def test_get_BQ():
"""
Simulate data similar to observed
"""
T = 160
S, J = 40, 2
r = 0.5 + 0.5 * np.random.rand(T).reshape(T, 1)
b_splus1 = 0.06 + 7 * np.random.rand(T, S, J)
# normalize across S and J axes
omega = 0.5 * np.random.rand(T * S).reshape(T, S, 1)
omega = omega / omega.sum(axis=1).reshape(T, 1, 1)
lambdas = 0.4 + 0.2 * np.random.rand(J).reshape(1, 1, J)
lambdas = lambdas / lambdas.sum()
assert np.allclose(lambdas.sum(), 1.0)
assert np.allclose(omega.sum(), T)
rho = np.random.rand(S).reshape(1, S, 1)
g_n = 0.1 * np.random.rand(T).reshape(T, 1)
BQ_presum = b_splus1 * omega * rho * lambdas
factor = (1.0 + r) / (1.0 + g_n)
# test SS
BQ = aggr.get_BQ(r[0], b_splus1[0],
(omega[0], lambdas[0], rho[0], g_n[0], "SS"))
assert np.allclose(BQ_presum[0].sum(0) * factor[0], BQ)
# test TPI
BQ = aggr.get_BQ(r, b_splus1, (omega, lambdas, rho, g_n, "TPI"))
assert np.allclose(BQ_presum.sum(1) * factor, BQ)
def test_SS_solver(baseline, param_updates, filename, dask_client):
# Test SS.SS_solver function. Provide inputs to function and
# ensure that output returned matches what it has been before.
p = Specifications(baseline=baseline,
client=dask_client,
num_workers=NUM_WORKERS)
p.update_specifications(param_updates)
p.output_base = CUR_PATH
p.get_tax_function_parameters(None, run_micro=False)
b_guess = np.ones((p.S, p.J)) * 0.07
n_guess = np.ones((p.S, p.J)) * .35 * p.ltilde
if p.zeta_K[-1] == 1.0:
rguess = p.world_int_rate[-1]
else:
rguess = 0.06483431412921253
TRguess = 0.05738932081035772
factorguess = 139355.1547340256
BQguess = aggregates.get_BQ(rguess, b_guess, None, p, 'SS', False)
Yguess = 0.6376591201150815
test_dict = SS.SS_solver(b_guess, n_guess, rguess, BQguess, TRguess,
factorguess, Yguess, p, None, False)
expected_dict = utils.safe_read_pickle(
os.path.join(CUR_PATH, 'test_io_data', filename))
for k, v in expected_dict.items():
print('Testing ', k)
assert (np.allclose(test_dict[k], v, atol=1e-07, equal_nan=True))
def find_moments(p, client):
b_guess = np.ones((p.S, p.J)) * 0.07
n_guess = np.ones((p.S, p.J)) * .4 * p.ltilde
rguess = 0.08961277823002804 # 0.09
T_Hguess = 0.12
factorguess = 12.73047710050195 # 7.7 #70000 # Modified
BQguess = aggr.get_BQ(rguess, b_guess, None, p, 'SS', False)
exit_early = [0, -1] # 2nd value gives number of valid labor moments to consider before exiting SS_fsolve
# Put -1 to run to SS
ss_params_baseline = (b_guess, n_guess, None, None, p, client, exit_early)
guesses = [rguess] + list(BQguess) + [T_Hguess, factorguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS.SS_fsolve, guesses, args=ss_params_baseline,
xtol=p.mindist_SS, full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-2]
T_Hss = solutions_fsolve[-2]
factor_ss = solutions_fsolve[-1]
Yss = T_Hss/p.alpha_T[-1]
fsolve_flag = True
try:
output = SS.SS_solver(b_guess, n_guess, rss, BQss, T_Hss,
factor_ss, Yss, p, client, fsolve_flag)
except:
print('RuntimeError: Steady state aggregate resource constraint not satisfied')
print('Luckily we caught the error, so minstat_init_calibrate will continue')
return 1e10
model_moments = np.array(output['nssmat'].mean(axis=1)[:45]) # calc_moments(output, p.omega_SS, p.lambdas, p.S, p.J)
return model_moments
def minstat_init_calibrate(params, *args):
a0, a1, a2, a3, a4 = params
p, client, data_moments, W, ages = args
chi_n = np.ones(p.S)
chi_n[:p.S // 2 + 5] = chebyshev_func(ages, a0, a1, a2, a3, a4)
slope = chi_n[p.S // 2 + 5 - 1] - chi_n[p.S // 2 + 5 - 2]
chi_n[p.S // 2 + 5 -
1:] = (np.linspace(65, 100, 36) - 65) * slope + chi_n[p.S // 2 + 5 -
1]
chi_n[chi_n < 0.5] = 0.5
p.chi_n = chi_n
