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

[gsanchez@stata.com]

Svein Olav wrote:

> I am trying to have no constant in the cointegration vector in the VEC
> model.
>
> â?¦ 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 â??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 â??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
equationsâ?? (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 â??trend(none)â?? 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 â??trend()â?? 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 â??bconstraints()â?? 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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