def run_TPI(p, client=None):
'''
Solve for transition path equilibrium of OG-USA.
Args:
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with transition path solution
results
'''
# unpack tuples of parameters
initial_values, ss_vars, theta, baseline_values = get_initial_SS_values(p)
(B0, b_sinit, b_splus1init, factor, initial_b, initial_n) =\
initial_values
(TRbaseline, Gbaseline, D0_baseline) = baseline_values
print('Government spending breakpoints are tG1: ', p.tG1, '; and tG2:',
p.tG2)
# Initialize guesses at time paths
# Make array of initial guesses for labor supply and savings
guesses_b = utils.get_initial_path(initial_b, ss_vars['bssmat_splus1'], p,
'ratio')
guesses_n = utils.get_initial_path(initial_n, ss_vars['nssmat'], p,
'ratio')
b_mat = guesses_b
n_mat = guesses_n
ind = np.arange(p.S)
# Get path for aggregate savings and labor supply`
L_init = np.ones((p.T + p.S, )) * ss_vars['Lss']
B_init = np.ones((p.T + p.S, )) * ss_vars['Bss']
L_init[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B_init[1:p.T] = aggr.get_B(b_mat[:p.T], p, 'TPI', False)[:p.T - 1]
B_init[0] = B0
K_init = B_init * ss_vars['Kss'] / ss_vars['Bss']
K = K_init
K_d = K_init * ss_vars['K_d_ss'] / ss_vars['Kss']
K_f = K_init * ss_vars['K_f_ss'] / ss_vars['Kss']
L = L_init
B = B_init
Y = np.zeros_like(K)
Y[:p.T] = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
Y[p.T:] = ss_vars['Yss']
r = np.zeros_like(Y)
r[:p.T] = firm.get_r(Y[:p.T], K[:p.T], p, 'TPI')
r[p.T:] = ss_vars['rss']
# For case where economy is small open econ
r[p.zeta_K == 1] = p.world_int_rate[p.zeta_K == 1]
# Compute other interest rates
r_gov = fiscal.get_r_gov(r, p)
r_hh = aggr.get_r_hh(r, r_gov, K, ss_vars['Dss'])
# compute w
w = np.zeros_like(r)
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
w[p.T:] = ss_vars['wss']
# initial guesses at fiscal vars
if p.budget_balance:
if np.abs(ss_vars['TR_ss']) < 1e-13:
TR_ss2 = 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 pct changes below
else:
TR_ss2 = ss_vars['TR_ss']
TR = np.ones(p.T + p.S) * TR_ss2
total_tax_revenue = TR - ss_vars['agg_pension_outlays']
G = np.zeros(p.T + p.S)
D = np.zeros(p.T + p.S)
D_d = np.zeros(p.T + p.S)
D_f = np.zeros(p.T + p.S)
else:
if p.baseline_spending:
TR = TRbaseline
G = Gbaseline
G[p.T:] = ss_vars['Gss']
else:
TR = p.alpha_T * Y
G = np.ones(p.T + p.S) * ss_vars['Gss']
D = np.ones(p.T + p.S) * ss_vars['Dss']
D_d = D * ss_vars['D_d_ss'] / ss_vars['Dss']
D_f = D * ss_vars['D_f_ss'] / ss_vars['Dss']
total_tax_revenue = np.ones(p.T + p.S) * ss_vars['total_tax_revenue']
# Initialize bequests
BQ0 = aggr.get_BQ(r_hh[0], initial_b, None, p, 'SS', True)
if not p.use_zeta:
BQ = np.zeros((p.T + p.S, p.J))
for j in range(p.J):
BQ[:, j] = (list(np.linspace(BQ0[j], ss_vars['BQss'][j], p.T)) +
[ss_vars['BQss'][j]] * p.S)
BQ = np.array(BQ)
else:
BQ = (list(np.linspace(BQ0, ss_vars['BQss'], p.T)) +
[ss_vars['BQss']] * p.S)
BQ = np.array(BQ)
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
TPIdist_vec = np.zeros(p.maxiter)
# TPI loop
while (TPIiter < p.maxiter) and (TPIdist >= p.mindist_TPI):
r_gov[:p.T] = fiscal.get_r_gov(r[:p.T], p)
if not p.budget_balance:
K[:p.T] = firm.get_K_from_Y(Y[:p.T], r[:p.T], p, 'TPI')
r_hh[:p.T] = aggr.get_r_hh(r[:p.T], r_gov[:p.T], K[:p.T], D[:p.T])
outer_loop_vars = (r, w, r_hh, BQ, TR, theta)
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
lazy_values = []
for j in range(p.J):
guesses = (guesses_b[:, :, j], guesses_n[:, :, j])
lazy_values.append(
delayed(inner_loop)(guesses, outer_loop_vars, initial_values,
j, ind, p))
if client:
futures = client.compute(lazy_values, num_workers=p.num_workers)
results = client.gather(futures)
else:
results = results = compute(*lazy_values,
scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
for j, result in enumerate(results):
euler_errors[:, :, j], b_mat[:, :, j], n_mat[:, :, j] = result
bmat_s = np.zeros((p.T, p.S, p.J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:p.T - 1, :-1, :]
bmat_splus1 = np.zeros((p.T, p.S, p.J))
bmat_splus1[:, :, :] = b_mat[:p.T, :, :]
etr_params_4D = np.tile(
p.etr_params.reshape(p.T, p.S, 1, p.etr_params.shape[2]),
(1, 1, p.J, 1))
bqmat = household.get_bq(BQ, None, p, 'TPI')
trmat = household.get_tr(TR, None, p, 'TPI')
tax_mat = tax.net_taxes(r_hh[:p.T], w[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], factor, trmat[:p.T, :, :],
theta, 0, None, False, 'TPI', p.e,
etr_params_4D, p)
r_hh_path = utils.to_timepath_shape(r_hh)
wpath = utils.to_timepath_shape(w)
c_mat = household.get_cons(r_hh_path[:p.T, :, :], wpath[:p.T, :, :],
bmat_s, bmat_splus1, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], tax_mat, p.e,
p.tau_c[:p.T, :, :], p)
y_before_tax_mat = household.get_y(r_hh_path[:p.T, :, :],
wpath[:p.T, :, :],
bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], p)
(total_tax_rev, iit_payroll_tax_revenue, agg_pension_outlays,
bequest_tax_revenue, wealth_tax_revenue, cons_tax_revenue,
business_tax_revenue, payroll_tax_revenue,
iit_revenue) = aggr.revenue(r_hh[:p.T], w[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat[:p.T, :, :],
c_mat[:p.T, :, :], Y[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p,
'TPI')
total_tax_revenue[:p.T] = total_tax_rev
dg_fixed_values = (Y, total_tax_revenue, agg_pension_outlays, TR,
Gbaseline, D0_baseline)
(Dnew, G[:p.T], D_d[:p.T], D_f[:p.T], new_borrowing,
debt_service, new_borrowing_f) =\
fiscal.D_G_path(r_gov, dg_fixed_values, p)
L[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B[1:p.T] = aggr.get_B(bmat_splus1[:p.T], p, 'TPI', False)[:p.T - 1]
K_demand_open = firm.get_K(L[:p.T], p.world_int_rate[:p.T], p, 'TPI')
K[:p.T], K_d[:p.T], K_f[:p.T] = aggr.get_K_splits(
B[:p.T], K_demand_open, D_d[:p.T], p.zeta_K[:p.T])
Ynew = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
rnew = r.copy()
rnew[:p.T] = firm.get_r(Ynew[:p.T], K[:p.T], p, 'TPI')
# For case where economy is small open econ
r[p.zeta_K == 1] = p.world_int_rate[p.zeta_K == 1]
r_gov_new = fiscal.get_r_gov(rnew, p)
r_hh_new = aggr.get_r_hh(rnew[:p.T], r_gov_new[:p.T], K[:p.T],
Dnew[:p.T])
# compute w
wnew = firm.get_w_from_r(rnew[:p.T], p, 'TPI')
b_mat_shift = np.append(np.reshape(initial_b, (1, p.S, p.J)),
b_mat[:p.T - 1, :, :],
axis=0)
BQnew = aggr.get_BQ(r_hh_new[:p.T], b_mat_shift, None, p, 'TPI', False)
bqmat_new = household.get_bq(BQnew, None, p, 'TPI')
(total_tax_rev, iit_payroll_tax_revenue, agg_pension_outlays,
bequest_tax_revenue, wealth_tax_revenue, cons_tax_revenue,
business_tax_revenue, payroll_tax_revenue,
iit_revenue) = aggr.revenue(r_hh_new[:p.T], wnew[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat_new[:p.T, :, :],
c_mat[:p.T, :, :], Ynew[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p,
'TPI')
total_tax_revenue[:p.T] = total_tax_rev
TR_new = fiscal.get_TR(Ynew[:p.T], TR[:p.T], G[:p.T],
total_tax_revenue[:p.T],
agg_pension_outlays[:p.T], p, 'TPI')
# update vars for next iteration
w[:p.T] = wnew[:p.T]
r[:p.T] = utils.convex_combo(rnew[:p.T], r[:p.T], p.nu)
BQ[:p.T] = utils.convex_combo(BQnew[:p.T], BQ[:p.T], p.nu)
D[:p.T] = Dnew[:p.T]
Y[:p.T] = utils.convex_combo(Ynew[:p.T], Y[:p.T], p.nu)
if not p.baseline_spending:
TR[:p.T] = utils.convex_combo(TR_new[:p.T], TR[:p.T], p.nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, p.nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, p.nu)
print('r diff: ', (rnew[:p.T] - r[:p.T]).max(),
(rnew[:p.T] - r[:p.T]).min())
print('BQ diff: ', (BQnew[:p.T] - BQ[:p.T]).max(),
(BQnew[:p.T] - BQ[:p.T]).min())
print('TR diff: ', (TR_new[:p.T] - TR[:p.T]).max(),
(TR_new[:p.T] - TR[:p.T]).min())
print('Y diff: ', (Ynew[:p.T] - Y[:p.T]).max(),
(Ynew[:p.T] - Y[:p.T]).min())
if not p.baseline_spending:
if TR.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(TR_new[:p.T], TR[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(np.abs(TR[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(Ynew[:p.T], Y[:p.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)
# Compute effective and marginal tax rates for all agents
mtrx_params_4D = np.tile(
p.mtrx_params.reshape(p.T, p.S, 1, p.mtrx_params.shape[2]),
(1, 1, p.J, 1))
mtry_params_4D = np.tile(
p.mtry_params.reshape(p.T, p.S, 1, p.mtry_params.shape[2]),
(1, 1, p.J, 1))
e_3D = np.tile(p.e.reshape(1, p.S, p.J), (p.T, 1, 1))
mtry_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
True, e_3D, etr_params_4D, mtry_params_4D, p)
mtrx_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
False, e_3D, etr_params_4D, mtrx_params_4D, p)
etr_path = tax.ETR_income(r_hh_path[:p.T], wpath[:p.T], bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, e_3D, etr_params_4D,
p)
C = aggr.get_C(c_mat, p, 'TPI')
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d = aggr.get_I(bmat_splus1[:p.T], K_d[1:p.T + 1], K_d[:p.T], p, 'TPI')
I = aggr.get_I(bmat_splus1[:p.T], K[1:p.T + 1], K[:p.T], p, 'TPI')
# solve resource constraint
# foreign debt service costs
debt_service_f = fiscal.get_debt_service_f(r_hh, D_f)
RC_error = aggr.resource_constraint(Y[:p.T - 1], C[:p.T - 1], G[:p.T - 1],
I_d[:p.T - 1], K_f[:p.T - 1],
new_borrowing_f[:p.T - 1],
debt_service_f[:p.T - 1],
r_hh[:p.T - 1], p)
# Compute total investment (not just domestic)
I_total = aggr.get_I(None, K[1:p.T + 1], K[:p.T], p, 'total_tpi')
# Compute resource constraint error
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 range(p.T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_mat[t], t,
p.ltilde)
eul_savings = euler_errors[:, :p.S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, p.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[:p.T],
'B': B,
'K': K,
'K_f': K_f,
'K_d': K_d,
'L': L,
'C': C,
'I': I,
'I_total': I_total,
'I_d': I_d,
'BQ': BQ,
'total_tax_revenue': total_tax_revenue,
'business_tax_revenue': business_tax_revenue,
'iit_payroll_tax_revenue': iit_payroll_tax_revenue,
'iit_revenue': iit_revenue,
'payroll_tax_revenue': payroll_tax_revenue,
'TR': TR,
'agg_pension_outlays': agg_pension_outlays,
'bequest_tax_revenue': bequest_tax_revenue,
'wealth_tax_revenue': wealth_tax_revenue,
'cons_tax_revenue': cons_tax_revenue,
'G': G,
'D': D,
'D_f': D_f,
'D_d': D_d,
'r': r,
'r_gov': r_gov,
'r_hh': r_hh,
'w': w,
'bmat_splus1': bmat_splus1,
'bmat_s': bmat_s[:p.T, :, :],
'n_mat': n_mat[:p.T, :, :],
'c_path': c_mat,
'bq_path': bqmat,
'tr_path': trmat,
'y_before_tax_mat': y_before_tax_mat,
'tax_path': tax_mat,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure,
'resource_constraint_error': RC_error,
'new_borrowing_f': new_borrowing_f,
'debt_service_f': debt_service_f,
'etr_path': etr_path,
'mtrx_path': mtrx_path,
'mtry_path': mtry_path
}
tpi_dir = os.path.join(p.output_base, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
with open(tpi_vars, "wb") as f:
pickle.dump(output, f)
if np.any(G) < 0:
print('Government spending is negative along transition path' +
' to satisfy budget')
if (((TPIiter >= p.maxiter) or (np.absolute(TPIdist) > p.mindist_TPI))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found' +
' (TPIdist)')
if ((np.any(np.absolute(RC_error) >= p.mindist_TPI * 10))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(RC_error)')
if ((np.any(np.absolute(eul_savings) >= p.mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > p.mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(eulers)')
return output
def inner_loop(guesses, outer_loop_vars, initial_values, j, ind, p):
'''
Solves inner loop of TPI. Given path of economic aggregates and
factor prices, solves household problem.