print("-----------------------------------------------------")
print('PARAMS AT START' + str(params))
print("-----------------------------------------------------")
b_guess = np.ones((p.S, p.J)) * 0.07
n_guess = np.ones((p.S, p.J)) * .4 * p.ltilde
rguess = 0.09
T_Hguess = 0.12
factorguess = 7.7 #70000 # Modified
BQguess = aggr.get_BQ(rguess, b_guess, None, p, 'SS', False)
exit_early = [
0, 2
] # 2nd value gives number of valid labor moments to consider before exiting SS_fsolve
ss_params_baseline = (b_guess, n_guess, None, None, p, client, exit_early)
guesses = [rguess] + list(BQguess) + [T_Hguess, factorguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS.SS_fsolve, guesses, args=ss_params_baseline,
xtol=p.mindist_SS, full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-2]
T_Hss = solutions_fsolve[-2]
factor_ss = solutions_fsolve[-1]
Yss = T_Hss / p.alpha_T[-1]
fsolve_flag = True
try:
output = SS.SS_solver(b_guess, n_guess, rss, BQss, T_Hss, factor_ss,
Yss, p, client, fsolve_flag)
except:
print(
'RuntimeError: Steady state aggregate resource constraint not satisfied'
)
print(
'Luckily we caught the error, so minstat_init_calibrate will continue'
)
return 1e10
model_moments = calc_moments(output, p.omega_SS, p.lambdas, p.S, p.J)
print('Model moments:', model_moments)
print("-----------------------------------------------------")
distance = np.dot(
np.dot((np.array(model_moments[:9]) - np.array(data_moments)).T, W),
np.array(model_moments[:9]) - np.array(data_moments))
print('DATA and MODEL DISTANCE: ', distance)
return distance
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 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, 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 test_get_BQ(r, b_splus1, j, p, method, PreTP, expected):
"""
Test of aggregate bequest function.
"""
BQ = aggr.get_BQ(r, b_splus1, j, p, method, PreTP)
assert np.allclose(BQ, expected)
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 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 run_SS(p, client=None):
'''
--------------------------------------------------------------------
Solve for SS of OG-USA.
--------------------------------------------------------------------
INPUTS:
p = Specifications class with parameterization of model
income_tax_parameters = length 5 tuple, (tax_func_type,
analytical_mtrs, etr_params,
mtrx_params, mtry_params)
ss_parameters = length 21 tuple, (J, S, T, BW, beta, sigma, alpha,
gamma, epsilon, Z, delta, ltilde, nu, g_y, g_n_ss,
tau_payroll, retire, mean_income_data, h_wealth,
p_wealth, m_wealth, b_ellipse, upsilon)
iterative_params = [2,] vector, vector with max iterations and
tolerance for SS solution
baseline = boolean, =True if run is for baseline tax policy
calibrate_model = boolean, =True if run calibration of chi parameters
output_dir = string, path to save output from current model run
baseline_dir = string, path where baseline results located
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
SS_fsolve()
SS_fsolve_reform()
SS_solver
OBJECTS CREATED WITHIN FUNCTION:
chi_params = [J+S,] vector, chi_b and chi_n stacked together
b_guess = [S,J] array, initial guess at savings
n_guess = [S,J] array, initial guess at labor supply
wguess = scalar, initial guess at SS real wage rate
rguess = scalar, initial guess at SS real interest rate
T_Hguess = scalar, initial guess at SS lump sum transfers
factorguess = scalar, initial guess at SS factor adjustment (to
scale model units to dollars)
output
RETURNS: output
OUTPUT: None
--------------------------------------------------------------------
'''
