John D. Levendis <[email protected]> wrote that he was having trouble
specifying a constraint on an exogenous variable when using -var-.
The short answer is that the space between the equation name and coefficient
name in the constraint define statement is what is causing the problem.
Instead of
. constraint define 1 [Q] X1 = 0
John should type
. constraint define 1 [Q]X1 = 0
Note the lack of a space between [Q] and X1 in the second constraint define
statement.
Now for a longer answer that provides some details.
John wrote that the model of interest can be expressed as
> P = B1*P(t-1) + B2*Q(t-1) + B3*X1(t) + B4*X2(t) + e(t)
> Q = B5*P(t-1) + B6*Q(t-1) + B7*X1(t) + B8*X2(t) + e(t)
Since X2 is superfluous to the example, allow me restrict the example to the
system
P = B1*P(t-1) + B2*Q(t-1) + B3*X1(t) + e(t)
Q = B4*P(t-1) + B5*Q(t-1) + B6*X1(t) + e(t)
John wants to constrain the coefficient on X1 in the Q equation to be zero.
He wrote that
> If the Xs were endogenous variables, I could have done:
> constraint define 1 [Q] X1 = 0
> var P Q, exog(X1 X2) constraint(1)
Unfortunately, this is not quite correct. The space between [Q] and X1
would cause the constraint define statement to specify something besides
what John had intended. If the Xs were endogenous, John could have
specified:
constraint define 1 [Q]X1 = 0
Note that there is no space between [Q] and X1.
The same logic applies when X1 is exogenous. If John wants to use the
syntax
constraint define # exp=exp
then there cannot be a space between an equation name and a coefficient
name when referring to a coefficient. Here is an example using the lutkepohl
dataset used in the [TS] var manual entry.
. 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 1 [dlincome]dlconsumption = 0
. var dlinvestment dlincome , exog(dlconsumption) constraint(1)
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
--------------------------------------------------------------------------
Equation Obs Parms RMSE R-sq chi2 P
--------------------------------------------------------------------------
dlinvestment 89 6 .04131 0.1552 16.03491 0.0067
dlincome 89 5 .011078 0.1027 10.1916 0.0373
--------------------------------------------------------------------------
Model lag order selection statistics
------------------------------------
FPE AIC HQIC SBIC LL Det(Sigma_ml)
2.682e-07 -9.4336017 -9.2983526 -9.0980553 431.79528 2.094e-07
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlinvestment |
dlinvestment |
L1 | -.2108975 .101412 -2.08 0.038 -.4096613 -.0121337
L2 | -.1755615 .1041221 -1.69 0.092 -.379637 .0285141
dlincome |
L1 | .5383786 .3850028 1.40 0.162 -.216213 1.29297
L2 | .1844466 .3982752 0.46 0.643 -.5961584 .9650515
dlconsumpt~n | 1.180586 .4456346 2.65 0.008 .307158 2.054013
_cons | -.0125696 .0115283 -1.09 0.276 -.0351647 .0100254
-------------+----------------------------------------------------------------
dlincome |
dlinvestment |
L1 | .0597466 .0271441 2.20 0.028 .0065451 .1129481
L2 | .0563513 .0272629 2.07 0.039 .002917 .1097855
dlincome |
L1 | .0209461 .1017687 0.21 0.837 -.1785169 .220409
L2 | .0833252 .1014303 0.82 0.411 -.1154745 .2821249
dlconsumpt~n | 6.09e-17 1.33e-17 4.59 0.000 3.49e-17 8.69e-17
_cons | .0150368 .0028704 5.24 0.000 .0094108 .0206627
------------------------------------------------------------------------------
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.
. 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
--------------------------------------------------------------------------
Equation Obs Parms RMSE R-sq chi2 P
--------------------------------------------------------------------------
dlinvestment 89 6 .04131 0.1552 16.03491 0.0067
dlincome 89 5 .011078 0.1027 10.1916 0.0373
--------------------------------------------------------------------------
Model lag order selection statistics
------------------------------------
FPE AIC HQIC SBIC LL Det(Sigma_ml)
2.682e-07 -9.4336017 -9.2983526 -9.0980553 431.79528 2.094e-07
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dlinvestment |
dlinvestment |
L1 | -.2108975 .101412 -2.08 0.038 -.4096613 -.0121337
L2 | -.1755615 .1041221 -1.69 0.092 -.379637 .0285141
dlincome |
L1 | .5383786 .3850028 1.40 0.162 -.216213 1.29297
L2 | .1844466 .3982752 0.46 0.643 -.5961584 .9650515
dlconsumpt~n | 1.180586 .4456346 2.65 0.008 .307158 2.054013
_cons | -.0125696 .0115283 -1.09 0.276 -.0351647 .0100254
-------------+----------------------------------------------------------------
dlincome |
dlinvestment |
L1 | .0597466 .0271441 2.20 0.028 .0065451 .1129481
L2 | .0563513 .0272629 2.07 0.039 .002917 .1097855
dlincome |
L1 | .0209461 .1017687 0.21 0.837 -.1785169 .220409
L2 | .0833252 .1014303 0.82 0.411 -.1154745 .2821249
dlconsumpt~n | 6.09e-17 1.33e-17 4.59 0.000 3.49e-17 8.69e-17
_cons | .0150368 .0028704 5.24 0.000 .0094108 .0206627
------------------------------------------------------------------------------
I hope that this helps.
David
[email protected]
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