91 lines
3.2 KiB
Matlab
91 lines
3.2 KiB
Matlab
function [ys_, params, info] = rbcii_steadystate(ys_, exo_, M_, options_)
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params = M_.params;
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% Flag initialization (equal to zero if the deterministic steady state exists)
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info = 0;
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% efficiency
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ys_(13)=0;
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% Efficiency
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ys_(12)=params(8);
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% Steady state ratios
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Output_per_unit_of_Capital=((1/params(1)-1+params(6))/params(4))^(1/(1-params(5)));
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Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-params(6);
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Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/ys_(12))^params(5)-params(4))/(1-params(4)))^(1/params(5));
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Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
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Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
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% Steady state share of capital revenues in total revenues (calibration check)
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ShareOfCapital=params(4)/(params(4)+(1-params(4))*Labour_per_unit_of_Capital^params(5));
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% Steady state level of labour
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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))));
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% Steady state level of consumption
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ys_(4)=Consumption_per_unit_of_Labour*ys_(3);
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% Steady state level of physical capital stock
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ys_(1)=ys_(3)/Labour_per_unit_of_Capital;
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% Steady state level of output
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ys_(2)=Output_per_unit_of_Capital*ys_(1);
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% Steady state level of investment
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ys_(5)=params(6)*ys_(1);
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% Steady state level of the expected term appearing in the Euler equation
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ys_(14)=(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));
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% Steady state level of output in the unconstrained regime (positive investment)
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ys_(6)=ys_(2);
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% Steady state level of labour in the unconstrained regime
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ys_(7)=ys_(3);
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% Steady state level of consumption in the unconstrained regime
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ys_(8)=ys_(4);
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% Steady state level of labour in the constrained regime (noinvestment)
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[lss,info] = l_solver(ys_(3),params(4),params(5),params(2),params(8),ys_(1),100);
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if info, return, end
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ys_(10) = lss;
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% Steady state level of consumption in the constrained regime
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ys_(11)=params(8)*(params(4)*ys_(1)^params(5)+(1-params(4))*ys_(10)^params(5))^(1/params(5));
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% Steady state level of output in the constrained regime
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ys_(9)=ys_(11);
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end
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function r = p0(labour,alpha,psi,theta,effstar,kstar)
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r = labour * ( alpha*kstar^psi/labour^psi + 1-alpha + theta*(1-alpha)/(1-theta)/effstar^psi ) - theta*(1-alpha)/(1-theta)/effstar^psi;
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end
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function d = p1(labour,alpha,psi,theta,effstar,kstar)
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d = alpha*(1-psi)*kstar^psi/labour^psi + 1-alpha + theta*(1-alpha)/(1-alpha)/effstar^psi;
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end
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function [labour,info] = l_solver(labour,alpha,psi,theta,effstar,kstar,maxiter)
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iteration = 1; info = 0;
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r = p0(labour,alpha,psi,theta,effstar,kstar);
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condition = abs(r);
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while condition
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if iteration==maxiter
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info = 1;
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break
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end
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d = p1(labour,alpha,psi,theta,effstar,kstar);
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labour = labour - r/d;
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r = p0(labour,alpha,psi,theta,effstar,kstar);
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condition = abs(r)>1e-9;
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iteration = iteration + 1;
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end
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end
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