# st: Constraints in VAR models

 From "Falko Juessen" To Subject st: Constraints in VAR models Date Thu, 06 May 2004 13:45:54 +0200

```Dear statalisters,

I have a question concerning constraints (exclusion restrictions) in VAR
models. David M. Drukker, Stata Corp, posted on Fri, 27 Jun 2003:

'As described in [R] constraint, there is an alternative syntax when
specifying exclusion restrictions.  The syntax constraint define #
[equation_name] coefficient_list defines exclusion restrictions for all
the coefficients named in coefficient_list in the specified equation.  To
illustrate, I repeat the previous example using this syntax.

. clear
. use http://www.stata-press.com/data/r8/lutkepohl
(Quarterly SA West German macro data, Bil DM, from Lutkepohl 1993 Table
E.1)
. constraint define 2 [dlincome] dlconsumption
. var dlinvestment dlincome , exog(dlconsumption)  constraint(2)

Estimating VAR coefficients

Iteration 1:   tolerance =    .009279
Iteration 2:   tolerance =  .00221815
Iteration 3:   tolerance =   .0005265
Iteration 4:   tolerance =  .00012476
Iteration 5:   tolerance =  .00002955
Iteration 6:   tolerance =  6.999e-06
Iteration 7:   tolerance =  1.658e-06
Iteration 8:   tolerance =  3.926e-07

Vector autoregression

Constraints:
( 1)  [dlincome]dlconsumption = 0
Sample:  1960q4   1982q4

(output omitted)'

So far, so good.

Now I would like to include more than one variable in the
coefficient_list. For example, L.dlincome also should have no effect on
the [dlincome] equation. Syntax:

constraint define 3 [dlincome] dlconsumption L.dlincome

. var dlinvestment dlincome , exog(dlconsumption)  constraint(3)
Estimating VAR coefficients

Iteration 1:   tolerance =  .00095522
Iteration 2:   tolerance =  .00022329
Iteration 3:   tolerance =  .00005216
Iteration 4:   tolerance =  .00001218
Iteration 5:   tolerance =  2.845e-06
Iteration 6:   tolerance =  6.643e-07

Vector autoregression

Constraints:
( 1)  [dlincome]dlconsumption = 0
( 2)  [dlinvestment]L.dlincome = 0
( 3)  [dlincome]L.dlincome = 0
Sample:  1960q4   1982q4
(output omitted)

Why does stata include a third constraint in the estimation?

Thank you very much for your help.

Falko Juessen.
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```