def test_MTR_wealth():
# Test marginal tax rate on wealth
b = np.array([0.2, 0.6, 0.8])
h_wealth = 3
p_wealth = 4
m_wealth = 5
tau_w_prime = tax.MTR_wealth(b, (h_wealth, p_wealth, m_wealth))
assert np.allclose(tau_w_prime,
np.array([1.91326531, 1.29757785, 1.09569028]))
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\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 tranfers 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]
else:
chi_b = p.chi_b
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.total_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])) - p.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
def test_MTR_wealth(b, p, expected):
# Test marginal tax rate on wealth
tau_w_prime = tax.MTR_wealth(b, p.h_wealth[:p.T], p.m_wealth[:p.T],
p.p_wealth[:p.T])
assert np.allclose(tau_w_prime, expected)