 # Equity Premium in a DSGE Model

Dear all,

Several papers try to replicate the equity premium from asset market data within DSGE models.
Some authors introduce habit persistence preferences as well as adjustment costs (of investment or capital).

Where can I exactly observe this equity premium in a DSGE model? Directly after a production shock?

In the non-stochastic steady-state there is no risk. Adjustment cost do not exist and the ratio of the
Lagrange multipliers from budget constraint and capital accumulation process is unity. Therefore, I have no
variation in capital accumulation process and in conclusion no premium?

Many thanks in advance!

You need to use a second order approximation. You might be interested in https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Jermann_1998

Many thanks! That’s very helpful for me

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

I did not give this file too much thought. For consistency, you should simply request theoretical moments at `order=2`. That should give almost exactly the same as the simulated moments. The reason I did the simulation part is that the original paper also used simulations. But that is generally not necessary.

Ok I see. Thank you!