def inner_loop(r, w, Y, x, params):
'''
--------------------------------------------------------------------
Given values for r and w, solve for equilibrium errors from the two
first order conditions of the firm
--------------------------------------------------------------------
INPUTS:
r = scalar > 0, guess at steady-state interest rate
w = scalar > 0, guess at steady-state wage
Y = scalar > 0, guess steady-state output
x = scalar > 0, guess as steady-state transfers per household
params = length 16 tuple, (c1_init, S, beta, sigma, l_tilde, b_ellip,
upsilon, chi_n_vec, A, alpha, delta, tax_params,
fiscal_params, diff, hh_fsolve, SS_tol)
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
hh.bn_solve()
hh.c1_bSp1err()
hh.get_cnb_vecs()
aggr.get_K()
aggr.get_L()
firms.get_r()
firms.get_w()
OBJECTS CREATED WITHIN FUNCTION:
c1_init = scalar > 0, initial guess for c1
S = integer >= 3, number of periods in individual lifetime
beta = scalar in (0,1), discount factor
sigma = scalar >= 1, coefficient of relative risk aversion
l_tilde = scalar > 0, per-period time endowment for every agent
b_ellip = scalar > 0, fitted value of b for elliptical disutility
of labor
upsilon = scalar > 1, fitted value of upsilon for elliptical
disutility of labor
chi_n_vec = (S,) vector, values for chi^n_s
A = scalar > 0, total factor productivity parameter in
firms' production function
alpha = scalar in (0,1), capital share of income
delta = scalar in [0,1], model-period depreciation rate of
capital
tax_params = length 3 tuple, (tau_l, tau_k, tau_c)
fiscal_params = length 7 tuple, (tG1, tG2, alpha_X, alpha_G, rho_G,
alpha_D, alpha_D0)
diff = boolean, =True if simple difference Euler errors,
otherwise percent deviation Euler errors
hh_fsolve = boolean, =True if solve inner-loop household problem by
choosing c_1 to set final period savings b_{S+1}=0.
Otherwise, solve the household problem as multivariate
root finder with 2S-1 unknowns and equations
SS_tol = scalar > 0, tolerance level for steady-state fsolve
tau_l = scalar, marginal tax rate on labor income
tau_k = scalar, marginal tax rate on capital income
tau_c = scalar, marginal tax rate on corporate income
tG1 = integer, model period when budget closure rule begins
tG2 = integer, model period when budget is closed
alpha_X = scalar, ratio of lump sum transfers to GDP
alpha_G = scalar, ratio of government spending to GDP prior to
budget closure rule beginning
rho_G = scalar in (0,1), rate of convergence to SS budget
alpha_D = scalar, steady-state debt to GDP ratio
alpha_D0 = scalar, debt to GDP ratio in the initial period
r_params = length 3 tuple, args to pass into get_r()
w_params = length 2 tuple, args to pass into get_w()
Y_params = length 2 tuple, args to pass into get_Y()
b_init = (S-1,) vector, initial guess at distribution of savings
n_init = (S,) vector, initial guess at distribution of labor supply
guesses = (2S-1,) vector, initial guesses at b and n
bn_params = length 12 tuple, parameters to pass to solve_bn_path()
(r, w, x, S, beta, sigma, l_tilde,
b_ellip, upsilon, chi_n_vec, tax_params, diff)
euler_errors = (2S-1,) vector, Euler errors for FOCs for b and n
b_splus1_vec = (S,) vector, optimal savings choice
nvec = (S,) vector, optimal labor supply choice
b_Sp1 = scalar, last period savings
b_s_vec = (S,) vector, wealth enter period with
cvec = (S,) vector, optimal consumption
rpath = (S,) vector, lifetime path of interest rates
wpath = (S,) vector, lifetime path of wages
c1_args = length 10 tuple, args to pass into c1_bSp1err()
