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TPI.py
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TPI.py
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# imports
import numpy as np
import pickle
import scipy.optimize as opt
from dask import delayed, compute
import dask.multiprocessing
from ogcore import tax, utils, household, firm, fiscal
from ogcore import aggregates as aggr
from ogcore.constants import SHOW_RUNTIME
import os
import warnings
if not SHOW_RUNTIME:
warnings.simplefilter("ignore", RuntimeWarning)
"""
Set minimizer tolerance
"""
MINIMIZER_TOL = 1e-13
"""
Set flag for enforcement of solution check
"""
ENFORCE_SOLUTION_CHECKS = True
"""
A global future for the Parameters object for client workers.
This is scattered once and place at module scope, then used
by the client in the inner loop.
"""
scattered_p = None
def get_initial_SS_values(p):
"""
Get values of variables for the initial period and the steady state
equilibrium values.
Args:
p (OG-Core Specifications object): model parameters
Returns:
(tuple): initial period and steady state values:
* initial_values (tuple): initial period variable values,
(b_sinit, b_splus1init, factor, initial_b, initial_n)
* ss_vars (dictionary): dictionary with steady state
solution results
* theta (Numpy array): steady-state retirement replacement
rates, length J
* baseline_values (tuple): (TRbaseline, Gbaseline,
D0_baseline), lump sum transfer and government spending
amounts from the baseline model run
"""
baseline_ss = os.path.join(p.baseline_dir, "SS", "SS_vars.pkl")
ss_baseline_vars = utils.safe_read_pickle(baseline_ss)
factor = ss_baseline_vars["factor_ss"]
B0 = aggr.get_B(ss_baseline_vars["bssmat_splus1"], p, "SS", True)
initial_b = ss_baseline_vars["bssmat_splus1"] * (
ss_baseline_vars["Bss"] / B0
)
initial_n = ss_baseline_vars["nssmat"]
TRbaseline = None
Gbaseline = None
Ig_baseline = None
if p.baseline_spending:
baseline_tpi = os.path.join(p.baseline_dir, "TPI", "TPI_vars.pkl")
tpi_baseline_vars = utils.safe_read_pickle(baseline_tpi)
TRbaseline = tpi_baseline_vars["TR"]
Gbaseline = tpi_baseline_vars["G"]
Ig_baseline = tpi_baseline_vars["I_g"]
if p.baseline:
ss_vars = ss_baseline_vars
else:
reform_ss_path = os.path.join(p.output_base, "SS", "SS_vars.pkl")
ss_vars = utils.safe_read_pickle(reform_ss_path)
theta = ss_vars["theta"]
"""
------------------------------------------------------------------------
Set other parameters and initial values
------------------------------------------------------------------------
"""
# Get an initial distribution of wealth with the initial population
# distribution. When small_open=True, the value of K0 is used as a
# placeholder for first-period wealth
B0 = aggr.get_B(initial_b, p, "SS", True)
b_sinit = np.array(
list(np.zeros(p.J).reshape(1, p.J)) + list(initial_b[:-1])
)
b_splus1init = initial_b
# Intial gov't debt and capital stock must match that in the baseline
if not p.baseline:
baseline_tpi = os.path.join(p.baseline_dir, "TPI", "TPI_vars.pkl")
tpi_baseline_vars = utils.safe_read_pickle(baseline_tpi)
D0_baseline = tpi_baseline_vars["D"][0]
Kg0_baseline = tpi_baseline_vars["K_g"][0]
else:
D0_baseline = None
Kg0_baseline = None
initial_values = (B0, b_sinit, b_splus1init, factor, initial_b, initial_n)
baseline_values = (
TRbaseline,
Gbaseline,
Ig_baseline,
D0_baseline,
Kg0_baseline,
)
return initial_values, ss_vars, theta, baseline_values
def firstdoughnutring(
guesses, r, w, p_tilde, 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
p_tilde (scalar): composite good price
