baseline_v1: An open Economy DSGE model

baseline_v1.mod

% ----- --------------------------------------------------------------
% Model Attempt 1
% ----- --------------------------------------------------------------
% Solving the model without calculating the steady state! Closing large open economy models
 
% ----- --------------------------------------------------------------
% Endogenous Variables
% ----- --------------------------------------------------------------
var 	nubeta  nun  nuc    nui  nup  tauyd  taun  tauk  taud  taum  gd  gm  g  pid  pi  pidopt  psigma  f  gpr  x  c  cd  cm  n  w  r  k  i  yd  lambda2  mc  lambda1  ydn
        nubetas nuns nucs   nuis nups tauyds tauns tauks tauds taums gds gms gs pids pis pidopts psigmas fs gprs xs cs cds cms ns ws rs ks is yds lambda2s mcs lambda1s ydns
        num     icu  ygapcu picu tau  ycu    ycun
; 
 
 
% ----- --------------------------------------------------------------
% Exogenous Variables 
% ----- --------------------------------------------------------------
varexo ebeta en ec ei ep etauyd etaun etauk etaud etaum
	   epsg
	  ebetas ens ecs eis eps etauyds etauns etauks etauds etaums
	   epsgs
	  em
; 
 
 
% ----- --------------------------------------------------------------
% Parameters 
% ----- --------------------------------------------------------------
parameters rhob rhon rhoc rhoi rhop rhotauyd rhotaun rhotauk rhotaud rhotaum eg omg rhog xi mun pidss om muc sigma beta h kappa ej N alpha delta el
egs omgs oms
rhom psiygap rhoicu psipi
;
 
 
% ----- --------------------------------------------------------------
% Parameters Values (Calibrated Parameters)
% ----- --------------------------------------------------------------
rhob = 0.9;
rhob = rhon;
rhob = rhoc;
rhob = rhoi;
rhob = rhop;
rhob  = rhotauyd;
rhob  = rhotaun;
rhob  = rhotauk;
rhob = rhotaud;
rhob = rhotaum ;
el = 1.1;
eg = el;
ej = 0.6;
om = 0.3;
omg = 0.3;
rhog = 0.8;
xi = 0.4;
mun = 0.023;
pidss = 0.02;
muc = 0.001;
sigma = 0.6;
beta = 0.9987;
h = 0.8; 
kappa = 4.00; % Sims (2016)
ej = 2; % Doubt
N = 1/3;
alpha = 1/3;
delta = 0.025;
egs = eg;
oms = 0.2;
omgs = oms;
rhom = 0.7;
psiygap = 1;
psipi = 2.5;
rhoicu = 0.8;





% ----- --------------------------------------------------------------
% Model Block
% ----- --------------------------------------------------------------
 
 
 
