steady state from fsolve to calculate parameters in dynare

[nk178]

Dear all,

I use fsolve to calculate the steady-state values of my model. I want to "transfer" these values to my dynare .mod file directly. However, my model is log-linearised by hand, so I know that the ss values (initvals) in the .mod file are all zero. The reason I need the steady-state values from my fsolve .m file to be delivered directly to the .mod file is to calculate some structural parameters of the model and also to make some loops for some parameters that I want to compare.

Please do not confuse this with the standard problem of using the fsolve m. file to calculate the steady state values of the .mod file.

Best regards,

Nick

[jpfeifer]

Use a dedicated steady state file. Within that file you can call any Matlab function and set any parameter you need. An example is the NK_baseline.mod in the Dynare examples folder.

[nk178]

Great,

I will have a look on the example. Thank you a lot once again jpfeifer.

Best,

[nk178]

Dear jpfeifer,

I have some problems to do that. I have created a dedicated _steadystate.m file in which I successfully used the fsolve to calculate some particular steady-state values. The problem still remains. These steady-state values are just parameters to my .mod file model as I have log-linearised by hand (that is in the .mod file I still have to write down initvals which are all zero of course). However, when I run my .mod file model, it seems that it does not load the calculated values from the _steadystate.m file. Can you please tell me how I can do that? (which function I have to write and to which file .m or .mod, please).

Thank you very much in advance. I am really sorry for this inconvenience.

Best,

[nk178]

I found it. I used the save my_parameters.mat parm1 parm2 (matlab) and then load my_parameters.mat (dynare). If it is useful to anyone, please follow the link

viewtopic.php?f=1&t=327

Best,

nk

[nk178]

Use a dedicated steady state file. Within that file you can call any Matlab function and set any parameter you need. An example is the NK_baseline.mod in the Dynare examples folder.

Dear jpfeifer,

As I said to my latest post, I managed to load the parameter values from matlab to dynare. However now I face another problem. In the mod-file, I use the initvals; to set the steady state (that is as all variables are zero as the model is log-linearised by hand). When, I run dynare, while the parameter values are loaded correctly from the m-file, (I check this on the right hand side of the screen), I get the following message:

Error using print_info (line 80)
The steady state contains NaN or Inf
Error in resid (line 112)
print_info(info,options_.noprint, options_)
Error in NK_f3f (line 483)
resid(1);
Error in dynare (line 180)
evalin('base',fname) ;

I run the model diagnostics and it says that model diagnostic can't obtain the steady state!

However, I created another mod-file in which I set the parameter values manually (copied from the m-file) and the model runs!!
Any indication on where the problem is ?

I copy the mod-file and then the dedicated steady-state file, thank you very much in advance.

mod-file:

%variables
var
y %output tilde, where tilde is the gap from the natural rate
k %capital tilde
psi %quality of capital
r %real interest rate
rn %natural interest rate
Pi %inflation
a %productivity
y_f %natural level of output
k_f %natural level of capital
q %price of capital
q_f
inv %investment tilde
inv_f %natural level of investments
theta_hat %leverage ratio
nw %net worth
s_p %total securities tilde
s
v_hat
mu_hat
Omega_hat
r_k
z_hat
z_fhat
s_g
d_hat
varrho_hat
phi_ct
qnom
theta_fhat %leverage ratio
nw_f %net worth
s_fp %total securities tilde
s_f
v_fhat
mu_fhat
Omega_fhat
r_fk
s_fg
d_fhat
varrho_fhat
phi_fct
spread_t;

varexo
e_a %stochastic component of productivity
e_psi; %stochastic component of quality of capital

