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VFiteration.f90
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VFiteration.f90
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!===== VF SINGLES =================================================================================
subroutine VFSingles()
use Globals
use GlobalsSingles
use Utils
implicit none
integer, parameter :: maxIter = 5000, showError = 500
real(8), parameter :: tolerance = 1.0d-4
integer :: iter, ind_a, ind_z, ind_g, ind_b
real(8) :: error_N_vf, error_U_vf, error_W_vf, error_J_vf, error_V_vf, error_N_pf, error_U_pf, error_W_pf, error_vf, error_pf
real(8), dimension(gp_a,gp_z) :: new_N_vf, new_N_pf, exp_N, new_W_vf, new_W_pf, exp_W
real(8), dimension(gp_a,gp_z,0:1) :: exp_U
real(8), dimension(gp_a,gp_z,gp_gamma,0:1) :: new_U_vf, new_J_vf, new_U_pf, new_V_vf
! Guess a value for global value functions
call random_number(N_vf) ! Assign random numbers to N_vf
call random_number(U_vf)
call random_number(W_vf)
call ValueFunctions(N_vf,U_vf,W_vf,J_vf,V_vf)
! Initialise new value functions
new_N_vf = 0.d0
new_U_vf = 0.d0
new_W_vf = 0.d0
new_J_vf = 0.d0
new_V_vf = 0.d0
! Initialise global policy functions
N_pf = 0.d0
U_pf = 0.d0
W_pf = 0.d0
! Initialise new policy functions
new_N_pf = 1.d0
new_U_pf = 1.d0
new_W_pf = 1.d0
! Value function iteration
do iter = 1, maxIter
! Compute expected values
call ExpectedValuesS(exp_N, exp_U, exp_W)
! Iterate over all states TODAY
do ind_a = 1, gp_a
do ind_z = 1, gp_z
call value_N(ind_a, exp_N(:,ind_z), new_N_pf(ind_a,ind_z), new_N_vf(ind_a,ind_z))
call value_W(ind_a, ind_z, exp_W(:,ind_z), &
new_W_pf(ind_a,ind_z), new_W_vf(ind_a,ind_z))
do ind_b = 0, 1
do ind_g = 1, gp_gamma
call value_U(ind_a, ind_z, ind_g, ind_b, exp_U(:,ind_z,ind_b), &
new_U_pf(ind_a,ind_z,ind_g,ind_b), new_U_vf(ind_a,ind_z,ind_g,ind_b))
end do
end do
end do
end do
! Compute new J and new V
call ValueFunctions(new_N_vf,new_U_vf,new_W_vf,new_J_vf,new_V_vf)
! Compute errors
error_N_vf = maxval(abs(new_N_vf-N_vf))
error_U_vf = maxval(abs(new_U_vf-U_vf))
error_W_vf = maxval(abs(new_W_vf-W_vf))
error_J_vf = maxval(abs(new_J_vf-J_vf))
error_V_vf = maxval(abs(new_V_vf-V_vf))
error_vf = max(error_N_vf, error_U_vf, error_W_vf, error_J_vf, error_V_vf)
error_N_pf = maxval(abs(new_N_pf-N_pf))
error_U_pf = maxval(abs(new_U_pf-U_pf))
error_W_pf = maxval(abs(new_W_pf-W_pf))
error_pf = max(error_N_pf, error_U_pf, error_W_pf)
! Update value functions and decision rules
N_vf = new_N_vf
U_vf = new_U_vf
W_vf = new_W_vf
J_vf = new_J_vf
V_vf = new_V_vf
N_pf = new_N_pf
U_pf = new_U_pf
W_pf = new_W_pf
if ((error_vf.lt.tolerance).and.(error_pf.lt.tolerance)) then
print *, "Value function iteration finished at iteration:", iter
print *, ""
exit
elseif (mod(iter,showError).eq.0) then
print *, "Current value function iteration errors, at iteration:", iter
print *, "Error for N is:", error_N_vf
print *, "Error for U is:", error_U_vf
print *, "Error for W is:", error_W_vf
print *, "Error for J is:", error_J_vf
print *, "Error for V is:", error_V_vf
print *, "Error for N's policy function is:", error_N_pf
print *, "Error for U's policy function is:", error_U_pf
print *, "Error for W's policy function is:", error_W_pf
print *, ""
end if
end do
end subroutine VFSingles