model;
% 1st equation
nubeta *lambda1 = beta* nubeta(+1)*(1+icu)*lambda1(+1) *(1+pi)^(-1);
% 2nd equation
x = c - h * c(-1);
% 3rd equation
mun * n * nun = lambda1 * w * (1-taun);
% 4th equation
lambda1 = (x - muc*nuc)^(-sigma);
% 5th equation
lambda1*(1+pi(+1))*nubeta = lambda1s * (1+pis(+1))*nubetas;
% 6th equation
lambda1 = (lambda2 * (1-nui*(1- (kappa/2)*((i/i(-1)) - 1))^2 + (nui*i/i(-1))*kappa*((i/i(-1)) - 1))) + (beta * nubeta(+1) * lambda2(+1) * kappa * ((i(+1)/i) - 1)*(i(+1)/i)^2);
% 7th equation
lambda2 = beta* (nubeta(+1)/nubeta)*(r(+1)*lambda1(+1)*(1-tauk(+1))+lambda2*(1-delta));
% 8th equation
(1+pid)^(1-ej) = ( xi*(1+pidss)^(1-ej) + (1-xi)*(1+pidopt)^(1-ej) );
% 9th Equation
tau = ((1+pids)/(1+pid))* tau(-1);
%10th equation
(1+pi)^(1-el) = ( (((1-om)*(1+taud)^(1-el)+om*(1+taum)^(1-el)*tau^(1-el)))/(((1-om)*(1+taud(-1))^(1-el)+om*(1+taum(-1))^(1-el)*tau(-1)^(1-el))) ) * (1+pid)^(1-el);
% 11th Equation
yd = cd + gd + i + ((1-N)/N)*(cms + gms);
% 12th equation
cd = (((1-om)* x)/((1+taud)^(el))) * ((1-om)*(1+taud)^(1-el)+om*(1+taum)^(1-el)*tau^(1-el))^(el/(1-el));
% 13 th equation
cm =  (((om)* x)/((1+taum)^(el))) * ((1-om)*(1+taud)^(1-el)+om*(1+taum)^(1-el)*tau^(1-el))^(el/(1-el));
% 14th equation
gd = (((1-omg)* g)/((1+taud)^(eg))) * ((1-omg)*(1+taud)^(1-eg)+omg*(1+taum)^(1-eg)*tau^(1-eg))^(eg/(1-eg));
%15th equation
gm = (((omg)* g)/((1+taum)^(eg))) * ((1-omg)*(1+taud)^(1-eg)+omg*(1+taum)^(1-eg)*tau^(1-eg))^(eg/(1-eg));
%16th equation
k(+1) = i + k*(1-delta) - nui*(1-(kappa/2)*((i/i(-1)) - 1)^2)*i;
% 17the equation
psigma = (1-tauyd)^(ej)*((1-xi)*((1+pidopt)/(1+pid))^(-ej) + xi* ((1+pid)/(1+pidss))^(ej)*psigma(-1));
% 18th equation
(w*alpha)/(r*(1-alpha)) = (k/n);
% 19th equation
mc = (1/nup)*((n/k)^(alpha))*(w/(1-alpha));
% 20th equation
f = nubeta*lambda1*(1-tauyd)^(ej)*mc*yd + xi*beta*((1+pid(+1))/(1+pidss))^(ej)*f(+1);
% 21st equation
gpr = nubeta*lambda1*(1-tauyd)^(ej)*yd + xi*beta*((1+pid(+1))/(1+pidss))^(ej)*gpr(+1);
% 22nd euqation
(1+pidopt) = (ej/(ej-1))*(f/gpr)*(1+pid);
% 23rd equation
taud = rhotaud*taud(-1) + etaud;
% 24th equation
taum = rhotaum*taum(-1) + etaum;
% 25th equation
tauk = rhotauk*tauk(-1) + etauk;
% 26th equation
taun = rhotaun*taun(-1)+ etaun;
% 27th equation
tauyd = rhotauyd * tauyd(-1) + etauyd;
%28th equation
g = rhog * g(-1) + epsg;
% 29th equation
icu = max(0, psiygap*(1-rhoicu)*ygapcu + psipi*(1-rhoicu)*picu + rhoicu*icu(-1)+num);
% 30th equation
nuc = rhoc*nuc(-1) + ec;
%31st equation
nun = rhon*nuc(-1) + en;
% 32nd equation
nubeta = rhob*nubeta(-1) + ebeta;
% 33rd equation
nui = rhoi*nui(-1) + ei;
% 34th equation
nup = rhop*nup(-1) + ep;
% 35
num = rhom*num(-1) + em;
% 36
nubetas*lambda1s = beta* nubetas(+1)*(1+icu)*lambda1s(+1) *(1+pis)^(-1);
% 37
xs = cs - h*cs(-1);
% 38
mun * ns * nuns = lambda1s * ws * (1-tauns);
% 39
lambda1s = (xs - muc * nucs)^(-sigma);
% 40
lambda1s = (lambda2s *(1-nuis*(1- (kappa/2)*((is/is(-1)) - 1))^2 + (nuis*is/is(-1))*kappa*((is/is(-1)) - 1))) + (beta * nubetas(+1) * lambda2s(+1) * kappa * ((is(+1)/is) - 1) * (is(+1)/is)^2);
% 41 
lambda2s = beta* (nubetas(+1)/nubetas)*(rs(+1)*lambda1s(+1)*(1-tauks(+1))+lambda2s*(1-delta));
% 42
(1+pids)^(1-ej) = ( xi*(1+pidss)^(1-ej) + (1-xi)*(1+pidopts)^(1-ej) );
% 43
(1+pis)^(1-el) = ( (((1-oms)*(1+tauds)^(1-el)+oms*(1+taums)^(1-el)*tau^(-1+el)))/(((1-oms)*(1+tauds(-1))^(1-el)+oms*(1+taums(-1))^(1-el)*tau(-1)^(-1+el))) ) * (1+pids)^(1-el);
% 44
yds = cds + gds + is + (N/(1-N))*(cm + gm);
% 45
cms =  (((oms)* xs)/((1+taums)^(el))) * ((1-oms)*(1+tauds)^(1-el)+oms*(1+taums)^(1-el)*tau^(-1+el))^(el/(1-el));
% 46
cds = (((1-oms)* xs)/((1+tauds)^(el))) * ((1-oms)*(1+tauds)^(1-el)+oms*(1+taums)^(1-el)*tau^(-1+el))^(el/(1-el));
% 47
gms = (((omgs)* gs)/((1+taums)^(eg))) * ((1-omgs)*(1+tauds)^(1-eg)+omgs*(1+taums)^(1-eg)*tau^(-1+eg))^(eg/(1-eg));
% 48
gds = (((1-omgs)* gs)/((1+tauds)^(eg))) * ((1-omgs)*(1+tauds)^(1-eg)+omgs*(1+taums)^(1-eg)*tau^(-1+eg))^(eg/(1-eg));
% 49
ks(+1) = is + ks*(1-delta) - nuis*(1-(kappa/2)*((is/is(-1)) - 1)^2)*is;
% 50
psigmas = (1-tauyds)^(ej)*((1-xi)*((1+pidopts)/(1+pids))^(-ej) + xi* ((1+pids)/(1+pidss))^(ej)*psigmas(-1));
% 51
(ws*alpha)/(rs*(1-alpha)) = (ks/ns);
% 52
mcs = (1/nups)*((ns/ks)^(alpha))*(ws/(1-alpha));
% 53
fs = nubetas*lambda1s*(1-tauyds)^(ej)*mcs*yds + xi*beta*((1+pids(+1))/(1+pidss))^(ej)*fs(+1);
% 54
gprs = nubetas*lambda1s*(1-tauyds)^(ej)*yds + xi*beta*((1+pids(+1))/(1+pidss))^(ej-1)*gprs(+1);
% 55
(1+pidopts) = (ej/(ej-1))*(fs/gprs)*(1+pids);
% 56
tauds = rhotaud*tauds(-1) + etauds;
% 57
taums = rhotaum*taums(-1) + etaums;
% 58
tauks = rhotauk*tauks(-1) + etauks;
% 59
tauns = rhotaun*tauns(-1)+ etauns;
% 60
tauyds = rhotauyd * tauyds(-1) + etauyds;
% 61
gs = rhog * gs(-1) + epsgs;
% 62
picu = N*pi + (1-N)* pis;
% 63
nubetas = rhob*nubetas(-1) + ebetas;
% 64
nuns = rhon*nucs(-1) + ens;
% 65
nucs = rhoc*nucs(-1) + ecs;
% 66
nuis = rhoi*nuis(-1) + eis;
% 67
nups = rhop*nups(-1) + eps;
% 68
ygapcu = ycu - ycun;
% 69
ycun = n * ydn + (1-n) * ydns;
% 70
ycu = n * yd + (1-n) * yds;
% 71
ydns = 0;
% 72
ydn = 0;
% 73 Equation linking intermediate output and domestic output (used for natural rate purposes)
nup*(k/n)^(alpha) * n = yd*(1-tauyd)^(ej)*psigma^(-1);

