# Solow with endogenous growth

I’m currently working on a Solow model variation with endogenous growth, developed by Romer P., Grossman, Helpman and others, as specified in the book “Advanced Macroeconomics, Fourth Edition” by Romer, D. (p. 101). Which specifies technology as endogenous variables with its own production sector. And this technology is labor augmenting. And there’s population exogenous growth.

The question is, as this model is non-stationary, and there’s no way to de-trend the model (as in regular Solow with population and technology exogenous growth), is it possible to simulate the model with Dynare tools, or is there a way to represent the model in a de-tended way maybe. I just want the model the be able (if possible) to run, no matter if have to make some algebra or ratio variables, or know even if it’s not possible.

K_{t+1}=s[(1-a_K)K_t]^\alpha[(1-a_L)A_tL_t]^{1-\alpha}+(1-\delta)K_t
A_{t+1}=B[a_KK_t]^\beta[a_LL_t]^\gamma A_t^\theta+A_t

0<a_K,a_L<1 \;\;\;\;B>0 \;\;\;\; \beta,\gamma>0\;\;\;\;\theta\ne0

Let me know if you want some specifics of the model equations or something.

Some idea I got was to assume \theta=1\;\;\;\beta=\gamma=0 (hard assumption this last one), and de-trend capital converting it to effective form, and I can even get a closed form for the steady-state for \hat{k_t}, but still having the problem with A_t. (If you could advice me a better way to solve this, if possible withouth the assumption on \gamma and \beta would be better.)

Thank you!

Yes, that should be possible as the model features constant long-run growth. You should be able to detrend the respective variables with their respective long-run growth rates.

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