Var Post-estimation: Extract and manipulate coefficients to create new series

[Charlie Clarke]

I am trying to replicate the variance decomposition from a vector autoregression (1 lag) found in "Bad Beta, Good Beta" by John Campbell and Tuomo Vuolteenaho (using Stata 12). On page 10 of the version linked, the authors set the following var system:

z_t+1 = a + G z_t + u_t+1

where G is gamma, a matrix of coefficients for the var set up don't include the constant term. In my set up, I have 4 state variables in z, so G is 4 by 4.

I need to define a lambda: L = p*G*(I - pG)^-1
where p is a constant, I is the identity (in my case 4x4), and the last term (I - pG)^-1 means the inverse of the matrix.

Using L, I will create two series:
let e1' be a row vector of 1 and zeros, in my case: [1 0 0 0]

N1 = e1' L u_t+1
N2 = (e1' + e1'L)u_t+1

So N1, is taking the first row of L and multiplying by the innovations in the var. Ideally, I'd end up with N1 and N2 tacked onto my original data set as two new series. I don't need the matrices beyond that.

So I start with the VAR(1) which is easy enough:

var y x1 x2 x3, lags(1)

but I'm not sure what to do from here. Can anyone help?

[Charlie Clarke]

Sorry, if the question is poorly posed. I think probably there is a way to use mata and put the coefficients in a matrix. If someone could push me in that direction, maybe I could figure out the correct matrix manipulations.

[Andres Salman]

Charlie Clarke By any chance were you able to reproduce this study in Stata? I'm in the same boat. Unfortunately I have not found any other references to this study using Stata.