c1_options = length 1 dict, options for c1_bSp1err()
results_c1 = results object, results from c1_bSp1err()
c1 = scalar > 0, optimal initial period consumption given r
and w
cnb_args = length 8 tuple, args to pass into get_cnb_vecs()
cvec = (S,) vector, lifetime consumption (c1, c2, ...cS)
nvec = (S,) vector, lifetime labor supply (n1, n2, ...nS)
bvec = (S,) vector, lifetime savings (b1, b2, ...bS) with b1=0
b_Sp1 = scalar, final period savings, should be close to zero
B = scalar > 0, aggregate savings
B_cnstr = boolean, =True if B < 0
L = scalar > 0, aggregate labor
debt = scalar, total government debt
K = scalar > 0, aggregate capital stock
K_cnstr = boolean, =True if K < 0
r_new = scalar > 0, implied steady-state interest rate
w_new = scalar > 0, implied steady-state wage
Y_new = scalar >0, implied steady-state output
x_new = scalar >=0, implied transfers per household
FILES CREATED BY THIS FUNCTION: None
RETURNS: B, K, L, Y_new, debt, cvec, nvec, b_s_vec, b_splus1_vec,
b_Sp1, x_new, r_new, w_new
--------------------------------------------------------------------
'''
c1_init, S, beta, sigma, l_tilde, b_ellip, upsilon,\
chi_n_vec, A, alpha, delta, tax_params, fiscal_params,\
diff, hh_fsolve, SS_tol = params
tau_l, tau_k, tau_c = tax_params
tG1, tG2, alpha_X, alpha_G, rho_G, alpha_D, alpha_D0 = fiscal_params
r_params = (A, alpha, delta, tau_c)
w_params = (A, alpha)
Y_params = (A, alpha)
if hh_fsolve:
b_init = np.ones((S - 1, 1)) * 0.05
n_init = np.ones((S, 1)) * 0.4
guesses = np.append(b_init, n_init)
bn_params = (r, w, x, S, beta, sigma, l_tilde, b_ellip, upsilon,
chi_n_vec, tax_params, diff)
[solutions, infodict, ier, message] = \
opt.fsolve(hh.bn_solve, guesses, args=bn_params,
xtol=SS_tol, full_output=True)
euler_errors = infodict['fvec']
print('Max Euler errors: ', np.absolute(euler_errors).max())
b_splus1_vec = np.append(solutions[:S - 1], 0.0)
nvec = solutions[S - 1:]
b_Sp1 = 0.0
b_s_vec = np.append(0.0, b_splus1_vec[:-1])
cvec = hh.get_cons(r, w, b_s_vec, b_splus1_vec, nvec, x, tax_params)
else:
rpath = r * np.ones(S)
wpath = w * np.ones(S)
xpath = x * np.ones(S)
c1_options = {'maxiter': 500}
c1_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
tax_params, xpath, rpath, wpath, diff)
results_c1 = \
opt.root(hh.c1_bSp1err, c1_init, args=(c1_args),
method='lm', tol=SS_tol,
options=(c1_options))
c1_new = results_c1.x
cnb_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
tax_params, diff)
cvec, nvec, b_s_vec, b_Sp1 = \
hh.get_cnb_vecs(c1_new, rpath, wpath, xpath, cnb_args)
b_splus1_vec = np.append(b_s_vec[1:], b_Sp1)
B, B_cnstr = aggr.get_K(b_s_vec)
L = aggr.get_L(nvec)
L = np.maximum(0.0001, L)
debt = alpha_D * Y
K = B - debt
K_cnstr = K < 0
if K_cnstr:
print('Aggregate capital constraint is violated K<=0 for ' +
'in the steady state.')
r_new = firms.get_r(r_params, K, L)
w_new = firms.get_w(w_params, K, L)
Y_new = aggr.get_Y(Y_params, K, L)
x_new = (alpha_X * Y_new) / S
return B, K, L, Y_new, debt, cvec, nvec, b_s_vec, b_splus1_vec, \
b_Sp1, x_new, r_new, w_new
def get_cnbpath(params, rpath, wpath):
'''
--------------------------------------------------------------------
Given time paths for interest rates and wages, this function
generates matrices for the time path of the distribution of
individual consumption, labor supply, savings, the corresponding
Euler errors for the labor supply decision and the savings decision,
and the residual error of end-of-life savings associated with
solving each lifetime decision.
