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Re: st: Restrictions in SVAR


From   "David M. Drukker" <ddrukker@stata.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Restrictions in SVAR
Date   Wed, 7 Jun 2006 18:21:48 -0500 (CDT)

Alvaro <aa314@cam.ac.uk> asked how

to impose that two elements of matrix A in the SVAR estimation are equal.

as [a_3_1]_cons = [a_3_2]_cons

The short answer is to use the -acns()- on -svar-.

This option is complicated, so let's repeat what the help file has to say.


-acns(matrix_acns)- specifies a matrix that defines a set of exclusion or
cross-parameter equality constraints on A. This matrix must be square
with dimension equal to the number of equations in the underlying VAR.
Each element of this matrix must be -missing-, 0, or a positive integer.
A missing value in the (i,j) element of this matrix specifies that no
constraint be placed on this element of A. A zero in the (i,j) element
of this matrix constrains the (i,j) element of A to be zero. Any
strictly positive integers must be in two or more elements of this
matrix. A strictly positive integer in the (i,j) element of this matrix
constrains the (i,j) element of A to be equal to all the other elements
of A that correspond to elements in this matrix that contain the same
integer. For example, consider the matrix

- -
A = | . 1 |
| 1 0 |
- -

Specifying, -acns(A)- in a two-equation SVAR constrains
A[2,1]=A[1,2], A[2,2]=0 while leaving A[1,1] free.

The following example uses the above A in an SVAR.


. webuse lutkepohl
(Quarterly SA West German macro data, Bil DM, from Lutkepohl 1993 Table E.1)

. matrix A = ( ., 1\ 1, 0)

. . svar dlincome dlconsumption, acns(A)
Estimating short-run parameters

Iteration 0: log likelihood = -159.19754 Iteration 1: log likelihood = 491.87116 Iteration 2: log likelihood = 542.40175 Iteration 3: log likelihood = 572.88512 Iteration 4: log likelihood = 573.16306 Iteration 5: log likelihood = 573.17262 Iteration 6: log likelihood = 573.17354 Iteration 7: log likelihood = 573.17364 Iteration 8: log likelihood = 573.17365

Structural vector autoregression

Constraints:
( 1) [a_2_2]_cons = 0
( 2) - [a_2_1]_cons + [a_1_2]_cons = 0
( 3) [b_1_1]_cons = 1
( 4) [b_1_2]_cons = 0
( 5) [b_2_1]_cons = 0
( 6) [b_2_2]_cons = 1

Sample: 1960q4 1982q4 No. of obs = 89
Overidentified model Log likelihood = 573.1737

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/a_1_1 | -53.00645 11.31905 -4.68 0.000 -75.19138 -30.82152
/a_2_1 | 103.4424 5.482438 18.87 0.000 92.69705 114.1878
/a_1_2 | 103.4424 5.482438 18.87 0.000 92.69705 114.1878
/a_2_2 | 0 . . . . .
-------------+----------------------------------------------------------------
/b_1_1 | 1 . . . . .
/b_2_1 | 0 . . . . .
/b_1_2 | 0 . . . . .
/b_2_2 | 1 . . . . .
------------------------------------------------------------------------------
LR test of identifying restrictions: chi2( 1)= 10.21 Prob > chi2 = 0.001

--David
ddrukker@stata.com
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