Growth rates changing through time

Perfect foresight simulations
1

Good evening,

I want to simulate a model with labor-augmenting (A_L) and demographic growth (A_N). The growth rate of each can change through time (see it as shocks). I am aware of https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_growth_rate_changes.mod . But this file does not consider growth rate as changing through time. That file does: https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_growth_rate_changes.mod . But The model is stationary.

Can I somewhat combine the two structures, i.e. non-stationarity and changing rates? Or should I put everything in per efficient unit of labor and reproduce https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_growth_rate_changes.mod ?

If I stay in a non-stationary form, the labor-augmenting technology and labour would be declared as endogenous variables, growth rates as exogenous variables, and initial growth rates as parameters (?). I would also specify the equation for the labor-augmenting technology and “labor” in model-block, being:

  • A_L=1*(1+g_l)*(@{simulation_periods})
  • A_N=1*(1+g_n)*(@{simulation_periods})

And putting in the intival block:
g_n=g_n_init;
g_l=g_l_init;
A_L=1*(1+g_l)^0; %A_L_0
A_N=1*(1+g_n)^0; %A_N_0

Finally, specifying jumps in the rates in the shock-block.

Am I right ?

Furthermore, what is shock_vals_L=cumprod((1+g_n)*ones(@{simulation_periods},1)) in your file https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Solow_model/Solow_nonstationary.mod ?

Thank you.

Best

2

In the end, you will have a standard problem. You need to define an initial and terminal steady state using initval and endval-blocks and fill in the period growth rates as shocks.
shock_vals_A=cumprod((1+g)*ones(@{simulation_periods},1))
does just that. Starting from the first period. It defines A_t growing exponentially as A_t=A_0(1+g_A)^t

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3

That’s clear enough.

Would you recommend to write down the model in intensive or extensive form in Dynare? (for simplicity and computational purposes let’s say).

Thanks.

Best

4

In your case, I would probably go for the extensive form version. That seems to be less complicated.

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