Shock to expectations

[eta]

Hi,
I am in a deterministic setup, so everything should be easy, but I am new to Dynare ... The problem is the following one: in period 0 there is a revision in expectations that results in an inflation rate below the target rate (i.e. 2%), say 1,98 %. This is the shock I want to model. I wrote the initial condition for pi (inflation rate) and the shock (the new value), but this is incorrect. What would you suggest to do ? Thanks in advance.

[jpfeifer]

Could you please be more precise. Why is your approach incorrect? What exactly are you trying to achieve? For example, I don't understand how you can have shocks to expectations in deterministic perfect foresight models.

[eta]

Ok. I'm trying to compute the perfect-foresight equilibrium path of different variables (among which there is inflation) because I have to replicate the results of a working paper. There is a shock to inflation modeled as an initial value of pi below the target rate (i.e. 2%). I think this model is deterministic, otherwise I don't know how they could include in the model occasionally binding constraints, such as DNWR or the ZLB in the Taylor rule (by the way, there is no problem in doing that in such a context, isn't there ?) and they explicitly say that the set of perfect-foresight equilibrium conditions involves only deterministic sequences. So we are not talking about expected inflation but inflation itself. Thanks.

[jpfeifer]

We are getting closer. As documented in the manual, you can only set exogenous variables or endogenous states. Inflation typically is not a state in our models. So there must be some trick like a negative cost-push shock or something like this that makes inflation be below steady state at time 0.

[eta]

Yes, there must be. However, in the simple model they present it seems taht there is no cost-push shock. I don't know whether they are implicitly considering the usual NKPC p_t=betaE_t p_t+1+kx_t +u_t. If this is the case, I only have to shock u_t, including inflation in var, right ?

[eta]

In case you are interested, the model I am talking about is from the wp of Schmitt-Grohé and Uribe (2013). I am trying to replicate it as part of the learning process.

[eta]

No, they are not considering the NKPC, because the parameter k is not calibrated, so there must be another trick.

[eta]

What could make the inflation rate be below the target at period 0 if it's not a cost push shock ?

[jpfeifer]

Which of the SGU 2013 papers are you talking about?

[eta]

It's "The Making of a Great Contraction...", a working paper.

[jpfeifer]

I only had a quick look at the paper, but it seems to allow for multiple equilibria and thus for confidence shocks that are not determined within the model as they are "sunspot" shocks.

[eta]

It's true, there are 2 nonstochastic steady states. So, how would you model this confidence shock ? Using the usual NKPC I would shock u, but here I cannot write this equation since I want the dynamics of the original nonlinear model. I'm a bit confused and I don't know how to proceed.

[jpfeifer]

As I said, I don't know. But if there are sunspot shocks, you cannot proceed as in the usual case where everything is determinate. In this case, there is something outside of the model you need to specify. I have no idea what exactly they did there, but also I don't have the time to deeply look at this. But you could ask them for their code.

[eta]

OK, thank you for your useful comments, but I don't think they will provide the code.