Restrictions on short-run VAR

[Gianluca Cafiso]

Dear Statalisters,

I am estimating a Structural VAR:
A(I_K − A₁L − A₂L² − · · · − A_pL^p )y_t = Ae_t = Bet

I have set the restrictions I need on the A matrix (contemporaneous effects). Let's say that one of those restrictions is a₂₃=0; to wit, I am imposing no contemporaneous effect of the shock to variable 3 on variable 2.

Up to this point, everything is smooth in STATA: short-run constraints.

My problem is that I have to set the same restriction also on the matrices A₁, ..., A_p. This is because I want that variable 3 does not impact on variable 2 also from lag 1 onwards. I need to shut down the effect of variable 3 on 2 for any time period. This is for a counterfactual as done in:

• Ludvigson-Steindel-Lettau 2002 (Monetary Policy Transmission through the Consumption-Wealth Channel, FRBNY Economic Policy Review / May 2002)
• Giuliodori 2005 (Monetary Policy Shocks and the Role of House Prices Across European Countries)

Is there any way to do that in STATA svar command? I tend to belive no...
………………..

As an alternative solution: Do you think it would be the same to set constraints on the coefficients of the reduced-form VAR from which the Structural VAR is retrieved?
Reduced-form VAR: Y_t= v + B₁Y_t-1+…+ B_pY_t-p +u_t

To wit: I could impose that the coefficients of variable 3 in the equation of variable 2 in the VAR are equal to zero for any lag (b₂₃=0 in B₁,...,B_p).
Although, these are not the structural coefficients, perhaps this would make the trick, namely, this would shut any effect of variable 3 on 2. But I am not sure how this could alter the conclusion from the analysis.

I would really appreciate any suggestion about this.
Thanks

[Eric de Souza]

The example below should give you an idea of how to proceed:

webuse lutkepohl2

var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), lags(1/2)

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

matrix B =(1,0,0\0,1,0\0,0,1)
matrix list B

svar dln_inv dln_inc dln_consump if qtr<=tq(1978q4), aeq(A) beq(B) var dfk


*******************************

constraint 1 [dln_inv]L2.dln_inv = 0
constraint 2 [dln_inv]L.dln_inc = 0
constraint 3 [dln_inv]L2.dln_inc = 0
constraint 4 [dln_inv]L2.dln_consump = 0
constraint 5 [dln_inc]L2.dln_inv = 0
constraint 6 [dln_inc]L2.dln_inc = 0
constraint 7 [dln_inc]L2.dln_consump = 0
constraint 8 [dln_consump]L.dln_inv = 0
constraint 9 [dln_consump]L2.dln_consump = 0

*******************************
svar dln_inv dln_inc dln_consump if qtr<=tq(1978q4), aeq(A) beq(B) var varconst(1/9) dfk

On edit: Note that Stata sometimes produces very small numbers for the coefficients instead of a zero

[Gianluca Cafiso]

I am aware of this example. This is what I meant by "an alternative".

The issue is: through the "constraint X" lines one imposes constraints on the lagged coefficient-matrices in the Reduced-Form (B in my previous text), not in the Structural-Form.
In the example the restrictions on the structural-form matices are set through "aeq(A)", but that works only for the contemporaneous effects, not for the lagged.

Theoretically, I would need to impose restrictions on the lagged coefficient-matrices of the Structural Form (A_p in my previous text)

[Eric de Souza]

The constraints 1 to 9 in my example are constraints on the A1 to Ap matrices. So I don't understand what you mean.

[Gianluca Cafiso]

You report example 3 from the "var svar" command (STATA TS manual)

>Structural VAR: A(I_K − A₁L − A₂L² − · · · − A_pL^p )y_t = Ae_t = Bet
>Reduced-form VAR: Y_t= v + B₁Y_t-1+…+ B_pY_t-p +u_t

The constraints you set and include through the varconst(1/9) are on the coefficient matrices of the Reduced-Form (B matrices), not on the matrices of the Structural-Form (A matrices)

If you read the example: "svar also allows us to palce constraints ont he parametners of the Underlyign VAR..."

Have a look at page 11: http://www.stata.com/manuals13/tsvarsvar.pdf

Although, I don't know whether imposing restrictions on B_i is equivalent to imposing restrictions on A_i

[Eric de Souza]

After having had a look at the two papers to which you refer as well as the technical appendix to Ludvigson et al paper (the technical appendix is available on her website), I fear that this is something you will have to program yourself. Giulidori used RATS and I get the impression that he also had to program it himself.

[Gianluca Cafiso]

Dear Eric,
thank you very much for your interest on my post.

Yes, I believe I have to switch to another software.

Regards,
g