def SS_TPI_firstdoughnutring(guesses, winit, rinit, BQinit, T_H_init, initial_b, factor_ss, j, tax_params, parameters, theta, tau_bq):
'''
Solves the first entries of the upper triangle of the twist doughnut. This is
separate from the main TPI function because the the values of b and n are scalars,
so it is easier to just have a separate function for these cases.
Inputs:
guesses = guess for b and n (2x1 list)
winit = initial wage rate (scalar)
rinit = initial rental rate (scalar)
BQinit = initial aggregate bequest (scalar)
T_H_init = initial lump sum tax (scalar)
initial_b = initial distribution of capital (SxJ array)
factor_ss = steady state scaling factor (scalar)
j = which ability type is being solved for (scalar)
parameters = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rates (Jx1 array)
Output:
euler errors (2x1 list)
'''
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = parameters
analytical_mtrs, etr_params, mtrx_params, mtry_params = tax_params
b2 = float(guesses[0])
n1 = float(guesses[1])
b1 = float(initial_b[-2, j])
# Euler 1 equations
tax1_params = (J, S, retire, etr_params[-1,0,:], h_wealth, p_wealth, m_wealth, tau_payroll)
tax1 = tax.total_taxes(rinit, b1, winit, e[-1, j], n1, BQinit, lambdas[
j], factor_ss, T_H_init, j, 'TPI_scalar', False, tax1_params, theta, tau_bq)
cons1 = household.get_cons(
rinit, b1, winit, e[-1, j], n1, BQinit, lambdas[j], b2, parameters, tax1)
bequest_ut = rho[-1] * np.exp(-sigma * g_y) * chi_b[-1, j] * b2 ** (-sigma)
error1 = household.marg_ut_cons(cons1, parameters) - bequest_ut
# Euler 2 equations
income2 = (rinit * b1 + winit * e[-1, j] * n1) * factor_ss
deriv2 = 1 - tau_payroll - tax.MTR_labor(rinit, b1, winit, e[-1, j], n1, factor_ss, analytical_mtrs, etr_params[-1,0,:], mtrx_params[-1,0,:])
error2 = household.marg_ut_cons(cons1, parameters) * winit * \
e[-1, j] * deriv2 - household.marg_ut_labor(n1, chi_n[-1], parameters)
if n1 <= 0 or n1 >= 1:
error2 += 1e12
if b2 <= 0:
error1 += 1e12
if cons1 <= 0:
error1 += 1e12
return [error1] + [error2]
def SS_TPI_firstdoughnutring(guesses, winit, rinit, BQinit, T_H_init,
initial_b, factor_ss, j, parameters, theta,
tau_bq):
'''
Solves the first entries of the upper triangle of the twist doughnut. This is
separate from the main TPI function because the the values of b and n are scalars,
so it is easier to just have a separate function for these cases.
Inputs:
guesses = guess for b and n (2x1 list)
winit = initial wage rate (scalar)
rinit = initial rental rate (scalar)
BQinit = initial aggregate bequest (scalar)
T_H_init = initial lump sum tax (scalar)
initial_b = initial distribution of capital (SxJ array)
factor_ss = steady state scaling factor (scalar)
j = which ability type is being solved for (scalar)
parameters = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rates (Jx1 array)
Output:
euler errors (2x1 list)
'''
b2 = float(guesses[0])
n1 = float(guesses[1])
b1 = float(initial_b[-2, j])
# Euler 1 equations
tax1 = tax.total_taxes(rinit, b1, winit, e[-1, j], n1, BQinit, lambdas[j],
factor_ss, T_H_init, j, 'TPI_scalar', False,
parameters, theta, tau_bq)
cons1 = household.get_cons(rinit, b1, winit, e[-1, j], n1, BQinit,
lambdas[j], b2, parameters, tax1)
bequest_ut = rho[-1] * np.exp(-sigma * g_y) * chi_b[-1, j] * b2**(-sigma)
