def euler_savings_func(w, r, e, n_guess, b_s, b_splus1, b_splus2, BQ, factor,
T_H, chi_b, params, theta, tau_bq, rho, lambdas):
'''
This function is usually looped through over J, so it does one ability group at a time.
Inputs:
w = wage rate (scalar)
r = rental rate (scalar)
e = ability levels (Sx1 array)
n_guess = labor distribution (Sx1 array)
b_s = wealth holdings at the start of a period (Sx1 array)
b_splus1 = wealth holdings for the next period (Sx1 array)
b_splus2 = wealth holdings for 2 periods ahead (Sx1 array)
BQ = aggregate bequests for a certain ability (scalar)
factor = scaling factor to convert to dollars (scalar)
T_H = lump sum tax (scalar)
chi_b = chi^b_j for a certain ability (scalar)
params = parameter list (list)
theta = replacement rate for a certain ability (scalar)
tau_bq = bequest tax rate (scalar)
rho = mortality rate (Sx1 array)
lambdas = ability weight (scalar)
Output:
euler = Value of savings euler error (Sx1 array)
'''
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
# In order to not have 2 savings euler equations (one that solves the first S-1 equations, and one that solves the last one),
# we combine them. In order to do this, we have to compute a consumption term in period t+1, which requires us to have a shifted
# e and n matrix. We append a zero on the end of both of these so they will be the right size. We could append any value to them,
# since in the euler equation, the coefficient on the marginal utility of
# consumption for this term will be zero (since rho is one).
e_extended = np.array(list(e) + [0])
n_extended = np.array(list(n_guess) + [0])
tax1 = tax.total_taxes(r, b_s, w, e, n_guess, BQ, lambdas, factor, T_H,
None, 'SS', False, params, theta, tau_bq)
tax2 = tax.total_taxes(r, b_splus1, w, e_extended[1:], n_extended[1:], BQ,
lambdas, factor, T_H, None, 'SS', True, params,
theta, tau_bq)
cons1 = get_cons(r, b_s, w, e, n_guess, BQ, lambdas, b_splus1, params,
tax1)
cons2 = get_cons(r, b_splus1, w, e_extended[1:], n_extended[1:], BQ,
lambdas, b_splus2, params, tax2)
income = (r * b_splus1 + w * e_extended[1:] * n_extended[1:]) * factor
deriv = (1 + r *
(1 - tax.tau_income(r, b_splus1, w, e_extended[1:],
n_extended[1:], factor, params) -
tax.tau_income_deriv(r, b_splus1, w, e_extended[1:],
n_extended[1:], factor, params) * income) -
tax.tau_w_prime(b_splus1, params) * b_splus1 -
tax.tau_wealth(b_splus1, params))
savings_ut = rho * np.exp(-sigma * g_y) * chi_b * b_splus1**(-sigma)
# Again, not who in this equation, the (1-rho) term will zero out in the last period, so the last entry of cons2 can be complete
# gibberish (which it is). It just has to exist so cons2 is the right
# size to match all other arrays in the equation.
euler = marg_ut_cons(cons1,
params) - beta * (1 - rho) * deriv * marg_ut_cons(
cons2, params) * np.exp(-sigma * g_y) - savings_ut
return euler
def euler_labor_leisure_func(w, r, e, n_guess, b_s, b_splus1, BQ, factor, T_H,
chi_n, params, theta, tau_bq, lambdas):
'''
This function is usually looped through over J, so it does one ability group at a time.
Inputs:
w = wage rate (scalar)
r = rental rate (scalar)
e = ability levels (Sx1 array)
n_guess = labor distribution (Sx1 array)
b_s = wealth holdings at the start of a period (Sx1 array)
b_splus1 = wealth holdings for the next period (Sx1 array)
BQ = aggregate bequests for a certain ability (scalar)
factor = scaling factor to convert to dollars (scalar)
T_H = lump sum tax (scalar)
chi_n = chi^n_s (Sx1 array)
params = parameter list (list)
theta = replacement rate for a certain ability (scalar)
tau_bq = bequest tax rate (scalar)
lambdas = ability weight (scalar)
Output:
euler = Value of labor leisure euler error (Sx1 array)
'''
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
tax1 = tax.total_taxes(r, b_s, w, e, n_guess, BQ, lambdas, factor, T_H,
None, 'SS', False, params, theta, tau_bq)
cons = get_cons(r, b_s, w, e, n_guess, BQ, lambdas, b_splus1, params, tax1)
income = (r * b_s + w * e * n_guess) * factor
deriv = 1 - tau_payroll - tax.tau_income(
r, b_s, w, e, n_guess, factor, params) - tax.tau_income_deriv(
r, b_s, w, e, n_guess, factor, params) * income
euler = marg_ut_cons(cons, params) * w * deriv * e - \
marg_ut_labor(n_guess, chi_n, params)
return euler
def euler_labor_leisure_func(w, r, e, n_guess, b_s, b_splus1, BQ, factor, T_H, chi_n, params, theta, tau_bq, lambdas):
"""
This function is usually looped through over J, so it does one ability group at a time.
Inputs:
w = wage rate (scalar)
r = rental rate (scalar)
e = ability levels (Sx1 array)
n_guess = labor distribution (Sx1 array)
b_s = wealth holdings at the start of a period (Sx1 array)
b_splus1 = wealth holdings for the next period (Sx1 array)
BQ = aggregate bequests for a certain ability (scalar)
factor = scaling factor to convert to dollars (scalar)
T_H = lump sum tax (scalar)
chi_n = chi^n_s (Sx1 array)
params = parameter list (list)
theta = replacement rate for a certain ability (scalar)
tau_bq = bequest tax rate (scalar)
lambdas = ability weight (scalar)
Output:
euler = Value of labor leisure euler error (Sx1 array)
"""
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
)
tax1 = tax.total_taxes(r, b_s, w, e, n_guess, BQ, lambdas, factor, T_H, None, "SS", False, params, theta, tau_bq)
cons = get_cons(r, b_s, w, e, n_guess, BQ, lambdas, b_splus1, params, tax1)
income = (r * b_s + w * e * n_guess) * factor
deriv = (
1
- tau_payroll
- tax.tau_income(r, b_s, w, e, n_guess, factor, params)
- tax.tau_income_deriv(r, b_s, w, e, n_guess, factor, params) * income
)
euler = marg_ut_cons(cons, params) * w * deriv * e - marg_ut_labor(n_guess, chi_n, params)
return euler
def euler_savings_func(w, r, e, n_guess, b_s, b_splus1, b_splus2, BQ, factor, T_H, chi_b, params, theta, tau_bq, rho, lambdas):
'''
This function is usually looped through over J, so it does one ability group at a time.
Inputs:
w = wage rate (scalar)
r = rental rate (scalar)
e = ability levels (Sx1 array)
n_guess = labor distribution (Sx1 array)
b_s = wealth holdings at the start of a period (Sx1 array)
b_splus1 = wealth holdings for the next period (Sx1 array)
b_splus2 = wealth holdings for 2 periods ahead (Sx1 array)
BQ = aggregate bequests for a certain ability (scalar)
factor = scaling factor to convert to dollars (scalar)
T_H = lump sum tax (scalar)
chi_b = chi^b_j for a certain ability (scalar)
params = parameter list (list)
theta = replacement rate for a certain ability (scalar)
tau_bq = bequest tax rate (scalar)
rho = mortality rate (Sx1 array)
lambdas = ability weight (scalar)
Output:
euler = Value of savings euler error (Sx1 array)
'''
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
# In order to not have 2 savings euler equations (one that solves the first S-1 equations, and one that solves the last one),
# we combine them. In order to do this, we have to compute a consumption term in period t+1, which requires us to have a shifted
# e and n matrix. We append a zero on the end of both of these so they will be the right size. We could append any value to them,
# since in the euler equation, the coefficient on the marginal utility of consumption for this term will be zero (since rho is one).
e_extended = np.array(list(e) + [0])
n_extended = np.array(list(n_guess) + [0])
tax1 = tax.total_taxes(r, b_s, w, e, n_guess, BQ, lambdas, factor, T_H, None, 'SS', False, params, theta, tau_bq)
tax2 = tax.total_taxes(r, b_splus1, w, e_extended[1:], n_extended[1:], BQ, lambdas, factor, T_H, None, 'SS', True, params, theta, tau_bq)
cons1 = get_cons(r, b_s, w, e, n_guess, BQ, lambdas, b_splus1, params, tax1)
cons2 = get_cons(r, b_splus1, w, e_extended[1:], n_extended[1:], BQ, lambdas, b_splus2, params, tax2)
income = (r * b_splus1 + w * e_extended[1:] * n_extended[1:]) * factor
deriv = (
1 + r*(1-tax.tau_income(r, b_splus1, w, e_extended[1:], n_extended[1:], factor, params)-tax.tau_income_deriv(
r, b_splus1, w, e_extended[1:], n_extended[1:], factor, params)*income)-tax.tau_w_prime(b_splus1, params)*b_splus1-tax.tau_wealth(b_splus1, params))
savings_ut = rho * np.exp(-sigma * g_y) * chi_b * b_splus1 ** (-sigma)
# Again, not who in this equation, the (1-rho) term will zero out in the last period, so the last entry of cons2 can be complete
# gibberish (which it is). It just has to exist so cons2 is the right size to match all other arrays in the equation.
euler = marg_ut_cons(cons1, params) - beta * (1-rho) * deriv * marg_ut_cons(
cons2, params) * np.exp(-sigma * g_y) - savings_ut
return euler
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 = 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 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, imm_rates, e, retire, mean_income_data,\
factor, T_H_baseline, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = 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]
# Errors from FOC for savings
foc_save_params = (e_s, sigma, beta, g_y, chi_b[j], theta, tau_bq,
rho[-(length):], lambdas[j], j, J, S,
analytical_mtrs, etr_params, mtry_params,
h_wealth, p_wealth, m_wealth, tau_payroll,
retire, 'TPI')
error1 = household.FOC_savings(r_s, w_s, b_s, b_splus1, b_splus2,
n_s, BQ_s, factor, T_H_s,
foc_save_params)
# Errors from FOC for labor supply
foc_labor_params = (e_s, sigma, g_y, theta, b_ellipse, upsilon,
chi_n[-length:], ltilde, tau_bq, lambdas[j], j,
J, S, analytical_mtrs, etr_params, mtrx_params,
h_wealth, p_wealth, m_wealth, tau_payroll,
retire, 'TPI')
error2 = household.FOC_labor(r_s, w_s, b_s, b_splus1, n_s, BQ_s,
factor, T_H_s, foc_labor_params)
tax_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_params)
cons_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_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
mask5 = b_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())
def FOC_savings(r, w, b, b_splus1, b_splus2, n, BQ, factor, T_H, params):
'''
Computes Euler errors for the FOC for savings in the steady state.
This function is usually looped through over J, so it does one lifetime income group at a time.
Inputs:
r = scalar, interest rate
w = scalar, wage rate
b = [S,J] array, distribution of wealth/capital holdings
b_splus1 = [S,J] array, distribution of wealth/capital holdings one period ahead
b_splus2 = [S,J] array, distribution of wealth/capital holdings two periods ahead
n = [S,J] array, distribution of labor supply
BQ = [J,] vector, aggregate bequests by lifetime income group
factor = scalar, scaling factor to convert model income to dollars
T_H = scalar, lump sum transfer
params = length 18 tuple (e, sigma, beta, g_y, chi_b, theta, tau_bq, rho, lambdas,
J, S, etr_params, mtry_params, h_wealth, p_wealth,
m_wealth, tau_payroll, tau_bq)
e = [S,J] array, effective labor units
sigma = scalar, coefficient of relative risk aversion
beta = scalar, discount factor
g_y = scalar, exogenous labor augmenting technological growth
chi_b = [J,] vector, utility weight on bequests for each lifetime income group
theta = [J,] vector, replacement rate for each lifetime income group
tau_bq = scalar, bequest tax rate (scalar)
rho = [S,] vector, mortality rates
lambdas = [J,] vector, ability weights
J = integer, number of lifetime income groups
S = integer, number of economically active periods in lifetime
etr_params = [S,10] array, parameters of effective income tax rate function
mtry_params = [S,10] array, parameters of marginal tax rate on capital income function
h_wealth = scalar, parameter in wealth tax function
p_wealth = scalar, parameter in wealth tax function
m_wealth = scalar, parameter in wealth tax function
tau_payroll = scalar, payroll tax rate
tau_bq = scalar, bequest tax rate
Functions called:
get_cons
marg_ut_cons
tax.total_taxes
tax.MTR_capital
Objects in function:
tax1 = [S,J] array, net taxes in the current period
tax2 = [S,J] array, net taxes one period ahead
cons1 = [S,J] array, consumption in the current period
cons2 = [S,J] array, consumption one period ahead
deriv = [S,J] array, after-tax return on capital
savings_ut = [S,J] array, marginal utility from savings
euler = [S,J] array, Euler error from FOC for savings
Returns: euler
'''
e, sigma, beta, g_y, chi_b, theta, tau_bq, rho, lambdas, J, S, \
analytical_mtrs, etr_params, mtry_params, h_wealth, p_wealth, m_wealth, tau_payroll, retire, method = params
# In order to not have 2 savings euler equations (one that solves the first S-1 equations, and one that solves the last one),
# we combine them. In order to do this, we have to compute a consumption term in period t+1, which requires us to have a shifted
# e and n matrix. We append a zero on the end of both of these so they will be the right size. We could append any value to them,
# since in the euler equation, the coefficient on the marginal utility of
# consumption for this term will be zero (since rho is one).
if method == 'TPI_scalar':
e_extended = np.array([e] + [0])
n_extended = np.array([n] + [0])
etr_params_to_use = etr_params
mtry_params_to_use = mtry_params
else:
e_extended = np.array(list(e) + [0])
n_extended = np.array(list(n) + [0])
etr_params_to_use = np.append(etr_params,
np.reshape(etr_params[-1, :],
(1, etr_params.shape[1])),
axis=0)[1:, :]
mtry_params_to_use = np.append(mtry_params,
np.reshape(mtry_params[-1, :],
(1, mtry_params.shape[1])),
axis=0)[1:, :]
# tax1_params = (e, lambdas, method, retire, etr_params, h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
# tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, None, False, tax1_params)
# tax2_params = (e_extended[1:], lambdas, method, retire,
# np.append(etr_params,np.reshape(etr_params[-1,:],(1,etr_params.shape[1])),axis=0)[1:,:],
# h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
# tax2 = tax.total_taxes(r, w, b_splus1, n_extended[1:], BQ, factor, T_H, None, True, tax2_params)
# cons1_params = (e, lambdas, g_y)
# cons1 = get_cons(r, w, b, b_splus1, n, BQ, tax1, cons1_params)
# cons2_params = (e_extended[1:], lambdas, g_y)
# cons2 = get_cons(r, w, b_splus1, b_splus2, n_extended[1:], BQ, tax2, cons2_params)
# mtr_cap_params = (e_extended[1:], np.append(etr_params,np.reshape(etr_params[-1,:],(1,etr_params.shape[1])),axis=0)[1:,:],
# np.append(mtry_params,np.reshape(mtry_params[-1,:],(1,mtry_params.shape[1])),axis=0)[1:,:],analytical_mtrs)
# deriv = (1+r) - r*(tax.MTR_capital(r, w, b_splus1, n_extended[1:], factor, mtr_cap_params))
tax1_params = (e, lambdas, method, retire, etr_params, h_wealth, p_wealth,
m_wealth, tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, None, False,
tax1_params)
tax2_params = (e_extended[1:], lambdas, method, retire, etr_params_to_use,
h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J,
S)
tax2 = tax.total_taxes(r, w, b_splus1, n_extended[1:], BQ, factor, T_H,
None, True, tax2_params)
cons1_params = (e, lambdas, g_y)
cons1 = get_cons(r, w, b, b_splus1, n, BQ, tax1, cons1_params)
cons2_params = (e_extended[1:], lambdas, g_y)
cons2 = get_cons(r, w, b_splus1, b_splus2, n_extended[1:], BQ, tax2,
cons2_params)
mtr_cap_params = (e_extended[1:], etr_params_to_use, mtry_params_to_use,
analytical_mtrs)
deriv = (1 + r) - r * (tax.MTR_capital(r, w, b_splus1, n_extended[1:],
factor, mtr_cap_params))
savings_ut = rho * np.exp(-sigma * g_y) * chi_b * b_splus1**(-sigma)
# Again, note timing in this equation, the (1-rho) term will zero out in the last period, so the last entry of cons2 can be complete
# gibberish (which it is). It just has to exist so cons2 is the right
# size to match all other arrays in the equation.
euler = marg_ut_cons(cons1,
sigma) - beta * (1 - rho) * deriv * marg_ut_cons(
cons2, sigma) * np.exp(-sigma * g_y) - savings_ut
return euler
def run_TPI(income_tax_params, tpi_params, iterative_params, initial_values, SS_values, output_dir="./OUTPUT"):
# unpack tuples of parameters
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
maxiter, mindist_SS, mindist_TPI = iterative_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
K0, b_sinit, b_splus1init, L0, Y0,\
w0, r0, BQ0, T_H_0, factor, tax0, c0, initial_b, initial_n = initial_values
Kss, Lss, rss, wss, BQss, T_Hss, bssmat_splus1, nssmat = SS_values
TPI_FIG_DIR = output_dir
# Initialize guesses at time paths
domain = np.linspace(0, T, T)
K_init = (-1 / (domain + 1)) * (Kss - K0) + Kss
K_init[-1] = Kss
K_init = np.array(list(K_init) + list(np.ones(S) * Kss))
L_init = np.ones(T + S) * Lss
K = K_init
L = L_init
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
w = firm.get_w(Y, L, alpha)
r_params = (alpha, delta)
r = firm.get_r(Y, K, r_params)
BQ = np.zeros((T + S, J))
for j in xrange(J):
BQ[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQ = np.array(BQ)
if T_Hss < 1e-13 and T_Hss > 0.0 :
T_Hss2 = 0.0 # sometimes SS is very small but not zero, even if taxes are zero, this get's rid of the approximation error, which affects the perc changes below
else:
T_Hss2 = T_Hss
T_H = np.ones(T + S) * T_Hss2
# Make array of initial guesses for labor supply and savings
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = np.zeros((T + S, S, J))
n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
TPIiter = 0
TPIdist = 10
PLOT_TPI = False
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
K_plot = list(K) + list(np.ones(10) * Kss)
L_plot = list(L) + list(np.ones(10) * Lss)
plt.figure()
plt.axhline(
y=Kss, color='black', linewidth=2, label=r"Steady State $\hat{K}$", ls='--')
plt.plot(np.arange(
T + 10), Kpath_plot[:T + 10], 'b', linewidth=2, label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_K"))
# Uncomment the following print statements to make sure all euler equations are converging.
# If they don't, then you'll have negative consumption or consumption spikes. If they don't,
# it is the initial guesses. You might need to scale them differently. It is rather delicate for the first
# few periods and high ability groups.
# 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,))
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, K, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, theta, ind)
# Solve HH problem in inner loop
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars, inner_loop_params)
# if euler_errors.max() > 1e-6:
# print 't-loop:', euler_errors.max()
# Force the initial distribution of capital to be as given above.
b_mat[0, :, :] = initial_b
K_params = (omega[:T].reshape(T, S, 1), lambdas.reshape(1, 1, J), g_n_vector[:T], 'TPI')
K[:T] = household.get_K(b_mat[:T], K_params)
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(n_mat[:T], L_params)
Y_params = (alpha, Z)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
wnew = firm.get_w(Ynew[:T], L[:T], alpha)
r_params = (alpha, delta)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
BQ_params = (omega[:T].reshape(T, S, 1), lambdas.reshape(1, 1, J), rho.reshape(1, S, 1),
g_n_vector[:T].reshape(T, 1), 'TPI')
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat[:T,:,:], BQ_params)
bmat_s = np.zeros((T, S, J))
bmat_s[:, 1:, :] = b_mat[:T, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[1:T + 1, :, :]
TH_tax_params = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
TH_tax_params[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
T_H_params = (np.tile(e.reshape(1, S, J),(T,1,1)), BQ_dist, lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
TH_tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
T_H_new = np.array(list(tax.get_lump_sum(np.tile(rnew[:T].reshape(T, 1, 1),(1,S,J)), np.tile(wnew[:T].reshape(T, 1, 1),(1,S,J)),
bmat_s, n_mat[:T,:,:], BQnew[:T].reshape(T, 1, J), factor, T_H_params)) + [T_Hss] * S)
w[:T] = utils.convex_combo(wnew[:T], w[:T], nu)
r[:T] = utils.convex_combo(rnew[:T], r[:T], nu)
BQ[:T] = utils.convex_combo(BQnew[:T], BQ[:T], nu)
T_H[:T] = utils.convex_combo(T_H_new[:T], T_H[:T], nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, nu)
if T_H.all() != 0:
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) + list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) + list(
utils.pct_diff_func(wnew[:T], w[:T])) + list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
else:
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) + list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) + list(
utils.pct_diff_func(wnew[:T], w[:T])) + list(np.abs(T_H_new[:T], T_H[:T]))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
# if TPIiter > 10:
# if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
# nu /= 2
# print 'New Value of nu:', nu
TPIiter += 1
print '\tIteration:', TPIiter
print '\t\tDistance:', TPIdist
if ((TPIiter >= maxiter) or (np.absolute(TPIdist) > mindist_TPI)) and ENFORCE_SOLUTION_CHECKS :
raise RuntimeError("Transition path equlibrium not found")
Y[:T] = Ynew
# Solve HH problem in inner loop
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, K, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, theta, ind)
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars, inner_loop_params)
b_mat[0, :, :] = initial_b
K_params = (omega[:T].reshape(T, S, 1), lambdas.reshape(1, 1, J), g_n_vector[:T], 'TPI')
K[:T] = household.get_K(b_mat[:T], K_params) # this is what old code does, but it's strange - why use
# b_mat -- what is going on with initial period, etc.
etr_params_path = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_path_params = (np.tile(e.reshape(1, S, J),(T,1,1)), BQ_dist, lambdas, 'TPI', retire, etr_params_path, h_wealth,
p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax_path = tax.total_taxes(np.tile(r[:T].reshape(T, 1, 1),(1,S,J)), np.tile(w[:T].reshape(T, 1, 1),(1,S,J)), bmat_s,
n_mat[:T,:,:], BQ[:T, :].reshape(T, 1, J), factor, T_H[:T].reshape(T, 1, 1), None, False, tax_path_params)
cons_params = (e.reshape(1, S, J), BQ_dist, lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(omega[:T].reshape(T,S,1), r[:T].reshape(T, 1, 1), w[:T].reshape(T, 1, 1), bmat_s, bmat_splus1, n_mat[:T,:,:],
BQ[:T].reshape(T, 1, J), tax_path, cons_params)
C_params = (omega[:T].reshape(T, S, 1), lambdas, 'TPI')
C = household.get_C(c_path, C_params)
I_params = (delta, g_y, g_n_vector[:T])
I = firm.get_I(K[1:T+1], K[:T], I_params)
print 'Resource Constraint Difference:', Y[:T] - C[:T] - I[:T]
print'Checking time path for violations of constaints.'