# For initial guesses of w, r, T_H, and factor, we use values that
# are close to some steady state values.
if p.baseline:
b_guess = np.ones((p.S, p.J)) * 0.07
n_guess = np.ones((p.S, p.J)) * .4 * p.ltilde
if p.small_open:
rguess = p.firm_r[-1]
else:
rguess = 0.09
T_Hguess = 0.12
factorguess = 70000
BQguess = aggr.get_BQ(rguess, b_guess, None, p, 'SS', False)
ss_params_baseline = (b_guess, n_guess, None, None, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [T_Hguess, factorguess]
else:
guesses = [rguess] + list(BQguess) + [T_Hguess, factorguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses, args=ss_params_baseline,
xtol=p.mindist_SS, full_output=True)
if ENFORCE_SOLUTION_CHECKS and not ier == 1:
raise RuntimeError('Steady state equilibrium not found')
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-2]
T_Hss = solutions_fsolve[-2]
factor_ss = solutions_fsolve[-1]
Yss = T_Hss/p.alpha_T[-1] # may not be right - if budget_balance
# = True, but that's ok - will be fixed in SS_solver
fsolve_flag = True
# Return SS values of variables
output = SS_solver(b_guess, n_guess, rss, BQss, T_Hss,
factor_ss, Yss, p, client, fsolve_flag)
else:
# Use the baseline solution to get starting values for the reform
baseline_ss_dir = os.path.join(p.baseline_dir, 'SS/SS_vars.pkl')
ss_solutions = pickle.load(open(baseline_ss_dir, 'rb'),
encoding='latin1')
(b_guess, n_guess, rguess, BQguess, T_Hguess, Yguess, factor) =\
(ss_solutions['bssmat_splus1'], ss_solutions['nssmat'],
ss_solutions['rss'], ss_solutions['BQss'],
ss_solutions['T_Hss'], ss_solutions['Yss'],
ss_solutions['factor_ss'])
if p.baseline_spending:
T_Hss = T_Hguess
ss_params_reform = (b_guess, n_guess, T_Hss, factor, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [Yguess]
else:
guesses = [rguess] + list(BQguess) + [Yguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses,
args=ss_params_reform, xtol=p.mindist_SS,
full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-1]
Yss = solutions_fsolve[-1]
else:
ss_params_reform = (b_guess, n_guess, None, factor, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [T_Hguess]
else:
guesses = [rguess] + list(BQguess) + [T_Hguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses,
args=ss_params_reform, xtol=p.mindist_SS,
full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-1]
T_Hss = solutions_fsolve[-1]
Yss = T_Hss/p.alpha_T[-1] # may not be right - if
# budget_balance = True, but that's ok - will be fixed in
# SS_solver
if ENFORCE_SOLUTION_CHECKS and not ier == 1:
raise RuntimeError('Steady state equilibrium not found')
# Return SS values of variables
fsolve_flag = True
# Return SS values of variables
output = SS_solver(b_guess, n_guess, rss, BQss, T_Hss, factor,
Yss, p, client, fsolve_flag)
if output['Gss'] < 0.:
warnings.warn('Warning: The combination of the tax policy '
+ 'you specified and your target debt-to-GDP '
+ 'ratio results in an infeasible amount of '
+ 'government spending in order to close the '
+ 'budget (i.e., G < 0)')
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 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 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 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_SS(p, client=None):
'''
Solve for steady-state equilibrium of OG-USA.
