Risk Premium in Epstein-Zin Models

[hamedgh]

Hi, I am using Dynare++ (with orders 4-6) to solve asset pricing models, with recursive preferences. I know the history of discussions about the (in)accuracy of perturbation methods for risk premium in this class of models and this makes me worry that the results might be off. Does anyone here has the experience of working with EZ models (higher orders, in ++) and getting reasonable risk premium results?

[JerseyBoy1910]

Were you referring to asset prices in a production economy or a consumption based model? How were you able to resolve these issues?

I am computing a production-based asset pricing model in Dynare (up to order 3) and am running into some difficulties getting the asset prices correct. The macro moments are generally right though. Do you know whether Dynare, in particular, does a poor job with asset prices?

[japoorva]

Hi,
I am trying to solve two country model with Epstein Zin Preferences. I was stuck about how to enter objective block in Dynare ++ ? Any guidance will be helpful.
My idea was as follows:

objective: U
beta =1;

model block:
K = U^(1-gamma);
((1-beta)*c^(1-p) + beta*(K(+1))^((1-p)/(1-gamma)))^(1/(1-p));
.
.
followed by other conditions




Any suggestion?

Thanks

[jpfeifer]

This seems to be the logical extension. Define the objective in the model-block and then let the planner target it using an identity mapping. The only problem I see is the non-separability. Usually one defines the per-period felicity function and a discount factor for the planner. Now, the concept is already the present discounted value of lifetime utility. I am not sure whether letting the planner maximize the undiscounted sum of lifetime utilities of every period is what you are trying to achieve.

[japoorva]

Thanks for the reply. That is exactly the problem. My current period utility is weighted average of utility from current consumption and utility from future utility. And the weights are beta and (1-beta) respectively. So the current felicity is computed already after discounting the future utility. Then to apply beta in "discounting block" would mean like double discounting.
Also my fear is that once I enter U in objective block, dynare would understand it as \sum[beta^t*(U_t)] which is clearly wrong.
Any comments?

Thanks

[jpfeifer]

If you can check correctness, I would try putting the planner discount to 0 and use the Epstein-Zin utility in the planner objective. That way, having
\sum_t=0^\infty [beta^t*(U_t)]=U_t
which is just lifetime utility.

[japoorva]

Thanks. That is an intelligent suggestion. I will try going that way.