Regression within the model

Stochastic simulations
1

Dear Professor,

I am working on a DSGE model and I want to perform the following regression within the model:
E_t e_{t+s}= \zeta_s + \beta_s(r_t)+ u_t^s for s=1,...,120
where the variables e, r and u are already defined in the model. I need to see how the slope coefficient (\beta's) change with the horizon for the three different shocks in the model.

Thank you in anticipation.

Best Regards
Sahil

2

Not sure of what ‘perform regression’ means here though. But I guess you want to simulate that equation together with the other equations in the model by changing beta?

3

You mean you want to do 120 population regressions within the model?

4

Yes. In the model, instead of the equation above, I have: e_t= r_t+u_t, so I will have the simulated data for these variables and can compute the beta coefficient. However, I need to see how this coefficient changes with the horizon. For example, If I have 364 data points and take a lag of three, I do regression from period 4 to period 120 so I get beta_1, then period 5 to 121 so I get beta_2, and so on.

5

Do you want to run such a regression based on simulated data from the model? Or do you want agents in the model to solve such a regression (like a learning type exercise)?

6

Using simulated data will produce a sampling error, so I defined the lags in the model like r_t(-1), r_t(-2), r_t(-3),… and then e_t=e_t(-1), e_t=r_t(-2),… so I obtained the coefficients manually. But, now my question is if there is a better way to do this?
Thank you

7

Sorry, but I still don’t get what exactly you are doing. What do you mean with