# Regression within the model

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

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?

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

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.

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)?

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

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