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 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 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 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 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,
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_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