# 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:

\frac{R_t}{R}=\left(\frac{R_{t-1}}{R}\right)^{\phi_R}{\left(\left(\frac{\Pi_t}{\Pi^T}\right)^{\phi_\pi}\left(\frac{Y_t}{Y}\right)^{\phi_y}\left({dS}_t\right)^{\phi_s}\right)}^{1-\phi_R}

then in the steady state I would have:

1=\left(\frac{\Pi}{\Pi^T}\right)^{\phi_\pi}

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?

\frac{R_t}{R^T}=\left(\frac{R_{t-1}}{R^T}\right)^{\phi_R}{\left(\left(\frac{\Pi_t}{\Pi^T}\right)^{\phi_\pi}\left(\frac{Y_t}{Y}\right)^{\phi_y}\left({dS}_t\right)^{\phi_s}\right)}^{1-\phi_R}

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

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?

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.