def solve_ss(r_init, params):
'''
Solves for the steady-state equlibrium of the OG model
'''
beta, sigma, n, alpha, A, delta, xi = params
ss_dist = 7.0
ss_tol = 1e-8
ss_iter = 0
ss_max_iter = 300
r = r_init
while (ss_dist > ss_tol) & (ss_iter < ss_max_iter):
# get w
w = firm.get_w(r, alpha, A, delta)
# solve HH problem
foc_args = (beta, sigma, r, w, n, 0.0)
b_sp1_guess = [0.05, 0.05]
result = opt.root(hh.FOCs, b_sp1_guess, args=foc_args)
b_sp1 = result.x
euler_errors = result.fun
b_s = np.append(0.0, b_sp1)
# use market clearing
L = agg.get_L(n)
K = agg.get_K(b_s)
# find implied r
r_prime = firm.get_r(L, K, alpha, A, delta)
# check distance
ss_dist = np.absolute(r - r_prime)
print('Iteration = ', ss_iter, ', Distance = ', ss_dist, ', r = ', r)
# update r
r = xi * r_prime + (1 - xi) * r
# update iteration counter
ss_iter += 1
return r, b_sp1, euler_errors
def solve_tp(r_path_init, params):
'''
Solves for the time path equlibrium using TPI
'''
(beta, sigma, n, alpha, A, delta, T, xi, b_sp1_pre, r_ss,
b_sp1_ss) = params
tpi_dist = 7.0
tpi_tol = 1e-8
tpi_iter = 0
tpi_max_iter = 300
r_path = np.append(r_path_init, np.ones(2) * r_ss)
while (tpi_dist > tpi_tol) & (tpi_iter < tpi_max_iter):
w_path = firm.get_w(r_path, alpha, A, delta)
# Solve HH problem
b_sp1_mat = np.zeros((T + 2, 2))
euler_errors_mat = np.zeros((T + 2, 2))
# solve upper right corner
foc_args = (beta, sigma, r_path[:2], w_path[:2], n[-2:], b_sp1_pre[0])
b_sp1_guess = b_sp1_ss[-1]
result = opt.root(hh.FOCs, b_sp1_guess, args=foc_args)
b_sp1_mat[0, -1] = result.x
euler_errors_mat[0, -1] = result.fun
# solve all full lifetimes
DiagMaskb = np.eye(2, dtype=bool)
for t in range(T):
foc_args = (beta, sigma, r_path[t:t + 3], w_path[t:t + 3], n, 0.0)
b_sp1_guess = b_sp1_ss
result = opt.root(hh.FOCs, b_sp1_guess, args=foc_args)
b_sp1_mat[t:t + 2, :] = (DiagMaskb * result.x +
b_sp1_mat[t:t + 2, :])
euler_errors_mat[t:t + 2, :] = (DiagMaskb * result.fun +
euler_errors_mat[t:t + 2, :])
# create a b_s_mat
b_s_mat = np.zeros((T, 3))
b_s_mat[0, 1:] = b_sp1_pre
b_s_mat[1:, 1:] = b_sp1_mat[:T - 1, :]
# use market clearing
L_path = np.ones(T) * agg.get_L(n)
K_path = agg.get_K(b_s_mat)
# find implied r
r_path_prime = firm.get_r(L_path, K_path, alpha, A, delta)
# check distance
tpi_dist = np.absolute(r_path[:T] - r_path_prime[:T]).max()
print('Iteration = ', tpi_iter, ', Distance = ', tpi_dist)
# update r
r_path[:T] = xi * r_path_prime[:T] + (1 - xi) * r_path[:T]
# update iteration counter
tpi_iter += 1
if tpi_iter < tpi_max_iter:
print('The time path solved')
else:
print('The time path did not solve')
return r_path[:T], euler_errors_mat[:T, :]
def test_get_r():
'''
Teset of the firm.get_r() function
'''
A = 1.0
alpha = 0.5
delta = 0.1
L = 4.0
K = 16.0
expected_value = 0.15
test_value = firm.get_r(L, K, alpha, A, delta)
assert np.allclose(test_value, expected_value)
def solve_ss(r_init, params):
'''
Solves for the steady-state equlibrium of the OG model
'''
beta, sigma, alpha, A, delta, xi, omega_SS, imm_rates_SS, S = params
ss_dist = 7.0
ss_tol = 1e-8
ss_iter = 0
ss_max_iter = 300
r = r_init
# w = w_init
# Why do we need w as well? Are we not going to get it by providing r_init to firm.get_w()?
# I think Jason said this too and I'm going to stick to what we did in class.
while (ss_dist > ss_tol) & (ss_iter < ss_max_iter):
# get w
w = firm.get_w(r, alpha, A, delta)
# solve HH problem
foc_args = (beta, sigma, r, w, 0.0)
n_s_guess = np.ones(S)
b_sp1_guess = np.ones(S - 1) * 0.5
HH_guess = np.append(b_sp1_guess, n_s_guess)
result = opt.root(hh.FOCs, HH_guess, args=foc_args)
b_sp1 = result.x[0:S - 1]
n_s = result.x[S - 1:]
euler_errors = result.fun
b_s = np.append(0.0, b_sp1)
# use market clearing
L = agg.get_L(n_s, omega_SS)
K = agg.get_K(b_s, omega_SS, imm_rates_SS)
# find implied r
r_prime = firm.get_r(L, K, alpha, A, delta)
# find implied w
w_prime = firm.get_w(r, alpha, A, delta)
# check distance
ss_dist_r = np.absolute(r - r_prime)
ss_dist_w = np.absolute(w - w_prime)
print('Iteration = ', ss_iter, ', Distance r = ', ss_dist_r, ', r = ',
r, ', w = ', w)
# update r
r = xi * r_prime + (1 - xi) * r
# update iteration counter
ss_iter += 1
return r, w, b_sp1, euler_errors
def solve_ss(r_init, w_init, params):
'''
Solves for the steady-state equlibrium of the OG model
'''
beta, sigma, n, alpha, A, delta, xi = params
ss_dist = 7.0
ss_tol = 1e-8
ss_iter = 0
ss_max_iter = 300
r = r_init
w = w_init
while (ss_dist > ss_tol) & (ss_iter < ss_max_iter):
# solve HH problem
foc_args = (beta, sigma, r, w, 0.0)
n_s_guess = np.ones(S)
b_sp1_guess = np.ones(S-1) * 0.5
HH_guess = np.append(b_sp1_guess, n_s_guess)
result = opt.root(hh.FOCs, HH_guess, args=foc_args)
b_sp1 = result.x[0: S-1]
n_s = result.x[S-1:]
euler_errors = result.fun
b_s = np.append(0.0, b_sp1)
# use market clearing
L = agg.get_L(n)
K = agg.get_K(b_s)
# find implied r
r_prime = firm.get_r(L, K, alpha, A, delta)
# find implied w
w_prime = firm.get_w(L, K, G, alpha, A)
# check distance
ss_dist_r = np.absolute(r - r_prime)
ss_dist_w = np.absolute(w - w_prime)
print('Iteration = ', ss_iter, ', Distance r = ', ss_dist_r,
', Disrance w = ' ss_dist_w,
', r = ', r, ', w = ', w)
# update r
r = xi * r_prime + (1 - xi) * r
# update w
w = xi * w_prime + (1 - xi) * w
# update iteration counter
ss_iter += 1
return r, w, b_sp1, euler_errors
def solve_ss(r_init, params):
'''
Solves for the steady-state equlibrium of the OG model
'''
beta, sigma, alpha, A, delta, xi, l_tilde, chi, theta, omega_SS, imm_rates_SS, rho_s, S = params
ss_dist = 7.0
ss_tol = 1e-8
ss_iter = 0
ss_max_iter = 300
r = r_init
while (ss_dist > ss_tol) & (ss_iter < ss_max_iter):
# get w
w = firm.get_w(r, alpha, A, delta)
# solve HH problem
foc_args = (beta, sigma, r, w, 0.0, l_tilde, chi, theta, omega_SS, rho_s)
n_s_guess = np.ones(S)
b_sp1_guess = np.ones(S-1) * 0.5
HH_guess = np.append(b_sp1_guess, n_s_guess)
result = opt.root(hh.FOCs, HH_guess, args=foc_args)
b_sp1 = result.x[0: S-1]
n_s = result.x[S-1:]
euler_errors = result.fun
b_s = np.append(0.0, b_sp1)
# use market clearing
L = agg.get_L(n_s, omega_SS)
K = agg.get_K(b_s, omega_SS, imm_rates_SS)
# find implied r
r_prime = firm.get_r(L, K, alpha, A, delta)
# check distance
ss_dist_r = np.absolute(r - r_prime)
print('Iteration = ', ss_iter, ', Distance r = ', ss_dist_r,
', r = ', r)
# update r
r = xi * r_prime + (1 - xi) * r
# update iteration counter
ss_iter += 1
return ss_iter, r, w, b_sp1, euler_errors
