def test_net_taxes(r, w, b, n, bq, factor, tr, theta, t, j, shift,
method, e, etr_params, p, expected):
# Test function that computes total net taxes for the household
# method = ss
net_taxes = tax.net_taxes(r, w, b, n, bq, factor, tr, theta, t,
j, shift, method, e, etr_params, p)
assert np.allclose(net_taxes, expected)
def euler_equation_solver(guesses, *args):
'''
Finds the euler errors for certain b and n, one ability type at a
time.
Args:
guesses (Numpy array): initial guesses for b and n, lenth 2S
args (tuple): tuple of arguments (r, w, bq, TR, factor, j, p)
w (scalar): real wage rate
bq (Numpy array): bequest amounts by age, length S
tr (scalar): government transfer amount by age, length S
factor (scalar): scaling factor converting model units to dollars
p (OG-USA Specifications object): model parameters
Returns:
errros (Numpy array): errors from FOCs, length 2S
'''
(r, w, bq, tr, factor, j, p) = args
b_guess = np.array(guesses[:p.S])
n_guess = np.array(guesses[p.S:])
b_s = np.array([0] + list(b_guess[:-1]))
b_splus1 = b_guess
theta = tax.replacement_rate_vals(n_guess, w, factor, j, p)
error1 = household.FOC_savings(r, w, b_s, b_splus1, n_guess, bq, factor,
tr, theta, p.e[:, j], p.rho,
p.tau_c[-1, :, j], p.etr_params[-1, :, :],
p.mtry_params[-1, :, :], None, j, p, 'SS')
error2 = household.FOC_labor(r, w, b_s, b_splus1, n_guess, bq, factor, tr,
theta, p.chi_n, p.e[:, j], p.tau_c[-1, :, j],
p.etr_params[-1, :, :],
p.mtrx_params[-1, :, :], None, j, p, 'SS')
# Put in constraints for consumption and savings.
# According to the euler equations, they can be negative. When
# Chi_b is large, they will be. This prevents that from happening.
# I'm not sure if the constraints are needed for labor.
# But we might as well put them in for now.
mask1 = n_guess < 0
mask2 = n_guess > p.ltilde
mask3 = b_guess <= 0
mask4 = np.isnan(n_guess)
mask5 = np.isnan(b_guess)
error2[mask1] = 1e14
error2[mask2] = 1e14
error1[mask3] = 1e14
error1[mask5] = 1e14
error2[mask4] = 1e14
taxes = tax.net_taxes(r, w, b_s, n_guess, bq, factor, tr, theta, None, j,
False, 'SS', p.e[:, j], p.etr_params[-1, :, :], p)
cons = household.get_cons(r, w, b_s, b_splus1, n_guess, bq, taxes,
p.e[:, j], p.tau_c[-1, :, j], p)
mask6 = cons < 0
error1[mask6] = 1e14
errors = np.hstack((error1, error2))
return errors
def run_TPI(p, client=None):
'''
Solve for transition path equilibrium of OG-USA.
