st: SVAR Blanchard and Perotti approach - Impulse response function

[Safis-Moustafa Chatzouz <shajjouz@gmail.com>]

Hi,

I am estimating a SVAR, between three variables real per capita 
government spending, real per capita tax revenues and real per capita 
income.
The variables are transformed in logs. Actually, i am trying to 
reproduce the results in Blanchard and Perotti (2002). I will try to 
describe shortly what i do and what i need.

my variables are gdp, gov and tax (quarterly data)

Var specification is: X(t)=A0+A(L)X(t-1)+dummy+trend + U

In the first step I estimated a var with four lags a dummy variable 
linear trend. So I used this command

var tax gov gdp, lags(1/4) exog( trend dummy)

i get the residuals from each equation. By the way, I could not find a 
command to get the residuals from each equation, simultaneously, after 
the var. So i run OLS for each equation and use:

predict e, residuals (for example I name the residuals as: u_t, u_g, u_y)

The identification as the authors say is as follows

u_t=a1*u_y  +  a2*e_g  + e_t    (1)
u_g=b1*u_y + b2*e_t   +e_g     (2)
u_y=c1*u_t + c2*u_g   +e_y      (3)

Where e_ denotes the structural shocks that need to be recovered. The 
restrictions are, b1=0, a1=2.08 and b2=0.
Then they construct the following two variables after the above 
restrictions

T=u_t - 2.08*u_y   (4)
G= u_g                    (5)

The authors write: "we use T and G as instruments to estimate c1 and c2 
in a regression of u_y on u_t and u_g". So what i do is the following

ivregress 2sls u_y (u_t  u_g = T G)

My first question is whether the above IV regression is the correct one 
to express what the authors say. I am saying this because i receive an 
error in STATA, although if i understood correctly the endogenous 
variables here should be  u_t  u_g

My second problem now is the following. Assume that someone here helped 
me with the above step and i have estimated c1 and c2, then is still 
missing the estimation of a2. So what i was planning to do is to have 
the svar estimation with the usual set up, i.e:

matrix A =
matrix B =
svar tax gov gdp, lags (1/4) exog (dummy trend) aeg(A) beq(B)

However, I need to make a rescaling or transformation for the whole 
estimated coefficients including the coefficients for the impulse response.
Since the variables are in logs i need to make a rescaling to denote 
multipliers, i.e dollar per dollar change. The authors do not say how 
they do the transformation but i guess they divide by the mean of the 
ratio y/g and y/t to recover the spending and tax multiplier respectively.

My next question is how to do this rescaling for impulse responses so 
as, instead of the 1% deviation to have the 1 unit dollar increase and 
therefore get the multipliers at each quarter.

Can you please help me. I will also appreciate whether there is any code 
and welcome any suggestions or corrections to what I did.

Looking forward for your reply.

Kind regards
Safis



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