Hello, I have a conceptual question regarding the pure random walk shock and the de-trending process in a model.

Specifically, I am trying to replicate the model of Eric Swanson in this paper, which features recursive preferences and a pure random walk for productivity.

When I de-trend all variables by A_t (and value function by log(A_t)), the de-trended variables only include the next period’s shock (eps_A(+1)), but not eps_A.

Since Dynare only allows for shocks to occur in the current period, these shocks appear to have no effect on the economy after de-trending.

On the other hand, if I do not de-trend the variables and put them into Dynare and perform Stoch_simul, the shock to eps_A does seem to have an effect on the model. However, this is very puzzling to me since eps_A do not appear in the de-trended equations.

Am I missing something in the de-trending process, or is there another way to properly handle these shocks in the model? Can this be due to multiple equilibrium?

Thank you in advance for your help!

- Attached, the Detrended.mod gives the one de-trended by hand; the nondetrended one gives the non-linear equations as in the paper WITHOUT detrending. Again, I believe they should yield the same results, but in the former one the detrended variable does not move; on the latter, it moves.

EZ_Detrended.mod (2.5 KB)

EZ_Notdetrended.mod (2.5 KB)