def TPI_fsolve(guesses, 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):
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
# create full time paths with guesses and SS values
rinit = np.zeros(T+S)
winit = np.zeros(T+S)
T_H_init = np.zeros(T+S)
BQinit = np.zeros((T+S,J))
rinit[:T] = guesses[0:T].reshape(T)
winit[:T] = guesses[T:2*T].reshape(T)
rinit[T:] = rss
winit[T:] = wss
T_H_init[:T] = guesses[2*T:3*T].reshape(T)
BQinit[:T,:] = guesses[3*T:].reshape(T,J)
T_H_init[T:] = T_Hss
BQinit[T:,:] = BQss
# Make array of initial guesses for distribution of
# savings and labor supply
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)
euler_errors = np.zeros((T, 2 * S, J))
# Solve hh problem over time path:
# 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, income_tax_params, 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))
# 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
# 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])
# 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))
# 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')
# Plotting of Kpath and Lpath to check convergence
# make vectors of Kpath and Lpath to plot
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
TPI_FIG_DIR = output_dir
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"))
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, :]
# initialize array
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_new = np.array(list(tax.get_lump_sum(np.tile(rnew.reshape(T, 1, 1),(1,S,J)), bmat_s, np.tile(wnew.reshape(
T, 1, 1),(1,S,J)), np.tile(e.reshape(1, S, J),(T,1,1)), n_mat[:T,:,:], BQnew.reshape(T, 1, J), lambdas.reshape(
1, 1, J), factor_ss, omega_stationary[:T].reshape(T, S, 1), 'TPI', TH_tax_params, parameters, theta, tau_bq)) + [T_Hss] * S)
error1 = rinit[:T]-rnew[:T]
error2 = winit[:T]-wnew[:T]
error3 = T_H_init[:T]-T_H_new[:T]
error4 = BQinit[:T] - BQnew[:T]
# Check and punish constraing violations
mask1 = rinit[:T] <= 0
mask2 = winit[:T] <= 0
mask3 = np.isnan(rinit[:T])
mask4 = np.isnan(winit[:T])
error1[mask1] = 1e14
error2[mask2] = 1e14
error1[mask3] = 1e14
error2[mask4] = 1e14
mask5 = T_H_init[:T] < 0
mask6 = np.isnan(T_H_init[:T])
mask7 = BQinit[:T] < 0
mask8 = np.isnan(BQinit[:T])
error3[mask5] = 1e14
error3[mask6] = 1e14
error4[mask7] = 1e14
error4[mask8] = 1e14
errors = np.array(list(error1) +list(error2) + list(error3) + list(error4.flatten()))
print '\t\tDistance:', np.absolute(errors).max()
return errors
def run_time_path_iteration(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):
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
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)
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_init = np.ones(T + S) * T_Hss2
# 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, income_tax_params, 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))
# 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
# 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])
# 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))
# 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, :]
# initialize array
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_new = np.array(list(tax.get_lump_sum(np.tile(rnew.reshape(T, 1, 1),(1,S,J)), bmat_s, np.tile(wnew.reshape(
T, 1, 1),(1,S,J)), np.tile(e.reshape(1, S, J),(T,1,1)), n_mat[:T,:,:], BQnew.reshape(T, 1, J), lambdas.reshape(
1, 1, J), factor_ss, omega_stationary[:T].reshape(T, S, 1), 'TPI', TH_tax_params, parameters, theta, tau_bq)) + [T_Hss] * S)
winit[:T] = utils.convex_combo(wnew, winit[:T], nu)
rinit[:T] = utils.convex_combo(rnew, rinit[:T], nu)
BQinit[:T] = utils.convex_combo(BQnew, BQinit[:T], nu)
T_H_init[:T] = utils.convex_combo(T_H_new[:T], T_H_init[: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_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
return winit[:T], rinit[:T], T_H_init[:T], BQinit[:T], Yinit
def inner_loop(outer_loop_vars, params):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, T_H, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
T_H = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
household.get_K()
firm.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
household.get_BQ()
tax.replacement_rate_vals()
tax.get_lump_sum()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
bssmat, nssmat, r, w, T_H, factor = outer_loop_vars
ss_params, income_tax_params, chi_params = params
J, S, T, BQ_dist, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, lambdas, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
etr_params = np.tile(np.reshape(etr_params,(S,1,etr_params.shape[1])),(1,J,1))
mtrx_params = np.tile(np.reshape(mtrx_params,(S,1,mtrx_params.shape[1])),(1,J,1))
mtry_params = np.tile(np.reshape(mtry_params,(S,1,mtry_params.shape[1])),(1,J,1))
euler_errors = np.zeros((2*S,J))
guesses = np.hstack((bssmat, nssmat))
euler_params = [r, w, T_H, factor, J, S, BQ_dist, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solutions, infodict, ier, message] = opt.fsolve(euler_equation_solver, guesses * .9,
args=euler_params, xtol=MINIMIZER_TOL, full_output=True)
euler_errors = infodict['fvec']
print 'Max Euler errors: ', np.absolute(euler_errors).max()
euler_errors = euler_errors.reshape(S, 2 *J)
solutions = solutions.reshape(S, 2*J)
bssmat = solutions[:, :J]
nssmat = solutions[:, J:]
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), g_n_ss, 'SS')
K = household.get_K(bssmat, K_params)
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = firm.get_L(nssmat, L_params)
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
new_r = firm.get_r(Y, K, r_params)
new_w = firm.get_w(Y, L, alpha)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
new_factor = mean_income_data / average_income_model
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = household.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, J, omega_SS.reshape(S, 1), lambdas)
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, theta_params)
T_H_params = (e, BQ_dist, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS', etr_params, theta, tau_bq,
tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
new_T_H = tax.get_lump_sum(new_r, new_w, b_s, nssmat, new_BQ, factor, T_H_params)
return euler_errors, bssmat, nssmat, new_r, new_w, \
new_T_H, new_factor, new_BQ, average_income_model
def inner_loop(outer_loop_vars, params, baseline):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, T_H, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