--------------------------------------------------------------------
INPUTS:
params = length 11 tuple, (S, T2, beta, sigma, l_tilde, b_ellip,
upsilon, chi_n_vec, bvec1, TPI_tol, diff)
rpath = (T2+S-1,) vector, equilibrium time path of interest rate
wpath = (T2+S-1,) vector, equilibrium time path of the real wage
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
hh.c1_bSp1err()
hh.get_cnb_vecs()
hh.get_n_errors()
hh.get_b_errors()
OBJECTS CREATED WITHIN FUNCTION:
S = integer in [3,80], number of periods an individual
lives
T2 = integer > S, number of periods until steady state
beta = scalar in (0,1), discount factor
sigma = scalar > 0, coefficient of relative risk aversion
l_tilde = scalar > 0, time endowment for each agent each
period
b_ellip = scalar > 0, fitted value of b for elliptical
disutility of labor
upsilon = scalar > 1, fitted value of upsilon for elliptical
disutility of labor
chi_n_vec = (S,) vector, values for chi^n_s
bvec1 = (S,) vector, initial period savings distribution
TPI_tol = scalar > 0, tolerance level for fsolve's in TPI
diff = boolean, =True if want difference version of Euler
errors beta*(1+r)*u'(c2) - u'(c1), =False if want
ratio version [beta*(1+r)*u'(c2)]/[u'(c1)] - 1
cpath = (S, T2+S-1) matrix, time path of the distribution of
consumption
npath = (S, T2+S-1) matrix, time path of the distribution of
labor supply
bpath = (S, T2+S-1) matrix, time path of the distribution of
savings
n_err_path = (S, T2+S-1) matrix, time path of distribution of
labor supply Euler errors
b_err_path = (S, T2+S-1) matrix, time path of distribution of
savings Euler errors
bSp1_err_path = (S, T2) matrix, residual last period savings, which
should be close to zero in equilibrium. Nonzero
elements of matrix should only be in first column
and first row
c1_options = length 1 dict, options for
opt.root(hh.c1_bSp1err,...)
b_err_params = length 2 tuple, args to pass into
hh.get_b_errors()
p = integer in [1, S-1], index representing number of
periods remaining in a lifetime, used to solve
incomplete lifetimes
c1_init = scalar > 0, guess for initial period consumption
c1_args = length 10 tuple, args to pass into
opt.root(hh.c1_bSp1err,...)
results_c1 = results object, solution from
opt.root(hh.c1_bSp1err,...)
c1 = scalar > 0, optimal initial consumption
cnb_args = length 8 tuple, args to pass into
hh.get_cnb_vecs()
cvec = (p,) vector, individual lifetime consumption
decisions
nvec = (p,) vector, individual lifetime labor supply
decisions
bvec = (p,) vector, individual lifetime savings decisions
b_Sp1 = scalar, savings in last period for next period.