for t in xrange(T):
household.constraint_checker_TPI(
b_mat[t], n_mat[t], c_path[t], t, ltilde)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
print 'Max Euler error, savings: ', eul_savings
print 'Max Euler error labor supply: ', eul_laborleisure
if ((np.any(np.absolute(eul_savings) >= mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError("Transition path equlibrium not found")
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {'Y': Y, 'K': K, 'L': L, 'C': C, 'I': I, 'BQ': BQ,
'T_H': T_H, 'r': r, 'w': w, 'b_mat': b_mat, 'n_mat': n_mat,
'c_path': c_path, 'tax_path': tax_path,
'eul_savings': eul_savings, 'eul_laborleisure': eul_laborleisure}
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
macro_output = {'Y': Y, 'K': K, 'L': L, 'C': C, 'I': I,
'BQ': BQ, 'T_H': T_H, 'r': r, 'w': w,
'tax_path': tax_path}
# Non-stationary output
# macro_ns_output = {'K_ns_path': K_ns_path, 'C_ns_path': C_ns_path, 'I_ns_path': I_ns_path,
# 'L_ns_path': L_ns_path, 'BQ_ns_path': BQ_ns_path,
# 'rinit': rinit, 'Y_ns_path': Y_ns_path, 'T_H_ns_path': T_H_ns_path,
# 'w_ns_path': w_ns_path}
return output, macro_output
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 run_TPI(income_tax_params,
tpi_params,
iterative_params,
initial_values,
SS_values,
fix_transfers=False,
output_dir="./OUTPUT"):
# unpack tuples of parameters
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
maxiter, mindist_SS, mindist_TPI = iterative_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, imm_rates, e, retire, mean_income_data,\
factor, T_H_baseline, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = tpi_params
K0, b_sinit, b_splus1init, factor, initial_b, initial_n, omega_S_preTP = initial_values
Kss, Lss, rss, wss, BQss, T_Hss, Gss, bssmat_splus1, nssmat = SS_values
TPI_FIG_DIR = output_dir
# Initialize guesses at time paths
domain = np.linspace(0, T, T)
r = np.ones(T + S) * rss
BQ = np.zeros((T + S, J))
BQ0_params = (omega_S_preTP.reshape(S, 1), lambdas, rho.reshape(S, 1),
g_n_vector[0], 'SS')
BQ0 = household.get_BQ(r[0], initial_b, BQ0_params)
for j in xrange(J):
BQ[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQ = np.array(BQ)
# print "BQ values = ", BQ[0, :], BQ[100, :], BQ[-1, :], BQss
# print "K0 vs Kss = ", K0-Kss
if fix_transfers:
T_H = T_H_baseline
else:
if np.abs(T_Hss) < 1e-13:
T_Hss2 = 0.0 # sometimes SS is very small but not zero, even if taxes are zero, this get's rid of the approximation error, which affects the perc changes below
else:
T_Hss2 = T_Hss
T_H = np.ones(T + S) * T_Hss2 * (r / rss)
G = np.ones(T + S) * Gss
# # print "T_H values = ", T_H[0], T_H[100], T_H[-1], T_Hss
# # print "omega diffs = ", (omega_S_preTP-omega[-1]).max(), (omega[10]-omega[-1]).max()
#
# Make array of initial guesses for labor supply and savings
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
# print 'diff btwn start and end b: ', (guesses_b[0]-guesses_b[-1]).max()
#
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
# b_mat = np.zeros((T + S, S, J))
# n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
# # print 'diff btwn start and end n: ', (guesses_n[0]-guesses_n[-1]).max()
#
# # find economic aggregates
K = np.zeros(T + S)
L = np.zeros(T + S)
K[0] = K0
K_params = (omega[:T - 1].reshape(T - 1, S, 1), lambdas.reshape(1, 1, J),
imm_rates[:T - 1].reshape(T - 1, S, 1), g_n_vector[1:T], 'TPI')
K[1:T] = household.get_K(guesses_b[:T - 1], K_params)
K[T:] = Kss
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1),
lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(guesses_n[:T], L_params)
L[T:] = Lss
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
r[:T] = firm.get_r(Y[:T], K[:T], r_params)
# uncomment lines below if want to use starting values from prior run
r = TPI_START_VALUES['r']
K = TPI_START_VALUES['K']
L = TPI_START_VALUES['L']
Y = TPI_START_VALUES['Y']
T_H = TPI_START_VALUES['T_H']
BQ = TPI_START_VALUES['BQ']
G = TPI_START_VALUES['G']
guesses_b = TPI_START_VALUES['b_mat']
guesses_n = TPI_START_VALUES['n_mat']
TPIiter = 0
TPIdist = 10
PLOT_TPI = False
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
# print 'analytical mtrs in tpi = ', analytical_mtrs
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
K_plot = list(K) + list(np.ones(10) * Kss)
L_plot = list(L) + list(np.ones(10) * Lss)
plt.figure()
plt.axhline(y=Kss,
color='black',
linewidth=2,
label=r"Steady State $\hat{K}$",
ls='--')
plt.plot(np.arange(T + 10),
Kpath_plot[:T + 10],
'b',
linewidth=2,
label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_K"))
guesses = (guesses_b, guesses_n)
w_params = (Z, alpha, delta)
w = firm.get_w_from_r(r, w_params)
# print 'r and rss diff = ', r-rss
# print 'w and wss diff = ', w-wss
# print 'BQ and BQss diff = ', BQ-BQss
# print 'T_H and T_Hss diff = ', T_H - T_Hss
# print 'guess b and bss = ', (bssmat_splus1 - guesses_b).max()
# print 'guess n and nss = ', (nssmat - guesses_n).max()
outer_loop_vars = (r, w, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values,
ind)
# Solve HH problem in inner loop
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars,
inner_loop_params)
# print 'guess b and bss = ', (b_mat - guesses_b).max()
# print 'guess n and nss over time = ', (n_mat - guesses_n).max(axis=2).max(axis=1)
# print 'guess n and nss over age = ', (n_mat - guesses_n).max(axis=0).max(axis=1)
# print 'guess n and nss over ability = ', (n_mat - guesses_n).max(axis=0).max(axis=0)
# quit()
print 'Max Euler error: ', (np.abs(euler_errors)).max()
bmat_s = np.zeros((T, S, J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:T - 1, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[:T, :, :]
K[0] = K0
K_params = (omega[:T - 1].reshape(T - 1, S,
1), lambdas.reshape(1, 1, J),
imm_rates[:T - 1].reshape(T - 1, S,
1), g_n_vector[1:T], 'TPI')
K[1:T] = household.get_K(bmat_splus1[:T - 1], K_params)
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1),
lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(n_mat[:T], L_params)
# print 'K diffs = ', K-K0
# print 'L diffs = ', L-L[0]
Y_params = (alpha, Z)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
r_params = (alpha, delta)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
wnew = firm.get_w_from_r(rnew, w_params)
omega_shift = np.append(omega_S_preTP.reshape(1, S),
omega[:T - 1, :],
axis=0)
BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J),
rho.reshape(1, S, 1), g_n_vector[:T].reshape(T, 1), 'TPI')
# b_mat_shift = np.append(np.reshape(initial_b, (1, S, J)),
# b_mat[:T-1, :, :], axis=0)
b_mat_shift = bmat_splus1[:T, :, :]
# print 'b diffs = ', (bmat_splus1[100, :, :] - initial_b).max(), (bmat_splus1[0, :, :] - initial_b).max(), (bmat_splus1[1, :, :] - initial_b).max()
# print 'r diffs = ', rnew[1]-r[1], rnew[100]-r[100], rnew[-1]-r[-1]
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat_shift,
BQ_params)
BQss2 = np.empty(J)
for j in range(J):
BQss_params = (omega[1, :], lambdas[j], rho, g_n_vector[1], 'SS')
BQss2[j] = household.get_BQ(rnew[1], bmat_splus1[1, :, j],
BQss_params)
# print 'BQ test = ', BQss2-BQss, BQss-BQnew[1], BQss-BQnew[100], BQss-BQnew[-1]
total_tax_params = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
total_tax_params[:, :, :, i] = np.tile(
np.reshape(np.transpose(etr_params[:, :T, i]), (T, S, 1)),
(1, 1, J))
tax_receipt_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)),
lambdas.reshape(1, 1,
J), omega[:T].reshape(T, S,
1), 'TPI',
total_tax_params, theta, tau_bq, tau_payroll,
h_wealth, p_wealth, m_wealth, retire, T, S, J)
net_tax_receipts = np.array(
list(
tax.get_lump_sum(np.tile(rnew[:T].reshape(T, 1, 1), (
1, S, J)), np.tile(wnew[:T].reshape(T, 1, 1), (
1, S, J)), bmat_s, n_mat[:T, :, :], BQnew[:T].reshape(
T, 1, J), factor, tax_receipt_params)) +
[T_Hss] * S)
r[:T] = utils.convex_combo(rnew[:T], r[:T], nu)
BQ[:T] = utils.convex_combo(BQnew[:T], BQ[:T], nu)
if fix_transfers:
T_H_new = T_H
G[:T] = net_tax_receipts[:T] - T_H[:T]
else:
T_H_new = net_tax_receipts
T_H[:T] = utils.convex_combo(T_H_new[:T], T_H[:T], nu)
G[:T] = 0.0
etr_params_path = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:, :, :, i] = np.tile(
np.reshape(np.transpose(etr_params[:, :T, i]), (T, S, 1)),
(1, 1, J))
tax_path_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)), lambdas,
'TPI', retire, etr_params_path, h_wealth, p_wealth,
m_wealth, tau_payroll, theta, tau_bq, J, S)
b_to_use = np.zeros((T, S, J))
b_to_use[0, 1:, :] = initial_b[:-1, :]
b_to_use[1:, 1:, :] = b_mat[:T - 1, :-1, :]
tax_path = tax.total_taxes(np.tile(r[:T].reshape(T, 1, 1), (1, S, J)),
np.tile(w[:T].reshape(T, 1, 1),
(1, S, J)), b_to_use,
n_mat[:T, :, :], BQ[:T, :].reshape(T, 1, J),
factor, T_H[:T].reshape(T, 1, 1), None,
False, tax_path_params)
y_path = (np.tile(r[:T].reshape(T, 1, 1),
(1, S, J)) * b_to_use[:T, :, :] +
np.tile(w[:T].reshape(T, 1, 1),
(1, S, J)) * np.tile(e.reshape(1, S, J),
(T, 1, 1)) * n_mat[:T, :, :])
cons_params = (e.reshape(1, S, J), lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(r[:T].reshape(T, 1,
1), w[:T].reshape(T, 1, 1),
b_to_use[:T, :, :], b_mat[:T, :, :],
n_mat[:T, :, :], BQ[:T].reshape(T, 1, J),
tax_path, cons_params)
guesses_b = utils.convex_combo(b_mat, guesses_b, nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, nu)
if T_H.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:T], r[:T])) +
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) +
list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
print 'r dist = ', np.array(
list(utils.pct_diff_func(rnew[:T], r[:T]))).max()
print 'BQ dist = ', np.array(
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten())).max()
print 'T_H dist = ', np.array(
list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
print 'T_H path = ', T_H[:20]
# print 'r old = ', r[:T]
# print 'r new = ', rnew[:T]
# print 'K old = ', K[:T]
# print 'L old = ', L[:T]
# print 'income = ', y_path[:, :, -1]
# print 'taxes = ', tax_path[:, :, -1]
# print 'labor supply = ', n_mat[:, :, -1]
# print 'max and min labor = ', n_mat.max(), n_mat.min()
# print 'max and min labor = ', np.argmax(n_mat), np.argmin(n_mat)
# print 'max and min labor, j = 7 = ', n_mat[:,:,-1].max(), n_mat[:,:,-1].min()
# print 'max and min labor, j = 6 = ', n_mat[:,:,-2].max(), n_mat[:,:,-2].min()
# print 'max and min labor, j = 5 = ', n_mat[:,:,4].max(), n_mat[:,:,4].min()
# print 'max and min labor, j = 4 = ', n_mat[:,:,3].max(), n_mat[:,:,3].min()
# print 'max and min labor, j = 3 = ', n_mat[:,:,2].max(), n_mat[:,:,2].min()
# print 'max and min labor, j = 2 = ', n_mat[:,:,1].max(), n_mat[:,:,1].min()
# print 'max and min labor, j = 1 = ', n_mat[:,:,0].max(), n_mat[:,:,0].min()
# print 'max and min labor, S = 80 = ', n_mat[:,-1,-1].max(), n_mat[:,-1,-1].min()
# print "number > 1 = ", (n_mat > 1).sum()
# print "number < 0, = ", (n_mat < 0).sum()
# print "number > 1, j=7 = ", (n_mat[:T,:,-1] > 1).sum()
# print "number < 0, j=7 = ", (n_mat[:T,:,-1] < 0).sum()
# print "number > 1, s=80, j=7 = ", (n_mat[:T,-1,-1] > 1).sum()
# print "number < 0, s=80, j=7 = ", (n_mat[:T,-1,-1] < 0).sum()
# print "number > 1, j= 7, age 80= ", (n_mat[:T,-1,-1] > 1).sum()
# print "number < 0, j = 7, age 80= ", (n_mat[:T,-1,-1] < 0).sum()
# print "number > 1, j= 7, age 80, period 0 to 10= ", (n_mat[:30,-1,-1] > 1).sum()
# print "number < 0, j = 7, age 80, period 0 to 10= ", (n_mat[:30,-1,-1] < 0).sum()
# print "number > 1, j= 7, age 70-79, period 0 to 10= ", (n_mat[:30,70:80,-1] > 1).sum()
# print "number < 0, j = 7, age 70-79, period 0 to 10= ", (n_mat[:30,70:80 ,-1] < 0).sum()
# diag_dict = {'n_mat': n_mat, 'b_mat': b_mat, 'y_path': y_path, 'c_path': c_path}
# pickle.dump(diag_dict, open('tpi_iter1.pkl', 'wb'))
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:T], r[:T])) +
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) +
list(np.abs(T_H_new[:T] - T_H[:T]))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
# if TPIiter > 10:
# if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
# nu /= 2
# print 'New Value of nu:', nu
TPIiter += 1
print '\tIteration:', TPIiter
print '\t\tDistance:', TPIdist
Y[:T] = Ynew
# Solve HH problem in inner loop
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, ind)
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars,
inner_loop_params)
bmat_s = np.zeros((T, S, J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:T - 1, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[:T, :, :]
K[0] = K0
K_params = (omega[:T - 1].reshape(T - 1, S, 1), lambdas.reshape(1, 1, J),
imm_rates[:T - 1].reshape(T - 1, S, 1), g_n_vector[1:T], 'TPI')
K[1:T] = household.get_K(bmat_splus1[:T - 1], K_params)
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1),
lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(n_mat[:T], L_params)
Y_params = (alpha, Z)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
r_params = (alpha, delta)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
wnew = firm.get_w_from_r(rnew, w_params)
omega_shift = np.append(omega_S_preTP.reshape(1, S),
omega[:T - 1, :],
axis=0)
BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J),
rho.reshape(1, S, 1), g_n_vector[:T].reshape(T, 1), 'TPI')
b_mat_shift = np.append(np.reshape(initial_b, (1, S, J)),
b_mat[:T - 1, :, :],
axis=0)
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat_shift, BQ_params)
total_tax_params = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
total_tax_params[:, :, :, i] = np.tile(
np.reshape(np.transpose(etr_params[:, :T, i]), (T, S, 1)),
(1, 1, J))
tax_receipt_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)),
lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1),
'TPI', total_tax_params, theta, tau_bq, tau_payroll,
h_wealth, p_wealth, m_wealth, retire, T, S, J)
net_tax_receipts = np.array(
list(
tax.get_lump_sum(np.tile(rnew[:T].reshape(T, 1, 1), (
1, S, J)), np.tile(wnew[:T].reshape(T, 1, 1), (
1, S, J)), bmat_s, n_mat[:T, :, :], BQnew[:T].reshape(
T, 1, J), factor, tax_receipt_params)) + [T_Hss] * S)
if fix_transfers:
G[:T] = net_tax_receipts[:T] - T_H[:T]
else:
T_H[:T] = net_tax_receipts[:T]
G[:T] = 0.0
etr_params_path = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:, :, :, i] = np.tile(
np.reshape(np.transpose(etr_params[:, :T, i]), (T, S, 1)),
(1, 1, J))
tax_path_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)), lambdas, 'TPI',
retire, etr_params_path, h_wealth, p_wealth, m_wealth,
tau_payroll, theta, tau_bq, J, S)
tax_path = tax.total_taxes(np.tile(r[:T].reshape(T, 1, 1), (1, S, J)),
np.tile(w[:T].reshape(T, 1, 1),
(1, S, J)), bmat_s, n_mat[:T, :, :],
BQ[:T, :].reshape(T, 1, J), factor,
T_H[:T].reshape(T, 1, 1), None, False,
tax_path_params)
cons_params = (e.reshape(1, S, J), lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(r[:T].reshape(T, 1, 1), w[:T].reshape(T, 1, 1),
bmat_s, bmat_splus1, n_mat[:T, :, :],
BQ[:T].reshape(T, 1, J), tax_path, cons_params)
C_params = (omega[:T].reshape(T, S, 1), lambdas, 'TPI')
C = household.get_C(c_path, C_params)
I_params = (delta, g_y, omega[:T].reshape(T, S, 1), lambdas,
imm_rates[:T].reshape(T, S, 1), g_n_vector[1:T + 1], 'TPI')
I = firm.get_I(bmat_splus1[:T], K[1:T + 1], K[:T], I_params)
rc_error = Y[:T] - C[:T] - I[:T] - G[:T]
print 'Resource Constraint Difference:', rc_error
# compute utility
u_params = (sigma, np.tile(chi_n.reshape(1, S, 1),
(T, 1, J)), b_ellipse, ltilde, upsilon,
np.tile(rho.reshape(1, S, 1),
(T, 1, J)), np.tile(chi_b.reshape(1, 1, J), (T, S, 1)))
utility_path = household.get_u(c_path[:T, :, :], n_mat[:T, :, :],
bmat_splus1[:T, :, :], u_params)
# compute before and after-tax income
y_path = (np.tile(r[:T].reshape(T, 1, 1), (1, S, J)) * bmat_s[:T, :, :] +
np.tile(w[:T].reshape(T, 1, 1),
(1, S, J)) * np.tile(e.reshape(1, S, J),
(T, 1, 1)) * n_mat[:T, :, :])
inctax_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)), etr_params_path)
y_aftertax_path = (y_path - tax.tau_income(
np.tile(r[:T].reshape(T, 1, 1),
(1, S, J)), np.tile(w[:T].reshape(T, 1, 1), (1, S, J)),
bmat_s[:T, :, :], n_mat[:T, :, :], factor, inctax_params))
# compute after-tax wealth
wtax_params = (h_wealth, p_wealth, m_wealth)
b_aftertax_path = bmat_s[:T, :, :] - tax.tau_wealth(
bmat_s[:T, :, :], wtax_params)
print 'Checking time path for violations of constaints.'
