def SS_solver(bmat, nmat, r, BQ, T_H, factor, Y, p, client,
fsolve_flag=False):
'''
--------------------------------------------------------------------
Solves for the steady state distribution of capital, labor, as well
as w, r, T_H and the scaling factor, using a bisection method
similar to TPI.
--------------------------------------------------------------------
INPUTS:
b_guess_init = [S,J] array, initial guesses for savings
n_guess_init = [S,J] array, initial guesses for labor supply
wguess = scalar, initial guess for SS real wage rate
rguess = scalar, initial guess for SS real interest rate
T_Hguess = scalar, initial guess for lump sum transfer
factorguess = scalar, initial guess for scaling factor to dollars
chi_b = [J,] vector, chi^b_j, the utility weight on bequests
chi_n = [S,] vector, chi^n_s utility weight on labor supply
params = length X tuple, list of parameters
iterative_params = length X tuple, list of parameters that determine
the convergence of the while loop
tau_bq = [J,] vector, bequest tax rate
rho = [S,] vector, mortality rates by age
lambdas = [J,] vector, fraction of population with each ability type
omega = [S,] vector, stationary population weights
e = [S,J] array, effective labor units by age and ability type
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
euler_equation_solver()
aggr.get_K()
aggr.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
aggr.get_BQ()
tax.replacement_rate_vals()
aggr.revenue()
utils.convex_combo()
utils.pct_diff_func()
OBJECTS CREATED WITHIN FUNCTION:
b_guess = [S,] vector, initial guess at household savings
n_guess = [S,] vector, initial guess at household labor supply
b_s = [S,] vector, wealth enter period with
b_splus1 = [S,] vector, household savings
b_splus2 = [S,] vector, household savings one period ahead
BQ = scalar, aggregate bequests to lifetime income group
theta = scalar, replacement rate for social security benenfits
error1 = [S,] vector, errors from FOC for savings
error2 = [S,] vector, errors from FOC for labor supply
tax1 = [S,] vector, total income taxes paid
cons = [S,] vector, household consumption
OBJECTS CREATED WITHIN FUNCTION - SMALL OPEN ONLY
Bss = scalar, aggregate household wealth in the steady state
BIss = scalar, aggregate household net investment in the steady state
RETURNS: solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
OUTPUT: None
--------------------------------------------------------------------
'''
# Rename the inputs
if not p.budget_balance:
if not p.baseline_spending:
Y = T_H / p.alpha_T[-1]
if p.small_open:
r = p.hh_r[-1]
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag:
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, T_H, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, T_H, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_hh,
new_w, new_T_H, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
# bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
# nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
if not p.baseline_spending:
T_H = utils.convex_combo(new_T_H, T_H, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_T_H, T_H)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absolute difference
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[abs(new_Y - Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
print('Iteration: %02d' % iteration, ' Distance: ', dist)
'''
------------------------------------------------------------------------
Generate the SS values of variables, including euler errors
------------------------------------------------------------------------
'''
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
if p.budget_balance:
r_hh_ss = rss
Dss = 0.0
else:
