106 lines
2.9 KiB
Modula-2
106 lines
2.9 KiB
Modula-2
close all
|
|
|
|
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 = 1.0;
|
|
PopulationGrowth_ss = 1.0;
|
|
|
|
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;
|
|
|
|
|
|
shocks;
|
|
var e_x = 0.005;
|
|
var e_n = 0.001;
|
|
end;
|
|
|
|
/*
|
|
** FIRST APPROACH (PASS A DSERIES OBJECT FOR THE INITIAL CONDITION)
|
|
*/
|
|
|
|
// Define a dseries object.
|
|
ds = dseries(repmat([1, .5, 1, .5, 0, 1], 10, 1), 1990Q1, M_.endo_names, M_.endo_names_tex);
|
|
|
|
// Alternatively we could build this object with a stochastic simulation of the model.
|
|
//oo_ = simul_backward_model(rand(6,1), 10, options_, M_, oo_);
|
|
|
|
// Set the initial condition for the IRFs using observation 1991Q1 in ds.
|
|
set_historical_values ds 1991Q1;
|
|
|
|
// Define the shocks for which we want to compute the IRFs
|
|
listofshocks = {'e_x', 'e_n'};
|
|
|
|
// Define the variables for which we want to compute the IRFs
|
|
listofvariables = {'Efficiency', 'Population', 'Output'};
|
|
|
|
// Compute the IRFs
|
|
irfs = backward_model_irf(1991Q1, listofshocks, listofvariables, 50); // 10 is the number of periods (default value is 40).
|
|
|
|
// Plot an IRF (shock on technology)
|
|
figure(1)
|
|
plot(irfs.e_x.Output)
|
|
legend('Output')
|
|
title('IRF (shock on the growth rate of efficiency)')
|
|
|
|
/*
|
|
** SECOND APPROACH (USE THE HISTVAL BLOCK FOR SETTING THE INITIAL CONDITION)
|
|
**
|
|
** In this case the first argument of the backward_model_irf routine is a date object (for specifying
|
|
** the period of the initial condition).
|
|
*/
|
|
|
|
histval;
|
|
Efficiency(0) = 1;
|
|
EfficiencyGrowth(0) = .5;
|
|
Population(0) = 1;
|
|
PopulationGrowth(0) = .5;
|
|
PhysicalCapitalStock(0) = 1;
|
|
end;
|
|
|
|
// Define the shocks for which we want to compute the IRFs
|
|
listofshocks = {'e_x', 'e_n'};
|
|
|
|
// Define the variables for which we want to compute the IRFs
|
|
listofvariables = {'Efficiency', 'Population', 'Output'};
|
|
|
|
// Compute the IRFs
|
|
irfs = backward_model_irf(1991Q1, listofshocks, listofvariables, 50); // 10 is the number of periods (default value is 40).
|
|
|
|
// Plot an IRF (shock on technology)
|
|
figure(2)
|
|
plot(irfs.e_x.Output)
|
|
legend('Output')
|
|
title('IRF (shock on the growth rate of efficiency)')
|
|
|
|
/* REMARK
|
|
** ------
|
|
**
|
|
** This model is nonlinear and non stationary. For different initial conditions the IRFs may look quite different.
|
|
*/ |