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:
firstdoughnutring()
twist_doughnut()
Objects in function:
Returns: euler_errors, b_mat, n_mat
'''
# unpack variables and parameters pass to function
(K0, b_sinit, b_splus1init, factor, initial_b, initial_n,
D0) = initial_values
guesses_b, guesses_n = guesses
r, w, r_hh, BQ, T_H, theta = outer_loop_vars
# compute w
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
# compute bq
bq = household.get_bq(BQ, None, p, 'TPI')
# initialize arrays
b_mat = np.zeros((p.T + p.S, p.S))
n_mat = np.zeros((p.T + p.S, p.S))
euler_errors = np.zeros((p.T, 2 * p.S))
b_mat[0, -1], n_mat[0, -1] =\
np.array(opt.fsolve(firstdoughnutring, [guesses_b[0, -1],
guesses_n[0, -1]],
args=(r_hh[0], w[0], bq[0, -1, j], T_H[0],
theta * p.replacement_rate_adjust[0],
factor, j, initial_b, p),
xtol=MINIMIZER_TOL))
for s in range(p.S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[:p.S, :], p.S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:p.S, :], p.S - (s + 2))
theta_to_use = theta[j] * p.replacement_rate_adjust[:p.S]
bq_to_use = np.diag(bq[:p.S, :, j], p.S - (s + 2))
tau_c_to_use = np.diag(p.tau_c[:p.S, :, j], p.S - (s + 2))
length_diag =\
np.diag(p.etr_params[:p.S, :, 0], p.S-(s + 2)).shape[0]
etr_params_to_use = np.zeros((length_diag, p.etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag, p.mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag, p.mtry_params.shape[2]))
for i in range(p.etr_params.shape[2]):
etr_params_to_use[:, i] =\
np.diag(p.etr_params[:p.S, :, i], p.S - (s + 2))
mtrx_params_to_use[:, i] =\
np.diag(p.mtrx_params[:p.S, :, i], p.S - (s + 2))
mtry_params_to_use[:, i] =\
np.diag(p.mtry_params[:p.S, :, i], p.S - (s + 2))
solutions = opt.fsolve(twist_doughnut,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(r_hh, w, bq_to_use, T_H, theta_to_use,
factor, j, s, 0, tau_c_to_use,
etr_params_to_use, mtrx_params_to_use,
mtry_params_to_use, initial_b, p),
xtol=MINIMIZER_TOL)
b_vec = solutions[:int(len(solutions) / 2)]
b_mat[ind2, p.S - (s + 2) + ind2] = b_vec
n_vec = solutions[int(len(solutions) / 2):]
n_mat[ind2, p.S - (s + 2) + ind2] = n_vec
for t in range(0, p.T):
b_guesses_to_use = .75 * \
np.diag(guesses_b[t:t + p.S, :])
n_guesses_to_use = np.diag(guesses_n[t:t + p.S, :])
theta_to_use = theta[j] * p.replacement_rate_adjust[t:t + p.S]
bq_to_use = np.diag(bq[t:t + p.S, :, j])
tau_c_to_use = np.diag(p.tau_c[t:t + p.S, :, j])
# initialize array of diagonal elements
etr_params_TP = np.zeros((p.T + p.S, p.S, p.etr_params.shape[2]))
etr_params_TP[:p.T, :, :] = p.etr_params
etr_params_TP[p.T:, :, :] = p.etr_params[-1, :, :]
mtrx_params_TP = np.zeros((p.T + p.S, p.S, p.mtrx_params.shape[2]))
mtrx_params_TP[:p.T, :, :] = p.mtrx_params
mtrx_params_TP[p.T:, :, :] = p.mtrx_params[-1, :, :]
mtry_params_TP = np.zeros((p.T + p.S, p.S, p.mtry_params.shape[2]))
mtry_params_TP[:p.T, :, :] = p.mtry_params
mtry_params_TP[p.T:, :, :] = p.mtry_params[-1, :, :]
length_diag =\
np.diag(etr_params_TP[t:t + p.S, :, 0]).shape[0]
etr_params_to_use = np.zeros((length_diag, p.etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag, p.mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag, p.mtry_params.shape[2]))
for i in range(p.etr_params.shape[2]):
etr_params_to_use[:, i] = np.diag(etr_params_TP[t:t + p.S, :, i])
mtrx_params_to_use[:, i] = np.diag(mtrx_params_TP[t:t + p.S, :, i])
mtry_params_to_use[:, i] = np.diag(mtry_params_TP[t:t + p.S, :, i])
#
# TPI_solver_params = (inc_tax_params_TP, tpi_params, None)
[solutions, infodict, ier, message] =\
opt.fsolve(twist_doughnut, list(b_guesses_to_use) +
list(n_guesses_to_use),
args=(r_hh, w, bq_to_use, T_H,
theta_to_use, factor,
j, None, t, tau_c_to_use,
etr_params_to_use, mtrx_params_to_use,
mtry_params_to_use, initial_b, p),
xtol=MINIMIZER_TOL, full_output=True)
euler_errors[t, :] = infodict['fvec']
b_vec = solutions[:p.S]
b_mat[t + ind, ind] = b_vec
n_vec = solutions[p.S:]
n_mat[t + ind, ind] = n_vec
print('Type ', j, ' max euler error = ', euler_errors.max())
return euler_errors, b_mat, n_mat
def test_get_bq(BQ, j, p, method, expected):
# Test the get_bq function
test_value = household.get_bq(BQ, j, p, method)
print('Test value = ', test_value)
assert np.allclose(test_value, expected)
def inner_loop(guesses, outer_loop_vars, initial_values, j, ind, p):
'''
Given path of economic aggregates and factor prices, solves
household problem. This has been termed the inner-loop (in
constrast to the outer fixed point loop that soves for GE factor
prices and economic aggregates).
Args:
guesses (tuple): initial guesses for b and n, (guesses_b,
guesses_n)
outer_loop_vars (tuple): values for factor prices and economic
aggregates used in household problem (r, w, r_hh, BQ, TR,
theta)
r (Numpy array): real interest rate on private capital
w (Numpy array): real wage rate
r (Numpy array): real interest rate on household portfolio
BQ (array_like): aggregate bequest amounts
TR (Numpy array): lump sum transfer amount
theta (Numpy array): retirement replacement rates, length J
initial_values (tuple): initial period variable values,
(b_sinit, b_splus1init, factor, initial_b, initial_n,
D0_baseline)
j (int): index of ability type
ind (Numpy array): integers from 0 to S-1
p (OG-USA Specifications object): model parameters
Returns:
(tuple): household solution results:
* euler_errors (Numpy array): errors from FOCs, size = Tx2S
* b_mat (Numpy array): savings amounts, size = TxS
* n_mat (Numpy array): labor supply amounts, size = TxS
'''
# unpack variables and parameters pass to function
(K0, b_sinit, b_splus1init, factor, initial_b, initial_n) =\
initial_values
guesses_b, guesses_n = guesses
r, w, r_hh, BQ, TR, theta = outer_loop_vars
# compute w
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
# compute bq
bq = household.get_bq(BQ, None, p, 'TPI')
# compute tr
tr = household.get_tr(TR, None, p, 'TPI')
# initialize arrays
b_mat = np.zeros((p.T + p.S, p.S))
n_mat = np.zeros((p.T + p.S, p.S))
euler_errors = np.zeros((p.T, 2 * p.S))
b_mat[0, -1], n_mat[0, -1] =\
np.array(opt.fsolve(firstdoughnutring, [guesses_b[0, -1],
guesses_n[0, -1]],
args=(r_hh[0], w[0], bq[0, -1, j],
tr[0, -1, j],
theta * p.replacement_rate_adjust[0],
factor, j, initial_b, p),
xtol=MINIMIZER_TOL))
for s in range(p.S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[:p.S, :], p.S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:p.S, :], p.S - (s + 2))
theta_to_use = theta[j] * p.replacement_rate_adjust[:p.S]
bq_to_use = np.diag(bq[:p.S, :, j], p.S - (s + 2))
tr_to_use = np.diag(tr[:p.S, :, j], p.S - (s + 2))
tau_c_to_use = np.diag(p.tau_c[:p.S, :, j], p.S - (s + 2))
length_diag =\
np.diag(p.etr_params[:p.S, :, 0], p.S-(s + 2)).shape[0]
etr_params_to_use = np.zeros((length_diag, p.etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag, p.mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag, p.mtry_params.shape[2]))
for i in range(p.etr_params.shape[2]):
etr_params_to_use[:, i] =\
np.diag(p.etr_params[:p.S, :, i], p.S - (s + 2))
mtrx_params_to_use[:, i] =\
np.diag(p.mtrx_params[:p.S, :, i], p.S - (s + 2))
mtry_params_to_use[:, i] =\
np.diag(p.mtry_params[:p.S, :, i], p.S - (s + 2))
solutions = opt.fsolve(
twist_doughnut,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(r_hh, w, bq_to_use, tr_to_use, theta_to_use, factor, j, s, 0,
tau_c_to_use, etr_params_to_use, mtrx_params_to_use,
mtry_params_to_use, initial_b, p),
xtol=MINIMIZER_TOL)
b_vec = solutions[:int(len(solutions) / 2)]
b_mat[ind2, p.S - (s + 2) + ind2] = b_vec
n_vec = solutions[int(len(solutions) / 2):]
n_mat[ind2, p.S - (s + 2) + ind2] = n_vec
for t in range(0, p.T):
b_guesses_to_use = .75 * \
np.diag(guesses_b[t:t + p.S, :])
n_guesses_to_use = np.diag(guesses_n[t:t + p.S, :])
theta_to_use = theta[j] * p.replacement_rate_adjust[t:t + p.S]
bq_to_use = np.diag(bq[t:t + p.S, :, j])
tr_to_use = np.diag(tr[t:t + p.S, :, j])
tau_c_to_use = np.diag(p.tau_c[t:t + p.S, :, j])
# initialize array of diagonal elements
etr_params_TP = np.zeros((p.T + p.S, p.S, p.etr_params.shape[2]))
etr_params_TP[:p.T, :, :] = p.etr_params
etr_params_TP[p.T:, :, :] = p.etr_params[-1, :, :]
mtrx_params_TP = np.zeros((p.T + p.S, p.S, p.mtrx_params.shape[2]))
mtrx_params_TP[:p.T, :, :] = p.mtrx_params
mtrx_params_TP[p.T:, :, :] = p.mtrx_params[-1, :, :]
mtry_params_TP = np.zeros((p.T + p.S, p.S, p.mtry_params.shape[2]))
mtry_params_TP[:p.T, :, :] = p.mtry_params
mtry_params_TP[p.T:, :, :] = p.mtry_params[-1, :, :]
length_diag =\
np.diag(etr_params_TP[t:t + p.S, :, 0]).shape[0]
etr_params_to_use = np.zeros((length_diag, p.etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag, p.mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag, p.mtry_params.shape[2]))
for i in range(p.etr_params.shape[2]):
etr_params_to_use[:, i] = np.diag(etr_params_TP[t:t + p.S, :, i])
mtrx_params_to_use[:, i] = np.diag(mtrx_params_TP[t:t + p.S, :, i])
mtry_params_to_use[:, i] = np.diag(mtry_params_TP[t:t + p.S, :, i])
[solutions, infodict, ier, message] =\
opt.fsolve(twist_doughnut, list(b_guesses_to_use) +
list(n_guesses_to_use),
args=(r_hh, w, bq_to_use, tr_to_use,
theta_to_use, factor,
j, None, t, tau_c_to_use,
etr_params_to_use, mtrx_params_to_use,
mtry_params_to_use, initial_b, p),
xtol=MINIMIZER_TOL, full_output=True)
euler_errors[t, :] = infodict['fvec']
b_vec = solutions[:p.S]
b_mat[t + ind, ind] = b_vec
n_vec = solutions[p.S:]
n_mat[t + ind, ind] = n_vec
print('Type ', j, ' max euler error = ', np.absolute(euler_errors).max())
return euler_errors, b_mat, n_mat
def inner_loop(guesses, outer_loop_vars, initial_values, j, ind, p):
'''
Solves inner loop of TPI. Given path of economic aggregates and
factor prices, solves household problem.
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:
firstdoughnutring()
twist_doughnut()
Objects in function:
Returns: euler_errors, b_mat, n_mat
'''
# unpack variables and parameters pass to function
(K0, b_sinit, b_splus1init, factor, initial_b, initial_n,
D0) = initial_values
guesses_b, guesses_n = guesses
r, w, r_hh, BQ, T_H, theta = outer_loop_vars
# compute w
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
# compute bq
bq = household.get_bq(BQ, None, p, 'TPI')
# initialize arrays
b_mat = np.zeros((p.T + p.S, p.S))
n_mat = np.zeros((p.T + p.S, p.S))
euler_errors = np.zeros((p.T, 2 * p.S))
b_mat[0, -1], n_mat[0, -1] =\
np.array(opt.fsolve(firstdoughnutring, [guesses_b[0, -1],
guesses_n[0, -1]],
args=(r_hh[0], w[0], bq[0, -1, j], T_H[0],
theta * p.replacement_rate_adjust[0],
factor, j, initial_b, p),
xtol=MINIMIZER_TOL))
for s in range(p.S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[:p.S, :], p.S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[:p.S, :], p.S - (s + 2))
theta_to_use = theta[j] * p.replacement_rate_adjust[:p.S]
bq_to_use = np.diag(bq[:p.S, :, j], p.S - (s + 2))
tau_c_to_use = np.diag(p.tau_c[:p.S, :, j], p.S - (s + 2))
length_diag =\
np.diag(p.etr_params[:p.S, :, 0], p.S-(s + 2)).shape[0]
etr_params_to_use = np.zeros((length_diag, p.etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag, p.mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag, p.mtry_params.shape[2]))
for i in range(p.etr_params.shape[2]):
etr_params_to_use[:, i] =\
np.diag(p.etr_params[:p.S, :, i], p.S - (s + 2))
mtrx_params_to_use[:, i] =\
np.diag(p.mtrx_params[:p.S, :, i], p.S - (s + 2))
mtry_params_to_use[:, i] =\
np.diag(p.mtry_params[:p.S, :, i], p.S - (s + 2))
solutions = opt.fsolve(twist_doughnut,
list(b_guesses_to_use) +
list(n_guesses_to_use),
args=(r_hh, w, bq_to_use, T_H, theta_to_use,
factor, j, s, 0, tau_c_to_use,
etr_params_to_use,
mtrx_params_to_use,
mtry_params_to_use, initial_b, p),
xtol=MINIMIZER_TOL)
b_vec = solutions[:int(len(solutions) / 2)]
b_mat[ind2, p.S - (s + 2) + ind2] = b_vec
n_vec = solutions[int(len(solutions) / 2):]
n_mat[ind2, p.S - (s + 2) + ind2] = n_vec
for t in range(0, p.T):
b_guesses_to_use = .75 * \
np.diag(guesses_b[t:t + p.S, :])
n_guesses_to_use = np.diag(guesses_n[t:t + p.S, :])
theta_to_use = theta[j] * p.replacement_rate_adjust[t:t + p.S]
bq_to_use = np.diag(bq[t:t + p.S, :, j])
tau_c_to_use = np.diag(p.tau_c[t:t + p.S, :, j])
# initialize array of diagonal elements
etr_params_TP = np.zeros((p.T + p.S, p.S, p.etr_params.shape[2]))
etr_params_TP[:p.T, :, :] = p.etr_params
etr_params_TP[p.T:, :, :] = p.etr_params[-1, :, :]
mtrx_params_TP = np.zeros((p.T + p.S, p.S, p.mtrx_params.shape[2]))
mtrx_params_TP[:p.T, :, :] = p.mtrx_params
mtrx_params_TP[p.T:, :, :] = p.mtrx_params[-1, :, :]
mtry_params_TP = np.zeros((p.T + p.S, p.S, p.mtry_params.shape[2]))
mtry_params_TP[:p.T, :, :] = p.mtry_params
mtry_params_TP[p.T:, :, :] = p.mtry_params[-1, :, :]
length_diag =\
np.diag(etr_params_TP[t:t + p.S, :, 0]).shape[0]
etr_params_to_use = np.zeros((length_diag, p.etr_params.shape[2]))
mtrx_params_to_use = np.zeros((length_diag, p.mtrx_params.shape[2]))
mtry_params_to_use = np.zeros((length_diag, p.mtry_params.shape[2]))
for i in range(p.etr_params.shape[2]):
etr_params_to_use[:, i] = np.diag(etr_params_TP[t:t + p.S, :, i])
mtrx_params_to_use[:, i] = np.diag(mtrx_params_TP[t:t + p.S, :, i])
mtry_params_to_use[:, i] = np.diag(mtry_params_TP[t:t + p.S, :, i])
#
# TPI_solver_params = (inc_tax_params_TP, tpi_params, None)
[solutions, infodict, ier, message] =\
opt.fsolve(twist_doughnut, list(b_guesses_to_use) +
list(n_guesses_to_use),
args=(r_hh, w, bq_to_use, T_H,
theta_to_use, factor,
j, None, t, tau_c_to_use,
etr_params_to_use, mtrx_params_to_use,
mtry_params_to_use, initial_b, p),
xtol=MINIMIZER_TOL, full_output=True)
euler_errors[t, :] = infodict['fvec']
b_vec = solutions[:p.S]
b_mat[t + ind, ind] = b_vec
n_vec = solutions[p.S:]
n_mat[t + ind, ind] = n_vec
print('Type ', j, ' max euler error = ', euler_errors.max())
return euler_errors, b_mat, n_mat
def run_TPI(p, client=None):
# unpack tuples of parameters
initial_values, SS_values, baseline_values = get_initial_SS_values(p)
(B0, b_sinit, b_splus1init, factor, initial_b, initial_n,
D0) = initial_values
(Kss, Bss, Lss, rss, wss, BQss, T_Hss, total_revenue_ss, bssmat_splus1,
nssmat, Yss, Gss, theta) = SS_values
(T_Hbaseline, Gbaseline) = baseline_values
print('Government spending breakpoints are tG1: ', p.tG1,