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]),
np.array([p_tilde]),
b_s,
np.array([b_splus1]),
np.array([n]),
np.array([bq]),
factor,
np.array([tr]),
np.array([ubi]),
theta[j],
p.rho[0, -1],
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]),
np.array([p_tilde]),
b_s,
b_splus1,
np.array([n]),
np.array([bq]),
factor,
np.array([tr]),
np.array([ubi]),
theta[j],
p.chi_n[0, -1],
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 twist_doughnut(
guesses,
r,
w,
p_tilde,
bq,
tr,
theta,
factor,
ubi,
j,
s,
t,
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 (list): initial guesses for b and n, length 2s
r (Numpy array): real interest rate
w (Numpy array): real wage rate
p_tilde (Numpy array): composite good price
bq (Numpy array): bequest amounts by age, length s
tr (Numpy array): government transfer amount
theta (Numpy array): retirement replacement rates, length J
factor (scalar): scaling factor converting model units to dollars
ubi (Numpy 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
etr_params (list): ETR function parameters,
list of lists with size = sxsxnum_params
mtrx_params (list): labor income MTR function parameters,
list of lists with size = sxsxnum_params
mtry_params (list): capital income MTR function
parameters, lists of lists with 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]
p_tilde_s = p_tilde[t : t + length]
n_s = n_guess
chi_n_s = np.diag(p.chi_n[t : t + p.S, :], max(p.S - length, 0))
rho_s = np.diag(p.rho[t : t + p.S, :], max(p.S - length, 0))
error1 = household.FOC_savings(
r_s,
w_s,
p_tilde_s,
b_s,
b_splus1,
n_s,
bq,
factor,
tr,
ubi,
theta,
rho_s,
etr_params,
mtry_params,
t,
j,
p,
"TPI",
)
error2 = household.FOC_labor(
r_s,
w_s,
p_tilde_s,
b_s,
b_splus1,
n_s,
bq,
factor,
tr,
ubi,
theta,
chi_n_s,
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())
def inner_loop(guesses, outer_loop_vars, initial_values, ubi, j, ind, p):
"""
Given path of economic aggregates and factor prices, solves
household problem. This has been termed the inner-loop (in
contrast to the outer fixed point loop that solves for GE factor
prices and economic aggregates).
Args:
guesses (tuple): initial guesses for b and n, (guesses_b,
guesses_n)
outer_loop_vars (tuple): values for factor prices and economic
aggregates used in household problem (r_p, r, w, p+m, BQ, TR,
theta)
r_p (Numpy array): real interest rate on household portfolio
r (Numpy array): real interest rate on private capital
w (Numpy array): real wage rate
p_m (Numpy array): output goods prices
BQ (array_like): aggregate bequest amounts
TR (Numpy array): lump sum transfer amount
theta (Numpy array): retirement replacement rates, length J
initial_values (tuple): initial period variable values,
(b_sinit, b_splus1init, factor, initial_b, initial_n,
D0_baseline)
ubi (array_like): T+S x S x J array time series of UBI transfers in
model units for each type-j age-s household in every period t
j (int): index of ability type
ind (Numpy array): integers from 0 to S-1
p (OG-Core Specifications object): model parameters
Returns:
(tuple): household solution results:
* euler_errors (Numpy array): errors from FOCs, size = Tx2S
* b_mat (Numpy array): savings amounts, size = TxS
* n_mat (Numpy array): labor supply amounts, size = TxS
"""
(K0, b_sinit, b_splus1init, factor, initial_b, initial_n) = initial_values
guesses_b, guesses_n = guesses
r_p, r, w, p_m, BQ, TR, theta = outer_loop_vars
# compute composite good price
p_i = (
np.tile(p.io_matrix.reshape(1, p.I, p.M), (p.T + p.S, 1, 1))
