Forward guidance in Rotemberg NKmodel

Perfect foresight simulations
1

Hi

I am trying to implement a forward guidance using NK model with Rotemberg sticky price. unfortunately when I run the model in perfect foresight it is unable to compute the steady state. Even though I find a “non conventional” way to get the steady state by adding the excess residual to the equation the rank condition is not verified and so the model fail. I thus have two questions:

1 - I guessed that the problem comes maybe from the initval of the nominal interest or the way the steady state model is parameterized, but I still don’t have any clue on what’s going on. Do any one have an idea on how to solve the problem?

2 - In perfect foresight there is no need to linearize the model for the simulation. But I was wondering if it is possible to use higher order approximation with the simul command so that I could capture the difference between Rotemberg and Calvo?

Thank you

testFG.mod (8.7 KB)

2
  1. Your model has a unit root. That implies that the terminal steady state will be different from the initial one and that you need to provide the terminal steady state.
  2. If your interest rate is purely exogenously set, what assures a unique inflation rate? Pure interest pegs typically violate the Taylor principle.
3

Thank you for the answer

First of all sorry for the cross post.

Thank you for your first remark. For the terminal steady state you refer to the endval section? I guess that the easiest and convenient way to solve it without no need of these terminal steady state is thus to express the model in term of inflation to get rid of the price level and the unit root? or will I still need to provide terminal steady state?

For the second remark I understand the violation of the Taylor rule. In the literature I figure out that multiple equilibria in the NK model results from a monetary policy not sufficiently responsive to insure the equilibrium uniqueness (coefficients on inflation and output are 0 in the Taylor rule). This is the same case in my model I guess. Though this mean that I still don’t get the proper way to capture the forward guidance implementation in Dynare. To my understanding it is not possible to define the interest rate as exogenous and endogenous variables at the same time. So how do I implement a deterministic shock with the Taylor rule in the model?
I already tried your example for TFP shock in RBC model but it does bot produce the contemporaneous response of the macro variables. I did implement the result I wanted in a linear SOE NK model even though I have rank condition problem. I attached the file so that you can see if I had the good approach?

Thank you

G_SOENK_news1.mod (8.2 KB)

paranews1.m (8.0 KB)

4
  1. Yes, working with inflation rates instead of levels typically helps.
  2. With indeterminacy, there are infinitely many possible paths. A terminal condition will typically select one of those paths. So that may be one solution. Looking at the rank condition from a linearized, infinite-horizon stationary perspective will be misleading in this case.
    You may want to ask @fcbs about this solution to Forward guidance shock
5

Thank you very much for your answer. I will ask.
One last question is is possible to have higher order approximation in pure perfect foresight model. I’m asking due to the fact that there’s is no need to linearize the model in Dynare to do the perfect foresight simulation (correct me if I’m wrong)

Thank you

6

Perfect foresight is solving a nonlinear equation system. There is no approximation involved.

7

Hi dear @jpfeifer

I have again 2 question regarding the Rotemberg pricing NK with monetary shock.

1 - when I apply a 1 percent annualized contractionary shock, the nominal interest rate fall, but the real interest rate increases. Playing with the parameter I found out that the persistence parameter for the shock is the cause of this wrong response. for rho_nu < 5 the nominal rate goes up. Conversely in Calvo for rho_nu > 6 it goes down. Is it a problem insight the code itself or just as you mentioned in this topic just and endogenous response of the Taylor rule Please help see my code

2 - When there is interest rate smoothing in the taylor rule
R=R(-1)^rho_r*(1/bettaPi^phi_pi(Y/steady_state(Y))^phi_y)^(1-rho_r)*exp(nu);
is the monetary shock still autoregressive or just iid?

thank you

testenvoi1.mod (13.5 KB)

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  1. This seems to indeed be the result of the endogenous response.
  2. Usually, the MP shock is considered to be iid if there is interest rate smoothing.
9

ok Thank you for the reply