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