error1 = household.marg_ut_cons(cons1, parameters) - bequest_ut
# Euler 2 equations
income2 = (rinit * b1 + winit * e[-1, j] * n1) * factor_ss
deriv2 = 1 - tau_payroll - tax.tau_income(
rinit, b1, winit, e[-1, j],
n1, factor_ss, parameters) - tax.tau_income_deriv(
rinit, b1, winit, e[-1, j], n1, factor_ss, parameters) * income2
error2 = household.marg_ut_cons(cons1, parameters) * winit * \
e[-1, j] * deriv2 - household.marg_ut_labor(n1, chi_n[-1], parameters)
if n1 <= 0 or n1 >= 1:
error2 += 1e12
if b2 <= 0:
error1 += 1e12
if cons1 <= 0:
error1 += 1e12
return [error1] + [error2]
def twist_doughnut(guesses, r, w, BQ, T_H, j, s, t, params):
'''
Parameters:
guesses = distribution of capital and labor (various length list)
w = wage rate ((T+S)x1 array)
r = rental rate ((T+S)x1 array)
BQ = aggregate bequests ((T+S)x1 array)
T_H = lump sum tax over time ((T+S)x1 array)
factor = scaling factor (scalar)
j = which ability type is being solved for (scalar)
s = which upper triangle loop is being solved for (scalar)
t = which diagonal is being solved for (scalar)
params = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rate (Jx1 array)
rho = mortality rate (Sx1 array)
lambdas = ability weights (Jx1 array)
e = ability type (SxJ array)
initial_b = capital stock distribution in period 0 (SxJ array)
chi_b = chi^b_j (Jx1 array)
chi_n = chi^n_s (Sx1 array)
Output:
Value of Euler error (various length list)
'''
income_tax_params, tpi_params, initial_b = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
J, S, T, BQ_dist, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_vector, tau_payroll, tau_bq, rho, omega, N_tilde, lambdas, e, retire, mean_income_data,\
factor, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n = tpi_params
length = len(guesses) / 2
b_guess = np.array(guesses[:length])
n_guess = np.array(guesses[length:])
if length == S:
b_s = np.array([0] + list(b_guess[:-1]))
else:
b_s = np.array([(initial_b[-(s + 3), j])] + list(b_guess[:-1]))
b_splus1 = b_guess
b_splus2 = np.array(list(b_guess[1:]) + [0])
w_s = w[t:t + length]
w_splus1 = w[t + 1:t + length + 1]
r_s = r[t:t + length]
r_splus1 = r[t + 1:t + length + 1]
n_s = n_guess
n_extended = np.array(list(n_guess[1:]) + [0])
e_s = e[-length:, j]
e_extended = np.array(list(e[-length + 1:, j]) + [0])
BQ_s = BQ[t:t + length]
BQ_splus1 = BQ[t + 1:t + length + 1]
T_H_s = T_H[t:t + length]
T_H_splus1 = T_H[t + 1:t + length + 1]
omega = omega[t, -length:]
BQ_dist = BQ_dist[-length:, j]
# Savings euler equations
# theta_params = (e[-1, j], 1, omega[0].reshape(S, 1), lambdas[j])
# theta = tax.replacement_rate_vals(n, w, factor, theta_params)
theta = np.zeros((J,))
tax_s_params = (e_s, BQ_dist, lambdas[j], 'TPI', retire, etr_params, h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax_s = tax.total_taxes(r_s, w_s, b_s, n_s, BQ_s, factor, T_H_s, j, False, tax_s_params)
etr_params_sp1 = np.append(etr_params,np.reshape(etr_params[-1,:],(1,etr_params.shape[1])),axis=0)[1:,:]
taxsp1_params = (e_extended, BQ_dist, lambdas[j], 'TPI', retire, etr_params_sp1, h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax_splus1 = tax.total_taxes(r_splus1, w_splus1, b_splus1, n_extended, BQ_splus1, factor, T_H_splus1, j, True, taxsp1_params)
cons_s_params = (e_s, BQ_dist, lambdas[j], g_y)