T_H = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
household.get_K()
firm.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
household.get_BQ()
tax.replacement_rate_vals()
tax.get_lump_sum()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
bssmat, nssmat, r, w, T_H, BQ, theta, factor = outer_loop_vars
ss_params, income_tax_params, chi_params = params
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, lambdas, imm_rates, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
# bssmat = START_VALUES['bssmat_splus1']
# nssmat = START_VALUES['nssmat']
cssmat = np.zeros((S,J))
euler_errors = np.zeros((2*S,J))
for j in xrange(J):
# Solve the euler equations
if j == 0:
b_Sp1_guess = bssmat[-1, j]
else:
b_Sp1_guess = bssmat[-1, j-1]*10
euler_params = [r, w, T_H, BQ, theta, factor, j, J, S, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
j, chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solution, infodict, ier, message] = opt.fsolve(lc_error, b_Sp1_guess,
args=euler_params, xtol=MINIMIZER_TOL, full_output=True)
# [x0, r_out] = opt.bisect(lc_error, -1.0, 10.0, args=euler_params, xtol=MINIMIZER_TOL, full_output=True, disp=False)
print 'j = ', j
print 'b[0] error = ', infodict['fvec']
print 'message: ', message
# print 'b[S]= ', x0
# print 'converged= ', r_out.converged
b_out, nssmat[:, j], cssmat[:, j] = lifecycle_solver(solution,euler_params)
bssmat[:, j] = b_out[1:]
# print solutions
# quit()
#
# euler_errors[:,j] = infodict['fvec']
# print 'j = ', j
# print 'Max Euler errors: ', np.absolute(euler_errors[:,j]).max()
# print 'bssmat: ', bssmat
# print 'nssmat: ', nssmat
# print 'cssmat: ', cssmat
quit()
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), imm_rates, g_n_ss, 'SS')
K = household.get_K(bssmat, K_params)
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = firm.get_L(nssmat, L_params)
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
new_r = firm.get_r(Y, K, r_params)
new_w = firm.get_w(Y, L, alpha)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
if baseline:
new_factor = mean_income_data / average_income_model
else:
new_factor = factor
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = household.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, S, J, omega_SS.reshape(S, 1), lambdas,retire)
new_theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, theta_params)
T_H_params = (e, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS', etr_params, theta, tau_bq,
tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
new_T_H = tax.get_lump_sum(new_r, new_w, b_s, nssmat, new_BQ, factor, T_H_params)
print 'Inner Loop Max Euler Error: ', (np.absolute(euler_errors)).max()
# print 'K: ', K
# print 'L: ', L
#print 'bssmat: ', bssmat
return euler_errors, bssmat, nssmat, new_r, new_w, \
new_T_H, new_BQ, new_theta, new_factor, average_income_model
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 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 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 inner_loop(outer_loop_vars, params, baseline, baseline_spending=False):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, Y, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
Y = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
household.get_K()
firm.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
household.get_BQ()
tax.replacement_rate_vals()
tax.revenue()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
ss_params, income_tax_params, chi_params, small_open_params = params
J, S, T, BW, beta, sigma, alpha, gamma, epsilon, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, budget_balance, \
alpha_T, debt_ratio_ss, tau_b, delta_tau,\
lambdas, imm_rates, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
small_open, ss_firm_r, ss_hh_r = small_open_params
if budget_balance:
bssmat, nssmat, r, w, T_H, factor = outer_loop_vars
else:
bssmat, nssmat, r, w, Y, T_H, factor = outer_loop_vars
euler_errors = np.zeros((2*S,J))
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j-1], nssmat[:, j-1])
euler_params = [r, w, T_H, factor, j, J, S, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
j, chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solutions, infodict, ier, message] = opt.fsolve(euler_equation_solver, guesses * .9,
args=euler_params, xtol=MINIMIZER_TOL, full_output=True)
euler_errors[:,j] = infodict['fvec']
# print 'Max Euler errors: ', np.absolute(euler_errors[:,j]).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = firm.get_L(nssmat, L_params)
if small_open == False:
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), imm_rates, g_n_ss, 'SS')
B = household.get_K(bssmat, K_params)
if budget_balance:
K = B
else:
K = B - debt_ratio_ss*Y
else:
K_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
K = firm.get_K(L, ss_firm_r, K_params)
# Y_params = (alpha, Z)
Y_params = (Z, gamma, epsilon)
new_Y = firm.get_Y(K, L, Y_params)
#print 'inner K, L, Y: ', K, L, new_Y
if budget_balance:
Y = new_Y
if small_open == False:
r_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
new_r = firm.get_r(Y, K, r_params)
else:
new_r = ss_hh_r
w_params = (Z, gamma, epsilon)
new_w = firm.get_w(Y, L, w_params)
print 'inner factor prices: ', new_r, new_w
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
if baseline:
new_factor = mean_income_data / average_income_model
else:
new_factor = factor
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = household.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, S, retire)
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, theta_params)
if budget_balance:
T_H_params = (e, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS', etr_params, theta, tau_bq,
tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J, tau_b, delta_tau)
new_T_H = tax.revenue(new_r, new_w, b_s, nssmat, new_BQ, new_Y, L, K, factor, T_H_params)
elif baseline_spending:
new_T_H = T_H
else:
new_T_H = alpha_T*new_Y
return euler_errors, bssmat, nssmat, new_r, new_w, \
new_T_H, new_Y, new_factor, new_BQ, average_income_model
def SS_solver(b_guess_init,
n_guess_init,
wguess,
rguess,
T_Hguess,
factorguess,
chi_n,
chi_b,
tax_params,
params,
iterative_params,
tau_bq,
rho,
lambdas,
weights,
e,
fsolve_flag=False):
'''
Solves for the steady state distribution of capital, labor, as well as
w, r, T_H and the scaling factor, using an iterative method similar to TPI.
