
Hello, folks. I have a DSGE model with 'nb' number of backwardlooking variables and 'nf' number of forwardlooking variables. I've been digging into IRIS filter algos and was wondering if you could help me clarify how the forecast of backwardlooking
variables is generated.
From the quasi upper triangular matrix T (of size [nb + nf] by nb) one could conclude that backwardlooking variables dynamics are not being affected by forwardlooking variables, and that forwardlooking variables dynamics are affected by backwardlooking
variables ONLY.
Could you confirm this is the case? In other words, could one use the upper triangular portion of T to forecast backwardlooking variables without the need to forecast forwardlooking variables? The source of my confusion is that when we write the model equations
in the model file, we write such equations so that backwardlooking variables ARE affected by forwardlooking variables.
Any enlightening words will be appreciated!



Hi
You're absolutely correct. You can decouple the dynamics of bkwlooking variables (xb) from frwlooking variables (xf). Note that in IRIS solution matrices. the bkwlooking variables are placed in the lower part.
You're also right that in the original model equations, everything is interdependent. But this interdepency is sorted out when the below final solution is computed using the generalized Schur decomposition. Then, the effect of frwlooking variables is integrated
away, and effectively replaced directly with expectations of future exogenous things, which means anticipated shocks in IRIS.
The IRIS transition equation (in its vector/matrix form) is, in fact, given by
[ xf; xb ] = [ Tf; Tb ] * xb(1) + [ Rf0; Rb0 ] * e + [ Rf1; Rb1 ] * E[e(+1)] + ... [ Rfk; Rbk ] * E[e(+k)] + ...
where Tf, Tb, Rf0, Rb0, ... are matrices (only Tb is square, all other matrices can be rectangular in general), and e the vector of current shocks, and E[e(+k)] means the expectations of shocks at t+k (which is implicitly assumed zero if not specified otherwise
by the user, through anticipated shocks).
Note that the first term on the RHS refers to xb(1) only, and not to xf(1).
Hope this helps.
Jaromir



Thank you!

