Commit 7d4a7b1b authored by MichelJuillard's avatar MichelJuillard
Browse files

adding test for computing Ramsey policy in a model using the

expectation operator.
parent ff4285d6
//MODEL:
//test on Dynare to find the lagrangean multipliers.
//We consider a standard NK model. We use the FOCS of the competitive economy and we aim at calculating the Ramsey optimal problem.
//------------------------------------------------------------------------------------------------------------------------
//1. Variable declaration
//------------------------------------------------------------------------------------------------------------------------
var pai, c, n, r, a;
//4 variables + 1 shock
varexo u;
//------------------------------------------------------------------------------------------------------------------------
// 2. Parameter declaration and calibration
//-------------------------------------------------------------------------------------------------------------------------
parameters beta, rho, epsilon, omega, phi, gamma;
beta=0.99;
gamma=3; //Frish elasticity
omega=17; //price stickyness
epsilon=8; //elasticity for each variety of consumption
phi=1; //coefficient associated to labor effort disutility
rho=0.95; //coefficient associated to productivity shock
//-----------------------------------------------------------------------------------------------------------------------
// 3. The model
//-----------------------------------------------------------------------------------------------------------------------
model;
a=rho*(a(-1))+u;
1/c=beta*(1/(c(+1)))*(r/expectation(0)(pai(+1))); //euler
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
(exp(a))*n=c+(omega/2)*((pai-1)^2);
end;
//--------------------------------------------------------------------------------------------------------------------------
// 4. Steady state
//---------------------------------------------------------------------------------------------------------------------------
initval;
pai=1;
r=1/beta;
c=0.9671684882;
n=0.9671684882;
a=0;
end;
//---------------------------------------------------------------------------------------------------------------------------
// 5. shocks
//---------------------------------------------------------------------------------------------------------------------------
shocks;
var u; stderr 0.008;
end;
//--------------------------------------------------------------------------------------------------------------------------
// 6. Ramsey problem
//--------------------------------------------------------------------------------------------------------------------------
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
write_latex_static_model;
write_latex_dynamic_model;
ramsey_policy(planner_discount=0.99);
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