parameters
beta %static discount factor
alpha %capital share
varphi %Frisch inverse elasticity of labour
delta %depreciation of capital
gamma %elasticity of substitution among the differentiated goods (to match the markup)
M %markup
chi %parameter in convex adjustment cost function
Psi %steady-state of quality of capital shock
A %steady-state of productivity shock
Q %price of new-capital good (tobin's q) steady-state, calculated from capital good producers optimal decision
phi %price flexibility value of real marginal cost (inverse of mark-up)
omega %degree of nominal price rigidity, to match quarterly data
rho_a %degree of autocorrelation, productivity shock
rho_psi %degree of autocorrelation, capital quality shock
sigma %survival rate of bankers
xi %transfer to entering bankers, perfect interbank
lambda %fraction of divertable assets
theta %levarage ratio, fixed according Gerlter Kiyotaki/ Gertler Karadi
R %real interest rate steady state
Qnom %from fischer equation, steady state value of nominal interest rate determination
Omega
mu %excess value
V
R_k %steady state value of intrabanking rate
Z %steady state value of Z
yk %ratios useful to calculate the steady state of quantity variables (like RBC)
ck
N %steady state of employment
K %steady state of capital
Y %steady state of output
C %steady state of consumption
S_p %steady state of private securities
S_g
S
NW %steady state of net worth
I %steady state of investments
D %steady state of deposits
rho_q %smoothing parameter of interest rate
kappa_pi %taylor rule weight on inflation
kappa_y %taylor rule weight on output
kappa_varrho %credit policy parameter
kappa_varrhof %credit policy parameter
varrho %steady state of credit policy tool
kappa_i
kappa_k
kappa_yi
kappa_yk
delta_1
delta_2
delta_3
delta_4
delta_5
delta_6
delta_7
delta_8
delta_9
delta_10
delta_11
delta_12
delta_13
alpha_1
alpha_2
alpha_3
delta_p %elasticity of inflation wrt the real marginal cost
nwk
dk
spread;

%Parameter values

load my_parameters.mat

model (linear);

%standard equations of NK with capital
%spread
spread_t=r_k-r;

%dynamic IS with capital (deviations from natural rate)
y=y(+1)-I/Y*(inv(+1)-inv)-(r - rn);

%natural interest rate
rn=y_f(+1)-y_f- I/Y*(inv_f(+1)-inv_f);

%flexible price equilibrium
0=-(((alpha+varphi)/(1-alpha))+(Y/C))*y_f + (I/C)*inv_f + ((alpha*(1+varphi))/(1-alpha))*k_f(-1) + ((1+varphi)/(1-alpha))*a;

%NKPC with capital (deviations from natural rate)
Pi=beta*Pi(+1) + delta_p*(((Y/C)+((alpha+varphi)/(1-alpha)))*y - (I/C)*inv - ((alpha*(1+varphi))/(1-alpha))*k(-1));

%Fischer equation
r=qnom - Pi(+1);

%Interest rate rule(Taylor), characterisation of monetary policy
qnom=rho_q*qnom(-1) + (1-rho_q)*(kappa_pi*Pi + kappa_y*y + kappa_i*inv + kappa_k*k);

%law of motion of capital efficient
inv_f=(1/delta)*(k_f-(1-delta)*k_f(-1)-psi(+1));
inv=(1/delta)*k-((1-delta)/(delta))*k(-1);

%AR(1) technology shock
a=rho_a*a(-1)-e_a;

%asset price determination
q=chi*(inv-inv(-1))-beta*chi*(inv(+1)-inv);
q_f=chi*(inv_f-inv_f(-1))-beta*chi*(inv_f(+1)-inv_f);

%Demand for total bank assets
q+s=phi_ct+nw;
phi_ct=theta_hat+((varrho)/(1-varrho))*varrho_hat;

q_f + s_f=phi_fct + nw_f;
phi_fct=theta_fhat+((varrho)/(1-varrho))*varrho_fhat;

%determination of gross earnings from capital
z_hat=(Y/C+((1+varphi)/(1-alpha)))*y-(I/C)*inv-((1+(alpha*varphi))/(1-alpha))*k(-1);
z_fhat=y_f-k_f(-1);

%determination of leverage ratio net of interbank borrowing, theta_hat
theta_hat=v_hat+(mu/(lambda-mu))*mu_hat;
theta_fhat=v_fhat+(mu/(lambda-mu))*mu_fhat;

%linearity condition 1
v_hat=Omega_hat(+1);
v_fhat=Omega_fhat(+1);