!===== EXPECTED VALUES SINGLES ====================================================================
subroutine ExpectedValuesS(exp_N, exp_U, exp_W)
! Computes auxiliary vector to store the expected value for each level of assets tomorrow
use Globals
use GlobalsSingles
implicit none
integer :: ind_z, ind_b, ind_ap, ind_zp, ind_gp, ind_bp
real(8) :: prob_N, prob_U, prob_W
real(8), dimension(gp_a,gp_z), intent(out) :: exp_N, exp_W
real(8), dimension(gp_a,gp_z,0:1), intent(out) :: exp_U
! Initialise arrays to 0
exp_N = 0.d0
exp_U = 0.d0
exp_W = 0.d0
! Iterate over values of z TODAY
do ind_z = 1, gp_z
! Iterate over all values of assets, z, and gammas tomorrow
do ind_ap = 1, gp_a
do ind_zp = 1, gp_z
do ind_gp = 1, gp_gamma
prob_N = z_trans(ind_z,ind_zp)*gamma_trans(ind_gp)
exp_N(ind_ap,ind_z) = exp_N(ind_ap,ind_z) + prob_N*(&
(lambda_n*V_vf(ind_ap,ind_zp,ind_gp,0)) + &
((1.d0-lambda_n)*J_vf(ind_ap,ind_zp,ind_gp,0)))
prob_W = prob_N
exp_W(ind_ap,ind_z) = exp_W(ind_ap,ind_z) + prob_W*(&
((1.d0-sigma)*V_vf(ind_ap,ind_zp,ind_gp,0)) + &
(sigma*(1.d0-lambda_u)*J_vf(ind_ap,ind_zp,ind_gp,1)) + &
(sigma*lambda_u*V_vf(ind_ap,ind_zp,ind_gp,1)))
! Iterate over values of UI TODAY and TOMORROW
do ind_b = 0, 1
do ind_bp = 0, 1
prob_U = prob_W*IB_trans(ind_b,ind_bp)
exp_U(ind_ap,ind_z,ind_b) = exp_U(ind_ap,ind_z,ind_b) + prob_U*(&
(lambda_u*V_vf(ind_ap,ind_zp,ind_gp,ind_bp)) + &
((1.d0-lambda_u)*J_vf(ind_ap,ind_zp,ind_gp,ind_bp)))
end do
end do
end do
end do
end do
end do
end subroutine ExpectedValuesS
!===== OLF ========================================================================================
subroutine value_N(ind_a, aux_exp, pf, vf)
use Globals
use GlobalsSingles
use Utils
implicit none
integer, intent(in) :: ind_a
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_N, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_N(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_N = u(cons) + beta*aux_inter
end function valor_N
end subroutine value_N
!===== EMPLOYED ===================================================================================
subroutine value_W(ind_a, ind_z, aux_exp, pf, vf)
use Globals
use GlobalsSingles
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + (1.d0-tau)*wage*z_values(ind_z)
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_W, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_W(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_W = u(cons) - alpha + beta*aux_inter
end function valor_W
end subroutine value_W
!===== EMPLOYED ===================================================================================
subroutine value_U(ind_a, ind_z, ind_g, ind_b, aux_exp, pf, vf)
use Globals
use GlobalsSingles
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z, ind_g, ind_b
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + (1.d0-tau)*real(ind_b)*benefits(z_values(ind_z))
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_U, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_U(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_U = u(cons) - gamma_values(ind_g) + beta*aux_inter
end function valor_U
end subroutine value_U
!===== VF MARRIED =================================================================================
subroutine VFMarried()
use Globals
use GlobalsMarried
use Utils
