107 lines
3.5 KiB
Modula-2
107 lines
3.5 KiB
Modula-2
//MODEL:
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// test for using expectation operator with Ramsey policy
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// Here, the expected variable is replaced manually with an auxiliary variable (epai)
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// We check that the result is the same as with an explicit expectation operator in nk_ramsey_expectation.mod
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// Note that the example doesn't make any sense from an economic point of view.
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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, epai;
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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/epai); //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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epai = pai(+1);
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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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% this is the exact steady state under optimal policy
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%important for the comparison
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pai=1;
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epai=1;
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r=1/beta;
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c=((epsilon-1)/(epsilon*phi))^(1/(1+gamma));
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n=c;
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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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options_.solve_tolf=1e-12;
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ramsey_model(planner_discount=0.99);
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stoch_simul(order=1,irf=0);
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evaluate_planner_objective;
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o1=load(['nk_ramsey_expectation' filesep 'Output' filesep 'nk_ramsey_expectation_results']);
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if (norm(o1.oo_.dr.ghx-oo_.dr.ghx,inf) > 1e-12)
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error('ghx doesn''t match')
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end
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if (norm(o1.oo_.dr.ghu-oo_.dr.ghu,inf) > 1e-12)
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error('ghu doesn''t match')
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end
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if (abs(o1.oo_.planner_objective_value(1)-oo_.planner_objective_value(1)) > 1e-12)
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error('planner objective value doesn''t match')
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end
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