Added integration test...

For nonlinear simul_backward_model. Use a Solow model with varying
growth rates of efficiency and population.

tests/Makefile.am

@@ -240,6 +240,7 @@ MODFILES = \
 	ep/linearmodel1.mod \
 	stochastic-backward-models/solow_cd.mod \
 	stochastic-backward-models/solow_ces.mod \
+	stochastic-backward-models/solow_cd_with_steadystate.mod \
 	stochastic-backward-models/backward_linear.mod \
 	deterministic_simulations/purely_forward/ar1.mod \
         deterministic_simulations/purely_forward/nk.mod \

tests/stochastic-backward-models/solow_cd_with_steadystate.mod

@@ -0,0 +1,67 @@
+var Efficiency $A$
+    EfficiencyGrowth $X$
+    Population $L$
+    PopulationGrowth $N$
+    Output $Y$
+    PhysicalCapitalStock $K$ ;
+
+varexo e_x $\varepsilon_x$
+       e_n $\varepsilon_n$;
+
+parameters alpha $\alpha$
+	   delta $\delta$
+	   s $s$
+           rho_x $\rho_x$
+           rho_n $\rho_n$
+           EfficiencyGrowth_ss $X^{\star}$
+           PopulationGrowth_ss $N^{\star}$ ;
+
+alpha = .33;
+delta = .02;
+s     = .20;
+rho_x = .90;
+rho_n = .95;
+EfficiencyGrowth_ss = 1.00; // Do not change this calibration
+PopulationGrowth_ss = 1.00; // Do not change this calibration
+
+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 = PhysicalCapitalStock(-1)^alpha*(Efficiency*Population)^(1-alpha);
+    PhysicalCapitalStock = (1-delta)*PhysicalCapitalStock(-1) + s*Output;
+end;
+
+histval;
+    Efficiency(0) = .5;
+    EfficiencyGrowth(0) = 1.02;
+    Population(0) = 1;
+    PopulationGrowth(0) = 1.02;
+    PhysicalCapitalStock(0) = 1;
+end;
+
+LongRunEfficiency = M_.endo_histval(1)*M_.endo_histval(2)^(rho_x/(1-rho_x));
+LongRunPopulation = M_.endo_histval(3)*M_.endo_histval(4)^(rho_n/(1-rho_n));
+LongRunEfficiencyGrowth = EfficiencyGrowth_ss; 
+LongRunPopulationGrowth = PopulationGrowth_ss;
+LongRunIntensiveCapitalStock = LongRunEfficiencyGrowth*LongRunPopulationGrowth*(s/(LongRunEfficiencyGrowth*LongRunPopulationGrowth-1+delta))^(1/(1-alpha));
+
+precision = 1e-6;
+T = 5*floor(log(precision)/log(max(rho_x, rho_n)));
+
+oo_ = simul_backward_model(M_.endo_histval, T, options_, M_, oo_, zeros(T+1,2));
+
+if abs(oo_.endo_simul(1,end)-LongRunEfficiency)>1e-10
+    error('Wrong long run level!')
+end
+
+if abs(oo_.endo_simul(3,end)-LongRunPopulation)>1e-10
+    error('Wrong long run level!')
+end
+
+IntensiveCapitalStock = oo_.endo_simul(6,1:end)./(oo_.endo_simul(1,1:end).*oo_.endo_simul(3,1:end));
+
+if abs(IntensiveCapitalStock-LongRunIntensiveCapitalStock)>1e-6
+    error('Wrong long run level!')
+end