98 lines
1.6 KiB
Modula-2
98 lines
1.6 KiB
Modula-2
var c, h, pi, w, R, r_e, y, gdp, gdp_hat, k, u, g, c_hat, w_hat, y_hat, h_hat;
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varexo d, z, eta;
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parameters alpha, beta, sigma, gamma, theta, ni, tau_w, phi_p, phi_y;
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beta = 0.997;
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sigma = 2;
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gamma = 25;
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theta = 7.67;
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tau_w = 0.2;
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ni = 0.28;
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phi_p = 1.5;
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phi_y = 0.125;
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alpha = 0.064;
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model;
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// log-deviation of _ from its steady state value
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gdp_hat=log(gdp)-log(steady_state(gdp));
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c_hat=log(c)-log(steady_state(c));
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w_hat=log(w)-log(steady_state(w));
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y_hat=log(y)-log(steady_state(y));
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h_hat=log(h)-log(steady_state(h));
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// real interest rate
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r_e=1/(beta*d(+1))-1;
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//FOC labor
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c^sigma*h^ni=w*(1-tau_w);
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//Euler equation 1
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1=beta*d(+1)*(1+R)/(1+pi(+1))*(c/c(+1))^sigma;
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//Euler equation 2
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0=1/(1-alpha)*(steady_state(w)/z)*h^alpha-1-gamma/theta*pi*(1+pi)+beta*d(+1)*(c/c(+1))^sigma * y(+1)/y*gamma/theta*pi(+1)*(1+pi(+1));
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// Taylor rule with ZLB
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R=max(0,r_e+phi_p*pi+phi_y*gdp_hat);
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//output
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y=z*h^(1-alpha);
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//aggregate resource constraint
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c=(1-k-eta)*y;
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// resource cost of price adjustment
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k=(gamma/2)*(pi^2);
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//government purchases
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g=eta*y;
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// GDP
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gdp=(1-k)*y;
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//utility
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u=(c^(1-sigma))/(1-sigma)-(h^(1+ni))/(1+ni);
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end;
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initval;
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z=1;
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d=1;
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pi=0;
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k=(gamma/2)*(pi^2);
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r_e=1/(beta*d)-1;
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eta=0.2;
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h=1;
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y=z*h;
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g=eta*y;
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c=(1-k-eta)*y;
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w=z;
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gdp=(1-k)*y;
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R=r_e;
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end;
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steady;
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check;
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shocks;
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//5% preference shock
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var d;
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periods 1:10;
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values 1.05;
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//technology shock
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var z;
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periods 1:10;
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values 1.05;
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end;
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perfect_foresight_setup(periods=40);
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perfect_foresight_solver(maxit=1000);
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rplot gdp_hat;
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rplot R;
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if oo_.deterministic_simulation.status~=1
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error('This model has no solution');
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end
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