Inputs:
b_guess_init = guesses for b (SxJ array)
n_guess_init = guesses for n (SxJ array)
wguess = guess for wage rate (scalar)
rguess = guess for rental rate (scalar)
T_Hguess = guess for lump sum tax (scalar)
factorguess = guess for scaling factor to dollars (scalar)
chi_n = chi^n_s (Sx1 array)
chi_b = chi^b_j (Jx1 array)
params = list of parameters (list)
iterative_params = list of parameters that determine the convergence
of the while loop (list)
tau_bq = bequest tax rate (Jx1 array)
rho = mortality rates (Sx1 array)
lambdas = ability weights (Jx1 array)
weights = population weights (Sx1 array)
e = ability levels (SxJ array)
Outputs:
solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
'''
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 = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = tax_params
maxiter, mindist_SS = iterative_params
# Rename the inputs
w = wguess
r = rguess
T_H = T_Hguess
factor = factorguess
bssmat = b_guess_init
nssmat = n_guess_init
dist = 10
iteration = 0
dist_vec = np.zeros(maxiter)
if fsolve_flag == True:
maxiter = 1
while (dist > mindist_SS) and (iteration < maxiter):
# Solve for the steady state levels of b and n, given w, r, T_H and
# factor
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j - 1], nssmat[:, j - 1])
args_ = (r, w, T_H, factor, j, tax_params, params, chi_b, chi_n,
tau_bq, rho, lambdas, weights, e)
[solutions, infodict, ier,
message] = opt.fsolve(Euler_equation_solver,
guesses * .9,
args=args_,
xtol=1e-13,
full_output=True)
print 'Max Euler errors: ', np.absolute(infodict['fvec']).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
# print np.array(Euler_equation_solver(np.append(bssmat[:, j],
# nssmat[:, j]), r, w, T_H, factor, j, params, chi_b, chi_n,
# theta, tau_bq, rho, lambdas, e)).max()
K = household.get_K(bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), g_n_ss, 'SS')
L = firm.get_L(e, nssmat, weights.reshape(S, 1), lambdas.reshape(1, J),
'SS')
Y = firm.get_Y(K, L, params)
new_r = firm.get_r(Y, K, params)
new_w = firm.get_w(Y, L, params)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
weights.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
new_factor = mean_income_data / average_income_model
new_BQ = household.get_BQ(new_r, bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), rho.reshape(S, 1),
g_n_ss, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, e, J,
weights.reshape(S, 1), lambdas)
# lump_sum_tax_params = (a_etr_income, b_etr_income, c_etr_income, d_etr_income,
# e_etr_income, f_etr_income, min_x_etr_income, max_x_etr_income,
# min_y_etr_income, max_y_etr_income)
new_T_H = tax.get_lump_sum(new_r, b_s, new_w, e, nssmat, new_BQ,
lambdas.reshape(1, J), factor,
weights.reshape(S, 1), 'SS', etr_params,
params, theta, tau_bq)
r = utils.convex_combo(new_r, r, nu)
w = utils.convex_combo(new_w, w, nu)
factor = utils.convex_combo(new_factor, factor, nu)
T_H = utils.convex_combo(new_T_H, T_H, nu)
if T_H != 0:
dist = np.array([utils.perc_dif_func(new_r, r)] +
[utils.perc_dif_func(new_w, w)] +
[utils.perc_dif_func(new_T_H, T_H)] +
[utils.perc_dif_func(new_factor, factor)]).max()
else:
# If T_H is zero (if there are no taxes), a percent difference
# will throw NaN's, so we use an absoluate difference
dist = np.array([utils.perc_dif_func(new_r, r)] +
[utils.perc_dif_func(new_w, w)] +
[abs(new_T_H - T_H)] +
[utils.perc_dif_func(new_factor, factor)]).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu /= 2.0
print 'New value of nu:', nu
iteration += 1
print "Iteration: %02d" % iteration, " Distance: ", dist
eul_errors = np.ones(J)
b_mat = np.zeros((S, J))
n_mat = np.zeros((S, J))
# Given the final w, r, T_H and factor, solve for the SS b and n (if you
# don't do a final fsolve, there will be a slight mismatch,
# with high euler errors)
for j in xrange(J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
args_ = (r, w, T_H, factor, j, tax_params, params, chi_b, chi_n,
tau_bq, rho, lambdas, weights, e)
[solutions1, infodict, ier,
message] = opt.fsolve(Euler_equation_solver,
guesses * .9,
args=args_,
xtol=1e-13,
full_output=True)
eul_errors[j] = np.array(infodict['fvec']).max()
print 'Max Euler errors: ', np.absolute(infodict['fvec']).max()
b_mat[:, j] = solutions1[:S]
n_mat[:, j] = solutions1[S:]
print 'SS fsolve euler error:', eul_errors.max()
solutions = np.append(b_mat.flatten(), n_mat.flatten())
other_vars = np.array([w, r, factor, T_H])
solutions = np.append(solutions, other_vars)
return solutions
def SS_fsolve(guesses, b_guess_init, n_guess_init, chi_n, chi_b, tax_params,
params, iterative_params, tau_bq, rho, lambdas, weights, e):
'''
Solves for the steady state distribution of capital, labor, as well as
w, r, T_H and the scaling factor, using an iterative method similar to TPI.
Inputs:
b_guess_init = guesses for b (SxJ array)
n_guess_init = guesses for n (SxJ array)
wguess = guess for wage rate (scalar)
rguess = guess for rental rate (scalar)
T_Hguess = guess for lump sum tax (scalar)
factorguess = guess for scaling factor to dollars (scalar)
chi_n = chi^n_s (Sx1 array)
chi_b = chi^b_j (Jx1 array)
params = list of parameters (list)
iterative_params = list of parameters that determine the convergence
of the while loop (list)
tau_bq = bequest tax rate (Jx1 array)
rho = mortality rates (Sx1 array)
lambdas = ability weights (Jx1 array)
weights = population weights (Sx1 array)
e = ability levels (SxJ array)
Outputs:
solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
'''
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 = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = tax_params
maxiter, mindist_SS = iterative_params
# Rename the inputs
w = guesses[0]
r = guesses[1]
T_H = guesses[2]
factor = guesses[3]
bssmat = b_guess_init
nssmat = n_guess_init
# Solve for the steady state levels of b and n, given w, r, T_H and
# factor
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j - 1], nssmat[:, j - 1])
args_ = (r, w, T_H, factor, j, tax_params, params, chi_b, chi_n,
tau_bq, rho, lambdas, weights, e)
[solutions, infodict, ier, message] = opt.fsolve(Euler_equation_solver,
guesses * .9,
args=args_,
xtol=1e-13,
full_output=True)
print 'Max Euler errors: ', np.absolute(infodict['fvec']).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
# print np.array(Euler_equation_solver(np.append(bssmat[:, j],
# nssmat[:, j]), r, w, T_H, factor, j, params, chi_b, chi_n,
# theta, tau_bq, rho, lambdas, e)).max()
K = household.get_K(bssmat, weights.reshape(S, 1), lambdas.reshape(1, J),
g_n_ss, 'SS')
L = firm.get_L(e, nssmat, weights.reshape(S, 1), lambdas.reshape(1, J),
'SS')
Y = firm.get_Y(K, L, params)
new_r = firm.get_r(Y, K, params)
new_w = firm.get_w(Y, L, params)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
weights.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
new_factor = mean_income_data / average_income_model
new_BQ = household.get_BQ(new_r, bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), rho.reshape(S, 1), g_n_ss,
'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, e, J,