Dss = p.debt_ratio_ss * Y
Lss = aggr.get_L(nssmat, p, 'SS')
Bss = aggr.get_K(bssmat_splus1, p, 'SS', False)
K_demand_open_ss = firm.get_K(Lss, p.firm_r[-1], p, 'SS')
D_f_ss = p.zeta_D[-1] * Dss
D_d_ss = Dss - D_f_ss
K_d_ss = Bss - D_d_ss
if not p.small_open:
K_f_ss = p.zeta_K[-1] * (K_demand_open_ss - Bss + D_d_ss)
Kss = K_f_ss + K_d_ss
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
else:
K_d_ss = Bss - D_d_ss
K_f_ss = K_demand_open_ss - Bss + D_d_ss
Kss = K_f_ss + K_d_ss
InvestmentPlaceholder = np.zeros(bssmat_splus1.shape)
Iss = aggr.get_I(InvestmentPlaceholder, Kss, Kss, p, 'SS')
BIss = aggr.get_I(bssmat_splus1, Bss, Bss, p, 'BI_SS')
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
r_hh_ss = aggr.get_r_hh(rss, r_gov_ss, Kss, Dss)
wss = new_w
BQss = new_BQ
factor_ss = factor
T_Hss = T_H
bqssmat = household.get_bq(BQss, None, p, 'SS')
Yss = firm.get_Y(Kss, Lss, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.total_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, T_Hss, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
yss_before_tax_mat = r_hh_ss * bssmat_s + wss * p.e * nssmat
Css = aggr.get_C(cssmat, p, 'SS')
(total_revenue_ss, T_Iss, T_Pss, T_BQss, T_Wss, T_Css,
business_revenue) =\
aggr.revenue(r_hh_ss, wss, bssmat_s, nssmat, bqssmat, cssmat,
Yss, Lss, Kss, factor, theta, etr_params_3D, p,
'SS')
debt_service_ss = r_gov_ss * Dss
new_borrowing = Dss * ((1 + p.g_n_ss) * np.exp(p.g_y) - 1)
# government spends such that it expands its debt at the same rate as GDP
if p.budget_balance:
Gss = 0.0
else:
Gss = total_revenue_ss + new_borrowing - (T_Hss + debt_service_ss)
print('G components = ', new_borrowing, T_Hss, debt_service_ss)
# Compute total investment (not just domestic)
Iss_total = ((1 + p.g_n_ss) * np.exp(p.g_y) - 1 + p.delta) * Kss
# solve resource constraint
# net foreign borrowing
print('Foreign debt holdings = ', D_f_ss)
print('Foreign capital holdings = ', K_f_ss)
new_borrowing_f = D_f_ss * (np.exp(p.g_y) * (1 + p.g_n_ss) - 1)
debt_service_f = D_f_ss * r_hh_ss
RC = aggr.resource_constraint(Yss, Css, Gss, I_d_ss, K_f_ss,
new_borrowing_f, debt_service_f, r_hh_ss,
p)
print('resource constraint: ', RC)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(RC) >
p.mindist_SS):
print('Resource Constraint Difference:', RC)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
'''
------------------------------------------------------------------------
Return dictionary of SS results
------------------------------------------------------------------------
'''
output = {'Kss': Kss, 'K_f_ss': K_f_ss, 'K_d_ss': K_d_ss,
'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'I_d_ss': I_d_ss, 'nssmat': nssmat,
'Yss': Yss, 'Dss': Dss, 'D_f_ss': D_f_ss,
'D_d_ss': D_d_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'yss_before_tax_mat': yss_before_tax_mat,
'bqssmat': bqssmat, 'T_Hss': T_Hss, 'Gss': Gss,
'total_revenue_ss': total_revenue_ss,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Iss,
'T_Pss': T_Pss, 'T_BQss': T_BQss, 'T_Wss': T_Wss,
'T_Css': T_Css, 'euler_savings': euler_savings,
'debt_service_f': debt_service_f,
'new_borrowing_f': new_borrowing_f,
'debt_service_ss': debt_service_ss,
'new_borrowing': new_borrowing,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': RC,
'etr_ss': etr_ss, 'mtrx_ss': mtrx_ss, 'mtry_ss': mtry_ss}
return output
def test_constraint_checker_SS(bssmat, nssmat, cssmat, ltilde):
household.constraint_checker_SS(bssmat, nssmat, cssmat, ltilde)
assert True
def SS_solver(bmat, nmat, r, BQ, TR, factor, Y, p, client,
fsolve_flag=False):
'''
Solves for the steady state distribution of capital, labor, as well
as w, r, TR and the scaling factor, using functional iteration.
