionable because the two series are likely to have unit roots. If we take the results as given, we would conclude that nominal money does not cause real GDP at conventional significance levels. Alternatively, we would conclude that GDP is exogenous in its relationship with nominal money.

The final form of the test (Geweke-Meese-Dent) does not have the same problem with non-standard asymptotics. Note that, like the Sims test, this involves running a regression with FM1 as the dependent variable, not GDPH as is done in the Granger test.

The example GRANGERBOOTSTRAP.RPF does a bootstrap calculation of the Granger test on the same pair of series, using the bootstrap to approximate the actual distribution of the Granger test given the unit root behavior of the series.

Full Program

cal(m) 1959:1
allocate 2006:4
open data haversample.rat
data(format=rats) / gdph fm1
log gdph
log fm1
*
* Granger test
*
linreg gdph
# constant gdph{1 to 8} fm1{1 to 8}
exclude(title="Granger Causality Test")
# fm1{1 to 8}
*
* Sims' test
*
set filtm1 = fm1-1.50*fm1{1}+.5625*fm1{2}
set filtgdp = gdph-1.50*gdph{1}+.5625*gdph{2}
*
linreg filtm1
# constant filtgdp{-4 to 8}
exclude(title="Sims Causality Test")
# filtgdp{-4 to -1}
*
* Geweke-Meese-Dent variation
*
linreg fm1
# constant gdph{-4 to 8} fm1{1 to 8}
exclude(title="Geweke-Meese-Dent Causality Test")
# gdph{-4 to -1}

Output

Linear Regression - Estimation by Least Squares

Dependent Variable GDPH

Monthly Data From 1959:09 To 2006:04

Usable Observations 560

Degrees of Freedom 543

Centered R^2 0.9998727

R-Bar^2 0.9998690

Uncentered R^2 0.9999997

Mean of Dependent Variable 8.6164000918

Std Error of Dependent Variable 0.4292900688

Standard Error of Estimate 0.0049143190

Sum of Squared Residuals 0.0131137386

Regression F(16,543) 266570.1573

Significance Level of F 0.0000000

Log Likelihood 2190.7633

Durbin-Watson Statistic 2.0025

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 0.023142815 0.014229033 1.62645 0.10443405

2. GDPH{1} 0.940383062 0.042858514 21.94157 0.00000000

3. GDPH{2} -0.000883539 0.057097152 -0.01547 0.98765947

4. GDPH{3} 0.407260257 0.054792388 7.43279 0.00000000

5. GDPH{4} -0.396927291 0.057617485 -6.88901 0.00000000

6. GDPH{5} -0.027798562 0.057349379 -0.48472 0.62806833

7. GDPH{6} 0.339090345 0.054252004 6.25028 0.00000000

8. GDPH{7} -0.304312283 0.056174589 -5.41726 0.00000009

9. GDPH{8} 0.039326930 0.041986340 0.93666 0.34934981

10. FM1{1} 0.016799145 0.041821282 0.40169 0.68807105

11. FM1{2} -0.027559411 0.064160473 -0.42954 0.66770156

12. FM1{3} -0.018693171 0.064310750 -0.29067 0.77141511

13. FM1{4} 0.103736453 0.064374031 1.61146 0.10765963

14. FM1{5} 0.028629003 0.064466030 0.44409 0.65715126

15. FM1{6} -0.137395564 0.064439150 -2.13218 0.03344054

16. FM1{7} -0.002644040 0.064632703 -0.04091 0.96738372

17. FM1{8} 0.039022044 0.042078339 0.92737 0.35414826

Granger Causality Test

Null Hypothesis : The Following Coefficients Are Zero

FM1 Lag(s) 1 to 8

F(8,543)= 1.63750 with Significance Level 0.11131014

Linear Regression - Estimation by Least Squares

Dependent Variable FILTM1

Monthly Data From 1959:11 To 2005:12

Usable Observations 554

Degrees of Freedom 540

Centered R^2 0.9558178

R-Bar^2 0.9547541

Uncentered R^2 0.9993122

Mean of Dependent Variable 0.3853800897

Std Error of Dependent Variable 0.0485059223

Standard Error of Estimate 0.0103177337

Sum of Squared Residuals 0.0574860390

Regression F(13,540) 898.6235

Significance Level of F 0.0000000

Log Likelihood 1754.9337

Durbin-Watson Statistic 0.7176

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -0.581372238 0.009019101 -64.46011 0.00000000