Should be zero in equilibrium
DiagMaskc = (p, p) boolean identity matrix
DiagMaskb = (p-1, p-1) boolean identity matrix
n_err_params = length 5 tuple, args to pass into hh.get_n_errors()
n_err_vec = (p,) vector, individual lifetime labor supply Euler
errors
b_err_vec = (p-1,) vector, individual lifetime savings Euler
errors
t = integer in [0,T2-1], index of time period (minus 1)
FILES CREATED BY THIS FUNCTION: None
RETURNS: cpath, npath, bpath, n_err_path, b_err_path, bSp1_err_path
--------------------------------------------------------------------
'''
(S, T2, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec, bvec1, TPI_tol,
diff) = params
cpath = np.zeros((S, T2 + S - 1))
npath = np.zeros((S, T2 + S - 1))
bpath = np.append(bvec1.reshape((S, 1)), np.zeros((S, T2 + S - 2)), axis=1)
n_err_path = np.zeros((S, T2 + S - 1))
b_err_path = np.zeros((S, T2 + S - 1))
bSp1_err_path = np.zeros((S, T2))
# Solve the incomplete remaining lifetime decisions of agents alive
# in period t=1 but not born in period t=1
c1_options = {'maxiter': 500}
b_err_params = (beta, sigma)
for p in range(1, S):
c1_init = 0.1
c1_args = (bvec1[-p], beta, sigma, l_tilde, b_ellip, upsilon,
chi_n_vec[-p:], rpath[:p], wpath[:p], diff)
results_c1 = \
opt.root(hh.c1_bSp1err, c1_init, args=(c1_args),
method='lm', tol=TPI_tol, options=(c1_options))
c_1 = results_c1.x
cnb_args = (bvec1[-p], beta, sigma, l_tilde, b_ellip, upsilon,
chi_n_vec[-p:], diff)
cvec, nvec, bvec, b_Sp1 = \
hh.get_cnb_vecs(c_1, rpath[:p], wpath[:p], cnb_args)
DiagMaskc = np.eye(p, dtype=bool)
DiagMaskb = np.eye(p - 1, dtype=bool)
cpath[-p:, :p] = DiagMaskc * cvec + cpath[-p:, :p]
npath[-p:, :p] = DiagMaskc * nvec + npath[-p:, :p]
n_err_args = (wpath[:p], cvec, sigma, l_tilde, chi_n_vec[-p:], b_ellip,
upsilon, diff)
n_err_vec = hh.get_n_errors(nvec, n_err_args)
n_err_path[-p:, :p] = (DiagMaskc * n_err_vec + n_err_path[-p:, :p])
bSp1_err_path[-p, 0] = b_Sp1
if p > 1:
bpath[S - p + 1:,
1:p] = (DiagMaskb * bvec[1:] + bpath[S - p + 1:, 1:p])
b_err_vec = hh.get_b_errors(b_err_params, rpath[1:p], cvec, diff)
b_err_path[S - p + 1:, 1:p] = (DiagMaskb * b_err_vec +
b_err_path[S - p + 1:, 1:p])
# print('p=', p, ', max. abs. all errs: ',
# np.hstack((n_err_vec, b_err_vec, b_Sp1)).max())
# Solve the remaining lifetime decisions of agents born between
# period t=1 and t=T (complete lifetimes)
DiagMaskc = np.eye(S, dtype=bool)
DiagMaskb = np.eye(S - 1, dtype=bool)
for t in range(T2): # Go from periods 1 to T (columns 0 to T-1)
if t == 0:
c1_init = 0.1
else:
c1_init = cpath[0, t - 1]
c1_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
rpath[t:t + S], wpath[t:t + S], diff)
results_c1 = \
opt.root(hh.c1_bSp1err, c1_init, args=(c1_args),
method='lm', tol=TPI_tol, options=(c1_options))
c_1 = results_c1.x
cnb_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
diff)
cvec, nvec, bvec, b_Sp1 = \
hh.get_cnb_vecs(c_1, rpath[t:t + S], wpath[t:t + S],
cnb_args)
cpath[:, t:t + S] = DiagMaskc * cvec + cpath[:, t:t + S]
npath[:, t:t + S] = DiagMaskc * nvec + npath[:, t:t + S]
n_err_args = (wpath[t:t + S], cvec, sigma, l_tilde, chi_n_vec, b_ellip,
upsilon, diff)
n_err_vec = hh.get_n_errors(nvec, n_err_args)
n_err_path[:,
t:t + S] = (DiagMaskc * n_err_vec + n_err_path[:, t:t + S])
bpath[:, t:t + S] = DiagMaskc * bvec + bpath[:, t:t + S]
