3rd order perturbation and volatility of consumptoin

Hello Professor Johannes,

Background: SOE RBC models, 3rd order perturbation with pruning stationary TFP shocks using GHH preferences. When I lower the gamma (risk aversion (exponent in GHH utility functions) say, 2.5 to 2. I noticed that standard deviation for consumption is decreased sufficiently.

If risk aversion is large, it means that the household will want consumption (in expectation) to be very smooth. At gamma =2, Initial response of consumption is greater after TFP shocks in IRFs starting at EMAS than gamma =2.5. That’s make sense to me however,

I am looking for economic intuition why at higher gamma there is greater volatility of consumption than the at lower gamma.

Is it that at higher gamma there more smoothness in consumption, at 3rd order certainty equivalence also break, so precautionary motive is there already. With higher gamma, this precautionary motive further go up. As smoothness is large period of time, so, it result in increasing in the volatility of consumption than at gamma=2.?

Best Regards,

The volatility will depend on the initial response and the persistence over time. A higher risk aversion usually means a bigger smoothing, i.e. a bigger persistence.

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Thanks a lot, Though, Initial response in consumption is lower at higher risk aversion. But decreasing risk aversion from 2.5 to 2 decrease volatility of consumption by 47%. I think, using pruning option is also adding more persistence. As without pruning option, decreasing the value of risk aversion parameter does not make any significant change in the volatility of consumption. (almost same).

Second question is related to pruning which I discussed earlier.

I want to a bit dig deeper now to see how pruning is creating persistence. How can I do so? I think, starting point would to look into state space model? But which variable I need to look into? How can get access to state space of model in 3rd order.

Thanks a lot.