%linearity condition 2
mu_hat=((Omega*beta*R_k)/mu)*r_k-(((Omega*beta*R)/mu)+1)*r+Omega_hat(+1);
mu_fhat=((Omega*beta*R_k)/mu)*r_fk-(((Omega*beta*R)/mu)+1)*r+Omega_fhat(+1);

%marginal value of net worth
Omega_hat=((sigma*V)/Omega)*v_hat+((sigma*theta*mu)/Omega)*(theta_hat+mu_hat);
Omega_fhat=((sigma*V)/Omega)*v_fhat+((sigma*theta*mu)/Omega)*(theta_fhat+mu_fhat);

%gross rate of return on bank assets
r_k = psi(+1)-q+(Z/R_k)*z_hat(+1)+((1-delta)/R_k)*q(+1);
r_fk = psi(+1)-q_f+(Z/R_k)*z_fhat(+1)+((1-delta)/R_k)*q_f(+1);

%Total securities on investing and non investing islands
s=delta*inv+(1-delta)*k(-1);
s_f=delta*inv_f+(1-delta)*k_f(-1);

%deposits
d_hat=(Q*S/D)*(q+s_p)-(NW/D)*nw;
d_fhat=(Q*S/D)*(q_f+s_fp)-(NW/D)*nw_f;

%law of motion of net worth
nw=((sigma+xi)/NW)*(Z*z_hat+(1-delta)*Q*q+(Z+(1-delta)*Q)*Psi*S*(psi+s_p(-1)))-((sigma*R*D)/NW)*(r(-1)+d_hat(-1));
nw_f=((sigma+xi)/NW)*(Z*z_fhat+(1-delta)*Q*q_f+(Z+(1-delta)*Q)*Psi*S*(psi+s_fp(-1)))-((sigma*R*D)/NW)*(rn(-1)+d_fhat(-1));

%credit policy
s_g= varrho_hat + s;
s=(S_p/S)*s_p+(S_g/S)*s_g;
varrho_hat=kappa_varrho*(r_k-r);

s_fg=varrho_fhat + s_f;
s_f=(S_p/S)*s_fp+(S_g/S)*s_fg;
varrho_fhat=kappa_varrhof*(r_fk-rn);

%AR(1) quality of capital shock
psi=rho_psi*psi(-1)-e_psi;

end;

initval;
y=0; %output tilde, where tilde is the gap from the natural rate
k=0; %capital tilde
psi=0; %quality of capital
r=0; %real interest rate
rn=0; %natural interest rate
Pi=0; %inflation
qnom=0; %nominal interest rate
a=0; %productivity
y_f=0; %natural level of output
k_f=0; %natural level of capital
q=0; %price of capital
q_f=0;
inv_f=0; %natural level of investments
inv=0;
theta_hat=0; %leverage ratio
nw=0; %net worth
s_p=0; %private securities
s=0;
v_hat=0;
mu_hat=0;
Omega_hat=0;
r_k=0;
z_hat=0;
z_fhat=0;
s_g=0;
d_hat=0;
varrho_hat=0;
spread_t=0;
phi_ct=0;
theta_fhat=0;
nw_f=0;
s_fp=0;
s_f=0;
v_fhat=0;
mu_fhat=0;
Omega_fhat=0;
r_fk=0;
s_fg=0;
d_fhat=0;
varrho_fhat=0;
phi_fct=0;
end;

resid(1);
steady;
check;

shocks;
var e_a;
stderr 0;
var e_psi;
stderr 0.05;
var e_a, e_psi= 0*0.0624*0.05;
end;

check;

stoch_simul(order=1,nomoments,periods=3000,irf=50)y Pi k inv q r_k r spread_t nw theta_hat s s_p s_g d_hat qnom;


Dedicated steady-state-m-file

function [ys,check] = NK_f3f_steadystate(ys,exo);
% function [ys,check] = NK_f3f_steadystate(ys,exo)
% computes the steady state for the NK_baseline.mod and uses a numerical
% solver to do so
% Inputs:
% - ys [vector] vector of initial values for the steady state of
% the endogenous variables
% - exo [vector] vector of values for the exogenous variables
%
% Output:
% - ys [vector] vector of steady state values fpr the the endogenous variables
% - check [scalar] set to 0 if steady state computation worked and to
% 1 of not (allows to impos restriction on parameters)