'; and tG2:', p.tG2)
# Initialize guesses at time paths
# Make array of initial guesses for labor supply and savings
domain = np.linspace(0, p.T, p.T)
domain2 = np.tile(domain.reshape(p.T, 1, 1), (1, p.S, p.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, p.S, p.J), (p.S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, p.T).reshape(p.T, 1, 1), (1, p.S, p.J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, p.S, p.J), (p.S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = guesses_b # np.zeros((p.T + p.S, p.S, p.J))
n_mat = guesses_n # np.zeros((p.T + p.S, p.S, p.J))
ind = np.arange(p.S)
L_init = np.ones((p.T + p.S,)) * Lss
B_init = np.ones((p.T + p.S,)) * Bss
L_init[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B_init[1:p.T] = aggr.get_K(b_mat[:p.T], p, 'TPI', False)[:p.T - 1]
B_init[0] = B0
if not p.small_open:
if p.budget_balance:
K_init = B_init
else:
K_init = B_init * Kss / Bss
else:
K_init = firm.get_K(L_init, p.firm_r, p, 'TPI')
K = K_init
L = L_init
B = B_init
Y = np.zeros_like(K)
Y[:p.T] = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
Y[p.T:] = Yss
r = np.zeros_like(Y)
if not p.small_open:
r[:p.T] = firm.get_r(Y[:p.T], K[:p.T], p, 'TPI')
r[p.T:] = rss
else:
r = p.firm_r
# compute w
w = np.zeros_like(r)
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
w[p.T:] = wss
r_gov = fiscal.get_r_gov(r, p)
if p.budget_balance:
r_hh = r
else:
r_hh = aggr.get_r_hh(r, r_gov, K, p.debt_ratio_ss * Y)
if p.small_open:
r_hh = p.hh_r
BQ0 = aggr.get_BQ(r[0], initial_b, None, p, 'SS', True)
if not p.use_zeta:
BQ = np.zeros((p.T + p.S, p.J))
for j in range(p.J):
BQ[:, j] = (list(np.linspace(BQ0[j], BQss[j], p.T)) +
[BQss[j]] * p.S)
BQ = np.array(BQ)
else:
BQ = (list(np.linspace(BQ0, BQss, p.T)) + [BQss] * p.S)
BQ = np.array(BQ)
if p.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(p.T + p.S) * T_Hss2
total_revenue = T_H
G = np.zeros(p.T + p.S)
elif not p.baseline_spending:
T_H = p.alpha_T * Y
elif p.baseline_spending:
T_H = T_Hbaseline
T_H_new = p.T_H # Need to set T_H_new for later reference
G = Gbaseline
G_0 = Gbaseline[0]
# Initialize some starting value
if p.budget_balance:
D = 0.0 * Y
else:
D = p.debt_ratio_ss * Y
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
TPIdist_vec = np.zeros(p.maxiter)
print('analytical mtrs in tpi = ', p.analytical_mtrs)
print('tax function type in tpi = ', p.tax_func_type)
# TPI loop
while (TPIiter < p.maxiter) and (TPIdist >= p.mindist_TPI):
r_gov[:p.T] = fiscal.get_r_gov(r[:p.T], p)
if p.budget_balance:
r_hh[:p.T] = r[:p.T]
else:
K[:p.T] = firm.get_K_from_Y(Y[:p.T], r[:p.T], p, 'TPI')
r_hh[:p.T] = aggr.get_r_hh(r[:p.T], r_gov[:p.T], K[:p.T], D[:p.T])
if p.small_open:
r_hh[:p.T] = p.hh_r[:p.T]
outer_loop_vars = (r, w, r_hh, BQ, T_H, theta)
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
lazy_values = []
for j in range(p.J):
guesses = (guesses_b[:, :, j], guesses_n[:, :, j])
lazy_values.append(
delayed(inner_loop)(guesses, outer_loop_vars,
initial_values, j, ind, p))
results = compute(*lazy_values, scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
for j, result in enumerate(results):
euler_errors[:, :, j], b_mat[:, :, j], n_mat[:, :, j] = result
bmat_s = np.zeros((p.T, p.S, p.J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:p.T-1, :-1, :]
bmat_splus1 = np.zeros((p.T, p.S, p.J))
bmat_splus1[:, :, :] = b_mat[:p.T, :, :]
L[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B[1:p.T] = aggr.get_K(bmat_splus1[:p.T], p, 'TPI',
False)[:p.T - 1]
if np.any(B) < 0:
print('B has negative elements. B[0:9]:', B[0:9])
print('B[T-2:T]:', B[p.T - 2, p.T])
etr_params_4D = np.tile(
p.etr_params.reshape(p.T, p.S, 1, p.etr_params.shape[2]),
(1, 1, p.J, 1))
bqmat = household.get_bq(BQ, None, p, 'TPI')
tax_mat = tax.total_taxes(r_hh[:p.T], w[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat[:p.T, :, :],
factor, T_H[:p.T], theta, 0, None,
False, 'TPI', p.e, etr_params_4D, p)
r_hh_path = utils.to_timepath_shape(r_hh, p)
wpath = utils.to_timepath_shape(w, p)
c_mat = household.get_cons(r_hh_path[:p.T, :, :], wpath[:p.T, :, :],
bmat_s, bmat_splus1,
n_mat[:p.T, :, :], bqmat[:p.T, :, :],
tax_mat, p.e, p.tau_c[:p.T, :, :], p)
if not p.small_open:
if p.budget_balance:
K[:p.T] = B[:p.T]
else:
if not p.baseline_spending:
Y = T_H / p.alpha_T # maybe unecessary
(total_rev, T_Ipath, T_Ppath, T_BQpath, T_Wpath,
T_Cpath, business_revenue) = aggr.revenue(
r_hh[:p.T], w[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], c_mat[:p.T, :, :], Y[:p.T],
L[:p.T], K[:p.T], factor, theta, etr_params_4D,
p, 'TPI')
total_revenue = np.array(list(total_rev) +
[total_revenue_ss] * p.S)
# set intial debt value
if p.baseline:
D_0 = p.initial_debt_ratio * Y[0]
else:
D_0 = D0
if not p.baseline_spending:
G_0 = p.alpha_G[0] * Y[0]
dg_fixed_values = (Y, total_revenue, T_H, D_0, G_0)
Dnew, G = fiscal.D_G_path(r_gov, dg_fixed_values,
Gbaseline, p)
K[:p.T] = B[:p.T] - Dnew[:p.T]
if np.any(K < 0):
print('K has negative elements. Setting them ' +
'positive to prevent NAN.')
K[:p.T] = np.fmax(K[:p.T], 0.05 * B[:p.T])
else:
K[:p.T] = firm.get_K(L[:p.T], p.firm_r[:p.T], p, 'TPI')
Ynew = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
if not p.small_open:
rnew = firm.get_r(Ynew[:p.T], K[:p.T], p, 'TPI')
else:
rnew = r.copy()
r_gov_new = fiscal.get_r_gov(rnew, p)
if p.budget_balance:
r_hh_new = rnew[:p.T]
else:
r_hh_new = aggr.get_r_hh(rnew, r_gov_new, K[:p.T],
Dnew[:p.T])
if p.small_open:
r_hh_new = p.hh_r[:p.T]
# compute w
wnew = firm.get_w_from_r(rnew[:p.T], p, 'TPI')
b_mat_shift = np.append(np.reshape(initial_b, (1, p.S, p.J)),
b_mat[:p.T - 1, :, :], axis=0)
BQnew = aggr.get_BQ(r_hh_new[:p.T], b_mat_shift, None, p,
'TPI', False)
bqmat_new = household.get_bq(BQnew, None, p, 'TPI')
(total_rev, T_Ipath, T_Ppath, T_BQpath, T_Wpath, T_Cpath,
business_revenue) = aggr.revenue(
r_hh_new[:p.T], wnew[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat_new[:p.T, :, :], c_mat[:p.T, :, :], Ynew[:p.T],
L[:p.T], K[:p.T], factor, theta, etr_params_4D, p, 'TPI')
total_revenue = np.array(list(total_rev) +
[total_revenue_ss] * p.S)
if p.budget_balance:
T_H_new = total_revenue
elif not p.baseline_spending:
T_H_new = p.alpha_T[:p.T] * Ynew[:p.T]
# If baseline_spending==True, no need to update T_H, it's fixed
if p.small_open and not p.budget_balance:
# Loop through years to calculate debt and gov't spending.
# This is done earlier when small_open=False.
if p.baseline:
D_0 = p.initial_debt_ratio * Y[0]
else:
D_0 = D0
if not p.baseline_spending:
G_0 = p.alpha_G[0] * Ynew[0]
dg_fixed_values = (Ynew, total_revenue, T_H, D_0, G_0)
Dnew, G = fiscal.D_G_path(r_gov_new, dg_fixed_values, Gbaseline, p)
if p.budget_balance:
Dnew = D
w[:p.T] = wnew[:p.T]
r[:p.T] = utils.convex_combo(rnew[:p.T], r[:p.T], p.nu)
BQ[:p.T] = utils.convex_combo(BQnew[:p.T], BQ[:p.T], p.nu)
D = Dnew
Y[:p.T] = utils.convex_combo(Ynew[:p.T], Y[:p.T], p.nu)
if not p.baseline_spending:
T_H[:p.T] = utils.convex_combo(T_H_new[:p.T], T_H[:p.T], p.nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, p.nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, p.nu)
print('r diff: ', (rnew[:p.T] - r[:p.T]).max(),
(rnew[:p.T] - r[:p.T]).min())
print('BQ diff: ', (BQnew[:p.T] - BQ[:p.T]).max(),
(BQnew[:p.T] - BQ[:p.T]).min())
print('T_H diff: ', (T_H_new[:p.T]-T_H[:p.T]).max(),
(T_H_new[:p.T] - T_H[:p.T]).min())
print('Y diff: ', (Ynew[:p.T]-Y[:p.T]).max(),
(Ynew[:p.T] - Y[:p.T]).min())
if not p.baseline_spending:
if T_H.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T],
BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(wnew[:p.T], w[:p.T])) +
list(utils.pct_diff_func(T_H_new[:p.T],
T_H[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T],
BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(wnew[:p.T], w[:p.T])) +
list(np.abs(T_H[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten())
+ list(utils.pct_diff_func(wnew[:p.T], w[:p.T])) +
list(utils.pct_diff_func(Ynew[:p.T], Y[:p.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)
# Compute effective and marginal tax rates for all agents
mtrx_params_4D = np.tile(
p.mtrx_params.reshape(p.T, p.S, 1, p.mtrx_params.shape[2]),
(1, 1, p.J, 1))
mtry_params_4D = np.tile(
p.mtry_params.reshape(p.T, p.S, 1, p.mtry_params.shape[2]),
(1, 1, p.J, 1))
e_3D = np.tile(p.e.reshape(1, p.S, p.J), (p.T, 1, 1))
mtry_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, True,
e_3D, etr_params_4D, mtry_params_4D, p)
mtrx_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, False,
e_3D, etr_params_4D, mtrx_params_4D, p)
etr_path = tax.ETR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, e_3D,
etr_params_4D, p)
C = aggr.get_C(c_mat, p, 'TPI')
if not p.small_open:
I = aggr.get_I(bmat_splus1[:p.T], K[1:p.T + 1], K[:p.T], p, 'TPI')
rc_error = Y[:p.T] - C[:p.T] - I[:p.T] - G[:p.T]
else:
I = ((1 + np.squeeze(np.hstack((p.g_n[1:p.T], p.g_n_ss)))) *
np.exp(p.g_y) * K[1:p.T + 1] - (1.0 - p.delta) * K[:p.T])
BI = aggr.get_I(bmat_splus1[:p.T], B[1:p.T + 1], B[:p.T], p, 'TPI')
new_borrowing = (D[1:p.T] * (1 + p.g_n[1:p.T]) *
np.exp(p.g_y) - D[:p.T - 1])
rc_error = (Y[:p.T - 1] + new_borrowing - (
C[:p.T - 1] + BI[:p.T - 1] + G[:p.T - 1]) +
(p.hh_r[:p.T - 1] * B[:p.T - 1] - (
p.delta + p.firm_r[:p.T - 1]) * K[:p.T - 1] -
p.hh_r[:p.T - 1] * D[:p.T - 1]))
# Compute total investment (not just domestic)
I_total = ((1 + p.g_n[:p.T]) * np.exp(p.g_y) * K[1:p.T + 1] -
(1.0 - p.delta) * K[:p.T])
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 range(p.T):
household.constraint_checker_TPI(
b_mat[t], n_mat[t], c_mat[t], t, p.ltilde)
eul_savings = euler_errors[:, :p.S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, p.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[:p.T], 'B': B, 'K': K, 'L': L, 'C': C, 'I': I,
'I_total': I_total, 'BQ': BQ, 'total_revenue': total_revenue,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Ipath, 'T_H': T_H,
'T_P': T_Ppath, 'T_BQ': T_BQpath, 'T_W': T_Wpath,
'T_C': T_Cpath, 'G': G, 'D': D, 'r': r, 'r_gov': r_gov,
'r_hh': r_hh, 'w': w, 'bmat_splus1': bmat_splus1,
'bmat_s': bmat_s[:p.T, :, :], 'n_mat': n_mat[:p.T, :, :],
'c_path': c_mat, 'bq_path': bqmat,
'tax_path': tax_mat, 'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure,
'resource_constraint_error': rc_error,
'etr_path': etr_path, 'mtrx_path': mtrx_path,
'mtry_path': mtry_path}
tpi_dir = os.path.join(p.output_base, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
if np.any(G) < 0:
print('Government spending is negative along transition path' +
' to satisfy budget')
if (((TPIiter >= p.maxiter) or
(np.absolute(TPIdist) > p.mindist_TPI)) and
ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found' +
' (TPIdist)')
if ((np.any(np.absolute(rc_error) >= p.mindist_TPI * 10)) and
ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(rc_error)')
if ((np.any(np.absolute(eul_savings) >= p.mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > p.mindist_TPI))) and
ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(eulers)')
return output
def inner_loop(outer_loop_vars, p, client):
'''
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 to pass to function
if p.budget_balance:
bssmat, nssmat, r, BQ, T_H, factor = outer_loop_vars
else:
bssmat, nssmat, r, BQ, Y, T_H, factor = outer_loop_vars
euler_errors = np.zeros((2 * p.S, p.J))
w = firm.get_w_from_r(r, p, 'SS')
r_gov = fiscal.get_r_gov(r, p)
if p.budget_balance:
r_hh = r
D = 0
else:
D = p.debt_ratio_ss * Y
K = firm.get_K_from_Y(Y, r, p, 'SS')
r_hh = aggr.get_r_hh(r, r_gov, K, D)
if p.small_open:
r_hh = p.hh_r[-1]
bq = household.get_bq(BQ, None, p, 'SS')
lazy_values = []
for j in range(p.J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = (r_hh, w, bq[:, j], T_H, factor, j, p)
lazy_values.append(delayed(opt.fsolve)(euler_equation_solver,
guesses * .9,
args=euler_params,
xtol=MINIMIZER_TOL,
full_output=True))
results = compute(*lazy_values, scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
# for j, result in results.items():
for j, result in enumerate(results):
[solutions, infodict, ier, message] = result
euler_errors[:, j] = infodict['fvec']
bssmat[:, j] = solutions[:p.S]
nssmat[:, j] = solutions[p.S:]
L = aggr.get_L(nssmat, p, 'SS')
B = aggr.get_K(bssmat, p, 'SS', False)
K_demand_open = firm.get_K(L, p.firm_r[-1], p, 'SS')
D_f = p.zeta_D[-1] * D
D_d = D - D_f
if not p.small_open:
K_d = B - D_d
K_f = p.zeta_K[-1] * (K_demand_open - B + D_d)
K = K_f + K_d
else:
# can remove this else statement by making small open the case where zeta_K = 1
K_d = B - D_d
K_f = K_demand_open - B + D_d
K = K_f + K_d
new_Y = firm.get_Y(K, L, p, 'SS')
if p.budget_balance:
Y = new_Y
if not p.small_open:
new_r = firm.get_r(Y, K, p, 'SS')
else:
new_r = p.firm_r[-1]
new_w = firm.get_w_from_r(new_r, p, 'SS')
b_s = np.array(list(np.zeros(p.J).reshape(1, p.J)) +
list(bssmat[:-1, :]))
new_r_gov = fiscal.get_r_gov(new_r, p)
new_r_hh = aggr.get_r_hh(new_r, new_r_gov, K, D)
average_income_model = ((new_r_hh * b_s + new_w * p.e * nssmat) *
p.omega_SS.reshape(p.S, 1) *
p.lambdas.reshape(1, p.J)).sum()
if p.baseline:
new_factor = p.mean_income_data / average_income_model
else:
new_factor = factor
new_BQ = aggr.get_BQ(new_r_hh, bssmat, None, p, 'SS', False)
new_bq = household.get_bq(new_BQ, None, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, None, p)
if p.budget_balance:
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])),
(1, p.J, 1))
taxss = tax.total_taxes(new_r_hh, new_w, b_s, nssmat, new_bq,
factor, T_H, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(new_r_hh, new_w, b_s, bssmat,
nssmat, new_bq, taxss,
p.e, p.tau_c[-1, :, :], p)
new_T_H, _, _, _, _, _, _ = aggr.revenue(
new_r_hh, new_w, b_s, nssmat, new_bq, cssmat, new_Y, L, K,
factor, theta, etr_params_3D, p, 'SS')
elif p.baseline_spending:
new_T_H = T_H
else:
new_T_H = p.alpha_T[-1] * new_Y
return euler_errors, bssmat, nssmat, new_r, new_r_gov, new_r_hh, \
new_w, new_T_H, new_Y, new_factor, new_BQ, average_income_model
def inner_loop(outer_loop_vars, p, client):
'''
This function solves for the inner loop of the SS. That is, given
the guesses of the outer loop variables (r, w, TR, factor) this
function solves the households' problems in the SS.