b_err_vec = hh.get_b_errors(b_err_params, rpath[t + 1:t + S], cvec,
diff)
b_err_path[1:, t + 1:t + S] = (DiagMaskb * b_err_vec +
b_err_path[1:, t + 1:t + S])
bSp1_err_path[0, t] = b_Sp1
# print('t=', t, ', max. abs. all errs: ',
# np.absolute(np.hstack((n_err_vec, b_err_vec,
# b_Sp1))).max())
return cpath, npath, bpath, n_err_path, b_err_path, bSp1_err_path
def rBQ_errors(rBQ_vals, *args):
'''
--------------------------------------------------------------------
Generate interest rate and wage errors from labor market clearing
and capital market clearing conditions
--------------------------------------------------------------------
INPUTS:
rBQ_vals = (2,) vector, steady-state r value and BQ value
args = length 2 tuple, (nb_guess, p)
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
firms.get_wt()
hh.get_cnb_vecs()
aggr.get_Lt()
aggr.get_Kt()
firms.get_rt()
aggr.get_BQt()
OBJECTS CREATED WITHIN FUNCTION:
nb_buess = (2S,) vector, initial guesses for n_s and b_sp1
p = parameters class object
r_init = scalar, initial guess for steady-state interest rate
BQ_init = scalar, initial guess for steady-state total bequests
w = scalar, steady-state wage implied by r_init
b_init = scalar = 0, initial wealth of initial age individuals
r_path = (S,) vector, constant interest rate time path over
lifetime of individual
w_path = (S,) vector, constant wage time path over lifetime of
individual
BQ_path = (S,) vector, constant total bequests time path over
lifetime of individual
c_s = (S,) vector, steady-state consumption by age
n_s = (S,) vector, steady-state labor supply by age
b_s = (S+1,) vector, steady-state wealth or savings by age
n_errors = (S,) vector, errors associated with optimal labor
supply solution
b_errors = (S,) vector, errors associated with optimal savings
solution
L = scalar, aggregate labor implied by household and firm
optimization
K = scalar, aggregate capital implied by household and firm
optimization
r_new = scalar, new value of r implied by household and firm
optimization
BQ_new = scalar, new value of BQ implied by household and firm
optimization
r_error = scalar, difference between r_new and r_init
BQ_error = scalar, difference between BQ_new and BQ_init
rBQ_errors = (2,) vector, r_error and BQ_error
FILES CREATED BY THIS FUNCTION: None
RETURNS: rBQ_errors
--------------------------------------------------------------------
'''
(nb_guess, p) = args
r_init, BQ_init = rBQ_vals
# Solve for steady-state wage w implied by r
w = firms.get_wt(r_init, p)
# Solve for household steady-state decisions c_s, n_s, b_{s+1} given
# r, w, and BQ
b_init = 0.0
r_path = r_init * np.ones(p.S)
w_path = w * np.ones(p.S)
BQ_path = BQ_init * np.ones(p.S)
c_s, n_s, b_s, n_errors, b_errors = \
hh.get_cnb_vecs(nb_guess, b_init, r_path, w_path, BQ_path,
p.rho_ss, p.SS_EulDif, p, p.SS_EulTol)
# Solve for aggregate labor and aggregate capital
L = aggr.get_Lt(n_s, p)
K = aggr.get_Kt(b_s[1:], p)
# Solve for updated values of the interest rate r and total bequests
# BQ
r_new = firms.get_rt(K, L, p)
BQ_new = aggr.get_BQt(b_s[1:], r_init, p)
# solve for errors in interest rate and total bequests guesses
r_error = r_new - r_init
BQ_error = BQ_new - BQ_init
rBQ_errors = np.array([r_error, BQ_error])
return rBQ_errors
def get_SS(rBQ_init, p, graphs=False):
'''