Args:
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with transition path solution
results
'''
# unpack tuples of parameters
initial_values, ss_vars, theta, baseline_values = get_initial_SS_values(p)
(B0, b_sinit, b_splus1init, factor, initial_b, initial_n) =\
initial_values
(TRbaseline, Gbaseline, D0_baseline) = baseline_values
print('Government spending breakpoints are tG1: ', p.tG1, '; and tG2:',
p.tG2)
# Initialize guesses at time paths
# Make array of initial guesses for labor supply and savings
guesses_b = utils.get_initial_path(initial_b, ss_vars['bssmat_splus1'], p,
'ratio')
guesses_n = utils.get_initial_path(initial_n, ss_vars['nssmat'], p,
'ratio')
b_mat = guesses_b
n_mat = guesses_n
ind = np.arange(p.S)
# Get path for aggregate savings and labor supply`
L_init = np.ones((p.T + p.S, )) * ss_vars['Lss']
B_init = np.ones((p.T + p.S, )) * ss_vars['Bss']
L_init[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B_init[1:p.T] = aggr.get_B(b_mat[:p.T], p, 'TPI', False)[:p.T - 1]
B_init[0] = B0
K_init = B_init * ss_vars['Kss'] / ss_vars['Bss']
K = K_init
K_d = K_init * ss_vars['K_d_ss'] / ss_vars['Kss']
K_f = K_init * ss_vars['K_f_ss'] / ss_vars['Kss']
L = L_init
B = B_init
Y = np.zeros_like(K)
Y[:p.T] = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
Y[p.T:] = ss_vars['Yss']
r = np.zeros_like(Y)
r[:p.T] = firm.get_r(Y[:p.T], K[:p.T], p, 'TPI')
r[p.T:] = ss_vars['rss']
# For case where economy is small open econ
r[p.zeta_K == 1] = p.world_int_rate[p.zeta_K == 1]
# Compute other interest rates
r_gov = fiscal.get_r_gov(r, p)
r_hh = aggr.get_r_hh(r, r_gov, K, ss_vars['Dss'])
# compute w
w = np.zeros_like(r)
w[:p.T] = firm.get_w_from_r(r[:p.T], p, 'TPI')
w[p.T:] = ss_vars['wss']
# initial guesses at fiscal vars
if p.budget_balance:
if np.abs(ss_vars['TR_ss']) < 1e-13:
TR_ss2 = 0.0 # sometimes SS is very small but not zero,
# even if taxes are zero, this get's rid of the
# approximation error, which affects the pct changes below
else:
TR_ss2 = ss_vars['TR_ss']
TR = np.ones(p.T + p.S) * TR_ss2
total_tax_revenue = TR - ss_vars['agg_pension_outlays']
G = np.zeros(p.T + p.S)
D = np.zeros(p.T + p.S)
D_d = np.zeros(p.T + p.S)
D_f = np.zeros(p.T + p.S)
else:
if p.baseline_spending:
TR = TRbaseline
G = Gbaseline
G[p.T:] = ss_vars['Gss']
else:
TR = p.alpha_T * Y
G = np.ones(p.T + p.S) * ss_vars['Gss']
D = np.ones(p.T + p.S) * ss_vars['Dss']
D_d = D * ss_vars['D_d_ss'] / ss_vars['Dss']
D_f = D * ss_vars['D_f_ss'] / ss_vars['Dss']
total_tax_revenue = np.ones(p.T + p.S) * ss_vars['total_tax_revenue']
# Initialize bequests
BQ0 = aggr.get_BQ(r_hh[0], initial_b, None, p, 'SS', True)
if not p.use_zeta:
BQ = np.zeros((p.T + p.S, p.J))
for j in range(p.J):
BQ[:, j] = (list(np.linspace(BQ0[j], ss_vars['BQss'][j], p.T)) +
[ss_vars['BQss'][j]] * p.S)
BQ = np.array(BQ)
else:
BQ = (list(np.linspace(BQ0, ss_vars['BQss'], p.T)) +
[ss_vars['BQss']] * p.S)
BQ = np.array(BQ)
TPIiter = 0
TPIdist = 10
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
TPIdist_vec = np.zeros(p.maxiter)
# TPI loop
while (TPIiter < p.maxiter) and (TPIdist >= p.mindist_TPI):
r_gov[:p.T] = fiscal.get_r_gov(r[:p.T], p)
if not p.budget_balance:
K[:p.T] = firm.get_K_from_Y(Y[:p.T], r[:p.T], p, 'TPI')
r_hh[:p.T] = aggr.get_r_hh(r[:p.T], r_gov[:p.T], K[:p.T], D[:p.T])
outer_loop_vars = (r, w, r_hh, BQ, TR, theta)
