# How to simulate deterministic growth model

**URL:** <https://forum.dynare.org/t/how-to-simulate-deterministic-growth-model/21547>\
**Category:** Perfect foresight simulations\
**Created:** [28 November 2022 18:43 UTC](https://forum.dynare.org/t/how-to-simulate-deterministic-growth-model/21547 "2022-11-28T18:43:03Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![bkaplowitz](https://forum.dynare.org/letter_avatar_proxy/v4/letter/b/da6949/32.png) [@bkaplowitz](https://forum.dynare.org/u/bkaplowitz)\
**Post date:** [28 November 2022 18:43 UTC](https://forum.dynare.org/t/how-to-simulate-deterministic-growth-model/21547/1 "2022-11-28T18:43:03Z")

</div>

Hi, I am trying to simulate a Ramsey-Kass-Koopmans model that has deterministic growth and plot process of convergence to steady state. I can compute the de-trended steady state easily, however plotting the actual convergence I haven’t yet figured out. My code currently reads:

```auto
%%file Dynare_model\NGM\NGM_approx.mod
@#define periods=100

parameters beta delta gamma alpha g;

periods = @{periods};
varexo Z;
%trend_var(growth_factor=1+g) Z;
% Equation is: k'=A^(1-alpha) k^alpha -c +(1-delta-g)k
% if we normalize, divide by A:
%var(deflator=Z) k;
%var(deflator=Z) c;
var k;
var c;

beta = 0.98;
delta = 0.01;
alpha = 0.3;
gamma = 2.0;
g=0.05;

model;
(c)^(1-gamma)/c = beta*((c(+1))^(1-gamma)/c(+1))*(1+alpha*Z(-1)^(1-alpha)*k(-1)^(alpha)/k(-1)-delta-g);
k = Z(-1)^(1-alpha)*k(-1)^alpha - c + (1-delta-g)*k(-1);
end;

initval;
k = 0.7;
c = 1.0;
end;

shock_vals_Z = cumprod((1+g)*ones(@{periods},1));
shocks;
    var Z;
    periods 1:@{periods};
    values (shock_vals_Z);
end;

endval;
    Z = 1*(1+g)^(@{periods}+1);
    k =Z*(1+g)*(delta+g)^(1/alpha-1);
end;

steady(solve_algo=1);

stoch_simul(periods=@{periods});
%perfect_foresight_setup(periods=@{periods});

%perfect_foresight_solver;
rplot k c;

```

any suggestions?

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<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [28 November 2022 21:12 UTC](https://forum.dynare.org/t/how-to-simulate-deterministic-growth-model/21547/2 "2022-11-28T21:12:05Z")

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You cannot call `steady` to compute a steady state in a trending model.

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<div class="post-metadata">

**Author:** ![bkaplowitz](https://forum.dynare.org/letter_avatar_proxy/v4/letter/b/da6949/32.png) [@bkaplowitz](https://forum.dynare.org/u/bkaplowitz)\
**Post date:** [29 November 2022 15:51 UTC](https://forum.dynare.org/t/how-to-simulate-deterministic-growth-model/21547/3 "2022-11-29T15:51:49Z")

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Thanks so much for the reply.

Then how do I compute the detrended model and plot convergence to the detrended steady state? If you look at the commented-out section I tried to do exactly this with a trend\_var and the perfect\_foresight\_solver. This does not actually let me track convergence though. Do I need to manually detrend? I’ve tried this too, with no luck.

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<div class="post-metadata">

**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [6 December 2022 15:38 UTC](https://forum.dynare.org/t/how-to-simulate-deterministic-growth-model/21547/4 "2022-12-06T15:38:29Z")

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One approach is at [DSGE\_mod/Ramsey\_Cass\_Koopmans at master · JohannesPfeifer/DSGE\_mod · GitHub](https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Ramsey_Cass_Koopmans)