--------------------------------------------------------------------
Solve for the steady-state solution of the S-period-lived agent OG
model with endogenous labor supply and multiple industries using the
root finder method in r and w for the outer loop
--------------------------------------------------------------------
INPUTS:
rBQ_init = (2,) vector, initial guesses for (rss_init, BQss_init)
p = parameters class object
graphs = boolean, =True if output steady-state graphs
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
rBQ_errors()
firms.get_wt()
hh.get_cnb_vecs()
aggr.get_Lt()
aggr.get_Kt()
firms.get_Yt()
C_ss = aggr.get_Ct()
I_ss = aggr.get_It()
NX_ss = aggr.get_NXt()
utils.print_time()
ss_graphs()
OBJECTS CREATED WITHIN FUNCTION:
start_time = scalar > 0, clock time at beginning of program
nvec_guess = (S,) vector, initial guess for optimal household labor
supply n_s
bvec_guess = (S,) vector, initial guess for optimal household
savings b_sp1
nb_guess = (2S,) vector, initial guesses for optimal household
labor supply and savings (n_s, b_sp1)
rBQ_args = length 2 tuple, (nb_guess, p)
results_rBQ = root results object
err_msg = string, error message text string
r_ss = scalar > -delta, steady-state interest rate
BQ_ss = scalar > 0, steady-state total bequests
r_err_ss = scalar, error in steady-state optimal solution firm
first order condition for r_ss
BQ_err_ss = scalar, error in steady-state optimal solution
bequests law of motion for BQ_ss
w_ss = scalar > 0, steady-state wage
b_init = scalar = 0, initial wealth of initial age individuals
r_path = (S,) vector, constant interest rate time path over
lifetime of individual
w_path = (S,) vector, constant wage time path over lifetime of
individual
BQ_path = (S,) vector, constant total bequests time path over
lifetime of individual
c_ss = (S,) vector, steady-state consumption by age
n_ss = (S,) vector, steady-state labor supply by age
b_ss = (S+1,) vector, steady-state wealth or savings by age
n_err_ss = (S,) vector, errors associated with optimal labor
supply solution
b_err_ss = (S,) vector, errors associated with optimal savings
solution
L_ss = scalar > 0, steady-state aggregate labor
K_ss = scalar > 0, steady-state aggregate capital stock
Y_ss = scalar > 0, steady-state aggregate output
C_ss = scalar > 0, steady-state aggregate consumption
I_ss = scalar, steady-state aggregate investment
NX_ss = scalar, steady-state net exports
RCerr_ss = scalar, steady-state resource constraint (goods market
clearing) error
ss_time = scalar, seconds elapsed for steady-state computation
ss_output = length 18 dictionary, steady-state output {c_ss, n_ss,
b_ss, n_err_ss, b_err_ss, r_ss, w_ss, BQ_ss, r_err_ss,
BQ_err_ss, L_ss, K_ss, Y_ss, C_ss, I_ss, NX_ss,
RCerr_ss, ss_time}
FILES CREATED BY THIS FUNCTION: None
RETURNS: ss_output
--------------------------------------------------------------------
'''
start_time = time.clock()
nvec_guess = 0.4 * p.l_tilde * np.ones(p.S)
bvec_guess = 0.1 * np.ones(p.S)
nb_guess = np.append(nvec_guess, bvec_guess)
rBQ_args = (nb_guess, p)
results_rBQ = opt.root(rBQ_errors,
rBQ_init,
args=rBQ_args,
tol=p.SS_OutTol)
if not results_rBQ.success:
err_msg = ('SS Error: Steady-state root finder did not ' +
'solve. results_rBQ.success=False')
raise ValueError(err_msg)
else:
print('SS SUCESSS: steady-state solution converged.')