Args:
outer_loop_vars (tuple): tuple of outer loop variables,
(bssmat, nssmat, r, BQ, TR, factor) or
(bssmat, nssmat, r, BQ, Y, TR, factor)
bssmat (Numpy array): initial guess at savings, size = SxJ
nssmat (Numpy array): initial guess at labor supply, size = SxJ
BQ (array_like): aggregate bequest amount(s)
Y (scalar): real GDP
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
w (scalar): real wage rate
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
(tuple): results from household solution:
* euler_errors (Numpy array): errors terms from FOCs,
size = 2SxJ
* bssmat (Numpy array): savings, size = SxJ
* nssmat (Numpy array): labor supply, size = SxJ
* new_r (scalar): real interest rate on firm capital
* new_r_gov (scalar): real interest rate on government debt
* new_r_hh (scalar): real interest rate on household
portfolio
* new_w (scalar): real wage rate
* new_TR (scalar): lump sum transfer amount
* new_Y (scalar): real GDP
* new_factor (scalar): scaling factor converting model
units to dollars
* new_BQ (array_like): aggregate bequest amount(s)
* average_income_model (scalar): average income in model
units
'''
# unpack variables to pass to function
if p.budget_balance:
bssmat, nssmat, r, BQ, TR, factor = outer_loop_vars
r_hh = r
Y = 1.0 # placeholder
K = 1.0 # placeholder
else:
bssmat, nssmat, r, BQ, Y, TR, factor = outer_loop_vars
K = firm.get_K_from_Y(Y, r, p, 'SS')
# initialize array for euler errors
euler_errors = np.zeros((2 * p.S, p.J))
w = firm.get_w_from_r(r, p, 'SS')
r_gov = fiscal.get_r_gov(r, p)
D, D_d, D_f, new_borrowing, debt_service, new_borrowing_f =\
fiscal.get_D_ss(r_gov, Y, p)
r_hh = aggr.get_r_hh(r, r_gov, K, D)
bq = household.get_bq(BQ, None, p, 'SS')
tr = household.get_tr(TR, None, p, 'SS')
lazy_values = []
for j in range(p.J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = (r_hh, w, bq[:, j], tr[:, j], factor, j, p)
lazy_values.append(delayed(opt.fsolve)(euler_equation_solver,
guesses * .9,
args=euler_params,
xtol=MINIMIZER_TOL,
full_output=True))
if client:
futures = client.compute(lazy_values, num_workers=p.num_workers)
results = client.gather(futures)
else:
results = results = compute(
*lazy_values, scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
# for j, result in results.items():
for j, result in enumerate(results):
[solutions, infodict, ier, message] = result
euler_errors[:, j] = infodict['fvec']
bssmat[:, j] = solutions[:p.S]
nssmat[:, j] = solutions[p.S:]
L = aggr.get_L(nssmat, p, 'SS')
B = aggr.get_B(bssmat, p, 'SS', False)
K_demand_open = firm.get_K(L, p.world_int_rate[-1], p, 'SS')
K, K_d, K_f = aggr.get_K_splits(B, K_demand_open, D_d, p.zeta_K[-1])
Y = firm.get_Y(K, L, p, 'SS')
if p.zeta_K[-1] == 1.0:
new_r = p.world_int_rate[-1]
else:
new_r = firm.get_r(Y, K, p, 'SS')
new_w = firm.get_w_from_r(new_r, p, 'SS')
b_s = np.array(list(np.zeros(p.J).reshape(1, p.J)) +
list(bssmat[:-1, :]))
new_r_gov = fiscal.get_r_gov(new_r, p)
new_r_hh = aggr.get_r_hh(new_r, new_r_gov, K, D)
average_income_model = ((new_r_hh * b_s + new_w * p.e * nssmat) *
p.omega_SS.reshape(p.S, 1) *
p.lambdas.reshape(1, p.J)).sum()
if p.baseline:
new_factor = p.mean_income_data / average_income_model
else:
new_factor = factor
new_BQ = aggr.get_BQ(new_r_hh, bssmat, None, p, 'SS', False)
new_bq = household.get_bq(new_BQ, None, p, 'SS')
tr = household.get_tr(TR, None, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, None, p)
etr_params_3D = np.tile(
np.reshape(p.etr_params[-1, :, :],
(p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
taxss = tax.net_taxes(
new_r_hh, new_w, b_s, nssmat, new_bq, factor, tr, theta, None,
None, False, 'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(
new_r_hh, new_w, b_s, bssmat, nssmat, new_bq, taxss, p.e,
p.tau_c[-1, :, :], p)
total_tax_revenue, _, agg_pension_outlays, _, _, _, _, _, _ =\
aggr.revenue(new_r_hh, new_w, b_s, nssmat, new_bq, cssmat, Y, L,
K, factor, theta, etr_params_3D, p, 'SS')
G = fiscal.get_G_ss(Y, total_tax_revenue, agg_pension_outlays, TR,
new_borrowing, debt_service, p)
new_TR = fiscal.get_TR(Y, TR, G, total_tax_revenue,
agg_pension_outlays, p, 'SS')
return euler_errors, bssmat, nssmat, new_r, new_r_gov, new_r_hh, \
new_w, new_TR, Y, new_factor, new_BQ, average_income_model
def inner_loop(outer_loop_vars, p, client):
'''
This function solves for the inner loop of the SS. That is, given
the guesses of the outer loop variables (r, w, TR, factor) this
function solves the households' problems in the SS.
Args:
outer_loop_vars (tuple): tuple of outer loop variables,
(bssmat, nssmat, r, BQ, TR, factor) or
(bssmat, nssmat, r, BQ, Y, TR, factor)
bssmat (Numpy array): initial guess at savings, size = SxJ
nssmat (Numpy array): initial guess at labor supply, size = SxJ
BQ (array_like): aggregate bequest amount(s)
Y (scalar): real GDP
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
w (scalar): real wage rate
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
(tuple): results from household solution:
* euler_errors (Numpy array): errors terms from FOCs,
size = 2SxJ
* bssmat (Numpy array): savings, size = SxJ
* nssmat (Numpy array): labor supply, size = SxJ
* new_r (scalar): real interest rate on firm capital
* new_r_gov (scalar): real interest rate on government debt
* new_r_hh (scalar): real interest rate on household
portfolio
* new_w (scalar): real wage rate
* new_TR (scalar): lump sum transfer amount
* new_Y (scalar): real GDP
* new_factor (scalar): scaling factor converting model
units to dollars
* new_BQ (array_like): aggregate bequest amount(s)
* average_income_model (scalar): average income in model
units
'''
# unpack variables to pass to function
if p.budget_balance:
bssmat, nssmat, r, BQ, TR, factor = outer_loop_vars
else:
bssmat, nssmat, r, BQ, Y, TR, factor = outer_loop_vars
euler_errors = np.zeros((2 * p.S, p.J))
w = firm.get_w_from_r(r, p, 'SS')
r_gov = fiscal.get_r_gov(r, p)
if p.budget_balance:
r_hh = r
D = 0
else:
D = p.debt_ratio_ss * Y
K = firm.get_K_from_Y(Y, r, p, 'SS')
r_hh = aggr.get_r_hh(r, r_gov, K, D)
if p.small_open:
r_hh = p.hh_r[-1]
bq = household.get_bq(BQ, None, p, 'SS')
tr = household.get_tr(TR, None, p, 'SS')
lazy_values = []
for j in range(p.J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = (r_hh, w, bq[:, j], tr[:, j], factor, j, p)
lazy_values.append(delayed(opt.fsolve)(euler_equation_solver,
guesses * .9,
args=euler_params,
xtol=MINIMIZER_TOL,
full_output=True))
results = compute(*lazy_values, scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
# for j, result in results.items():
for j, result in enumerate(results):
[solutions, infodict, ier, message] = result
euler_errors[:, j] = infodict['fvec']
bssmat[:, j] = solutions[:p.S]
nssmat[:, j] = solutions[p.S:]
L = aggr.get_L(nssmat, p, 'SS')
B = aggr.get_B(bssmat, p, 'SS', False)
K_demand_open = firm.get_K(L, p.firm_r[-1], p, 'SS')
D_f = p.zeta_D[-1] * D
D_d = D - D_f
if not p.small_open:
K_d = B - D_d
K_f = p.zeta_K[-1] * (K_demand_open - B + D_d)
K = K_f + K_d
else:
# can remove this else statement by making small open the case
# where zeta_K = 1
K_d = B - D_d
K_f = K_demand_open - B + D_d
K = K_f + K_d
new_Y = firm.get_Y(K, L, p, 'SS')
if p.budget_balance:
Y = new_Y
if not p.small_open:
new_r = firm.get_r(Y, K, p, 'SS')
else:
new_r = p.firm_r[-1]
new_w = firm.get_w_from_r(new_r, p, 'SS')
b_s = np.array(list(np.zeros(p.J).reshape(1, p.J)) +
list(bssmat[:-1, :]))
new_r_gov = fiscal.get_r_gov(new_r, p)
new_r_hh = aggr.get_r_hh(new_r, new_r_gov, K, D)
average_income_model = ((new_r_hh * b_s + new_w * p.e * nssmat) *
p.omega_SS.reshape(p.S, 1) *
p.lambdas.reshape(1, p.J)).sum()
if p.baseline:
new_factor = p.mean_income_data / average_income_model
else:
new_factor = factor
new_BQ = aggr.get_BQ(new_r_hh, bssmat, None, p, 'SS', False)
new_bq = household.get_bq(new_BQ, None, p, 'SS')
tr = household.get_tr(TR, None, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, None, p)
if p.budget_balance:
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])),
(1, p.J, 1))
taxss = tax.total_taxes(new_r_hh, new_w, b_s, nssmat, new_bq,
factor, tr, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(new_r_hh, new_w, b_s, bssmat,
nssmat, new_bq, taxss,
p.e, p.tau_c[-1, :, :], p)
new_TR, _, _, _, _, _, _ = aggr.revenue(
new_r_hh, new_w, b_s, nssmat, new_bq, cssmat, new_Y, L, K,
factor, theta, etr_params_3D, p, 'SS')
elif p.baseline_spending:
new_TR = TR
else:
new_TR = p.alpha_T[-1] * new_Y
return euler_errors, bssmat, nssmat, new_r, new_r_gov, new_r_hh, \
new_w, new_TR, new_Y, new_factor, new_BQ, average_income_model
def run_TPI(p, client=None):
# unpack tuples of parameters
initial_values, ss_vars, theta, baseline_values = get_initial_SS_values(p)
(B0, b_sinit, b_splus1init, factor, initial_b, initial_n,
D0) = initial_values
(T_Hbaseline, Gbaseline) = baseline_values
print('Government spending breakpoints are tG1: ', p.tG1, '; and tG2:',
p.tG2)
# Initialize guesses at time paths
# Make array of initial guesses for labor supply and savings
domain = np.linspace(0, p.T, p.T)
domain2 = np.tile(domain.reshape(p.T, 1, 1), (1, p.S, p.J))
ending_b = ss_vars['bssmat_splus1']
guesses_b = (-1 / (domain2 + 1)) * (ending_b - initial_b) + ending_b
ending_b_tail = np.tile(ending_b.reshape(1, p.S, p.J), (p.S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, p.T).reshape(p.T, 1, 1), (1, p.S, p.J))
guesses_n = domain3 * (ss_vars['nssmat'] - initial_n) + initial_n
ending_n_tail = np.tile(ss_vars['nssmat'].reshape(1, p.S, p.J),
(p.S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = guesses_b
n_mat = guesses_n
ind = np.arange(p.S)
L_init = np.ones((p.T + p.S, )) * ss_vars['Lss']
B_init = np.ones((p.T + p.S, )) * ss_vars['Bss']
L_init[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B_init[1:p.T] = aggr.get_K(b_mat[:p.T], p, 'TPI', False)[:p.T - 1]
B_init[0] = B0
if not p.small_open:
if p.budget_balance:
K_init = B_init
else:
K_init = B_init * ss_vars['Kss'] / ss_vars['Bss']
else:
K_init = firm.get_K(L_init, p.firm_r, p, 'TPI')
K = K_init
K_d = K_init * ss_vars['K_d_ss'] / ss_vars['Kss']
K_f = K_init * ss_vars['K_f_ss'] / ss_vars['Kss']
L = L_init
B = B_init
Y = np.zeros_like(K)
Y[:p.T] = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
Y[p.T:] = ss_vars['Yss']
r = np.zeros_like(Y)
if not p.small_open:
r[:p.T] = firm.get_r(Y[:p.T], K[:p.T], p, 'TPI')
r[p.T:] = ss_vars['rss']
else:
r = p.firm_r
# compute w
w = np.zeros_like(r)
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
w[p.T:] = ss_vars['wss']
r_gov = fiscal.get_r_gov(r, p)
if p.budget_balance:
r_hh = r
else:
r_hh = aggr.get_r_hh(r, r_gov, K, ss_vars['Dss'])
if p.small_open:
r_hh = p.hh_r
BQ0 = aggr.get_BQ(r[0], initial_b, None, p, 'SS', True)
if not p.use_zeta:
BQ = np.zeros((p.T + p.S, p.J))
for j in range(p.J):
BQ[:, j] = (list(np.linspace(BQ0[j], ss_vars['BQss'][j], p.T)) +
[ss_vars['BQss'][j]] * p.S)
BQ = np.array(BQ)
else:
BQ = (list(np.linspace(BQ0, ss_vars['BQss'], p.T)) +
[ss_vars['BQss']] * p.S)
BQ = np.array(BQ)
if p.budget_balance:
if np.abs(ss_vars['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 = ss_vars['T_Hss']
T_H = np.ones(p.T + p.S) * T_Hss2
total_revenue = T_H
G = np.zeros(p.T + p.S)
elif not p.baseline_spending:
T_H = p.alpha_T * Y
G = np.ones(p.T + p.S) * ss_vars['Gss']
elif p.baseline_spending:
T_H = T_Hbaseline
T_H_new = p.T_H # Need to set T_H_new for later reference
G = Gbaseline
G_0 = Gbaseline[0]
# Initialize some starting values
if p.budget_balance:
D = np.zeros(p.T + p.S)
else:
D = np.ones(p.T + p.S) * ss_vars['Dss']
if ss_vars['Dss'] == 0:
D_d = np.zeros(p.T + p.S)
D_f = np.zeros(p.T + p.S)
else:
D_d = D * ss_vars['D_d_ss'] / ss_vars['Dss']
D_f = D * ss_vars['D_f_ss'] / ss_vars['Dss']
total_revenue = np.ones(p.T + p.S) * ss_vars['total_revenue_ss']
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
TPIdist_vec = np.zeros(p.maxiter)
# TPI loop
while (TPIiter < p.maxiter) and (TPIdist >= p.mindist_TPI):
r_gov[:p.T] = fiscal.get_r_gov(r[:p.T], p)
if p.budget_balance:
r_hh[:p.T] = r[:p.T]
else:
K[:p.T] = firm.get_K_from_Y(Y[:p.T], r[:p.T], p, 'TPI')
r_hh[:p.T] = aggr.get_r_hh(r[:p.T], r_gov[:p.T], K[:p.T], D[:p.T])
if p.small_open:
r_hh[:p.T] = p.hh_r[:p.T]
outer_loop_vars = (r, w, r_hh, BQ, T_H, theta)
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
lazy_values = []
for j in range(p.J):
guesses = (guesses_b[:, :, j], guesses_n[:, :, j])
lazy_values.append(
delayed(inner_loop)(guesses, outer_loop_vars, initial_values,
j, ind, p))
results = compute(*lazy_values,
scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
for j, result in enumerate(results):
euler_errors[:, :, j], b_mat[:, :, j], n_mat[:, :, j] = result
bmat_s = np.zeros((p.T, p.S, p.J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:p.T - 1, :-1, :]
bmat_splus1 = np.zeros((p.T, p.S, p.J))
bmat_splus1[:, :, :] = b_mat[:p.T, :, :]
etr_params_4D = np.tile(