Args:
bmat (Numpy array): initial guess at savings, size = SxJ
nmat (Numpy array): initial guess at labor supply, size = SxJ
r (scalar): real interest rate
BQ (array_like): aggregate bequest amount(s)
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
Y (scalar): real GDP
p (OG-USA Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with steady state solution
results
'''
# Rename the inputs
if not p.budget_balance:
if not p.baseline_spending:
Y = TR / p.alpha_T[-1]
if p.small_open:
r = p.hh_r[-1]
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag:
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, TR, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, TR, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_hh,
new_w, new_TR, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
# bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
# nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
if not p.baseline_spending:
TR = utils.convex_combo(new_TR, TR, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_TR, TR)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absolute difference
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[abs(new_Y - Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
print('Iteration: %02d' % iteration, ' Distance: ', dist)
# Generate the SS values of variables, including euler errors
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
if p.budget_balance:
r_hh_ss = rss
Dss = 0.0
else:
Dss = p.debt_ratio_ss * Y
Lss = aggr.get_L(nssmat, p, 'SS')
Bss = aggr.get_B(bssmat_splus1, p, 'SS', False)
K_demand_open_ss = firm.get_K(Lss, p.firm_r[-1], p, 'SS')
D_f_ss = p.zeta_D[-1] * Dss
D_d_ss = Dss - D_f_ss
K_d_ss = Bss - D_d_ss
if not p.small_open:
K_f_ss = p.zeta_K[-1] * (K_demand_open_ss - Bss + D_d_ss)
Kss = K_f_ss + K_d_ss
# Note that implicity in this computation is that immigrants'
# wealth is all in the form of private capital
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
else:
K_d_ss = Bss - D_d_ss
K_f_ss = K_demand_open_ss - Bss + D_d_ss
Kss = K_f_ss + K_d_ss
InvestmentPlaceholder = np.zeros(bssmat_splus1.shape)
Iss = aggr.get_I(InvestmentPlaceholder, Kss, Kss, p, 'SS')
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, 'SS')
r_hh_ss = aggr.get_r_hh(rss, r_gov_ss, Kss, Dss)
wss = new_w
BQss = new_BQ
factor_ss = factor
TR_ss = TR
bqssmat = household.get_bq(BQss, None, p, 'SS')
trssmat = household.get_tr(TR_ss, None, p, 'SS')
Yss = firm.get_Y(Kss, Lss, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.total_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, trssmat, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
yss_before_tax_mat = r_hh_ss * bssmat_s + wss * p.e * nssmat
Css = aggr.get_C(cssmat, p, 'SS')
(total_revenue_ss, T_Iss, T_Pss, T_BQss, T_Wss, T_Css,
business_revenue) =\
aggr.revenue(r_hh_ss, wss, bssmat_s, nssmat, bqssmat, cssmat,
Yss, Lss, Kss, factor, theta, etr_params_3D, p,
'SS')
debt_service_ss = r_gov_ss * Dss
new_borrowing = Dss * ((1 + p.g_n_ss) * np.exp(p.g_y) - 1)
# government spends such that it expands its debt at the same rate as GDP
if p.budget_balance:
Gss = 0.0
else:
Gss = total_revenue_ss + new_borrowing - (TR_ss + debt_service_ss)
print('G components = ', new_borrowing, TR_ss, debt_service_ss)
# Compute total investment (not just domestic)
Iss_total = ((1 + p.g_n_ss) * np.exp(p.g_y) - 1 + p.delta) * Kss
# solve resource constraint
# net foreign borrowing
print('Foreign debt holdings = ', D_f_ss)
print('Foreign capital holdings = ', K_f_ss)
new_borrowing_f = D_f_ss * (np.exp(p.g_y) * (1 + p.g_n_ss) - 1)
debt_service_f = D_f_ss * r_hh_ss
RC = aggr.resource_constraint(Yss, Css, Gss, I_d_ss, K_f_ss,
new_borrowing_f, debt_service_f, r_hh_ss,
p)
print('resource constraint: ', RC)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(RC) >
p.mindist_SS):
print('Resource Constraint Difference:', RC)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
# Return dictionary of SS results
output = {'Kss': Kss, 'K_f_ss': K_f_ss, 'K_d_ss': K_d_ss,
'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'I_d_ss': I_d_ss, 'nssmat': nssmat,
'Yss': Yss, 'Dss': Dss, 'D_f_ss': D_f_ss,
'D_d_ss': D_d_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'yss_before_tax_mat': yss_before_tax_mat,
'bqssmat': bqssmat, 'TR_ss': TR_ss, 'trssmat': trssmat,
'Gss': Gss, 'total_revenue_ss': total_revenue_ss,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Iss,
'T_Pss': T_Pss, 'T_BQss': T_BQss, 'T_Wss': T_Wss,
'T_Css': T_Css, 'euler_savings': euler_savings,
'debt_service_f': debt_service_f,
'new_borrowing_f': new_borrowing_f,
'debt_service_ss': debt_service_ss,
'new_borrowing': new_borrowing,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': RC,
'etr_ss': etr_ss, 'mtrx_ss': mtrx_ss, 'mtry_ss': mtry_ss}
return output
def SS_solver(bmat, nmat, r, BQ, T_H, factor, Y, p, client,
fsolve_flag=False):
'''
--------------------------------------------------------------------
Solves for the steady state distribution of capital, labor, as well
as w, r, T_H and the scaling factor, using a bisection method
similar to TPI.
