def test_get_D_ss(budget_balance, expected_tuple):
'''
Test of the fiscla.get_D_ss() function.
'''
r_gov = 0.03
Y = 1.176255339
p = Specifications()
p.debt_ratio_ss = 1.2
p.budget_balance = budget_balance
p.g_n_ss = 0.02
test_tuple = fiscal.get_D_ss(r_gov, Y, p)
for i, v in enumerate(test_tuple):
assert np.allclose(v, expected_tuple[i])
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-Core 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_p (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_p = 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_p = aggr.get_r_p(r, r_gov, K, D)
bq = household.get_bq(BQ, None, p, 'SS')
tr = household.get_tr(TR, None, p, 'SS')
ubi = p.ubi_nom_array[-1, :, :] / factor
lazy_values = []
for j in range(p.J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = (r_p, w, bq[:, j], tr[:, j], ubi[:, 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_p = aggr.get_r_p(new_r, new_r_gov, K, D)
average_income_model = ((new_r_p * 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_p, 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_p, new_w, b_s, nssmat, new_bq, factor, tr, ubi,
theta, None, None, False, 'SS', p.e, etr_params_3D,
p)
cssmat = household.get_cons(new_r_p, new_w, b_s, bssmat, nssmat, new_bq,
taxss, p.e, p.tau_c[-1, :, :], p)
total_tax_revenue, _, agg_pension_outlays, UBI_outlays, _, _, _, _, _, _ =\
aggr.revenue(new_r_p, new_w, b_s, nssmat, new_bq, cssmat, Y, L,
K, factor, ubi, theta, etr_params_3D, p, 'SS')
G = fiscal.get_G_ss(Y, total_tax_revenue, agg_pension_outlays, TR,
UBI_outlays, new_borrowing, debt_service, p)
new_TR = fiscal.get_TR(Y, TR, G, total_tax_revenue, agg_pension_outlays,
UBI_outlays, p, 'SS')
return euler_errors, bssmat, nssmat, new_r, new_r_gov, new_r_p, \
new_w, new_TR, Y, new_factor, new_BQ, average_income_model
def SS_solver(bmat, nmat, r, BQ, TR, factor, Y, p, client, fsolve_flag=False):
'''
Solves for the steady state distribution of capital, labor, as well
as w, r, TR and the scaling factor, using functional iteration.
Args:
bmat (Numpy array): initial guess at savings, size = SxJ
nmat (Numpy array): initial guess at labor supply, size = SxJ
r (scalar): real interest rate
BQ (array_like): aggregate bequest amount(s)
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
Y (scalar): real GDP
p (OG-Core Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with steady state solution
results
'''
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag: # case where already solved via SS_fsolve
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, TR, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, TR, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_p,
new_w, new_TR, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
if p.baseline_spending:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array(
[utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absolute difference
dist = np.array(
[utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) + [abs(new_Y - Y)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
TR = utils.convex_combo(new_TR, TR, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_TR, TR)] +
[utils.pct_diff_func(new_factor, factor)]).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
if VERBOSE:
print('Iteration: %02d' % iteration, ' Distance: ', dist)
# Generate the SS values of variables, including euler errors
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
TR_ss = TR
Lss = aggr.get_L(nssmat, p, 'SS')
Bss = aggr.get_B(bssmat_splus1, p, 'SS', False)
(Dss, D_d_ss, D_f_ss, new_borrowing, debt_service,
new_borrowing_f) = fiscal.get_D_ss(r_gov_ss, Y, p)
K_demand_open_ss = firm.get_K(Lss, p.world_int_rate[-1], p, 'SS')
