Structural VAR model in Stata

[Tirupam Goel]

I am trying to estimate the structural VAR model shown in the figure below.

I am using the following set of STATA commands, where v_inf is the first variable, v_ste is the second, and v_lte is the third in the model above.

constraint 1 [v_inf]L.v_ste = 0
constraint 2 [v_inf]L.v_lte = 0
matrix A = (1,.,.\0,1,0\0,0,1)
matrix B = (.,0,0\.,.,0\.,.,.)
svar v_inf v_ste v_lte, lags(1) varconstraints(1 2) aeq(A) beq(B)

I get the following error when running the command.

Estimating VAR coefficients

Iteration 1:   tolerance =   .3625846
Iteration 2:   tolerance =  .07657791
Iteration 3:   tolerance =   .0143273
Iteration 4:   tolerance =  .00284507
Iteration 5:   tolerance =  .00057143
Iteration 6:   tolerance =  .00011503
Iteration 7:   tolerance =  .00002317
Iteration 8:   tolerance =  4.666e-06
Iteration 9:   tolerance =  9.399e-07

With the current starting values, the constraints are not sufficient for identification
The constraints placed on A and B are 
  1999:  [a_1_1]_cons = 1
  1998:  [a_2_1]_cons = 0
  1997:  [a_2_2]_cons = 1
  1996:  [a_2_3]_cons = 0
  1995:  [a_3_1]_cons = 0
  1994:  [a_3_2]_cons = 0
  1993:  [a_3_3]_cons = 1
  1992:  [b_1_2]_cons = 0
  1991:  [b_1_3]_cons = 0
  1990:  [b_2_3]_cons = 0
These constraints place 10 independent constraints on A and B
The order condition requires at least 12 constraints.
Identification requires a rank of 18, but the identification matrix only has rank 16
r(498);

This is despite having checked that the model is exactly identified. That is, if I run the following command to estimate the reduced form VAR parameters, I can back out A, A1 and B exactly by solving some linear equations manually

var v_inf v_ste v_lte, lags(1)

Any help regarding what I am not doing correctly with the svar implementation of my model is much appreciated.

[Eric de Souza]

Stata does not take into account the restrictions on the matrix A1 for identification, only the restrictions on A and B.
Also - but this is not relevant to your problem - there is a typo in your definition of the B matrix in your code: see the second row.

[Tirupam Goel]

Dear Eric, many thanks for your kind response. This was my hunch, and it is good to have confirmation.

[Tirupam Goel]

My end goal is to compute IRFs.

The "irf create" command in Stata enables a user to compute IRFs under different Cholesky orderings of variables in VAR model.

But is it possible to compute IRFs based on a user-defined identification strategy (one that is not a Cholesky identification)?

[Eric de Souza]

I don't remember all the details but it is explained in the Stata manuals.
The command "irf create" creates various kinds of irf's and stores them in memory which you can then call up.

After an SVAR "irf create" creates and stores:
simple IRFs
cumulative IRFs
orthogonalized IRFs
cumulative orthogonalized IRFs
structural IRFs

You can then clall them with "irf graph" or "irf table"
irf graph irf,
irf graph cirf
irf graph oirf
irf graph coirf

and in addition after a SVAR
irf grpah sirf

The same for irf table

[On edit] The magnitude of the shock for orthogonalised IRFs and for structural IRFs is equal to one standard deviation in Stata

[Tirupam Goel]

Thanks much Eric.

[haiyan lin]

Why there is no csirf option after SVAR to draw the cumulative impulse responses?