implicit none
integer, parameter :: maxIter = 5000, showError = 500
real(8), parameter :: tolerance = 1.0d-04
integer :: iter, ind_a, ind_z, ind_b, ind_g, ind_b_f, ind_g_f
real(8) :: error_WW_vf, error_WU_vf, error_WN_vf, error_UW_vf, error_UU_vf, error_UN_vf, &
error_NW_vf, error_NU_vf, error_NN_vf, error_WW_pf, error_WU_pf, error_WN_pf, &
error_UW_pf, error_UU_pf, error_UN_pf, error_NW_pf, error_NU_pf, error_NN_pf, &
error_JJ_vf, error_VJ_vf, error_JV_vf, error_VV_vf, error_vf, error_pf
real(8), dimension(gp_a,gp_z2) :: new_NN_vf, new_NN_pf, new_WW_vf, new_WW_pf, new_WN_vf, &
new_WN_pf, new_NW_vf, new_NW_pf, &
exp_WW, exp_WN, exp_NN, exp_NW
real(8), dimension(gp_a,gp_z2,0:1) :: exp_WU, exp_UW, exp_NU, exp_UN
real(8), dimension(gp_a,gp_z2,0:1,0:1) :: exp_UU
real(8), dimension(gp_a,gp_z2,gp_gamma,0:1) :: new_WU_vf, new_WU_pf, new_UW_vf, new_UW_pf, &
new_NU_vf, new_NU_pf, new_UN_vf, new_UN_pf
real(8), dimension(gp_a,gp_z2,gp_gamma,gp_gamma,0:1,0:1) :: new_UU_vf, new_UU_pf, new_JJ_vf, &
new_VJ_vf, new_JV_vf, new_VV_vf
! Guess a value for global value functions
call random_number(WW_vf)
call random_number(WU_vf)
call random_number(WN_vf)
call random_number(UW_vf)
call random_number(UU_vf)
call random_number(UN_vf)
call random_number(NW_vf)
call random_number(NU_vf)
call random_number(NN_vf)
call ValueFunctions(WW_vf,WU_vf,WN_vf,UW_vf,UU_vf,UN_vf,NW_vf,NU_vf,NN_vf,JJ_vf,VJ_vf,JV_vf,VV_vf)
! Initialise new value functions
new_WW_vf = 0.d0
new_WU_vf = 0.d0
new_WN_vf = 0.d0
new_UW_vf = 0.d0
new_UU_vf = 0.d0
new_UN_vf = 0.d0
new_NW_vf = 0.d0
new_NU_vf = 0.d0
new_NN_vf = 0.d0
! Initialise global policy functions
WW_pf = 0.d0
WU_pf = 0.d0
WN_pf = 0.d0
UW_pf = 0.d0
UU_pf = 0.d0
UN_pf = 0.d0
NW_pf = 0.d0
NU_pf = 0.d0
NN_pf = 0.d0
! Initialise new policy functions
new_WW_pf = 1.d0
new_WU_pf = 1.d0
new_WN_pf = 1.d0
new_UW_pf = 1.d0
new_UU_pf = 1.d0
new_UN_pf = 1.d0
new_NW_pf = 1.d0
new_NU_pf = 1.d0
new_NN_pf = 1.d0
! Value function iteration
do iter = 1, maxIter
! Compute expected values
call ExpectedValuesM(exp_WW,exp_WU,exp_WN,exp_UW,exp_UU,exp_UN,exp_NW,exp_NU,exp_NN)
! Iterate over all states TODAY
do ind_a = 1, gp_a
do ind_z = 1, gp_z2
call value_NN(ind_a, exp_NN(:,ind_z), new_NN_pf(ind_a,ind_z), new_NN_vf(ind_a,ind_z))
call value_WN(ind_a, ind_z, exp_WN(:,ind_z), &
new_WN_pf(ind_a,ind_z), new_WN_vf(ind_a,ind_z))
call value_NW(ind_a, ind_z, exp_NW(:,ind_z), &
new_NW_pf(ind_a,ind_z), new_NW_vf(ind_a,ind_z))
call value_WW(ind_a, ind_z, exp_WW(:,ind_z), &
new_WW_pf(ind_a,ind_z), new_WW_vf(ind_a,ind_z))
do ind_b = 0, 1
do ind_g = 1, gp_gamma
call value_NU(ind_a, ind_z, ind_g, ind_b, exp_NU(:,ind_z,ind_b), &
new_NU_pf(ind_a,ind_z,ind_g,ind_b), new_NU_vf(ind_a,ind_z,ind_g,ind_b))
call value_UN(ind_a, ind_z, ind_g, ind_b, exp_UN(:,ind_z,ind_b), &
new_UN_pf(ind_a,ind_z,ind_g,ind_b), new_UN_vf(ind_a,ind_z,ind_g,ind_b))
call value_WU(ind_a, ind_z, ind_g, ind_b, exp_WU(:,ind_z,ind_b), &
new_WU_pf(ind_a,ind_z,ind_g,ind_b), new_WU_vf(ind_a,ind_z,ind_g,ind_b))
call value_UW(ind_a, ind_z, ind_g, ind_b, exp_UW(:,ind_z,ind_b), &
new_UW_pf(ind_a,ind_z,ind_g,ind_b), new_UW_vf(ind_a,ind_z,ind_g,ind_b))
do ind_b_f = 0, 1
do ind_g_f = 1, gp_gamma
call value_UU(ind_a, ind_z, ind_g, ind_g_f, ind_b, ind_b_f, exp_UU(:,ind_z,ind_b,ind_b_f),&
