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Replace LMMCP test with another one that converges 

Incidentally the new one takes far less time, especially on Octave.
time-shift
Sébastien Villemot 2018-07-18 14:38:11 +02:00
parent 5361325ba9
commit 9c3ce0350d
1 changed files with 46 additions and 53 deletions
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99
tests/lmmcp/rbcii.mod
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@ -1,74 +1,67 @@
var Capital, Output, Labour, Consumption, Investment, Efficiency, efficiency, residual, marginal_utility;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma;
/*
** Calibration
*/
var k, y, L, c, i, A, a, mu;
varexo epsilon;
parameters beta, theta, tau, alpha, psi, delta, rho, Astar, sigma;
beta = 0.990;
theta = 0.357;
tau = 2.000;
alpha = 0.450;
psi = -0.200;
psi = -2.500;
delta = 0.020;
rho = 0.800;
effstar = 1.000;
rho = 0.998;
Astar = 1.000;
sigma = 0.100;
model;
a = rho*a(-1) + sigma*epsilon;
A = Astar*exp(a);
(c^theta*(1-L)^(1-theta))^(1-tau)/c - mu = beta*((c(+1)^theta*(1-L(+1))^(1-theta))^(1-tau)/c(+1)*(alpha*(y(+1)/k)^(1-psi)+1-delta)-mu(+1)*(1-delta));
((1-theta)/theta)*(c/(1-L)) - (1-alpha)*(y/L)^(1-psi);
y = A*(alpha*(k(-1)^psi)+(1-alpha)*(L^psi))^(1/psi);
k = y-c+(1-delta)*k(-1);
i = k-(1-delta)*k(-1);
efficiency = rho*efficiency(-1) + sigma*EfficiencyInnovation;
Efficiency = effstar*exp(efficiency);
[mcp = 'Investment > 0',name='Investment Euler Equation']
-(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption + beta*((((Consumption(+1)^theta)*((1-Labour(+1))^(1-theta)))^(1-tau))/Consumption(+1))*(alpha*((Output(+1)/Capital)^(1-psi))+1-delta);
residual = (((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption - beta*((((Consumption(+1)^theta)*((1-Labour(+1))^(1-theta)))^(1-tau))/Consumption(+1))*(alpha*((Output(+1)/Capital)^(1-psi))+1-delta);
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
Output = Consumption + Investment;
Investment = Capital - (1-delta)*Capital(-1);
marginal_utility = (((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption;
[ mcp = 'i > 0' ]
mu = 0;
end;
steady_state_model;
Efficiency = effstar;
y_k = (Efficiency^(-psi)*(1/beta-1+delta)/alpha)^(1/(1-psi));
c_k = y_k - delta;
n_k = (((y_k/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
y_n = y_k/n_k;
c_n = c_k/n_k;
Labour = y_k*(1-alpha)/(((1-theta)/theta)*c_k*(alpha*n_k^(-psi)+1-alpha)+y_k*(1-alpha));
Capital = Labour/n_k;
Consumption = c_n*Labour;
Output = Efficiency*(alpha*Capital^psi+(1-alpha)*Labour^psi)^(1/psi);
Investment = delta*Capital;
residual = 0;
marginal_utility = (((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption;
end;
a=0;
mu=0;
A=Astar;
resid;
steady;
// Steady state ratios
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/A)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
L=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
c=Consumption_per_unit_of_Labour*L;
k=L/Labour_per_unit_of_Capital;
y=Output_per_unit_of_Capital*k;
i=delta*k;
end;
shocks;
var EfficiencyInnovation;
periods 1;
values -4;
var epsilon;
periods 10;
values -1;
end;
perfect_foresight_setup(periods=100);
steady;
perfect_foresight_solver(lmmcp);
perfect_foresight_setup(periods=400);
perfect_foresight_solver(lmmcp, maxit=200);
rplot Investment;
n = 40;
figure(2);
subplot(3,2,1); plot(1:n,A(1:n)); title('A');
subplot(3,2,2); plot(2:n,y(2:n)); title('y');
subplot(3,2,3); plot(2:n,L(2:n)); title('L');
subplot(3,2,4); plot(1:n,k(1:n)); title('k');
subplot(3,2,5); plot(2:n,c(2:n)); title('c');
subplot(3,2,6); plot(2:n, y(2:n)-c(2:n)); title('i');
rplot residual;