euler_errors = np.zeros((p.T, 2 * p.S, p.J))
lazy_values = []
for j in range(p.J):
guesses = (guesses_b[:, :, j], guesses_n[:, :, j])
lazy_values.append(
delayed(inner_loop)(guesses, outer_loop_vars, initial_values,
j, ind, p))
if client:
futures = client.compute(lazy_values, num_workers=p.num_workers)
results = client.gather(futures)
else:
results = results = compute(*lazy_values,
scheduler=dask.multiprocessing.get,
num_workers=p.num_workers)
for j, result in enumerate(results):
euler_errors[:, :, j], b_mat[:, :, j], n_mat[:, :, j] = result
bmat_s = np.zeros((p.T, p.S, p.J))
bmat_s[0, 1:, :] = initial_b[:-1, :]
bmat_s[1:, 1:, :] = b_mat[:p.T - 1, :-1, :]
bmat_splus1 = np.zeros((p.T, p.S, p.J))
bmat_splus1[:, :, :] = b_mat[:p.T, :, :]
etr_params_4D = np.tile(
p.etr_params.reshape(p.T, p.S, 1, p.etr_params.shape[2]),
(1, 1, p.J, 1))
bqmat = household.get_bq(BQ, None, p, 'TPI')
trmat = household.get_tr(TR, None, p, 'TPI')
tax_mat = tax.net_taxes(r_hh[:p.T], w[:p.T], bmat_s, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], factor, trmat[:p.T, :, :],
theta, 0, None, False, 'TPI', p.e,
etr_params_4D, p)
r_hh_path = utils.to_timepath_shape(r_hh)
wpath = utils.to_timepath_shape(w)
c_mat = household.get_cons(r_hh_path[:p.T, :, :], wpath[:p.T, :, :],
bmat_s, bmat_splus1, n_mat[:p.T, :, :],
bqmat[:p.T, :, :], tax_mat, p.e,
p.tau_c[:p.T, :, :], p)
y_before_tax_mat = household.get_y(r_hh_path[:p.T, :, :],
wpath[:p.T, :, :],
bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], p)
(total_tax_rev, iit_payroll_tax_revenue, agg_pension_outlays,
bequest_tax_revenue, wealth_tax_revenue, cons_tax_revenue,
business_tax_revenue, payroll_tax_revenue,
iit_revenue) = aggr.revenue(r_hh[:p.T], w[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat[:p.T, :, :],
c_mat[:p.T, :, :], Y[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p,
'TPI')
total_tax_revenue[:p.T] = total_tax_rev
dg_fixed_values = (Y, total_tax_revenue, agg_pension_outlays, TR,
Gbaseline, D0_baseline)
(Dnew, G[:p.T], D_d[:p.T], D_f[:p.T], new_borrowing,
debt_service, new_borrowing_f) =\
fiscal.D_G_path(r_gov, dg_fixed_values, p)
L[:p.T] = aggr.get_L(n_mat[:p.T], p, 'TPI')
B[1:p.T] = aggr.get_B(bmat_splus1[:p.T], p, 'TPI', False)[:p.T - 1]
K_demand_open = firm.get_K(L[:p.T], p.world_int_rate[:p.T], p, 'TPI')
K[:p.T], K_d[:p.T], K_f[:p.T] = aggr.get_K_splits(
B[:p.T], K_demand_open, D_d[:p.T], p.zeta_K[:p.T])
Ynew = firm.get_Y(K[:p.T], L[:p.T], p, 'TPI')
rnew = r.copy()
rnew[:p.T] = firm.get_r(Ynew[:p.T], K[:p.T], p, 'TPI')
# For case where economy is small open econ
r[p.zeta_K == 1] = p.world_int_rate[p.zeta_K == 1]
r_gov_new = fiscal.get_r_gov(rnew, p)
r_hh_new = aggr.get_r_hh(rnew[:p.T], r_gov_new[:p.T], K[:p.T],
Dnew[:p.T])
# compute w
wnew = firm.get_w_from_r(rnew[:p.T], p, 'TPI')
b_mat_shift = np.append(np.reshape(initial_b, (1, p.S, p.J)),
b_mat[:p.T - 1, :, :],
axis=0)
BQnew = aggr.get_BQ(r_hh_new[:p.T], b_mat_shift, None, p, 'TPI', False)
bqmat_new = household.get_bq(BQnew, None, p, 'TPI')
(total_tax_rev, iit_payroll_tax_revenue, agg_pension_outlays,
bequest_tax_revenue, wealth_tax_revenue, cons_tax_revenue,
business_tax_revenue, payroll_tax_revenue,
iit_revenue) = aggr.revenue(r_hh_new[:p.T], wnew[:p.T], bmat_s,
n_mat[:p.T, :, :], bqmat_new[:p.T, :, :],
c_mat[:p.T, :, :], Ynew[:p.T], L[:p.T],