new_UU_pf(ind_a,ind_z,ind_g,ind_g_f,ind_b,ind_b_f), &
new_UU_vf(ind_a,ind_z,ind_g,ind_g_f,ind_b,ind_b_f))
end do
end do
end do
end do
end do
end do
! Compute new JJ, VJ, JV, and VV
call ValueFunctions(new_WW_vf,new_WU_vf,new_WN_vf,new_UW_vf,new_UU_vf,new_UN_vf,new_NW_vf,&
new_NU_vf,new_NN_vf,new_JJ_vf,new_VJ_vf,new_JV_vf,new_VV_vf)
! Compute errors
error_WW_vf = maxval(abs(new_WW_vf-WW_vf))
error_WU_vf = maxval(abs(new_WU_vf-WU_vf))
error_WN_vf = maxval(abs(new_WN_vf-WN_vf))
error_UW_vf = maxval(abs(new_UW_vf-UW_vf))
error_UU_vf = maxval(abs(new_UU_vf-UU_vf))
error_UN_vf = maxval(abs(new_UN_vf-UN_vf))
error_NW_vf = maxval(abs(new_NW_vf-NW_vf))
error_NU_vf = maxval(abs(new_NU_vf-NU_vf))
error_NN_vf = maxval(abs(new_NN_vf-NN_vf))
error_JJ_vf = maxval(abs(new_JJ_vf-JJ_vf))
error_VJ_vf = maxval(abs(new_VJ_vf-VJ_vf))
error_JV_vf = maxval(abs(new_JV_vf-JV_vf))
error_VV_vf = maxval(abs(new_VV_vf-VV_vf))
error_vf = max(error_WW_vf, error_WU_vf, error_WN_vf, error_UW_vf, error_UU_vf, error_UN_vf, &
error_NW_vf, error_NU_vf, error_NN_vf, error_JJ_vf, error_VJ_vf, error_JV_vf, &
error_VV_vf)
error_WW_pf = maxval(abs(new_WW_pf-WW_pf))
error_WU_pf = maxval(abs(new_WU_pf-WU_pf))
error_WN_pf = maxval(abs(new_WN_pf-WN_pf))
error_UW_pf = maxval(abs(new_UW_pf-UW_pf))
error_UU_pf = maxval(abs(new_UU_pf-UU_pf))
error_UN_pf = maxval(abs(new_UN_pf-UN_pf))
error_NW_pf = maxval(abs(new_NW_pf-NW_pf))
error_NU_pf = maxval(abs(new_NU_pf-NU_pf))
error_NN_pf = maxval(abs(new_NN_pf-NN_pf))
error_pf = max(error_WW_pf, error_WU_pf, error_WN_pf, error_UW_pf, error_UU_pf, error_UN_pf, &
error_NW_pf, error_NU_pf, error_NN_pf)
! Update value functions and decision rules
WW_vf = new_WW_vf
WU_vf = new_WU_vf
WN_vf = new_WN_vf
UW_vf = new_UW_vf
UU_vf = new_UU_vf
UN_vf = new_UN_vf
NW_vf = new_NW_vf
NU_vf = new_NU_vf
NN_vf = new_NN_vf
JJ_vf = new_JJ_vf
VJ_vf = new_VJ_vf
JV_vf = new_JV_vf
VV_vf = new_VV_vf
WW_pf = new_WW_pf
WU_pf = new_WU_pf
WN_pf = new_WN_pf
UW_pf = new_UW_pf
UU_pf = new_UU_pf
UN_pf = new_UN_pf
NW_pf = new_NW_pf
NU_pf = new_NU_pf
NN_pf = new_NN_pf
if ((error_vf.lt.tolerance).and.(error_pf.lt.tolerance)) then
print *, "Value function iteration finished at iteration:", iter
print *, ""
exit
elseif (mod(iter,showError).eq.0) then
print *, "Current value function iteration errors, at iteration:", iter
print *, "Error for WW is:", error_WW_vf
print *, "Error for WU is:", error_WU_vf
print *, "Error for WN is:", error_WN_vf
print *, "Error for UW is:", error_UW_vf
print *, "Error for UU is:", error_UU_vf
print *, "Error for UN is:", error_UN_vf
print *, "Error for NW is:", error_NW_vf
print *, "Error for NU is:", error_NU_vf
print *, "Error for NN is:", error_NN_vf
print *, "Error for JJ is:", error_JJ_vf
print *, "Error for VJ is:", error_VJ_vf
print *, "Error for JV is:", error_JV_vf
print *, "Error for VV is:", error_VV_vf
print *, "Error for WW's policy function is:", error_WW_pf
print *, "Error for WU's policy function is:", error_WU_pf
print *, "Error for WN's policy function is:", error_WN_pf
print *, "Error for UW's policy function is:", error_UW_pf
print *, "Error for UU's policy function is:", error_UU_pf
print *, "Error for UN's policy function is:", error_UN_pf
print *, "Error for NW's policy function is:", error_NW_pf
print *, "Error for NU's policy function is:", error_NU_pf
