dynare/tests/stochastic-backward-models/solow_ces.mod

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Modula-2
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var Efficiency $A$
EfficiencyGrowth $X$
Population $L$
PopulationGrowth $N$
Output $Y$
PhysicalCapitalStock $K$ ;
varexo e_x $\varepsilon_x$
e_n $\varepsilon_n$;
parameters alpha $\alpha$
epsilon $\varepsilon$
delta $\delta$
s $s$
rho_x $\rho_x$
rho_n $\rho_n$
EfficiencyGrowth_ss $X^{\star}$
PopulationGrowth_ss $N^{\star}$ ;
alpha = .33;
epsilon = .70;
delta = .02;
s = .20;
rho_x = .90;
rho_n = .95;
EfficiencyGrowth_ss = 1.02;
PopulationGrowth_ss = 1.02;
model;
Efficiency = EfficiencyGrowth*Efficiency(-1);
EfficiencyGrowth/EfficiencyGrowth_ss = (EfficiencyGrowth(-1)/EfficiencyGrowth_ss)^(rho_x)*exp(e_x);
Population = PopulationGrowth*Population(-1);
PopulationGrowth/PopulationGrowth_ss = (PopulationGrowth(-1)/PopulationGrowth_ss)^(rho_n)*exp(e_n);
Output = (alpha*PhysicalCapitalStock(-1)^((epsilon-1)/epsilon)+(1-alpha)*(Efficiency*Population)^((epsilon-1)/epsilon))^(epsilon/(epsilon-1));
PhysicalCapitalStock = (1-delta)*PhysicalCapitalStock(-1) + s*Output;
end;
histval;
Efficiency(0) = 1;
EfficiencyGrowth(0) = 1.02;
Population(0) = 1;
PopulationGrowth(0) = 1.02;
PhysicalCapitalStock(0) = 1;
end;
shocks;
var e_x = 0.005;
var e_n = 0.001;
end;
oo_ = simul_backward_nonlinear_model([], 5000, options_, M_, oo_);