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# st: error correction model with quarterly data and dummies

 From "Sabina Kummer" To statalist@hsphsun2.harvard.edu Subject st: error correction model with quarterly data and dummies Date Thu, 20 Dec 2012 09:28:51 +0100 (CET)

Dear all,

I am not used to estimation of models with quarterly data and I would need some help.

I would like to estimate an error correction model with quarterly data. I use raw (and not seasonnaly adjusted) data and introduce dummy variables (for three quarters) to take into account the quarterly effects of the series. I follow the “Engle & Granger” procedure. In the long-run equation, one of the dummy variables was not significantly different from zero so that the long-run equation contains only two of them:

log(Yt)=c(1)+c(2)*log(Xt)+c(3)*dum4+c(4)*dum3

In the full equation (that contains the error correction term and the short-run effects), I then include the dummy variable that was dropped from the long-run equation and that is now significantly different from zero. Thus, the final specification is:

dlog(Yt)=c(1)*dlog(Xt)+c(2)*[log(Yt-1)-c(3)-c(4)*log(Xt-1)-c(5)*dum3-c(6)*dum4]+c(7)*dum2+c(8)*dlog(Yt-1)+c(9)*dlog(Yt-2)+c(10)*dlog(Yt-3)

dlog: first difference of the log of the variable X or Y
dum2: dummy = 1 if quarter = 2
dum3: dummy = 1 if quarter = 3
dum4: dummy = 1 if quarter = 4
The error correction term is in brackets [ ]

My questions are the following:
-           Is it ok to exclude one of the three dummies from the long-run equation or must this equation obligatory contains the three dummy variables in order to correctly capture the effects of each quarter?
-           Is it ok to have one dummy in the full specification and the two others in the error correction term?

FYI,  here is the EViews output:

Coefficient       Std. Error        t-Statistic         Prob.

C(2)     1.019572         1.998954         0.510053         0.6116
C(3)     -1.054762       0.494412         -2.133364       0.0363
C(4)     -4.004634       0.983247         -4.072867       0.0001
C(5)     1.131626         0.083556         13.54329         0.0000
C(6)     0.000219         0.064984         0.003377         0.9973
C(7)     0.228694         0.131190         1.743223         0.0855
C(9)     0.420972         0.139663         3.014199         0.0035
C(11)   -0.015446       0.433398         -0.035640       0.9717
C(12)   -0.359115       0.262654         -1.367252       0.1757
C(13)   -0.402420       0.182734         -2.202218       0.0308

R-squared       0.930911             Mean dependent var          -5.56E-05
Adjusted R-squared    0.922393             S.D. dependent var 0.603876
S.E. of regression       0.168228             Akaike info criterion            -0.614411
Sum squared resid     2.065947             Schwarz criterion    -0.322985
Log likelihood  35.49806             Hannan-Quinn criter.          -0.497332
Durbin-Watson stat     1.795317

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