SVAR - Exact Zero Restrictions

[ospiridonova]

Hello!

I identify a SVAR model. The "householder" identifiation method lets me impose only sign restrictions. How can I impose an exact zero restriction in addition to sign restrictions? The option when I just add "== 0" to the logical expression ("test=") does not work.

My code example:

    v = VAR(list_1);
    [v, var_db] = estimate(v, db_raw, estStartDate:estEndDate, 'order=', p, 'const=', false, ...
        'covParameters=', true, 'BVAR=', litterman, 'stdize=', true, 'A=', constrA, 'timeWeights=', db_raw.w);     %This part works well:)
    test_string = [ ...
     ' S(4,1,1) > 0 ', ...
     '&& S(1,1,1) > 0 ', ...
     '&& S(1,5,1) < 0 ',...
     '&& S(2,2,1) < 0 ',...
      '&& S(6,1,1) == 0 ',...
      '&& S(2,1,1) > 0 '];
     [s3,sd3] = SVAR(v,var_db,'method=', 'householder', 'test=', test_string, 'ndraw=', 1000,'maxIter=',Inf,'progress=',true);

If I remove '&& S(6,1,1) == 0 ', then everything works fine, but the constraint is not satisfied. How can I add this restriction?

[jaromir-benes]

Hi Olga

This is because of the random sampling nature of the algorithm. In other words, the probability that a random number will be exactly equal to your desired value, is zero, and hence this algorithm cannot be used in that instance. As a workaround, you can specify some (rather narrow) interval around zero, e.g. S(6,1,1)<0.1 && S(6,1,1)>-0.1. The narrower the interval, the larger number of draws is needed, though.

Hope this helps. Best Jaromir

On Tue, Jan 18, 2022 at 12:04 PM Olga Spiridonova @.***> wrote:

Hello!

I identify a SVAR model. The "householder" identifiation method lets me impose only sign restrictions. How can I impose an exact zero restriction in addition to sign restrictions? The option when I just add "== 0" to the logical expression ("test=") does not work.

My code example:

v = VAR(list_1);
[v, var_db] = estimate(v, db_raw, estStartDate:estEndDate, 'order=', p, 'const=', false, ...
    'covParameters=', true, 'BVAR=', litterman, 'stdize=', true, 'A=', constrA, 'timeWeights=', db_raw.w);     %This part works well:)
test_string = [ ...
 ' S(4,1,1) > 0 ', ...
 '&& S(1,1,1) > 0 ', ...
 '&& S(1,5,1) < 0 ',...
 '&& S(2,2,1) < 0 ',...
  '&& S(6,1,1) == 0 ',...
  '&& S(2,1,1) > 0 '];
 [s3,sd3] = SVAR(v,var_db,'method=', 'householder', 'test=', test_string, 'ndraw=', 1000,'maxIter=',Inf,'progress=',true);

If I remove '&& S(6,1,1) == 0 ', then everything works fine, but the constraint is not satisfied. How can I add this restriction?

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[AndreyDO]

Olga,

I recommend looking at the algorithm in "Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications" by Arias, Rubio‐Ramírez, Waggoner (2018). There, the authors draw from the posterior distribution conditional on zero restrictions and then do the sign restrictions. The BEAR Toolbox has it implemented.

Andrey

[ospiridonova]

Thanks for the answers!