Taylor Rule and price level targeting

[homayoun]

Hi,

Thank you so much for your reply.
I have some difficulties in understanding the mechanism and it would be great if you can help me with that. I have already read your post here:

@jpfeifer

All I am saying is that it could be a feature and not a bug. I did not check your model.

The mechanism is the following: Assume the initial monetary policy shock increases the nominal and thus the real interest rate. The central bank then reacts to lower output and inflation endogenously by lowering the nominal interest rate. If the response is strong enough, it overcompensates the initial increase due to the shock. The only thing you know is that the real interest rate increases, so that the shock is still contractionary, although the nominal interest rate goes down. This is one of the reasons why you cannot look at interest rates to determine whether monetary policy is expansionary.

If we consider a simple taylor rule such as
R_t/R_{ss}=(Π_t/Π_{ss})^{ϕ_Π}S_t

Where S follows

ln(S_t)=rhoS∗ln(S_t(−1))+(1−rhoS)∗ln(S_{ss}))+EPS_{R,t}

1. A change in EPS_R in the above equation, means a contradictionary mondetary policy shock as its sign is positive in the equation and it definitely increases the real interest rate (r_t=R_t-\Pi_t) no matter if we can see a posive or negative nominal interest rate (R_t). Is this true?

2. The IRF of Real Interest rate with respect to the above shock is negative (I added the following equation in my nonlinear model : r_t=R_t/\Pi_{t+1}) in the model. Is this OK or it must be positive as the result of the contradictionary policy?

3. I know in the NK models, the Euler equation pins down the nominal interest rate ,R_t, and the Taylor rule pins down the inflation , \Pi_t but how these equation reacts when we have a contradictionary monetary policy shock? I thought the shock starts to propagate into the model through the Taylor rule and it increases R_t and then the increase in the nominal interest rate would decrease the current consumption and so on.

4. It there any formal way (adding a term or removing a variableother than changing the parameters) to be followed in order to get rid of the overcompensation (of the initial increase due to the shock) you mentioned in your reply to get the nominal and real interest rate in the same direction?

Thank you in advance for your time