print *, "Error for NN's policy function is:", error_NN_pf
print *, ""
end if
end do
end subroutine VFMarried
!===== EXPECTED VALUES MARRIED ====================================================================
subroutine ExpectedValuesM(exp_WW,exp_WU,exp_WN,exp_UW,exp_UU,exp_UN,exp_NW,exp_NU,exp_NN)
use Globals
use GlobalsMarried
implicit none
integer :: ind_z, ind_b_f, ind_ap, ind_zp, ind_gp_m, ind_gp_f, ind_b, ind_bp, ind_bp_f
real(8) :: prob_WW, prob_WU, prob_WN, prob_UW, prob_UU, prob_UN, prob_NW, prob_NU, prob_NN
real(8), dimension(gp_a,gp_z2), intent(out) :: exp_WW, exp_WN, exp_NN, exp_NW
real(8), dimension(gp_a,gp_z2,0:1), intent(out) :: exp_WU, exp_UW, exp_NU, exp_UN
real(8), dimension(gp_a,gp_z2,0:1,0:1), intent(out) :: exp_UU
! Initialise arrays to 0
exp_WW = 0.d0
exp_WU = 0.d0
exp_WN = 0.d0
exp_UW = 0.d0
exp_UU = 0.d0
exp_UN = 0.d0
exp_NW = 0.d0
exp_NU = 0.d0
exp_NN = 0.d0
! Iterate over values of z TODAY
do ind_z = 1, gp_z2
! Iterate over values of assets, z, and gammas TOMORROW
do ind_ap = 1, gp_a
do ind_zp = 1, gp_z2
do ind_gp_m = 1, gp_gamma
do ind_gp_f = 1, gp_gamma
prob_NN = z_trans(ind_z,ind_zp)*gamma_trans(male,ind_gp_m)*gamma_trans(female,ind_gp_f)
exp_NN(ind_ap,ind_z) = exp_NN(ind_ap,ind_z) + prob_NN*( &
(lambda_n(male)*lambda_n(female)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
(lambda_n(male)*(1.d0-lambda_n(female))*VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
((1.d0-lambda_n(male))*lambda_n(female)*JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
((1.d0-lambda_n(male))*(1.d0-lambda_n(female))*JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0)))
prob_WN = prob_NN
exp_WN(ind_ap,ind_z) = exp_WN(ind_ap,ind_z) + prob_WN*( &
((1.d0-sigma(male))*lambda_n(female)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
((1.d0-sigma(male))*(1.d0-lambda_n(female))*VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
(sigma(male)*lambda_u(male)*lambda_n(female)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,0))+&
(sigma(male)*lambda_u(male)*(1.d0-lambda_n(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,0))+&
(sigma(male)*(1.d0-lambda_u(male))*lambda_n(female)*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,0))+&
(sigma(male)*(1.d0-lambda_u(male))*(1.d0-lambda_n(female))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,0)))
prob_NW = prob_WN
exp_NW(ind_ap,ind_z) = exp_NW(ind_ap,ind_z) + prob_NW*( &
((1.d0-sigma(female))*lambda_n(male)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
((1.d0-sigma(female))*(1.d0-lambda_n(male))*JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
(sigma(female)*lambda_u(female)*lambda_n(male)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,1))+&
(sigma(female)*lambda_u(female)*(1.d0-lambda_n(male))*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,1))+&
(sigma(female)*(1.d0-lambda_u(female))*lambda_n(male)*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,1))+&
(sigma(female)*(1.d0-lambda_u(female))*(1.d0-lambda_n(male))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,1)))
prob_WW = prob_NW
exp_WW(ind_ap,ind_z) = exp_WW(ind_ap,ind_z) + prob_WW*( &
((1.d0-sigma(male))*(1.d0-sigma(female))*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,0))+&
((1.d0-sigma(male))*sigma(female)*lambda_u(female)*&
VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,1))+&
((1.d0-sigma(male))*sigma(female)*(1.d0-lambda_u(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,1))+&
(sigma(male)*lambda_u(male)*(1.d0-sigma(female))*&
VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,0))+&
(sigma(male)*lambda_u(male)*sigma(female)*lambda_u(female)*&
VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,1))+&
(sigma(male)*lambda_u(male)*sigma(female)*(1.d0-lambda_u(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,1))+&
(sigma(male)*(1.d0-lambda_u(male))*(1.d0-sigma(female))*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,0))+&
(sigma(male)*(1.d0-lambda_u(male))*sigma(female)*lambda_u(female)*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,1))+&
(sigma(male)*(1.d0-lambda_u(male))*sigma(female)*(1.d0-lambda_u(female))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,1)))
! Iterate over values of UI TODAY and TOMORROW
do ind_b = 0, 1
do ind_bp = 0, 1
prob_NU = prob_WW*IB_trans(ind_b,ind_bp)
exp_NU(ind_ap,ind_z,ind_b) = exp_NU(ind_ap,ind_z,ind_b) + prob_NU*( &
(lambda_n(male)*lambda_u(female)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,ind_bp))+&
(lambda_n(male)*(1.d0-lambda_u(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,ind_bp))+&
((1.d0-lambda_n(male))*lambda_u(female)*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,ind_bp))+&
((1.d0-lambda_n(male))*(1.d0-lambda_u(female))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,ind_bp)))
prob_UN = prob_NU
exp_UN(ind_ap,ind_z,ind_b) = exp_UN(ind_ap,ind_z,ind_b) + prob_UN*( &
(lambda_n(female)*lambda_u(male)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,0))+&
(lambda_n(female)*(1.d0-lambda_u(male))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,0))+&
((1.d0-lambda_n(female))*lambda_u(male)*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,0))+&
((1.d0-lambda_n(female))*(1.d0-lambda_u(male))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,0)))
prob_WU = prob_NU
exp_WU(ind_ap,ind_z,ind_b) = exp_WU(ind_ap,ind_z,ind_b) + prob_WU*( &
((1.d0-sigma(male))*lambda_u(female)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,ind_bp))+&
((1.d0-sigma(male))*(1.d0-lambda_u(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,0,ind_bp))+&
(sigma(male)*lambda_u(male)*lambda_u(female)*&
VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,ind_bp))+&
(sigma(male)*lambda_u(male)*(1.d0-lambda_u(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,ind_bp))+&
(sigma(male)*(1.d0-lambda_u(male))*lambda_u(female)*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,ind_bp))+&
(sigma(male)*(1.d0-lambda_u(male))*(1.d0-lambda_u(female))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,1,ind_bp)))
prob_UW = prob_UN
exp_UW(ind_ap,ind_z,ind_b) = exp_UW(ind_ap,ind_z,ind_b) + prob_UW*( &
((1.d0-sigma(female))*lambda_u(male)*VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,0))+&
((1.d0-sigma(female))*(1.d0-lambda_u(male))*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,0))+&
(sigma(female)*lambda_u(female)*lambda_u(male)*&
VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,1))+&
(sigma(female)*lambda_u(female)*(1.d0-lambda_u(male))*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,1))+&
