def equations(state, policy_state):
E_t = State.E_t_gen(state, policy_state)
loss_dict = {}
betaK = Definitions.betaK(state, policy_state)
# original eq 1
loss_dict['eq_1'] = lambday_norm - (
State.nux(state) /
(Cy_norm)) + beta * b_habit * E_t(lambda s, ps: State.nux(s) /
(Definitions.Cy_norm(s, ps)))
loss_dict['eq_2'] = lambday_norm - beta * (
1.0 + iy) * E_t(lambda s, ps: Definitions.lambday_norm(s, ps) *
(1.0 / (1.0 + Definitions.piy_norm(s, ps))))
loss_dict['eq_3'] = lambday_norm - muy_norm * State.Zx(state) * (
(1.0 - kappa / 2.0 * (Iy_norm / State.Ix(state) - 1.0)**2.0) - kappa *
(Iy_norm / State.Ix(state) - 1.0) * Iy_norm / State.Ix(state)
) - beta * E_t(lambda s, ps: Definitions.muy_norm(s, ps) * State.Zx(
s) * kappa * (Definitions.Iy_norm(s, ps) / Iy_norm - 1.0) *
(Definitions.Iy_norm(s, ps) / Iy_norm)**2.0)
return loss_dict
def policy_step(prev_state, policy_state):
# coming from the lagged policy / definition
policy_step = tf.zeros_like(prev_state)
#policy_step = State.update(policy_step, "Kx",PolicyState.Ky(policy_state))
policy_step = State.update(policy_step, "Kx",
Definitions.Ky(prev_state, policy_state))
policy_step = State.update(
policy_step, "Cx", (Definitions.Cy_norm(prev_state, policy_state) +
Parameters.b_habit * State.Cx(prev_state)))
policy_step = State.update(
policy_step, "Ix", (Definitions.Iy_norm(prev_state, policy_state)))
policy_step = State.update(
policy_step, "Yx", Definitions.Yy_norm(prev_state, policy_state))
policy_step = State.update(
policy_step, "wx", Definitions.wy_norm(prev_state, policy_state))
policy_step = State.update(
policy_step, "nupx", Definitions.nupy_norm(prev_state,
policy_state))
policy_step = State.update(
policy_step, "pix", Definitions.piy_norm(prev_state, policy_state))
return State.update(policy_step, "ix",
Definitions.iy(prev_state, policy_state))
def equations(state, policy_state):
E_t = State.E_t_gen(state, policy_state)
loss_dict = {}
weight = 1.0
weight2 = 1.0
Ky = Definitions.Ky(state, policy_state)
iy = Definitions.iy(state, policy_state)
lambday_norm = Definitions.lambday_norm(state, policy_state)
Cy_norm = Definitions.Cy_norm(state, policy_state)
piy_norm = Definitions.piy_norm(state, policy_state)
pihashy_norm = Definitions.pihashy_norm(state, policy_state)
muy_norm = Definitions.muy_norm(state, policy_state)
Iy_norm = Definitions.Iy_norm(state, policy_state)
Ry_norm = Definitions.Ry_norm(state, policy_state)
h1y_norm = Definitions.h1y_norm(state, policy_state)
h2y_norm = Definitions.h2y_norm(state, policy_state)
whashy_norm = Definitions.whashy_norm(state, policy_state)
wy_norm = Definitions.wy_norm(state, policy_state)
Ny_norm = Definitions.Ny_norm(state, policy_state)
mcy_norm = Definitions.mcy_norm(state, policy_state)
x1y_norm = Definitions.x1y_norm(state, policy_state)
x2y_norm = Definitions.x2y_norm(state, policy_state)
Yy_norm = Definitions.Yy_norm(state, policy_state)
nupy_norm = Definitions.nupy_norm(state, policy_state)
#loss_dict['eq_1'] = 1600*E_t(lambda s, ps: Cy_norm * Definitions.Cy_norm(s, ps) * lambday_norm - Definitions.Cy_norm(s, ps) * State.nux(state) + Cy_norm * beta * b_habit * State.nux (s))
