Dear Forum,

I am working with a DSGE asset pricing model with stochastic volatility. Somebody suggests me a third-order perturbation should be the minimum requirement. The reason is, in the second-order perturbation, only constant volatility affects the decision rule.

However, in Caldara et al (2012RED)'s case, the second-order and third-order perturbation shares almost the same result in the benchmark calibration. In my own research, the second-order perturbation with stochastic volatility can match the equity premium. Once I turn off the stochastic volatility or second-order perturbation to be first-order, the high equity premia and volatility disappear.

My question is, if, in a second-order perturbation, merely the constant volatility drives the equity premia. Why does the mere original TFP shock fail to produce the sizable equity premia? Why Caldara et al (2012RED) suggests that second-order perturbation is acceptable?

Or, the second and third-order perturbation, who is the minimum requirement? why?

If I adopt the second-order perturbation, is there any negative effects in terms of asset pricing research?

All comments are welcome.