* np.tile(p_m.reshape(p.T + p.S, 1, p.M), (1, p.I, 1))
).sum(axis=2)
p_tilde = aggr.get_ptilde(p_i[:, :], p.tau_c[:, :], p.alpha_c, "TPI")
# compute bq
bq = household.get_bq(BQ, None, p, "TPI")
# compute tr
tr = household.get_tr(TR, None, p, "TPI")
# initialize arrays
b_mat = np.zeros((p.T + p.S, p.S))
n_mat = np.zeros((p.T + p.S, p.S))
euler_errors = np.zeros((p.T, 2 * p.S))
solutions = opt.root(
firstdoughnutring,
[guesses_b[0, -1], guesses_n[0, -1]],
args=(
r_p[0],
w[0],
p_tilde[0],
bq[0, -1, j],
tr[0, -1, j],
theta * p.replacement_rate_adjust[0],
factor,
ubi[0, -1, j],
j,
initial_b,
p,
),
method=p.FOC_root_method,
tol=MINIMIZER_TOL,
)
b_mat[0, -1], n_mat[0, -1] = solutions.x[0], solutions.x[1]
for s in range(p.S - 2): # Upper triangle
ind2 = np.arange(s + 2)
b_guesses_to_use = np.diag(guesses_b[: p.S, :], p.S - (s + 2))
n_guesses_to_use = np.diag(guesses_n[: p.S, :], p.S - (s + 2))
theta_to_use = theta[j] * p.replacement_rate_adjust[: p.S]
bq_to_use = np.diag(bq[: p.S, :, j], p.S - (s + 2))
tr_to_use = np.diag(tr[: p.S, :, j], p.S - (s + 2))
ubi_to_use = np.diag(ubi[: p.S, :, j], p.S - (s + 2))
num_params = len(p.etr_params[0][0])
temp_etr = [
[p.etr_params[t][p.S - s - 2 + t][i] for i in range(num_params)]
for t in range(s + 2)
]
etr_params_to_use = [
[temp_etr[i][j] for j in range(num_params)] for i in range(s + 2)
]
temp_mtrx = [
[p.mtrx_params[t][p.S - s - 2 + t][i] for i in range(num_params)]
for t in range(s + 2)
]
mtrx_params_to_use = [
[temp_mtrx[i][j] for j in range(num_params)] for i in range(s + 2)
]
temp_mtry = [
[p.mtry_params[t][p.S - s - 2 + t][i] for i in range(num_params)]
for t in range(s + 2)
]
mtry_params_to_use = [
[temp_mtry[i][j] for j in range(num_params)] for i in range(s + 2)
]
solutions = opt.root(
twist_doughnut,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(
r_p,
w,
p_tilde,
bq_to_use,
tr_to_use,
theta_to_use,
factor,
ubi_to_use,
j,
s,
0,
etr_params_to_use,
mtrx_params_to_use,
mtry_params_to_use,
initial_b,
p,
),
method=p.FOC_root_method,
tol=MINIMIZER_TOL,
)
b_vec = solutions.x[: int(len(solutions.x) / 2)]
b_mat[ind2, p.S - (s + 2) + ind2] = b_vec
n_vec = solutions.x[int(len(solutions.x) / 2) :]
n_mat[ind2, p.S - (s + 2) + ind2] = n_vec
for t in range(0, p.T):
b_guesses_to_use = 0.75 * np.diag(guesses_b[t : t + p.S, :])
n_guesses_to_use = np.diag(guesses_n[t : t + p.S, :])
theta_to_use = theta[j] * p.replacement_rate_adjust[t : t + p.S]
bq_to_use = np.diag(bq[t : t + p.S, :, j])
tr_to_use = np.diag(tr[t : t + p.S, :, j])
ubi_to_use = np.diag(ubi[t : t + p.S, :, j])
# initialize array of diagonal elements
num_params = len(p.etr_params[t][0])
etr_params_to_use = [
[p.etr_params[t + s][s][i] for i in range(num_params)]
for s in range(p.S)
]
mtrx_params_to_use = [
[p.mtrx_params[t + s][s][i] for i in range(num_params)]
for s in range(p.S)
]
mtry_params_to_use = [
[p.mtry_params[t + s][s][i] for i in range(num_params)]
for s in range(p.S)
]
solutions = opt.root(
twist_doughnut,
list(b_guesses_to_use) + list(n_guesses_to_use),
args=(
r_p,
w,
p_tilde,
bq_to_use,
tr_to_use,
theta_to_use,
factor,
ubi_to_use,
j,
None,
t,
etr_params_to_use,
mtrx_params_to_use,
mtry_params_to_use,
initial_b,
p,
),
method=p.FOC_root_method,
tol=MINIMIZER_TOL,
)
euler_errors[t, :] = solutions.fun
b_vec = solutions.x[: p.S]
b_mat[t + ind, ind] = b_vec
n_vec = solutions.x[p.S :]
n_mat[t + ind, ind] = n_vec
# print('Type ', j, ' max euler error = ',
# np.absolute(euler_errors).max())
return euler_errors, b_mat, n_mat
def run_TPI(p, client=None):
"""
Solve for transition path equilibrium of OG-Core.