for t in xrange(T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_path[t], t,
ltilde)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
print 'Max Euler error, savings: ', eul_savings
print 'Max Euler error labor supply: ', eul_laborleisure
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {
'Y': Y,
'K': K,
'L': L,
'C': C,
'I': I,
'BQ': BQ,
'G': G,
'T_H': T_H,
'r': r,
'w': w,
'b_mat': b_mat,
'n_mat': n_mat,
'c_path': c_path,
'tax_path': tax_path,
'bmat_s': bmat_s,
'utility_path': utility_path,
'b_aftertax_path': b_aftertax_path,
'y_aftertax_path': y_aftertax_path,
'y_path': y_path,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure
}
macro_output = {
'Y': Y,
'K': K,
'L': L,
'C': C,
'I': I,
'BQ': BQ,
'G': G,
'T_H': T_H,
'r': r,
'w': w,
'tax_path': tax_path
}
# if ((TPIiter >= maxiter) or (np.absolute(TPIdist) > mindist_TPI)) and ENFORCE_SOLUTION_CHECKS :
# raise RuntimeError("Transition path equlibrium not found")
#
# if ((np.any(np.absolute(rc_error) >= 1e-6))
# and ENFORCE_SOLUTION_CHECKS):
# raise RuntimeError("Transition path equlibrium not found")
#
# if ((np.any(np.absolute(eul_savings) >= mindist_TPI) or
# (np.any(np.absolute(eul_laborleisure) > mindist_TPI)))
# and ENFORCE_SOLUTION_CHECKS):
# raise RuntimeError("Transition path equlibrium not found")
return output, macro_output
def run_time_path_iteration(Kss,
Lss,
Yss,
BQss,
theta,
parameters,
g_n_vector,
omega_stationary,
K0,
b_sinit,
b_splus1init,
L0,
Y0,
r0,
BQ0,
T_H_0,
tax0,
c0,
initial_b,
initial_n,
factor_ss,
tau_bq,
chi_b,
chi_n,
get_baseline=False,
output_dir="./OUTPUT",
**kwargs):
TPI_FIG_DIR = output_dir
# Initialize Time paths
domain = np.linspace(0, T, T)
Kinit = (-1 / (domain + 1)) * (Kss - K0) + Kss
Kinit[-1] = Kss
Kinit = np.array(list(Kinit) + list(np.ones(S) * Kss))
Linit = np.ones(T + S) * Lss
Yinit = firm.get_Y(Kinit, Linit, parameters)
winit = firm.get_w(Yinit, Linit, parameters)
rinit = firm.get_r(Yinit, Kinit, parameters)
BQinit = np.zeros((T + S, J))
for j in xrange(J):
BQinit[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQinit = np.array(BQinit)
T_H_init = np.ones(T + S) * T_Hss
# Make array of initial guesses
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = np.zeros((T + S, S, J))
n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
Kpath_TPI = list(Kinit) + list(np.ones(10) * Kss)
Lpath_TPI = list(Linit) + list(np.ones(10) * Lss)
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
plt.figure()
plt.axhline(y=Kss,
color='black',
linewidth=2,
label=r"Steady State $\hat{K}$",
ls='--')
plt.plot(np.arange(T + 10),
Kpath_TPI[:T + 10],
'b',
linewidth=2,
label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_K"))
# Uncomment the following print statements to make sure all euler equations are converging.
# If they don't, then you'll have negative consumption or consumption spikes. If they don't,
# it is the initial guesses. You might need to scale them differently. It is rather delicate for the first
# few periods and high ability groups.
for j in xrange(J):
b_mat[1, -1, j], n_mat[0, -1, j] = np.array(
opt.fsolve(SS_TPI_firstdoughnutring,
[guesses_b[1, -1, j], guesses_n[0, -1, j]],
args=(winit[1], rinit[1], BQinit[1, j], T_H_init[1],
initial_b, factor_ss, j, parameters, theta,
tau_bq),
xtol=1e-13))
# if np.array(SS_TPI_firstdoughnutring([b_mat[1, -1, j], n_mat[0, -1, j]], winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b, factor_ss, j, parameters, theta, tau_bq)).max() > 1e-6:
# print 'minidoughnut:',
# np.array(SS_TPI_firstdoughnutring([b_mat[1, -1, j], n_mat[0, -1,
# j]], winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b,
# factor_ss, j, parameters, theta, tau_bq)).max()
for s in xrange(S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[1:S + 1, :, j],
S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:S, :, j], S - (s + 2))
solutions = opt.fsolve(
Steady_state_TPI_solver,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(winit, rinit, BQinit[:, j], T_H_init, factor_ss, j,
s, 0, parameters, theta, tau_bq, rho, lambdas, e,
initial_b, chi_b, chi_n),
xtol=1e-13)
b_vec = solutions[:len(solutions) / 2]
b_mat[1 + ind2, S - (s + 2) + ind2, j] = b_vec
n_vec = solutions[len(solutions) / 2:]
n_mat[ind2, S - (s + 2) + ind2, j] = n_vec
# if abs(np.array(Steady_state_TPI_solver(solutions, winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, s, 0, parameters, theta, tau_bq, rho, lambdas, e, initial_b, chi_b, chi_n))).max() > 1e-6:
# print 's-loop:',
# abs(np.array(Steady_state_TPI_solver(solutions, winit, rinit,
# BQinit[:, j], T_H_init, factor_ss, j, s, 0, parameters,
# theta, tau_bq, rho, lambdas, e, initial_b, chi_b,
# chi_n))).max()
for t in xrange(0, T):
b_guesses_to_use = .75 * \
np.diag(guesses_b[t + 1:t + S + 1, :, j])
n_guesses_to_use = np.diag(guesses_n[t:t + S, :, j])
solutions = opt.fsolve(
Steady_state_TPI_solver,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(winit, rinit, BQinit[:, j], T_H_init, factor_ss, j,
None, t, parameters, theta, tau_bq, rho, lambdas, e,
None, chi_b, chi_n),
xtol=1e-13)
b_vec = solutions[:S]
b_mat[t + 1 + ind, ind, j] = b_vec
n_vec = solutions[S:]
n_mat[t + ind, ind, j] = n_vec
inputs = list(solutions)
euler_errors[t, :, j] = np.abs(
Steady_state_TPI_solver(inputs, winit, rinit, BQinit[:, j],
T_H_init, factor_ss, j, None, t,
parameters, theta, tau_bq, rho,
lambdas, e, None, chi_b, chi_n))
# if euler_errors.max() > 1e-6:
# print 't-loop:', euler_errors.max()
# Force the initial distribution of capital to be as given above.
b_mat[0, :, :] = initial_b
Kinit = household.get_K(b_mat[:T],
omega_stationary[:T].reshape(T, S, 1),
lambdas.reshape(1, 1,
J), g_n_vector[:T], 'TPI')
Linit = firm.get_L(e.reshape(1, S, J), n_mat[:T],
omega_stationary[:T, :].reshape(T, S, 1),
lambdas.reshape(1, 1, J), 'TPI')
Ynew = firm.get_Y(Kinit, Linit, parameters)
wnew = firm.get_w(Ynew, Linit, parameters)
rnew = firm.get_r(Ynew, Kinit, parameters)
# the following needs a g_n term
BQnew = household.get_BQ(rnew.reshape(T, 1), b_mat[:T],
omega_stationary[:T].reshape(T, S, 1),
lambdas.reshape(1, 1,
J), rho.reshape(1, S, 1),
g_n_vector[:T].reshape(T, 1), 'TPI')
bmat_s = np.zeros((T, S, J))
bmat_s[:, 1:, :] = b_mat[:T, :-1, :]
T_H_new = np.array(
list(
tax.get_lump_sum(
rnew.reshape(T, 1, 1), bmat_s, wnew.reshape(T, 1, 1),
e.reshape(1, S, J), n_mat[:T], BQnew.reshape(T, 1, J),
lambdas.reshape(1, 1, J), factor_ss, omega_stationary[:T].
reshape(T, S, 1), 'TPI', parameters, theta, tau_bq)) +
[T_Hss] * S)
winit[:T] = utils.convex_combo(wnew, winit[:T], parameters)
rinit[:T] = utils.convex_combo(rnew, rinit[:T], parameters)
BQinit[:T] = utils.convex_combo(BQnew, BQinit[:T], parameters)
T_H_init[:T] = utils.convex_combo(T_H_new[:T], T_H_init[:T],
parameters)
guesses_b = utils.convex_combo(b_mat, guesses_b, parameters)
guesses_n = utils.convex_combo(n_mat, guesses_n, parameters)
if T_H_init.all() != 0:
TPIdist = np.array(
list(utils.perc_dif_func(rnew, rinit[:T])) +
list(utils.perc_dif_func(BQnew, BQinit[:T]).flatten()) +
list(utils.perc_dif_func(wnew, winit[:T])) +
list(utils.perc_dif_func(T_H_new, T_H_init))).max()
else:
TPIdist = np.array(
list(utils.perc_dif_func(rnew, rinit[:T])) +
list(utils.perc_dif_func(BQnew, BQinit[:T]).flatten()) +
list(utils.perc_dif_func(wnew, winit[:T])) +
list(np.abs(T_H_new, T_H_init))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
if TPIiter > 10:
if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
nu /= 2
print 'New Value of nu:', nu
TPIiter += 1
print '\tIteration:', TPIiter
print '\t\tDistance:', TPIdist
print 'Computing final solutions'
# As in SS, you need the final distributions of b and n to match the final
# w, r, BQ, etc. Otherwise the euler errors are large. You need one more
# fsolve.
for j in xrange(J):
b_mat[1, -1, j], n_mat[0, -1, j] = np.array(
opt.fsolve(SS_TPI_firstdoughnutring,
[guesses_b[1, -1, j], guesses_n[0, -1, j]],
args=(winit[1], rinit[1], BQinit[1, j], T_H_init[1],
initial_b, factor_ss, j, parameters, theta,
tau_bq),
xtol=1e-13))
for s in xrange(S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[1:S + 1, :, j], S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:S, :, j], S - (s + 2))
solutions = opt.fsolve(
Steady_state_TPI_solver,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, s, 0,
parameters, theta, tau_bq, rho, lambdas, e, initial_b,
chi_b, chi_n),
xtol=1e-13)
b_vec = solutions[:len(solutions) / 2]
b_mat[1 + ind2, S - (s + 2) + ind2, j] = b_vec
n_vec = solutions[len(solutions) / 2:]
n_mat[ind2, S - (s + 2) + ind2, j] = n_vec
for t in xrange(0, T):
b_guesses_to_use = .75 * np.diag(guesses_b[t + 1:t + S + 1, :, j])
n_guesses_to_use = np.diag(guesses_n[t:t + S, :, j])
solutions = opt.fsolve(
Steady_state_TPI_solver,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None,
t, parameters, theta, tau_bq, rho, lambdas, e, None,
chi_b, chi_n),
xtol=1e-13)
b_vec = solutions[:S]
b_mat[t + 1 + ind, ind, j] = b_vec
n_vec = solutions[S:]
n_mat[t + ind, ind, j] = n_vec
inputs = list(solutions)
euler_errors[t, :, j] = np.abs(
Steady_state_TPI_solver(inputs, winit, rinit, BQinit[:, j],
T_H_init, factor_ss, j, None, t,
parameters, theta, tau_bq, rho,
lambdas, e, None, chi_b, chi_n))
b_mat[0, :, :] = initial_b
'''
------------------------------------------------------------------------
Generate variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
Kpath_TPI = np.array(list(Kinit) + list(np.ones(10) * Kss))
Lpath_TPI = np.array(list(Linit) + list(np.ones(10) * Lss))
BQpath_TPI = np.array(list(BQinit) + list(np.ones((10, J)) * BQss))
b_s = np.zeros((T, S, J))
b_s[:, 1:, :] = b_mat[:T, :-1, :]
b_splus1 = np.zeros((T, S, J))
b_splus1[:, :, :] = b_mat[1:T + 1, :, :]
tax_path = tax.total_taxes(rinit[:T].reshape(T, 1, 1),
b_s, winit[:T].reshape(T, 1, 1),
e.reshape(1, S, J), n_mat[:T],
BQinit[:T, :].reshape(T, 1, J), lambdas,
factor_ss, T_H_init[:T].reshape(T, 1, 1), None,
'TPI', False, parameters, theta, tau_bq)
c_path = household.get_cons(rinit[:T].reshape(T, 1, 1),
b_s, winit[:T].reshape(T, 1, 1),
e.reshape(1, S, J), n_mat[:T],
BQinit[:T].reshape(T, 1, J),
lambdas.reshape(1, 1, J), b_splus1, parameters,
tax_path)
Y_path = firm.get_Y(Kpath_TPI[:T], Lpath_TPI[:T], parameters)
C_path = household.get_C(c_path, omega_stationary[:T].reshape(T, S, 1),
lambdas, 'TPI')
I_path = firm.get_I(Kpath_TPI[1:T + 1], Kpath_TPI[:T], delta, g_y,
g_n_vector[:T])
print 'Resource Constraint Difference:', Y_path - C_path - I_path
print 'Checking time path for violations of constaints.'
for t in xrange(T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_path[t], t,
parameters)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {
'Kpath_TPI': Kpath_TPI,
'b_mat': b_mat,
'c_path': c_path,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure,
'Lpath_TPI': Lpath_TPI,
'BQpath_TPI': BQpath_TPI,
'n_mat': n_mat,
'rinit': rinit,
'Yinit': Yinit,
'T_H_init': T_H_init,
'tax_path': tax_path,
'winit': winit
}
if get_baseline:
tpi_init_dir = os.path.join(output_dir, "TPIinit")
utils.mkdirs(tpi_init_dir)
tpi_init_vars = os.path.join(tpi_init_dir, "TPIinit_vars.pkl")
pickle.dump(output, open(tpi_init_vars, "wb"))
else:
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
def run_TPI(income_tax_params, tpi_params, iterative_params,
initial_values, SS_values, fix_transfers=False,
output_dir="./OUTPUT"):
# unpack tuples of parameters
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
maxiter, mindist_SS, mindist_TPI = iterative_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, imm_rates, e, retire, mean_income_data,\
factor, T_H_baseline, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = tpi_params
K0, b_sinit, b_splus1init, factor, initial_b, initial_n, omega_S_preTP = initial_values
Kss, Lss, rss, wss, BQss, T_Hss, Gss, bssmat_splus1, nssmat = SS_values
TPI_FIG_DIR = output_dir
# Initialize guesses at time paths
domain = np.linspace(0, T, T)
r = np.ones(T + S) * rss
BQ = np.zeros((T + S, J))
BQ0_params = (omega_S_preTP.reshape(S, 1), lambdas, rho.reshape(S, 1), g_n_vector[0], 'SS')
BQ0 = household.get_BQ(r[0], initial_b, BQ0_params)
for j in xrange(J):
BQ[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQ = np.array(BQ)
# print "BQ values = ", BQ[0, :], BQ[100, :], BQ[-1, :], BQss
# print "K0 vs Kss = ", K0-Kss
if fix_transfers:
T_H = T_H_baseline
else:
if np.abs(T_Hss) < 1e-13 :
T_Hss2 = 0.0 # sometimes SS is very small but not zero, even if taxes are zero, this get's rid of the approximation error, which affects the perc changes below
else:
T_Hss2 = T_Hss
T_H = np.ones(T + S) * T_Hss2 * (r/rss)
G = np.ones(T + S) * Gss
# # print "T_H values = ", T_H[0], T_H[100], T_H[-1], T_Hss
# # print "omega diffs = ", (omega_S_preTP-omega[-1]).max(), (omega[10]-omega[-1]).max()
#
# Make array of initial guesses for labor supply and savings
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
# print 'diff btwn start and end b: ', (guesses_b[0]-guesses_b[-1]).max()
#
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
# b_mat = np.zeros((T + S, S, J))
# n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
# # print 'diff btwn start and end n: ', (guesses_n[0]-guesses_n[-1]).max()
#
# # find economic aggregates
K = np.zeros(T+S)
L = np.zeros(T+S)
K[0] = K0
K_params = (omega[:T-1].reshape(T-1, S, 1), lambdas.reshape(1, 1, J), imm_rates[:T-1].reshape(T-1,S,1), g_n_vector[1:T], 'TPI')
K[1:T] = household.get_K(guesses_b[:T-1], K_params)
K[T:] = Kss
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(guesses_n[:T], L_params)
L[T:] = Lss
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
r[:T] = firm.get_r(Y[:T], K[:T], r_params)
# uncomment lines below if want to use starting values from prior run
r = TPI_START_VALUES['r']
K = TPI_START_VALUES['K']
L = TPI_START_VALUES['L']
Y = TPI_START_VALUES['Y']
T_H = TPI_START_VALUES['T_H']
BQ = TPI_START_VALUES['BQ']
G = TPI_START_VALUES['G']
guesses_b = TPI_START_VALUES['b_mat']
guesses_n = TPI_START_VALUES['n_mat']
TPIiter = 0
TPIdist = 10
PLOT_TPI = False
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
# print 'analytical mtrs in tpi = ', analytical_mtrs
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
K_plot = list(K) + list(np.ones(10) * Kss)
L_plot = list(L) + list(np.ones(10) * Lss)
plt.figure()
plt.axhline(
y=Kss, color='black', linewidth=2, label=r"Steady State $\hat{K}$", ls='--')
plt.plot(np.arange(
T + 10), Kpath_plot[:T + 10], 'b', linewidth=2, label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_K"))
guesses = (guesses_b, guesses_n)
w_params = (Z, alpha, delta)
w = firm.get_w_from_r(r, w_params)
# print 'r and rss diff = ', r-rss
# print 'w and wss diff = ', w-wss
# print 'BQ and BQss diff = ', BQ-BQss
# print 'T_H and T_Hss diff = ', T_H - T_Hss
# print 'guess b and bss = ', (bssmat_splus1 - guesses_b).max()
# print 'guess n and nss = ', (nssmat - guesses_n).max()
outer_loop_vars = (r, w, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, ind)
# Solve HH problem in inner loop
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars, inner_loop_params)
# print 'guess b and bss = ', (b_mat - guesses_b).max()
# print 'guess n and nss over time = ', (n_mat - guesses_n).max(axis=2).max(axis=1)
# print 'guess n and nss over age = ', (n_mat - guesses_n).max(axis=0).max(axis=1)
# print 'guess n and nss over ability = ', (n_mat - guesses_n).max(axis=0).max(axis=0)
# quit()
print 'Max Euler error: ', (np.abs(euler_errors)).max()
bmat_s = np.zeros((T, S, J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:T-1, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[:T, :, :]
K[0] = K0
K_params = (omega[:T-1].reshape(T-1, S, 1), lambdas.reshape(1, 1, J),
imm_rates[:T-1].reshape(T-1, S, 1), g_n_vector[1:T], 'TPI')
K[1:T] = household.get_K(bmat_splus1[:T-1], K_params)
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1),
lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(n_mat[:T], L_params)
# print 'K diffs = ', K-K0
# print 'L diffs = ', L-L[0]
Y_params = (alpha, Z)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
r_params = (alpha, delta)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
wnew = firm.get_w_from_r(rnew, w_params)
omega_shift = np.append(omega_S_preTP.reshape(1, S),
omega[:T-1, :], axis=0)
BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J),
rho.reshape(1, S, 1), g_n_vector[:T].reshape(T, 1), 'TPI')
# b_mat_shift = np.append(np.reshape(initial_b, (1, S, J)),
# b_mat[:T-1, :, :], axis=0)
b_mat_shift = bmat_splus1[:T, :, :]
# print 'b diffs = ', (bmat_splus1[100, :, :] - initial_b).max(), (bmat_splus1[0, :, :] - initial_b).max(), (bmat_splus1[1, :, :] - initial_b).max()
# print 'r diffs = ', rnew[1]-r[1], rnew[100]-r[100], rnew[-1]-r[-1]
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat_shift,
BQ_params)
BQss2 = np.empty(J)
for j in range(J):
BQss_params = (omega[1, :], lambdas[j], rho, g_n_vector[1], 'SS')
BQss2[j] = household.get_BQ(rnew[1], bmat_splus1[1, :, j],
BQss_params)
# print 'BQ test = ', BQss2-BQss, BQss-BQnew[1], BQss-BQnew[100], BQss-BQnew[-1]
total_tax_params = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
total_tax_params[:, :, :, i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_receipt_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
total_tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
net_tax_receipts = np.array(list(tax.get_lump_sum(np.tile(rnew[:T].reshape(T, 1, 1),(1,S,J)), np.tile(wnew[:T].reshape(T, 1, 1),(1,S,J)),
bmat_s, n_mat[:T,:,:], BQnew[:T].reshape(T, 1, J), factor, tax_receipt_params)) + [T_Hss] * S)
r[:T] = utils.convex_combo(rnew[:T], r[:T], nu)
BQ[:T] = utils.convex_combo(BQnew[:T], BQ[:T], nu)
if fix_transfers:
T_H_new = T_H
G[:T] = net_tax_receipts[:T] - T_H[:T]
else:
T_H_new = net_tax_receipts
T_H[:T] = utils.convex_combo(T_H_new[:T], T_H[:T], nu)
G[:T] = 0.0
etr_params_path = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:,:,:,i] = np.tile(
np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_path_params = (np.tile(e.reshape(1, S, J),(T,1,1)),
lambdas, 'TPI', retire, etr_params_path, h_wealth,
p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
b_to_use = np.zeros((T, S, J))
b_to_use[0, 1:, :] = initial_b[:-1, :]
b_to_use[1:, 1:, :] = b_mat[:T-1, :-1, :]
tax_path = tax.total_taxes(
np.tile(r[:T].reshape(T, 1, 1),(1,S,J)),
np.tile(w[:T].reshape(T, 1, 1),(1,S,J)), b_to_use,
n_mat[:T,:,:], BQ[:T, :].reshape(T, 1, J), factor,
T_H[:T].reshape(T, 1, 1), None, False, tax_path_params)
y_path = (np.tile(r[:T].reshape(T, 1, 1), (1, S, J)) * b_to_use[:T, :, :] +
np.tile(w[:T].reshape(T, 1, 1), (1, S, J)) *
np.tile(e.reshape(1, S, J), (T, 1, 1)) * n_mat[:T, :, :])
cons_params = (e.reshape(1, S, J), lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(r[:T].reshape(T, 1, 1), w[:T].reshape(T, 1, 1), b_to_use[:T,:,:], b_mat[:T,:,:], n_mat[:T,:,:],
BQ[:T].reshape(T, 1, J), tax_path, cons_params)
guesses_b = utils.convex_combo(b_mat, guesses_b, nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, nu)
if T_H.all() != 0:
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) +
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) +
list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
print 'r dist = ', np.array(list(utils.pct_diff_func(rnew[:T], r[:T]))).max()
print 'BQ dist = ', np.array(list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten())).max()
print 'T_H dist = ', np.array(list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
print 'T_H path = ', T_H[:20]
# print 'r old = ', r[:T]
# print 'r new = ', rnew[:T]
# print 'K old = ', K[:T]
# print 'L old = ', L[:T]
# print 'income = ', y_path[:, :, -1]
# print 'taxes = ', tax_path[:, :, -1]
# print 'labor supply = ', n_mat[:, :, -1]
# print 'max and min labor = ', n_mat.max(), n_mat.min()
# print 'max and min labor = ', np.argmax(n_mat), np.argmin(n_mat)
# print 'max and min labor, j = 7 = ', n_mat[:,:,-1].max(), n_mat[:,:,-1].min()
# print 'max and min labor, j = 6 = ', n_mat[:,:,-2].max(), n_mat[:,:,-2].min()
# print 'max and min labor, j = 5 = ', n_mat[:,:,4].max(), n_mat[:,:,4].min()
# print 'max and min labor, j = 4 = ', n_mat[:,:,3].max(), n_mat[:,:,3].min()
# print 'max and min labor, j = 3 = ', n_mat[:,:,2].max(), n_mat[:,:,2].min()
# print 'max and min labor, j = 2 = ', n_mat[:,:,1].max(), n_mat[:,:,1].min()
# print 'max and min labor, j = 1 = ', n_mat[:,:,0].max(), n_mat[:,:,0].min()
# print 'max and min labor, S = 80 = ', n_mat[:,-1,-1].max(), n_mat[:,-1,-1].min()
# print "number > 1 = ", (n_mat > 1).sum()
# print "number < 0, = ", (n_mat < 0).sum()
# print "number > 1, j=7 = ", (n_mat[:T,:,-1] > 1).sum()
# print "number < 0, j=7 = ", (n_mat[:T,:,-1] < 0).sum()
# print "number > 1, s=80, j=7 = ", (n_mat[:T,-1,-1] > 1).sum()
# print "number < 0, s=80, j=7 = ", (n_mat[:T,-1,-1] < 0).sum()
# print "number > 1, j= 7, age 80= ", (n_mat[:T,-1,-1] > 1).sum()
# print "number < 0, j = 7, age 80= ", (n_mat[:T,-1,-1] < 0).sum()
# print "number > 1, j= 7, age 80, period 0 to 10= ", (n_mat[:30,-1,-1] > 1).sum()
# print "number < 0, j = 7, age 80, period 0 to 10= ", (n_mat[:30,-1,-1] < 0).sum()
# print "number > 1, j= 7, age 70-79, period 0 to 10= ", (n_mat[:30,70:80,-1] > 1).sum()
# print "number < 0, j = 7, age 70-79, period 0 to 10= ", (n_mat[:30,70:80 ,-1] < 0).sum()
# diag_dict = {'n_mat': n_mat, 'b_mat': b_mat, 'y_path': y_path, 'c_path': c_path}
# pickle.dump(diag_dict, open('tpi_iter1.pkl', 'wb'))
else:
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) +
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) +
list(np.abs(T_H_new[:T]-T_H[:T]))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
# if TPIiter > 10:
# if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
# nu /= 2
# print 'New Value of nu:', nu
TPIiter += 1
print '\tIteration:', TPIiter
print '\t\tDistance:', TPIdist
Y[:T] = Ynew
# Solve HH problem in inner loop
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, ind)
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars, inner_loop_params)
bmat_s = np.zeros((T, S, J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:T-1, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[:T, :, :]
K[0] = K0
K_params = (omega[:T-1].reshape(T-1, S, 1), lambdas.reshape(1, 1, J), imm_rates[:T-1].reshape(T-1,S,1), g_n_vector[1:T], 'TPI')
K[1:T] = household.get_K(bmat_splus1[:T-1], K_params)
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(n_mat[:T], L_params)
Y_params = (alpha, Z)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
r_params = (alpha, delta)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
wnew = firm.get_w_from_r(rnew, w_params)
omega_shift = np.append(omega_S_preTP.reshape(1,S),omega[:T-1,:],axis=0)
BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J), rho.reshape(1, S, 1),
g_n_vector[:T].reshape(T, 1), 'TPI')
b_mat_shift = np.append(np.reshape(initial_b,(1,S,J)),b_mat[:T-1,:,:],axis=0)
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat_shift, BQ_params)
total_tax_params = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
total_tax_params[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_receipt_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
total_tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
net_tax_receipts = np.array(list(tax.get_lump_sum(np.tile(rnew[:T].reshape(T, 1, 1),(1,S,J)), np.tile(wnew[:T].reshape(T, 1, 1),(1,S,J)),
bmat_s, n_mat[:T,:,:], BQnew[:T].reshape(T, 1, J), factor, tax_receipt_params)) + [T_Hss] * S)
if fix_transfers:
G[:T] = net_tax_receipts[:T] - T_H[:T]
else:
T_H[:T] = net_tax_receipts[:T]
G[:T] = 0.0
etr_params_path = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_path_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas, 'TPI', retire, etr_params_path, h_wealth,
p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax_path = tax.total_taxes(np.tile(r[:T].reshape(T, 1, 1),(1,S,J)), np.tile(w[:T].reshape(T, 1, 1),(1,S,J)), bmat_s,
n_mat[:T,:,:], BQ[:T, :].reshape(T, 1, J), factor, T_H[:T].reshape(T, 1, 1), None, False, tax_path_params)
cons_params = (e.reshape(1, S, J), lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(r[:T].reshape(T, 1, 1), w[:T].reshape(T, 1, 1), bmat_s, bmat_splus1, n_mat[:T,:,:],
BQ[:T].reshape(T, 1, J), tax_path, cons_params)
C_params = (omega[:T].reshape(T, S, 1), lambdas, 'TPI')
C = household.get_C(c_path, C_params)
I_params = (delta, g_y, omega[:T].reshape(T, S, 1), lambdas, imm_rates[:T].reshape(T, S, 1), g_n_vector[1:T+1], 'TPI')
I = firm.get_I(bmat_splus1[:T], K[1:T+1], K[:T], I_params)
rc_error = Y[:T] - C[:T] - I[:T] - G[:T]
print 'Resource Constraint Difference:', rc_error
# compute utility
u_params = (sigma, np.tile(chi_n.reshape(1, S, 1), (T, 1, J)),
b_ellipse, ltilde, upsilon,
np.tile(rho.reshape(1, S, 1), (T, 1, J)),
np.tile(chi_b.reshape(1, 1, J), (T, S, 1)))
utility_path = household.get_u(c_path[:T, :, :], n_mat[:T, :, :],
bmat_splus1[:T, :, :], u_params)
# compute before and after-tax income
y_path = (np.tile(r[:T].reshape(T, 1, 1), (1, S, J)) * bmat_s[:T, :, :] +
np.tile(w[:T].reshape(T, 1, 1), (1, S, J)) *
np.tile(e.reshape(1, S, J), (T, 1, 1)) * n_mat[:T, :, :])
inctax_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)), etr_params_path)
y_aftertax_path = (y_path -
tax.tau_income(np.tile(r[:T].reshape(T, 1, 1), (1, S, J)),
np.tile(w[:T].reshape(T, 1, 1), (1, S, J)),
bmat_s[:T,:,:], n_mat[:T,:,:], factor, inctax_params))
# compute after-tax wealth
wtax_params = (h_wealth, p_wealth, m_wealth)
b_aftertax_path = bmat_s[:T,:,:] - tax.tau_wealth(bmat_s[:T,:,:], wtax_params)
print'Checking time path for violations of constaints.'
