Real or Nominal Variables, Does it Matter for the Impulse Response?

This paper analyzes impulse response functions of vector autoregression models for variables that are linearly transformed. These impulse responses are equal to the linear transformation of the original impulse responses only if the shocks are equal to the linear transformation of the original shocks. Sufficient conditions are derived both for shocks in one error term only, orthogonalized shocks and generalized shocks. A vector autoregression model with ination, the overnight target rate and a real interest rate that replaces the corresponding nominal interest rate, illustrates the applicability of our results for the empirical researcher.