Re: st: RE: Noconst in cointegration relationship in VECM

[Svein Olav Krakstad <sveinolavkrakstad@gmail.com>]

Thank you all for helping me. Then I understand why Stata does not
allow me to do what i want. :-)

(I can mentioned that if one are only interested in the cointegration vector,
johans y x1 x2, noconst lags(3) exog(z1 z2 ... zn)
does the trick.)

Have a nice day.
Svein Olav

2011/4/28  <gsanchez@stata.com>:
> Svein Olav wrote:
>
>> I am trying to have no constant in the cointegration vector in the VEC
>> model.
>>
>> … if I restrict (i.e.) the variable lnrent:
>>
>> constraint define 1 [_ce1]lnrent=1
>> vec lnprice lnrent lnAM, rank(1) lags(2) trend(constant) bconstraints(1)
>>
>> It works fine.
>> Then I am thinking that it should only be to restrict the constant in the
>> same way:
>>
>> constraint define 1 [_ce1]_cons=0
>> vec lnprice lnrent lnAM, rank(1) lags(2) trend(constant) bconstraints(1)
>>
>> But this do not work.
>
> The –vec- command provides five different options to restrict the
> deterministic components included in the VEC model specification. The five
> alternatives were referred by Eric de Souza in his response to Svein Olav
>
>>  trend(constant) include an unrestricted constant in model; the default
>>  trend(rconstant) include a restricted constant in model
>>  trend(trend) include a linear trend in the cointegrating equations and a
>>  quadratic trend in the undifferenced data
>>  trend(rtrend) include a restricted trend in model
>>  trend(none) do not include a trend or a constant
>> See page 477 of the time series manual for a detailed explanation
>
> Those five alternatives imply “different asymptotic distributions of the
> statistics used for inference on the number of cointegrating equations and a
> different asymptotic distribution of the ML estimator of the cointegrating
> equations” (see pages 480-1 in the time-series manual [TS]). This is discussed
> in Johansen (1995, chap. 11).
>
> Svein Olav may consider specifying the option ‘trend(none)’ to restrict the
> constant in the cointegrating equation to zero. However, that option would
> also restrict to zero the constant in the differenced portion of the model and
> it would exclude linear trends in the differenced data and linear trends in
> the cointegrating equations (page 477 in the [TS] provides additional details
> for the ‘trend()’ option).
>
> There is not an option to restrict the constant in the cointegrating equation
> without imposing any constraints in the other deterministic components of the
> model. That alternative is not allowed with the ‘bconstraints()’ option
> because it would modify the asymptotic distributions referred above and,
> therefore, it would invalidate the estimation and inference on the
> cointegrating equations.
>
> Reference:
>
>  Johansen, S. 1995. Likelihood-Based Inference in Cointegrated Vector
>        Autoregressive Models. Oxford: Oxford University Press.
>
>
>
> Gustavo Sanchez
> gsanchez@stata.com
>
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