Dynare can solve models with time-varying vol of shocks?

May I ask a question on using dynare to solve models with time-varying volatility? Such models is shown to be solved by log-linearization approximation (Bansal, Kiku and Yaron(2007)) or perturbation method, for instance, Malkhozov and Shamloo (2010).

However, I meet with some problems by soving it in dynare. Please have a look at the attached folder. I use a simple example – a consumption based asset pricing model with Epstein-Zin preference and time-varying volatility of consumption, following an AR(1) process. As in Bansal, Yaron and Kiku (2009), consumption variance is a state variable. However, after dynare solving the model, I get the results which does not make much sense.

First, the price-to-dividend ratio is constant, and does not related to the state variable “consumption vol”.
Second, I get strange impulse response functions with respect to vol shock, which are hard to interpret.

The attached folder contains three files:

“LRR_example.mod” is the model file.
“Model.pdf” describes the simple model with time varying volatility.
“LRR_example_IRF_e2.pdf” contains the IRF w.r.t the voaltility shock e2.

Thank you!
TimeVaryingVol.zip (52.6 KB)

I do not know a solution, but have two suggestions:

1.) In models with time-varying volatility, sometimes a higher-order approximation than 2 is needed (e.g. Fernandez-Villaverde/Guerron-Quintana/Rubio-Ramirez/Martin Uribe (2009) “Risk Matters: The Real Effects of Volatility Shocks” do a third order approximation)
2.) Is the timing of your predetermined states correct as a wrong timing sometimes leads to the oscillating IRFs as in your case.

See also [K_order_perturbation error)