I have recently been replicating Gourio, F. (2012). "Disaster Risk and Business Cycles." American Economic Review, 102, 2734–2766. https://doi.org/10.1257/aer.102.6.2734.
However, I encountered problems calculating risk aversion and IES under the EZ preference. In Gourio (2012), the representative consumer has recursive preferences (Epstein and Zin 1989): $$ V_t=\left(U_t^{1-\psi}+\beta E_t\left(V_{t+1}^{1-\gamma}\right)^{\frac{1-\psi}{1-\gamma}}\right)^{\frac{1}{1-\psi}} $$ where the utility index $U_t$ depends on consumption $C_t$ as well as hours worked $N_t$, and takes the following standard Cobb-Douglas form, consistent with balanced growth: $$ U_t=u\left(C_t, N_t\right)=C_t\left(1-N_t\right)^v $$ For this specification, $\gamma$ is the risk aversion coefficient and the parameter $\psi$ is inversely related to elasticity of substitution (IES). Specifically, the IES is $1 / \hat{\psi}$, where $\hat{\psi}=1-(1+v)(1-\psi)$, and it is larger than unity if and only if $\psi$ <1 .
I successfully calculated the discount factor by referring to this slides , but when I computed IES according to the formula, I found that IES is exactly $\frac{1}{\psi}$, which is the erroneous result emphasized by Gourio (2012). Moreover, I am unsure how to calculate risk aversion; in fact, the risk aversion I calculated seems to have no relation to $\gamma$ at all.
I hope someone can point me in the right direction! Thank you in advance!
