Computing level-impulse responses of log-specified VAR systems

Impulse response functions (IRFs) are often used to analyze the dynamic behavior of a vector autoregressive (VAR) system. In many applications of VAR modelling, the variables are log-transformed before the model is estimated. If this is the case, the results of the IRFs do not have a direct interpretation, since they are also log-transformed. In this paper, we present explicit expressions for computing impulse response functions that are expressed in the levels of the variables, given a log-log transformed model. We illustrate the methodology by an application in marketing.