causality granger test

[Nabtheberliner]

Hi Tom,
My question is which test do i have to trust between those two?

According to what says W.Enders in his RATS HANDBOOK FOR ECONOMETRICS TIME SERIES p.131 WITH THE FILE US.PRN:

and the causality granger test explained in the users guide UG-85

Code: Select all

* VAR2.PRG 
cal 60 1 4
all 10 91:4
open data a:\us.prn
data(format=prn,org=obs) / m1 gdpdef tbill
set gm1 = log(m1) - log(m1{1})
set inf = log(gdpdef) - log(gdpdef{1})
diff tbill / dtbill
seasonal seasons

system 1 to 3                           
vars gm1 inf dtbill              
lags 1 to 4                             
det constant seasons{-2 to 0} 
end(system)

estimate(print,outsigma=V) 61:2 91:4 1

OUTPUT I KEEP JUST THE REG ON DTBILL VARIABLE:

F-Tests, Dependent Variable DTBILL
Variable F-Statistic Signif
*******************************************************
GM1 2.8679 0.0265898
INF 3.3814 0.0120133
DTBILL 6.3197 0.0001326

As Enders concludes: DTBILL granger-causes all variables

Now if i check the same system with the test explained in the users guide UG-85 with the reg on the DTBILL variable

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linreg DTBILL
# constant DTBILL {1 to 4} inf {1 to 4} gm1{1 to 4}
exclude(title="granger causality test")
# inf {1 to 4} 
exclude(title="granger causality test")
# gm1{1 to 4}

OUTPUT:

Code: Select all

granger causality test

Null Hypothesis : The Following Coefficients Are Zero
INF              Lag(s) 1 to 4
F(4,110)=      3.47912 with Significance Level [b]0.01024311[/b]

granger causality test

Null Hypothesis : The Following Coefficients Are Zero
GM1 Lag(s) 1 to 4
F(4,110)= 1.75396 with Significance Level 0.14334028

At a 10% level, the null hypothesis DTBILL doesn't cause granger gm1 is not rejected

What do you think? my intuition is to trust the second test but still it remains the doubt why Enders treats the causality granger test in the RATS HANDBOOK...this way?

[TomDoan]

Your interpretation of the last result is backwards---you would conclude that GM1 doesn't cause DTBILL, not the other way around. However, that is still giving a different conclusion than in the book. The reason is that GM1 and INFL are both not-seasonally-adjusted. Enders' model includes seasonal dummies; your LINREG doesn't. If the GM1 coefficients are non-zero, running a regression without doing something to deal with the seasonality will bias the estimates towards zero, since non-zero coefficients will put a seasonal pattern into the residuals.

[Nabtheberliner]

Ok sorry for the interpretation indeed it's clear in the users guide:

[quote][/quote]Granger’s procedure: regress M1 on lags of GDP and M1. Test the lags of GDP

Also this is much better that way:

Code: Select all

linreg DTBILL
# constant DTBILL {1 to 4} inf {1 to 4} gm1{1 to 4} seasons{-2 to 0}

exclude(title="granger causality test")
# inf {1 to 4}
exclude(title="granger causality test")
# gm1{1 to 4}

OUTPUT:

Code: Select all

granger causality test

Null Hypothesis : The Following Coefficients Are Zero
GM1 Lag(s) 1 to 4
F(4,107)= 2.86786 with Significance Level 0.02658978

So if take another example: file E2 2 variables y1 y2 attached:
I wanna test the hypothesis Ho: y2 does not granger-causes y1, i run the test like this: after estimation and the variables are in first diff

Code: Select all

linreg Y1
# constant Y2{1} Y1{1}
exclude(title="granger causality test")
# Y2{1}
granger causality test

Null Hypothesis : The Following Coefficients Are Zero
Y2 Lag(s) 1
t(100)= -1.277303 or F(1,100)= 1.631502 with Significance Level 0.20445306


The correct interpretation is not to reject Ho: y2 does not granger-causes y1
Is that correct?

Finally, back to my first question: both tests are equivalent?
Thanks Tom

[TomDoan]

You're having a hard time with the Code tags. Put the code in first, select it then hit the "code" button. It looks like you're hitting "code" first, then inputting the information.

Yes, you would accept H0 that y2 doesn't Granger cause y1.

Yes. They are identical if set up the same. ESTIMATE does OLS equation by equation and the block F's are just exclusions on the lags for the preceding regression.