// Endogenous and Exogenous Variables
var cT cN yT yN hT hN w pT g d phi tau h h_ssT p_ssX;
varexo pX;

// Parameters
parameters a xi alpha gamma r aT aN hbar epsilon W;

// Parameter Values
a = 0.7; // Cobb-Douglas Utility Weight
xi = 0.5; // Substitution parameter between cT and cN
alpha = 0.33; // Labour share in production
gamma = 0.2; // Government Spending Parameter
r = 0.04; // World interest rate
aT = 1; // Productivity in the tradable sector
aN = 1; // Productivity in the nontradable sector
hbar = 1; // Total labour endowment
epsilon = 1; // Exchange Rate
W = 1; // Nominal Wage Rate 

// Model equations
model;

// HOUSEHOLDS 

// Household Budget Constraint
cT + pT * cN + d + tau = w * h + phi + d(+1)/(1+r);

// Household Optimality
pT = (1-a)/a * (cT/cN)^(1/xi);




// FIRMS 

// Tradable Firm Production Function
yT = aT * hT^(1-alpha);

// Non-tradable Firm Production Function
yN = aN * hN^(1-alpha);

// Tradable Labour Demand
w = pX * aT * (1-alpha) * hT^(-alpha);

// Non-tradable Labour Demand
w = pT * aN * (1-alpha) * hN^(-alpha);



// GOVERNMENT

// Government Budget Constraint
tau = g * (gamma + pT);


// MARKET CLEARING

//Non-tradable Market Clearing
cN + g = yN;

//Labour Market Clearing
h = hT + hN;

// External Debt Evolution
cT + gamma*g + d = pX * yT + d(+1)/(1+r);




// STEADY STATE

pT = (1-a)/a * ((cT/((h - hT)^(1-alpha) - g))^(1/xi));

pT = (W/epsilon)/((1-alpha)*(h-hT)^(-alpha));

pX * (1-alpha) * (hT)^(-alpha) = W/epsilon;

cT + gamma*r/(1+r) * g = r/(1+r) * pX * (hT)^(1-alpha) + 1/(1+r) * p_ssX * (h_ssT)^(1-alpha);

(1-a)/a * ((cT/((hbar - h_ssT)^(1-alpha)))^(1/xi)) = (p_ssX * (1-alpha) * h_ssT^(-alpha))/((1-alpha) * (hbar - h_ssT)^(-alpha));



end;


// EXOGENOUS SHOCKS
shocks;
var pX; stderr 1;
end;

stoch_simul(order=1, irf=20);