for t in xrange(T):
household.constraint_checker_TPI(
b_mat[t], n_mat[t], c_path[t], t, ltilde)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
print 'Max Euler error, savings: ', eul_savings
print 'Max Euler error labor supply: ', eul_laborleisure
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {'Y': Y, 'K': K, 'L': L, 'C': C, 'I': I, 'BQ': BQ, 'G': G,
'T_H': T_H, 'r': r, 'w': w, 'b_mat': b_mat, 'n_mat': n_mat,
'c_path': c_path, 'tax_path': tax_path, 'bmat_s': bmat_s,
'utility_path': utility_path, 'b_aftertax_path': b_aftertax_path,
'y_aftertax_path': y_aftertax_path, 'y_path': y_path,
'eul_savings': eul_savings, 'eul_laborleisure': eul_laborleisure}
macro_output = {'Y': Y, 'K': K, 'L': L, 'C': C, 'I': I,
'BQ': BQ, 'G': G, 'T_H': T_H, 'r': r, 'w': w,
'tax_path': tax_path}
# if ((TPIiter >= maxiter) or (np.absolute(TPIdist) > mindist_TPI)) and ENFORCE_SOLUTION_CHECKS :
# raise RuntimeError("Transition path equlibrium not found")
#
# if ((np.any(np.absolute(rc_error) >= 1e-6))
# and ENFORCE_SOLUTION_CHECKS):
# raise RuntimeError("Transition path equlibrium not found")
#
# if ((np.any(np.absolute(eul_savings) >= mindist_TPI) or
# (np.any(np.absolute(eul_laborleisure) > mindist_TPI)))
# and ENFORCE_SOLUTION_CHECKS):
# raise RuntimeError("Transition path equlibrium not found")
return output, macro_output
def FOC_savings(r, w, b, b_splus1, b_splus2, n, BQ, factor, T_H,
params):
'''
Computes Euler errors for the FOC for savings in the steady state.
This function is usually looped through over J, so it does one
lifetime income group at a time.
Inputs:
r = scalar, interest rate
w = scalar, wage rate
b = [S,J] array, distribution of wealth/capital
b_splus1 = [S,J] array, distribution of wealth/capital,
one period ahead
b_splus2 = [S,J] array, distribution of wealth/capital, two
periods ahead
n = [S,J] array, distribution of labor supply
BQ = [J,] vector, aggregate bequests by lifetime income
group
factor = scalar, scaling factor to convert model income to
dollars
T_H = scalar, lump sum transfer
params = length 18 tuple (e, sigma, beta, g_y, chi_b,
theta, tau_bq, rho, lambdas, J,
S, etr_params, mtry_params,
h_wealth, p_wealth, m_wealth,
tau_payroll, tau_bq)
e = [S,J] array, effective labor units
sigma = scalar, coefficient of relative risk aversion
beta = scalar, discount factor
g_y = scalar, exogenous labor augmenting technological
growth
chi_b = [J,] vector, utility weight on bequests for each
lifetime income group
theta = [J,] vector, replacement rate for each lifetime
income group
tau_bq = scalar, bequest tax rate (scalar)
rho = [S,] vector, mortality rates
lambdas = [J,] vector, ability weights
J = integer, number of lifetime income groups
S = integer, number of economically active periods in
lifetime
etr_params = [S,12] array, parameters of effective income tax
rate function
mtry_params = [S,12] array, parameters of marginal tax rate on
capital income function
h_wealth = scalar, parameter in wealth tax function
p_wealth = scalar, parameter in wealth tax function
m_wealth = scalar, parameter in wealth tax function
tau_payroll = scalar, payroll tax rate
tau_bq = scalar, bequest tax rate
Functions called:
get_cons
marg_ut_cons
tax.total_taxes
tax.MTR_capital
Objects in function:
tax1 = [S,J] array, net taxes in the current period
tax2 = [S,J] array, net taxes one period ahead
cons1 = [S,J] array, consumption in the current period
cons2 = [S,J] array, consumption one period ahead
deriv = [S,J] array, after-tax return on capital
savings_ut = [S,J] array, marginal utility from savings
euler = [S,J] array, Euler error from FOC for savings
Returns: euler
'''
(e, sigma, beta, g_y, chi_b, theta, tau_bq, rho, lambdas, j, J, S,
analytical_mtrs, etr_params, mtry_params, h_wealth, p_wealth,
m_wealth, tau_payroll, retire, method) = params
# In order to not have 2 savings euler equations (one that solves
# the first S-1 equations, and one that solves the last one), we
# combine them. In order to do this, we have to compute a
# consumption term in period t+1, which requires us to have a shifted
# e and n matrix. We append a zero on the end of both of these so
# they will be the right size. We could append any value to them,
# since in the euler equation, the coefficient on the marginal
# utility of consumption for this term will be zero (since rho is
# one).
e_extended = np.array(list(e) + [0])
n_extended = np.array(list(n) + [0])
etr_params_extended = np.append(etr_params,
np.reshape(etr_params[-1, :],
(1, etr_params.shape[1])),
axis=0)[1:, :]
mtry_params_extended = np.append(mtry_params,
np.reshape(mtry_params[-1, :],
(1, mtry_params.shape[1])),
axis=0)[1:, :]
if method == 'TPI':
r_extended = np.append(r, r[-1])
w_extended = np.append(w, w[-1])
BQ_extended = np.append(BQ, BQ[-1])
T_H_extended = np.append(T_H, T_H[-1])
elif method == 'SS':
r_extended = np.array([r, r])
w_extended = np.array([w, w])
BQ_extended = np.array([BQ, BQ])
T_H_extended = np.array([T_H, T_H])
tax1_params = (e, lambdas, method, retire, etr_params, h_wealth,
p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, j, False,
tax1_params)
tax2_params = (e_extended[1:], lambdas, method, retire,
etr_params_extended, h_wealth, p_wealth, m_wealth,
tau_payroll, theta, tau_bq, J, S)
tax2 = tax.total_taxes(r_extended[1:], w_extended[1:], b_splus1,
n_extended[1:], BQ_extended[1:], factor,
T_H_extended[1:], j, True, tax2_params)
cons1_params = (e, lambdas, g_y)
cons1 = get_cons(r, w, b, b_splus1, n, BQ, tax1, cons1_params)
cons2_params = (e_extended[1:], lambdas, g_y)
cons2 = get_cons(r_extended[1:], w_extended[1:], b_splus1, b_splus2,
n_extended[1:], BQ_extended[1:], tax2,
cons2_params)
cons2[-1] = 0.01 # set to small positive number to avoid exception
# errors when negative b/c this period value doesn't matter -
# it's consumption after the last period of life
mtr_cap_params = (e_extended[1:], etr_params_extended,
mtry_params_extended, analytical_mtrs)
deriv = ((1 + r_extended[1:]) - r_extended[1:] *
(tax.MTR_capital(r_extended[1:], w_extended[1:], b_splus1,
n_extended[1:], factor, mtr_cap_params)) -
(tax.tau_w_prime(b_splus1, (h_wealth, p_wealth, m_wealth)) *
b_splus1) - tax.tau_wealth(b_splus1, (h_wealth, p_wealth,
m_wealth)))
savings_ut = (rho * np.exp(-sigma * g_y) * chi_b * b_splus1 **
(-sigma))
euler_error = (marg_ut_cons(cons1, sigma) - beta * (1 - rho) *
deriv * marg_ut_cons(cons2, sigma) *
np.exp(-sigma * g_y) - savings_ut)
return euler_error
def run_TPI(income_tax_params, tpi_params, iterative_params, small_open_params, initial_values, SS_values, fiscal_params, biz_tax_params, output_dir="./OUTPUT", baseline_spending=False):
# unpack tuples of parameters
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
maxiter, mindist_SS, mindist_TPI = iterative_params
J, S, T, BW, beta, sigma, alpha, gamma, epsilon, Z, delta, ltilde, nu, g_y,\
g_n_vector, tau_payroll, tau_bq, rho, omega, N_tilde, lambdas, imm_rates, e, retire, mean_income_data,\
factor, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = tpi_params
# K0, b_sinit, b_splus1init, L0, Y0,\
# w0, r0, BQ0, T_H_0, factor, tax0, c0, initial_b, initial_n, omega_S_preTP = initial_values
small_open, tpi_firm_r, tpi_hh_r = small_open_params
B0, b_sinit, b_splus1init, factor, initial_b, initial_n, omega_S_preTP, initial_debt = initial_values
Kss, Bss, Lss, rss, wss, BQss, T_Hss, revenue_ss, bssmat_splus1, nssmat, Yss, Gss = SS_values
tau_b, delta_tau = biz_tax_params
if baseline_spending==False:
budget_balance, ALPHA_T, ALPHA_G, tG1, tG2, rho_G, debt_ratio_ss = fiscal_params
else:
budget_balance, ALPHA_T, ALPHA_G, tG1, tG2, rho_G, debt_ratio_ss, T_Hbaseline, Gbaseline = fiscal_params
print 'Government spending breakpoints are tG1: ', tG1, '; and tG2:', tG2
TPI_FIG_DIR = output_dir
# Initialize guesses at time paths
# Make array of initial guesses for labor supply and savings
domain = np.linspace(0, T, T)
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = guesses_b#np.zeros((T + S, S, J))
n_mat = guesses_n#np.zeros((T + S, S, J))
ind = np.arange(S)
L_init = np.ones((T+S,))*Lss
B_init = np.ones((T+S,))*Bss
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI')
L_init[:T] = firm.get_L(n_mat[:T], L_params)
B_params = (omega[:T-1].reshape(T-1, S, 1), lambdas.reshape(1, 1, J), imm_rates[:T-1].reshape(T-1,S,1), g_n_vector[1:T], 'TPI')
B_init[1:T] = household.get_K(b_mat[:T-1], B_params)
B_init[0] = B0
if small_open == False:
if budget_balance:
K_init = B_init
else:
K_init = B_init * Kss/Bss
else:
K_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
K_init = firm.get_K(L_init, tpi_firm_r, K_params)
K = K_init
# if np.any(K < 0):
# print 'K_init has negative elements. Setting them positive to prevent NAN.'
# K[:T] = np.fmax(K[:T], 0.05*B[:T])
L = L_init
B = B_init
Y_params = (Z, gamma, epsilon)
Y = firm.get_Y(K, L, Y_params)
w_params = (Z, gamma, epsilon)
w = firm.get_w(Y, L, w_params)
if small_open == False:
r_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
r = firm.get_r(Y, K, r_params)
else:
r = tpi_hh_r
BQ = np.zeros((T + S, J))
BQ0_params = (omega_S_preTP.reshape(S, 1), lambdas, rho.reshape(S, 1), g_n_vector[0], 'SS')
BQ0 = household.get_BQ(r[0], initial_b, BQ0_params)
for j in xrange(J):
BQ[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQ = np.array(BQ)
if budget_balance:
if np.abs(T_Hss) < 1e-13 :
T_Hss2 = 0.0 # sometimes SS is very small but not zero, even if taxes are zero, this get's rid of the approximation error, which affects the perc changes below
else:
T_Hss2 = T_Hss
T_H = np.ones(T + S) * T_Hss2
REVENUE = T_H
G = np.zeros(T + S)
elif baseline_spending==False:
T_H = ALPHA_T * Y
elif baseline_spending==True:
T_H = T_Hbaseline
T_H_new = T_H # Need to set T_H_new for later reference
G = Gbaseline
G_0 = Gbaseline[0]
# Initialize some inputs
# D = np.zeros(T + S)
D = debt_ratio_ss*Y
omega_shift = np.append(omega_S_preTP.reshape(1,S),omega[:T-1,:],axis=0)
BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J), rho.reshape(1, S, 1),
g_n_vector[:T].reshape(T, 1), 'TPI')
tax_params = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
tax_params[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
REVENUE_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J, tau_b, delta_tau)
# print 'D/Y:', D[:T]/Y[:T]
# print 'T/Y:', T_H[:T]/Y[:T]
# print 'G/Y:', G[:T]/Y[:T]
# print 'Int payments to GDP:', (r[:T]*D[:T])/Y[:T]
# quit()
TPIiter = 0
TPIdist = 10
PLOT_TPI = False
report_tG1 = False
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
print 'analytical mtrs in tpi = ', analytical_mtrs
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
#K_plot = list(K) + list(np.ones(10) * Kss)
D_plot = list(D) + list(np.ones(10) * Yss * debt_ratio_ss)
plt.figure()
plt.axhline(
y=Kss, color='black', linewidth=2, label=r"Steady State $\hat{K}$", ls='--')
plt.plot(np.arange(
T + 10), D_plot[:T + 10], 'b', linewidth=2, label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_D"))
if report_tG1 is True:
print '\tAt time tG1-1:'
print '\t\tG = ', G[tG1-1]
print '\t\tK = ', K[tG1-1]
print '\t\tr = ', r[tG1-1]
print '\t\tD = ', D[tG1-1]
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, K, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, ind)
# Solve HH problem in inner loop
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars, inner_loop_params)
bmat_s = np.zeros((T, S, J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:T-1, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[:T, :, :]
#L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI') # defined above
L[:T] = firm.get_L(n_mat[:T], L_params)
#B_params = (omega[:T-1].reshape(T-1, S, 1), lambdas.reshape(1, 1, J), imm_rates[:T-1].reshape(T-1,S,1), g_n_vector[1:T], 'TPI') # defined above
B[1:T] = household.get_K(bmat_splus1[:T-1], B_params)
if np.any(B) < 0:
print 'B has negative elements. B[0:9]:', B[0:9]
print 'B[T-2:T]:', B[T-2,T]
if small_open == False:
if budget_balance:
K[:T] = B[:T]
else:
if baseline_spending == False:
Y = T_H/ALPHA_T #SBF 3/3: This seems totally unnecessary as both these variables are defined above.
# tax_params = np.zeros((T,S,J,etr_params.shape[2]))
# for i in range(etr_params.shape[2]):
# tax_params[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
# REVENUE_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
# tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J, tau_b, delta_tau) # define above
REVENUE = np.array(list(tax.revenue(np.tile(r[:T].reshape(T, 1, 1),(1,S,J)), np.tile(w[:T].reshape(T, 1, 1),(1,S,J)),
bmat_s, n_mat[:T,:,:], BQ[:T].reshape(T, 1, J), Y[:T], L[:T], K[:T], factor, REVENUE_params)) + [revenue_ss] * S)
D_0 = initial_debt * Y[0]
other_dg_params = (T, r, g_n_vector, g_y)
if baseline_spending==False:
G_0 = ALPHA_G[0] * Y[0]
dg_fixed_values = (Y, REVENUE, T_H, D_0,G_0)
Dnew, G = fiscal.D_G_path(dg_fixed_values, fiscal_params, other_dg_params, baseline_spending=baseline_spending)
K[:T] = B[:T] - Dnew[:T]
if np.any(K < 0):
print 'K has negative elements. Setting them positive to prevent NAN.'