p.etr_params.reshape(p.T, p.S, 1, p.etr_params.shape[2]),
(1, 1, p.J, 1))
bqmat = household.get_bq(BQ, None, p, 'TPI')
tax_mat = tax.total_taxes(r_hh[:p.T], w[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat[:p.T, :, :], factor,
T_H[:p.T], theta, 0, None, False, 'TPI', p.e,
etr_params_4D, p)
r_hh_path = utils.to_timepath_shape(r_hh, p)
wpath = utils.to_timepath_shape(w, p)
c_mat = household.get_cons(r_hh_path[:p.T, :, :], wpath[:p.T, :, :],
bmat_s, bmat_splus1, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], tax_mat, p.e,
p.tau_c[:p.T, :, :], p)
y_before_tax_mat = (r_hh_path[:p.T, :, :] * bmat_s[:p.T, :, :] +
wpath[:p.T, :, :] * p.e * n_mat[:p.T, :, :])
if not p.baseline_spending and not p.budget_balance:
Y[:p.T] = T_H[:p.T] / p.alpha_T[:p.T] # maybe unecessary
(total_rev, T_Ipath, T_Ppath, T_BQpath,
T_Wpath, T_Cpath, business_revenue) = aggr.revenue(
r_hh[:p.T], w[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], c_mat[:p.T, :, :], Y[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p, 'TPI')
total_revenue[:p.T] = total_rev
# set intial debt value
if p.baseline:
D0 = p.initial_debt_ratio * Y[0]
if not p.baseline_spending:
G_0 = p.alpha_G[0] * Y[0]
dg_fixed_values = (Y, total_revenue, T_H, D0, G_0)
Dnew, G[:p.T] = fiscal.D_G_path(r_gov, dg_fixed_values, Gbaseline,
p)
# Fix initial amount of foreign debt holding
D_f[0] = p.initial_foreign_debt_ratio * Dnew[0]
for t in range(1, p.T):
D_f[t + 1] = (D_f[t] / (np.exp(p.g_y) * (1 + p.g_n[t + 1])) +
p.zeta_D[t] * (Dnew[t + 1] -
(Dnew[t] / (np.exp(p.g_y) *
(1 + p.g_n[t + 1])))))
D_d[:p.T] = Dnew[:p.T] - D_f[:p.T]
else: # if budget balance
Dnew = np.zeros(p.T + 1)
G[:p.T] = np.zeros(p.T)
D_f[:p.T] = np.zeros(p.T)
D_d[:p.T] = np.zeros(p.T)
L[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B[1:p.T] = aggr.get_K(bmat_splus1[:p.T], p, 'TPI', False)[:p.T - 1]
K_demand_open = firm.get_K(L[:p.T], p.firm_r[:p.T], p, 'TPI')
K_d[:p.T] = B[:p.T] - D_d[:p.T]
if np.any(K_d < 0):
print('K_d has negative elements. Setting them ' +
'positive to prevent NAN.')
K_d[:p.T] = np.fmax(K_d[:p.T], 0.05 * B[:p.T])
K_f[:p.T] = p.zeta_K[:p.T] * (K_demand_open - B[:p.T] + D_d[:p.T])
K = K_f + K_d
if np.any(B) < 0:
print('B has negative elements. B[0:9]:', B[0:9])
print('B[T-2:T]:', B[p.T - 2, p.T])
if p.small_open:
K[:p.T] = K_demand_open
Ynew = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
rnew = r.copy()
if not p.small_open:
rnew[:p.T] = firm.get_r(Ynew[:p.T], K[:p.T], p, 'TPI')
else:
rnew[:p.T] = r[:p.T].copy()
r_gov_new = fiscal.get_r_gov(rnew, p)
if p.budget_balance:
r_hh_new = rnew[:p.T]
else:
r_hh_new = aggr.get_r_hh(rnew[:p.T], r_gov_new[:p.T], K[:p.T],
Dnew[:p.T])
if p.small_open:
r_hh_new = p.hh_r[:p.T]
# compute w
wnew = firm.get_w_from_r(rnew[:p.T], p, 'TPI')
b_mat_shift = np.append(np.reshape(initial_b, (1, p.S, p.J)),
b_mat[:p.T - 1, :, :],
axis=0)
BQnew = aggr.get_BQ(r_hh_new[:p.T], b_mat_shift, None, p, 'TPI', False)
bqmat_new = household.get_bq(BQnew, None, p, 'TPI')
(total_rev, T_Ipath, T_Ppath, T_BQpath,
T_Wpath, T_Cpath, business_revenue) = aggr.revenue(
r_hh_new[:p.T], wnew[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat_new[:p.T, :, :], c_mat[:p.T, :, :], Ynew[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p, 'TPI')
total_revenue[:p.T] = total_rev
if p.budget_balance:
T_H_new = total_revenue
elif not p.baseline_spending:
T_H_new = p.alpha_T[:p.T] * Ynew[:p.T]
# If baseline_spending==True, no need to update T_H, it's fixed
# update vars for next iteration
w[:p.T] = wnew[:p.T]
r[:p.T] = utils.convex_combo(rnew[:p.T], r[:p.T], p.nu)
BQ[:p.T] = utils.convex_combo(BQnew[:p.T], BQ[:p.T], p.nu)
D[:p.T] = Dnew[:p.T]
Y[:p.T] = utils.convex_combo(Ynew[:p.T], Y[:p.T], p.nu)
if not p.baseline_spending:
T_H[:p.T] = utils.convex_combo(T_H_new[:p.T], T_H[:p.T], p.nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, p.nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, p.nu)
print('r diff: ', (rnew[:p.T] - r[:p.T]).max(),
(rnew[:p.T] - r[:p.T]).min())
print('BQ diff: ', (BQnew[:p.T] - BQ[:p.T]).max(),
(BQnew[:p.T] - BQ[:p.T]).min())
print('T_H diff: ', (T_H_new[:p.T] - T_H[:p.T]).max(),
(T_H_new[:p.T] - T_H[:p.T]).min())
print('Y diff: ', (Ynew[:p.T] - Y[:p.T]).max(),
(Ynew[:p.T] - Y[:p.T]).min())
if not p.baseline_spending:
if T_H.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(T_H_new[:p.T], T_H[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(np.abs(T_H[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(Ynew[:p.T], Y[:p.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)
# Compute effective and marginal tax rates for all agents
mtrx_params_4D = np.tile(
p.mtrx_params.reshape(p.T, p.S, 1, p.mtrx_params.shape[2]),
(1, 1, p.J, 1))
mtry_params_4D = np.tile(
p.mtry_params.reshape(p.T, p.S, 1, p.mtry_params.shape[2]),
(1, 1, p.J, 1))
e_3D = np.tile(p.e.reshape(1, p.S, p.J), (p.T, 1, 1))
mtry_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
True, e_3D, etr_params_4D, mtry_params_4D, p)
mtrx_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
False, e_3D, etr_params_4D, mtrx_params_4D, p)
etr_path = tax.ETR_income(r_hh_path[:p.T], wpath[:p.T], bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, e_3D, etr_params_4D,
p)
C = aggr.get_C(c_mat, p, 'TPI')
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d = aggr.get_I(bmat_splus1[:p.T], K_d[1:p.T + 1], K_d[:p.T], p, 'TPI')
I = aggr.get_I(bmat_splus1[:p.T], K[1:p.T + 1], K[:p.T], p, 'TPI')
# solve resource constraint
# net foreign borrowing
new_borrowing_f = (D_f[1:p.T + 1] * np.exp(p.g_y) *
(1 + p.g_n[1:p.T + 1]) - D_f[:p.T])
debt_service_f = D_f * r_hh
RC_error = aggr.resource_constraint(Y[:p.T - 1], C[:p.T - 1], G[:p.T - 1],
I_d[:p.T - 1], K_f[:p.T - 1],
new_borrowing_f[:p.T - 1],
debt_service_f[:p.T - 1],
r_hh[:p.T - 1], p)
# Compute total investment (not just domestic)
I_total = ((1 + p.g_n[:p.T]) * np.exp(p.g_y) * K[1:p.T + 1] -
(1.0 - p.delta) * K[:p.T])
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 range(p.T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_mat[t], t,
p.ltilde)
eul_savings = euler_errors[:, :p.S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, p.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[:p.T],
'B': B,
'K': K,
'K_f': K_f,
'K_d': K_d,
'L': L,
'C': C,
'I': I,
'I_total': I_total,
'I_d': I_d,
'BQ': BQ,
'total_revenue': total_revenue,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Ipath,
'T_H': T_H,
'T_P': T_Ppath,
'T_BQ': T_BQpath,
'T_W': T_Wpath,
'T_C': T_Cpath,
'G': G,
'D': D,
'D_f': D_f,
'D_d': D_d,
'r': r,
'r_gov': r_gov,
'r_hh': r_hh,
'w': w,
'bmat_splus1': bmat_splus1,
'bmat_s': bmat_s[:p.T, :, :],
'n_mat': n_mat[:p.T, :, :],
'c_path': c_mat,
'bq_path': bqmat,
'y_before_tax_mat': y_before_tax_mat,
'tax_path': tax_mat,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure,
'resource_constraint_error': RC_error,
'new_borrowing_f': new_borrowing_f,
'debt_service_f': debt_service_f,
'etr_path': etr_path,
'mtrx_path': mtrx_path,
'mtry_path': mtry_path
}
tpi_dir = os.path.join(p.output_base, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
if np.any(G) < 0:
print('Government spending is negative along transition path' +
' to satisfy budget')
if (((TPIiter >= p.maxiter) or (np.absolute(TPIdist) > p.mindist_TPI))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found' +
' (TPIdist)')
if ((np.any(np.absolute(RC_error) >= p.mindist_TPI * 10))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(RC_error)')
if ((np.any(np.absolute(eul_savings) >= p.mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > p.mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(eulers)')
return output
def SS_solver(bmat, nmat, r, BQ, TR, factor, Y, p, client,
fsolve_flag=False):
'''
Solves for the steady state distribution of capital, labor, as well
as w, r, TR and the scaling factor, using functional iteration.
Args:
bmat (Numpy array): initial guess at savings, size = SxJ
nmat (Numpy array): initial guess at labor supply, size = SxJ
r (scalar): real interest rate
BQ (array_like): aggregate bequest amount(s)
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
Y (scalar): real GDP
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with steady state solution
results
'''
# Rename the inputs
if not p.budget_balance:
if not p.baseline_spending:
Y = TR / p.alpha_T[-1]
if p.small_open:
r = p.hh_r[-1]
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag:
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, TR, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, TR, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_hh,
new_w, new_TR, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
# bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
# nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
if not p.baseline_spending:
TR = utils.convex_combo(new_TR, TR, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_TR, TR)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absolute difference
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[abs(new_Y - Y)] +
[utils.pct_diff_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_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
print('Iteration: %02d' % iteration, ' Distance: ', dist)
# Generate the SS values of variables, including euler errors
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
if p.budget_balance:
r_hh_ss = rss
Dss = 0.0
else:
Dss = p.debt_ratio_ss * Y
Lss = aggr.get_L(nssmat, p, 'SS')
Bss = aggr.get_B(bssmat_splus1, p, 'SS', False)
K_demand_open_ss = firm.get_K(Lss, p.firm_r[-1], p, 'SS')
D_f_ss = p.zeta_D[-1] * Dss
D_d_ss = Dss - D_f_ss
K_d_ss = Bss - D_d_ss
if not p.small_open:
K_f_ss = p.zeta_K[-1] * (K_demand_open_ss - Bss + D_d_ss)
Kss = K_f_ss + K_d_ss
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
else:
K_d_ss = Bss - D_d_ss
K_f_ss = K_demand_open_ss - Bss + D_d_ss
Kss = K_f_ss + K_d_ss
InvestmentPlaceholder = np.zeros(bssmat_splus1.shape)
Iss = aggr.get_I(InvestmentPlaceholder, Kss, Kss, p, 'SS')
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
r_hh_ss = aggr.get_r_hh(rss, r_gov_ss, Kss, Dss)
wss = new_w
BQss = new_BQ
factor_ss = factor
TR_ss = TR
bqssmat = household.get_bq(BQss, None, p, 'SS')
trssmat = household.get_tr(TR_ss, None, p, 'SS')
Yss = firm.get_Y(Kss, Lss, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.total_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, trssmat, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
yss_before_tax_mat = r_hh_ss * bssmat_s + wss * p.e * nssmat
Css = aggr.get_C(cssmat, p, 'SS')
(total_revenue_ss, T_Iss, T_Pss, T_BQss, T_Wss, T_Css,
business_revenue) =\
aggr.revenue(r_hh_ss, wss, bssmat_s, nssmat, bqssmat, cssmat,
Yss, Lss, Kss, factor, theta, etr_params_3D, p,
'SS')
debt_service_ss = r_gov_ss * Dss
new_borrowing = Dss * ((1 + p.g_n_ss) * np.exp(p.g_y) - 1)
# government spends such that it expands its debt at the same rate as GDP
if p.budget_balance:
Gss = 0.0
else:
Gss = total_revenue_ss + new_borrowing - (TR_ss + debt_service_ss)
print('G components = ', new_borrowing, TR_ss, debt_service_ss)
# Compute total investment (not just domestic)
Iss_total = ((1 + p.g_n_ss) * np.exp(p.g_y) - 1 + p.delta) * Kss
# solve resource constraint
# net foreign borrowing
print('Foreign debt holdings = ', D_f_ss)
print('Foreign capital holdings = ', K_f_ss)
new_borrowing_f = D_f_ss * (np.exp(p.g_y) * (1 + p.g_n_ss) - 1)
debt_service_f = D_f_ss * r_hh_ss
RC = aggr.resource_constraint(Yss, Css, Gss, I_d_ss, K_f_ss,
new_borrowing_f, debt_service_f, r_hh_ss,
p)
print('resource constraint: ', RC)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(RC) >
p.mindist_SS):
print('Resource Constraint Difference:', RC)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
# Return dictionary of SS results
output = {'Kss': Kss, 'K_f_ss': K_f_ss, 'K_d_ss': K_d_ss,
'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'I_d_ss': I_d_ss, 'nssmat': nssmat,
'Yss': Yss, 'Dss': Dss, 'D_f_ss': D_f_ss,
'D_d_ss': D_d_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'yss_before_tax_mat': yss_before_tax_mat,
'bqssmat': bqssmat, 'TR_ss': TR_ss, 'trssmat': trssmat,
'Gss': Gss, 'total_revenue_ss': total_revenue_ss,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Iss,
'T_Pss': T_Pss, 'T_BQss': T_BQss, 'T_Wss': T_Wss,
'T_Css': T_Css, 'euler_savings': euler_savings,
'debt_service_f': debt_service_f,
'new_borrowing_f': new_borrowing_f,
'debt_service_ss': debt_service_ss,
'new_borrowing': new_borrowing,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': RC,
'etr_ss': etr_ss, 'mtrx_ss': mtrx_ss, 'mtry_ss': mtry_ss}
return output
def SS_solver(bmat, nmat, r, BQ, T_H, factor, Y, p, client,
fsolve_flag=False):
'''
--------------------------------------------------------------------
Solves for the steady state distribution of capital, labor, as well
as w, r, T_H and the scaling factor, using a bisection method
similar to TPI.
