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docs: v_t defined as function of v_t ? #235
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yes, it is a general updating equation. It is there to
accommodate nonseparable value function like epstein-zin formulation.
It is also defined as such in the recipes file
https://github.com/EconForge/dolo.py/blob/master/dolo/compiler/recipes.yaml
For the "reward" there is an additional `felicity` function which is purely
intratemporal.
In any case, this could use some dust cleaning, or some name
renormalization: the VFI algorithm was never very advanced in dolo
…On Wed, Apr 5, 2023 at 4:37 PM Sebastian Benthall ***@***.***> wrote:
In the documentation of the (non-separable) value function, the signature
is given as:
$v_t = w(s_t,x_t,v_t,s_{t+1},x_{t+1},v_{t+1}$
Note that $v_t$ is repeated on both sides of the equation.
Is that intentional?
See:
https://github.com/EconForge/dolo.py/blob/master/docs/model_specification.md#value
https://dolo.readthedocs.io/en/latest/model_specification.html#value
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I'm sorry if this is a dense question, but isn't |
Actually the way I did Epstein-Zin a while ago was by iterating on two variables: V_t <- U(c_t) + \beta (V_{t+1}/EV_t^{1/alpha})^{-\gamma} In equilibrium, EV_t is of course the same on the left and on the right. I admit it is a little bit of a corner case .... In other applications, I used arbitrage equations for the same purpose (treating left and right hand side in the same way) but that is also not super satisfying. |
Oh, I see. So with some solution algorithms, you might run this to convergence to solve for a single period, before incrementing So there's two update/convergence loops? Is the solution algorithm for this in the repository? |
In the documentation of the (non-separable) value function, the signature is given as:
Note that$v_t$ is repeated on both sides of the equation.
Is that intentional?
See:
https://github.com/EconForge/dolo.py/blob/master/docs/model_specification.md#value
https://dolo.readthedocs.io/en/latest/model_specification.html#value
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