Commit e75a54d3 authored by Stéphane Adjemian's avatar Stéphane Adjemian
Browse files

Fixed steady state in rbcii.mod (steady state levels in the unconstrained regime were wrong).

parent a219a4b9
......@@ -60,38 +60,14 @@ model;
end;
steady_state_model;
efficiency = 0;
Efficiency = effstar*exp(efficiency-mean_preserving_spread(rho,sigma2));
// Compute steady state ratios.
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
// Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
/// Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption = Consumption_per_unit_of_Labour*Labour;
Capital = Labour/Labour_per_unit_of_Capital;
Output = Output_per_unit_of_Capital*Capital;
Investment = delta*Capital;
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital)^(1-psi))+1-delta);
Output1 = Output;
Output2 = Output;
Labour1 = Labour;
Labour2 = Labour;
Consumption1 = Consumption;
Consumption2 = Consumption;
end;
// Write analytical steady state file (without globals)
options_.steadystate_flag = 2;
copyfile('rbcii_steady_state.m','rbcii_steadystate2.m');
@#if extended_path_version
shocks;
var EfficiencyInnovation = sigma2;
var EfficiencyInnovation = 1;
end;
steady(nocheck);
......
function [ys_, params, info] = rbcii_steadystate2(ys_, exo_, params)
% Flag initialization (equal to zero if the deterministic steady state exists)
info = 0;
% efficiency
ys_(13)=0;
% Efficiency
ys_(12)=params(8);
% Steady state ratios
Output_per_unit_of_Capital=((1/params(1)-1+params(6))/params(4))^(1/(1-params(5)));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-params(6);
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/ys_(12))^params(5)-params(4))/(1-params(4)))^(1/params(5));
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Steady state share of capital revenues in total revenues (calibration check)
ShareOfCapital=params(4)/(params(4)+(1-params(4))*Labour_per_unit_of_Capital^params(5));
% Steady state level of labour
ys_(3)=1/(1+Consumption_per_unit_of_Labour/((1-params(4))*params(2)/(1-params(2))*Output_per_unit_of_Labour^(1-params(5))));
% Steady state level of consumption
ys_(4)=Consumption_per_unit_of_Labour*ys_(3);
% Steady state level of physical capital stock
ys_(1)=ys_(3)/Labour_per_unit_of_Capital;
% Steady state level of output
ys_(2)=Output_per_unit_of_Capital*ys_(1);
% Steady state level of investment
ys_(5)=params(6)*ys_(1);
% Steady state level of the expected term appearing in the Euler equation
ys_(14)=params(1)*(ys_(4)^params(2)*(1-ys_(3))^(1-params(2)))^(1-params(3))/ys_(4)*(1+params(4)*(ys_(2)/ys_(1))^(1-params(5))-params(6));
% Steady state level of output in the unconstrained regime (positive investment)
ys_(6)=ys_(2);
% Steady state level of labour in the unconstrained regime
ys_(7)=ys_(3);
% Steady state level of consumption in the unconstrained regime
ys_(8)=ys_(4);
% Steady state level of labour in the constrained regime (noinvestment)
[lss,info] = l_solver(ys_(3),params(4),params(5),params(2),params(8),ys_(1),100);
if info, return, end
ys_(10) = lss;
% Steady state level of consumption in the constrained regime
ys_(11)=params(8)*(params(4)*ys_(1)^params(5)+(1-params(4))*ys_(10)^params(5))^(1/params(5));
% Steady state level of output in the constrained regime
ys_(9)=ys_(11);
end
function r = p0(labour,alpha,psi,theta,effstar,kstar)
r = labour * ( alpha*kstar^psi/labour^psi + 1-alpha + theta*(1-alpha)/(1-theta)/effstar^psi ) - theta*(1-alpha)/(1-theta)/effstar^psi;
end
function d = p1(labour,alpha,psi,theta,effstar,kstar)
d = alpha*(1-psi)*kstar^psi/labour^psi + 1-alpha + theta*(1-alpha)/(1-alpha)/effstar^psi;
end
function [labour,info] = l_solver(labour,alpha,psi,theta,effstar,kstar,maxiter)
iteration = 1; info = 0;
r = p0(labour,alpha,psi,theta,effstar,kstar);
condition = abs(r);
while condition
if iteration==maxiter
info = 1;
break
end
d = p1(labour,alpha,psi,theta,effstar,kstar);
labour = labour - r/d;
r = p0(labour,alpha,psi,theta,effstar,kstar);
condition = abs(r)>1e-9;
iteration = iteration + 1;
end
end
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