SVAR model, interpretation matter

[Morad Bali]

Dear Statalist community,

It is the first time that I am trying to use the SVAR with the help of STATA. And I would be sure to understand well the results.
I have read the STATA help, the examples, an also the related questions on this forum. I therefore can't find an answer to my issue, and I start to be lost.

I want to know the impact of variable S on variables X and Y.

S is an index of favorable diplomatic measures ; X and Y are GDP of considered economies. X and Y are first differenced ln.

Data are run quarterly, from 1995q1 to 2015q4. Data are seasonally adjusted,

Here is what I have done:

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

. matrix B = (.,0,0\0,.,0\0,0,.)

. svar s x y, aeq(A) beq(B)
Estimating short-run parameters

Iteration 0:   log likelihood =  -299.8563  
Iteration 1:   log likelihood = -147.47074  
Iteration 2:   log likelihood = -122.12662  
Iteration 3:   log likelihood = -50.376469  
Iteration 4:   log likelihood =   99.25067  
Iteration 5:   log likelihood =  254.43141  
Iteration 6:   log likelihood =  388.92237  
Iteration 7:   log likelihood =  451.48461  
Iteration 8:   log likelihood =  464.37819  
Iteration 9:   log likelihood =  466.25805  
Iteration 10:  log likelihood =  466.26709  
Iteration 11:  log likelihood =  466.26709  

Structural vector autoregression

 ( 1)  [a_1_1]_cons = 1
 ( 2)  [a_1_2]_cons = 0
 ( 3)  [a_1_3]_cons = 0
 ( 4)  [a_2_2]_cons = 1
 ( 5)  [a_2_3]_cons = 0
 ( 6)  [a_3_3]_cons = 1
 ( 7)  [b_1_2]_cons = 0
 ( 8)  [b_1_3]_cons = 0
 ( 9)  [b_2_1]_cons = 0
 (10)  [b_2_3]_cons = 0
 (11)  [b_3_1]_cons = 0
 (12)  [b_3_2]_cons = 0

Sample:  1995q4 - 2015q4                           No. of obs      =        81
Exactly identified model                           Log likelihood  =  466.2671

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      /a_1_1 |          1  (constrained)
      /a_2_1 |   .0002574   .0007334     0.35   0.726      -.00118    .0016948
      /a_3_1 |  -.0005385   .0023946    -0.22   0.822    -.0052319    .0041548
      /a_1_2 |          0  (constrained)
      /a_2_2 |          1  (constrained)
      /a_3_2 |   -.952645   .3625158    -2.63   0.009    -1.663163   -.2421271
      /a_1_3 |          0  (constrained)
      /a_2_3 |          0  (constrained)
      /a_3_3 |          1  (constrained)
-------------+----------------------------------------------------------------
      /b_1_1 |   .6805628   .0534701    12.73   0.000     .5757634    .7853622
      /b_2_1 |          0  (constrained)
      /b_3_1 |          0  (constrained)
      /b_1_2 |          0  (constrained)
      /b_2_2 |    .004492   .0003529    12.73   0.000     .0038003    .0051838
      /b_3_2 |          0  (constrained)
      /b_1_3 |          0  (constrained)
      /b_2_3 |          0  (constrained)
      /b_3_3 |   .0146559   .0011515    12.73   0.000      .012399    .0169127
------------------------------------------------------------------------------

. matlist e(A)

             |         s          x          y
-------------+---------------------------------
           s |         1          0          0
           x |  .0002574          1          0
           y | -.0005385   -.952645          1

. matlist e(B)

             |         s          x          y
-------------+---------------------------------
           s |  .6805628                      
           x |         0    .004492            
           y |         0          0   .0146559

.

1) If I understand well the reading of mat(A) : S has a negative impact on X (even if a little one) and S has a positive impact on y (bigger than the impact on x).
But what is the % interpretation ?

2) I would like to be able to know the loss / win of GDP % point due to S, quarter on quarter, from 2014q1 to 2015q4. What do I have to enter to find it out ?

3) Same than 2), but this time compared to a situation where all the values of S are equal to 0 : like if there is no favorable diplomatic measure at all on the studied period.
I have to gen a new data S2, replace values by 0 and run the same than 2) ?

4) Which graph can I use in order to observe the impact of S on X and Y ?

5) How to interpret the values of mat(B) ?

THANK YOU VERY MUCH for your kind help and time !

This is very important for my research.

Best regards,
M.B

[Morad Bali]

UP

[Julian Reyes Troncoso]

Hi Morad,

Do you have information about the sign interpretation of matrix A? I could not find any sources on the matter besides some blog comments.
I hope you can answer this quickly, as it is of great relevance to my research.

Cordially,
Julian Reyes

[Morad Bali]

Hi Morad,

Do you have information about the sign interpretation of matrix A? I could not find any sources on the matter besides some blog comments.
I hope you can answer this quickly, as it is of great relevance to my research.

Cordially,
Julian Reyes

Dear Julian,

Did you read the two articles present on the STATA blog? One about VAR, another about SVAR.

If it doesn't answer your question, create a new post with your code and results.

[Julian Reyes Troncoso]

Dear Julian,

Did you read the two articles present on the STATA blog? One about VAR, another about SVAR.

If it doesn't answer your question, create a new post with your code and results.

I read an article from David Schenck (https://blog.stata.com/2016/09/20/st...ession-models/) on SVAR models. However, I'm failing to see the sign interpretation on the coefficients from matrix A, as David states that "unemployment rate will decline slightly on impact after an inflation shock", with the coefficient being positive. You as well stated that you understand the sign interpretation on your first entry of this post, and at first glance I think one should interpret the coefficient with the opposite sign. Maybe it's a basic question, but I would like to know more about the sign interpretation as to put it correctly on my research.

PS: I hope someone has solved your question from this post, as I hung to this post.

[Morad Bali]

I read an article from David Schenck (https://blog.stata.com/2016/09/20/st...ession-models/) on SVAR models. However, I'm failing to see the sign interpretation on the coefficients from matrix A, as David states that "unemployment rate will decline slightly on impact after an inflation shock", with the coefficient being positive. You as well stated that you understand the sign interpretation on your first entry of this post, and at first glance I think one should interpret the coefficient with the opposite sign. Maybe it's a basic question, but I would like to know more about the sign interpretation as to put it correctly on my research.

PS: I hope someone has solved your question from this post, as I hung to this post.

I have just checked his blog paper, it is indeed strange. I don't see why signs should be reversed, but there is maybe something that I am missing here.

Frankly speaking, what I am usuallly doing is creating an IRF file, so I can specify the step number.
Then I just run OIRF to see how each variable reacts to the considered shock.
You can also table OIRF and FEVD once you have this IRF file, which is really useful.
Did you try that to see if that's in line with matlist e(A)?

[Julian Reyes Troncoso]

I listed matrix A, and is not in line with what I've found with the IRF graphs. I think that you got a sense of the reversed sign as you said that "S has a negative impact on X" even when the coefficient is positive in this same post. That's why I asked about the sign interpretation.

[Julian Reyes Troncoso]

Also, it seems that in SVAR models literature, coefficients of A and B aren't of much relevance as researchers tend to concentrate on IRF and FEVD

[Morad Bali]

Also, it seems that in SVAR models literature, coefficients of A and B aren't of much relevance as researchers tend to concentrate on IRF and FEVD

That's one the real advantage of SVAR.

About the sign, I honestly really don't remember what led me to this conclusion. I am mostly working with the help of IRF and FEVD nowadays.

[Julian Reyes Troncoso]

Don't worry. Thanks for helping this undergrad, Morad. I hope you're doing well