Equity premium (asset pricing) in DSGE model

Dear all,

I’d like to know how to calculate equity premium in DSGE models.
I have the same problem that Cybueh posted before.
My understanding is as same as the following.
Could you please comment and complement my interpretation of how to calculate equity premium in DSGE models.?

https://forum.dynare.org/t/equity-premium-in-a-dsge-model/11740

I’m building my own DSGE model with equity premium considerations.

Could you please comment and complement my interpretation of the procedure used in the file?

In a first step, you simulate the calibrated (deflated) nonlinear model (1st order approximation) to observe macroeconomic variables’ behavior (growth of output, consumption, investment). In particular, the theoretical moments are of interest to evaluate the model’s ability to replicate stylized business cycle facts.
In a second step, you simulate the model for 50000 quarters (2nd order approximation) to observe financial variables (risk-free return, asset return, dividends, price of capital stock). This is necessary because we don’t have risk (and therefore no equity premium) in steady-state. We need simulations to find the unconditional mean. For these variables theoretical moments do not exist, that’s why we have to take the moments of simulated variables.
Why don’t you, for example, use a 3rd order approximation?

Thank you in advance!

I mean if Equity premium in the steady state equals to zero,
How do you calculate it ?
Huh_and_Kim_July_16_2018.pdf (370.0 KB)

page 22 they report the equity premium on table 2.
How shoud I repliciate? Isn’t it steady state, is it?

thank you

Why do theoretical moments not exist for those variables?

Hi budoka

Some important things:

  • The steady-state is deterministic by definition. There is no risk in steady-state.
  • When you do a first-order approximation, certainty equivalence holds (e.g. in the model output you can see that the return on the risky asset is the same as the risk-free bond return, irrespectively if you do a first-order approximation of theoretical or simulated variables). When certainty equivalence holds, the individual does not care about risk.
  • The simulation has nothing to do with the equity premium itself, it’s just to produce an unconditional mean of the equity premium. Therefore, key is the second-order approximation. You need a second-order approximation to incorporate the curvature of preferences.
  • To produce a substantial equity premium, several model modifications are necessary to increase the curvature of preferences (habits for example: the individual cares much more about consumption volatility. We would like to amplify risk aversion). As soon as you do a second-order approximation, you’ll see in the model output that the risky asset differs from the risk-free asset.

:four_leaf_clover:

@Cybueh That is all correct, but @budoka stated that a second order approximation was used. The big question is why the following happens:

@budoka, @jpfeifer For me it’s not possible to figure out why theoretical moments do not exist when using a second order approximation of a nonlinear model.

Check:

Nonlinearity of the model?
Interpretation of adjustment cost parameter?
Return on equity or return on capital? -> Are zero dividend payments the issue?
(Log-)Return formula?

@budoka We would need to see the codes. The only reason for moments to not exist is a unit root.