olg_zin_index_PT_no_money_total.mod

//This mod file was finalised on 9 Feb 2014 (written by M. Hatcher)

var A, b, bd, co, cy, g, k, mu, muy, pi, pro, R, rm, rn, v, q, out, eco, w, rf, rk, btotd, btot, bi, bid, utility, g_ratio, ri, irp, piind;

varexo e, u, u1;
 
parameters alpha, beta, rho, delta, pstar, promean, eps, sharei, N, t, tk;

alpha = 0.263;  //capital share in output
beta = 0.70;    //private discount factor
rho = 0.400;    //persistence in TFP
delta = -15;    //(negative of) coefficient of relative risk aversion
pstar = 0.02;   //yearly inflation target
promean = 1;    //mean of TFP
eps = -0.35;    //intertemporal elasticity of substitution = 1/(1-eps)
//Parameters below are tax rates (t and tk), indexation share (sharei) and a scaling parameter (N) which prevents large numbers
//t and sharei are replaced in each simulation


t = 1.264600e-001; 
sharei = 1; 
tk = 2.3*t; 
N = 100000;

model;

//Budget constraint of young consumers
cy = w*(1-t) - btotd - k; 

//Budget constraint of old consumers
co = (1-tk)*A*k(-1) + ( sharei*rf(-1)*rm*piind + (1-sharei)*R(-1)*rm )*btotd(-1);

//Government budget constraint
g = w*t + tk*A*k(-1) + b - R(-1)*rm*b(-1) + bi - rf(-1)*rm*piind*bi(-1);

//Government spending to output ratio
g_ratio = g/out;

//Total demand for bonds
btotd = bd + bid;

//Nominal bonds market clearing
bd = b;

//Indexed bonds market clearing
bid = bi;

//Supply of indexed bonds
bi = sharei*btot;

//Supply of nominal bonds
b = (1-sharei)*btot;

//Total bond supply equation (ie eq for btot)
muy = mu(+1);

//Inflation shock
v = u;

//Shock to indexed inflation
q = u1;

//Money supply rule
//Horizon of 1 year
1+pi = ( (1+pstar)^20 )*(1+v)/(1+v(-1));

//Indexed inflation
piind =( (1+pstar)^20 )*(1+q)/(1+q(-1));

//Productivity (ie TFP)
pro = exp(e)*(pro(-1)^rho)*(promean^(1-rho));

//Euler equation for capital
muy = beta*(1-tk)*mu(+1)*pro(+1)*alpha*k^(alpha-1);

//Real return on money balances
rm = 1/(1+pi);

//Euler equation for nominal bonds 
muy = beta*R*mu(+1)*rm(+1);

//Euler equation for indexed bonds
muy = beta*rf*mu(+1)*rm(+1)*piind(+1);

//Real return on nominal bonds
rn = R(-1)*rm;

//Real return on indexed bonds
ri = rf(-1)*rm*piind;

//Real return on capital
A = pro*alpha*k(-1)^(alpha-1);

//Equation to calculate average annual after-tax risk premium on capital
rk = ( ((1-tk)*A)^(1/20) - 1 ) - (ri^(1/20) - 1);

//Equation to calculate the average diff between the inflation risk premium on nominal and indexed debt
irp = rn - ri;

//LHS term of Euler equation
//Scaling by 1/N prevents large numbers
muy = (1/N)*cy^(eps-1);

//RHS term of Euler equation
//Scaled and unscaled by 10^(1+delta) due to definition of eco (see below)
//Scaling by 1/N prevents large numbers
mu = (1/N)*( co^delta )/ ( (eco(-1) / (10^(1+delta)) )^((1-eps+delta)/(1+delta)) );

//Expected consumption term in utility
//Scaling by 10 prevents large numbers
eco = (10*co(+1))^(1+delta);

//Epstein-Zin preferences
//Scaling by 1/(10^30) mean that initial value for utility does not need to changed with small changes on calibration 
//The same scaling is applied under IT
utility = (1/(10^30))*(1/(1+delta))*( (cy)^(eps) + beta*(eco/(10^(1+delta)))^(eps/(1+delta)) )^((1+delta)/eps);

//Aggregate output
out = pro*k(-1)^alpha; 

//Wages
w = out - A*k(-1);

end;

initval;
btotd = 0.0557;
btot = btotd;
bid = 0.0111;
bd = 0.0446;
bi = bid;
b = bd;
k = 0.0674;
rn = 1/beta;
cy = 0.1842; 
R = 2.5877;
co = cy;
muy = 0.0000982;
mu = muy; 
pi = 0.8114;
pro = promean;
rm = 0.5521;
A = 1.9195;
g = 0.0563;
utility = -0.000000000023;
out = 0.4920;
eco = 0.000194;
w = 0.3626;
rf = rn;
ri = rn;
rk = 0;
g_ratio = 0.1146;
irp = 0;
v = 0;
q = 0;
piind = 1+pi;
t = 0.11;
tk = 2.3*t;
end;vcov = [3.100000e-003 0 0; 0 1.100000e-004 0; 0 0 1.100000e-004];