Linearly Transforming Variables in the VAR Model, How Does it Change the Impulse Response?

Abstract This paper analyzes the impulse response function of vector autoregression models for variables that are linearly transformed. The impulse response is equal to the linear transformation of the original impulse response if and only if the shock is equal to the linear transformation of the original shock. In particular, we consider shocks in one error term only, generalized shocks, structural shocks identified by short-run recursive restrictions and structural shocks identified by long-run recursive restrictions. A vector autoregression model with expected inflation, the overnight rate and a long term ex-ante real interest rate that replaces the corresponding long term nominal interest rate, illustrates our results.