--------------------------------------------------------------------
INPUTS:
b_guess_init = [S,J] array, initial guesses for savings
n_guess_init = [S,J] array, initial guesses for labor supply
wguess = scalar, initial guess for SS real wage rate
rguess = scalar, initial guess for SS real interest rate
T_Hguess = scalar, initial guess for lump sum transfer
factorguess = scalar, initial guess for scaling factor to dollars
chi_b = [J,] vector, chi^b_j, the utility weight on bequests
chi_n = [S,] vector, chi^n_s utility weight on labor supply
params = length X tuple, list of parameters
iterative_params = length X tuple, list of parameters that determine
the convergence of the while loop
tau_bq = [J,] vector, bequest tax rate
rho = [S,] vector, mortality rates by age
lambdas = [J,] vector, fraction of population with each ability type
omega = [S,] vector, stationary population weights
e = [S,J] array, effective labor units by age and ability type
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
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()
utils.convex_combo()
utils.pct_diff_func()
OBJECTS CREATED WITHIN FUNCTION:
b_guess = [S,] vector, initial guess at household savings
n_guess = [S,] vector, initial guess at household labor supply
b_s = [S,] vector, wealth enter period with
b_splus1 = [S,] vector, household savings
b_splus2 = [S,] vector, household savings one period ahead
BQ = scalar, aggregate bequests to lifetime income group
theta = scalar, replacement rate for social security benenfits
error1 = [S,] vector, errors from FOC for savings
error2 = [S,] vector, errors from FOC for labor supply
tax1 = [S,] vector, total income taxes paid
cons = [S,] vector, household consumption
OBJECTS CREATED WITHIN FUNCTION - SMALL OPEN ONLY
Bss = scalar, aggregate household wealth in the steady state
BIss = scalar, aggregate household net investment in the steady state
RETURNS: solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
OUTPUT: None
--------------------------------------------------------------------
'''
# Rename the inputs
if not p.budget_balance:
if not p.baseline_spending:
Y = T_H / p.alpha_T[-1]
if p.small_open:
r = p.hh_r[-1]
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag:
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, T_H, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, T_H, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_hh,
new_w, new_T_H, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
# bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
# nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
if p.budget_balance:
T_H = utils.convex_combo(new_T_H, T_H, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_T_H, T_H)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absoluate difference
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[abs(new_Y - Y)] +
[utils.pct_diff_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_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
print('Iteration: %02d' % iteration, ' Distance: ', dist)
'''
------------------------------------------------------------------------
Generate the SS values of variables, including euler errors
------------------------------------------------------------------------
'''
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
if p.budget_balance:
r_hh_ss = rss
debt_ss = 0.0
else:
debt_ss = p.debt_ratio_ss * Y
Lss = aggr.get_L(nssmat, p, 'SS')
if not p.small_open:
Bss = aggr.get_K(bssmat_splus1, p, 'SS', False)
Kss = Bss - debt_ss
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
else:
# Compute capital (K) and wealth (B) separately
Kss = firm.get_K(Lss, p.firm_r[-1], p, 'SS')
InvestmentPlaceholder = np.zeros(bssmat_splus1.shape)
Iss = aggr.get_I(InvestmentPlaceholder, Kss, Kss, p, 'SS')
Bss = aggr.get_K(bssmat_splus1, p, 'SS', False)
BIss = aggr.get_I(bssmat_splus1, Bss, Bss, p, 'BI_SS')
if p.budget_balance:
r_hh_ss = rss
else:
r_hh_ss = aggr.get_r_hh(rss, r_gov_ss, Kss, debt_ss)
if p.small_open:
r_hh_ss = p.hh_r[-1]
wss = new_w
BQss = new_BQ
factor_ss = factor
T_Hss = T_H
bqssmat = household.get_bq(BQss, None, p, 'SS')
Yss = firm.get_Y(Kss, Lss, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.total_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, T_Hss, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
Css = aggr.get_C(cssmat, p, 'SS')
(total_revenue_ss, T_Iss, T_Pss, T_BQss, T_Wss, T_Css,
business_revenue) =\
aggr.revenue(r_hh_ss, wss, bssmat_s, nssmat, bqssmat, cssmat,
Yss, Lss, Kss, factor, theta, etr_params_3D, p,
'SS')
debt_service_ss = r_gov_ss * p.debt_ratio_ss * Yss
new_borrowing = p.debt_ratio_ss * Yss * ((1 + p.g_n_ss) *
np.exp(p.g_y) - 1)
# government spends such that it expands its debt at the same rate as GDP
if p.budget_balance:
Gss = 0.0
else:
Gss = total_revenue_ss + new_borrowing - (T_Hss + debt_service_ss)
print('G components = ', new_borrowing, T_Hss, debt_service_ss)
# Compute total investment (not just domestic)
Iss_total = p.delta * Kss
# solve resource constraint
if p.small_open:
# include term for current account
resource_constraint = (Yss + new_borrowing - (Css + BIss + Gss)
+ (p.hh_r[-1] * Bss -
(p.delta + p.firm_r[-1]) *
Kss - debt_service_ss))
print('Yss= ', Yss, '\n', 'Css= ', Css, '\n', 'Bss = ', Bss,
'\n', 'BIss = ', BIss, '\n', 'Kss = ', Kss, '\n', 'Iss = ',
Iss, '\n', 'Lss = ', Lss, '\n', 'T_H = ', T_H, '\n',
'Gss= ', Gss)
print('D/Y:', debt_ss / Yss, 'T/Y:', T_Hss / Yss, 'G/Y:',
Gss / Yss, 'Rev/Y:', total_revenue_ss / Yss,
'Int payments to GDP:', (r_gov_ss * debt_ss) / Yss)
print('resource constraint: ', resource_constraint)
else:
resource_constraint = Yss - (Css + Iss + Gss)
print('Yss= ', Yss, '\n', 'Gss= ', Gss, '\n', 'Css= ', Css, '\n',
'Kss = ', Kss, '\n', 'Iss = ', Iss, '\n', 'Lss = ', Lss,
'\n', 'Debt service = ', debt_service_ss)
print('D/Y:', debt_ss / Yss, 'T/Y:', T_Hss / Yss, 'G/Y:',
Gss / Yss, 'Rev/Y:', total_revenue_ss / Yss, 'business rev/Y: ',
business_revenue / Yss, 'Int payments to GDP:',
(r_gov_ss * debt_ss) / Yss)
print('Check SS budget: ', Gss - (np.exp(p.g_y) *
(1 + p.g_n_ss) - 1 - r_gov_ss)
* debt_ss - total_revenue_ss + T_Hss)
print('resource constraint: ', resource_constraint)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(resource_constraint) >
p.mindist_SS):
print('Resource Constraint Difference:', resource_constraint)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
'''
------------------------------------------------------------------------
Return dictionary of SS results
------------------------------------------------------------------------
'''
output = {'Kss': Kss, 'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'nssmat': nssmat, 'Yss': Yss,
'Dss': debt_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'bqssmat': bqssmat, 'T_Hss': T_Hss, 'Gss': Gss,
'total_revenue_ss': total_revenue_ss,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Iss,
'T_Pss': T_Pss, 'T_BQss': T_BQss, 'T_Wss': T_Wss,
'T_Css': T_Css, 'euler_savings': euler_savings,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': resource_constraint,
'etr_ss': etr_ss, 'mtrx_ss': mtrx_ss, 'mtry_ss': mtry_ss}
return output
def inner_loop(outer_loop_vars, p, client):
'''
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 to pass to function
if p.budget_balance:
bssmat, nssmat, r, BQ, T_H, factor = outer_loop_vars
else:
bssmat, nssmat, r, BQ, Y, T_H, factor = outer_loop_vars
euler_errors = np.zeros((2 * p.S, p.J))
w = firm.get_w_from_r(r, p, 'SS')
r_gov = fiscal.get_r_gov(r, p)
if p.budget_balance:
r_hh = r
D = 0
else:
D = p.debt_ratio_ss * Y
K = firm.get_K_from_Y(Y, r, p, 'SS')
r_hh = aggr.get_r_hh(r, r_gov, K, D)
if p.small_open:
r_hh = p.hh_r[-1]
bq = household.get_bq(BQ, None, p, 'SS')
lazy_values = []
for j in range(p.J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = (r_hh, w, bq[:, j], T_H, factor, j, p)
lazy_values.append(delayed(opt.fsolve)(euler_equation_solver,
guesses * .9,
args=euler_params,
xtol=MINIMIZER_TOL,
full_output=True))
results = compute(*lazy_values, scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
# for j, result in results.items():
for j, result in enumerate(results):
[solutions, infodict, ier, message] = result
euler_errors[:, j] = infodict['fvec']
bssmat[:, j] = solutions[:p.S]
nssmat[:, j] = solutions[p.S:]
L = aggr.get_L(nssmat, p, 'SS')
if not p.small_open:
B = aggr.get_K(bssmat, p, 'SS', False)
if p.budget_balance:
K = B
else:
K = B - D
else:
K = firm.get_K(L, r, p, 'SS')
new_Y = firm.get_Y(K, L, p, 'SS')
if p.budget_balance:
Y = new_Y
if not p.small_open:
new_r = firm.get_r(Y, K, p, 'SS')
else:
new_r = p.firm_r[-1]
new_w = firm.get_w_from_r(new_r, p, 'SS')
print('inner factor prices: ', new_r, new_w)
b_s = np.array(list(np.zeros(p.J).reshape(1, p.J)) +
list(bssmat[:-1, :]))
new_r_gov = fiscal.get_r_gov(new_r, p)
if p.small_open:
new_r_hh = p.hh_r[-1]
else:
new_r_hh = aggr.get_r_hh(new_r, new_r_gov, K, D)
average_income_model = ((new_r_hh * b_s + new_w * p.e * nssmat) *
p.omega_SS.reshape(p.S, 1) *
p.lambdas.reshape(1, p.J)).sum()
if p.baseline:
new_factor = p.mean_income_data / average_income_model
else:
new_factor = factor
new_BQ = aggr.get_BQ(new_r_hh, bssmat, None, p, 'SS', False)
new_bq = household.get_bq(new_BQ, None, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, None, p)
if p.budget_balance:
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])),
(1, p.J, 1))
taxss = tax.total_taxes(new_r_hh, new_w, b_s, nssmat, new_bq,
factor, T_H, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(new_r_hh, new_w, b_s, bssmat,
nssmat, new_bq, taxss,
p.e, p.tau_c[-1, :, :], p)
new_T_H, _, _, _, _, _, _ = aggr.revenue(
new_r_hh, new_w, b_s, nssmat, new_bq, cssmat, new_Y, L, K,
factor, theta, etr_params_3D, p, 'SS')
elif p.baseline_spending:
new_T_H = T_H
else:
new_T_H = p.alpha_T[-1] * new_Y
return euler_errors, bssmat, nssmat, new_r, new_r_gov, new_r_hh, \
new_w, new_T_H, new_Y, new_factor, new_BQ, average_income_model
def run_TPI(p, client=None):
# unpack tuples of parameters
initial_values, SS_values, baseline_values = get_initial_SS_values(p)
(B0, b_sinit, b_splus1init, factor, initial_b, initial_n,
D0) = initial_values
(Kss, Bss, Lss, rss, wss, BQss, T_Hss, total_revenue_ss, bssmat_splus1,
nssmat, Yss, Gss, theta) = SS_values
(T_Hbaseline, Gbaseline) = baseline_values
print('Government spending breakpoints are tG1: ', p.tG1, '; and tG2:',
p.tG2)
# Initialize guesses at time paths
# Make array of initial guesses for labor supply and savings
domain = np.linspace(0, p.T, p.T)
domain2 = np.tile(domain.reshape(p.T, 1, 1), (1, p.S, p.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, p.S, p.J), (p.S, 1, 1))
guesses_b = np.append(guesses_b, ending_b_tail, axis=0)
domain3 = np.tile(np.linspace(0, 1, p.T).reshape(p.T, 1, 1), (1, p.S, p.J))
guesses_n = domain3 * (nssmat - initial_n) + initial_n
