VARCAUSE.RPF

VARCAUSE.RPF is an example of a block exogeneity test (Granger causality test involving more than two variables).

The five variable VAR has three real variables (real GDP, unemployment and real investment), and two nominal ones (M2 and price level). All but unemployment are included in log form. The block exogeneity test is to see if the three real variables are exogenous relative to the two nominal ones. This involves running a system on just those three variables with (unrestricted) and without (restricted) the two nominal variables. The likelihood ratio test (with a minor adjustment of the "T" multiplier to deal with loss of degrees of freedom) is used as the test statistic.

Note that, like a two variable Granger test, this is subject to having a non-standard asymptotic distribution due to unit roots. If it weren't for the fact that the result is way out in the tails (non-causality is overwhelming rejected using the standard chi-squared asymptotics), this would probably deserve a more careful approach.

Full Program

open data haversample.rat
calendar(q) 1959
data(format=rats) 1959:1 2006:4 dgnp fm2 gdph ih lr
*
set loggdp = log(gdph)
set logm2 = log(fm2)
set logp   = log(dgnp)
set logi   = log(ih)
set unemp = lr
*
system(model=unrestricted)
variables loggdp unemp logi
lags 1 to 4
det constant logp{1 to 4} logm2{1 to 4}
end(system)
estimate(resids=unresids)
compute ntotal=%nregsystem,mcorr=%nreg,loglunr=%logl
compute logdetunr=%logdet
*
system(model=restricted)
variables loggdp unemp logi
lags 1 to 4
det constant
end(system)
estimate(resids=resresids)
compute loglres=%logl
compute logdetres=%logdet
*
* Using RATIO
*
ratio(degrees=ntotal-%nregsystem,mcorr=mcorr,$
   title="Exogeneity of Real Variables")
# unresids
# resresids
*
* Using %LOGDET statistics:
*
compute teststat=(%nobs-mcorr)*(logdetres-logdetunr)
cdf(title="Exogeneity of Real Variables") chisqr $
   teststat ntotal-%nregsystem
*
* Using %LOGL statistics. The standard LR test of -2*(L(R)-L(U)) is
* adjusted by multiplying by (T-c)/T to implement the multiplier
* correction.
*
compute teststat=-2.0*(%nobs-mcorr)/%nobs*(loglres-loglunr)
cdf(title="Exogeneity of Real Variables") chisqr $
   teststat ntotal-%nregsystem