Args:
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with steady-state solution
results
'''
# For initial guesses of w, r, TR, and factor, we use values that
# are close to some steady state values.
if p.baseline:
b_guess = np.ones((p.S, p.J)) * 0.07
n_guess = np.ones((p.S, p.J)) * .4 * p.ltilde
if p.small_open:
rguess = p.firm_r[-1]
else:
rguess = 0.09
TRguess = 0.12
factorguess = 70000
BQguess = aggr.get_BQ(rguess, b_guess, None, p, 'SS', False)
ss_params_baseline = (b_guess, n_guess, None, None, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [TRguess, factorguess]
else:
guesses = [rguess] + list(BQguess) + [TRguess, factorguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses, args=ss_params_baseline,
xtol=p.mindist_SS, full_output=True)
if ENFORCE_SOLUTION_CHECKS and not ier == 1:
raise RuntimeError('Steady state equilibrium not found')
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-2]
TR_ss = solutions_fsolve[-2]
factor_ss = solutions_fsolve[-1]
Yss = TR_ss/p.alpha_T[-1] # may not be right - if budget_balance
# = True, but that's ok - will be fixed in SS_solver
fsolve_flag = True
# Return SS values of variables
output = SS_solver(b_guess, n_guess, rss, BQss, TR_ss,
factor_ss, Yss, p, client, fsolve_flag)
else:
# Use the baseline solution to get starting values for the reform
baseline_ss_dir = os.path.join(p.baseline_dir, 'SS/SS_vars.pkl')
ss_solutions = pickle.load(open(baseline_ss_dir, 'rb'),
encoding='latin1')
(b_guess, n_guess, rguess, BQguess, TRguess, Yguess, factor) =\
(ss_solutions['bssmat_splus1'], ss_solutions['nssmat'],
ss_solutions['rss'], ss_solutions['BQss'],
ss_solutions['TR_ss'], ss_solutions['Yss'],
ss_solutions['factor_ss'])
if p.baseline_spending:
TR_ss = TRguess
ss_params_reform = (b_guess, n_guess, TR_ss, factor, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [Yguess]
else:
guesses = [rguess] + list(BQguess) + [Yguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses,
args=ss_params_reform, xtol=p.mindist_SS,
full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-1]
Yss = solutions_fsolve[-1]
else:
ss_params_reform = (b_guess, n_guess, None, factor, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [TRguess]
else:
guesses = [rguess] + list(BQguess) + [TRguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses,
args=ss_params_reform, xtol=p.mindist_SS,
full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-1]
TR_ss = solutions_fsolve[-1]
Yss = TR_ss/p.alpha_T[-1] # may not be right - if
# budget_balance = True, but that's ok - will be fixed in
# SS_solver
if ENFORCE_SOLUTION_CHECKS and not ier == 1:
raise RuntimeError('Steady state equilibrium not found')
# Return SS values of variables
fsolve_flag = True
# Return SS values of variables
output = SS_solver(b_guess, n_guess, rss, BQss, TR_ss, factor,
Yss, p, client, fsolve_flag)
if output['Gss'] < 0.:
warnings.warn('Warning: The combination of the tax policy '
+ 'you specified and your target debt-to-GDP '
+ 'ratio results in an infeasible amount of '
+ 'government spending in order to close the '
+ 'budget (i.e., G < 0)')
return output
def run_SS(p, client=None):
'''
--------------------------------------------------------------------
Solve for SS of OG-USA.
--------------------------------------------------------------------
INPUTS:
p = Specifications class with parameterization of model
income_tax_parameters = length 5 tuple, (tax_func_type,
analytical_mtrs, etr_params,
mtrx_params, mtry_params)
ss_parameters = length 21 tuple, (J, S, T, BW, beta, sigma, alpha,
gamma, epsilon, Z, delta, ltilde, nu, g_y, g_n_ss,
tau_payroll, retire, mean_income_data, h_wealth,
p_wealth, m_wealth, b_ellipse, upsilon)
iterative_params = [2,] vector, vector with max iterations and
tolerance for SS solution
baseline = boolean, =True if run is for baseline tax policy
calibrate_model = boolean, =True if run calibration of chi parameters
output_dir = string, path to save output from current model run
baseline_dir = string, path where baseline results located
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
SS_fsolve()
SS_fsolve_reform()
SS_solver
OBJECTS CREATED WITHIN FUNCTION:
chi_params = [J+S,] vector, chi_b and chi_n stacked together
b_guess = [S,J] array, initial guess at savings
n_guess = [S,J] array, initial guess at labor supply
wguess = scalar, initial guess at SS real wage rate
rguess = scalar, initial guess at SS real interest rate
T_Hguess = scalar, initial guess at SS lump sum transfers
factorguess = scalar, initial guess at SS factor adjustment (to
scale model units to dollars)
output
RETURNS: output
OUTPUT: None
--------------------------------------------------------------------
'''