ending_n_tail = np.tile(nssmat.reshape(1, p.S, p.J), (p.S, 1, 1))
guesses_n = np.append(guesses_n, ending_n_tail, axis=0)
b_mat = guesses_b # np.zeros((p.T + p.S, p.S, p.J))
n_mat = guesses_n # np.zeros((p.T + p.S, p.S, p.J))
ind = np.arange(p.S)
L_init = np.ones((p.T + p.S, )) * Lss
B_init = np.ones((p.T + p.S, )) * Bss
L_init[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B_init[1:p.T] = aggr.get_K(b_mat[:p.T], p, 'TPI', False)[:p.T - 1]
B_init[0] = B0
if not p.small_open:
if p.budget_balance:
K_init = B_init
else:
K_init = B_init * Kss / Bss
else:
K_init = firm.get_K(L_init, p.firm_r, p, 'TPI')
K = K_init
L = L_init
B = B_init
Y = np.zeros_like(K)
Y[:p.T] = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
Y[p.T:] = Yss
r = np.zeros_like(Y)
if not p.small_open:
r[:p.T] = firm.get_r(Y[:p.T], K[:p.T], p, 'TPI')
r[p.T:] = rss
else:
r = p.firm_r
# compute w
w = np.zeros_like(r)
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
w[p.T:] = wss
r_gov = fiscal.get_r_gov(r, p)
if p.budget_balance:
r_hh = r
else:
r_hh = aggr.get_r_hh(r, r_gov, K, p.debt_ratio_ss * Y)
if p.small_open:
r_hh = p.hh_r
BQ0 = aggr.get_BQ(r[0], initial_b, None, p, 'SS', True)
if not p.use_zeta:
BQ = np.zeros((p.T + p.S, p.J))
for j in range(p.J):
BQ[:,
j] = (list(np.linspace(BQ0[j], BQss[j], p.T)) + [BQss[j]] * p.S)
BQ = np.array(BQ)
else:
BQ = (list(np.linspace(BQ0, BQss, p.T)) + [BQss] * p.S)
BQ = np.array(BQ)
if p.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(p.T + p.S) * T_Hss2
total_revenue = T_H
G = np.zeros(p.T + p.S)
elif not p.baseline_spending:
T_H = p.alpha_T * Y
elif p.baseline_spending:
T_H = T_Hbaseline
T_H_new = p.T_H # Need to set T_H_new for later reference
G = Gbaseline
G_0 = Gbaseline[0]
# Initialize some starting value
if p.budget_balance:
D = 0.0 * Y
else:
D = p.debt_ratio_ss * Y
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
TPIdist_vec = np.zeros(p.maxiter)
print('analytical mtrs in tpi = ', p.analytical_mtrs)
print('tax function type in tpi = ', p.tax_func_type)
# TPI loop
while (TPIiter < p.maxiter) and (TPIdist >= p.mindist_TPI):
r_gov[:p.T] = fiscal.get_r_gov(r[:p.T], p)
if p.budget_balance:
r_hh[:p.T] = r[:p.T]
else:
K[:p.T] = firm.get_K_from_Y(Y[:p.T], r[:p.T], p, 'TPI')
r_hh[:p.T] = aggr.get_r_hh(r[:p.T], r_gov[:p.T], K[:p.T], D[:p.T])
if p.small_open:
r_hh[:p.T] = p.hh_r[:p.T]
outer_loop_vars = (r, w, r_hh, BQ, T_H, theta)
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
lazy_values = []
for j in range(p.J):
guesses = (guesses_b[:, :, j], guesses_n[:, :, j])
lazy_values.append(
delayed(inner_loop)(guesses, outer_loop_vars, initial_values,
j, ind, p))
results = compute(*lazy_values,
scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
for j, result in enumerate(results):
euler_errors[:, :, j], b_mat[:, :, j], n_mat[:, :, j] = result
bmat_s = np.zeros((p.T, p.S, p.J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:p.T - 1, :-1, :]
bmat_splus1 = np.zeros((p.T, p.S, p.J))
bmat_splus1[:, :, :] = b_mat[:p.T, :, :]
L[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B[1:p.T] = aggr.get_K(bmat_splus1[:p.T], p, 'TPI', False)[:p.T - 1]
if np.any(B) < 0:
print('B has negative elements. B[0:9]:', B[0:9])
print('B[T-2:T]:', B[p.T - 2, p.T])
etr_params_4D = np.tile(
p.etr_params.reshape(p.T, p.S, 1, p.etr_params.shape[2]),
(1, 1, p.J, 1))
bqmat = household.get_bq(BQ, None, p, 'TPI')
tax_mat = tax.total_taxes(r_hh[:p.T], w[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat[:p.T, :, :], factor,
T_H[:p.T], theta, 0, None, False, 'TPI', p.e,
etr_params_4D, p)
r_hh_path = utils.to_timepath_shape(r_hh, p)
wpath = utils.to_timepath_shape(w, p)
c_mat = household.get_cons(r_hh_path[:p.T, :, :], wpath[:p.T, :, :],
bmat_s, bmat_splus1, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], tax_mat, p.e,
p.tau_c[:p.T, :, :], p)
if not p.small_open:
if p.budget_balance:
K[:p.T] = B[:p.T]
else:
if not p.baseline_spending:
Y = T_H / p.alpha_T # maybe unecessary
(total_rev, T_Ipath, T_Ppath, T_BQpath, T_Wpath,
T_Cpath, business_revenue) = aggr.revenue(
r_hh[:p.T], w[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], c_mat[:p.T, :, :], Y[:p.T],
L[:p.T], K[:p.T], factor, theta, etr_params_4D, p,
'TPI')
total_revenue = np.array(
list(total_rev) + [total_revenue_ss] * p.S)
# set intial debt value
if p.baseline:
D_0 = p.initial_debt_ratio * Y[0]
else:
D_0 = D0
if not p.baseline_spending:
G_0 = p.alpha_G[0] * Y[0]
dg_fixed_values = (Y, total_revenue, T_H, D_0, G_0)
Dnew, G = fiscal.D_G_path(r_gov, dg_fixed_values, Gbaseline, p)
K[:p.T] = B[:p.T] - Dnew[:p.T]
if np.any(K < 0):
print('K has negative elements. Setting them ' +
'positive to prevent NAN.')
K[:p.T] = np.fmax(K[:p.T], 0.05 * B[:p.T])
else:
K[:p.T] = firm.get_K(L[:p.T], p.firm_r[:p.T], p, 'TPI')
Ynew = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
if not p.small_open:
rnew = firm.get_r(Ynew[:p.T], K[:p.T], p, 'TPI')
else:
rnew = r.copy()
r_gov_new = fiscal.get_r_gov(rnew, p)
if p.budget_balance:
r_hh_new = rnew[:p.T]
else:
r_hh_new = aggr.get_r_hh(rnew, r_gov_new, K[:p.T], Dnew[:p.T])
if p.small_open:
r_hh_new = p.hh_r[:p.T]
# compute w
wnew = firm.get_w_from_r(rnew[:p.T], p, 'TPI')
b_mat_shift = np.append(np.reshape(initial_b, (1, p.S, p.J)),
b_mat[:p.T - 1, :, :],
axis=0)
BQnew = aggr.get_BQ(r_hh_new[:p.T], b_mat_shift, None, p, 'TPI', False)
bqmat_new = household.get_bq(BQnew, None, p, 'TPI')
(total_rev, T_Ipath, T_Ppath, T_BQpath,
T_Wpath, T_Cpath, business_revenue) = aggr.revenue(
r_hh_new[:p.T], wnew[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat_new[:p.T, :, :], c_mat[:p.T, :, :], Ynew[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p, 'TPI')
total_revenue = np.array(list(total_rev) + [total_revenue_ss] * p.S)
if p.budget_balance:
T_H_new = total_revenue
elif not p.baseline_spending:
T_H_new = p.alpha_T[:p.T] * Ynew[:p.T]
# If baseline_spending==True, no need to update T_H, it's fixed
if p.small_open and not p.budget_balance:
# Loop through years to calculate debt and gov't spending.
# This is done earlier when small_open=False.
if p.baseline:
D_0 = p.initial_debt_ratio * Y[0]
else:
D_0 = D0
if not p.baseline_spending:
G_0 = p.alpha_G[0] * Ynew[0]
dg_fixed_values = (Ynew, total_revenue, T_H, D_0, G_0)
Dnew, G = fiscal.D_G_path(r_gov_new, dg_fixed_values, Gbaseline, p)
if p.budget_balance:
Dnew = D
w[:p.T] = wnew[:p.T]
r[:p.T] = utils.convex_combo(rnew[:p.T], r[:p.T], p.nu)
BQ[:p.T] = utils.convex_combo(BQnew[:p.T], BQ[:p.T], p.nu)
D = Dnew
Y[:p.T] = utils.convex_combo(Ynew[:p.T], Y[:p.T], p.nu)
if not p.baseline_spending:
T_H[:p.T] = utils.convex_combo(T_H_new[:p.T], T_H[:p.T], p.nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, p.nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, p.nu)
print('r diff: ', (rnew[:p.T] - r[:p.T]).max(),
(rnew[:p.T] - r[:p.T]).min())
print('BQ diff: ', (BQnew[:p.T] - BQ[:p.T]).max(),
(BQnew[:p.T] - BQ[:p.T]).min())
print('T_H diff: ', (T_H_new[:p.T] - T_H[:p.T]).max(),
(T_H_new[:p.T] - T_H[:p.T]).min())
print('Y diff: ', (Ynew[:p.T] - Y[:p.T]).max(),
(Ynew[:p.T] - Y[:p.T]).min())
if not p.baseline_spending:
if T_H.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(wnew[:p.T], w[:p.T])) +
list(utils.pct_diff_func(T_H_new[:p.T], T_H[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(wnew[:p.T], w[:p.T])) +
list(np.abs(T_H[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(wnew[:p.T], w[:p.T])) +
list(utils.pct_diff_func(Ynew[:p.T], Y[:p.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)
# Compute effective and marginal tax rates for all agents
mtrx_params_4D = np.tile(
p.mtrx_params.reshape(p.T, p.S, 1, p.mtrx_params.shape[2]),
(1, 1, p.J, 1))
mtry_params_4D = np.tile(
p.mtry_params.reshape(p.T, p.S, 1, p.mtry_params.shape[2]),
(1, 1, p.J, 1))
e_3D = np.tile(p.e.reshape(1, p.S, p.J), (p.T, 1, 1))
mtry_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
True, e_3D, etr_params_4D, mtry_params_4D, p)
mtrx_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
False, e_3D, etr_params_4D, mtrx_params_4D, p)
etr_path = tax.ETR_income(r_hh_path[:p.T], wpath[:p.T], bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, e_3D, etr_params_4D,
p)
C = aggr.get_C(c_mat, p, 'TPI')
if not p.small_open:
I = aggr.get_I(bmat_splus1[:p.T], K[1:p.T + 1], K[:p.T], p, 'TPI')
rc_error = Y[:p.T] - C[:p.T] - I[:p.T] - G[:p.T]
else:
I = ((1 + np.squeeze(np.hstack(
(p.g_n[1:p.T], p.g_n_ss)))) * np.exp(p.g_y) * K[1:p.T + 1] -
(1.0 - p.delta) * K[:p.T])
BI = aggr.get_I(bmat_splus1[:p.T], B[1:p.T + 1], B[:p.T], p, 'TPI')
new_borrowing = (D[1:p.T] * (1 + p.g_n[1:p.T]) * np.exp(p.g_y) -
D[:p.T - 1])
rc_error = (Y[:p.T - 1] + new_borrowing -
(C[:p.T - 1] + BI[:p.T - 1] + G[:p.T - 1]) +
(p.hh_r[:p.T - 1] * B[:p.T - 1] -
(p.delta + p.firm_r[:p.T - 1]) * K[:p.T - 1] -
p.hh_r[:p.T - 1] * D[:p.T - 1]))
# Compute total investment (not just domestic)
I_total = ((1 + p.g_n[:p.T]) * np.exp(p.g_y) * K[1:p.T + 1] -
(1.0 - p.delta) * K[:p.T])
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 range(p.T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_mat[t], t,
p.ltilde)
eul_savings = euler_errors[:, :p.S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, p.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[:p.T],
'B': B,
'K': K,
'L': L,
'C': C,
'I': I,
'I_total': I_total,
'BQ': BQ,
'total_revenue': total_revenue,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Ipath,
'T_H': T_H,
'T_P': T_Ppath,
'T_BQ': T_BQpath,
'T_W': T_Wpath,
'T_C': T_Cpath,
'G': G,
'D': D,
'r': r,
'r_gov': r_gov,
'r_hh': r_hh,
'w': w,
'bmat_splus1': bmat_splus1,
'bmat_s': bmat_s[:p.T, :, :],
'n_mat': n_mat[:p.T, :, :],
'c_path': c_mat,
'bq_path': bqmat,
'tax_path': tax_mat,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure,
'resource_constraint_error': rc_error,
'etr_path': etr_path,
'mtrx_path': mtrx_path,
'mtry_path': mtry_path
}
tpi_dir = os.path.join(p.output_base, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
pickle.dump(output, open(tpi_vars, "wb"))
if np.any(G) < 0:
print('Government spending is negative along transition path' +
' to satisfy budget')
if (((TPIiter >= p.maxiter) or (np.absolute(TPIdist) > p.mindist_TPI))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found' +
' (TPIdist)')
if ((np.any(np.absolute(rc_error) >= p.mindist_TPI * 10))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(rc_error)')
if ((np.any(np.absolute(eul_savings) >= p.mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > p.mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(eulers)')
return output
def SS_solver(bmat, nmat, r, BQ, T_H, factor, Y, p, client,
fsolve_flag=False):
'''
--------------------------------------------------------------------
Solves for the steady state distribution of capital, labor, as well
as w, r, T_H and the scaling factor, using a bisection method
similar to TPI.
