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?
I kindly thank you in advance for your help and your relply
.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