% initialize indicator
check=0;

x0 =[4; 0.003; 5; 1.025; 0.0025; 10;];
options = optimset('TolFun',1e-8,'TolX',1e-8,'MaxIter', 5000,'MaxFunEvals', 5000, 'Display','final');
[x]=fsolve(@fun_NK_f3f,x0,options);

nwk=x(1);
mu=x(2);
Omega=x(3);
R_k=x(4);
spread=x(5);

beta=0.99; %static discount factor
R=1/beta; %euler equation
sigma=0.97; %survival rate of bankers
xi=0.003; %transfer to entering bankers, perfect interbank
lambda=0.381; %fraction of divertable assets
theta=1/nwk;
mu= max(0,lambda-(Omega*nwk));


Qnom=R-1; %Fischer equation
alpha=0.33; %capital share
varphi=2; %Frisch inverse elasticity of labour
delta=0.025; %depreciation of capital
gamma=6; %elasticity of substitution among the differentiated goods (to match the markup)
M=gamma/(gamma-1); %markup

omega=0.75; %degree of nominal price rigidity, to match quarterly data
delta_p=((1-omega*beta)*(1-omega)/(omega)); %elasticity of inflation wrt the real marginal cost

%steady-state values
chi=1; %parameter in convex adjustment cost function
Psi=1; %steady-state of quality of capital shock
A=1; %steady-state of productivity shock
Q=1; %price of new-capital good (tobin's q) steady-state, calculated from capital good producers optimal decision
phi=1/M; %price flexibility value of real marginal cost (inverse of mark-up)

V=Omega;
Z=(R_k - (1-delta))*Q;
yk=(1/(alpha*phi))*Z;
ck=yk - delta;
N=(phi*(1-alpha)*yk*(ck)^(-1))^(1/(1+varphi));
K=N*(yk)^((-1/(1-alpha)));
I=delta*K;
C=ck*K;
Y=yk*K;
spread=R_k-R;
S=K;
NW=nwk*K;
dk=1-nwk;
D=dk*K;

kappa_pi=1.5;
kappa_y=0.5/4;
kappa_i=0;
kappa_k=0;
kappa_yi=0;
kappa_yk=0;
kappa_varrho=50;
kappa_varrhof=0;

rho_a=0.95;
rho_psi=0.75;
rho_q=0.2;
varrho=0.1;

S_p=(1-varrho)*S;
S_g=S-S_p;

delta_1 = (gamma/2)*(delta_p/(1-delta_p));
delta_2 = (1/2)*(Y/C)*(((alpha+varphi)/(1-alpha)));
delta_3 = (1/2)*(I*Y)/(C^2);
delta_4 = (1/2)*((1+varphi)/(1-alpha))*(alpha^2)*(Y/C);
delta_5 = (alpha*Y/C)*((1+varphi)/(1-alpha));
delta_6 = ((I*Y)/(C^2));
delta_7=delta_5*(1/(1-delta));
delta_8=delta_5*(delta/(1-delta));
delta_9=delta_6*(alpha/(1-delta));
delta_10=delta_6*((alpha*delta)/(1-delta));
delta_11=delta_4*(1/((1-delta)^2));
delta_12=2*delta_4*((delta/((1-delta)^2)));
delta_13=delta_4*(((delta^2)/((1-delta)^2)));
alpha_1=delta_3+delta_13;
alpha_2=delta_8-delta_6;
alpha_3=delta_6+delta_10;

save my_parameters.mat beta alpha varphi delta gamma M Psi A Q phi omega rho_a rho_psi sigma xi lambda theta R Qnom Omega V R_k Z yk ck N K Y C S_p S_g S NW I D rho_q kappa_pi kappa_y kappa_varrho kappa_varrhof varrho kappa_i kappa_k kappa_yi kappa_yk delta_1 delta_2 delta_3 delta_4 delta_5 delta_6 delta_7 delta_8 delta_9 delta_10 delta_11 delta_12 delta_13 alpha_1 alpha_2 alpha_3 delta_p nwk dk spread
end