Kss, K_d_ss, K_f_ss = aggr.get_K_splits(Bss, K_demand_open_ss, D_d_ss,
p.zeta_K[-1])
Yss = firm.get_Y(Kss, Lss, p, 'SS')
r_p_ss = aggr.get_r_p(rss, r_gov_ss, Kss, Dss)
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
wss = new_w
BQss = new_BQ
factor_ss = factor
bqssmat = household.get_bq(BQss, None, p, 'SS')
trssmat = household.get_tr(TR_ss, None, p, 'SS')
ubissmat = p.ubi_nom_array[-1, :, :] / factor_ss
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(
np.reshape(p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])),
(1, p.J, 1))
mtrx_params_3D = np.tile(
np.reshape(p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(
np.reshape(p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_p_ss, wss, bssmat_s, nssmat, factor, True, p.e,
etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_p_ss, wss, bssmat_s, nssmat, factor, False, p.e,
etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_p_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.net_taxes(r_p_ss, wss, bssmat_s, nssmat, bqssmat, factor_ss,
trssmat, ubissmat, theta, None, None, False, 'SS',
p.e, etr_params_3D, p)
cssmat = household.get_cons(r_p_ss, wss, bssmat_s, bssmat_splus1, nssmat,
bqssmat, taxss, p.e, p.tau_c[-1, :, :], p)
yss_before_tax_mat = household.get_y(r_p_ss, wss, bssmat_s, nssmat, p)
Css = aggr.get_C(cssmat, p, 'SS')
(total_tax_revenue, iit_payroll_tax_revenue, agg_pension_outlays,
UBI_outlays, bequest_tax_revenue, wealth_tax_revenue, cons_tax_revenue,
business_tax_revenue, payroll_tax_revenue,
iit_revenue) = aggr.revenue(r_p_ss, wss, bssmat_s, nssmat, bqssmat,
cssmat, Yss, Lss, Kss, factor, ubissmat,
theta, etr_params_3D, p, 'SS')
Gss = fiscal.get_G_ss(Yss, total_tax_revenue, agg_pension_outlays, TR_ss,
UBI_outlays, new_borrowing, debt_service, p)
# Compute total investment (not just domestic)
Iss_total = aggr.get_I(None, Kss, Kss, p, 'total_ss')
# solve resource constraint
# net foreign borrowing
debt_service_f = fiscal.get_debt_service_f(r_p_ss, D_f_ss)
RC = aggr.resource_constraint(Yss, Css, Gss, I_d_ss, K_f_ss,
new_borrowing_f, debt_service_f, r_p_ss, p)
if VERBOSE:
print('Foreign debt holdings = ', D_f_ss)
print('Foreign capital holdings = ', K_f_ss)
print('resource constraint: ', RC)
if Gss < 0:
print('Steady state government spending is negative to satisfy' +
' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(RC) > p.mindist_SS):
print('Resource Constraint Difference:', RC)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
if VERBOSE:
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
# Return dictionary of SS results
output = {
'Kss': Kss,
'K_f_ss': K_f_ss,
'K_d_ss': K_d_ss,
'Bss': Bss,
'Lss': Lss,
'Css': Css,
'Iss': Iss,
'Iss_total': Iss_total,
'I_d_ss': I_d_ss,
'nssmat': nssmat,
'Yss': Yss,
'Dss': Dss,
'D_f_ss': D_f_ss,
'D_d_ss': D_d_ss,
'wss': wss,
'rss': rss,
'total_taxes_ss': taxss,
'ubissmat': ubissmat,
'r_gov_ss': r_gov_ss,
'r_p_ss': r_p_ss,
'theta': theta,
'BQss': BQss,
'factor_ss': factor_ss,
'bssmat_s': bssmat_s,
'cssmat': cssmat,
'bssmat_splus1': bssmat_splus1,
'yss_before_tax_mat': yss_before_tax_mat,
'bqssmat': bqssmat,
'TR_ss': TR_ss,
'trssmat': trssmat,
'Gss': Gss,
'total_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,
'agg_pension_outlays': agg_pension_outlays,
'UBI_outlays_SS': UBI_outlays,
'bequest_tax_revenue': bequest_tax_revenue,
'wealth_tax_revenue': wealth_tax_revenue,
'cons_tax_revenue': cons_tax_revenue,
'euler_savings': euler_savings,
'debt_service_f': debt_service_f,
'new_borrowing_f': new_borrowing_f,
'debt_service': debt_service,
'new_borrowing': new_borrowing,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': RC,
'etr_ss': etr_ss,
'mtrx_ss': mtrx_ss,
'mtry_ss': mtry_ss
}
return output