cons_s = household.get_cons(omega, r_s, w_s, b_s, b_splus1, n_s,
BQ_s, tax_s, cons_s_params)
cons_sp1_params = (e_extended, BQ_dist, lambdas[j], g_y)
cons_splus1 = household.get_cons(omega, r_splus1, w_splus1, b_splus1, b_splus2, n_extended,
BQ_splus1, tax_splus1, cons_sp1_params)
income_splus1 = (r_splus1 * b_splus1 + w_splus1 *
e_extended * n_extended) * factor
savings_ut = rho[-(length):] * np.exp(-sigma * g_y) * \
chi_b[j] * b_splus1 ** (-sigma)
mtry_params_sp1 = np.append(mtry_params,np.reshape(mtry_params[-1,:],(1,mtry_params.shape[1])),axis=0)[1:,:]
mtr_capital_params = (e_extended, etr_params_sp1, mtry_params_sp1, analytical_mtrs)
deriv_savings = 1 + r_splus1 * (1 - tax.MTR_capital(r_splus1, w_splus1, b_splus1, n_extended, factor, mtr_capital_params))
error1 = household.marg_ut_cons(cons_s, sigma) - beta * (1 - rho[-(length):]) * np.exp(-sigma * g_y) * deriv_savings * household.marg_ut_cons(
cons_splus1, sigma) - savings_ut
# Labor leisure euler equations
income_s = (r_s * b_s + w_s * e_s * n_s) * factor
mtr_labor_params = (e_s, etr_params, mtrx_params, analytical_mtrs)
deriv_laborleisure = 1 - tau_payroll - tax.MTR_labor(r_s, w_s, b_s, n_s, factor, mtr_labor_params)
mu_labor_params = (b_ellipse, upsilon, ltilde, chi_n[-length:])
error2 = household.marg_ut_cons(cons_s, sigma) * w_s * e[-(
length):, j] * deriv_laborleisure - household.marg_ut_labor(n_s, mu_labor_params)
# Check and punish constraint violations
mask1 = n_guess < 0
error2[mask1] += 1e12
mask2 = n_guess > ltilde
error2[mask2] += 1e12
mask3 = cons_s < 0
error2[mask3] += 1e12
mask4 = b_guess <= 0
error2[mask4] += 1e12
mask5 = cons_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())
def firstdoughnutring(guesses, r, w, b, BQ, T_H, j, params):
'''
Solves the first entries of the upper triangle of the twist doughnut. This is
separate from the main TPI function because the the values of b and n are scalars,
so it is easier to just have a separate function for these cases.
Inputs:
guesses = guess for b and n (2x1 list)
winit = initial wage rate (scalar)
rinit = initial rental rate (scalar)
BQinit = initial aggregate bequest (scalar)
T_H_init = initial lump sum tax (scalar)
initial_b = initial distribution of capital (SxJ array)
factor = steady state scaling factor (scalar)
j = which ability type is being solved for (scalar)
parameters = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rates (Jx1 array)
Output:
euler errors (2x1 list)
'''
# unpack tuples of parameters
income_tax_params, tpi_params, initial_b = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
J, S, T, BQ_dist, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_vector, tau_payroll, tau_bq, rho, omega, N_tilde, lambdas, e, retire, mean_income_data,\
factor, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n = tpi_params
b_splus1 = float(guesses[0])
n = float(guesses[1])
b_s = float(initial_b[-2, j])
# Euler 1 equations
# theta_params = (e[-1, j], 1, omega[0].reshape(S, 1), lambdas[j])
# theta = tax.replacement_rate_vals(n, w, factor, theta_params)
theta = np.zeros((J,))
tax1_params = (e[-1, j], BQ_dist[-1, j], lambdas[j], 'TPI_scalar', retire, etr_params[-1,0,:], h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b_s, n, BQ, factor, T_H, j, False, tax1_params)
cons_params = (e[-1, j], BQ_dist[-1, j], lambdas[j], g_y)