K[:p.T], factor, theta, etr_params_4D, p,
'TPI')
total_tax_revenue[:p.T] = total_tax_rev
TR_new = fiscal.get_TR(Ynew[:p.T], TR[:p.T], G[:p.T],
total_tax_revenue[:p.T],
agg_pension_outlays[:p.T], p, 'TPI')
# update vars for next iteration
w[:p.T] = wnew[:p.T]
r[:p.T] = utils.convex_combo(rnew[:p.T], r[:p.T], p.nu)
BQ[:p.T] = utils.convex_combo(BQnew[:p.T], BQ[:p.T], p.nu)
D[:p.T] = Dnew[:p.T]
Y[:p.T] = utils.convex_combo(Ynew[:p.T], Y[:p.T], p.nu)
if not p.baseline_spending:
TR[:p.T] = utils.convex_combo(TR_new[:p.T], TR[:p.T], p.nu)
guesses_b = utils.convex_combo(b_mat, guesses_b, p.nu)
guesses_n = utils.convex_combo(n_mat, guesses_n, p.nu)
print('r diff: ', (rnew[:p.T] - r[:p.T]).max(),
(rnew[:p.T] - r[:p.T]).min())
print('BQ diff: ', (BQnew[:p.T] - BQ[:p.T]).max(),
(BQnew[:p.T] - BQ[:p.T]).min())
print('TR diff: ', (TR_new[:p.T] - TR[:p.T]).max(),
(TR_new[:p.T] - TR[:p.T]).min())
print('Y diff: ', (Ynew[:p.T] - Y[:p.T]).max(),
(Ynew[:p.T] - Y[:p.T]).min())
if not p.baseline_spending:
if TR.all() != 0:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(TR_new[:p.T], TR[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) + list(
utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(np.abs(TR[:p.T]))).max()
else:
TPIdist = np.array(
list(utils.pct_diff_func(rnew[:p.T], r[:p.T])) +
list(utils.pct_diff_func(BQnew[:p.T], BQ[:p.T]).flatten()) +
list(utils.pct_diff_func(Ynew[:p.T], Y[:p.T]))).max()
TPIdist_vec[TPIiter] = TPIdist
# After T=10, if cycling occurs, drop the value of nu
# wait til after T=10 or so, because sometimes there is a jump up
# in the first couple iterations
# if TPIiter > 10:
# if TPIdist_vec[TPIiter] - TPIdist_vec[TPIiter - 1] > 0:
# nu /= 2
# print 'New Value of nu:', nu
TPIiter += 1
print('Iteration:', TPIiter)
print('\tDistance:', TPIdist)
# Compute effective and marginal tax rates for all agents
mtrx_params_4D = np.tile(
p.mtrx_params.reshape(p.T, p.S, 1, p.mtrx_params.shape[2]),
(1, 1, p.J, 1))
mtry_params_4D = np.tile(
p.mtry_params.reshape(p.T, p.S, 1, p.mtry_params.shape[2]),
(1, 1, p.J, 1))
e_3D = np.tile(p.e.reshape(1, p.S, p.J), (p.T, 1, 1))
mtry_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
True, e_3D, etr_params_4D, mtry_params_4D, p)
mtrx_path = tax.MTR_income(r_hh_path[:p.T], wpath[:p.T],
bmat_s[:p.T, :, :], n_mat[:p.T, :, :], factor,
False, e_3D, etr_params_4D, mtrx_params_4D, p)
etr_path = tax.ETR_income(r_hh_path[:p.T], wpath[:p.T], bmat_s[:p.T, :, :],
n_mat[:p.T, :, :], factor, e_3D, etr_params_4D,
p)
C = aggr.get_C(c_mat, p, 'TPI')
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d = aggr.get_I(bmat_splus1[:p.T], K_d[1:p.T + 1], K_d[:p.T], p, 'TPI')
I = aggr.get_I(bmat_splus1[:p.T], K[1:p.T + 1], K[:p.T], p, 'TPI')
# solve resource constraint
# foreign debt service costs
debt_service_f = fiscal.get_debt_service_f(r_hh, D_f)
RC_error = aggr.resource_constraint(Y[:p.T - 1], C[:p.T - 1], G[:p.T - 1],
I_d[:p.T - 1], K_f[:p.T - 1],
new_borrowing_f[:p.T - 1],
debt_service_f[:p.T - 1],
r_hh[:p.T - 1], p)
# Compute total investment (not just domestic)
I_total = aggr.get_I(None, K[1:p.T + 1], K[:p.T], p, 'total_tpi')
# Compute resource constraint error
rce_max = np.amax(np.abs(RC_error))
print('Max absolute value resource constraint error:', rce_max)
print('Checking time path for violations of constraints.')