K[:T] = np.fmax(K[:T], 0.05*B[:T])
else:
# K_params previously set to = (Z, gamma, epsilon, delta, tau_b, delta_tau)
K[:T] = firm.get_K(L[:T], tpi_firm_r[:T], K_params)
Y_params = (Z, gamma, epsilon)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
Y = Ynew
w_params = (Z, gamma, epsilon)
wnew = firm.get_w(Ynew[:T], L[:T], w_params)
if small_open == False:
r_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
else:
rnew = r.copy()
print 'Y and T_H: ', Y[3], T_H[3]
# omega_shift = np.append(omega_S_preTP.reshape(1,S),omega[:T-1,:],axis=0) # defined above
# BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J), rho.reshape(1, S, 1),
# g_n_vector[:T].reshape(T, 1), 'TPI') # defined above
b_mat_shift = np.append(np.reshape(initial_b,(1,S,J)),b_mat[:T-1,:,:],axis=0)
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat_shift, BQ_params)
# tax_params = np.zeros((T,S,J,etr_params.shape[2]))
# for i in range(etr_params.shape[2]):
# tax_params[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
# REVENUE_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
# tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J, tau_b, delta_tau) # defined above
REVENUE = np.array(list(tax.revenue(np.tile(rnew[:T].reshape(T, 1, 1),(1,S,J)), np.tile(wnew[:T].reshape(T, 1, 1),(1,S,J)),
bmat_s, n_mat[:T,:,:], BQnew[:T].reshape(T, 1, J), Y[:T], L[:T], K[:T], factor, REVENUE_params)) + [revenue_ss] * S)
if budget_balance:
T_H_new = REVENUE
elif baseline_spending==False:
T_H_new = ALPHA_T[:T] * Y[:T]
# If baseline_spending==True, no need to update T_H, which remains fixed.
if small_open==True and budget_balance==False:
# Loop through years to calculate debt and gov't spending. This is done earlier when small_open=False.
D_0 = initial_debt * Y[0]
other_dg_params = (T, r, g_n_vector, g_y)
if baseline_spending==False:
G_0 = ALPHA_G[0] * Y[0]
dg_fixed_values = (Y, REVENUE, T_H, D_0,G_0)
Dnew, G = fiscal.D_G_path(dg_fixed_values, fiscal_params, other_dg_params, baseline_spending=baseline_spending)
w[:T] = utils.convex_combo(wnew[:T], w[:T], nu)
r[:T] = utils.convex_combo(rnew[:T], r[:T], nu)
BQ[:T] = utils.convex_combo(BQnew[:T], BQ[:T], nu)
# D[:T] = utils.convex_combo(Dnew[:T], D[:T], nu)
D = Dnew
Y[:T] = utils.convex_combo(Ynew[:T], Y[:T], nu)
if baseline_spending==False:
T_H[:T] = utils.convex_combo(T_H_new[:T], T_H[:T], nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, nu)
print 'r diff: ', (rnew[:T]-r[:T]).max(), (rnew[:T]-r[:T]).min()
print 'w diff: ', (wnew[:T]-w[:T]).max(), (wnew[:T]-w[:T]).min()
print 'BQ diff: ', (BQnew[:T]-BQ[:T]).max(), (BQnew[:T]-BQ[:T]).min()
print 'T_H diff: ', (T_H_new[:T]-T_H[:T]).max(), (T_H_new[:T]-T_H[:T]).min()
if baseline_spending==False:
if T_H.all() != 0:
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) + list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) + list(
utils.pct_diff_func(wnew[:T], w[:T])) + list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
else:
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) + list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) + list(
utils.pct_diff_func(wnew[:T], w[:T])) + list(np.abs(T_H[:T]))).max()
else:
# TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) + list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) + list(
# utils.pct_diff_func(wnew[:T], w[:T])) + list(utils.pct_diff_func(Dnew[:T], D[:T]))).max()
TPIdist = np.array(list(utils.pct_diff_func(rnew[:T], r[:T])) + list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) + list(
utils.pct_diff_func(wnew[:T], w[:T])) + list(utils.pct_diff_func(Ynew[:T], Y[:T]))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
# if TPIiter > 10:
# if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
# nu /= 2
# print 'New Value of nu:', nu
TPIiter += 1
print 'Iteration:', TPIiter
print '\tDistance:', TPIdist
# print 'D/Y:', (D[:T]/Ynew[:T]).max(), (D[:T]/Ynew[:T]).min(), np.median(D[:T]/Ynew[:T])
# print 'T/Y:', (T_H_new[:T]/Ynew[:T]).max(), (T_H_new[:T]/Ynew[:T]).min(), np.median(T_H_new[:T]/Ynew[:T])
# print 'G/Y:', (G[:T]/Ynew[:T]).max(), (G[:T]/Ynew[:T]).min(), np.median(G[:T]/Ynew[:T])
# print 'Int payments to GDP:', ((r[:T]*D[:T])/Ynew[:T]).max(), ((r[:T]*D[:T])/Ynew[:T]).min(), np.median((r[:T]*D[:T])/Ynew[:T])
#
# print 'D/Y:', (D[:T]/Ynew[:T])
# print 'T/Y:', (T_H_new[:T]/Ynew[:T])
# print 'G/Y:', (G[:T]/Ynew[:T])
#
# print 'deficit: ', REVENUE[:T] - T_H_new[:T] - G[:T]
# Loop through years to calculate debt and gov't spending. The re-assignment of G0 & D0 is necessary because Y0 may change in the TPI loop.
if budget_balance == False:
D_0 = initial_debt * Y[0]
other_dg_params = (T, r, g_n_vector, g_y)
if baseline_spending==False:
G_0 = ALPHA_G[0] * Y[0]
dg_fixed_values = (Y, REVENUE, T_H, D_0,G_0)
D, G = fiscal.D_G_path(dg_fixed_values, fiscal_params, other_dg_params, baseline_spending=baseline_spending)
# Solve HH problem in inner loop
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, K, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, ind)
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars, inner_loop_params)
bmat_s = np.zeros((T, S, J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:T-1, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[:T, :, :]
#L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI') # defined above
L[:T] = firm.get_L(n_mat[:T], L_params)
#B_params = (omega[:T-1].reshape(T-1, S, 1), lambdas.reshape(1, 1, J), imm_rates[:T-1].reshape(T-1,S,1), g_n_vector[1:T], 'TPI') # defined above
B[1:T] = household.get_K(bmat_splus1[:T-1], B_params)
if small_open == False:
K[:T] = B[:T] - D[:T]
else:
# K_params previously set to = (Z, gamma, epsilon, delta, tau_b, delta_tau)
K[:T] = firm.get_K(L[:T], tpi_firm_r[:T], K_params)
# Y_params previously set to = (Z, gamma, epsilon)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
# testing for change in Y
ydiff = Ynew[:T] - Y[:T]
ydiff_max = np.amax(np.abs(ydiff))
print 'ydiff_max = ', ydiff_max
w_params = (Z, gamma, epsilon)
wnew = firm.get_w(Ynew[:T], L[:T], w_params)
if small_open == False:
# r_params previously set to = (Z, gamma, epsilon, delta, tau_b, delta_tau)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
else:
rnew = r
# Note: previously, Y was not reassigned to equal Ynew at this point.
Y = Ynew[:]
# omega_shift = np.append(omega_S_preTP.reshape(1,S),omega[:T-1,:],axis=0)
# BQ_params = (omega_shift.reshape(T, S, 1), lambdas.reshape(1, 1, J), rho.reshape(1, S, 1),
# g_n_vector[:T].reshape(T, 1), 'TPI')
b_mat_shift = np.append(np.reshape(initial_b,(1,S,J)),b_mat[:T-1,:,:],axis=0)
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat_shift, BQ_params)
# tax_params = np.zeros((T,S,J,etr_params.shape[2]))
# for i in range(etr_params.shape[2]):
# tax_params[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
# REVENUE_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1), 'TPI',
# tax_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J, tau_b, delta_tau)
REVENUE = np.array(list(tax.revenue(np.tile(rnew[:T].reshape(T, 1, 1),(1,S,J)), np.tile(wnew[:T].reshape(T, 1, 1),(1,S,J)),
bmat_s, n_mat[:T,:,:], BQnew[:T].reshape(T, 1, J), Ynew[:T], L[:T], K[:T], factor, REVENUE_params)) + [revenue_ss] * S)
etr_params_path = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_path_params = (np.tile(e.reshape(1, S, J),(T,1,1)), lambdas, 'TPI', retire, etr_params_path, h_wealth,
p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax_path = tax.total_taxes(np.tile(r[:T].reshape(T, 1, 1),(1,S,J)), np.tile(w[:T].reshape(T, 1, 1),(1,S,J)), bmat_s,
n_mat[:T,:,:], BQ[:T, :].reshape(T, 1, J), factor, T_H[:T].reshape(T, 1, 1), None, False, tax_path_params)
cons_params = (e.reshape(1, S, J), lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(r[:T].reshape(T, 1, 1), w[:T].reshape(T, 1, 1), bmat_s, bmat_splus1, n_mat[:T,:,:],
BQ[:T].reshape(T, 1, J), tax_path, cons_params)
C_params = (omega[:T].reshape(T, S, 1), lambdas, 'TPI')
C = household.get_C(c_path, C_params)
if budget_balance==False:
D_0 = initial_debt * Y[0]
other_dg_params = (T, r, g_n_vector, g_y)
if baseline_spending==False:
G_0 = ALPHA_G[0] * Y[0]
dg_fixed_values = (Y, REVENUE, T_H, D_0,G_0)
D, G = fiscal.D_G_path(dg_fixed_values, fiscal_params, other_dg_params, baseline_spending=baseline_spending)
if small_open == False:
I_params = (delta, g_y, omega[:T].reshape(T, S, 1), lambdas, imm_rates[:T].reshape(T, S, 1), g_n_vector[1:T+1], 'TPI')
I = firm.get_I(bmat_splus1[:T], K[1:T+1], K[:T], I_params)
rc_error = Y[:T] - C[:T] - I[:T] - G[:T]
else:
#InvestmentPlaceholder = np.zeros(bmat_splus1[:T].shape)
#I_params = (delta, g_y, omega[:T].reshape(T, S, 1), lambdas, imm_rates[:T].reshape(T, S, 1), g_n_vector[1:T+1], 'TPI')
I = (1+g_n_vector[:T])*np.exp(g_y)*K[1:T+1] - (1.0 - delta) * K[:T] #firm.get_I(InvestmentPlaceholder, K[1:T+1], K[:T], I_params)
BI_params = (0.0, g_y, omega[:T].reshape(T, S, 1), lambdas, imm_rates[:T].reshape(T, S, 1), g_n_vector[1:T+1], 'TPI')
BI = firm.get_I(bmat_splus1[:T], B[1:T+1], B[:T], BI_params)
new_borrowing = D[1:T]*(1+g_n_vector[1:T])*np.exp(g_y) - D[:T-1]
rc_error = Y[:T-1] + new_borrowing - (C[:T-1] + BI[:T-1] + G[:T-1] ) + (tpi_hh_r[:T-1] * B[:T-1] - (delta + tpi_firm_r[:T-1])*K[:T-1] - tpi_hh_r[:T-1]*D[:T-1])
#print 'Y(T-1):', Y[T-1], '\n','C(T-1):', C[T-1], '\n','K(T-1):', K[T-1], '\n','B(T-1):', B[T-1], '\n','BI(T-1):', BI[T-1], '\n','I(T-1):', I[T-1]
rce_max = np.amax(np.abs(rc_error))
print 'Max absolute value resource constraint error:', rce_max
print'Checking time path for violations of constraints.'
for t in xrange(T):
household.constraint_checker_TPI(
b_mat[t], n_mat[t], c_path[t], t, ltilde)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
# print 'Max Euler error, savings: ', eul_savings
# print 'Max Euler error labor supply: ', eul_laborleisure
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {'Y': Y, 'K': K, 'L': L, 'C': C, 'I': I, 'BQ': BQ,
'REVENUE': REVENUE, 'T_H': T_H, 'G': G, 'D': D,
'r': r, 'w': w, 'b_mat': b_mat, 'n_mat': n_mat,
'c_path': c_path, 'tax_path': tax_path,
'eul_savings': eul_savings, 'eul_laborleisure': eul_laborleisure}
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
macro_output = {'Y': Y, 'K': K, 'L': L, 'C': C, 'I': I,
'BQ': BQ, 'T_H': T_H, 'r': r, 'w': w,
'tax_path': tax_path}
growth = (1+g_n_vector)*np.exp(g_y)
with open('TPI_output.csv', 'wb') as csvfile:
tpiwriter = csv.writer(csvfile)
tpiwriter.writerow(Y)
tpiwriter.writerow(D)
tpiwriter.writerow(REVENUE)
tpiwriter.writerow(G)
tpiwriter.writerow(T_H)
tpiwriter.writerow(C)
tpiwriter.writerow(K)
tpiwriter.writerow(I)
tpiwriter.writerow(r)
if small_open == True:
tpiwriter.writerow(B)
tpiwriter.writerow(BI)
tpiwriter.writerow(new_borrowing)
tpiwriter.writerow(growth)
tpiwriter.writerow(rc_error)
tpiwriter.writerow(ydiff)
if np.any(G) < 0:
print 'Government spending is negative along transition path to satisfy budget'
if ((TPIiter >= maxiter) or (np.absolute(TPIdist) > mindist_TPI)) and ENFORCE_SOLUTION_CHECKS :
raise RuntimeError("Transition path equlibrium not found (TPIdist)")
if ((np.any(np.absolute(rc_error) >= mindist_TPI))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError("Transition path equlibrium not found (rc_error)")
if ((np.any(np.absolute(eul_savings) >= mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError("Transition path equlibrium not found (eulers)")
# Non-stationary output
# macro_ns_output = {'K_ns_path': K_ns_path, 'C_ns_path': C_ns_path, 'I_ns_path': I_ns_path,
# 'L_ns_path': L_ns_path, 'BQ_ns_path': BQ_ns_path,
# 'rinit': rinit, 'Y_ns_path': Y_ns_path, 'T_H_ns_path': T_H_ns_path,
# 'w_ns_path': w_ns_path}
return output, macro_output
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, imm_rates, e, retire, mean_income_data,\
factor, T_H_baseline, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = tpi_params
b_splus1 = float(guesses[0])
n = float(guesses[1])
b_s = float(initial_b[-2, j])
# Find errors from FOC for savings and FOC for labor supply
retire_fd = 0 # this sets retire to true in these agents who are
# in last period in life
# Note using method = "SS" below because just for one period
foc_save_params = (np.array([e[-1, j]]), sigma, beta, g_y, chi_b[j],
theta[j], tau_bq[j], rho[-1], lambdas[j], j, J, S,
analytical_mtrs,
np.reshape(etr_params[-1, 0, :],
(1, etr_params.shape[2])),
np.reshape(mtry_params[-1, 0, :],
(1, mtry_params.shape[2])), h_wealth,
p_wealth, m_wealth, tau_payroll, retire_fd, 'SS')
error1 = household.FOC_savings(np.array([r]), np.array([w]), b_s, b_splus1,
0., np.array([n]), np.array([BQ]), factor,
np.array([T_H]), foc_save_params)
foc_labor_params = (np.array([e[-1, j]]), sigma, g_y, theta[j], b_ellipse,
upsilon, chi_n[-1], ltilde, tau_bq[j], lambdas[j], j,
J, S, analytical_mtrs,
np.reshape(etr_params[-1, 0, :],
(1, etr_params.shape[2])),
np.reshape(mtrx_params[-1, 0, :],
(1, mtrx_params.shape[2])), h_wealth,
p_wealth, m_wealth, tau_payroll, retire_fd, 'SS')
error2 = household.FOC_labor(np.array([r]), np.array([w]), b_s, b_splus1,
np.array([n]), np.array([BQ]), factor,
np.array([T_H]), foc_labor_params)
tax_params = (np.array([e[-1, j]]), lambdas[j], 'SS', retire_fd,
np.reshape(etr_params[-1, 0, :],
(1, etr_params.shape[2])), h_wealth, p_wealth,
m_wealth, tau_payroll, theta[j], tau_bq[j], J, S)
tax1 = tax.total_taxes(np.array([r]), np.array([w]), b_s, np.array([n]),
np.array([BQ]), factor, np.array([T_H]), j, False,
tax_params)
cons_params = (np.array([e[-1, j]]), lambdas[j], g_y)
cons = household.get_cons(np.array([r]), np.array([w]), b_s, b_splus1,
np.array([n]), np.array([BQ]), tax1, cons_params)
if n < 0 or n > ltilde:
error2 = 1e12
if b_splus1 <= 0:
error1 += 1e12
# if cons <= 0:
# error1 += 1e12
return [np.squeeze(error1)] + [np.squeeze(error2)]
def run_TPI(income_tax_params,
tpi_params,
iterative_params,
initial_values,
SS_values,
output_dir="./OUTPUT"):
# unpack tuples of parameters
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
maxiter, mindist_SS, mindist_TPI = iterative_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
K0, b_sinit, b_splus1init, L0, Y0,\
w0, r0, BQ0, T_H_0, factor, tax0, c0, initial_b, initial_n = initial_values
Kss, Lss, rss, wss, BQss, T_Hss, bssmat_splus1, nssmat = SS_values
TPI_FIG_DIR = output_dir
# Initialize guesses at time paths
domain = np.linspace(0, T, T)
K_init = (-1 / (domain + 1)) * (Kss - K0) + Kss
K_init[-1] = Kss
K_init = np.array(list(K_init) + list(np.ones(S) * Kss))
L_init = np.ones(T + S) * Lss
K = K_init
L = L_init
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
w = firm.get_w(Y, L, alpha)
r_params = (alpha, delta)
r = firm.get_r(Y, K, r_params)
BQ = np.zeros((T + S, J))
for j in xrange(J):
BQ[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQ = np.array(BQ)
if T_Hss < 1e-13 and T_Hss > 0.0:
T_Hss2 = 0.0 # sometimes SS is very small but not zero, even if taxes are zero, this get's rid of the approximation error, which affects the perc changes below
else:
T_Hss2 = T_Hss
T_H = np.ones(T + S) * T_Hss2
# Make array of initial guesses for labor supply and savings
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = np.zeros((T + S, S, J))
n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
TPIiter = 0
TPIdist = 10
PLOT_TPI = False
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
K_plot = list(K) + list(np.ones(10) * Kss)
L_plot = list(L) + list(np.ones(10) * Lss)
plt.figure()
plt.axhline(y=Kss,
color='black',
linewidth=2,
label=r"Steady State $\hat{K}$",
ls='--')
plt.plot(np.arange(T + 10),
Kpath_plot[:T + 10],
'b',
linewidth=2,
label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_K"))
# Uncomment the following print statements to make sure all euler equations are converging.
# If they don't, then you'll have negative consumption or consumption spikes. If they don't,
# it is the initial guesses. You might need to scale them differently. It is rather delicate for the first
# few periods and high ability groups.
# 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, ))
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, K, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values,
theta, ind)
# Solve HH problem in inner loop
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars,
inner_loop_params)
# if euler_errors.max() > 1e-6:
# print 't-loop:', euler_errors.max()
# Force the initial distribution of capital to be as given above.
b_mat[0, :, :] = initial_b
K_params = (omega[:T].reshape(T, S, 1), lambdas.reshape(1, 1, J),
g_n_vector[:T], 'TPI')
K[:T] = household.get_K(b_mat[:T], K_params)
L_params = (e.reshape(1, S, J), omega[:T, :].reshape(T, S, 1),
lambdas.reshape(1, 1, J), 'TPI')
L[:T] = firm.get_L(n_mat[:T], L_params)
Y_params = (alpha, Z)
Ynew = firm.get_Y(K[:T], L[:T], Y_params)
wnew = firm.get_w(Ynew[:T], L[:T], alpha)
r_params = (alpha, delta)
rnew = firm.get_r(Ynew[:T], K[:T], r_params)
BQ_params = (omega[:T].reshape(T, S, 1), lambdas.reshape(1, 1, J),
rho.reshape(1, S, 1), g_n_vector[:T].reshape(T, 1), 'TPI')
BQnew = household.get_BQ(rnew[:T].reshape(T, 1), b_mat[:T, :, :],
BQ_params)
bmat_s = np.zeros((T, S, J))
bmat_s[:, 1:, :] = b_mat[:T, :-1, :]
bmat_splus1 = np.zeros((T, S, J))
bmat_splus1[:, :, :] = b_mat[1:T + 1, :, :]
TH_tax_params = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
TH_tax_params[:, :, :, i] = np.tile(
np.reshape(np.transpose(etr_params[:, :T, i]), (T, S, 1)),
(1, 1, J))
T_H_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)),
lambdas.reshape(1, 1, J), omega[:T].reshape(T, S, 1),
'TPI', TH_tax_params, theta, tau_bq, tau_payroll,
h_wealth, p_wealth, m_wealth, retire, T, S, J)
T_H_new = np.array(
list(
tax.get_lump_sum(np.tile(rnew[:T].reshape(T, 1, 1), (
1, S, J)), np.tile(wnew[:T].reshape(T, 1, 1), (
1, S, J)), bmat_s, n_mat[:T, :, :], BQnew[:T].reshape(
T, 1, J), factor, T_H_params)) + [T_Hss] * S)
w[:T] = utils.convex_combo(wnew[:T], w[:T], nu)
r[:T] = utils.convex_combo(rnew[:T], r[:T], nu)
BQ[:T] = utils.convex_combo(BQnew[:T], BQ[:T], nu)
T_H[:T] = utils.convex_combo(T_H_new[:T], T_H[:T], nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, nu)
if T_H.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:T], r[:T])) +
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) +
list(utils.pct_diff_func(wnew[:T], w[:T])) +
list(utils.pct_diff_func(T_H_new[:T], T_H[:T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:T], r[:T])) +
list(utils.pct_diff_func(BQnew[:T], BQ[:T]).flatten()) +
list(utils.pct_diff_func(wnew[:T], w[:T])) +
list(np.abs(T_H_new[:T], T_H[:T]))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
# if TPIiter > 10:
# if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
# nu /= 2
# print 'New Value of nu:', nu
TPIiter += 1
print '\tIteration:', TPIiter
print '\t\tDistance:', TPIdist
if ((TPIiter >= maxiter) or
(np.absolute(TPIdist) > mindist_TPI)) and ENFORCE_SOLUTION_CHECKS:
raise RuntimeError("Transition path equlibrium not found")
Y[:T] = Ynew
# Solve HH problem in inner loop
guesses = (guesses_b, guesses_n)
outer_loop_vars = (r, w, K, BQ, T_H)
inner_loop_params = (income_tax_params, tpi_params, initial_values, theta,
ind)
euler_errors, b_mat, n_mat = inner_loop(guesses, outer_loop_vars,
inner_loop_params)
b_mat[0, :, :] = initial_b
K_params = (omega[:T].reshape(T, S, 1), lambdas.reshape(1, 1, J),
g_n_vector[:T], 'TPI')
K[:T] = household.get_K(
b_mat[:T],
K_params) # this is what old code does, but it's strange - why use
# b_mat -- what is going on with initial period, etc.
etr_params_path = np.zeros((T, S, J, etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:, :, :, i] = np.tile(
np.reshape(np.transpose(etr_params[:, :T, i]), (T, S, 1)),
(1, 1, J))
tax_path_params = (np.tile(e.reshape(1, S, J), (T, 1, 1)), lambdas, 'TPI',
retire, etr_params_path, h_wealth, p_wealth, m_wealth,
tau_payroll, theta, tau_bq, J, S)
tax_path = tax.total_taxes(np.tile(r[:T].reshape(T, 1, 1), (1, S, J)),
np.tile(w[:T].reshape(T, 1, 1),
(1, S, J)), bmat_s, n_mat[:T, :, :],
BQ[:T, :].reshape(T, 1, J), factor,
T_H[:T].reshape(T, 1, 1), None, False,
tax_path_params)
cons_params = (e.reshape(1, S, J), lambdas.reshape(1, 1, J), g_y)
c_path = household.get_cons(r[:T].reshape(T, 1, 1), w[:T].reshape(T, 1, 1),
bmat_s, bmat_splus1, n_mat[:T, :, :],
BQ[:T].reshape(T, 1, J), tax_path, cons_params)
C_params = (omega[:T].reshape(T, S, 1), lambdas, 'TPI')
C = household.get_C(c_path, C_params)
I_params = (delta, g_y, g_n_vector[:T])
I = firm.get_I(K[1:T + 1], K[:T], I_params)
print 'Resource Constraint Difference:', Y[:T] - C[:T] - I[:T]
print 'Checking time path for violations of constaints.'
for t in xrange(T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_path[t], t,
ltilde)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
print 'Max Euler error, savings: ', eul_savings
print 'Max Euler error labor supply: ', eul_laborleisure
if ((np.any(np.absolute(eul_savings) >= mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError("Transition path equlibrium not found")
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {
'Y': Y,
'K': K,
'L': L,
'C': C,
'I': I,
'BQ': BQ,
'T_H': T_H,
'r': r,
'w': w,
'b_mat': b_mat,
'n_mat': n_mat,
'c_path': c_path,
'tax_path': tax_path,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure
}
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
macro_output = {
'Y': Y,
'K': K,
'L': L,
'C': C,
'I': I,
'BQ': BQ,
'T_H': T_H,
'r': r,
'w': w,
'tax_path': tax_path
}
# Non-stationary output
# macro_ns_output = {'K_ns_path': K_ns_path, 'C_ns_path': C_ns_path, 'I_ns_path': I_ns_path,
# 'L_ns_path': L_ns_path, 'BQ_ns_path': BQ_ns_path,
# 'rinit': rinit, 'Y_ns_path': Y_ns_path, 'T_H_ns_path': T_H_ns_path,
# 'w_ns_path': w_ns_path}
return output, macro_output
def FOC_savings(r, w, b, b_splus1, b_splus2, n, BQ, factor, T_H, params):
'''
Computes Euler errors for the FOC for savings in the steady state.
