# EZ Preferences and Calvo pricing

Hi everyone, I am trying to solve a standard NK model with Calvo pricing (for ex. Ch 3 Gali 2015), but introducing Epstein-Zin preferences in the household. In order to solve the NK model, the optimality conditions of the intermediate producers are expressed as two recursive variables to get rid of the infinite sum (see for example https://www.sas.upenn.edu/~jesusfv/benchmark_DSGE.pdf). Now, deriving these recursive variables is straightforward with standard power utility preferences, it is not as easy with EZ preferences for the presence of the certainty equivalent operator in the SDF.

I tried to find references that implement EZ preferences and calvo prices, but did not find any. Is anyone aware of a dynare code that has EZ pref + calvo prices so that I could see how the recursive variables are expressed? Thanks a lot in advance.

Hi Luca,

The simplest example I can think of is in the appendix of Monetary policy, doubts and asset prices by Benigno and Paciello. In particular, you should look at their appendix, sections 1 and 2.
The equations that answer your question are (22), (23), (24), and (29), as they constitute the nonlinear pricing block of the model.
In the complete set of equilibrium conditions listed in section 2, the same equations are (35), (36), (39), (40) (notice that in (39) and (40)) real marginal costs have been substituted in.
You can easily write equations (35), (36), (39), (40) in Dynare, just as you would with standard power utility preferences.

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Thank you, very useful reference!