def test_ETR_wealth():
# Test wealth tax computation
b = np.array([0.1, 0.5, 0.9])
h_wealth = 2
p_wealth = 3
m_wealth = 4
tau_w_prime = tax.ETR_wealth(b, (h_wealth, p_wealth, m_wealth))
assert np.allclose(tau_w_prime, np.array([0.14285714, 0.6, 0.93103448]))
def test_ETR_wealth(b, p, expected):
# Test wealth tax computation
tau_w = tax.ETR_wealth(b, p.h_wealth[:p.T], p.m_wealth[:p.T],
p.p_wealth[:p.T])
assert np.allclose(tau_w, expected)
def revenue(r, w, b, n, bq, c, Y, L, K, factor, theta, etr_params,
p, method):
r'''
Calculate aggregate tax revenue.
.. math::
R_{t} = \sum_{s=E}^{E+S}\sum_{j=0}^{J}\omega_{s,t}\lambda_{j}(T_{j,s,t} + \tau^{p}_{t}w_{t}e_{j,s}n_{j,s,t} - \theta_{j}w_{t} + \tau^{bq}bq_{j,s,t} + \tau^{c}_{s,t}c_{j,s,t} + \tau^{w}_{t}b_{j,s,t}) + \tau^{b}_{t}(Y_{t}-w_{t}L_{t}) - \tau^{b}_{t}\delta^{\tau}_{t}K^{\tau}_{t}
Args:
r (array_like): the real interest rate
w (array_like): the real wage rate
b (Numpy array): household savings
n (Numpy array): household labor supply
bq (Numpy array): household bequests received
c (Numpy array): household consumption
Y (array_like): aggregate output
L (array_like): aggregate labor
K (array_like): aggregate capital
factor (scalar): factor (scalar): scaling factor converting
model units to dollars
theta (Numpy array): social security replacement rate for each
lifetime income group
etr_params (Numpy array): paramters of the effective tax rate
functions
p (OG-USA Specifications object): model parameters
method (str): adjusts calculation dimensions based on 'SS' or
'TPI'
Returns:
REVENUE (array_like): aggregate tax revenue
T_I (array_like): aggregate income tax revenue
T_P (array_like): aggregate net payroll tax revenue, revenues
minus social security benefits paid
T_BQ (array_like): aggregate bequest tax revenue
T_W (array_like): aggregate wealth tax revenue
T_C (array_like): aggregate consumption tax revenue
business_revenue (array_like): aggregate business tax revenue
'''
if method == 'SS':
I = r * b + w * p.e * n
T_I = np.zeros_like(I)
T_I = tax.ETR_income(r, w, b, n, factor, p.e, etr_params, p) * I
T_P = p.tau_payroll[-1] * w * p.e * n
T_P[p.retire[-1]:] -= theta * w
T_W = (tax.ETR_wealth(b, p.h_wealth[-1], p.m_wealth[-1],
p.p_wealth[-1]) * b)
T_BQ = p.tau_bq[-1] * bq
T_C = p.tau_c[-1, :, :] * c
business_revenue = tax.get_biz_tax(w, Y, L, K, p, method)
REVENUE = ((np.transpose(p.omega_SS * p.lambdas) *
(T_I + T_P + T_BQ + T_W + T_C)).sum() +
business_revenue)
elif method == 'TPI':
r_array = utils.to_timepath_shape(r)
w_array = utils.to_timepath_shape(w)
I = r_array * b + w_array * n * p.e
T_I = np.zeros_like(I)
T_I = tax.ETR_income(r_array, w_array, b, n, factor, p.e,
etr_params, p) * I
T_P = p.tau_payroll[:p.T].reshape(p.T, 1, 1) * w_array * n * p.e
for t in range(T_P.shape[0]):
T_P[t, p.retire[t]:, :] -= (theta.reshape(1, p.J) *
p.replacement_rate_adjust[t] *
w_array[t])
T_W = (tax.ETR_wealth(b, p.h_wealth[:p.T].reshape(p.T, 1, 1),
p.m_wealth[:p.T].reshape(p.T, 1, 1),
p.p_wealth[:p.T].reshape(p.T, 1, 1)) * b)
T_BQ = p.tau_bq[:p.T].reshape(p.T, 1, 1) * bq
T_C = p.tau_c[:p.T, :, :] * c
business_revenue = tax.get_biz_tax(w, Y, L, K, p, method)
REVENUE = ((((np.squeeze(p.lambdas)) *
np.tile(np.reshape(p.omega[:p.T, :], (p.T, p.S, 1)),
(1, 1, p.J)))
* (T_I + T_P + T_BQ + T_W + T_C)).sum(1).sum(1) +
business_revenue)
return REVENUE, T_I, T_P, T_BQ, T_W, T_C, business_revenue
def revenue(r, w, b, n, bq, c, Y, L, K, factor, theta, etr_params, p, method):
'''
Gives lump sum transfer value.