This function is usually looped through over J, so it does one lifetime income group at a time.
Inputs:
r = scalar, interest rate
w = scalar, wage rate
b = [S,J] array, distribution of wealth/capital holdings
b_splus1 = [S,J] array, distribution of wealth/capital holdings one period ahead
b_splus2 = [S,J] array, distribution of wealth/capital holdings two periods ahead
n = [S,J] array, distribution of labor supply
BQ = [J,] vector, aggregate bequests by lifetime income group
factor = scalar, scaling factor to convert model income to dollars
T_H = scalar, lump sum transfer
params = length 18 tuple (e, sigma, beta, g_y, chi_b, theta, tau_bq, rho, lambdas,
J, S, etr_params, mtry_params, h_wealth, p_wealth,
m_wealth, tau_payroll, tau_bq)
e = [S,J] array, effective labor units
sigma = scalar, coefficient of relative risk aversion
beta = scalar, discount factor
g_y = scalar, exogenous labor augmenting technological growth
chi_b = [J,] vector, utility weight on bequests for each lifetime income group
theta = [J,] vector, replacement rate for each lifetime income group
tau_bq = scalar, bequest tax rate (scalar)
rho = [S,] vector, mortality rates
lambdas = [J,] vector, ability weights
J = integer, number of lifetime income groups
S = integer, number of economically active periods in lifetime
etr_params = [S,10] array, parameters of effective income tax rate function
mtry_params = [S,10] array, parameters of marginal tax rate on capital income function
h_wealth = scalar, parameter in wealth tax function
p_wealth = scalar, parameter in wealth tax function
m_wealth = scalar, parameter in wealth tax function
tau_payroll = scalar, payroll tax rate
tau_bq = scalar, bequest tax rate
Functions called:
get_cons
marg_ut_cons
tax.total_taxes
tax.MTR_capital
Objects in function:
tax1 = [S,J] array, net taxes in the current period
tax2 = [S,J] array, net taxes one period ahead
cons1 = [S,J] array, consumption in the current period
cons2 = [S,J] array, consumption one period ahead
deriv = [S,J] array, after-tax return on capital
savings_ut = [S,J] array, marginal utility from savings
euler = [S,J] array, Euler error from FOC for savings
Returns: euler
'''
omega, e, sigma, BQ_dist, beta, g_y, chi_b, theta, tau_bq, rho, lambdas, J, S, \
analytical_mtrs, etr_params, mtry_params, h_wealth, p_wealth, m_wealth, tau_payroll, retire, method = params
# In order to not have 2 savings euler equations (one that solves the first S-1 equations, and one that solves the last one),
# we combine them. In order to do this, we have to compute a consumption term in period t+1, which requires us to have a shifted
# e and n matrix. We append a zero on the end of both of these so they will be the right size. We could append any value to them,
# since in the euler equation, the coefficient on the marginal utility of
# consumption for this term will be zero (since rho is one).
if method == 'TPI_scalar':
e_extended = np.array([e] + [0])
n_extended = np.array([n] + [0])
etr_params_to_use = etr_params
mtry_params_to_use = mtry_params
else:
zeros = np.zeros((1, J))
e_extended = np.vstack((e , zeros ))
n_extended = np.vstack((n ,zeros))
etr_params_to_use = etr_params
mtry_params_to_use = mtry_params
# etr_params_to_use = np.append(etr_params,np.reshape(etr_params[-1,:],(1,etr_params.shape[1])),axis=0)[1:,:]
# mtry_params_to_use = np.append(mtry_params,np.reshape(mtry_params[-1,:],(1,mtry_params.shape[1])),axis=0)[1:,:]
# tax1_params = (e, lambdas, method, retire, etr_params, h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
# tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, None, False, tax1_params)
# tax2_params = (e_extended[1:], lambdas, method, retire,
# np.append(etr_params,np.reshape(etr_params[-1,:],(1,etr_params.shape[1])),axis=0)[1:,:],
# h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
# tax2 = tax.total_taxes(r, w, b_splus1, n_extended[1:], BQ, factor, T_H, None, True, tax2_params)
# cons1_params = (e, lambdas, g_y)
# cons1 = get_cons(r, w, b, b_splus1, n, BQ, tax1, cons1_params)
# cons2_params = (e_extended[1:], lambdas, g_y)
# cons2 = get_cons(r, w, b_splus1, b_splus2, n_extended[1:], BQ, tax2, cons2_params)
# mtr_cap_params = (e_extended[1:], np.append(etr_params,np.reshape(etr_params[-1,:],(1,etr_params.shape[1])),axis=0)[1:,:],
# np.append(mtry_params,np.reshape(mtry_params[-1,:],(1,mtry_params.shape[1])),axis=0)[1:,:],analytical_mtrs)
# deriv = (1+r) - r*(tax.MTR_capital(r, w, b_splus1, n_extended[1:], factor, mtr_cap_params))
tax1_params = (e, BQ_dist, lambdas, method, retire, etr_params, h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, None, False, tax1_params)
tax2_params = (e_extended[1:, :], BQ_dist, lambdas, method, retire,
etr_params_to_use, h_wealth, p_wealth, m_wealth, tau_payroll, theta, tau_bq, J, S)
tax2 = tax.total_taxes(r, w, b_splus1, n_extended[1:, :], BQ, factor, T_H, None, True, tax2_params)
cons1_params = (e, BQ_dist, lambdas, g_y)
cons1 = get_cons(omega, r, w, b, b_splus1, n, BQ, tax1, cons1_params)
cons2_params = (e_extended[1:, :], BQ_dist, lambdas, g_y)
cons2 = get_cons(omega, r, w, b_splus1, b_splus2, n_extended[1:, :], BQ, tax2, cons2_params)
mtr_cap_params = (e_extended[1:, :], etr_params_to_use,
mtry_params_to_use, analytical_mtrs)
deriv = (1+r) - r*(tax.MTR_capital(r, w, b_splus1, n_extended[1:, :], factor, mtr_cap_params))
savings_ut = rho * np.exp(-sigma * g_y) * chi_b * b_splus1 ** (-sigma)
# Again, note timing in this equation, the (1-rho) term will zero out in the last period, so the last entry of cons2 can be complete
# gibberish (which it is). It just has to exist so cons2 is the right
# size to match all other arrays in the equation.
# print marg_ut_cons(cons1, sigma).shape, np.exp(-sigma * g_y).shape, savings_ut.shape, beta.shape, (1 - rho).shape, deriv.shape, marg_ut_cons(
# cons2, sigma).shape
euler = marg_ut_cons(cons1, sigma) - beta * (1 - rho) * deriv * marg_ut_cons(
cons2, sigma) * np.exp(-sigma * g_y) - savings_ut
return euler
def create_tpi_params(**sim_params):
'''
------------------------------------------------------------------------
Set factor and initial capital stock to SS from baseline
------------------------------------------------------------------------
'''
baseline_ss = os.path.join(sim_params['baseline_dir'], "SS/SS_vars.pkl")
ss_baseline_vars = pickle.load(open(baseline_ss, "rb"))
factor = ss_baseline_vars['factor_ss']
#initial_b = ss_baseline_vars['bssmat_s'] + ss_baseline_vars['BQss']/lambdas
initial_b = ss_baseline_vars['bssmat_splus1']
initial_n = ss_baseline_vars['nssmat']
SS_values = (ss_baseline_vars['Kss'], ss_baseline_vars['Lss'],
ss_baseline_vars['rss'], ss_baseline_vars['wss'],
ss_baseline_vars['BQss'], ss_baseline_vars['T_Hss'],
ss_baseline_vars['bssmat_splus1'], ss_baseline_vars['nssmat'])
# Make a vector of all one dimensional parameters, to be used in the
# following functions
wealth_tax_params = [
sim_params['h_wealth'], sim_params['p_wealth'], sim_params['m_wealth']
]
ellipse_params = [sim_params['b_ellipse'], sim_params['upsilon']]
chi_params = [sim_params['chi_b_guess'], sim_params['chi_n_guess']]
N_tilde = sim_params['omega'].sum(
1
) #this should just be one in each year given how we've constructed omega
sim_params['omega'] = sim_params['omega'] / N_tilde.reshape(
sim_params['T'] + sim_params['S'], 1)
tpi_params = [sim_params['J'], sim_params['S'], sim_params['T'], sim_params['BW'],
sim_params['beta'], sim_params['sigma'], sim_params['alpha'],
sim_params['Z'], sim_params['delta'], sim_params['ltilde'],
sim_params['nu'], sim_params['g_y'], sim_params['g_n_vector'],
sim_params['tau_payroll'], sim_params['tau_bq'], sim_params['rho'], sim_params['omega'], N_tilde,
sim_params['lambdas'], sim_params['e'], sim_params['retire'], sim_params['mean_income_data'], factor] + \
wealth_tax_params + ellipse_params + chi_params
iterative_params = [
sim_params['maxiter'], sim_params['mindist_SS'],
sim_params['mindist_TPI']
]
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
## Assumption for tax functions is that policy in last year of BW is
# extended permanently
etr_params_TP = np.zeros((S, T + S, sim_params['etr_params'].shape[2]))
etr_params_TP[:, :BW, :] = sim_params['etr_params']
etr_params_TP[:, BW:, :] = np.reshape(
sim_params['etr_params'][:, BW - 1, :],
(S, 1, sim_params['etr_params'].shape[2]))
mtrx_params_TP = np.zeros((S, T + S, sim_params['mtrx_params'].shape[2]))
mtrx_params_TP[:, :BW, :] = sim_params['mtrx_params']
mtrx_params_TP[:, BW:, :] = np.reshape(
sim_params['mtrx_params'][:, BW - 1, :],
(S, 1, sim_params['mtrx_params'].shape[2]))
mtry_params_TP = np.zeros((S, T + S, sim_params['mtry_params'].shape[2]))
mtry_params_TP[:, :BW, :] = sim_params['mtry_params']
mtry_params_TP[:, BW:, :] = np.reshape(
sim_params['mtry_params'][:, BW - 1, :],
(S, 1, sim_params['mtry_params'].shape[2]))
income_tax_params = (sim_params['analytical_mtrs'], etr_params_TP,
mtrx_params_TP, mtry_params_TP)
'''
------------------------------------------------------------------------
Set other parameters and initial values
------------------------------------------------------------------------
'''
# Get an initial distribution of capital with the initial population
# distribution
K0_params = (omega[0].reshape(S, 1), lambdas, g_n_vector[0], 'SS')
K0 = household.get_K(initial_b, K0_params)
b_sinit = np.array(list(np.zeros(J).reshape(1, J)) + list(initial_b[:-1]))
b_splus1init = initial_b
L0_params = (e, omega[0].reshape(S, 1), lambdas, 'SS')
L0 = firm.get_L(initial_n, L0_params)
Y0_params = (alpha, Z)
Y0 = firm.get_Y(K0, L0, Y0_params)
w0 = firm.get_w(Y0, L0, alpha)
r0_params = (alpha, delta)
r0 = firm.get_r(Y0, K0, r0_params)
BQ0_params = (omega[0].reshape(S, 1), lambdas, rho.reshape(S, 1),
g_n_vector[0], 'SS')
BQ0 = household.get_BQ(r0, initial_b, BQ0_params)
theta_params = (e, J, omega[0].reshape(S, 1), lambdas)
theta = tax.replacement_rate_vals(initial_n, w0, factor, theta_params)
T_H_params = (e, lambdas, omega[0].reshape(S, 1), 'SS',
etr_params_TP[:, 0, :], theta, tau_bq, tau_payroll, h_wealth,
p_wealth, m_wealth, retire, T, S, J)
T_H_0 = tax.get_lump_sum(r0, w0, b_sinit, initial_n, BQ0, factor,
T_H_params)
etr_params_3D = np.tile(
np.reshape(etr_params_TP[:, 0, :], (S, 1, etr_params_TP.shape[2])),
(1, J, 1))
tax0_params = (e, lambdas, 'SS', retire, etr_params_3D, h_wealth, p_wealth,
m_wealth, tau_payroll, theta, tau_bq, J, S)
tax0 = tax.total_taxes(r0, w0, b_sinit, initial_n, BQ0, factor, T_H_0,
None, False, tax0_params)
c0_params = (e, lambdas.reshape(1, J), g_y)
c0 = household.get_cons(r0, w0, b_sinit, b_splus1init, initial_n,
BQ0.reshape(1, J), tax0, c0_params)
initial_values = (K0, b_sinit, b_splus1init, L0, Y0, w0, r0, BQ0, T_H_0,
factor, tax0, c0, initial_b, initial_n)
return (income_tax_params, tpi_params, iterative_params, initial_values,
SS_values)
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, imm_rates, e, retire, mean_income_data,\
factor, T_H_baseline, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = 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]
# Errors from FOC for savings
foc_save_params = (e_s, sigma, beta, g_y, chi_b[j], theta, tau_bq,
rho[-(length):], lambdas[j], j, J, S, analytical_mtrs,
etr_params, mtry_params, h_wealth, p_wealth, m_wealth,
tau_payroll, retire, 'TPI')
error1 = household.FOC_savings(r_s, w_s, b_s, b_splus1, b_splus2, n_s,
BQ_s, factor, T_H_s, foc_save_params)
# Errors from FOC for labor supply
foc_labor_params = (e_s, sigma, g_y, theta, b_ellipse, upsilon,
chi_n[-length:], ltilde, tau_bq, lambdas[j], j, J, S,
analytical_mtrs, etr_params, mtrx_params, h_wealth,
p_wealth, m_wealth, tau_payroll, retire, 'TPI')
error2 = household.FOC_labor(r_s, w_s, b_s, b_splus1, n_s, BQ_s, factor,
T_H_s, foc_labor_params)
tax_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_params)
cons_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_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
mask5 = b_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())
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 create_tpi_params(analytical_mtrs, etr_params, mtrx_params, mtry_params,
b_ellipse, upsilon, J, S, T, BW, beta, sigma, alpha, Z,
delta, ltilde, nu, g_y, tau_payroll, retire,
mean_income_data, run_params,
input_dir="./OUTPUT", baseline_dir="./OUTPUT", **kwargs):
globals().update(run_params)
ss_init = os.path.join(input_dir, "SSinit/ss_init_vars.pkl")
variables = pickle.load(open(ss_init, "rb"))
for key in variables:
globals()[key] = variables[key]
'''
------------------------------------------------------------------------
Set factor and initial capital stock to SS from baseline
------------------------------------------------------------------------
'''
baseline_ss = os.path.join(baseline_dir, "SSinit/ss_init_vars.pkl")
ss_baseline_vars = pickle.load(open(baseline_ss, "rb"))
factor = ss_baseline_vars['factor_ss']
#initial_b = ss_baseline_vars['bssmat_s'] + ss_baseline_vars['BQss']/lambdas
initial_b= ss_baseline_vars['bssmat_splus1']
'''
------------------------------------------------------------------------
Set other parameters and initial values
------------------------------------------------------------------------
'''
# Make a vector of all one dimensional parameters, to be used in the
# following functions
# Put income tax parameters in a tuple
# Assumption here is that tax parameters of last year of budget
# window continue forever and so will be SS values
etr_params_TP = np.zeros((S,T+S,etr_params.shape[2]))
etr_params_TP[:,:BW,:] = etr_params
etr_params_TP[:,BW:,:] = np.reshape(etr_params[:,BW-1,:],(S,1,etr_params.shape[2]))
mtrx_params_TP = np.zeros((S,T+S,mtrx_params.shape[2]))
mtrx_params_TP[:,:BW,:] = mtrx_params
mtrx_params_TP[:,BW:,:] = np.reshape(mtrx_params[:,BW-1,:],(S,1,mtrx_params.shape[2]))
mtry_params_TP = np.zeros((S,T+S,mtry_params.shape[2]))
mtry_params_TP[:,:BW,:] = mtry_params
mtry_params_TP[:,BW:,:] = np.reshape(mtry_params[:,BW-1,:],(S,1,mtry_params.shape[2]))
income_tax_params = (analytical_mtrs, etr_params_TP, mtrx_params_TP, mtry_params_TP)
wealth_tax_params = [h_wealth, p_wealth, m_wealth]
ellipse_params = [b_ellipse, upsilon]
parameters = [J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y, g_n_ss, tau_payroll, retire,
mean_income_data] + wealth_tax_params + ellipse_params
N_tilde = omega.sum(1)
omega_stationary = omega / N_tilde.reshape(T + S, 1)
initial_n = nssmat
# Get an initial distribution of capital with the initial population
# distribution
K0 = household.get_K(initial_b, omega_stationary[
0].reshape(S, 1), lambdas, g_n_vector[0], 'SS')
b_sinit = np.array(list(np.zeros(J).reshape(1, J)) + list(initial_b[:-1]))
b_splus1init = initial_b
L0 = firm.get_L(e, initial_n, omega_stationary[
0].reshape(S, 1), lambdas, 'SS')
Y0 = firm.get_Y(K0, L0, parameters)
w0 = firm.get_w(Y0, L0, parameters)
r0 = firm.get_r(Y0, K0, parameters)
BQ0 = household.get_BQ(r0, initial_b, omega_stationary[0].reshape(
S, 1), lambdas, rho.reshape(S, 1), g_n_vector[0], 'SS')
T_H_0 = tax.get_lump_sum(r0, b_sinit, w0, e, initial_n, BQ0, lambdas, factor_ss, omega_stationary[
0].reshape(S, 1), 'SS', etr_params_TP[:,0,:], parameters, theta, tau_bq)
tax0_params = (J, S, retire, np.tile(np.reshape(etr_params_TP[:,0,:],(S,1,etr_params_TP.shape[2])),(1,J,1)),
h_wealth, p_wealth, m_wealth, tau_payroll)
tax0 = tax.total_taxes(r0, b_sinit, w0, e, initial_n, BQ0, lambdas,
factor_ss, T_H_0, None, 'SS', False, tax0_params, theta, tau_bq)
c0 = household.get_cons(r0, b_sinit, w0, e, initial_n, BQ0.reshape(
1, J), lambdas.reshape(1, J), b_splus1init, parameters, tax0)
return (income_tax_params, wealth_tax_params, ellipse_params, parameters,
N_tilde, omega_stationary, K0, b_sinit, b_splus1init, L0, Y0,
w0, r0, BQ0, T_H_0, factor, tax0, c0, initial_b, initial_n)
def create_tpi_params(a_tax_income,
b_tax_income,
c_tax_income,
d_tax_income,
b_ellipse,
upsilon,
J,
S,
T,
beta,
sigma,
alpha,
Z,
delta,
ltilde,
nu,
g_y,
tau_payroll,
retire,
mean_income_data,
get_baseline=True,
input_dir="./OUTPUT",
**kwargs):
if get_baseline:
ss_init = os.path.join(input_dir, "SSinit/ss_init_vars.pkl")
variables = pickle.load(open(ss_init, "rb"))
for key in variables:
globals()[key] = variables[key]
else:
params_path = os.path.join(input_dir,
"Saved_moments/params_changed.pkl")
variables = pickle.load(open(params_path, "rb"))
for key in variables:
globals()[key] = variables[key]
var_path = os.path.join(input_dir, "SS/ss_vars.pkl")
variables = pickle.load(open(var_path, "rb"))
for key in variables:
globals()[key] = variables[key]
init_tpi_vars = os.path.join(input_dir, "SSinit/ss_init_tpi_vars.pkl")
variables = pickle.load(open(init_tpi_vars, "rb"))
for key in variables:
globals()[key] = variables[key]
'''
------------------------------------------------------------------------
Set other parameters and initial values
------------------------------------------------------------------------
'''
# Make a vector of all one dimensional parameters, to be used in the
# following functions
income_tax_params = [
a_tax_income, b_tax_income, c_tax_income, d_tax_income
]
wealth_tax_params = [h_wealth, p_wealth, m_wealth]
ellipse_params = [b_ellipse, upsilon]
parameters = [
J, S, T, beta, sigma, alpha, Z, delta, ltilde, nu, g_y, g_n_ss,
tau_payroll, retire, mean_income_data
] + income_tax_params + wealth_tax_params + ellipse_params
N_tilde = omega.sum(1)
omega_stationary = omega / N_tilde.reshape(T + S, 1)
if get_baseline:
initial_b = bssmat_splus1
initial_n = nssmat
else:
initial_b = bssmat_init
initial_n = nssmat_init
# Get an initial distribution of capital with the initial population
# distribution
K0 = household.get_K(initial_b, omega_stationary[0].reshape(S, 1), lambdas,
g_n_vector[0], 'SS')
b_sinit = np.array(list(np.zeros(J).reshape(1, J)) + list(initial_b[:-1]))
b_splus1init = initial_b
L0 = firm.get_L(e, initial_n, omega_stationary[0].reshape(S, 1), lambdas,
'SS')
Y0 = firm.get_Y(K0, L0, parameters)
w0 = firm.get_w(Y0, L0, parameters)
r0 = firm.get_r(Y0, K0, parameters)
BQ0 = household.get_BQ(r0, initial_b, omega_stationary[0].reshape(S, 1),
lambdas, rho.reshape(S, 1), g_n_vector[0], 'SS')
T_H_0 = tax.get_lump_sum(r0, b_sinit, w0, e, initial_n, BQ0, lambdas,
factor_ss, omega_stationary[0].reshape(S, 1),
'SS', parameters, theta, tau_bq)
tax0 = tax.total_taxes(r0, b_sinit, w0, e, initial_n, BQ0, lambdas,
factor_ss, T_H_0, None, 'SS', False, parameters,
theta, tau_bq)
c0 = household.get_cons(r0, b_sinit, w0, e, initial_n, BQ0.reshape(1, J),
lambdas.reshape(1, J), b_splus1init, parameters,
tax0)
return (income_tax_params, wealth_tax_params, ellipse_params, parameters,
N_tilde, omega_stationary, K0, b_sinit, b_splus1init, L0, Y0, w0,
r0, BQ0, T_H_0, tax0, c0, initial_b, initial_n)
def TP_solutions(winit, rinit, T_H_init, BQinit2, Kss, Lss, Yss, BQss, theta, income_tax_params, wealth_tax_params, ellipse_params, parameters, g_n_vector,
omega_stationary, K0, b_sinit, b_splus1init, L0, Y0, r0, BQ0,
T_H_0, tax0, c0, initial_b, initial_n, factor_ss, tau_bq, chi_b,
chi_n, output_dir="./OUTPUT", **kwargs):
'''
This function returns the solutions for all variables along the time path.