Args:
p (OG-Core Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with transition path solution
results
"""
global scattered_p
if client:
scattered_p = client.scatter(p, broadcast=True)
else:
scattered_p = p
# 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,
Ig_baseline,
D0_baseline,
Kg0_baseline,
) = baseline_values
# Create time path of UBI household benefits and aggregate UBI outlays
ubi = p.ubi_nom_array / factor
UBI = aggr.get_L(ubi[: p.T], p, "TPI")
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
K_g = np.ones_like(K) * ss_vars["K_g_ss"]
Y = np.zeros_like(K)
Y[: p.T] = firm.get_Y(K[: p.T], K_g[: p.T], L[: p.T], p, "TPI")
Y[p.T :] = ss_vars["Yss"]
I_g = np.ones_like(Y) * ss_vars["I_g_ss"]
if p.baseline_spending:
I_g[: p.T] = Ig_baseline[: p.T]
else:
I_g = fiscal.get_I_g(Y, p.alpha_I)
if p.baseline:
K_g0 = p.initial_Kg_ratio * Y[0]
else:
K_g0 = Kg0_baseline
K_g = fiscal.get_K_g(K_g0, I_g, p, "TPI")
# path for industry specific aggregates
K_vec_init = np.ones((p.T + p.S, p.M)) * ss_vars["K_vec_ss"].reshape(
1, p.M
)
L_vec_init = np.ones((p.T + p.S, p.M)) * ss_vars["L_vec_ss"].reshape(
1, p.M
)
Y_vec_init = np.ones((p.T + p.S, p.M)) * ss_vars["Y_vec_ss"].reshape(
1, p.M
)
# compute w
w = np.ones_like(K) * ss_vars["wss"]
# compute goods prices
p_m = np.ones((p.T + p.S, p.M)) * ss_vars["p_m_ss"].reshape(1, p.M)
p_m[: p.T, :] = firm.get_pm(
w[: p.T], Y_vec_init[: p.T, :], L_vec_init[: p.T, :], p, "TPI"
)
p_m = p_m / p_m[:, -1].reshape(
p.T + p.S, 1
) # normalize prices by industry M
p_i = (
np.tile(p.io_matrix.reshape(1, p.I, p.M), (p.T + p.S, 1, 1))
* np.tile(p_m.reshape(p.T + p.S, 1, p.M), (1, p.I, 1))
).sum(axis=2)
p_tilde = aggr.get_ptilde(p_i[:, :], p.tau_c[:, :], p.alpha_c, "TPI")
if not any(p.zeta_K == 1):
w[: p.T] = np.squeeze(
firm.get_w(Y[: p.T], L[: p.T], p_m[: p.T, :], p, "TPI")
)
# repeat with updated w
p_m[: p.T, :] = firm.get_pm(
w[: p.T], Y_vec_init[: p.T, :], L_vec_init[: p.T, :], p, "TPI"
)
p_m = p_m / p_m[:, -1].reshape(
p.T + p.S, 1
) # normalize prices by industry M
p_i = (
np.tile(p.io_matrix.reshape(1, p.I, p.M), (p.T + p.S, 1, 1))
* np.tile(p_m.reshape(p.T + p.S, 1, p.M), (1, p.I, 1))
).sum(axis=2)
p_tilde = aggr.get_ptilde(p_i[:, :], p.tau_c[:, :], p.alpha_c, "TPI")
# path for interest rates
r = np.zeros_like(Y)
r[: p.T] = np.squeeze(
firm.get_r(Y[: p.T], K[: p.T], p_m[: 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]
# 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 = np.concatenate(
(TRbaseline[: p.T], np.ones(p.S) * ss_vars["TR_ss"])
)
G = np.concatenate(
(Gbaseline[: p.T], np.ones(p.S) * 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"]
# Compute other interest rates
r_gov = fiscal.get_r_gov(r, p, "TPI")