Output

VAR/System - Estimation by Least Squares

Quarterly Data From 1960:01 To 2006:04

Usable Observations 188

Dependent Variable LOGGDP

Mean of Dependent Variable 8.6324850619

Std Error of Dependent Variable 0.4316368147

Standard Error of Estimate 0.0072688036

Sum of Squared Residuals 0.0088235294

Durbin-Watson Statistic 1.9954

Variable Coeff Std Error T-Stat Signif

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

1. LOGGDP{1} 1.226399016 0.129072827 9.50160 0.00000000

2. LOGGDP{2} 0.040054697 0.166391941 0.24072 0.81006355

3. LOGGDP{3} -0.326842793 0.167162288 -1.95524 0.05222355

4. LOGGDP{4} 0.128053668 0.126251020 1.01428 0.31191722

5. UNEMP{1} -0.008004490 0.003016626 -2.65346 0.00873651

6. UNEMP{2} 0.013553738 0.004836842 2.80219 0.00567601

7. UNEMP{3} -0.006518079 0.004933922 -1.32107 0.18828378

8. UNEMP{4} 0.003119594 0.002936580 1.06232 0.28962328

9. LOGI{1} -0.077543012 0.024931750 -3.11021 0.00219888

10. LOGI{2} 0.031966831 0.028609304 1.11736 0.26544625

11. LOGI{3} 0.033342130 0.028797122 1.15783 0.24858723

12. LOGI{4} -0.011902589 0.022884582 -0.52011 0.60367300

13. Constant -0.302054702 0.135325331 -2.23206 0.02694087

14. LOGP{1} 0.153748818 0.214899740 0.71544 0.47533356

15. LOGP{2} -0.134761795 0.390824464 -0.34481 0.73066799

16. LOGP{3} -0.705687587 0.394476756 -1.78892 0.07544016

17. LOGP{4} 0.680507789 0.216394735 3.14475 0.00196801

18. LOGM2{1} 0.045612157 0.102316832 0.44579 0.65632397

19. LOGM2{2} 0.156381004 0.187761716 0.83287 0.40610787

20. LOGM2{3} -0.214481364 0.183580639 -1.16832 0.24434191

21. LOGM2{4} -0.001460064 0.099637390 -0.01465 0.98832589

F-Tests, Dependent Variable LOGGDP

Variable F-Statistic Signif

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

LOGGDP 336.6449 0.0000000

UNEMP 3.7040 0.0064544

LOGI 2.8241 0.0266142

Dependent Variable UNEMP

Mean of Dependent Variable 5.8732269504

Std Error of Dependent Variable 1.4427883606

Standard Error of Estimate 0.2234951514

Sum of Squared Residuals 8.3416638091

Durbin-Watson Statistic 1.9378

Variable Coeff Std Error T-Stat Signif

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

1. LOGGDP{1} -14.48423037 3.96862436 -3.64969 0.00035080

2. LOGGDP{2} 2.13279723 5.11608155 0.41688 0.67730081

3. LOGGDP{3} 3.67517648 5.13976757 0.71505 0.47557830

4. LOGGDP{4} 6.49867061 3.88186177 1.67411 0.09598047

5. UNEMP{1} 1.33581407 0.09275272 14.40189 0.00000000

6. UNEMP{2} -0.59270178 0.14871920 -3.98538 0.00010048

7. UNEMP{3} 0.24520413 0.15170415 1.61633 0.10791026

8. UNEMP{4} -0.08052958 0.09029153 -0.89188 0.37373833

9. LOGI{1} 2.34396054 0.76658079 3.05768 0.00259835

10. LOGI{2} -1.37968124 0.87965517 -1.56843 0.11867268

11. LOGI{3} 0.17668868 0.88543005 0.19955 0.84207432

12. LOGI{4} -0.42482830 0.70363617 -0.60376 0.54682157

13. Constant 10.79479976 4.16087119 2.59436 0.01031920

14. LOGP{1} -0.45707754 6.60755919 -0.06917 0.94493313

15. LOGP{2} -0.94203565 12.01674688 -0.07839 0.93760884

16. LOGP{3} 17.66204929 12.12904451 1.45618 0.14722084

17. LOGP{4} -15.98690516 6.65352604 -2.40277 0.01736760

18. LOGM2{1} 0.91423441 3.14595319 0.29061 0.77171287

19. LOGM2{2} -4.43343183 5.77314172 -0.76794 0.44360677

20. LOGM2{3} 3.76516967 5.64458543 0.66704 0.50566657

21. LOGM2{4} 0.13815090 3.06356794 0.04509 0.96408564

F-Tests, Dependent Variable UNEMP

Variable F-Statistic Signif

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

LOGGDP 5.3641 0.0004347

UNEMP 300.4806 0.0000000

LOGI 2.6856 0.0331745

Dependent Variable LOGI

Mean of Dependent Variable 6.6146375119

Std Error of Dependent Variable 0.5577696411

Standard Error of Estimate 0.0362100449

Sum of Squared Residuals 0.2189649480

Durbin-Watson Statistic 1.9556

Variable Coeff Std Error T-Stat Signif

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

1. LOGGDP{1} 2.223235132 0.642985164 3.45768 0.00069124

2. LOGGDP{2} -0.629732041 0.828892895 -0.75973 0.44848911

3. LOGGDP{3} -1.594754526 0.832730435 -1.91509 0.05719003

4. LOGGDP{4} 0.818584934 0.628928137 1.30156 0.19486098

5. UNEMP{1} -0.064674881 0.015027530 -4.30376 0.00002853

6. UNEMP{2} 0.088991341 0.024095059 3.69334 0.00029953

7. UNEMP{3} -0.034516292 0.024578672 -1.40432 0.16208101

8. UNEMP{4} 0.021585540 0.014628776 1.47555 0.14194674

9. LOGI{1} 0.261843964 0.124199227 2.10826 0.03650098

10. LOGI{2} 0.300206379 0.142519213 2.10643 0.03666181

11. LOGI{3} 0.228045346 0.143454844 1.58967 0.11380136

12. LOGI{4} -0.088720396 0.114001118 -0.77824 0.43752791

13. Constant -3.632768487 0.674132444 -5.38881 0.00000024

14. LOGP{1} 2.473520405 1.070537833 2.31054 0.02208126

15. LOGP{2} -3.677712411 1.946918945 -1.88899 0.06062647