weights.reshape(S, 1), lambdas)
new_T_H = tax.get_lump_sum(new_r, b_s, new_w, e, nssmat, new_BQ,
lambdas.reshape(1, J), factor,
weights.reshape(S, 1), 'SS', etr_params, params,
theta, tau_bq)
error1 = new_w - w
error2 = new_r - r
error3 = new_T_H - T_H
error4 = new_factor - factor
print 'errors: ', error1, error2, error3, error4
print 'T_H: ', new_T_H
print 'factor: ', new_factor
# Check and punish violations
if r <= 0:
error1 += 1e9
#if r > 1:
# error1 += 1e9
if w <= 0:
error2 += 1e9
return [error1, error2, error3, error4]
def inner_loop(outer_loop_vars, params):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, T_H, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
T_H = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
household.get_K()
firm.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
household.get_BQ()
tax.replacement_rate_vals()
tax.get_lump_sum()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
bssmat, nssmat, r, w, T_H, factor = outer_loop_vars
ss_params, income_tax_params, chi_params = params
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, lambdas, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
euler_errors = np.zeros((2*S,J))
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j-1], nssmat[:, j-1])
euler_params = [r, w, T_H, factor, j, J, S, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
j, chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solutions, infodict, ier, message] = opt.fsolve(euler_equation_solver, guesses * .9,
args=euler_params, xtol=MINIMIZER_TOL, full_output=True)
euler_errors[:,j] = infodict['fvec']
print 'Max Euler errors: ', np.absolute(euler_errors[:,j]).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), g_n_ss, 'SS')
K = household.get_K(bssmat, K_params)
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = firm.get_L(nssmat, L_params)
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
new_r = firm.get_r(Y, K, r_params)
new_w = firm.get_w(Y, L, alpha)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
new_factor = mean_income_data / average_income_model
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = household.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, J, omega_SS.reshape(S, 1), lambdas)
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, theta_params)
T_H_params = (e, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS', etr_params, theta, tau_bq,
tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
new_T_H = tax.get_lump_sum(new_r, new_w, b_s, nssmat, new_BQ, factor, T_H_params)
return euler_errors, bssmat, nssmat, new_r, new_w, \
new_T_H, new_factor, new_BQ, average_income_model
def inner_loop(outer_loop_vars, params, baseline, baseline_spending=False):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, Y, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
Y = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
aggr.get_K()
aggr.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
aggr.get_BQ()
tax.replacement_rate_vals()
aggr.revenue()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
ss_params, income_tax_params, chi_params, small_open_params = params
J, S, T, BW, beta, sigma, alpha, gamma, epsilon, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, budget_balance, \
alpha_T, debt_ratio_ss, tau_b, delta_tau,\
lambdas, imm_rates, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
small_open, ss_firm_r, ss_hh_r = small_open_params
if budget_balance:
bssmat, nssmat, r, w, T_H, factor = outer_loop_vars
else:
bssmat, nssmat, r, w, Y, T_H, factor = outer_loop_vars
euler_errors = np.zeros((2 * S, J))
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j - 1], nssmat[:, j - 1])
euler_params = [r, w, T_H, factor, j, J, S, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
j, chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solutions, infodict, ier, message] = opt.fsolve(euler_equation_solver,
guesses * .9,
args=euler_params,
xtol=MINIMIZER_TOL,
full_output=True)
euler_errors[:, j] = infodict['fvec']
# print 'Max Euler errors: ', np.absolute(euler_errors[:,j]).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = aggr.get_L(nssmat, L_params)
if small_open == False:
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), imm_rates,
g_n_ss, 'SS')
B = aggr.get_K(bssmat, K_params)
if budget_balance:
K = B
else:
K = B - debt_ratio_ss * Y
else:
K_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
K = firm.get_K(L, ss_firm_r, K_params)
# Y_params = (alpha, Z)
Y_params = (Z, gamma, epsilon)
new_Y = firm.get_Y(K, L, Y_params)
#print 'inner K, L, Y: ', K, L, new_Y
if budget_balance:
Y = new_Y
if small_open == False:
r_params = (Z, gamma, epsilon, delta, tau_b, delta_tau)
new_r = firm.get_r(Y, K, r_params)
else:
new_r = ss_hh_r
w_params = (Z, gamma, epsilon)
new_w = firm.get_w(Y, L, w_params)
print 'inner factor prices: ', new_r, new_w
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
if baseline:
new_factor = mean_income_data / average_income_model
else:
new_factor = factor
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J),
rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = aggr.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, S, retire)
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, theta_params)
if budget_balance:
T_H_params = (e, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS',
etr_params, theta, tau_bq, tau_payroll, h_wealth,
p_wealth, m_wealth, retire, T, S, J, tau_b, delta_tau)
new_T_H = aggr.revenue(new_r, new_w, b_s, nssmat, new_BQ, new_Y, L, K,
factor, T_H_params)
elif baseline_spending:
new_T_H = T_H
else:
new_T_H = alpha_T * new_Y
return euler_errors, bssmat, nssmat, new_r, new_w, \
new_T_H, new_Y, new_factor, new_BQ, average_income_model
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 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 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 solve_tp(g_n_path, omega_S_preTP, rho_s, imm_rates_path, omega_SS, omega_path_S, params):
'''
Solves for the time path equilibrium using TPI
'''
# Missing some elements of params
b_ss, r_ss, n_s, r_11, alpha, A, delta, beta, sigma, T, S = params
dist = 8.0
mindist = 1e-08
maxiter = 300
tpi_iter = 0
xi = 0.2
while dist > mindist and tpi_iter < maxiter:
# Define paths
b_11 = 1.1 * b_ss
BQ_params = (g_n_path[0], omega_S_preTP, rho_s)
K_params = (g_n_path[0], omega_S_preTP, imm_rates_path[0, :])
BQ_11 = agg.get_BQ(b_11, r_11, BQ_params, method = "TPI")
BQ_ss = agg.get_BQ(b_ss, r_ss, BQ_params, method = "SS")
K_11 = agg.get_K(b_11, K_params)
BQpath_init = np.zeros(T + S - 1)
BQpath_init[:T] = np.linspace(BQ_11, BQ_ss, T)
BQpath_init[T:] = BQ_ss
L_ss = agg.get_L(n_s, omega_SS)
r_11 = firm.get_r(L_ss, K_11, alpha, A, delta)
# I can't figure out how r_11 and r_path differ
''' Is r_11 an initial guess? Depending on how you're defining
r_11, the arguments passed to the function call above and below
will vary
'''
r_path = firm.get_r(L_ss, K_11, alpha, A, delta)
w_path = firm.get_w(r_path, alpha, A, delta)
bmat = np.zeros((S - 1, T + S - 1))
