# Using a linear Phillips curve in non-linear models

Can anybody help me please to understand something related to using Calvo price setting equations in Dynare?

By looking at Iacoviello Matteo 's replication codes, I realized that he always directly puts the log-linear (deviation from steady state) form of the Phillips curve in the non-linear forms of models programmed in Dynare.

In other words, instead of writing the non linear forms of Calvo price setting equations, he rather usually uses the linear Phillips curve while In my understanding we should use non-linear price setting equations in the models written as non-linears in Dynare.

I would like to know the rationale behind such a mixture of programming styles. Why do he uses this mixture? What are the implications on the model simulation results? Do this has no implications in terms of IRFs regardless the order of approximation?

1. At first order, it does not matter which one you use as long as you make sure that the variables defined are consistent. The reason is that the nonlinear equations will be linearized.
2. The problem with Calvo pricing is that the FOC involves an infinite sum that cannot be entered into the computer. One way out is to linearize the FOC, resulting in the New Keynesian Phillips Curve. The other way is to find a recursive representation (see https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Gali_2015). Apparently, Iacoviello went for the first way.
3. If you do higher order approximations, you need to use the nonlinear version, because a linear Phillips Curve is not equivalent to the nonlinear one.

Dear Johannes,
However, I programmed my model using the recusive form of the calvo price setting case, but the link between interest rate and inflation doesn’t work well regardless the parameters. Precisely, a hike in interest rate implies for example an increase in inflation. Where does this could come from? Herewith the simple version of the model.
Best,

Simple model.zip (553.8 KB)

A rise in interest rates is contractionary and should decrease inflation. So where is the problem?

Dear Johannes,
Sorry I did a mistake in my question, it is the opposite that the code provides.
I updated it: a hike in interest rate implies for example an increase in inflation. Where does this could come from? Herewith the simple version of the model.