107 lines
3.8 KiB
Matlab
107 lines
3.8 KiB
Matlab
function [ys,check] = NK_baseline_steadystate(ys,exo)
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% function [ys,check] = NK_baseline_steadystate(ys,exo)
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% computes the steady state for the NK_baseline.mod and uses a numerical
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% solver to do so
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% Inputs:
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% - ys [vector] vector of initial values for the steady state of
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% the endogenous variables
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% - exo [vector] vector of values for the exogenous variables
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%
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% Output:
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% - ys [vector] vector of steady state values fpr the the endogenous variables
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% - check [scalar] set to 0 if steady state computation worked and to
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% 1 of not (allows to impos restriction on parameters)
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global M_
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% read out parameters to access them with their name
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NumberOfParameters = M_.param_nbr;
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for ii = 1:NumberOfParameters
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paramname = M_.param_names{ii};
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eval([ paramname ' = M_.params(' int2str(ii) ');']);
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end
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% initialize indicator
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check = 0;
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%% Enter model equations here
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options=optimset(); % set options for numerical solver
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% the steady state computation follows FV (2006), section 4.1
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PI=PIbar;
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u=1;
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q=1;
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d=1;
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phi=1;
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m=0;
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zeta=1;
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LambdaYd= (LambdaA+alppha*Lambdamu)/(1-alppha);
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mu_z=exp(LambdaYd);
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mu_I=exp(Lambdamu);
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mu_A=exp(LambdaA);
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%set the parameter Lambdax
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Lambdax=mu_z;
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%set the parameter gammma1
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gammma1=mu_z*mu_I/betta-(1-delta);
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if gammma1<0 % parameter violates restriction; Preventing this cannot be implemented via prior restriction as it is a composite of different parameters and the valid prior region has unknown form
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check=1; %set failure indicator
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return; %return without updating steady states
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end
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r=1*gammma1;
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R=1+(PI*mu_z/betta-1);
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%set Rbar
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Rbar=R;
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PIstar=((1-thetap*PI^(-(1-epsilon)*(1-chi)))/(1-thetap))^(1/(1-epsilon));
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PIstarw=((1-thetaw*PI^(-(1-chiw)*(1-eta))*mu_z^(-(1-eta)))/(1-thetaw))^(1/(1-eta));
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mc=(epsilon-1)/epsilon*(1-betta*thetap*PI^((1-chi)*epsilon))/(1-betta*thetap*PI^(-(1-epsilon)*(1-chi)))*PIstar;
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w=(1-alppha)*(mc*(alppha/r)^alppha)^(1/(1-alppha));
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wstar=w*PIstarw;
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vp=(1-thetap)/(1-thetap*PI^((1-chi)*epsilon))*PIstar^(-epsilon);
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vw=(1-thetaw)/(1-thetaw*PI^((1-chiw)*eta)*mu_z^eta)*PIstarw^(-eta);
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tempvaromega=alppha/(1-alppha)*w/r*mu_z*mu_I;
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[ld,fval,exitflag]=fzero(@(ld)(1-betta*thetaw*mu_z^(eta-1)*PI^(-(1-chiw)*(1-eta)))/(1-betta*thetaw*mu_z^(eta*(1+gammma))*PI^(eta*(1-chiw)*(1+gammma)))...
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-(eta-1)/eta*wstar/(varpsi*PIstarw^(-eta*gammma)*ld^gammma)*((1-h*mu_z^(-1))^(-1)-betta*h*(mu_z-h)^(-1))*...
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((mu_A*mu_z^(-1)*vp^(-1)*tempvaromega^alppha-tempvaromega*(1-(1-delta)*(mu_z*mu_I)^(-1)))*ld-vp^(-1)*Phi)^(-1),0.25,options);
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if exitflag <1
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%indicate the SS computation was not sucessful; this would also be detected by Dynare
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%setting the indicator here shows how to use this functionality to
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%filter out parameter draws
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check=1; %set failure indicator
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return; %return without updating steady states
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end
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l=vw*ld;
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k=tempvaromega*ld;
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x=(1-(1-delta)*(mu_z*mu_I)^(-1))*k;
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yd=(mu_A/mu_z*k^alppha*ld^(1-alppha)-Phi)/vp;
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c=(mu_A*mu_z^(-1)*vp^(-1)*tempvaromega^alppha-tempvaromega*(1-(1-delta)*(mu_z*mu_I)^(-1)))*ld-vp^(-1)*Phi;
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lambda=(1-h*betta*mu_z^(-1))*(1-h/mu_z)^(-1)/c;
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F=yd-1/(1-alppha)*w*ld;
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f=(eta-1)/eta*wstar*PIstarw^(-eta)*lambda*ld/(1-betta*thetaw*mu_z^(eta-1)*PI^(-(1-chiw)*(1-eta)));
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f2=varpsi*d*phi*PIstarw^(-eta*(1+gammma))*ld^(1+gammma)/(1-betta*thetaw*(PI^chiw/PI)^(-eta*(1+gammma))*(wstar/wstar*mu_z)^(eta*(1+gammma)));
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g1=lambda*mc*yd/(1-betta*thetap*PI^((1-chi)*epsilon));
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g2=epsilon/(epsilon-1)*g1;
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%% end own model equations
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for iter = 1:length(M_.params) %update parameters set in the file
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eval([ 'M_.params(' num2str(iter) ') = ' M_.param_names{iter} ';' ])
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end
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NumberOfEndogenousVariables = M_.orig_endo_nbr; %auxiliary variables are set automatically
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for ii = 1:NumberOfEndogenousVariables
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varname = M_.endo_names{ii};
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eval(['ys(' int2str(ii) ') = ' varname ';']);
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end
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