'''
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 = income_tax_params
print 'Computing final solutions'
# Extend time paths past T
winit = np.array(list(winit) + list(np.ones(S) * wss))
rinit = np.array(list(rinit) + list(np.ones(S) * rss))
T_H_init = np.array(list(T_H_init) + list(np.ones(S) * T_Hss))
BQinit = np.zeros((T + S, J))
for j in xrange(J):
BQinit[:, j] = list(BQinit2[:,j]) + [BQss[j]] * S
BQinit = np.array(BQinit)
# Make array of initial guesses
domain = np.linspace(0, T, T)
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = np.zeros((T + S, S, J))
n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
# initialize array of Euler errors
euler_errors = np.zeros((T, 2 * S, J))
# As in SS, you need the final distributions of b and n to match the final
# w, r, BQ, etc. Otherwise the euler errors are large. You need one more
# fsolve.
for j in xrange(J):
b_mat[1, -1, j], n_mat[0, -1, j] = np.array(opt.fsolve(SS_TPI_firstdoughnutring, [guesses_b[1, -1, j], guesses_n[0, -1, j]],
args=(winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b, factor_ss,
j, income_tax_params, parameters, theta, tau_bq), xtol=1e-13))
for s in xrange(S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[1:S + 1, :, j], S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:S, :, j], S - (s + 2))
# initialize array of diagonal elements
length_diag = (np.diag(np.transpose(etr_params[:S,:,0]),S-(s+2))).shape[0]
etr_params_to_use = np.zeros((length_diag,etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag,mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag,mtry_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_to_use[:,i] = np.diag(np.transpose(etr_params[:S,:,i]),S-(s+2))
mtrx_params_to_use[:,i] = np.diag(np.transpose(mtrx_params[:S,:,i]),S-(s+2))
mtry_params_to_use[:,i] = np.diag(np.transpose(mtry_params[:S,:,i]),S-(s+2))
inc_tax_params_upper = (analytical_mtrs, etr_params_to_use, mtrx_params_to_use, mtry_params_to_use)
solutions = opt.fsolve(Steady_state_TPI_solver, list(
b_guesses_to_use) + list(n_guesses_to_use), args=(
winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, s, 0, inc_tax_params_upper, parameters, theta, tau_bq, rho, lambdas, e, initial_b, chi_b, chi_n), xtol=1e-13)
b_vec = solutions[:len(solutions) / 2]
b_mat[1 + ind2, S - (s + 2) + ind2, j] = b_vec
n_vec = solutions[len(solutions) / 2:]
n_mat[ind2, S - (s + 2) + ind2, j] = n_vec
for t in xrange(0, T):
b_guesses_to_use = .75 * np.diag(guesses_b[t + 1:t + S + 1, :, j])
n_guesses_to_use = np.diag(guesses_n[t:t + S, :, j])
# initialize array of diagonal elements
length_diag = (np.diag(np.transpose(etr_params[:,t:t+S,i]))).shape[0]
etr_params_to_use = np.zeros((length_diag,etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag,mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag,mtry_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_to_use[:,i] = np.diag(np.transpose(etr_params[:,t:t+S,i]))
mtrx_params_to_use[:,i] = np.diag(np.transpose(mtrx_params[:,t:t+S,i]))
mtry_params_to_use[:,i] = np.diag(np.transpose(mtry_params[:,t:t+S,i]))
inc_tax_params_TP = (analytical_mtrs, etr_params_to_use, mtrx_params_to_use, mtry_params_to_use)
solutions = opt.fsolve(Steady_state_TPI_solver, list(
b_guesses_to_use) + list(n_guesses_to_use), args=(
winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None, t, inc_tax_params_TP, parameters, theta, tau_bq, rho, lambdas, e, None, chi_b, chi_n), xtol=1e-13)
b_vec = solutions[:S]
b_mat[t + 1 + ind, ind, j] = b_vec
n_vec = solutions[S:]
n_mat[t + ind, ind, j] = n_vec
inputs = list(solutions)
euler_errors[t, :, j] = np.abs(Steady_state_TPI_solver(
inputs, winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None, t, inc_tax_params_TP, parameters, theta, tau_bq, rho, lambdas, e, None, chi_b, chi_n))
b_mat[0, :, :] = initial_b
'''
------------------------------------------------------------------------
Generate variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
Kinit = household.get_K(b_mat[:T], omega_stationary[:T].reshape(
T, S, 1), lambdas.reshape(1, 1, J), g_n_vector[:T], 'TPI')
Linit = firm.get_L(e.reshape(1, S, J), n_mat[:T], omega_stationary[
:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI')
Kpath_TPI = np.array(list(Kinit) + list(np.ones(10) * Kss))
Lpath_TPI = np.array(list(Linit) + list(np.ones(10) * Lss))
BQpath_TPI = np.array(list(BQinit) + list(np.ones((10, J)) * BQss))
b_s = np.zeros((T, S, J))
b_s[:, 1:, :] = b_mat[:T, :-1, :]
b_splus1 = np.zeros((T, S, J))
b_splus1[:, :, :] = b_mat[1:T + 1, :, :]
# initialize array
etr_params_path = np.zeros((T,S,J,etr_params.shape[2]))
for i in range(etr_params.shape[2]):
etr_params_path[:,:,:,i] = np.tile(np.reshape(np.transpose(etr_params[:,:T,i]),(T,S,1)),(1,1,J))
tax_path_params = J, S, retire, etr_params_path, h_wealth, p_wealth, m_wealth, tau_payroll
tax_path = tax.total_taxes(np.tile(rinit[:T].reshape(T, 1, 1),(1,S,J)), b_s, np.tile(winit[:T].reshape(T, 1, 1),(1,S,J)),
np.tile(e.reshape(1, S, J),(T,1,1)), n_mat[:T,:,:], BQinit[:T, :].reshape(T, 1, J), lambdas,
factor_ss, T_H_init[:T].reshape(T, 1, 1), None, 'TPI', False, tax_path_params, theta, tau_bq)
c_path = household.get_cons(rinit[:T].reshape(T, 1, 1), b_s, winit[:T].reshape(T, 1, 1), e.reshape(
1, S, J), n_mat[:T], BQinit[:T].reshape(T, 1, J), lambdas.reshape(1, 1, J), b_splus1, parameters, tax_path)
Y_path = firm.get_Y(Kpath_TPI[:T], Lpath_TPI[:T], parameters)
C_path = household.get_C(c_path, omega_stationary[
:T].reshape(T, S, 1), lambdas, 'TPI')
I_path = firm.get_I(Kpath_TPI[1:T + 1],
Kpath_TPI[:T], delta, g_y, g_n_vector[:T])
print 'Resource Constraint Difference:', Y_path - C_path - I_path
print'Checking time path for violations of constaints.'
hh_constraint_params = ltilde
for t in xrange(T):
household.constraint_checker_TPI(
b_mat[t], n_mat[t], c_path[t], t, hh_constraint_params)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
print 'Max Euler error, savings: ', eul_savings
print 'Max Euler error labor supply: ', eul_laborleisure
'''
------------------------------------------------------------------------
Create the unstationarized versions of the paths of macro aggregates
------------------------------------------------------------------------
'''
# tvec = np.linspace(0, len(C_path), len(C_path))
# growth_path = np.exp(g_y*tvec)
# pop_path = np.zeros(len(C_path))
# for i in range(0,len(C_path)):
# pop_path[i] = np.exp(g_n_vector[:i].sum()) # note that this normalizes the pop in the initial period to one
# growth_pop_path = growth_path*pop_path
# C_ns_path = C_path * growth_pop_path
# K_ns_path = Kinit * growth_pop_path
# BQ_ns_path = growth_pop_path * BQinit[:T]
# L_ns_path = Linit * pop_path
# T_H_ns_path = T_H_init[:T] * growth_pop_path
# w_ns_path = winit*growth_path
# I_ns_path = I_path * growth_pop_path
# Y_ns_path = Y_path * growth_pop_path
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {'Kpath_TPI': Kpath_TPI, 'b_mat': b_mat, 'c_path': c_path,
'eul_savings': eul_savings, 'eul_laborleisure': eul_laborleisure,
'Lpath_TPI': Lpath_TPI, 'BQpath_TPI': BQpath_TPI, 'n_mat': n_mat,
'rinit': rinit, 'Y_path': Y_path, 'T_H_init': T_H_init,
'tax_path': tax_path, 'winit': winit}
macro_output = {'Kpath_TPI': Kpath_TPI, 'C_path': C_path, 'I_path': I_path,
'Lpath_TPI': Lpath_TPI, 'BQpath_TPI': BQpath_TPI,
'rinit': rinit, 'Y_path': Y_path, 'T_H_init': T_H_init,
'winit': winit, 'tax_path': tax_path}
# macro_ns_output = {'K_ns_path': K_ns_path, 'C_ns_path': C_ns_path, 'I_ns_path': I_ns_path,
# 'L_ns_path': L_ns_path, 'BQ_ns_path': BQ_ns_path,
# 'rinit': rinit, 'Y_ns_path': Y_ns_path, 'T_H_ns_path': T_H_ns_path,
# 'w_ns_path': w_ns_path}
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_macro_vars.pkl")
pickle.dump(macro_output, open(tpi_vars, "wb"))
def FOC_labor(r, w, b, b_splus1, n, BQ, factor, T_H, params):
'''
Computes Euler errors for the FOC for labor supply in the steady state.
This function is usually looped through over J, so it does one lifetime income group at a time.
Inputs:
r = scalar, interest rate
w = scalar, wage rate
b = [S,J] array, distribution of wealth/capital holdings
b_splus1 = [S,J] array, distribution of wealth/capital holdings one period ahead
n = [S,J] array, distribution of labor supply
BQ = [J,] vector, aggregate bequests by lifetime income group
factor = scalar, scaling factor to convert model income to dollars
T_H = scalar, lump sum transfer
params = length 19 tuple (e, sigma, g_y, theta, b_ellipse, upsilon, ltilde,
chi_n, tau_bq, lambdas, J, S,
etr_params, mtrx_params, h_wealth, p_wealth,
m_wealth, tau_payroll, tau_bq)
e = [S,J] array, effective labor units
sigma = scalar, coefficient of relative risk aversion
g_y = scalar, exogenous labor augmenting technological growth
theta = [J,] vector, replacement rate for each lifetime income group
b_ellipse = scalar, scaling parameter in elliptical utility function
upsilon = curvature parameter in elliptical utility function
chi_n = [S,] vector, utility weights on disutility of labor
ltilde = scalar, upper bound of household labor supply
tau_bq = scalar, bequest tax rate (scalar)
lambdas = [J,] vector, ability weights
J = integer, number of lifetime income groups
S = integer, number of economically active periods in lifetime
etr_params = [S,10] array, parameters of effective income tax rate function
mtrx_params = [S,10] array, parameters of marginal tax rate on labor income function
h_wealth = scalar, parameter in wealth tax function
p_wealth = scalar, parameter in wealth tax function
m_wealth = scalar, parameter in wealth tax function
tau_payroll = scalar, payroll tax rate
tau_bq = scalar, bequest tax rate
Functions called:
get_cons
marg_ut_cons
marg_ut_labor
tax.total_taxes
tax.MTR_labor
Objects in function:
tax = [S,J] array, net taxes in the current period
cons = [S,J] array, consumption in the current period
deriv = [S,J] array, net of tax share of labor income
euler = [S,J] array, Euler error from FOC for labor supply
Returns: euler
'''
omega, e, BQ_dist, sigma, g_y, theta, b_ellipse, upsilon, chi_n, ltilde, tau_bq, lambdas, J, S, \
analytical_mtrs, etr_params, mtrx_params, h_wealth, p_wealth, m_wealth, tau_payroll, retire, method = params
tax1_params = (e, BQ_dist, lambdas, method, retire, etr_params, h_wealth, p_wealth,
m_wealth, tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, None, False, tax1_params)
cons_params = (e, BQ_dist, lambdas, g_y)
cons = get_cons(omega, r, w, b, b_splus1, n, BQ, tax1, cons_params)
mtr_lab_params = (e, etr_params, mtrx_params, analytical_mtrs)
deriv = (1 - tau_payroll - tax.MTR_labor(r, b, w, n, factor, mtr_lab_params))
lab_params = (b_ellipse, upsilon, ltilde, chi_n)
euler = marg_ut_cons(cons, sigma) * w * deriv * e - \
marg_ut_labor(n, lab_params)
return euler
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 = 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 run_time_path_iteration(Kss, Lss, Yss, BQss, theta, parameters, g_n_vector, omega_stationary, K0, b_sinit, b_splus1init, L0, Y0, r0, BQ0, T_H_0, tax0, c0, initial_b, initial_n, factor_ss, tau_bq, chi_b, chi_n, get_baseline=False, output_dir="./OUTPUT", **kwargs):
TPI_FIG_DIR = output_dir
# Initialize Time paths
domain = np.linspace(0, T, T)
Kinit = (-1 / (domain + 1)) * (Kss - K0) + Kss
Kinit[-1] = Kss
Kinit = np.array(list(Kinit) + list(np.ones(S) * Kss))
Linit = np.ones(T + S) * Lss
Yinit = firm.get_Y(Kinit, Linit, parameters)
winit = firm.get_w(Yinit, Linit, parameters)
rinit = firm.get_r(Yinit, Kinit, parameters)
BQinit = np.zeros((T + S, J))
for j in xrange(J):
BQinit[:, j] = list(np.linspace(BQ0[j], BQss[j], T)) + [BQss[j]] * S
BQinit = np.array(BQinit)
T_H_init = np.ones(T + S) * T_Hss
# Make array of initial guesses
domain2 = np.tile(domain.reshape(T, 1, 1), (1, S, J))
ending_b = bssmat_splus1
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, S, J), (S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, T).reshape(T, 1, 1), (1, S, J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, S, J), (S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = np.zeros((T + S, S, J))
n_mat = np.zeros((T + S, S, J))
ind = np.arange(S)
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((T, 2 * S, J))
TPIdist_vec = np.zeros(maxiter)
while (TPIiter < maxiter) and (TPIdist >= mindist_TPI):
Kpath_TPI = list(Kinit) + list(np.ones(10) * Kss)
Lpath_TPI = list(Linit) + list(np.ones(10) * Lss)
# Plot TPI for K for each iteration, so we can see if there is a
# problem
if PLOT_TPI is True:
plt.figure()
plt.axhline(
y=Kss, color='black', linewidth=2, label=r"Steady State $\hat{K}$", ls='--')
plt.plot(np.arange(
T + 10), Kpath_TPI[:T + 10], 'b', linewidth=2, label=r"TPI time path $\hat{K}_t$")
plt.savefig(os.path.join(TPI_FIG_DIR, "TPI_K"))
# Uncomment the following print statements to make sure all euler equations are converging.
# If they don't, then you'll have negative consumption or consumption spikes. If they don't,
# it is the initial guesses. You might need to scale them differently. It is rather delicate for the first
# few periods and high ability groups.
for j in xrange(J):
b_mat[1, -1, j], n_mat[0, -1, j] = np.array(opt.fsolve(SS_TPI_firstdoughnutring, [guesses_b[1, -1, j], guesses_n[0, -1, j]],
args=(winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b, factor_ss, j, parameters, theta, tau_bq), xtol=1e-13))
# if np.array(SS_TPI_firstdoughnutring([b_mat[1, -1, j], n_mat[0, -1, j]], winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b, factor_ss, j, parameters, theta, tau_bq)).max() > 1e-6:
# print 'minidoughnut:',
# np.array(SS_TPI_firstdoughnutring([b_mat[1, -1, j], n_mat[0, -1,
# j]], winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b,
# factor_ss, j, parameters, theta, tau_bq)).max()
for s in xrange(S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(
guesses_b[1:S + 1, :, j], S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:S, :, j], S - (s + 2))
solutions = opt.fsolve(Steady_state_TPI_solver, list(
b_guesses_to_use) + list(n_guesses_to_use), args=(
winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, s, 0, parameters, theta, tau_bq, rho, lambdas, e, initial_b, chi_b, chi_n), xtol=1e-13)
b_vec = solutions[:len(solutions) / 2]
b_mat[1 + ind2, S - (s + 2) + ind2, j] = b_vec
n_vec = solutions[len(solutions) / 2:]
n_mat[ind2, S - (s + 2) + ind2, j] = n_vec
# if abs(np.array(Steady_state_TPI_solver(solutions, winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, s, 0, parameters, theta, tau_bq, rho, lambdas, e, initial_b, chi_b, chi_n))).max() > 1e-6:
# print 's-loop:',
# abs(np.array(Steady_state_TPI_solver(solutions, winit, rinit,
# BQinit[:, j], T_H_init, factor_ss, j, s, 0, parameters,
# theta, tau_bq, rho, lambdas, e, initial_b, chi_b,
# chi_n))).max()
for t in xrange(0, T):
b_guesses_to_use = .75 * \
np.diag(guesses_b[t + 1:t + S + 1, :, j])
n_guesses_to_use = np.diag(guesses_n[t:t + S, :, j])
solutions = opt.fsolve(Steady_state_TPI_solver, list(
b_guesses_to_use) + list(n_guesses_to_use), args=(
winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None, t, parameters, theta, tau_bq, rho, lambdas, e, None, chi_b, chi_n), xtol=1e-13)
b_vec = solutions[:S]
b_mat[t + 1 + ind, ind, j] = b_vec
n_vec = solutions[S:]
n_mat[t + ind, ind, j] = n_vec
inputs = list(solutions)
euler_errors[t, :, j] = np.abs(Steady_state_TPI_solver(
inputs, winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None, t, parameters, theta, tau_bq, rho, lambdas, e, None, chi_b, chi_n))
