Log-linearized system and riginal system leads to different results


I am analyzing a standard RBC model with a CES production function. And I analyzed the model with the original format (see fun_simulation_rbc4.mod) and log-linearized system (see fun_simulation_rbc4_log.mod). Two questions confuse me:

First, in the original format, I define sp = w/v and ls = s/u, according to the irfs of w,v,s, and u; in period zero, w increases less than v, and s increases less than u, so both sp and ls should be decreasing. However, the irfs of sp and ls increase in the zero period. And there is no such problem in the result of the log-linearized system.

Second, although the results are similar between the two estimation methods, the magnitude of the responses is slightly different. As I set exactly the same parameters, and I am pretty sure the log-linearized equations are correct, why are the results differed between the two methods?

Best wishes
fun_simulation_rbc4.mod (1.9 KB)
fun_simulation_rbc4_log.mod (2.4 KB)
RBC model 4.pdf (112.8 KB)

You are comparing the levels in the nonlinear version to the logs in the log-linearized version. You may want to append the logs as auxiliary variables. But why do you even loglinearize by hand?

Hi Johannes,

Thank you very much for your reply. I log linearized the model because I have another model with sticky prices, in which the inflation equation is log linearized around the steady state, so to keep everything consistent, I log linearized all other equations around the steady state by hand.

I may not understand it right; to my understanding, these two versions are the same; both give the deviation from the steady state due to the shock, that’s why I think these two versions should generate the same results. So, do you mean it is normal to get different results from these two versions?

And I am still unsure why in the nonlinear system, in the irfs, variables sp and ls are initially increased while they should be decreasing according to sp=w/v and ls=s/u and the responses of w,v,s, and u. It confuses me a lot. (I have included the results)

Best wishes
RBC4-Simulation results.pdf (83.0 KB)