# For initial guesses of w, r, T_H, and factor, we use values that
# are close to some steady state values.
if p.baseline:
b_guess = np.ones((p.S, p.J)) * 0.07
n_guess = np.ones((p.S, p.J)) * .4 * p.ltilde
if p.small_open:
rguess = p.firm_r[-1]
else:
rguess = 0.09
T_Hguess = 0.12
factorguess = 70000
BQguess = aggr.get_BQ(rguess, b_guess, None, p, 'SS', False)
ss_params_baseline = (b_guess, n_guess, None, None, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [T_Hguess, factorguess]
else:
guesses = [rguess] + list(BQguess) + [T_Hguess, factorguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses, args=ss_params_baseline,
xtol=p.mindist_SS, full_output=True)
if ENFORCE_SOLUTION_CHECKS and not ier == 1:
raise RuntimeError('Steady state equilibrium not found')
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-2]
T_Hss = solutions_fsolve[-2]
factor_ss = solutions_fsolve[-1]
Yss = T_Hss/p.alpha_T[-1] # may not be right - if budget_balance
# = True, but that's ok - will be fixed in SS_solver
fsolve_flag = True
# Return SS values of variables
output = SS_solver(b_guess, n_guess, rss, BQss, T_Hss,
factor_ss, Yss, p, client, fsolve_flag)
else:
# Use the baseline solution to get starting values for the reform
baseline_ss_dir = os.path.join(p.baseline_dir, 'SS/SS_vars.pkl')
ss_solutions = pickle.load(open(baseline_ss_dir, 'rb'),
encoding='latin1')
(b_guess, n_guess, rguess, BQguess, T_Hguess, Yguess, factor) =\
(ss_solutions['bssmat_splus1'], ss_solutions['nssmat'],
ss_solutions['rss'], ss_solutions['BQss'],
ss_solutions['T_Hss'], ss_solutions['Yss'],
ss_solutions['factor_ss'])
if p.baseline_spending:
T_Hss = T_Hguess
ss_params_reform = (b_guess, n_guess, T_Hss, factor, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [Yguess]
else:
guesses = [rguess] + list(BQguess) + [Yguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses,
args=ss_params_reform, xtol=p.mindist_SS,
full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-1]
Yss = solutions_fsolve[-1]
else:
ss_params_reform = (b_guess, n_guess, None, factor, p, client)
if p.use_zeta:
guesses = [rguess] + list([BQguess]) + [T_Hguess]
else:
guesses = [rguess] + list(BQguess) + [T_Hguess]
[solutions_fsolve, infodict, ier, message] =\
opt.fsolve(SS_fsolve, guesses,
args=ss_params_reform, xtol=p.mindist_SS,
full_output=True)
rss = solutions_fsolve[0]
BQss = solutions_fsolve[1:-1]
T_Hss = solutions_fsolve[-1]
Yss = T_Hss/p.alpha_T[-1] # may not be right - if
# budget_balance = True, but that's ok - will be fixed in
# SS_solver
if ENFORCE_SOLUTION_CHECKS and not ier == 1:
raise RuntimeError('Steady state equilibrium not found')
# Return SS values of variables
fsolve_flag = True
# Return SS values of variables
output = SS_solver(b_guess, n_guess, rss, BQss, T_Hss, factor,
Yss, p, client, fsolve_flag)
if output['Gss'] < 0.:
warnings.warn('Warning: The combination of the tax policy '
+ 'you specified and your target debt-to-GDP '
+ 'ratio results in an infeasible amount of '
+ 'government spending in order to close the '
+ 'budget (i.e., G < 0)')
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