# What is b_1 supposed to be?
bmat[:, 0] = b_1
# Solve for households
for p in range(2, S):
b_guess = np.diagonal(bmat[S - p:, :p - 1])
b_init = bmat[S - p - 1, 0]
b_params = (b_init, n_s[-p:], r_path[:p], w_path[:p],
BQpath_init[:p], rho_s[-p:], beta, sigma)
results_bp = opt.root(hh.FOCs, b_guess, args=(b_params))
b_solve_p = results_bp.x
DiagMaskbp = np.eye(p - 1, dtype=bool)
bmat[S - p:, 1:p] = DiagMaskbp * b_solve_p + bmat[S - p:, 1:p]
for t in range(1, T + 1):
b_guess = np.diagonal(bmat[:, t - 1:t + S - 2])
b_init = 0.0
b_params = (b_init, n_s, r_path[t - 1:t + S - 1],
w_path[t - 1:t + S - 1], BQpath_init[t - 1:t + S - 1],
rho_s, beta, sigma)
results_bt = opt.root(hh.FOCs, b_guess, args=(b_params))
b_solve_t = results_bt.x
DiagMaskbt = np.eye(S - 1, dtype=bool)
bmat[:, t:t + S - 1] = (DiagMaskbt * b_solve_t +
bmat[:, t:t + S - 1])
new_Kpath = np.zeros(T)
new_Kpath[0] = K_11
new_Kpath[1:] = \
(1 / (omega_path_S[:T - 1, :-1]) *
bmat[:, 1:T].T +
imm_rates_path[:T - 1, 1:] *
omega_path_S[:T - 1, 1:] * bmat[:, 1:T].T).sum(axis=1)
new_BQpath = np.zeros(T)
new_BQpath[0] = BQ_11
new_BQpath[1:] = \
((1 + r_path[1:T]) / (rho_s[:-1]) *
omega_path_S[:T - 1, :-1] * bmat[:, 1:T].T).sum(axis=1)
dist = ((BQ_init - new_BQ) ** 2).sum()
BQpath_init[:T] = xi * new_BQpath[:T] + (1 - xi) * BQpath_init[:T]
# update iteration counter
tpi_iter += 1
if tpi_iter < maxiter:
print('The time path solved! ->', ' iter:', tpi_iter, ', dist: ', dist)
else:
print('The time path did not solve.')
return [new_Kpath, new_BQpath]
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 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 inner_loop(outer_loop_vars, params, baseline):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, T_H, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
T_H = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
household.get_K()
firm.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
household.get_BQ()
tax.replacement_rate_vals()
tax.get_lump_sum()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
bssmat, nssmat, r, w, T_H, BQ, theta, factor = outer_loop_vars
ss_params, income_tax_params, chi_params = params
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, lambdas, imm_rates, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
# bssmat = START_VALUES['bssmat_splus1']
# nssmat = START_VALUES['nssmat']
cssmat = np.zeros((S, J))
euler_errors = np.zeros((2 * S, J))
for j in xrange(J):
# Solve the euler equations
if j == 0:
b_Sp1_guess = bssmat[-1, j]
else:
b_Sp1_guess = bssmat[-1, j - 1] * 10
euler_params = [r, w, T_H, BQ, theta, factor, j, J, S, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
j, chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solution, infodict, ier, message] = opt.fsolve(lc_error,
b_Sp1_guess,
args=euler_params,
xtol=MINIMIZER_TOL,
full_output=True)
# [x0, r_out] = opt.bisect(lc_error, -1.0, 10.0, args=euler_params, xtol=MINIMIZER_TOL, full_output=True, disp=False)
print 'j = ', j
print 'b[0] error = ', infodict['fvec']
print 'message: ', message
# print 'b[S]= ', x0
# print 'converged= ', r_out.converged
b_out, nssmat[:,
j], cssmat[:,
j] = lifecycle_solver(solution, euler_params)
bssmat[:, j] = b_out[1:]
# print solutions
# quit()
#
# euler_errors[:,j] = infodict['fvec']
# print 'j = ', j
# print 'Max Euler errors: ', np.absolute(euler_errors[:,j]).max()
# print 'bssmat: ', bssmat
# print 'nssmat: ', nssmat
# print 'cssmat: ', cssmat
quit()
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), imm_rates,
g_n_ss, 'SS')
K = household.get_K(bssmat, K_params)
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = firm.get_L(nssmat, L_params)
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
new_r = firm.get_r(Y, K, r_params)
new_w = firm.get_w(Y, L, alpha)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
if baseline:
new_factor = mean_income_data / average_income_model
else:
new_factor = factor
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J),
rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = household.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, S, J, omega_SS.reshape(S, 1), lambdas, retire)
new_theta = tax.replacement_rate_vals(nssmat, new_w, new_factor,
theta_params)
T_H_params = (e, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS',
etr_params, theta, tau_bq, tau_payroll, h_wealth, p_wealth,
m_wealth, retire, T, S, J)
new_T_H = tax.get_lump_sum(new_r, new_w, b_s, nssmat, new_BQ, factor,
T_H_params)
print 'Inner Loop Max Euler Error: ', (np.absolute(euler_errors)).max()
# print 'K: ', K
# print 'L: ', L
#print 'bssmat: ', bssmat
return euler_errors, bssmat, nssmat, new_r, new_w, \
new_T_H, new_BQ, new_theta, new_factor, average_income_model
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 SS_fsolve(guesses, b_guess_init, n_guess_init, chi_n, chi_b, tax_params, params, iterative_params, tau_bq,
rho, lambdas, weights, e):
'''
Solves for the steady state distribution of capital, labor, as well as
w, r, T_H and the scaling factor, using an iterative method similar to TPI.
