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multisector.mod
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multisector.mod
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// This file replicates the model studied in:
// Krueger, Dirk, Harald Uhlig, and Taojun Xie (2020): "Macroeconomic
// Dynamics and Reallocation in an Epidemic", NBER Working Paper 27047.
@#define find_init_9sector = 0
@#define periods = 100
@#define phi1 = 0.2
@#define pi_a = 0 // 0.34
@#define kappa = 10
@#define alpha = .001
// Homogeneous vs heterogeneous sectors
// Autonomous infection
@#if pi_a == 0
@#define pi_s = 1.82e-6
@#else
@#define pi_s = 1.77e-7
@#endif
// Nine-sector scenario
@#if find_init_9sector == 1
@#define K = 9
@#else
@#define K = 2
@#endif
clc;
var n (long_name = 'Labor supply')
c (long_name = 'Agg. consumption')
lambda_tau (long_name = 'Lambda')
tau (long_name = 'Probability of infection')
I (long_name = 'Infected')
T (long_name = 'Newly infected')
S (long_name = 'Susceptible')
R (long_name = 'Recovered')
D (long_name = 'Deceased')
C (long_name = 'Agg. consumption')
N (long_name = 'Agg. labor')
Ui (long_name = 'Lifetime utility of infected')
Us (long_name = 'Lifetime utility of susceptible')
Ur (long_name = 'Lifetime utility of recovered')
dD (long_name = 'Weekly death')
@#for k in 1:K
c@{k}
c@{k}_dev
@#endfor
;
parameters pi_s ${\pi_s}$ (long_name = 'Probability of becoming infected')
pi_a ${\pi_a}$ (long_name = 'Probability of autonomous infection')
pi_r ${\pi_r}$ (long_name = 'Probability of recovery')
pi_d ${\pi_d}$ (long_name = 'Probability of death')
eta ${\eta}$ (long_name = 'Dlasticity of substitution')
theta ${\theta}$ (long_name = 'Labor supply parameter')
A ${A}$ (long_name = 'Productivity')
betta ${\beta}$ (long_name = 'Discount factor')
@#for k in 1:K
phi@{k} ${\phi_{@{k}}}$
ups@{k} ${\upsilon_{@{k}}}$
@#endfor
;
varexo eps
;
eta = 3;
pi_s = @{pi_s};
pi_a = @{pi_a};
pi_d = 7*@{alpha}/@{kappa};
pi_r = 7*(1-@{alpha})/@{kappa};
betta = 0.96^(1/52);
A = 39.835;
theta = 0.001275;
@#if K != 2
@#for k in 1:K
phi@{k} = 1/((@{K}+1)/2)*@{k};
ups@{k} = 1/@{K};
@#endfor
@#endif
@#if K == 2
phi1 = @{phi1};
ups1 = 0.5;
ups2 = 0.5;
phi2 = 2 - phi1;
@#endif
@#include "ModelEquations.mod"
steady_state_model;
tau = 0;
I = 0;
T = 0;
R = 0;
D = 0;
C = 0;
C_sum = 0;
N = 0;
n = 1/sqrt(theta);
lambda_b = theta/A*n;
c = A*n;
Us = (log(c)-theta/2*n^2)/(1-betta);
Ur = Us;
Ui = (log(c)-theta/2*n^2+betta*pi_r*Ur)/(1-betta*(1-pi_d-pi_r));
lambda_tau = betta * (Us - Ui);
S = 1;
dD = 0;
@#for k in 1:K
c@{k} = ups@{k} * c;
c@{k}_dev = 0;
@#endfor
end;
steady;
check;
//model_diagnostics;
shocks;
var eps;
periods 1:1;
values 0.0001;
end;
perfect_foresight_setup(periods = @{periods});
//
// SIMULATIONS
//
@#for value in 1e-7:2e-8:pi_s
clc;
pi_s = @{value};
disp(['pi_s = ' num2str(pi_s)]);
perfect_foresight_solver(stack_solve_algo=6);
@#endfor
@#if pi_a != 0
clc;
@#for value in 0:1e-2:(pi_a+1e-10)
clc;
pi_a = @{value};
disp(['pi_a = ' num2str(pi_a)]);
perfect_foresight_solver(stack_solve_algo=6);
@#endfor
@#endif
PlotResults;
clean_current_folder;