--------------------------------------------------------------------
INPUTS:
b_guess_init = [S,J] array, initial guesses for savings
n_guess_init = [S,J] array, initial guesses for labor supply
wguess = scalar, initial guess for SS real wage rate
rguess = scalar, initial guess for SS real interest rate
T_Hguess = scalar, initial guess for lump sum transfer
factorguess = scalar, initial guess for scaling factor to dollars
chi_b = [J,] vector, chi^b_j, the utility weight on bequests
chi_n = [S,] vector, chi^n_s utility weight on labor supply
params = length X tuple, list of parameters
iterative_params = length X tuple, list of parameters that determine
the convergence of the while loop
tau_bq = [J,] vector, bequest tax rate
rho = [S,] vector, mortality rates by age
lambdas = [J,] vector, fraction of population with each ability type
omega = [S,] vector, stationary population weights
e = [S,J] array, effective labor units by age and ability type
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
euler_equation_solver()
aggr.get_K()
aggr.get_L()
firm.get_Y()
firm.get_r()
firm.get_w()
aggr.get_BQ()
tax.replacement_rate_vals()
aggr.revenue()
utils.convex_combo()
utils.pct_diff_func()
OBJECTS CREATED WITHIN FUNCTION:
b_guess = [S,] vector, initial guess at household savings
n_guess = [S,] vector, initial guess at household labor supply
b_s = [S,] vector, wealth enter period with
b_splus1 = [S,] vector, household savings
b_splus2 = [S,] vector, household savings one period ahead
BQ = scalar, aggregate bequests to lifetime income group
theta = scalar, replacement rate for social security benenfits
error1 = [S,] vector, errors from FOC for savings
error2 = [S,] vector, errors from FOC for labor supply
tax1 = [S,] vector, total income taxes paid
cons = [S,] vector, household consumption
OBJECTS CREATED WITHIN FUNCTION - SMALL OPEN ONLY
Bss = scalar, aggregate household wealth in the steady state
BIss = scalar, aggregate household net investment in the steady state
RETURNS: solutions = steady state values of b, n, w, r, factor,
T_H ((2*S*J+4)x1 array)
OUTPUT: None
--------------------------------------------------------------------
'''
# Rename the inputs
if not p.budget_balance:
if not p.baseline_spending:
Y = T_H / p.alpha_T[-1]
if p.small_open:
r = p.hh_r[-1]
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag:
maxiter_ss = 1
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y and factor
if p.budget_balance:
outer_loop_vars = (bmat, nmat, r, BQ, T_H, factor)
else:
outer_loop_vars = (bmat, nmat, r, BQ, Y, T_H, factor)
(euler_errors, new_bmat, new_nmat, new_r, new_r_gov, new_r_hh,
new_w, new_T_H, new_Y, new_factor, new_BQ,
average_income_model) =\
inner_loop(outer_loop_vars, p, client)
r = utils.convex_combo(new_r, r, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
# bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
# nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
if p.budget_balance:
T_H = utils.convex_combo(new_T_H, T_H, nu_ss)