end;
 
% ----- --------------------------------------------------------------
% Initial Value ~ Helps Converge to Steady State
% ----- --------------------------------------------------------------
initval;
nubeta = 0;
 nun = 0;
 nuc = 0;
 nui = 0;
 nup = 0;
 tauyd = 0;
 taun = 0;
 tauk = 0;
 taud = 0;
 taum = 0;
 gd = 0;
 gm = 0;
 g = 0;
 pid = 0;
 pi = 0;
 pidopt = 0;
 psigma = 0;
 f = 0;
 gpr = 0;
 x = 0;
 c = 0;
 cd = 0;
 cm = 0;
 n = 0;
 w = 0;
 r = 0;
 k = 0;
 i = 0;
 yd = 0;
 lambda2 = 0;
 mc = 0;
 lambda1 = 0;
nubetas = 0;
 nuns= 0;
 nucs = 0;
 nuis = 0;
 nups = 0;
 tauyds = 0;
 tauns = 0;
 tauks = 0;
 tauds = 0;
 taums = 0;
 gds = 0;
 gms = 0;
 gs = 0;
 pids = 0;
 pis = 0;
 pidopts = 0;
 psigmas = 0;
 fs = 0;
 gprs = 0;
 xs = 0;
 cs = 0;
 cds = 0;
 cms = 0;
 ns = 0;
 ws = 0;
 rs = 0;
 ks = 0;
 is = 0;
yds = 0;
lambda2s = 0;
mcs = 0;
lambda1s = 0;
num = 0;
icu = 0;
ygapcu = 0;
picu = 0;
tau = 0;
end;
 
 
 
 
% ----- --------------------------------------------------------------
%       Shock Block
% ----- --------------------------------------------------------------
 
shocks;
var epsg;
stderr 0.009;
end;
 
% ---- ------------------------------------------------------------
%  Steady State Solver, Eigenvalues Checker
% ---- ------------------------------------------------------------
resid(1) ;
steady(solve_algo = 3);
check;
 
 
% -------- --------------------------------------------------------
%  Solution Block
% -------- --------------------------------------------------------
%extended_path(periods=100,order=10);
simul(order = 2, relative_irf, irf=30) yd;
%write_latex_dynamic_model ; 

The working version of the paper is here. The solutions need further work.
(A) Creating the steady state file.
(B) Estimating the parameters. (For now, the parameters are fixed according to the literature).

For information on the model, please email nikhil.damodaran@gmail.com