r_p = np.ones_like(r) * ss_vars["r_p_ss"]
MPKg = np.zeros((p.T, p.M))
for m in range(p.M):
MPKg[:, m] = np.squeeze(
firm.get_MPx(
Y_vec_init[: p.T, m], K_g[: p.T], p.gamma_g[m], p, "TPI", m
)
)
r_p[: p.T] = aggr.get_r_p(
r[: p.T],
r_gov[: p.T],
p_m[: p.T, :],
K_vec_init[: p.T, :],
K_g[: p.T],
D[: p.T],
MPKg,
p,
"TPI",
)
# Initialize bequests
BQ0 = aggr.get_BQ(r_p[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):
outer_loop_vars = (r_p, r, w, p_m, BQ, TR, theta)
# compute composite good price
p_i = (
np.tile(p.io_matrix.reshape(1, p.I, p.M), (p.T + p.S, 1, 1))
* np.tile(p_m.reshape(p.T + p.S, 1, p.M), (1, p.I, 1))
).sum(axis=2)
p_tilde = aggr.get_ptilde(p_i[:, :], p.tau_c[:, :], p.alpha_c, "TPI")
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,
ubi,
j,
ind,
scattered_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, :, :]
num_params = len(p.etr_params[0][0])
etr_params_4D = [
[
[
[p.etr_params[t][s][i] for i in range(num_params)]
for j in range(p.J)
]
for s in range(p.S)
]
for t in range(p.T)
]
bqmat = household.get_bq(BQ, None, p, "TPI")
trmat = household.get_tr(TR, None, p, "TPI")
tax_mat = tax.net_taxes(
r_p[: p.T],
w[: p.T],
bmat_s,
n_mat[: p.T, :, :],
bqmat[: p.T, :, :],
factor,
trmat[: p.T, :, :],
ubi[: p.T, :, :],
theta,
0,
None,
False,
"TPI",
p.e,
etr_params_4D,
p,
)
r_p_path = utils.to_timepath_shape(r_p)
p_tilde_path = utils.to_timepath_shape(p_tilde)
wpath = utils.to_timepath_shape(w)
c_mat = household.get_cons(
r_p_path[: p.T, :, :],
wpath[: p.T, :, :],
p_tilde_path[: p.T, :, :],
bmat_s,
bmat_splus1,
n_mat[: p.T, :, :],
bqmat[: p.T, :, :],
tax_mat,
p.e,
p,
)
C = aggr.get_C(c_mat, p, "TPI")
c_i = household.get_ci(
c_mat[: p.T, :, :],
p_i[: p.T, :],
p_tilde[: p.T],
p.tau_c[: p.T, :],
p.alpha_c,
"TPI",
)
y_before_tax_mat = household.get_y(
r_p_path[: p.T, :, :],
wpath[: p.T, :, :],
bmat_s[: p.T, :, :],
n_mat[: p.T, :, :],
p,
"TPI",
)
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]
w_open = firm.get_w_from_r(p.world_int_rate[: p.T], p, "TPI")
# Find output, labor demand, capital demand for M-1 industries
L_vec = np.zeros((p.T, p.M))
K_vec = np.zeros((p.T, p.M))
C_vec = np.zeros((p.T, p.I))
K_demand_open_vec = np.zeros((p.T, p.M))
for i_ind in range(p.I):
C_vec[:, i_ind] = aggr.get_C(c_i[: p.T, i_ind, :, :], p, "TPI")
Y_vec = (
np.tile(p.io_matrix.reshape(1, p.I, p.M), (p.T, 1, 1))
* np.tile(C_vec[: p.T, :].reshape(p.T, p.I, 1), (1, 1, p.M))
).sum(axis=1)
for m_ind in range(p.M - 1):
KYrat_m = firm.get_KY_ratio(
r[: p.T], p_m[: p.T, :], p, "TPI", m_ind
)
K_vec[:, m_ind] = KYrat_m * Y_vec[:, m_ind]
L_vec[:, m_ind] = firm.solve_L(
Y_vec[:, m_ind], K_vec[:, m_ind], K_g, p, "TPI", m_ind