Inputs:
b_guess_init = guesses for b (SxJ array)
n_guess_init = guesses for n (SxJ array)
wguess = guess for wage rate (scalar)
rguess = guess for rental rate (scalar)
T_Hguess = guess for lump sum tax (scalar)
factorguess = guess for scaling factor to dollars (scalar)
chi_n = chi^n_s (Sx1 array)
chi_b = chi^b_j (Jx1 array)
params = list of parameters (list)
iterative_params = list of parameters that determine the convergence
of the while loop (list)
tau_bq = bequest tax rate (Jx1 array)
rho = mortality rates (Sx1 array)
lambdas = ability weights (Jx1 array)
weights = population weights (Sx1 array)
e = ability levels (SxJ array)
Outputs:
solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
'''
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 = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = tax_params
maxiter, mindist_SS = iterative_params
# Rename the inputs
w = guesses[0]
r = guesses[1]
T_H = guesses[2]
factor = guesses[3]
bssmat = b_guess_init
nssmat = n_guess_init
# Solve for the steady state levels of b and n, given w, r, T_H and
# factor
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j-1], nssmat[:, j-1])
args_ = (r, w, T_H, factor, j, tax_params, params, chi_b, chi_n, tau_bq, rho,
lambdas, weights, e)
[solutions, infodict, ier, message] = opt.fsolve(Euler_equation_solver, guesses * .9,
args=args_, xtol=1e-13, full_output=True)
print 'Max Euler errors: ', np.absolute(infodict['fvec']).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
# print np.array(Euler_equation_solver(np.append(bssmat[:, j],
# nssmat[:, j]), r, w, T_H, factor, j, params, chi_b, chi_n,
# theta, tau_bq, rho, lambdas, e)).max()
K = household.get_K(bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), g_n_ss, 'SS')
L = firm.get_L(e, nssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), 'SS')
Y = firm.get_Y(K, L, params)
new_r = firm.get_r(Y, K, params)
new_w = firm.get_w(Y, L, params)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
weights.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
new_factor = mean_income_data / average_income_model
new_BQ = household.get_BQ(new_r, bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), rho.reshape(S, 1),
g_n_ss, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, e, J,
weights.reshape(S, 1), lambdas)
new_T_H = tax.get_lump_sum(new_r, b_s, new_w, e, nssmat, new_BQ,
lambdas.reshape(1, J), factor,
weights.reshape(S, 1), 'SS', etr_params, params, theta,
tau_bq)
error1 = new_w - w
error2 = new_r - r
error3 = new_T_H - T_H
error4 = new_factor - factor
print 'errors: ', error1, error2, error3, error4
print 'T_H: ', new_T_H
print 'factor: ', new_factor
# Check and punish violations
if r <= 0:
error1 += 1e9
#if r > 1:
# error1 += 1e9
if w <= 0:
error2 += 1e9
return [error1, error2, error3, error4]
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 solve_tp(g_n_path, omega_S_preTP, rho_s, imm_rates_path, params):
'''
Solves for the time path equilibrium using TPI
'''
# Missing some elements of params
b_ss, r_11, T, S = params
dist = 8.0
mindist = 1e-08
maxiter = 300
tpi_iter = 0
xi = 0.2
while dist > mindist and tpi_iter < maxiter:
# Define paths
b_11 = 1.1 * b_ss
BQ_params = (g_n_path[0], omega_S_preTP, rho_s)
K_params = (g_n_path[0], omega_S_preTP, imm_rates_path[0, :])
BQ_11 = agg.get_BQ(b_11, r_11, BQ_params)
K_11 = agg.get_K(b_11, K_params)
BQpath_init = np.zeros(T + S - 1)
BQpath_init[:T] = np.linspace(BQ_11, BQ_ss, T)
BQpath_init[T:] = BQ_ss
r_11 = firm.get_r(K_11, L_ss, r_params)
r_path = firm.get_r(L_ss, r_params)
w_path = firm.get_w(L_ss, w_params)
bmat = np.zeros((S - 1, T + S - 1))
bmat[:, 0] = b_1
# Solve for households
for p in range(2, S):
b_guess = np.diagonal(bmat[S - p:, :p - 1])
b_init = bmat[S - p - 1, 0]
b_params = (b_init, n[-p:], r_path[:p], w_path[:p],
BQpath_init[:p], rho_s[-p:], beta, sigma)
results_bp = opt.root(hh.FOCs, b_guess, args=(b_params))
b_solve_p = results_bp.x
DiagMaskbp = np.eye(p - 1, dtype=bool)
bmat[S - p:, 1:p] = DiagMaskbp * b_solve_p + bmat[S - p:, 1:p]
for t in range(1, T + 1):
b_guess = np.diagonal(bmat[:, t - 1:t + S - 2])
b_init = 0.0
b_params = (b_init, n, r_path[t - 1:t + S - 1],
w_path[t - 1:t + S - 1], BQpath_init[t - 1:t + S - 1],
rho_s, beta, sigma)
results_bt = opt.root(hh.FOCs, b_guess, args=(b_params))
b_solve_t = results_bt.x
DiagMaskbt = np.eye(S - 1, dtype=bool)
bmat[:,
t:t + S - 1] = (DiagMaskbt * b_solve_t + bmat[:, t:t + S - 1])
new_Kpath = np.zeros(T)
new_Kpath[0] = K_1
new_Kpath[1:] = \
(1 / (omega_path_S[:T - 1, :-1]) *
bmat[:, 1:T].T +
imm_rates_path[:T - 1, 1:] *
omega_path_S[:T - 1, 1:] * bmat[:, 1:T].T).sum(axis=1)
new_BQpath = np.zeros(T)
new_BQpath[0] = BQ_1
new_BQpath[1:] = \
((1 + r_path[1:T]) / (rho_s[:-1]) *
omega_path_S[:T - 1, :-1] * bmat[:, 1:T].T).sum(axis=1)
dist = ((BQ_init - new_BQ)**2).sum()
BQpath_init[:T] = xi * new_BQpath[:T] + (1 - xi) * BQpath_init[:T]
# update iteration counter
tpi_iter += 1
if tpi_iter < maxiter:
print('The time path solved! ->', ' iter:', tpi_iter, ', dist: ', dist)
else:
print('The time path did not solve.')
return [new_Kpath, new_BQpath]
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 SS_solver(b_guess_init, n_guess_init, wguess, rguess, T_Hguess,
factorguess, chi_n, chi_b, tax_params, params, iterative_params, tau_bq,
rho, lambdas, weights, e, fsolve_flag=False):
'''
Solves for the steady state distribution of capital, labor, as well as
w, r, T_H and the scaling factor, using an iterative method similar to TPI.
Inputs:
b_guess_init = guesses for b (SxJ array)
n_guess_init = guesses for n (SxJ array)
wguess = guess for wage rate (scalar)
rguess = guess for rental rate (scalar)
T_Hguess = guess for lump sum tax (scalar)
factorguess = guess for scaling factor to dollars (scalar)
chi_n = chi^n_s (Sx1 array)
chi_b = chi^b_j (Jx1 array)
params = list of parameters (list)
iterative_params = list of parameters that determine the convergence
of the while loop (list)
tau_bq = bequest tax rate (Jx1 array)
rho = mortality rates (Sx1 array)
lambdas = ability weights (Jx1 array)
weights = population weights (Sx1 array)
e = ability levels (SxJ array)
Outputs:
solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
'''
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 = params
analytical_mtrs, etr_params, mtrx_params, mtry_params = tax_params
maxiter, mindist_SS = iterative_params
# Rename the inputs
w = wguess
r = rguess
T_H = T_Hguess
factor = factorguess
bssmat = b_guess_init
nssmat = n_guess_init
dist = 10
iteration = 0
dist_vec = np.zeros(maxiter)
if fsolve_flag == True:
maxiter = 1
while (dist > mindist_SS) and (iteration < maxiter):
# Solve for the steady state levels of b and n, given w, r, T_H and
# factor
for j in xrange(J):
# Solve the euler equations
if j == 0:
guesses = np.append(bssmat[:, j], nssmat[:, j])