# original eq 1
loss_dict['eq_1'] = lambday_norm - (
State.nux(state) /
(Cy_norm)) + beta * b_habit * E_t(lambda s, ps: State.nux(s) /
(Definitions.Cy_norm(s, ps)))
loss_dict['eq_2'] = lambday_norm - beta * (
1.0 + iy) * E_t(lambda s, ps: Definitions.lambday_norm(s, ps) *
(1.0 / (1.0 + Definitions.piy_norm(s, ps))))
loss_dict['eq_3'] = lambday_norm - muy_norm * State.Zx(state) * (
(1.0 - kappa / 2.0 * (Iy_norm / State.Ix(state) - 1.0)**2.0) - kappa *
(Iy_norm / State.Ix(state) - 1.0) * Iy_norm / State.Ix(state)
) - beta * E_t(lambda s, ps: Definitions.muy_norm(s, ps) * State.Zx(
s) * kappa * (Definitions.Iy_norm(s, ps) / Iy_norm - 1.0) *
(Definitions.Iy_norm(s, ps) / Iy_norm)**2.0)
loss_dict['eq_4'] = muy_norm - beta * E_t(
lambda s, ps: Definitions.lambday_norm(s, ps) * Definitions.Ry_norm(
s, ps) + Definitions.muy_norm(s, ps) * (1.0 - delta_0))
loss_dict['eq_5'] = h1y_norm * whashy_norm**(
eps_w *
(1.0 + chi)) - State.nux(state) * State.psix(state) * wy_norm**(
eps_w * (1.0 + chi)) * Ny_norm**(1.0 + chi) - phi_w * beta * (
1.0 + piy_norm)**(-zeta_w * eps_w * (1.0 + chi)) * E_t(
lambda s, ps: (1.0 + Definitions.piy_norm(s, ps))**
(eps_w * (1.0 + chi)) * Definitions.whashy_norm(s, ps)**
(eps_w * (1.0 + chi)) * Definitions.h1y_norm(s, ps))
loss_dict[
'eq_6'] = h2y_norm * whashy_norm**eps_w - lambday_norm * wy_norm**eps_w * Ny_norm - phi_w * beta * (
1.0 - piy_norm)**(zeta_w * (1.0 - eps_w)) * E_t(
lambda s, ps: (1.0 + Definitions.piy_norm(s, ps))**
(eps_w - 1.0) * Definitions.whashy_norm(
s, ps)**eps_w * Definitions.h2y_norm(s, ps))
loss_dict['eq_7'] = whashy_norm * h2y_norm - (eps_w /
(eps_w - 1.0)) * h1y_norm
loss_dict['eq_8'] = wy_norm * Ny_norm - (
(1.0 - alpha) / alpha) * Ky * Ry_norm
loss_dict['eq_9'] = (1.0 - alpha) * State.Ax(
state) * mcy_norm * Ky**alpha - wy_norm * Ny_norm**alpha
loss_dict[
'eq_10'] = x1y_norm - lambday_norm * mcy_norm * Yy_norm - phi_p * beta * (
1.0 + piy_norm
)**(-zeta_p * eps_p) * E_t(lambda s, ps: (1.0 + Definitions.piy_norm(
s, ps))**eps_p * Definitions.x1y_norm(s, ps))
loss_dict['eq_11'] = x2y_norm - lambday_norm * Yy_norm - phi_p * beta * (
1.0 + piy_norm)**(zeta_p * (1.0 - eps_p)) * E_t(
lambda s, ps: (1.0 + Definitions.piy_norm(s, ps))**
(eps_p - 1.0) * Definitions.x2y_norm(s, ps))
loss_dict['eq_12'] = (1.0 + pihashy_norm) * x2y_norm - (
eps_p / (eps_p - 1.0)) * (1.0 + piy_norm) * x1y_norm
loss_dict['eq_13'] = Yy_norm - Cy_norm - b_habit * State.Cx(
state) - Iy_norm - State.Gx(state)
loss_dict['eq_14'] = State.Ax(state) * Ky**alpha * Ny_norm**(
1.0 - alpha) - F_prod - Yy_norm * nupy_norm
loss_dict['eq_15'] = nupy_norm * (1.0 + piy_norm)**(-eps_p) - (
1.0 - phi_p) * (1.0 + pihashy_norm)**(-eps_p) - (1.0 + State.pix(
state))**(-zeta_p * eps_p) * phi_p * State.nupx(state)
loss_dict['eq_16'] = (1.0 + piy_norm)**(
1.0 - eps_p) - (1.0 - phi_p) * (1.0 + pihashy_norm)**(1.0 - eps_p) - (
1.0 + State.pix(state))**(zeta_p * (1.0 - eps_p)) * phi_p
loss_dict['eq_17'] = wy_norm**(
1.0 - eps_w) - (1.0 - phi_w) * whashy_norm**(1.0 - eps_w) - (
1.0 + State.pix(state))**(zeta_w * (1.0 - eps_w)) * phi_w * (
1.0 + piy_norm)**(eps_w - 1.0) * State.wx(state)**(1.0 - eps_w)
return loss_dict