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_T_H, T_H)] +
[utils.pct_diff_func(new_factor, factor)]).max()
else:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[utils.pct_diff_func(new_Y, Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absoluate difference
dist = np.array([utils.pct_diff_func(new_r, r)] +
list(utils.pct_diff_func(new_BQ, BQ)) +
[abs(new_Y - Y)] +
[utils.pct_diff_func(new_factor,
factor)]).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu_ss /= 2.0
print('New value of nu:', nu_ss)
iteration += 1
print('Iteration: %02d' % iteration, ' Distance: ', dist)
'''
------------------------------------------------------------------------
Generate the SS values of variables, including euler errors
------------------------------------------------------------------------
'''
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = r
r_gov_ss = fiscal.get_r_gov(rss, p)
if p.budget_balance:
r_hh_ss = rss
debt_ss = 0.0
else:
debt_ss = p.debt_ratio_ss * Y
Lss = aggr.get_L(nssmat, p, 'SS')
if not p.small_open:
Bss = aggr.get_K(bssmat_splus1, p, 'SS', False)
Kss = Bss - debt_ss
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, 'SS')
else:
# Compute capital (K) and wealth (B) separately
Kss = firm.get_K(Lss, p.firm_r[-1], p, 'SS')
InvestmentPlaceholder = np.zeros(bssmat_splus1.shape)
Iss = aggr.get_I(InvestmentPlaceholder, Kss, Kss, p, 'SS')
Bss = aggr.get_K(bssmat_splus1, p, 'SS', False)
BIss = aggr.get_I(bssmat_splus1, Bss, Bss, p, 'BI_SS')
if p.budget_balance:
r_hh_ss = rss
else:
r_hh_ss = aggr.get_r_hh(rss, r_gov_ss, Kss, debt_ss)
if p.small_open:
r_hh_ss = p.hh_r[-1]
wss = new_w
BQss = new_BQ
factor_ss = factor
T_Hss = T_H
bqssmat = household.get_bq(BQss, None, p, 'SS')
Yss = firm.get_Y(Kss, Lss, p, 'SS')
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
etr_params_3D = np.tile(np.reshape(
p.etr_params[-1, :, :], (p.S, 1, p.etr_params.shape[2])), (1, p.J, 1))
mtrx_params_3D = np.tile(np.reshape(
p.mtrx_params[-1, :, :], (p.S, 1, p.mtrx_params.shape[2])),
(1, p.J, 1))
mtry_params_3D = np.tile(np.reshape(
p.mtry_params[-1, :, :], (p.S, 1, p.mtry_params.shape[2])),
(1, p.J, 1))
mtry_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, True,
p.e, etr_params_3D, mtry_params_3D, p)
mtrx_ss = tax.MTR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, False,
p.e, etr_params_3D, mtrx_params_3D, p)
etr_ss = tax.ETR_income(r_hh_ss, wss, bssmat_s, nssmat, factor, p.e,
etr_params_3D, p)
taxss = tax.total_taxes(r_hh_ss, wss, bssmat_s, nssmat, bqssmat,
factor_ss, T_Hss, theta, None, None, False,
'SS', p.e, etr_params_3D, p)
cssmat = household.get_cons(r_hh_ss, wss, bssmat_s, bssmat_splus1,
nssmat, bqssmat, taxss,
p.e, p.tau_c[-1, :, :], p)
Css = aggr.get_C(cssmat, p, 'SS')
(total_revenue_ss, T_Iss, T_Pss, T_BQss, T_Wss, T_Css,
business_revenue) =\
aggr.revenue(r_hh_ss, wss, bssmat_s, nssmat, bqssmat, cssmat,
Yss, Lss, Kss, factor, theta, etr_params_3D, p,
'SS')
debt_service_ss = r_gov_ss * p.debt_ratio_ss * Yss
new_borrowing = p.debt_ratio_ss * Yss * ((1 + p.g_n_ss) *
