# IRFs in annualised percentage points

I’m simulating a small open economy and its response to various shocks. I’m inputting the model in log-linearised form and want to plot the impulse response functions of the variables to the shocks. I want the impulse response functions of some variables to be in percentage deviations from the steady state, which I understand is the regular irf I’m being given when entering the model in log-linear form. However, I also want to display the irfs of some variables such as inflation and the nominal interest rate in annualised percentage points. I haven’t been able to figure out how to do this, please kindly assist me with this.

To add to this question, following section 4.4 of the Guide to Specifying Observation equations, I’ve put all variables apart from the ones I want to have in annualised percentage points into exp(). However, this had the effect that the coefficients on all variables put into exp() have been changed.

Are you working with a linearized model or a nonlinear one with exp()-substitution? Also, usually in nonlinear models you have gross interest and inflation rates. Their logged value will be approximately equal to net rates. Thus, the annualized rate is usually just 4 times the quarterly rate in a linearized model.

I’m working with a New Keynesian model that’s already linearised. I’m not sure conceptually how the moving to annualised percentage points works. Since the model is already linearised, I’m plotting percentage deviations from the steady state (which is zero trivially). If I then just multiply this by 4, wouldn’t this give me annualised percentage deviations from the steady state as opposed to the actual annualised inflation rate in percentage points for which I’d require the non-linearised steady state?

Are you interested in gross or net rates? I.e. gross inflation P_t/P_{t-1}= 1.02 or net inflation P_t/P_{t-1}-1= 0.02? Usually it’s the latter. And that what you get in a linearized model due to \ln(1+x)\approx x for small x.