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
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)
#original equation
loss_dict['eq_1'] = 1000 * E_t(
lambda s, ps: PolicyState.Cy(policy_state) * PolicyState.Cy(
ps) * PolicyState.lambday(policy_state) - PolicyState.Cy(
ps) * State.nux(state) + PolicyState.Cy(
policy_state) * beta * b_habit * State.nux(s))
# original eq 1
#loss_dict['eq_1'] = PolicyState.lambday(policy_state) - (State.nux(state) / (PolicyState.Cy(policy_state) )) + beta * b_habit * E_t(lambda s, ps: State.nux (s) / (PolicyState.Cy(ps)))
# original eq 1 1/C
#loss_dict['eq_1'] = PolicyState.lambday(policy_state) - (State.nux(state) / (PolicyState.Cy(policy_state) )) + beta * b_habit * E_t(lambda s, ps: State.nux (s) / ((weight*(PolicyState.Cy(ps)) + (1-weight)*0.025)))
## debug # replace (PolicyState.Cy(ps)) with (weight*(PolicyState.Cy(ps)) + (1-weight)*0.025) -- E()
#loss_dict['eq_1'] = E_t(lambda s, ps: PolicyState.Cy(policy_state) * (weight*(PolicyState.Cy(ps)) + (1-weight)*0.025) * PolicyState.lambday(policy_state) - (weight*(PolicyState.Cy(ps)) + (1-weight)*0.025) * State.nux(state) + PolicyState.Cy(policy_state) * beta * b_habit * State.nux (s))
#loss_dict['eq_2'] = PolicyState.lambday(policy_state) - beta * (1.0 + PolicyState.iy(policy_state)) * E_t(lambda s, ps: PolicyState.lambday(ps)*(1.0/(1.0 + PolicyState.piy(ps) )))
# debug: replace PolicyState.lambday(ps) with (weight*(PolicyState.lambday(ps)) + (1-weight)*2.6206)
loss_dict['eq_2'] = PolicyState.lambday(policy_state) - beta * (
1.0 + iy) * E_t(lambda s, ps: (weight * (PolicyState.lambday(ps)) +
(1 - weight) * 2.6206) *
(1.0 / (1.0 + PolicyState.piy(ps))))
loss_dict['eq_3'] = PolicyState.lambday(
policy_state
) - PolicyState.muy(policy_state) * State.Zx(state) * (
(1.0 - kappa / 2.0 *
(PolicyState.Iy(policy_state) / State.Ix(state) - 1.0)**2.0) - kappa *
(PolicyState.Iy(policy_state) / State.Ix(state) - 1.0) *
PolicyState.Iy(policy_state) / State.Ix(state)) - beta * E_t(
lambda s, ps: (weight * (PolicyState.muy(ps)) +
(1 - weight) * 2.6206) * State.Zx(s) * kappa *
((weight2 * (PolicyState.Iy(ps)) +
(1 - weight2) * 0.1881) / PolicyState.Iy(policy_state) - 1.0) *
((weight2 * (PolicyState.Iy(ps)) +
(1 - weight2) * 0.1881) / PolicyState.Iy(policy_state))**2.0)
# debug: replace PolicyState.muy(ps) with (weight*(PolicyState.muy(ps)) + (1-weight)*2.6206)
loss_dict['eq_4'] = PolicyState.muy(policy_state) - beta * E_t(
lambda s, ps: PolicyState.lambday(ps) * PolicyState.Ry(ps) +
(weight * (PolicyState.muy(ps)) +
(1 - weight) * 2.6206) * (1.0 - delta_0))
loss_dict['eq_5'] = 10 * (
PolicyState.h1y(policy_state) * PolicyState.whashy(policy_state)**
(eps_w * (1.0 + chi)) -
State.nux(state) * State.psix(state) * PolicyState.wy(policy_state)**
(eps_w * (1.0 + chi)) * PolicyState.Ny(policy_state)**(1.0 + chi) -
phi_w * beta * (1.0 + PolicyState.piy(policy_state))**
(-zeta_w * eps_w *
(1.0 + chi)) * E_t(lambda s, ps: (1.0 + PolicyState.piy(ps))**
(eps_w * (1.0 + chi)) * PolicyState.whashy(ps)**
(eps_w * (1.0 + chi)) * PolicyState.h1y(ps)))
loss_dict['eq_6'] = 10 * (
PolicyState.h2y(policy_state) * PolicyState.whashy(policy_state)**eps_w