cons = household.get_cons(omega[0,-1], r, w, b_s, b_splus1, n, BQ, tax1, cons_params)
bequest_ut = rho[-1] * np.exp(-sigma * g_y) * chi_b[j] * b_splus1 ** (-sigma)
error1 = household.marg_ut_cons(cons, sigma) - bequest_ut
# Euler 2 equations
income2 = (r * b_s + w * e[-1, j] * n) * factor
mtr_labor_params = (e[-1, j], etr_params[-1,0,:], mtrx_params[-1,0,:], analytical_mtrs)
deriv2 = 1 - tau_payroll - tax.MTR_labor(r, w, b_s, n, factor, mtr_labor_params)
mu_labor_params = (b_ellipse, upsilon, ltilde, chi_n[-1])
error2 = household.marg_ut_cons(cons, sigma) * w * \
e[-1, j] * deriv2 - household.marg_ut_labor(n, mu_labor_params)
#### TEST THESE FUNCS BELOW TO BE SURE GET SAME OUTPUT, but should use if so ***
# foc_save_params = (e[-1, j], sigma, beta, g_y, chi_b, theta, tau_bq, rho, lambdas, J, S,
# analytical_mtrs, etr_params[-1,0,:], mtry_params[-1,0,:], h_wealth, p_wealth, m_wealth, tau_payroll, retire, 'TPI')
# error3 = household.FOC_savings(r, w, b_s, b_splus1, 0., n, BQ, factor, T_H, foc_save_params)
# foc_labor_params = (e[-1, j], sigma, g_y, theta, b_ellipse, upsilon, chi_n, ltilde, tau_bq, lambdas, J, S,
# analytical_mtrs, etr_params[-1,0,:], mtrx_params[-1,0,:], h_wealth, p_wealth, m_wealth, tau_payroll, retire, 'TPI')
# error4 = household.FOC_labor(r, w, b, b_splus1, n, BQ, factor, T_H, foc_labor_params)
# print 'check1:', error2-error4
# print 'check2:', error1-error3
if n <= 0 or n >= 1:
error2 += 1e12
if b_splus1 <= 0:
error1 += 1e12
if cons <= 0:
error1 += 1e12
return [error1] + [error2]
def Steady_state_TPI_solver(guesses, winit, rinit, BQinit, T_H_init, factor, j,
s, t, params, theta, tau_bq, rho, lambdas, e,
initial_b, chi_b, chi_n):
'''
Parameters:
guesses = distribution of capital and labor (various length list)
winit = wage rate ((T+S)x1 array)
rinit = rental rate ((T+S)x1 array)
BQinit = aggregate bequests ((T+S)x1 array)
T_H_init = lump sum tax over time ((T+S)x1 array)
factor = scaling factor (scalar)
j = which ability type is being solved for (scalar)
s = which upper triangle loop is being solved for (scalar)
t = which diagonal is being solved for (scalar)
params = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rate (Jx1 array)
rho = mortalit rate (Sx1 array)
lambdas = ability weights (Jx1 array)
e = ability type (SxJ array)
initial_b = capital stock distribution in period 0 (SxJ array)
chi_b = chi^b_j (Jx1 array)
chi_n = chi^n_s (Sx1 array)
Output:
Value of Euler error (various length list)
'''
J, S, T, beta, sigma, alpha, Z, delta, ltilde, nu, g_y, g_n_ss, tau_payroll, retire, mean_income_data, \
a_tax_income, b_tax_income, c_tax_income, d_tax_income, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = params
length = len(guesses) / 2
b_guess = np.array(guesses[:length])
n_guess = np.array(guesses[length:])
if length == S:
b_s = np.array([0] + list(b_guess[:-1]))
else:
b_s = np.array([(initial_b[-(s + 3), j])] + list(b_guess[:-1]))
b_splus1 = b_guess
b_splus2 = np.array(list(b_guess[1:]) + [0])
w_s = winit[t:t + length]
w_splus1 = winit[t + 1:t + length + 1]
r_s = rinit[t:t + length]
r_splus1 = rinit[t + 1:t + length + 1]
n_s = n_guess
n_extended = np.array(list(n_guess[1:]) + [0])
e_s = e[-length:, j]
e_extended = np.array(list(e[-length + 1:, j]) + [0])
BQ_s = BQinit[t:t + length]
