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# Re: st: error correction model with quarterly data and dummies

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: error correction model with quarterly data and dummies Date Thu, 20 Dec 2012 10:57:53 +0000

```This is more a question about statistical style than about what is
indubitably, indisputably, infallibly correct. My own preference is to
consider the indicator variables (I recommend against "dummy" for
reasons often mentioned on this list) as a team and to use them all,
which here means three of them. To act otherwise is P-value fetishism
in my view, but I imagine that you will find other views if you ask
around enough.

Beyond that, using different sets of predictors requires a good
reason, and you don't seem to have one. More positively put, you have

Nick

On Thu, Dec 20, 2012 at 8:28 AM, Sabina Kummer <sabina.noo@postmail.ch> wrote:

> 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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