for t in range(p.T):
household.constraint_checker_TPI(b_mat[t], n_mat[t], c_mat[t], t,
p.ltilde)
eul_savings = euler_errors[:, :p.S, :].max(1).max(1)
eul_laborleisure = euler_errors[:, p.S:, :].max(1).max(1)
print('Max Euler error, savings: ', eul_savings)
print('Max Euler error labor supply: ', eul_laborleisure)
'''
------------------------------------------------------------------------
Save variables/values so they can be used in other modules
------------------------------------------------------------------------
'''
output = {
'Y': Y[:p.T],
'B': B,
'K': K,
'K_f': K_f,
'K_d': K_d,
'L': L,
'C': C,
'I': I,
'I_total': I_total,
'I_d': I_d,
'BQ': BQ,
'total_tax_revenue': total_tax_revenue,
'business_tax_revenue': business_tax_revenue,
'iit_payroll_tax_revenue': iit_payroll_tax_revenue,
'iit_revenue': iit_revenue,
'payroll_tax_revenue': payroll_tax_revenue,
'TR': TR,
'agg_pension_outlays': agg_pension_outlays,
'bequest_tax_revenue': bequest_tax_revenue,
'wealth_tax_revenue': wealth_tax_revenue,
'cons_tax_revenue': cons_tax_revenue,
'G': G,
'D': D,
'D_f': D_f,
'D_d': D_d,
'r': r,
'r_gov': r_gov,
'r_hh': r_hh,
'w': w,
'bmat_splus1': bmat_splus1,
'bmat_s': bmat_s[:p.T, :, :],
'n_mat': n_mat[:p.T, :, :],
'c_path': c_mat,
'bq_path': bqmat,
'tr_path': trmat,
'y_before_tax_mat': y_before_tax_mat,
'tax_path': tax_mat,
'eul_savings': eul_savings,
'eul_laborleisure': eul_laborleisure,
'resource_constraint_error': RC_error,
'new_borrowing_f': new_borrowing_f,
'debt_service_f': debt_service_f,
'etr_path': etr_path,
'mtrx_path': mtrx_path,
'mtry_path': mtry_path
}
tpi_dir = os.path.join(p.output_base, "TPI")
utils.mkdirs(tpi_dir)
tpi_vars = os.path.join(tpi_dir, "TPI_vars.pkl")
with open(tpi_vars, "wb") as f:
pickle.dump(output, f)
if np.any(G) < 0:
print('Government spending is negative along transition path' +
' to satisfy budget')
if (((TPIiter >= p.maxiter) or (np.absolute(TPIdist) > p.mindist_TPI))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found' +
' (TPIdist)')
if ((np.any(np.absolute(RC_error) >= p.mindist_TPI * 10))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(RC_error)')
if ((np.any(np.absolute(eul_savings) >= p.mindist_TPI) or
(np.any(np.absolute(eul_laborleisure) > p.mindist_TPI)))
and ENFORCE_SOLUTION_CHECKS):
raise RuntimeError('Transition path equlibrium not found ' +
'(eulers)')
return output
def inner_loop(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 SS_solver(bmat, nmat, r, BQ, TR, factor, Y, p, client,
fsolve_flag=False):
'''
Solves for the steady state distribution of capital, labor, as well
as w, r, TR and the scaling factor, using functional iteration.