--------------------------------------------------------------------
INPUTS:
b_guess_init = [S,J] array, initial guesses for savings
n_guess_init = [S,J] array, initial guesses for labor supply
wguess = scalar, initial guess for SS real wage rate
rguess = scalar, initial guess for SS real interest rate
T_Hguess = scalar, initial guess for lump sum transfer
factorguess = scalar, initial guess for scaling factor to dollars
chi_b = [J,] vector, chi^b_j, the utility weight on bequests
chi_n = [S,] vector, chi^n_s utility weight on labor supply
params = length X tuple, list of parameters
iterative_params = length X tuple, list of parameters that determine
the convergence of the while loop
tau_bq = [J,] vector, bequest tax rate
rho = [S,] vector, mortality rates by age
lambdas = [J,] vector, fraction of population with each ability type
omega = [S,] vector, stationary population weights
e = [S,J] array, effective labor units by age and ability type
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
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()
utils.convex_combo()
utils.pct_diff_func()
OBJECTS CREATED WITHIN FUNCTION:
b_guess = [S,] vector, initial guess at household savings
n_guess = [S,] vector, initial guess at household labor supply
b_s = [S,] vector, wealth enter period with
b_splus1 = [S,] vector, household savings
b_splus2 = [S,] vector, household savings one period ahead
BQ = scalar, aggregate bequests to lifetime income group
theta = scalar, replacement rate for social security benenfits
error1 = [S,] vector, errors from FOC for savings
error2 = [S,] vector, errors from FOC for labor supply
tax1 = [S,] vector, total income taxes paid
cons = [S,] vector, household consumption
OBJECTS CREATED WITHIN FUNCTION - SMALL OPEN ONLY
Bss = scalar, aggregate household wealth in the steady state
BIss = scalar, aggregate household net investment in the steady state
RETURNS: solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
OUTPUT: None
--------------------------------------------------------------------
'''
# Rename the inputs
if not p.budget_balance:
if not p.baseline_spending:
Y = T_H / p.alpha_T[-1]
if p.small_open:
r = p.hh_r[-1]
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag:
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, T_H, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, T_H, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_hh,
new_w, new_T_H, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
# bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
# nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
if not p.baseline_spending:
T_H = utils.convex_combo(new_T_H, T_H, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_T_H, T_H)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absolute difference
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[abs(new_Y - Y)] +
[utils.pct_diff_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_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
print('Iteration: %02d' % iteration, ' Distance: ', dist)
'''
------------------------------------------------------------------------
Generate the SS values of variables, including euler errors
------------------------------------------------------------------------
'''
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
if p.budget_balance:
r_hh_ss = rss
Dss = 0.0
else:
Dss = p.debt_ratio_ss * Y
Lss = aggr.get_L(nssmat, p, 'SS')
Bss = aggr.get_K(bssmat_splus1, p, 'SS', False)
K_demand_open_ss = firm.get_K(Lss, p.firm_r[-1], p, 'SS')
D_f_ss = p.zeta_D[-1] * Dss
D_d_ss = Dss - D_f_ss
K_d_ss = Bss - D_d_ss
if not p.small_open:
K_f_ss = p.zeta_K[-1] * (K_demand_open_ss - Bss + D_d_ss)
Kss = K_f_ss + K_d_ss
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
else:
K_d_ss = Bss - D_d_ss
K_f_ss = K_demand_open_ss - Bss + D_d_ss
Kss = K_f_ss + K_d_ss
InvestmentPlaceholder = np.zeros(bssmat_splus1.shape)
Iss = aggr.get_I(InvestmentPlaceholder, Kss, Kss, p, 'SS')
BIss = aggr.get_I(bssmat_splus1, Bss, Bss, p, 'BI_SS')
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
r_hh_ss = aggr.get_r_hh(rss, r_gov_ss, Kss, Dss)
wss = new_w
BQss = new_BQ
factor_ss = factor
T_Hss = T_H
bqssmat = household.get_bq(BQss, None, p, 'SS')
Yss = firm.get_Y(Kss, Lss, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.total_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, T_Hss, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
yss_before_tax_mat = r_hh_ss * bssmat_s + wss * p.e * nssmat
Css = aggr.get_C(cssmat, p, 'SS')
(total_revenue_ss, T_Iss, T_Pss, T_BQss, T_Wss, T_Css,
business_revenue) =\
aggr.revenue(r_hh_ss, wss, bssmat_s, nssmat, bqssmat, cssmat,
Yss, Lss, Kss, factor, theta, etr_params_3D, p,
'SS')
debt_service_ss = r_gov_ss * Dss
new_borrowing = Dss * ((1 + p.g_n_ss) * np.exp(p.g_y) - 1)
# government spends such that it expands its debt at the same rate as GDP
if p.budget_balance:
Gss = 0.0
else:
Gss = total_revenue_ss + new_borrowing - (T_Hss + debt_service_ss)
print('G components = ', new_borrowing, T_Hss, debt_service_ss)
# Compute total investment (not just domestic)
Iss_total = ((1 + p.g_n_ss) * np.exp(p.g_y) - 1 + p.delta) * Kss
# solve resource constraint
# net foreign borrowing
print('Foreign debt holdings = ', D_f_ss)
print('Foreign capital holdings = ', K_f_ss)
new_borrowing_f = D_f_ss * (np.exp(p.g_y) * (1 + p.g_n_ss) - 1)
debt_service_f = D_f_ss * r_hh_ss
RC = aggr.resource_constraint(Yss, Css, Gss, I_d_ss, K_f_ss,
new_borrowing_f, debt_service_f, r_hh_ss,
p)
print('resource constraint: ', RC)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(RC) >
p.mindist_SS):
print('Resource Constraint Difference:', RC)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
'''
------------------------------------------------------------------------
Return dictionary of SS results
------------------------------------------------------------------------
'''
output = {'Kss': Kss, 'K_f_ss': K_f_ss, 'K_d_ss': K_d_ss,
'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'I_d_ss': I_d_ss, 'nssmat': nssmat,
'Yss': Yss, 'Dss': Dss, 'D_f_ss': D_f_ss,
'D_d_ss': D_d_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'yss_before_tax_mat': yss_before_tax_mat,
'bqssmat': bqssmat, 'T_Hss': T_Hss, 'Gss': Gss,
'total_revenue_ss': total_revenue_ss,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Iss,
'T_Pss': T_Pss, 'T_BQss': T_BQss, 'T_Wss': T_Wss,
'T_Css': T_Css, 'euler_savings': euler_savings,
'debt_service_f': debt_service_f,
'new_borrowing_f': new_borrowing_f,
'debt_service_ss': debt_service_ss,
'new_borrowing': new_borrowing,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': RC,
'etr_ss': etr_ss, 'mtrx_ss': mtrx_ss, 'mtry_ss': mtry_ss}
return output
def test_euler_equation_solver():
# Test SS.inner_loop function. Provide inputs to function and
# ensure that output returned matches what it has been before.
input_tuple = utils.safe_read_pickle(
os.path.join(CUR_PATH, 'test_io_data/euler_eqn_solver_inputs.pkl'))
(guesses, params) = input_tuple
p = Specifications()
(r, w, T_H, factor, j, p.J, p.S, p.beta, p.sigma, p.ltilde, p.g_y,
p.g_n_ss, tau_payroll, retire, p.mean_income_data, h_wealth,
p_wealth, m_wealth, p.b_ellipse, p.upsilon, j, p.chi_b,
p.chi_n, tau_bq, p.rho, lambdas, p.omega_SS, p.e,
p.analytical_mtrs, etr_params, mtrx_params, mtry_params) = params
p.tau_bq = np.ones(p.T + p.S) * 0.0
p.tau_payroll = np.ones(p.T + p.S) * tau_payroll
p.h_wealth = np.ones(p.T + p.S) * h_wealth
p.p_wealth = np.ones(p.T + p.S) * p_wealth
p.m_wealth = np.ones(p.T + p.S) * m_wealth
p.retire = (np.ones(p.T + p.S) * retire).astype(int)
p.etr_params = np.transpose(etr_params.reshape(
p.S, 1, etr_params.shape[-1]), (1, 0, 2))
p.mtrx_params = np.transpose(mtrx_params.reshape(
p.S, 1, mtrx_params.shape[-1]), (1, 0, 2))
p.mtry_params = np.transpose(mtry_params.reshape(
p.S, 1, mtry_params.shape[-1]), (1, 0, 2))
p.tax_func_type = 'DEP'
p.lambdas = lambdas.reshape(p.J, 1)
b_splus1 = np.array(guesses[:p.S]).reshape(p.S, 1) + 0.005
BQ = aggregates.get_BQ(r, b_splus1, j, p, 'SS', False)
bq = household.get_bq(BQ, j, p, 'SS')
args = (r, w, bq, T_H, factor, j, p)
test_list = SS.euler_equation_solver(guesses, *args)
expected_list = np.array([
-3.62741663e+00, -6.30068841e+00, -6.76592886e+00,
-6.97731223e+00, -7.05777777e+00, -6.57305440e+00,
-7.11553046e+00, -7.30569622e+00, -7.45808107e+00,
-7.89984062e+00, -8.11466111e+00, -8.28230086e+00,
-8.79253862e+00, -8.86994311e+00, -9.31299476e+00,
-9.80834199e+00, -9.97333771e+00, -1.08349979e+01,
-1.13199826e+01, -1.22890930e+01, -1.31550471e+01,
-1.42753713e+01, -1.55721098e+01, -1.73811490e+01,
-1.88856303e+01, -2.09570569e+01, -2.30559500e+01,
-2.52127149e+01, -2.76119605e+01, -3.03141128e+01,
-3.30900203e+01, -3.62799730e+01, -3.91169706e+01,
-4.24246421e+01, -4.55740527e+01, -4.92914871e+01,
-5.30682805e+01, -5.70043846e+01, -6.06075991e+01,
-6.45251018e+01, -6.86128365e+01, -7.35896515e+01,
-7.92634608e+01, -8.34733231e+01, -9.29802390e+01,
-1.01179788e+02, -1.10437881e+02, -1.20569527e+02,
-1.31569973e+02, -1.43633399e+02, -1.57534056e+02,
-1.73244610e+02, -1.90066728e+02, -2.07980863e+02,
-2.27589046e+02, -2.50241670e+02, -2.76314755e+02,
-3.04930986e+02, -3.36196973e+02, -3.70907934e+02,
-4.10966644e+02, -4.56684022e+02, -5.06945218e+02,
-5.61838645e+02, -6.22617808e+02, -6.90840503e+02,
-7.67825713e+02, -8.54436805e+02, -9.51106365e+02,
-1.05780305e+03, -1.17435473e+03, -1.30045062e+03,
-1.43571221e+03, -1.57971603e+03, -1.73204264e+03,
-1.88430524e+03, -2.03403679e+03, -2.17861987e+03,
-2.31532884e+03, -8.00654731e+03, -5.21487172e-02,
-2.80234170e-01, 4.93894552e-01, 3.11884938e-01, 6.55799607e-01,
5.62182419e-01, 3.86074983e-01, 3.43741491e-01, 4.22461089e-01,
3.63707951e-01, 4.93150010e-01, 4.72813688e-01, 4.07390308e-01,
4.94974186e-01, 4.69900128e-01, 4.37562389e-01, 5.67370182e-01,
4.88965362e-01, 6.40728461e-01, 6.14619979e-01, 4.97173823e-01,
6.19549666e-01, 6.51193557e-01, 4.48906118e-01, 7.93091492e-01,
6.51249363e-01, 6.56307713e-01, 1.12948552e+00, 9.50018058e-01,
6.79613030e-01, 9.51359123e-01, 6.31059147e-01, 7.97896887e-01,
8.44620817e-01, 7.43683837e-01, 1.56693187e+00, 2.75630011e-01,
5.32956891e-01, 1.57110727e+00, 1.22674610e+00, 4.63932928e-01,
1.47225464e+00, 1.16948107e+00, 1.07965795e+00, -3.20557791e-01,
-1.17064127e+00, -7.84880649e-01, -7.60851182e-01, -1.61415945e+00,
-8.30363975e-01, -1.68459409e+00, -1.49260581e+00, -1.84257084e+00,
-1.72143079e+00, -1.43131579e+00, -1.63719219e+00, -1.43874851e+00,
-1.57207905e+00, -1.72909159e+00, -1.98778122e+00, -1.80843826e+00,
-2.12828312e+00, -2.24768762e+00, -2.36961877e+00, -2.49117258e+00,
-2.59914065e+00, -2.82309085e+00, -2.93613362e+00, -3.34446991e+00,
-3.45445086e+00, -3.74962140e+00, -3.78113417e+00, -4.55643800e+00,
-4.86929016e+00, -5.08657898e+00, -5.22054177e+00, -5.54606515e+00,
-5.78478304e+00, -5.93652041e+00, -6.11519786e+00])
assert(np.allclose(np.array(test_list), np.array(expected_list)))
def test_euler_equation_solver():
# Test SS.inner_loop function. Provide inputs to function and
# ensure that output returned matches what it has been before.
input_tuple = utils.safe_read_pickle(
os.path.join(CUR_PATH, 'test_io_data/euler_eqn_solver_inputs.pkl'))
(guesses, params) = input_tuple
p = Specifications()
(r, w, T_H, factor, j, p.J, p.S, p.beta, p.sigma, p.ltilde, p.g_y,
p.g_n_ss, tau_payroll, retire, p.mean_income_data, h_wealth,
p_wealth, m_wealth, p.b_ellipse, p.upsilon, j, p.chi_b,
p.chi_n, tau_bq, p.rho, lambdas, p.omega_SS, p.e,
p.analytical_mtrs, etr_params, mtrx_params, mtry_params) = params
p.tau_bq = np.ones(p.T + p.S) * 0.0
p.tau_payroll = np.ones(p.T + p.S) * tau_payroll
p.h_wealth = np.ones(p.T + p.S) * h_wealth
p.p_wealth = np.ones(p.T + p.S) * p_wealth
p.m_wealth = np.ones(p.T + p.S) * m_wealth
p.retire = (np.ones(p.T + p.S) * retire).astype(int)
p.etr_params = np.transpose(etr_params.reshape(
p.S, 1, etr_params.shape[-1]), (1, 0, 2))
p.mtrx_params = np.transpose(mtrx_params.reshape(
p.S, 1, mtrx_params.shape[-1]), (1, 0, 2))
p.mtry_params = np.transpose(mtry_params.reshape(
p.S, 1, mtry_params.shape[-1]), (1, 0, 2))
p.tax_func_type = 'DEP'
p.lambdas = lambdas.reshape(p.J, 1)
b_splus1 = np.array(guesses[:p.S]).reshape(p.S, 1) + 0.005
BQ = aggregates.get_BQ(r, b_splus1, j, p, 'SS', False)
bq = household.get_bq(BQ, j, p, 'SS')
args = (r, w, bq, T_H, factor, j, p)
test_list = SS.euler_equation_solver(guesses, *args)
expected_list = np.array([
-3.62741663e+00, -6.30068841e+00, -6.76592886e+00,
-6.97731223e+00, -7.05777777e+00, -6.57305440e+00,
-7.11553046e+00, -7.30569622e+00, -7.45808107e+00,
-7.89984062e+00, -8.11466111e+00, -8.28230086e+00,
-8.79253862e+00, -8.86994311e+00, -9.31299476e+00,
-9.80834199e+00, -9.97333771e+00, -1.08349979e+01,
-1.13199826e+01, -1.22890930e+01, -1.31550471e+01,
-1.42753713e+01, -1.55721098e+01, -1.73811490e+01,
-1.88856303e+01, -2.09570569e+01, -2.30559500e+01,
-2.52127149e+01, -2.76119605e+01, -3.03141128e+01,
-3.30900203e+01, -3.62799730e+01, -3.91169706e+01,
-4.24246421e+01, -4.55740527e+01, -4.92914871e+01,
-5.30682805e+01, -5.70043846e+01, -6.06075991e+01,
-6.45251018e+01, -6.86128365e+01, -7.35896515e+01,
-7.92634608e+01, -8.34733231e+01, -9.29802390e+01,
-1.01179788e+02, -1.10437881e+02, -1.20569527e+02,
-1.31569973e+02, -1.43633399e+02, -1.57534056e+02,
-1.73244610e+02, -1.90066728e+02, -2.07980863e+02,
-2.27589046e+02, -2.50241670e+02, -2.76314755e+02,
-3.04930986e+02, -3.36196973e+02, -3.70907934e+02,
-4.10966644e+02, -4.56684022e+02, -5.06945218e+02,
-5.61838645e+02, -6.22617808e+02, -6.90840503e+02,
-7.67825713e+02, -8.54436805e+02, -9.51106365e+02,
-1.05780305e+03, -1.17435473e+03, -1.30045062e+03,
-1.43571221e+03, -1.57971603e+03, -1.73204264e+03,
-1.88430524e+03, -2.03403679e+03, -2.17861987e+03,
-2.31532884e+03, -8.00654731e+03, -5.21487172e-02,
-2.80234170e-01, 4.93894552e-01, 3.11884938e-01, 6.55799607e-01,
5.62182419e-01, 3.86074983e-01, 3.43741491e-01, 4.22461089e-01,
3.63707951e-01, 4.93150010e-01, 4.72813688e-01, 4.07390308e-01,
4.94974186e-01, 4.69900128e-01, 4.37562389e-01, 5.67370182e-01,
4.88965362e-01, 6.40728461e-01, 6.14619979e-01, 4.97173823e-01,
6.19549666e-01, 6.51193557e-01, 4.48906118e-01, 7.93091492e-01,
6.51249363e-01, 6.56307713e-01, 1.12948552e+00, 9.50018058e-01,
6.79613030e-01, 9.51359123e-01, 6.31059147e-01, 7.97896887e-01,
8.44620817e-01, 7.43683837e-01, 1.56693187e+00, 2.75630011e-01,
5.32956891e-01, 1.57110727e+00, 1.22674610e+00, 4.63932928e-01,
1.47225464e+00, 1.16948107e+00, 1.07965795e+00, -3.20557791e-01,
-1.17064127e+00, -7.84880649e-01, -7.60851182e-01, -1.61415945e+00,
-8.30363975e-01, -1.68459409e+00, -1.49260581e+00, -1.84257084e+00,
-1.72143079e+00, -1.43131579e+00, -1.63719219e+00, -1.43874851e+00,
-1.57207905e+00, -1.72909159e+00, -1.98778122e+00, -1.80843826e+00,
-2.12828312e+00, -2.24768762e+00, -2.36961877e+00, -2.49117258e+00,
-2.59914065e+00, -2.82309085e+00, -2.93613362e+00, -3.34446991e+00,
-3.45445086e+00, -3.74962140e+00, -3.78113417e+00, -4.55643800e+00,
-4.86929016e+00, -5.08657898e+00, -5.22054177e+00, -5.54606515e+00,
-5.78478304e+00, -5.93652041e+00, -6.11519786e+00])
assert(np.allclose(np.array(test_list), np.array(expected_list)))