# print(results_rw)
r_ss, BQ_ss = results_rBQ.x
r_err_ss, BQ_err_ss = results_rBQ.fun
# Solve for steady-state wage w_ss implied by r_ss
w_ss = firms.get_wt(r_ss, p)
# Solve for household steady-state decisions c_s, n_s, b_{s+1} given
# r, w, and BQ
b_init = 0.0
r_path = r_ss * np.ones(p.S)
w_path = w_ss * np.ones(p.S)
BQ_path = BQ_ss * np.ones(p.S)
c_ss, n_ss, b_ss, n_err_ss, b_err_ss = \
hh.get_cnb_vecs(nb_guess, b_init, r_path, w_path, BQ_path,
p.rho_ss, p.SS_EulDif, p, p.SS_EulTol)
# Solve for steady-state aggregate labor and aggregate capital
L_ss = aggr.get_Lt(n_ss, p)
K_ss = aggr.get_Kt(b_ss[1:], p)
# Solve for steady-state aggregate output Y, consumption C,
# investment I, and net exports
Y_ss = firms.get_Yt(K_ss, L_ss, p)
C_ss = aggr.get_Ct(c_ss, p)
I_ss = aggr.get_It(K_ss, p)
NX_ss = aggr.get_NXt(b_ss[1:], p)
# Solve for steady-state resource constraint error
RCerr_ss = Y_ss - C_ss - I_ss - NX_ss
ss_time = time.clock() - start_time
ss_output = {
'c_ss': c_ss,
'n_ss': n_ss,
'b_ss': b_ss,
'n_err_ss': n_err_ss,
'b_err_ss': b_err_ss,
'r_ss': r_ss,
'w_ss': w_ss,
'BQ_ss': BQ_ss,
'r_err_ss': r_err_ss,
'BQ_err_ss': BQ_err_ss,
'L_ss': L_ss,
'K_ss': K_ss,
'Y_ss': Y_ss,
'C_ss': C_ss,
'I_ss': I_ss,
'NX_ss': NX_ss,
'RCerr_ss': RCerr_ss,
'ss_time': ss_time
}
print('n_ss=', n_ss)
print('b_ss=', b_ss)
print('K_ss=', K_ss)
print('L_ss=', L_ss)
print('r_ss=', r_ss, ', w_ss=', w_ss, ', BQ_ss=', BQ_ss)
print('Maximum abs. labor supply Euler error is: ',
np.absolute(n_err_ss).max())
print('Maximum abs. savings Euler error is: ', np.absolute(b_err_ss).max())
print('RC error is: ', RCerr_ss)
# Print SS computation time
utils.print_time(ss_time, 'SS')
if graphs:
ss_graphs(c_ss, n_ss, b_ss, p)
return ss_output
def inner_loop(r, w, args):
'''
--------------------------------------------------------------------
Given values for r and w, solve for equilibrium errors from the two
first order conditions of the firm
--------------------------------------------------------------------
INPUTS:
r = scalar > 0, guess at steady-state interest rate
w = scalar > 0, guess at steady-state wage
args = length 14 tuple, (c1_init, S, beta, sigma, l_tilde, b_ellip,
upsilon, chi_n_vec, A, alpha, delta, EulDiff, Eul_Tol,
c1_options)
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
hh.c1_bSp1err()
hh.get_cnb_vecs()
aggr.get_K()
aggr.get_L()
firms.get_r()
firms.get_w()
OBJECTS CREATED WITHIN FUNCTION:
c1_init = scalar > 0, initial guess for c1
S = integer >= 3, number of periods in individual lifetime
beta = scalar in (0,1), discount factor
sigma = scalar >= 1, coefficient of relative risk aversion
l_tilde = scalar > 0, per-period time endowment for every agent
b_ellip = scalar > 0, fitted value of b for elliptical disutility
of labor
upsilon = scalar > 1, fitted value of upsilon for elliptical
disutility of labor
chi_n_vec = (S,) vector, values for chi^n_s
A = scalar > 0, total factor productivity parameter in
firms' production function
alpha = scalar in (0,1), capital share of income
delta = scalar in [0,1], model-period depreciation rate of
capital
EulDiff = boolean, =True if simple difference Euler errors,
otherwise percent deviation Euler errors
SS_tol = scalar > 0, tolerance level for steady-state fsolve
c1_options = length 1 dict, options for c1_bSp1err()
rpath = (S,) vector, lifetime path of interest rates
wpath = (S,) vector, lifetime path of wages
c1_args = length 10 tuple, args to pass into hh.c1_bSp1err()
results_c1 = results object, results from c1_bSp1err()
c1 = scalar > 0, optimal initial period consumption given r
and w
