You are not defining the risk-free rate correctly as you are neglecting Jensen’s Inequality. You need to haver^f_t=\frac{1}{E_t\left(\beta\frac{C_{t+1}}{C_t}\right)} r^f_t=E_t\frac{1}{\beta\frac{C_{t+1}}{C_t}}
/*
* This file replicates some of the results in Jermann (1998): Asset pricing in production economies,
* Journal of Monetary Economics, 41, pp. 257-275
*
* THIS MOD-FILE REQUIRES DYNARE 4.5
*
* Notes:
* - While Jermann uses log-linear asset pricing, this implementation relies on a
* second order approximation
*
* This implementation was written by Johannes Pfeifer. In case you spot mistakes,
* email me at jpfeifer@gmx.de
*
* Please note that the following copyright notice only applies to this Dynare
* implementation of the model.
*/
/*
* Copyright (C) 2016-17 Johannes Pfeifer
*
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and
There is a good reason for this and it involves i)Jensen’s Inequality, ii) auxilary variables, and iii) the convention that there is a conditional expectation around every single equation you enter into Dynare.
What you have in your problem is basically an Euler equation with Omega being the stochastic discount factor. Say the SDF between t and t+1 is given by the standard
Omega=beta*(C(+1)/C)^(-sigma)
What you want to evaluate is
mu=E_t(SDF_{t,t+1} R_{t+1});
Note that the SDF depends on thin…