16. LOGP{3} -1.231625339 1.965113086 -0.62675 0.53168206

17. LOGP{4} 2.547308045 1.077985251 2.36303 0.01927715

18. LOGM2{1} -0.019866305 0.509698334 -0.03898 0.96895560

19. LOGM2{2} 1.048856045 0.935347902 1.12135 0.26374707

20. LOGM2{3} -0.893169482 0.914519580 -0.97665 0.33015296

21. LOGM2{4} -0.401542631 0.496350512 -0.80899 0.41967192

F-Tests, Dependent Variable LOGI

Variable F-Statistic Signif

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

LOGGDP 9.5537 0.0000006

UNEMP 7.0297 0.0000296

LOGI 39.2576 0.0000000

VAR/System - Estimation by Least Squares

Quarterly Data From 1960:01 To 2006:04

Usable Observations 188

Dependent Variable LOGGDP

Mean of Dependent Variable 8.6324850619

Std Error of Dependent Variable 0.4316368147

Standard Error of Estimate 0.0078019947

Sum of Squared Residuals 0.0106524463

Durbin-Watson Statistic 1.9498

Variable Coeff Std Error T-Stat Signif

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

1. LOGGDP{1} 1.257522686 0.126063422 9.97532 0.00000000

2. LOGGDP{2} 0.053842844 0.174572341 0.30843 0.75812418

3. LOGGDP{3} -0.285879374 0.173726501 -1.64557 0.10164690

4. LOGGDP{4} -0.011772623 0.130572148 -0.09016 0.92826173

5. UNEMP{1} -0.009362884 0.003161088 -2.96192 0.00348225

6. UNEMP{2} 0.014222985 0.005047060 2.81807 0.00538753

7. UNEMP{3} -0.004361986 0.005068926 -0.86053 0.39067191

8. UNEMP{4} 0.000058306 0.002862526 0.02037 0.98377254

9. LOGI{1} -0.060460216 0.023743851 -2.54635 0.01174759

10. LOGI{2} 0.020200868 0.029659353 0.68110 0.49671096

11. LOGI{3} 0.026230969 0.029715713 0.88273 0.37859280

12. LOGI{4} 0.002013921 0.022914268 0.08789 0.93006508

13. Constant -0.037697075 0.044930639 -0.83901 0.40261057

F-Tests, Dependent Variable LOGGDP

Variable F-Statistic Signif

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

LOGGDP 1582.3249 0.0000000

UNEMP 2.9292 0.0223658

LOGI 1.8965 0.1131166

Dependent Variable UNEMP

Mean of Dependent Variable 5.8732269504

Std Error of Dependent Variable 1.4427883606

Standard Error of Estimate 0.2321384781

Sum of Squared Residuals 9.4304477766

Durbin-Watson Statistic 1.9464

Variable Coeff Std Error T-Stat Signif

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

1. LOGGDP{1} -15.29976053 3.75085755 -4.07900 0.00006860

2. LOGGDP{2} 2.30364352 5.19417905 0.44350 0.65794845

3. LOGGDP{3} 2.54443638 5.16901214 0.49225 0.62316093

4. LOGGDP{4} 9.62677352 3.88500900 2.47793 0.01416311

5. UNEMP{1} 1.37383680 0.09405418 14.60687 0.00000000

6. UNEMP{2} -0.60050216 0.15016889 -3.99885 0.00009375

7. UNEMP{3} 0.20774767 0.15081949 1.37746 0.17012950

8. UNEMP{4} -0.01200261 0.08517084 -0.14092 0.88809214

9. LOGI{1} 1.94789751 0.70646824 2.75723 0.00644785

10. LOGI{2} -1.19870032 0.88247650 -1.35834 0.17610532

11. LOGI{3} 0.44186424 0.88415342 0.49976 0.61787208

12. LOGI{4} -0.61148601 0.68178505 -0.89689 0.37100992

13. Constant 3.73747264 1.33685430 2.79572 0.00575708

F-Tests, Dependent Variable UNEMP

Variable F-Statistic Signif

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

LOGGDP 7.9525 0.0000065

UNEMP 1090.7057 0.0000000

LOGI 2.5186 0.0430215

Dependent Variable LOGI

Mean of Dependent Variable 6.6146375119

Std Error of Dependent Variable 0.5577696411

Standard Error of Estimate 0.0396029944

Sum of Squared Residuals 0.2744695042

Durbin-Watson Statistic 1.9525

Variable Coeff Std Error T-Stat Signif

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

1. LOGGDP{1} 1.707520775 0.639899046 2.66842 0.00833715

2. LOGGDP{2} -0.459268273 0.886130750 -0.51828 0.60491410

3. LOGGDP{3} -1.268750717 0.881837258 -1.43876 0.15200510

4. LOGGDP{4} 0.215390517 0.662785381 0.32498 0.74558607

5. UNEMP{1} -0.068632392 0.016045712 -4.27730 0.00003106

6. UNEMP{2} 0.092402586 0.025618923 3.60681 0.00040420

7. UNEMP{3} -0.013957633 0.025729915 -0.54247 0.58818689

8. UNEMP{4} -0.008521701 0.014530208 -0.58648 0.55830760

9. LOGI{1} 0.493736735 0.120523999 4.09658 0.00006402

10. LOGI{2} 0.252133382 0.150551138 1.67474 0.09577217

11. LOGI{3} 0.178989953 0.150837222 1.18664 0.23697685

12. LOGI{4} -0.078104095 0.116313029 -0.67150 0.50278806

13. Constant -0.681276197 0.228068323 -2.98716 0.00322013

F-Tests, Dependent Variable LOGI

Variable F-Statistic Signif

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

LOGGDP 3.8844 0.0047634

UNEMP 5.1538 0.0005993

LOGI 70.4568 0.0000000

Exogeneity of Real Variables

Log Determinants are -21.122046 -20.731947

Chi-Squared(24)= 65.146518 with Significance Level 0.00001158

Exogeneity of Real Variables

Chi-Squared(24)= 65.146518 with Significance Level 0.00001158

Exogeneity of Real Variables

Chi-Squared(24)= 65.146518 with Significance Level 0.00001158