BQ_splus1 = BQinit[t + 1:t + length + 1]
T_H_s = T_H_init[t:t + length]
T_H_splus1 = T_H_init[t + 1:t + length + 1]
# Savings euler equations
tax_s = tax.total_taxes(r_s, b_s, w_s, e_s, n_s, BQ_s, lambdas[j], factor,
T_H_s, j, 'TPI', False, params, theta, tau_bq)
tax_splus1 = tax.total_taxes(r_splus1, b_splus1, w_splus1, e_extended,
n_extended, BQ_splus1, lambdas[j], factor,
T_H_splus1, j, 'TPI', True, params, theta,
tau_bq)
cons_s = household.get_cons(r_s, b_s, w_s, e_s, n_s, BQ_s, lambdas[j],
b_splus1, params, tax_s)
cons_splus1 = household.get_cons(r_splus1, b_splus1, w_splus1, e_extended,
n_extended, BQ_splus1, lambdas[j],
b_splus2, params, tax_splus1)
income_splus1 = (r_splus1 * b_splus1 +
w_splus1 * e_extended * n_extended) * factor
savings_ut = rho[-(length):] * np.exp(-sigma * g_y) * \
chi_b[-(length):, j] * b_splus1 ** (-sigma)
deriv_savings = 1 + r_splus1 * (
1 - tax.tau_income(r_splus1, b_splus1, w_splus1, e_extended,
n_extended, factor, params) -
tax.tau_income_deriv(r_splus1, b_splus1, w_splus1, e_extended,
n_extended, factor, params) * income_splus1
) - tax.tau_w_prime(b_splus1, params) * b_splus1 - tax.tau_wealth(
b_splus1, params)
error1 = household.marg_ut_cons(
cons_s, params) - beta * (1 - rho[-(length):]) * np.exp(
-sigma * g_y) * deriv_savings * household.marg_ut_cons(
cons_splus1, params) - savings_ut
# Labor leisure euler equations
income_s = (r_s * b_s + w_s * e_s * n_s) * factor
deriv_laborleisure = 1 - tau_payroll - tax.tau_income(
r_s, b_s, w_s, e_s, n_s, factor, params) - tax.tau_income_deriv(
r_s, b_s, w_s, e_s, n_s, factor, params) * income_s
error2 = household.marg_ut_cons(cons_s, params) * w_s * e[
-(length):, j] * deriv_laborleisure - household.marg_ut_labor(
n_s, chi_n[-length:], params)
# Check and punish constraint violations
mask1 = n_guess < 0
error2[mask1] += 1e12
mask2 = n_guess > ltilde
error2[mask2] += 1e12
mask3 = cons_s < 0
error2[mask3] += 1e12
mask4 = b_guess <= 0
error2[mask4] += 1e12
mask5 = cons_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())
def twist_doughnut(guesses, r, w, BQ, T_H, j, s, t, params):
'''
Parameters:
guesses = distribution of capital and labor (various length list)
w = wage rate ((T+S)x1 array)
r = rental rate ((T+S)x1 array)
BQ = aggregate bequests ((T+S)x1 array)
T_H = lump sum tax over time ((T+S)x1 array)
factor = scaling factor (scalar)
j = which ability type is being solved for (scalar)
s = which upper triangle loop is being solved for (scalar)
t = which diagonal is being solved for (scalar)
params = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rate (Jx1 array)
rho = mortalit rate (Sx1 array)
lambdas = ability weights (Jx1 array)
e = ability type (SxJ array)
initial_b = capital stock distribution in period 0 (SxJ array)
chi_b = chi^b_j (Jx1 array)
chi_n = chi^n_s (Sx1 array)
Output:
Value of Euler error (various length list)
'''
income_tax_params, tpi_params, initial_b = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_vector, tau_payroll, tau_bq, rho, omega, N_tilde, lambdas, e, retire, mean_income_data,\
factor, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n = tpi_params
length = len(guesses) / 2
b_guess = np.array(guesses[:length])
n_guess = np.array(guesses[length:])
if length == S:
b_s = np.array([0] + list(b_guess[:-1]))