else:
guesses = np.append(bssmat[:, j-1], nssmat[:, j-1])
args_ = (r, w, T_H, factor, j, tax_params, params, chi_b, chi_n, tau_bq, rho,
lambdas, weights, e)
[solutions, infodict, ier, message] = opt.fsolve(Euler_equation_solver, guesses * .9,
args=args_, xtol=1e-13, full_output=True)
print 'Max Euler errors: ', np.absolute(infodict['fvec']).max()
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
# print np.array(Euler_equation_solver(np.append(bssmat[:, j],
# nssmat[:, j]), r, w, T_H, factor, j, params, chi_b, chi_n,
# theta, tau_bq, rho, lambdas, e)).max()
K = household.get_K(bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), g_n_ss, 'SS')
L = firm.get_L(e, nssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), 'SS')
Y = firm.get_Y(K, L, params)
new_r = firm.get_r(Y, K, params)
new_w = firm.get_w(Y, L, params)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
weights.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
new_factor = mean_income_data / average_income_model
new_BQ = household.get_BQ(new_r, bssmat, weights.reshape(S, 1),
lambdas.reshape(1, J), rho.reshape(S, 1),
g_n_ss, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, e, J,
weights.reshape(S, 1), lambdas)
# lump_sum_tax_params = (a_etr_income, b_etr_income, c_etr_income, d_etr_income,
# e_etr_income, f_etr_income, min_x_etr_income, max_x_etr_income,
# min_y_etr_income, max_y_etr_income)
new_T_H = tax.get_lump_sum(new_r, b_s, new_w, e, nssmat, new_BQ,
lambdas.reshape(1, J), factor,
weights.reshape(S, 1), 'SS', etr_params, params, theta,
tau_bq)
r = utils.convex_combo(new_r, r, nu)
w = utils.convex_combo(new_w, w, nu)
factor = utils.convex_combo(new_factor, factor, nu)
T_H = utils.convex_combo(new_T_H, T_H, nu)
if T_H != 0:
dist = np.array([utils.perc_dif_func(new_r, r)] +
[utils.perc_dif_func(new_w, w)] +
[utils.perc_dif_func(new_T_H, T_H)] +
[utils.perc_dif_func(new_factor, factor)]).max()
else:
# If T_H is zero (if there are no taxes), a percent difference
# will throw NaN's, so we use an absoluate difference
dist = np.array([utils.perc_dif_func(new_r, r)] +
[utils.perc_dif_func(new_w, w)] +
[abs(new_T_H - T_H)] +
[utils.perc_dif_func(new_factor, factor)]).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu /= 2.0
print 'New value of nu:', nu
iteration += 1
print "Iteration: %02d" % iteration, " Distance: ", dist
eul_errors = np.ones(J)
b_mat = np.zeros((S, J))
n_mat = np.zeros((S, J))
# Given the final w, r, T_H and factor, solve for the SS b and n (if you
# don't do a final fsolve, there will be a slight mismatch,
# with high euler errors)
for j in xrange(J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
args_ = (r, w, T_H, factor, j, tax_params, params, chi_b, chi_n, tau_bq, rho,
lambdas, weights, e)
[solutions1, infodict, ier, message] = opt.fsolve(Euler_equation_solver, guesses * .9,
args=args_, xtol=1e-13, full_output=True)
eul_errors[j] = np.array(infodict['fvec']).max()
print 'Max Euler errors: ', np.absolute(infodict['fvec']).max()
b_mat[:, j] = solutions1[:S]
n_mat[:, j] = solutions1[S:]
print 'SS fsolve euler error:', eul_errors.max()
solutions = np.append(b_mat.flatten(), n_mat.flatten())
other_vars = np.array([w, r, factor, T_H])
solutions = np.append(solutions, other_vars)
return solutions
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 inner_loop(outer_loop_vars, params, baseline):
'''
This function solves for the inner loop of
the SS. That is, given the guesses of the
outer loop variables (r, w, T_H, factor)
this function solves the households'
problems in the SS.
Inputs:
r = [T,] vector, interest rate
w = [T,] vector, wage rate
b = [T,S,J] array, wealth holdings
n = [T,S,J] array, labor supply
BQ = [T,J] vector, bequest amounts
factor = scalar, model income scaling factor
T_H = [T,] vector, lump sum transfer amount(s)
Functions called:
euler_equation_solver()
household.get_K()
firm.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
household.get_BQ()
tax.replacement_rate_vals()
tax.get_lump_sum()
Objects in function:
Returns: euler_errors, bssmat, nssmat, new_r, new_w
new_T_H, new_factor, new_BQ
'''
# unpack variables and parameters pass to function
bssmat, nssmat, r, w, T_H, factor = outer_loop_vars
ss_params, income_tax_params, chi_params = params
J, S, T, BW, beta, sigma, alpha, Z, delta, ltilde, nu, g_y,\
g_n_ss, tau_payroll, tau_bq, rho, omega_SS, lambdas, imm_rates, e, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon = ss_params
analytical_mtrs, etr_params, mtrx_params, mtry_params = income_tax_params
chi_b, chi_n = chi_params
# bssmat = START_VALUES['bssmat_splus1']
# nssmat = START_VALUES['nssmat']
euler_errors = np.zeros((2*S,J))
for j in xrange(J):
# Solve the euler equations
# if j == 0:
# guesses = np.append(bssmat[:, j], nssmat[:, j])
# elif j == J - 1:
# guesses = np.append(bssmat[:, j-1]*2.0, nssmat[:, j-1])
# else:
# guesses = np.append(bssmat[:, j-1], nssmat[:, j-1])
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = [r, w, T_H, factor, j, J, S, beta, sigma, ltilde, g_y,\
g_n_ss, tau_payroll, retire, mean_income_data,\
h_wealth, p_wealth, m_wealth, b_ellipse, upsilon,\
j, chi_b, chi_n, tau_bq, rho, lambdas, omega_SS, e,\
analytical_mtrs, etr_params, mtrx_params,\
mtry_params]
[solutions, infodict, ier, message] = opt.fsolve(euler_equation_solver, guesses * .9,
args=euler_params, xtol=MINIMIZER_TOL, full_output=True)
euler_errors[:,j] = infodict['fvec']
bssmat[:, j] = solutions[:S]
nssmat[:, j] = solutions[S:]
K_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), imm_rates, g_n_ss, 'SS')
K = household.get_K(bssmat, K_params)
L_params = (e, omega_SS.reshape(S, 1), lambdas.reshape(1, J), 'SS')
L = firm.get_L(nssmat, L_params)
Y_params = (alpha, Z)
Y = firm.get_Y(K, L, Y_params)
r_params = (alpha, delta)
new_r = firm.get_r(Y, K, r_params)
new_w = firm.get_w(Y, L, alpha)
b_s = np.array(list(np.zeros(J).reshape(1, J)) + list(bssmat[:-1, :]))
average_income_model = ((new_r * b_s + new_w * e * nssmat) *
omega_SS.reshape(S, 1) *
lambdas.reshape(1, J)).sum()
if baseline:
new_factor = mean_income_data / average_income_model
else:
new_factor = factor
BQ_params = (omega_SS.reshape(S, 1), lambdas.reshape(1, J), rho.reshape(S, 1), g_n_ss, 'SS')
new_BQ = household.get_BQ(new_r, bssmat, BQ_params)
theta_params = (e, S, retire)
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, theta_params)
T_H_params = (e, lambdas.reshape(1, J), omega_SS.reshape(S, 1), 'SS', etr_params, theta, tau_bq,
tau_payroll, h_wealth, p_wealth, m_wealth, retire, T, S, J)
net_tax_receipts = tax.get_lump_sum(new_r, new_w, b_s, nssmat, new_BQ, factor, T_H_params)
print 'Inner Loop Max Euler Error: ', (np.absolute(euler_errors)).max()
return euler_errors, bssmat, nssmat, new_r, new_w, \
net_tax_receipts, new_factor, new_BQ, average_income_model