# Constraint on covariance matrix for shocks in VAR representation of DSGE model

Dear Johannes,
I have a question about var representation of dsge model in the following paper:

In this DSGE model, the prior mean of standard errors of shocks is set to 0.01 instead of 1. I have modified this model by replacing measurement error with another structural shock, so the number of observables equals the number of shocks
I can find a finite VAR representation for the modified DSGE model,
Define X_t as observable vector, U_t as reduced form shock vector, V_t as structural innovation vector
\Lambda is lag operator matrix, i have:
\Lambda X_t=U_t=\delta V_t, in order to identify this finite VAR representation of DSGE model, I impose constraint on variance-covariance matrix of V_t, Covariance Matrix of V_t=0.01 I,
However, in the literature, people impose covariance matrix of V_t=I, but their associated DSGE shock variance’s prior mean is 1 instead of 0.01
I have add 0.01 because my DSGE shock variance’s prior mean is 0.01 ,
My question is my imposed constraint of structural shocks V_t covariance matrix as 0.01 I right or wrong?
Thank you very much and look forward to hearing from you.
Jesse

Sorry, but I do not really understand the question. If you are consistent, you can use any normalization you like as the model is linear.