else:
b_s = np.array([(initial_b[-(s + 3), j])] + list(b_guess[:-1]))
b_splus1 = b_guess
b_splus2 = np.array(list(b_guess[1:]) + [0])
w_s = w[t:t + length]
w_splus1 = w[t + 1:t + length + 1]
r_s = r[t:t + length]
r_splus1 = r[t + 1:t + length + 1]
n_s = n_guess
n_extended = np.array(list(n_guess[1:]) + [0])
e_s = e[-length:, j]
e_extended = np.array(list(e[-length + 1:, j]) + [0])
BQ_s = BQ[t:t + length]
BQ_splus1 = BQ[t + 1:t + length + 1]
T_H_s = T_H[t:t + length]
T_H_splus1 = T_H[t + 1:t + length + 1]
# Savings euler equations
# theta_params = (e[-1, j], 1, omega[0].reshape(S, 1), lambdas[j])
# theta = tax.replacement_rate_vals(n, w, factor, theta_params)
theta = np.zeros((J, ))
tax_s_params = (e_s, lambdas[j], 'TPI', retire, etr_params, h_wealth,
p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax_s = tax.total_taxes(r_s, w_s, b_s, n_s, BQ_s, factor, T_H_s, j, False,
tax_s_params)
etr_params_sp1 = np.append(etr_params,
np.reshape(etr_params[-1, :],
(1, etr_params.shape[1])),
axis=0)[1:, :]
taxsp1_params = (e_extended, lambdas[j], 'TPI', retire, etr_params_sp1,
h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq,
J, S)
tax_splus1 = tax.total_taxes(r_splus1, w_splus1, b_splus1, n_extended,
BQ_splus1, factor, T_H_splus1, j, True,
taxsp1_params)
cons_s_params = (e_s, lambdas[j], g_y)
cons_s = household.get_cons(r_s, w_s, b_s, b_splus1, n_s, BQ_s, tax_s,
cons_s_params)
cons_sp1_params = (e_extended, lambdas[j], g_y)
cons_splus1 = household.get_cons(r_splus1, w_splus1, b_splus1, b_splus2,
n_extended, BQ_splus1, tax_splus1,
cons_sp1_params)
income_splus1 = (r_splus1 * b_splus1 +
w_splus1 * e_extended * n_extended) * factor
savings_ut = rho[-(length):] * np.exp(-sigma * g_y) * \
chi_b[j] * b_splus1 ** (-sigma)
mtry_params_sp1 = np.append(mtry_params,
np.reshape(mtry_params[-1, :],
(1, mtry_params.shape[1])),
axis=0)[1:, :]
mtr_capital_params = (e_extended, etr_params_sp1, mtry_params_sp1,
analytical_mtrs)
deriv_savings = 1 + r_splus1 * (1 - tax.MTR_capital(
r_splus1, w_splus1, b_splus1, n_extended, factor, mtr_capital_params))
error1 = household.marg_ut_cons(
cons_s, sigma) - beta * (1 - rho[-(length):]) * np.exp(
-sigma * g_y) * deriv_savings * household.marg_ut_cons(
cons_splus1, sigma) - savings_ut
# Labor leisure euler equations
income_s = (r_s * b_s + w_s * e_s * n_s) * factor
mtr_labor_params = (e_s, etr_params, mtrx_params, analytical_mtrs)
deriv_laborleisure = 1 - tau_payroll - tax.MTR_labor(
r_s, w_s, b_s, n_s, factor, mtr_labor_params)
mu_labor_params = (b_ellipse, upsilon, ltilde, chi_n[-length:])
error2 = household.marg_ut_cons(cons_s, sigma) * w_s * e[
-(length):, j] * deriv_laborleisure - household.marg_ut_labor(
n_s, mu_labor_params)
# Check and punish constraint violations
mask1 = n_guess < 0
error2[mask1] += 1e12
mask2 = n_guess > ltilde
error2[mask2] += 1e12
mask3 = cons_s < 0
error2[mask3] += 1e12
mask4 = b_guess <= 0
error2[mask4] += 1e12
mask5 = cons_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())
def firstdoughnutring(guesses, r, w, b, BQ, T_H, j, params):
'''
Solves the first entries of the upper triangle of the twist doughnut. This is
separate from the main TPI function because the the values of b and n are scalars,
so it is easier to just have a separate function for these cases.