(sigma(female)*(1.d0-lambda_u(female))*lambda_u(male)*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,1))+&
(sigma(female)*(1.d0-lambda_u(female))*(1.d0-lambda_u(male))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,1)))
! Iterate over value of UI TODAY and TOMORROW for both
do ind_b_f = 0, 1
do ind_bp_f = 0, 1
prob_UU = prob_NU*IB_trans(ind_b_f,ind_bp_f)
exp_UU(ind_ap,ind_z,ind_b,ind_b_f) = exp_UU(ind_ap,ind_z,ind_b,ind_b_f) + prob_UU*( &
(lambda_u(male)*lambda_u(female)*&
VV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,ind_bp_f))+&
(lambda_u(male)*(1.d0-lambda_u(female))*&
VJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,ind_bp_f))+&
((1.d0-lambda_u(male))*lambda_u(female)*&
JV_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,ind_bp_f))+&
((1.d0-lambda_u(male))*(1.d0-lambda_u(female))*&
JJ_vf(ind_ap,ind_zp,ind_gp_m,ind_gp_f,ind_bp,ind_bp_f)))
end do
end do
end do
end do
end do
end do
end do
end do
end do
end subroutine ExpectedValuesM
!===== NN =========================================================================================
subroutine value_NN(ind_a, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_NN, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_NN(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_NN = u(cons) + beta*aux_inter
end function valor_NN
end subroutine value_NN
!===== NU =========================================================================================
subroutine value_NU(ind_a, ind_z, ind_g_f, ind_b_f, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z, ind_g_f, ind_b_f
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*real(ind_b_f)*benefits(z_values(female,ind_z))
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_NU, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_NU(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_NU = u(cons) - gamma_values(female,ind_g_f) + beta*aux_inter
end function valor_NU
end subroutine value_NU
!===== NW =========================================================================================
subroutine value_NW(ind_a, ind_z, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*wage*z_values(female,ind_z)
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_NW, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_NW(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_NW = u(cons) - alpha(female) + beta*aux_inter
end function valor_NW
end subroutine value_NW
!===== UN =========================================================================================
subroutine value_UN(ind_a, ind_z, ind_g_m, ind_b_m, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z, ind_g_m, ind_b_m
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*real(ind_b_m)*benefits(z_values(male,ind_z))
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_UN, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_UN(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_UN = u(cons) - gamma_values(male,ind_g_m) + beta*aux_inter
end function valor_UN
end subroutine value_UN
!===== UU =========================================================================================
subroutine value_UU(ind_a, ind_z, ind_g_m, ind_g_f, ind_b_m, ind_b_f, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z, ind_g_m, ind_g_f, ind_b_m, ind_b_f
