def firstdoughnutring(guesses, r, w, bq, tr, theta, factor, ubi, j, initial_b,
p):
'''
Solves the first entries of the upper triangle of the twist doughnut. This
is separate from the main TPI function because the values of b and n are
scalars, so it is easier to just have a separate function for these cases.
Args:
guesses (Numpy array): initial guesses for b and n, length 2
r (scalar): real interest rate
w (scalar): real wage rate
bq (scalar): bequest amounts by age
tr (scalar): government transfer amount
theta (Numpy array): retirement replacement rates, length J
factor (scalar): scaling factor converting model units to dollars
ubi (scalar): individual UBI credit to household s=E+S of type j in
period 0
j (int): index of ability type
initial_b (Numpy array): SxJ matrix, savings of agents alive at T=0
p (OG-Core Specifications object): model parameters
Returns:
euler errors (Numpy array): errors from first order conditions,
length 2
'''
b_splus1 = float(guesses[0])
n = float(guesses[1])
b_s = float(initial_b[-2, j])
# Find errors from FOC for savings and FOC for labor supply
error1 = household.FOC_savings(np.array([r]), np.array([w]), b_s,
np.array([b_splus1]), np.array([n]),
np.array([bq]), factor, np.array([tr]),
np.array([ubi]), theta[j],
p.e[-1, j], p.rho[-1],
np.array([p.tau_c[0, -1,
j]]), p.etr_params[0,
-1, :],
p.mtry_params[0, -1, :], None, j, p,
'TPI_scalar')
error2 = household.FOC_labor(np.array([r]), np.array([w]), b_s, b_splus1,
np.array([n]), np.array([bq]), factor,
np.array([tr]), np.array([ubi]), theta[j],
p.chi_n[-1], p.e[-1, j],
np.array([p.tau_c[0, -1, j]]),
p.etr_params[0, -1, :], p.mtrx_params[0,
-1, :],
None, j, p, 'TPI_scalar')
if n <= 0 or n >= 1:
error2 += 1e12
if b_splus1 <= 0:
error1 += 1e12
return [np.squeeze(error1)] + [np.squeeze(error2)]
def test_FOC_labor(model_vars, params, expected):
# Test FOC condition for household's choice of labor supply
(r, w, b, b_splus1, n, bq, factor, tr, ubi, theta, tau_c, etr_params,
mtrx_params, t, j, method) = model_vars
test_value = household.FOC_labor(r, w, b, b_splus1, n, bq, factor, tr, ubi,
theta, params.chi_n, params.e[:, j],
tau_c, etr_params, mtrx_params, t, j,
params, method)
assert np.allclose(test_value, 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
ubi (vector): universal basic income (UBI) payment, length S
factor (scalar): scaling factor converting model units to dollars
p (OG-Core Specifications object): model parameters
Returns:
errros (Numpy array): errors from FOCs, length 2S
'''
(r, w, bq, tr, ubi, 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, ubi, 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,
ubi, 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, ubi, 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 twist_doughnut(guesses, r, w, bq, tr, theta, factor, ubi, j, s, t, tau_c,
etr_params, mtrx_params, mtry_params, initial_b, p):
'''
Solves the upper triangle of time path iterations. These are the agents who
are alive at time T=0 so that we do not solve for their full lifetime (so
of their life was before the model begins).
Args:
guesses (Numpy array): initial guesses for b and n, length 2s
r (scalar): real interest rate
w (scalar): real wage rate
bq (Numpy array): bequest amounts by age, length s
tr (scalar): government transfer amount
theta (Numpy array): retirement replacement rates, length J
factor (scalar): scaling factor converting model units to dollars
ubi (array): length remaining periods of life UBI payout to household
j (int): index of ability type
s (int): years of life remaining
t (int): model period
tau_c (Numpy array): consumption tax rates, size = sxJ
etr_params (Numpy array): ETR function parameters,
size = sxsxnum_params
mtrx_params (Numpy array): labor income MTR function parameters,
size = sxsxnum_params
mtry_params (Numpy array): capital income MTR function
parameters, size = sxsxnum_params
initial_b (Numpy array): savings of agents alive at T=0,
size = SxJ
p (OG-Core Specifications object): model parameters
Returns:
euler errors (Numpy array): errors from first order conditions,
length 2s
'''
length = int(len(guesses) / 2)
b_guess = np.array(guesses[:length])
n_guess = np.array(guesses[length:])
if length == p.S:
b_s = np.array([0] + list(b_guess[:-1]))
else:
b_s = np.array([(initial_b[-(s + 3), j])] + list(b_guess[:-1]))
b_splus1 = b_guess
w_s = w[t:t + length]
r_s = r[t:t + length]
n_s = n_guess
chi_n_s = p.chi_n[-length:]
e_s = p.e[-length:, j]
rho_s = p.rho[-length:]
error1 = household.FOC_savings(r_s, w_s, b_s, b_splus1, n_s, bq, factor,
tr, ubi, theta, e_s, rho_s, tau_c,
etr_params, mtry_params, t, j, p, 'TPI')
error2 = household.FOC_labor(r_s, w_s, b_s, b_splus1, n_s, bq, factor, tr,
ubi, theta, chi_n_s, e_s, tau_c, etr_params,
mtrx_params, t, j, p, 'TPI')
# Check and punish constraint violations
mask1 = n_guess < 0
error2[mask1] += 1e12
mask2 = n_guess > p.ltilde
error2[mask2] += 1e12
mask4 = b_guess <= 0
error2[mask4] += 1e12
mask5 = b_splus1 < 0
error2[mask5] += 1e12
return list(error1.flatten()) + list(error2.flatten())