# if euler_errors.max() > 1e-6:
# print 't-loop:', euler_errors.max()
# Force the initial distribution of capital to be as given above.
b_mat[0, :, :] = initial_b
Kinit = household.get_K(b_mat[:T], omega_stationary[:T].reshape(
T, S, 1), lambdas.reshape(1, 1, J), g_n_vector[:T], 'TPI')
Linit = firm.get_L(e.reshape(1, S, J), n_mat[:T], omega_stationary[
:T, :].reshape(T, S, 1), lambdas.reshape(1, 1, J), 'TPI')
Ynew = firm.get_Y(Kinit, Linit, parameters)
wnew = firm.get_w(Ynew, Linit, parameters)
rnew = firm.get_r(Ynew, Kinit, parameters)
# the following needs a g_n term
BQnew = household.get_BQ(rnew.reshape(T, 1), b_mat[:T], omega_stationary[:T].reshape(
T, S, 1), lambdas.reshape(1, 1, J), rho.reshape(1, S, 1), g_n_vector[:T].reshape(T, 1), 'TPI')
bmat_s = np.zeros((T, S, J))
bmat_s[:, 1:, :] = b_mat[:T, :-1, :]
T_H_new = np.array(list(tax.get_lump_sum(rnew.reshape(T, 1, 1), bmat_s, wnew.reshape(
T, 1, 1), e.reshape(1, S, J), n_mat[:T], BQnew.reshape(T, 1, J), lambdas.reshape(
1, 1, J), factor_ss, omega_stationary[:T].reshape(T, S, 1), 'TPI', parameters, theta, tau_bq)) + [T_Hss] * S)
winit[:T] = utils.convex_combo(wnew, winit[:T], parameters)
rinit[:T] = utils.convex_combo(rnew, rinit[:T], parameters)
BQinit[:T] = utils.convex_combo(BQnew, BQinit[:T], parameters)
T_H_init[:T] = utils.convex_combo(
T_H_new[:T], T_H_init[:T], parameters)
guesses_b = utils.convex_combo(b_mat, guesses_b, parameters)
guesses_n = utils.convex_combo(n_mat, guesses_n, parameters)
if T_H_init.all() != 0:
TPIdist = np.array(list(utils.perc_dif_func(rnew, rinit[:T])) + list(utils.perc_dif_func(BQnew, BQinit[:T]).flatten()) + list(
utils.perc_dif_func(wnew, winit[:T])) + list(utils.perc_dif_func(T_H_new, T_H_init))).max()
else:
TPIdist = np.array(list(utils.perc_dif_func(rnew, rinit[:T])) + list(utils.perc_dif_func(BQnew, BQinit[:T]).flatten()) + list(
utils.perc_dif_func(wnew, winit[:T])) + list(np.abs(T_H_new, T_H_init))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
if TPIiter > 10:
if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
nu /= 2
print 'New Value of nu:', nu
TPIiter += 1
print '\tIteration:', TPIiter
print '\t\tDistance:', TPIdist
print 'Computing final solutions'
# As in SS, you need the final distributions of b and n to match the final
# w, r, BQ, etc. Otherwise the euler errors are large. You need one more
# fsolve.
for j in xrange(J):
b_mat[1, -1, j], n_mat[0, -1, j] = np.array(opt.fsolve(SS_TPI_firstdoughnutring, [guesses_b[1, -1, j], guesses_n[0, -1, j]],
args=(winit[1], rinit[1], BQinit[1, j], T_H_init[1], initial_b, factor_ss, j, parameters, theta, tau_bq), xtol=1e-13))
for s in xrange(S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[1:S + 1, :, j], S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:S, :, j], S - (s + 2))
solutions = opt.fsolve(Steady_state_TPI_solver, list(
b_guesses_to_use) + list(n_guesses_to_use), args=(
winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, s, 0, parameters, theta, tau_bq, rho, lambdas, e, initial_b, chi_b, chi_n), xtol=1e-13)
b_vec = solutions[:len(solutions) / 2]
b_mat[1 + ind2, S - (s + 2) + ind2, j] = b_vec
n_vec = solutions[len(solutions) / 2:]
n_mat[ind2, S - (s + 2) + ind2, j] = n_vec
for t in xrange(0, T):
b_guesses_to_use = .75 * np.diag(guesses_b[t + 1:t + S + 1, :, j])
n_guesses_to_use = np.diag(guesses_n[t:t + S, :, j])
solutions = opt.fsolve(Steady_state_TPI_solver, list(
b_guesses_to_use) + list(n_guesses_to_use), args=(
winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None, t, parameters, theta, tau_bq, rho, lambdas, e, None, chi_b, chi_n), xtol=1e-13)
b_vec = solutions[:S]
b_mat[t + 1 + ind, ind, j] = b_vec
n_vec = solutions[S:]
n_mat[t + ind, ind, j] = n_vec
inputs = list(solutions)
euler_errors[t, :, j] = np.abs(Steady_state_TPI_solver(
inputs, winit, rinit, BQinit[:, j], T_H_init, factor_ss, j, None, t, parameters, theta, tau_bq, rho, lambdas, e, None, chi_b, chi_n))
b_mat[0, :, :] = initial_b
'''
------------------------------------------------------------------------
Generate variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
Kpath_TPI = np.array(list(Kinit) + list(np.ones(10) * Kss))
Lpath_TPI = np.array(list(Linit) + list(np.ones(10) * Lss))
BQpath_TPI = np.array(list(BQinit) + list(np.ones((10, J)) * BQss))
b_s = np.zeros((T, S, J))
b_s[:, 1:, :] = b_mat[:T, :-1, :]
b_splus1 = np.zeros((T, S, J))
b_splus1[:, :, :] = b_mat[1:T + 1, :, :]
tax_path = tax.total_taxes(rinit[:T].reshape(T, 1, 1), b_s, winit[:T].reshape(T, 1, 1), e.reshape(
1, S, J), n_mat[:T], BQinit[:T, :].reshape(T, 1, J), lambdas, factor_ss, T_H_init[:T].reshape(T, 1, 1), None, 'TPI', False, parameters, theta, tau_bq)
c_path = household.get_cons(rinit[:T].reshape(T, 1, 1), b_s, winit[:T].reshape(T, 1, 1), e.reshape(
1, S, J), n_mat[:T], BQinit[:T].reshape(T, 1, J), lambdas.reshape(1, 1, J), b_splus1, parameters, tax_path)
Y_path = firm.get_Y(Kpath_TPI[:T], Lpath_TPI[:T], parameters)
C_path = household.get_C(c_path, omega_stationary[
:T].reshape(T, S, 1), lambdas, 'TPI')
I_path = firm.get_I(Kpath_TPI[1:T + 1],
Kpath_TPI[:T], delta, g_y, g_n_vector[:T])
print 'Resource Constraint Difference:', Y_path - C_path - I_path
print'Checking time path for violations of constaints.'
for t in xrange(T):
household.constraint_checker_TPI(
b_mat[t], n_mat[t], c_path[t], t, parameters)
eul_savings = euler_errors[:, :S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, S:, :].max(1).max(1)
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {'Kpath_TPI': Kpath_TPI, 'b_mat': b_mat, 'c_path': c_path,
'eul_savings': eul_savings, 'eul_laborleisure': eul_laborleisure,
'Lpath_TPI': Lpath_TPI, 'BQpath_TPI': BQpath_TPI, 'n_mat': n_mat,
'rinit': rinit, 'Yinit': Yinit, 'T_H_init': T_H_init,
'tax_path': tax_path, 'winit': winit}
if get_baseline:
tpi_init_dir = os.path.join(output_dir, "TPIinit")
utils.mkdirs(tpi_init_dir)
tpi_init_vars = os.path.join(tpi_init_dir, "TPIinit_vars.pkl")
pickle.dump(output, open(tpi_init_vars, "wb"))
else:
tpi_dir = os.path.join(output_dir, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
def create_tpi_params(**sim_params):
'''
------------------------------------------------------------------------
Set factor and initial capital stock to SS from baseline
------------------------------------------------------------------------
'''
baseline_ss = os.path.join(sim_params['baseline_dir'], "SS/SS_vars.pkl")
ss_baseline_vars = pickle.load(open(baseline_ss, "rb"))
factor = ss_baseline_vars['factor_ss']
#initial_b = ss_baseline_vars['bssmat_s'] + ss_baseline_vars['BQss']/lambdas
initial_b = ss_baseline_vars['bssmat_splus1']
initial_n = ss_baseline_vars['nssmat']
SS_values = (ss_baseline_vars['Kss'],ss_baseline_vars['Lss'], ss_baseline_vars['rss'],
ss_baseline_vars['wss'], ss_baseline_vars['BQss'], ss_baseline_vars['T_Hss'],
ss_baseline_vars['bssmat_splus1'], ss_baseline_vars['nssmat'])
# Make a vector of all one dimensional parameters, to be used in the
# following functions
wealth_tax_params = [sim_params['h_wealth'], sim_params['p_wealth'], sim_params['m_wealth']]
ellipse_params = [sim_params['b_ellipse'], sim_params['upsilon']]
chi_params = [sim_params['chi_b_guess'], sim_params['chi_n_guess']]
N_tilde = sim_params['omega'].sum(1) #this should just be one in each year given how we've constructed omega
sim_params['omega'] = sim_params['omega'] / N_tilde.reshape(sim_params['T'] + sim_params['S'], 1)
tpi_params = [sim_params['J'], sim_params['S'], sim_params['T'], sim_params['BQ_dist'], sim_params['BW'],
sim_params['beta'], sim_params['sigma'], sim_params['alpha'],
sim_params['Z'], sim_params['delta'], sim_params['ltilde'],
sim_params['nu'], sim_params['g_y'], sim_params['g_n_vector'],
sim_params['tau_payroll'], sim_params['tau_bq'], sim_params['rho'], sim_params['omega'], N_tilde,
sim_params['lambdas'], sim_params['e'], sim_params['retire'], sim_params['mean_income_data'], factor] + \
wealth_tax_params + ellipse_params + chi_params
iterative_params = [sim_params['maxiter'], sim_params['mindist_SS'], sim_params['mindist_TPI']]
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
## Assumption for tax functions is that policy in last year of BW is
# extended permanently
etr_params_TP = np.zeros((S,T+S,sim_params['etr_params'].shape[2]))
etr_params_TP[:,:BW,:] = sim_params['etr_params']
etr_params_TP[:,BW:,:] = np.reshape(sim_params['etr_params'][:,BW-1,:],(S,1,sim_params['etr_params'].shape[2]))
mtrx_params_TP = np.zeros((S,T+S,sim_params['mtrx_params'].shape[2]))
mtrx_params_TP[:,:BW,:] = sim_params['mtrx_params']
mtrx_params_TP[:,BW:,:] = np.reshape(sim_params['mtrx_params'][:,BW-1,:],(S,1,sim_params['mtrx_params'].shape[2]))
mtry_params_TP = np.zeros((S,T+S,sim_params['mtry_params'].shape[2]))
mtry_params_TP[:,:BW,:] = sim_params['mtry_params']
mtry_params_TP[:,BW:,:] = np.reshape(sim_params['mtry_params'][:,BW-1,:],(S,1,sim_params['mtry_params'].shape[2]))
income_tax_params = (sim_params['analytical_mtrs'], etr_params_TP, mtrx_params_TP, mtry_params_TP)
'''
------------------------------------------------------------------------
Set other parameters and initial values
------------------------------------------------------------------------
'''
# Get an initial distribution of capital with the initial population
# distribution
K0_params = (omega[0].reshape(S, 1), lambdas, g_n_vector[0], 'SS')
K0 = household.get_K(initial_b, K0_params)
b_sinit = np.array(list(np.zeros(J).reshape(1, J)) + list(initial_b[:-1]))
b_splus1init = initial_b
L0_params = (e, omega[0].reshape(S, 1), lambdas, 'SS')
L0 = firm.get_L(initial_n, L0_params)
Y0_params = (alpha, Z)
Y0 = firm.get_Y(K0, L0, Y0_params)
w0 = firm.get_w(Y0, L0, alpha)
r0_params = (alpha, delta)
r0 = firm.get_r(Y0, K0, r0_params)
BQ0_params = (omega[0].reshape(S, 1), lambdas, rho.reshape(S, 1), g_n_vector[0], 'SS')
BQ0 = household.get_BQ(r0, initial_b, BQ0_params)
theta_params = (e, J, omega[0].reshape(S, 1), lambdas)
theta = tax.replacement_rate_vals(initial_n, w0, factor, theta_params)
T_H_params = (e, BQ_dist, lambdas, omega[0].reshape(S, 1), 'SS', etr_params_TP[:,0,:],
theta, tau_bq, tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
T_H_0 = tax.get_lump_sum(r0, w0, b_sinit, initial_n, BQ0, factor, T_H_params)
etr_params_3D = np.tile(np.reshape(etr_params_TP[:,0,:],(S,1,etr_params_TP.shape[2])),(1,J,1))
tax0_params = (e, BQ_dist, lambdas, 'SS', retire, etr_params_3D, h_wealth, p_wealth, m_wealth,
tau_payroll, theta, tau_bq, J, S)
tax0 = tax.total_taxes(r0, w0, b_sinit, initial_n, BQ0, factor, T_H_0, None, False, tax0_params)
c0_params = (e, BQ_dist, lambdas.reshape(1, J), g_y)
c0 = household.get_cons(omega[0].reshape(S, 1), r0, w0, b_sinit, b_splus1init, initial_n, BQ0.reshape(
1, J), tax0, c0_params)
initial_values = (K0, b_sinit, b_splus1init, L0, Y0,
w0, r0, BQ0, T_H_0, factor, tax0, c0, initial_b, initial_n)
return (income_tax_params, tpi_params, iterative_params, initial_values, SS_values)
def create_tpi_params(a_tax_income, b_tax_income, c_tax_income,
d_tax_income,
b_ellipse, upsilon, J, S, T, beta, sigma, alpha, Z,
delta, ltilde, nu, g_y, tau_payroll, retire,
mean_income_data, get_baseline=True, input_dir="./OUTPUT", **kwargs):
if get_baseline:
ss_init = os.path.join(input_dir, "SSinit/ss_init_vars.pkl")
variables = pickle.load(open(ss_init, "rb"))
for key in variables:
globals()[key] = variables[key]
else:
params_path = os.path.join(
input_dir, "Saved_moments/params_changed.pkl")
variables = pickle.load(open(params_path, "rb"))
for key in variables:
globals()[key] = variables[key]
var_path = os.path.join(input_dir, "SS/ss_vars.pkl")
variables = pickle.load(open(var_path, "rb"))
for key in variables:
globals()[key] = variables[key]
init_tpi_vars = os.path.join(input_dir, "SSinit/ss_init_tpi_vars.pkl")
variables = pickle.load(open(init_tpi_vars, "rb"))
for key in variables:
globals()[key] = variables[key]
'''
------------------------------------------------------------------------
Set other parameters and initial values
------------------------------------------------------------------------
'''
# Make a vector of all one dimensional parameters, to be used in the
# following functions
income_tax_params = [a_tax_income,
b_tax_income, c_tax_income, d_tax_income]
wealth_tax_params = [h_wealth, p_wealth, m_wealth]
ellipse_params = [b_ellipse, upsilon]
parameters = [J, S, T, beta, sigma, alpha, Z, delta, ltilde, nu, g_y, g_n_ss, tau_payroll, retire,
mean_income_data] + income_tax_params + wealth_tax_params + ellipse_params
N_tilde = omega.sum(1)
omega_stationary = omega / N_tilde.reshape(T + S, 1)
if get_baseline:
initial_b = bssmat_splus1
initial_n = nssmat
else:
initial_b = bssmat_init
initial_n = nssmat_init
# Get an initial distribution of capital with the initial population
# distribution
K0 = household.get_K(initial_b, omega_stationary[
0].reshape(S, 1), lambdas, g_n_vector[0], 'SS')
b_sinit = np.array(list(np.zeros(J).reshape(1, J)) + list(initial_b[:-1]))
b_splus1init = initial_b
L0 = firm.get_L(e, initial_n, omega_stationary[
0].reshape(S, 1), lambdas, 'SS')
Y0 = firm.get_Y(K0, L0, parameters)
w0 = firm.get_w(Y0, L0, parameters)
r0 = firm.get_r(Y0, K0, parameters)
BQ0 = household.get_BQ(r0, initial_b, omega_stationary[0].reshape(
S, 1), lambdas, rho.reshape(S, 1), g_n_vector[0], 'SS')
T_H_0 = tax.get_lump_sum(r0, b_sinit, w0, e, initial_n, BQ0, lambdas, factor_ss, omega_stationary[
0].reshape(S, 1), 'SS', parameters, theta, tau_bq)
tax0 = tax.total_taxes(r0, b_sinit, w0, e, initial_n, BQ0, lambdas,
factor_ss, T_H_0, None, 'SS', False, parameters, theta, tau_bq)
c0 = household.get_cons(r0, b_sinit, w0, e, initial_n, BQ0.reshape(
1, J), lambdas.reshape(1, J), b_splus1init, parameters, tax0)
return (income_tax_params, wealth_tax_params, ellipse_params, parameters,
N_tilde, omega_stationary, K0, b_sinit, b_splus1init, L0, Y0,
w0, r0, BQ0, T_H_0, tax0, c0, initial_b, initial_n)
def FOC_labor(r, w, b, b_splus1, n, BQ, factor, T_H, params):
'''
Computes Euler errors for the FOC for labor supply in the steady state.
This function is usually looped through over J, so it does one lifetime income group at a time.
Inputs:
r = scalar, interest rate
w = scalar, wage rate
b = [S,J] array, distribution of wealth/capital holdings
b_splus1 = [S,J] array, distribution of wealth/capital holdings one period ahead
n = [S,J] array, distribution of labor supply
BQ = [J,] vector, aggregate bequests by lifetime income group
factor = scalar, scaling factor to convert model income to dollars
T_H = scalar, lump sum transfer
params = length 19 tuple (e, sigma, g_y, theta, b_ellipse, upsilon, ltilde,
chi_n, tau_bq, lambdas, J, S,
etr_params, mtrx_params, h_wealth, p_wealth,
m_wealth, tau_payroll, tau_bq)
e = [S,J] array, effective labor units
sigma = scalar, coefficient of relative risk aversion
g_y = scalar, exogenous labor augmenting technological growth
theta = [J,] vector, replacement rate for each lifetime income group
b_ellipse = scalar, scaling parameter in elliptical utility function
upsilon = curvature parameter in elliptical utility function
chi_n = [S,] vector, utility weights on disutility of labor
ltilde = scalar, upper bound of household labor supply
tau_bq = scalar, bequest tax rate (scalar)
lambdas = [J,] vector, ability weights
J = integer, number of lifetime income groups
S = integer, number of economically active periods in lifetime
etr_params = [S,10] array, parameters of effective income tax rate function
mtrx_params = [S,10] array, parameters of marginal tax rate on labor income function
h_wealth = scalar, parameter in wealth tax function
p_wealth = scalar, parameter in wealth tax function
m_wealth = scalar, parameter in wealth tax function
tau_payroll = scalar, payroll tax rate
tau_bq = scalar, bequest tax rate
Functions called:
get_cons
marg_ut_cons
marg_ut_labor
tax.total_taxes
tax.MTR_labor
Objects in function:
tax = [S,J] array, net taxes in the current period
cons = [S,J] array, consumption in the current period
deriv = [S,J] array, net of tax share of labor income
euler = [S,J] array, Euler error from FOC for labor supply
Returns: euler
'''
e, sigma, g_y, theta, b_ellipse, upsilon, chi_n, ltilde, tau_bq, lambdas, J, S, \
analytical_mtrs, etr_params, mtrx_params, h_wealth, p_wealth, m_wealth, tau_payroll, retire, method = params
tax1_params = (e, lambdas, method, retire, etr_params, h_wealth, p_wealth,
m_wealth, tau_payroll, theta, tau_bq, J, S)
tax1 = tax.total_taxes(r, w, b, n, BQ, factor, T_H, None, False,
tax1_params)
cons_params = (e, lambdas, g_y)
cons = get_cons(r, w, b, b_splus1, n, BQ, tax1, cons_params)
mtr_lab_params = (e, etr_params, mtrx_params, analytical_mtrs)
deriv = (1 - tau_payroll -
tax.MTR_labor(r, b, w, n, factor, mtr_lab_params))
lab_params = (b_ellipse, upsilon, ltilde, chi_n)
euler = marg_ut_cons(cons, sigma) * w * deriv * e - \
marg_ut_labor(n, lab_params)
return euler
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, imm_rates, e, retire, mean_income_data,\
factor, T_H_baseline, h_wealth, p_wealth, m_wealth, b_ellipse, upsilon, chi_b, chi_n, theta = tpi_params
b_splus1 = float(guesses[0])
n = float(guesses[1])
b_s = float(initial_b[-2, j])
# Find errors from FOC for savings and FOC for labor supply
retire_fd = 0 # this sets retire to true in these agents who are
# in last period in life
# Note using method = "SS" below because just for one period
foc_save_params = (np.array([e[-1, j]]), sigma, beta, g_y, chi_b[j],
theta[j], tau_bq[j], rho[-1], lambdas[j], j, J,
S, analytical_mtrs,
np.reshape(etr_params[-1, 0, :],
(1, etr_params.shape[2])),
np.reshape(mtry_params[-1, 0, :],
(1, mtry_params.shape[2])), h_wealth,
p_wealth, m_wealth, tau_payroll, retire_fd, 'SS')
error1 = household.FOC_savings(np.array([r]), np.array([w]), b_s,
b_splus1, 0., np.array([n]),
np.array([BQ]), factor,
np.array([T_H]), foc_save_params)
foc_labor_params = (np.array([e[-1, j]]), sigma, g_y, theta[j],
b_ellipse, upsilon, chi_n[-1], ltilde,
tau_bq[j], lambdas[j], j, J, S, analytical_mtrs,
np.reshape(etr_params[-1, 0, :],
(1, etr_params.shape[2])),
np.reshape(mtrx_params[-1, 0, :],
(1, mtrx_params.shape[2])), h_wealth,
p_wealth, m_wealth, tau_payroll, retire_fd,
'SS')
error2 = household.FOC_labor(np.array([r]), np.array([w]), b_s,
b_splus1, np.array([n]),
np.array([BQ]), factor,
np.array([T_H]), foc_labor_params)
tax_params = (np.array([e[-1, j]]), lambdas[j], 'SS', retire_fd,
np.reshape(etr_params[-1, 0, :],
(1, etr_params.shape[2])), h_wealth,
p_wealth, m_wealth, tau_payroll, theta[j], tau_bq[j],
J, S)
tax1 = tax.total_taxes(np.array([r]), np.array([w]), b_s,
np.array([n]), np.array([BQ]), factor,
np.array([T_H]), j, False, tax_params)
cons_params = (np.array([e[-1, j]]), lambdas[j], g_y)
cons = household.get_cons(np.array([r]), np.array([w]), b_s, b_splus1,
np.array([n]), np.array([BQ]), tax1, cons_params)
if n < 0 or n > ltilde:
error2 = 1e12
if b_splus1 <= 0:
error1 += 1e12
# if cons <= 0:
# error1 += 1e12
return [np.squeeze(error1)] + [np.squeeze(error2)]