Inputs:
guesses = guess for b and n (2x1 list)
winit = initial wage rate (scalar)
rinit = initial rental rate (scalar)
BQinit = initial aggregate bequest (scalar)
T_H_init = initial lump sum tax (scalar)
initial_b = initial distribution of capital (SxJ array)
factor = steady state scaling factor (scalar)
j = which ability type is being solved for (scalar)
parameters = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rates (Jx1 array)
Output:
euler errors (2x1 list)
'''
# unpack tuples of parameters
income_tax_params, tpi_params, initial_b = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_vector, tau_payroll, tau_bq, rho, omega, N_tilde, lambdas, e, retire, mean_income_data,\
factor, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n = tpi_params
b_splus1 = float(guesses[0])
n = float(guesses[1])
b_s = float(initial_b[-2, j])
# Euler 1 equations
# theta_params = (e[-1, j], 1, omega[0].reshape(S, 1), lambdas[j])
# theta = tax.replacement_rate_vals(n, w, factor, theta_params)
theta = np.zeros((J, ))
tax1_params = (e[-1, j], lambdas[j], 'TPI_scalar', retire,
etr_params[-1, 0, :], h_wealth, p_wealth, m_wealth,
tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b_s, n, BQ, factor, T_H, j, False,
tax1_params)
cons_params = (e[-1, j], lambdas[j], g_y)
cons = household.get_cons(r, w, b_s, b_splus1, n, BQ, tax1, cons_params)
bequest_ut = rho[-1] * np.exp(-sigma * g_y) * chi_b[j] * b_splus1**(-sigma)
error1 = household.marg_ut_cons(cons, sigma) - bequest_ut
# Euler 2 equations
income2 = (r * b_s + w * e[-1, j] * n) * factor
mtr_labor_params = (e[-1, j], etr_params[-1, 0, :], mtrx_params[-1, 0, :],
analytical_mtrs)
deriv2 = 1 - tau_payroll - tax.MTR_labor(r, w, b_s, n, factor,
mtr_labor_params)
mu_labor_params = (b_ellipse, upsilon, ltilde, chi_n[-1])
error2 = household.marg_ut_cons(cons, sigma) * w * \
e[-1, j] * deriv2 - household.marg_ut_labor(n, mu_labor_params)
#### TEST THESE FUNCS BELOW TO BE SURE GET SAME OUTPUT, but should use if so ***
# foc_save_params = (e[-1, j], sigma, beta, g_y, chi_b, theta, tau_bq, rho, lambdas, J, S,
# analytical_mtrs, etr_params[-1,0,:], mtry_params[-1,0,:], h_wealth, p_wealth, m_wealth, tau_payroll, retire, 'TPI')
# error3 = household.FOC_savings(r, w, b_s, b_splus1, 0., n, BQ, factor, T_H, foc_save_params)
# foc_labor_params = (e[-1, j], sigma, g_y, theta, b_ellipse, upsilon, chi_n, ltilde, tau_bq, lambdas, J, S,
# analytical_mtrs, etr_params[-1,0,:], mtrx_params[-1,0,:], h_wealth, p_wealth, m_wealth, tau_payroll, retire, 'TPI')
# error4 = household.FOC_labor(r, w, b, b_splus1, n, BQ, factor, T_H, foc_labor_params)
# print 'check1:', error2-error4
# print 'check2:', error1-error3
if n <= 0 or n >= 1:
error2 += 1e12
if b_splus1 <= 0:
error1 += 1e12
if cons <= 0:
error1 += 1e12
return [error1] + [error2]
def Steady_state_TPI_solver(guesses, winit, rinit, BQinit, T_H_init, factor, j, s, t, params, theta, tau_bq, rho, lambdas, e, initial_b, chi_b, chi_n):
'''
Parameters:
guesses = distribution of capital and labor (various length list)
winit = wage rate ((T+S)x1 array)
rinit = rental rate ((T+S)x1 array)
BQinit = aggregate bequests ((T+S)x1 array)
T_H_init = lump sum tax over time ((T+S)x1 array)
factor = scaling factor (scalar)
j = which ability type is being solved for (scalar)
