Impulse Response Graph

[zhaoningru]

Will the impulse response graph be same no matter what kind of variables I use in DYNARE(For example, x(level variable) or exp(x)(log variable))? If I use linear model(do log-linearization by myself), will the impulse response graph be same with graph generated by using level variables or log variables in DYNARE?

[jpfeifer]

Of course not. In one case (variable in levels), the IRF will be for the total/absolute change in the level. If you use log variables through exp() substitution or log-linearize yourself, your IRF will be the percentage change in a variable relative from steady state. Thus, the two will only coincide for variables of steady state 1 as the normalization with the steady state does not do anything.

[zhaoningru]

Of course not. In one case (variable in levels), the IRF will be for the total/absolute change in the level. If you use log variables through exp() substitution or log-linearize yourself, your IRF will be the percentage change in a variable relative from steady state. Thus, the two will only coincide for variables of steady state 1 as the normalization with the steady state does not do anything.

That is what I think so. However, no matter percent change or level change, they should have the same direction. I mean if there is an increment for certain variable in level, there should be an increment in percent change in log. Am I correct?

[jpfeifer]

Yes, comovement must be the same.