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integration_A0.yaml
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integration_A0.yaml
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name: Partial Integration
description: capital
symbols:
exogenous: [A_1, A_2, E]
states: [k_1]
controls: [i_1, ew_1, w_1]
parameters: [beta, theta, gamma, psi, delta, rho_A, rho_E, min_b, max_b,
a1, a2, xi, sigma_A_1, sigma_A_2, sigma_E, kmin, kmax, min_bb, max_bb, spmin, spmax,
S_1, country, zeta, N_k, N_b, N_s]
definitions:
y_1: k_1**theta*exp(A_1)
c_1: y_1 - i_1
Phi_1: a1 + a2/(1-xi)*(i_1/k_1)^(1-xi)
Phi_1__p: a2*(i_1/k_1)^(-xi)
rho_1: ( exp(E(1))*w_1(1)/ew_1 )**(psi-gamma) * (exp(E(1))*c_1(1)/c_1)**(-psi)
equations:
transition:
- k_1 = ( (1-delta) + Phi_1(-1) )*k_1(-1) / exp(E)
arbitrage:
- beta*rho_1*( theta*(y_1(1)/k_1(1))*Phi_1__p + Phi_1__p/Phi_1__p(1)*( (1-delta) + Phi_1(1)-i_1(1)/k_1(1)*Phi_1__p(1))) - 1
- ( ew_1 )**(1-gamma) = ( w_1(1)*exp(E(1)) )**(1-gamma)
- beta*(ew_1)**(1-psi) - w_1**(1-psi) + (1-beta)*(c_1)**(1-psi)
############################
calibration:
# exogenous
# controls
i_1: ((1/beta-(1-delta))/theta)**(1/(theta-1)) * delta
p_1: beta
p_S_1: beta/(1-beta)*(theta*y_1-i_1)
E_p_S_1: (p_S_1 + theta*y_1-i_1)
roc_1: 1/beta
# states
A_1: 0
A_2: 0
E: 0
k_1: i_1/delta
sparsity: 1.0
#auxiliary
y_1: k_1**theta
c_1: (y_1 - delta*k_1)
Phi_1: a1 + a2/(1-xi)*(i_1/k_1)^(1-xi)
Phi_1__p: a2*(i_1/k_1)^(-xi)
w_1: c_1
ew_1: c_1
E: 0
r_S_1: 1/beta
beta: 0.96
theta: 0.3
delta: 0.08
gamma: 4
psi: 4
rho_A: 0.9
rho_E: 0.999
zeta: 0.0
tpb: 1
xi: 0.2
a2: delta^(xi)
a1: delta - a2/(1-xi)*delta^(1-xi)
sigma_A_1: 0.025
sigma_A_2: 0.05
sigma_E: 0.0
kmin: 2
kmax: 10
spmin: 0.5
spmax: 1.25
country: 1
min_b: -10.0
max_b: 10.0
min_bb: min_b
max_bb: max_b
S_1: 1
n_a: 2
n_e: 1
N_k: 1000
N_b: 50
N_s: 10
exogenous: !Product
p1: !VAR1
rho: rho_A
Sigma:
[ [sigma_A_1^2, zeta*sigma_A_1*sigma_A_2], [zeta*sigma_A_1*sigma_A_2, sigma_A_2^2] ]
N: n_a
p2: !VAR1
rho: rho_E
Sigma:
[ [sigma_E^2] ]
N: n_e
domain:
k_1: [kmin, kmax]
options:
grid: !Cartesian
orders: [50]