s = which upper triangle loop is being solved for (scalar)
t = which diagonal is being solved for (scalar)
params = list of parameters (list)
theta = replacement rates (Jx1 array)
tau_bq = bequest tax rate (Jx1 array)
rho = mortalit rate (Sx1 array)
lambdas = ability weights (Jx1 array)
e = ability type (SxJ array)
initial_b = capital stock distribution in period 0 (SxJ array)
chi_b = chi^b_j (Jx1 array)
chi_n = chi^n_s (Sx1 array)
Output:
Value of Euler error (various length list)
'''
J, S, T, beta, sigma, alpha, Z, delta, ltilde, nu, g_y, g_n_ss, tau_payroll, retire, mean_income_data, \
a_tax_income, b_tax_income, c_tax_income, d_tax_income, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = params
length = len(guesses) / 2
b_guess = np.array(guesses[:length])
n_guess = np.array(guesses[length:])
if length == S:
b_s = np.array([0] + list(b_guess[:-1]))
else:
b_s = np.array([(initial_b[-(s + 3), j])] + list(b_guess[:-1]))
b_splus1 = b_guess
b_splus2 = np.array(list(b_guess[1:]) + [0])
w_s = winit[t:t + length]
w_splus1 = winit[t + 1:t + length + 1]
r_s = rinit[t:t + length]
r_splus1 = rinit[t + 1:t + length + 1]
n_s = n_guess
n_extended = np.array(list(n_guess[1:]) + [0])
e_s = e[-length:, j]
e_extended = np.array(list(e[-length + 1:, j]) + [0])
BQ_s = BQinit[t:t + length]
BQ_splus1 = BQinit[t + 1:t + length + 1]
T_H_s = T_H_init[t:t + length]
T_H_splus1 = T_H_init[t + 1:t + length + 1]
# Savings euler equations
tax_s = tax.total_taxes(r_s, b_s, w_s, e_s, n_s, BQ_s, lambdas[
j], factor, T_H_s, j, 'TPI', False, params, theta, tau_bq)
tax_splus1 = tax.total_taxes(r_splus1, b_splus1, w_splus1, e_extended, n_extended, BQ_splus1, lambdas[
j], factor, T_H_splus1, j, 'TPI', True, params, theta, tau_bq)
cons_s = household.get_cons(r_s, b_s, w_s, e_s, n_s, BQ_s, lambdas[
j], b_splus1, params, tax_s)
cons_splus1 = household.get_cons(r_splus1, b_splus1, w_splus1, e_extended, n_extended, BQ_splus1, lambdas[
j], b_splus2, params, tax_splus1)
income_splus1 = (r_splus1 * b_splus1 + w_splus1 *
e_extended * n_extended) * factor
savings_ut = rho[-(length):] * np.exp(-sigma * g_y) * \
chi_b[-(length):, j] * b_splus1 ** (-sigma)
deriv_savings = 1 + r_splus1 * (1 - tax.tau_income(
r_splus1, b_splus1, w_splus1, e_extended, n_extended, factor, params) - tax.tau_income_deriv(
r_splus1, b_splus1, w_splus1, e_extended, n_extended, factor, params) * income_splus1) - tax.tau_w_prime(
b_splus1, params) * b_splus1 - tax.tau_wealth(b_splus1, params)
error1 = household.marg_ut_cons(cons_s, params) - beta * (1 - rho[-(length):]) * np.exp(-sigma * g_y) * deriv_savings * household.marg_ut_cons(
cons_splus1, params) - savings_ut
# Labor leisure euler equations
income_s = (r_s * b_s + w_s * e_s * n_s) * factor
deriv_laborleisure = 1 - tau_payroll - tax.tau_income(r_s, b_s, w_s, e_s, n_s, factor, params) - tax.tau_income_deriv(
r_s, b_s, w_s, e_s, n_s, factor, params) * income_s
error2 = household.marg_ut_cons(cons_s, params) * w_s * e[-(
length):, j] * deriv_laborleisure - household.marg_ut_labor(n_s, chi_n[-length:], params)
# Check and punish constraint violations
mask1 = n_guess < 0
error2[mask1] += 1e12
mask2 = n_guess > ltilde
error2[mask2] += 1e12
mask3 = cons_s < 0
error2[mask3] += 1e12
mask4 = b_guess <= 0
error2[mask4] += 1e12
mask5 = cons_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())
