RE: st: F test on VECM

[DE SOUZA Eric <eric.de_souza@coleurope.eu>]

Normally the following should work (but it does not in this case, see below why):
webuse rdinc
vec ln_ne ln_se
constraint 1 [_ce1]ln_se = -1
constraint 2 [_ce1]ln_ne = 1
vec ln_ne ln_se, bconstraints(1/2)
vec ln_ne ln_se ln_sw
vec ln_ne ln_se ln_sw, bconstraints(1 2)

The errror message one gets is the following:
there are at least as many constraints as parameters

This is a weakness of the program: it should go ahead and estimate and produce the likelihood ratio test.

Remember that without constraints, the beta coefficients are not identified. -vecrank- automatically imposes identification restrictions in order to able to estimate the model, what it calls the Johansen restrictions.

If the restrictions you wish to test are not constraining, then the maximum value of the likelihood function will be the same for both models. In this case, you cannot test the restrictions.

If the restrictions are constraining, you should always get a likelhood ratio test of the restrictions.

The following is the output (edited for length) from PcGive (OxMetrics)
The last line gives you the likelihood ratio test. The null is not rejected

SYS( 2) Cointegrated VAR (using rdinc.xls)
        The estimation sample is: 1950 - 2002

Cointegrated VAR (2) in:
[0] = ln_ne
[1] = ln_se
[2] = ln_sw
Unrestricted variables: 
[0] = Constant
Number of lags used in the analysis: 2

beta
ln_ne        1.0000
ln_se      -0.98233
ln_sw      0.037982

alpha
ln_ne      -0.44735
ln_se      -0.36762
ln_sw      -0.35322

. . . .

log-likelihood     465.501631  -

beta is not identified
No restrictions imposed

SYS( 3) Cointegrated VAR (using rdinc.xls)
        The estimation sample is: 1950 - 2002

Cointegrated VAR (2) in:
[0] = ln_ne
[1] = ln_se
[2] = ln_sw
Unrestricted variables: 
[0] = Constant
Number of lags used in the analysis: 2

General cointegration restrictions:
&3=1;
&4=-1;


beta
ln_ne        1.0000
ln_se       -1.0000
ln_sw      0.056902

. . . 

log-likelihood     465.500467 
no. long-run restrictions   1
beta is identified

LR test of restrictions: Chi^2(1) =0.0023272 [0.9615]  

In fact, this is a bad example because there is no cointegration, but it suffices for the purpose here

Eric de Souza
College of Europe
Brugge (Bruges), Belgium
http://www.coleurope.eu
 

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nat Tharnpanich
Sent: 07 April 2011 23:08
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: F test on VECM

Thanks so much Charles. However, I am afraid that this is not what I wanted. I want to do the F test on the cointegrating vector itself. For example, based on your online data, I want to test whether the estimated coefficient of ln_se which takes a value of -0.94 when ln_ne is constrained to be 1 is statistically different from, say, -1. Do you happen to know how to do that? Nat

On Apr 7 2011, Charles Koss wrote:

>you may try this:
>
>clear
>webuse rdinc
>vec ln_ne ln_se
>test [D_ln_se]L._ce1 == 0
>
>test [reference to the equation name ].{reference to the parameter} == 
>0
>
>did it work?
>
>Charles
>
>

--
Nat Tharnpanich
Downing College and Department of Land Economy University of Cambridge
CB2 1DQ
nt289@cam.ac.uk

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