Args:
bmat (Numpy array): initial guess at savings, size = SxJ
nmat (Numpy array): initial guess at labor supply, size = SxJ
r (scalar): real interest rate
BQ (array_like): aggregate bequest amount(s)
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
Y (scalar): real GDP
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with steady state solution
results
'''
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_hh,
new_w, new_TR, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
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
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_hh_ss = aggr.get_r_hh(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')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.net_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, trssmat, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
yss_before_tax_mat = household.get_y(
r_hh_ss, wss, bssmat_s, nssmat, p)
Css = aggr.get_C(cssmat, p, 'SS')
(total_tax_revenue, 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_ss, wss, bssmat_s, nssmat, bqssmat, cssmat, Yss, Lss, Kss,
factor, theta, etr_params_3D, p, 'SS')
Gss = fiscal.get_G_ss(
Yss, total_tax_revenue, agg_pension_outlays, TR_ss,
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
print('Foreign debt holdings = ', D_f_ss)
print('Foreign capital holdings = ', K_f_ss)
debt_service_f = fiscal.get_debt_service_f(r_hh_ss, D_f_ss)
RC = aggr.resource_constraint(
Yss, Css, Gss, I_d_ss, K_f_ss, new_borrowing_f, debt_service_f,
r_hh_ss, p)
print('resource constraint: ', RC)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(RC) >
p.mindist_SS):
print('Resource Constraint Difference:', RC)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
# Return dictionary of SS results
output = {'Kss': Kss, 'K_f_ss': K_f_ss, 'K_d_ss': K_d_ss,
'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'I_d_ss': I_d_ss, 'nssmat': nssmat,
'Yss': Yss, 'Dss': Dss, 'D_f_ss': D_f_ss,
'D_d_ss': D_d_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'yss_before_tax_mat': yss_before_tax_mat,
'bqssmat': bqssmat, 'TR_ss': TR_ss, 'trssmat': trssmat,
'Gss': Gss, 'total_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,
'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
def FOC_labor(r, w, b, b_splus1, n, bq, factor, tr, theta, chi_n, e, tau_c,
etr_params, mtrx_params, t, j, p, method):
r'''
Computes errors for the FOC for labor supply in the steady
state. This function is usually looped through over J, so it does
one lifetime income group at a time.
.. math::
w_t e_{j,s}\bigl(1 - \tau^{mtrx}_{s,t}\bigr)
(c_{j,s,t})^{-\sigma} = \chi^n_{s}
\biggl(\frac{b}{\tilde{l}}\biggr)\biggl(\frac{n_{j,s,t}}
{\tilde{l}}\biggr)^{\upsilon-1}\Biggl[1 -
\biggl(\frac{n_{j,s,t}}{\tilde{l}}\biggr)^\upsilon\Biggr]
^{\frac{1-\upsilon}{\upsilon}}
Args:
r (array_like): the real interest rate
w (array_like): the real wage rate
b (Numpy array): household savings
b_splus1 (Numpy array): household savings one period ahead
n (Numpy array): household labor supply
bq (Numpy array): household bequests received
factor (scalar): scaling factor converting model units to dollars
tr (Numpy array): government transfers to household
theta (Numpy array): social security replacement rate for each
lifetime income group
chi_n (Numpy array): utility weight on the disutility of labor
supply
e (Numpy array): effective labor units
tau_c (array_like): consumption tax rates
etr_params (Numpy array): parameters of the effective tax rate
functions
mtrx_params (Numpy array): parameters of the marginal tax rate
on labor income functions
t (int): model period
j (int): index of ability type
p (OG-USA Specifications object): model parameters
method (str): adjusts calculation dimensions based on 'SS' or
'TPI'
Returns:
FOC_error (Numpy array): error from FOC for labor supply
'''
if method == 'SS':
tau_payroll = p.tau_payroll[-1]
elif method == 'TPI_scalar': # for 1st donut ring only
tau_payroll = p.tau_payroll[0]
else:
length = r.shape[0]
tau_payroll = p.tau_payroll[t:t + length]
if method == 'TPI':
if b.ndim == 2:
r = r.reshape(r.shape[0], 1)
w = w.reshape(w.shape[0], 1)
tau_payroll = tau_payroll.reshape(tau_payroll.shape[0], 1)
taxes = tax.net_taxes(r, w, b, n, bq, factor, tr, theta, t, j, False,
method, e, etr_params, p)
cons = get_cons(r, w, b, b_splus1, n, bq, taxes, e, tau_c, p)
deriv = (1 - tau_payroll - tax.MTR_income(r, w, b, n, factor, False, e,
etr_params, mtrx_params, p))
FOC_error = (marg_ut_cons(cons, p.sigma) * (1 /
(1 + tau_c)) * w * deriv * e -
marg_ut_labor(n, chi_n, p))
return FOC_error
def FOC_savings(r, w, b, b_splus1, n, bq, factor, tr, theta, e, rho, tau_c,
etr_params, mtry_params, t, j, p, method):
r'''
Computes Euler errors for the FOC for savings in the steady state.
