Observable mean and steady state value

Hello everyone

I am working on a model with positive inflation in the steady state in a non-linear form. The central bank’s target inflation rate is 3% however the mean of inflation in the data is around 4% so if I assume in the model that \Pi=1.0075 (i.e. 3% annual net rate) it would not be consistent with the mean of inflation in the data. Some time ago I read in the forum that inflation in the steady state does not have to be the same as the target inflation (\Pi^T), however, if I assume that \Pi\neq\Pi^T and I have a Taylor rule of the following form:


then in the steady state I would have:


which obviously prevents the residuals of the equation from being zero in the steady state. Does this mean that I need to create a different parameter to replace R and adjust the residuals? Let’s call this new parameter R^T, so my taylor rule should look like this?


Therefore, in the steady state, rearranging terms I would have:

\frac{R}{R^T}=\left(\frac{\Pi}{\Pi^T}\right)^{\phi_\pi} which leads to R^T=\left(\frac{\Pi^T}{\Pi}\right)^{\phi_\pi}R

I don’t know if this is correct and I don’t know what economic meaning R^T would have, but if it is not correct, how do you make \Pi\neq\Pi^T without affecting the steady state of the Taylor rule?

Thanks in advance

You seem to be equating the mean in the data with the steady state, but that is only true in the very long run. In sample, the mean can be different from the steady state.

Thank you for your reply professor.

  1. Are you saying that the mean of the observable variables should not necessarily coincide with its value in the steady state suggested by the model?

  2. Another short question, I have three variables of the external sector, output, inflation and interest rate, the common thing is to model them as an AR process, however, I model the output and inflation as an AR process but the interest rate as a rule Taylor so that the interest rate responds endogenously to output and inflation and this affects the UIP. Is it correct to have a foreign Taylor rule even though output and inflation are AR processes? I have not seen such a thing in the literature.

Thanks again for your answer

  1. Yes. If the mean in a sample is supposed to be different from the steady state, then shocks in the sample need to account for the difference.
  2. From the perspective of the domestic economy, you don’t care where the foreign variables come from as you have to take them as given. Often a VAR process fits the data better than an imposed structural relationship. After all, central banks are not a Taylor rule, but that decision is up to you.