2. FILTGDP{-4} 0.125413682 0.091201555 1.37513 0.16966244

3. FILTGDP{-3} 0.112189547 0.103163939 1.08749 0.27730634

4. FILTGDP{-2} 0.196587384 0.104764051 1.87648 0.06112881

5. FILTGDP{-1} 0.195018167 0.107524845 1.81370 0.07027835

6. FILTGDP 0.234905857 0.108860259 2.15787 0.03137846

7. FILTGDP{1} 0.275649729 0.108964934 2.52971 0.01169896

8. FILTGDP{2} 0.116856390 0.112924051 1.03482 0.30121484

9. FILTGDP{3} 0.105792803 0.109930185 0.96236 0.33629775

10. FILTGDP{4} 0.053727907 0.108458102 0.49538 0.62053387

11. FILTGDP{5} 0.114008575 0.106827718 1.06722 0.28634982

12. FILTGDP{6} 0.131318262 0.104100584 1.26146 0.20768941

13. FILTGDP{7} 0.074273852 0.100585267 0.73842 0.46058200

14. FILTGDP{8} 0.057120440 0.088633089 0.64446 0.51955114

Sims Causality Test

Null Hypothesis : The Following Coefficients Are Zero

FILTGDP Lag(s) -4 to -1

F(4,540)= 1.78755 with Significance Level 0.12986402

Linear Regression - Estimation by Least Squares

Dependent Variable FM1

Monthly Data From 1959:09 To 2005:12

Usable Observations 556

Degrees of Freedom 534

Centered R^2 0.9999594

R-Bar^2 0.9999578

Uncentered R^2 0.9999994

Mean of Dependent Variable 6.1370722489

Std Error of Dependent Variable 0.7756055205

Standard Error of Estimate 0.0050407053

Sum of Squared Residuals 0.0135682513

Regression F(21,534) 625684.2182

Significance Level of F 0.0000000

Log Likelihood 2163.6501

Durbin-Watson Statistic 1.9982

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -0.015015555 0.014971093 -1.00297 0.31632968

2. GDPH{-4} 0.084123624 0.044523703 1.88941 0.05937810

3. GDPH{-3} -0.095035516 0.061129670 -1.55465 0.12062082

4. GDPH{-2} 0.010699385 0.061270683 0.17462 0.86144059

5. GDPH{-1} -0.011062650 0.062939675 -0.17577 0.86054448

6. GDPH 0.045536137 0.064328904 0.70786 0.47933835

7. GDPH{1} 0.039474558 0.064352234 0.61341 0.53986385

8. GDPH{2} -0.155906448 0.064320491 -2.42390 0.01568594

9. GDPH{3} 0.024715876 0.064311025 0.38432 0.70089585

10. GDPH{4} -0.007087366 0.064334004 -0.11017 0.91231977

11. GDPH{5} 0.048282602 0.062083878 0.77770 0.43709058

12. GDPH{6} 0.009546844 0.059691579 0.15994 0.87299181

13. GDPH{7} -0.042916760 0.059707020 -0.71879 0.47258523

14. GDPH{8} 0.053055158 0.043409673 1.22220 0.22217246

15. FM1{1} 1.163199959 0.043650341 26.64813 0.00000000

16. FM1{2} -0.078920098 0.066649342 -1.18411 0.23689664

17. FM1{3} 0.064304204 0.066613062 0.96534 0.33481187

18. FM1{4} -0.112706126 0.066605101 -1.69215 0.09119986

19. FM1{5} 0.029444034 0.066802477 0.44076 0.65956325

20. FM1{6} 0.091683781 0.067209930 1.36414 0.17309804

21. FM1{7} -0.130779585 0.067643415 -1.93337 0.05371917

22. FM1{8} -0.028327670 0.043940604 -0.64468 0.51941080

Geweke-Meese-Dent Causality Test

Null Hypothesis : The Following Coefficients Are Zero

GDPH Lag(s) -4 to -1

F(4,534)= 0.95652 with Significance Level 0.43097395