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] array, bequest amounts
factor = scalar, model income scaling factor
params = length 12 tuple, (e, lambdas, omega, method, etr_params,
theta, tau_bq, tau_payroll, h_wealth,
p_wealth, m_wealth, retire, T, S, J)
e = [T,S,J] array, effective labor units
lambdas = [J,] vector, population weights by lifetime income group
omega = [T,S] array, population weights by age
method = string, 'SS' or 'TPI'
etr_params = [T,S,J] array, effective tax rate function parameters
tax_func_types = string, type of tax function used
theta = [J,] vector, replacement rate values by lifetime
income group
tau_bq = scalar, bequest tax rate
h_wealth = scalar, wealth tax function parameter
p_wealth = scalar, wealth tax function parameter
m_wealth = scalar, wealth tax function parameter
tau_payroll = scalar, payroll tax rate
retire = integer, retirement age
T = integer, number of periods in transition path
S = integer, number of age groups
J = integer, number of lifetime income groups
Functions called:
ETR_income
ETR_wealth
Objects in function:
I = [T,S,J] array, total income
T_I = [T,S,J] array, total income taxes
T_P = [T,S,J] array, total payroll taxes
T_W = [T,S,J] array, total wealth taxes
T_BQ = [T,S,J] array, total bequest taxes
T_H = [T,] vector, lump sum transfer amount(s)
Returns: T_H
'''
if method == 'SS':
I = r * b + w * p.e * n
T_I = np.zeros_like(I)
T_I = tax.ETR_income(r, w, b, n, factor, p.e, etr_params, p) * I
T_P = p.tau_payroll[-1] * w * p.e * n
T_P[p.retire[-1]:] -= theta * w
T_W = (
tax.ETR_wealth(b, p.h_wealth[-1], p.m_wealth[-1], p.p_wealth[-1]) *
b)
T_BQ = p.tau_bq[-1] * bq
T_C = p.tau_c[-1, :, :] * c
business_revenue = tax.get_biz_tax(w, Y, L, K, p, method)
REVENUE = ((np.transpose(p.omega_SS * p.lambdas) *
(T_I + T_P + T_BQ + T_W + T_C)).sum() + business_revenue)
elif method == 'TPI':
r_array = utils.to_timepath_shape(r, p)
w_array = utils.to_timepath_shape(w, p)
I = r_array * b + w_array * n * p.e
T_I = np.zeros_like(I)
T_I = tax.ETR_income(r_array, w_array, b, n, factor, p.e, etr_params,
p) * I
T_P = p.tau_payroll[:p.T].reshape(p.T, 1, 1) * w_array * n * p.e
for t in range(T_P.shape[0]):
T_P[t,
p.retire[t]:, :] -= (theta.reshape(1, p.J) *
p.replacement_rate_adjust[t] * w_array[t])
T_W = (tax.ETR_wealth(
b, p.h_wealth[:p.T].reshape(p.T, 1, 1), p.m_wealth[:p.T].reshape(
p.T, 1, 1), p.p_wealth[:p.T].reshape(p.T, 1, 1)) * b)
T_BQ = p.tau_bq[:p.T].reshape(p.T, 1, 1) * bq
T_C = p.tau_c[:p.T, :, :] * c
business_revenue = tax.get_biz_tax(w, Y, L, K, p, method)
REVENUE = ((((np.squeeze(p.lambdas)) *
np.tile(np.reshape(p.omega[:p.T, :], (p.T, p.S, 1)),
(1, 1, p.J))) *
(T_I + T_P + T_BQ + T_W + T_C)).sum(1).sum(1) +
business_revenue)
return REVENUE, T_I, T_P, T_BQ, T_W, T_C, business_revenue