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*real(ind_b_m)*benefits(z_values(male,ind_z)) + &
(1.d0-tau)*real(ind_b_f)*benefits(z_values(female,ind_z))
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_UU, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_UU(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_UU = u(cons) - gamma_values(male,ind_g_m) - gamma_values(female,ind_g_f) + beta*aux_inter
end function valor_UU
end subroutine value_UU
!===== UW =========================================================================================
subroutine value_UW(ind_a, ind_z, ind_g_m, ind_b_m, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z, ind_g_m, ind_b_m
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*real(ind_b_m)*benefits(z_values(male,ind_z)) + &
(1.d0-tau)*wage*z_values(female,ind_z)
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_UW, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_UW(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_UW = u(cons) - gamma_values(male,ind_g_m) - alpha(female) + beta*aux_inter
end function valor_UW
end subroutine value_UW
!===== WN =========================================================================================
subroutine value_WN(ind_a, ind_z, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*wage*z_values(male,ind_z)
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_WN, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_WN(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_WN = u(cons) - alpha(male) + beta*aux_inter
end function valor_WN
end subroutine value_WN
!===== WU =========================================================================================
subroutine value_WU(ind_a, ind_z, ind_g_f, ind_b_f, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z, ind_g_f, ind_b_f
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*real(ind_b_f)*benefits(z_values(female,ind_z)) + &
(1.d0-tau)*wage*z_values(male,ind_z)
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_WU, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_WU(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_WU = u(cons) - gamma_values(female,ind_g_f) - alpha(male) + beta*aux_inter
end function valor_WU
end subroutine value_WU
!===== WW =========================================================================================
subroutine value_WW(ind_a, ind_z, aux_exp, pf, vf)
use Globals
use GlobalsMarried
use Utils
implicit none
integer, intent(in) :: ind_a, ind_z
real(8) :: aux_max_a, income
real(8), dimension(gp_a), intent(in) :: aux_exp
real(8), intent(out) :: pf, vf
! Compute income
income = (1.d0+int_rate)*a_values(ind_a) + T + &
(1.d0-tau)*wage*z_values(male,ind_z) + &
(1.d0-tau)*wage*z_values(female,ind_z)
! Compute upper bound for assets
aux_max_a = min(max_a-tiny, max(min_a, income))
! Find level of assets that maximised Bellman Equation
call golden_method(valor_WW, min_a, aux_max_a, pf, vf)
CONTAINS
real(8) function valor_WW(ap)
implicit none
real(8), intent(in) :: ap
real(8) :: aux_inter, cons
! Compute interpolated value for tomorrow
aux_inter = my_inter(a_values, aux_exp, gp_a, ap)
! Compute consumption
cons = income - ap
valor_WW = u(cons) - alpha(male) - alpha(female) - alpha(3) + beta*aux_inter
end function valor_WW
end subroutine value_WW