np.exp(p.g_y) - 1)
# government spends such that it expands its debt at the same rate as GDP
if p.budget_balance:
Gss = 0.0
else:
Gss = total_revenue_ss + new_borrowing - (T_Hss + debt_service_ss)
print('G components = ', new_borrowing, T_Hss, debt_service_ss)
# Compute total investment (not just domestic)
Iss_total = p.delta * Kss
# solve resource constraint
if p.small_open:
# include term for current account
resource_constraint = (Yss + new_borrowing - (Css + BIss + Gss)
+ (p.hh_r[-1] * Bss -
(p.delta + p.firm_r[-1]) *
Kss - debt_service_ss))
print('Yss= ', Yss, '\n', 'Css= ', Css, '\n', 'Bss = ', Bss,
'\n', 'BIss = ', BIss, '\n', 'Kss = ', Kss, '\n', 'Iss = ',
Iss, '\n', 'Lss = ', Lss, '\n', 'T_H = ', T_H, '\n',
'Gss= ', Gss)
print('D/Y:', debt_ss / Yss, 'T/Y:', T_Hss / Yss, 'G/Y:',
Gss / Yss, 'Rev/Y:', total_revenue_ss / Yss,
'Int payments to GDP:', (r_gov_ss * debt_ss) / Yss)
print('resource constraint: ', resource_constraint)
else:
resource_constraint = Yss - (Css + Iss + Gss)
print('Yss= ', Yss, '\n', 'Gss= ', Gss, '\n', 'Css= ', Css, '\n',
'Kss = ', Kss, '\n', 'Iss = ', Iss, '\n', 'Lss = ', Lss,
'\n', 'Debt service = ', debt_service_ss)
print('D/Y:', debt_ss / Yss, 'T/Y:', T_Hss / Yss, 'G/Y:',
Gss / Yss, 'Rev/Y:', total_revenue_ss / Yss, 'business rev/Y: ',
business_revenue / Yss, 'Int payments to GDP:',
(r_gov_ss * debt_ss) / Yss)
print('Check SS budget: ', Gss - (np.exp(p.g_y) *
(1 + p.g_n_ss) - 1 - r_gov_ss)
* debt_ss - total_revenue_ss + T_Hss)
print('resource constraint: ', resource_constraint)
if Gss < 0:
print('Steady state government spending is negative to satisfy'
+ ' budget')
if ENFORCE_SOLUTION_CHECKS and (np.absolute(resource_constraint) >
p.mindist_SS):
print('Resource Constraint Difference:', resource_constraint)
err = 'Steady state aggregate resource constraint not satisfied'
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[:p.S, :]
euler_labor_leisure = euler_errors[p.S:, :]
print('Maximum error in labor FOC = ',
np.absolute(euler_labor_leisure).max())
print('Maximum error in savings FOC = ',
np.absolute(euler_savings).max())
'''
------------------------------------------------------------------------
Return dictionary of SS results
------------------------------------------------------------------------
'''
output = {'Kss': Kss, 'Bss': Bss, 'Lss': Lss, 'Css': Css, 'Iss': Iss,
'Iss_total': Iss_total, 'nssmat': nssmat, 'Yss': Yss,
'Dss': debt_ss, 'wss': wss, 'rss': rss,
'r_gov_ss': r_gov_ss, 'r_hh_ss': r_hh_ss, 'theta': theta,
'BQss': BQss, 'factor_ss': factor_ss, 'bssmat_s': bssmat_s,
'cssmat': cssmat, 'bssmat_splus1': bssmat_splus1,
'bqssmat': bqssmat, 'T_Hss': T_Hss, 'Gss': Gss,
'total_revenue_ss': total_revenue_ss,
'business_revenue': business_revenue,
'IITpayroll_revenue': T_Iss,
'T_Pss': T_Pss, 'T_BQss': T_BQss, 'T_Wss': T_Wss,
'T_Css': T_Css, 'euler_savings': euler_savings,
'euler_labor_leisure': euler_labor_leisure,
'resource_constraint_error': resource_constraint,
'etr_ss': etr_ss, 'mtrx_ss': mtrx_ss, 'mtry_ss': mtry_ss}
return output