This function is usually looped through over J, so it does one
lifetime income group at a time.
.. math::
c_{j,s,t}^{-\sigma} = e^{-\sigma g_y}
\biggl[\chi^b_j\rho_s(b_{j,s+1,t+1})^{-\sigma} +
\beta_j\bigl(1 - \rho_s\bigr)\Bigl(1 + r_{t+1}
\bigl[1 - \tau^{mtry}_{s+1,t+1}\bigr]\Bigr)
(c_{j,s+1,t+1})^{-\sigma}\biggr]
Args:
r (array_like): the real interest rate
w (array_like): the real wage rate
b (Numpy array): household savings
b_splus1 (Numpy array): household savings one period ahead
b_splus2 (Numpy array): household savings two periods ahead
n (Numpy array): household labor supply
bq (Numpy array): household bequests received
factor (scalar): scaling factor converting model units to dollars
tr (Numpy array): government transfers to household
theta (Numpy array): social security replacement rate for each
lifetime income group
e (Numpy array): effective labor units
rho (Numpy array): mortality rates
tau_c (array_like): consumption tax rates
etr_params (Numpy array): parameters of the effective tax rate
functions
mtry_params (Numpy array): parameters of the marginal tax rate
on capital income functions
t (int): model period
j (int): index of ability type
p (OG-USA Specifications object): model parameters
method (str): adjusts calculation dimensions based on 'SS' or
'TPI'
Returns:
euler (Numpy array): Euler error from FOC for savings
'''
if j is not None:
chi_b = p.chi_b[j]
beta = p.beta[j]
else:
chi_b = p.chi_b
beta = p.beta
if method == 'SS':
h_wealth = p.h_wealth[-1]
m_wealth = p.m_wealth[-1]
p_wealth = p.p_wealth[-1]
else:
h_wealth = p.h_wealth[t]
m_wealth = p.m_wealth[t]
p_wealth = p.p_wealth[t]
taxes = tax.net_taxes(r, w, b, n, bq, factor, tr, theta, t, j, False,
method, e, etr_params, p)
cons = get_cons(r, w, b, b_splus1, n, bq, taxes, e, tau_c, p)
deriv = ((1 + r) - (r * tax.MTR_income(r, w, b, n, factor, True, e,
etr_params, mtry_params, p)) -
tax.MTR_wealth(b, h_wealth, m_wealth, p_wealth))
savings_ut = (rho * np.exp(-p.sigma * p.g_y) * chi_b *
b_splus1**(-p.sigma))
euler_error = np.zeros_like(n)
if n.shape[0] > 1:
euler_error[:-1] = (
marg_ut_cons(cons[:-1], p.sigma) * (1 / (1 + tau_c[:-1])) - beta *
(1 - rho[:-1]) * deriv[1:] * marg_ut_cons(cons[1:], p.sigma) *
(1 / (1 + tau_c[1:])) * np.exp(-p.sigma * p.g_y) - savings_ut[:-1])
euler_error[-1] = (marg_ut_cons(cons[-1], p.sigma) *
(1 / (1 + tau_c[-1])) - savings_ut[-1])
else:
euler_error[-1] = (marg_ut_cons(cons[-1], p.sigma) *
(1 / (1 + tau_c[-1])) - savings_ut[-1])
return euler_error