- PolicyState.lambday(policy_state) * PolicyState.wy(policy_state)**
eps_w * PolicyState.Ny(policy_state) - phi_w * beta *
(1.0 - PolicyState.piy(policy_state))**(zeta_w * (1.0 - eps_w)) *
E_t(lambda s, ps: (1.0 + PolicyState.piy(ps))**(eps_w - 1.0) *
PolicyState.whashy(ps)**eps_w * PolicyState.h2y(ps)))
loss_dict['eq_7'] = PolicyState.whashy(policy_state) * PolicyState.h2y(
policy_state) - (eps_w / (eps_w - 1.0)) * PolicyState.h1y(policy_state)
loss_dict['eq_8'] = PolicyState.wy(policy_state) * PolicyState.Ny(
policy_state) - (
(1.0 - alpha) / alpha) * Ky * PolicyState.Ry(policy_state)
loss_dict['eq_9'] = (1.0 - alpha) * State.Ax(state) * PolicyState.mcy(
policy_state) * Ky**alpha - PolicyState.wy(
policy_state) * PolicyState.Ny(policy_state)**alpha
loss_dict['eq_10'] = 100 * (
PolicyState.x1y(policy_state) - PolicyState.lambday(policy_state) *
PolicyState.mcy(policy_state) * PolicyState.Yy(policy_state) -
phi_p * beta *
(1.0 + PolicyState.piy(policy_state))**(-zeta_p * eps_p) *
E_t(lambda s, ps:
(1.0 + PolicyState.piy(ps))**eps_p * PolicyState.x1y(ps)))
loss_dict['eq_11'] = 10 * (
PolicyState.x2y(policy_state) - PolicyState.lambday(policy_state) *
PolicyState.Yy(policy_state) - phi_p * beta *
(1.0 + PolicyState.piy(policy_state))**
(zeta_p *
(1.0 - eps_p)) * E_t(lambda s, ps: (1.0 + PolicyState.piy(ps))**
(eps_p - 1.0) * PolicyState.x2y(ps)))
loss_dict['eq_12'] = 100 * (
(1.0 + PolicyState.pihashy(policy_state)) *
PolicyState.x2y(policy_state) - (eps_p / (eps_p - 1.0)) *
(1.0 + PolicyState.piy(policy_state)) * PolicyState.x1y(policy_state))
loss_dict['eq_13'] = PolicyState.Yy(policy_state) - PolicyState.Cy(
policy_state) - b_habit * State.Cx(state) - PolicyState.Iy(
policy_state) - State.Gx(state)
#original Eq.
#loss_dict['eq_14'] = PolicyState.Ky(policy_state) - State.Zx(state) * (1.0 - kappa/2.0 * (PolicyState.Iy(policy_state)/State.Ix(state) - 1.0 )**2.0) * PolicyState.Iy(policy_state) - (1.0 - delta_0) * State.Kx(state)
loss_dict['eq_14'] = State.Ax(state) * Ky**alpha * PolicyState.Ny(
policy_state)**(1.0 - alpha) - F_prod - PolicyState.Yy(
policy_state) * PolicyState.nupy(policy_state)
loss_dict['eq_15'] = PolicyState.nupy(policy_state) * (
1.0 + PolicyState.piy(policy_state))**(-eps_p) - (1.0 - phi_p) * (
1.0 + PolicyState.pihashy(policy_state))**(-eps_p) - (
1.0 + State.pix(state))**(-zeta_p *
eps_p) * phi_p * State.nupx(state)
loss_dict['eq_16'] = (1.0 + PolicyState.piy(policy_state))**(
1.0 -
eps_p) - (1.0 - phi_p) * (1.0 + PolicyState.pihashy(policy_state))**(
1.0 - eps_p) - (1.0 + State.pix(state))**(zeta_p *
(1.0 - eps_p)) * phi_p
loss_dict['eq_17'] = PolicyState.wy(policy_state)**(1.0 - eps_w) - (
1.0 - phi_w) * PolicyState.whashy(policy_state)**(1.0 - eps_w) - (
1.0 + State.pix(state))**(zeta_w * (1.0 - eps_w)) * phi_w * (
1.0 + PolicyState.piy(policy_state))**(
eps_w - 1.0) * State.wx(state)**(1.0 - eps_w)
#original Eq., substituted
#loss_dict['eq_18'] = PolicyState.iy(policy_state) - tf.math.maximum((1.0 - rho_i) * i_ss + rho_i * State.ix(state) + (1.0 - rho_i) * (phi_pi * (PolicyState.piy(policy_state) - pi_ss) + phi_y * (tf.math.log(PolicyState.Yy(policy_state)) - tf.math.log(State.Yx(state))) + State.mx(state)), i_LB )
return loss_dict