)
K_demand_open_vec[:, m_ind] = firm.get_K(
p.world_int_rate[: p.T],
w_open[: p.T],
L_vec[: p.T, m_ind],
p,
"TPI",
m_ind,
)
# Find output, labor demand, capital demand for last industry
L_M = np.maximum(
np.ones(p.T) * 0.001, L[: p.T] - L_vec[: p.T, :].sum(-1)
) # make sure L_M > 0
K_demand_open_vec[:, -1] = firm.get_K(
p.world_int_rate[: p.T], w_open[: p.T], L_M[: p.T], p, "TPI", -1
)
K[: p.T], K_d[: p.T], K_f[: p.T] = aggr.get_K_splits(
B[: p.T],
K_demand_open_vec[: p.T, :].sum(-1),
D_d[: p.T],
p.zeta_K[: p.T],
)
K_M = np.maximum(
np.ones(p.T) * 0.001, K[: p.T] - K_vec[: p.T, :].sum(-1)
) # make sure K_M > 0
L_vec[:, -1] = L_M
K_vec[:, -1] = K_M
Y_vec[:, -1] = firm.get_Y(
K_vec[: p.T, -1], K_g[: p.T], L_vec[: p.T, -1], p, "TPI", -1
)
Y = (p_m[: p.T, :] * Y_vec[: p.T, :]).sum(-1)
(
total_tax_rev,
iit_payroll_tax_revenue,
agg_pension_outlays,
UBI_outlays,
bequest_tax_revenue,
wealth_tax_revenue,
cons_tax_revenue,
business_tax_revenue,
payroll_tax_revenue,
iit_revenue,
) = aggr.revenue(
r_p[: p.T],
w[: p.T],
bmat_s,
n_mat[: p.T, :, :],
bqmat[: p.T, :, :],
c_i[: p.T, :, :, :],
Y_vec[: p.T, :],
L_vec[: p.T, :],
K_vec[: p.T, :],
p_m[: p.T, :],
factor,
ubi[: p.T, :, :],
theta,
etr_params_4D,
p.e,
p,
None,
"TPI",
)
total_tax_revenue[: p.T] = total_tax_rev
dg_fixed_values = (
Y,
total_tax_revenue,
agg_pension_outlays,
UBI_outlays,
TR,
I_g,
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)
K[: p.T], K_d[: p.T], K_f[: p.T] = aggr.get_K_splits(
B[: p.T], K_demand_open_vec.sum(-1), D_d[: p.T], p.zeta_K[: p.T]
)
if not p.baseline_spending:
I_g = fiscal.get_I_g(Y, p.alpha_I)
if p.baseline:
K_g0 = p.initial_Kg_ratio * Y[0]
K_g = fiscal.get_K_g(K_g0, I_g, p, "TPI")
rnew = r.copy()
rnew[: p.T] = np.squeeze(
firm.get_r(
Y_vec[: p.T, -1], K_vec[: p.T, -1], p_m[: p.T, :], p, "TPI", -1
)
)
# For case where economy is small open econ
rnew[p.zeta_K == 1] = p.world_int_rate[p.zeta_K == 1]
r_gov_new = fiscal.get_r_gov(rnew, p, "TPI")
MPKg_vec = np.zeros((p.T, p.M))
for m in range(p.M):
MPKg_vec[:, m] = np.squeeze(
firm.get_MPx(
Y_vec[: p.T, m], K_g[: p.T], p.gamma_g[m], p, "TPI", m
)
)
r_p_new = aggr.get_r_p(
rnew[: p.T],
r_gov_new[: p.T],
p_m[: p.T, :],
K_vec[: p.T, :],
K_g[: p.T],
Dnew[: p.T],
MPKg_vec,
p,
"TPI",
)
# compute w
wnew = np.squeeze(
firm.get_w(
Y_vec[: p.T, -1], L_vec[: p.T, -1], p_m[: p.T, :], p, "TPI", -1
)
)
# compute new prices
new_p_m = firm.get_pm(wnew, Y_vec, L_vec, p, "TPI")
new_p_m = new_p_m / new_p_m[:, -1].reshape(
p.T, 1
) # normalize prices by industry M
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_p_new[: p.T], b_mat_shift, None, p, "TPI", False)
bqmat_new = household.get_bq(BQnew, None, p, "TPI")
(