cnb_args = length 8 tuple, args to pass into get_cnb_vecs()
cvec = (S,) vector, lifetime consumption (c1, c2, ...cS)
nvec = (S,) vector, lifetime labor supply (n1, n2, ...nS)
bvec = (S,) vector, lifetime savings (b1, b2, ...bS) with b1=0
b_Sp1 = scalar, final period savings, should be close to zero
n_errors = (S,) vector, labor supply Euler errors
b_errors = (S-1,) vector, savings Euler errors
K = scalar > 0, aggregate capital stock
K_cstr = boolean, =True if K < epsilon
L = scalar > 0, aggregate labor
L_cstr = boolean, =True if L < epsilon
r_params = length 3 tuple, (A, alpha, delta)
w_params = length 2 tuple, (A, alpha)
r_new = scalar > 0, guess at steady-state interest rate
w_new = scalar > 0, guess at steady-state wage
FILES CREATED BY THIS FUNCTION: None
RETURNS: K, L, cvec, nvec, bvec, b_Sp1, r_new, w_new, n_errors,
b_errors
--------------------------------------------------------------------
'''
(c1_init, S, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec, A, alpha,
delta, EulDiff, SS_tol, c1_options) = args
rpath = r * np.ones(S)
wpath = w * np.ones(S)
c1_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec, rpath,
wpath, EulDiff)
results_c1 = \
opt.root(hh.c1_bSp1err, c1_init, args=(c1_args),
method='lm', tol=SS_tol, options=(c1_options))
c1 = results_c1.x
cnb_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
EulDiff)
cvec, nvec, bvec, b_Sp1, n_errors, b_errors = \
hh.get_cnb_vecs(c1, rpath, wpath, cnb_args)
K, K_cstr = aggr.get_K(bvec)
L, L_cstr = aggr.get_L(nvec)
r_params = (A, alpha, delta)
r_new = firms.get_r(K, L, r_params)
w_params = (A, alpha, delta)
w_new = firms.get_w(r_new, w_params)
return (K, L, cvec, nvec, bvec, b_Sp1, r_new, w_new, n_errors, b_errors)
def get_SS(init_vals, args, graphs=False):
'''
--------------------------------------------------------------------
Solve for the steady-state solution of the S-period-lived agent OG
model with endogenous labor supply and a small open economy.
--------------------------------------------------------------------
INPUTS:
init_vals = length 5 tuple,
(Kss_init, Lss_init, rss_init, wss_init,c1_init)
args = length 14 tuple, (S, beta, sigma, l_tilde, b_ellip,
upsilon, chi_n_vec, A, alpha, delta, SS_tol, EulDiff,
hh_fsolve, KL_outer)
graphs = boolean, =True if output steady-state graphs
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
firms.get_r()
firms.get_w()
hh.bn_solve()
hh.c1_bSp1err()
hh.get_cnb_vecs()
aggr.get_K()
aggr.get_L()
aggr.get_Y()
aggr.get_C()
hh.get_cons()
hh.get_n_errors()
hh.get_b_errors()
utils.print_time()
OBJECTS CREATED WITHIN FUNCTION:
start_time = scalar > 0, clock time at beginning of program
Kss_init = scalar > 0, initial guess for steady-state aggregate
capital stock supplied
Lss_init = scalar > 0, initial guess for steady-state aggregate
labor
rss_init = scalar > 0, initial guess for steady-state interest
rate
wss_init = scalar > 0, initial guess for steady-state wage
c1_init = scalar > 0, initial guess for first period consumpt'n
S = integer in [3, 80], number of periods an individual
lives
beta = scalar in (0,1), discount factor for each model per
sigma = scalar > 0, coefficient of relative risk aversion
l_tilde = scalar > 0, time endowment for each agent each period
b_ellip = scalar > 0, fitted value of b for elliptical
disutility of labor
upsilon = scalar > 1, fitted value of upsilon for elliptical
disutility of labor
chi_n_vec = (S,) vector, values for chi^n_s
A = scalar > 0, total factor productivity parameter in
firms' production function
alpha = scalar in (0,1), capital share of income
delta = scalar in [0,1], model-period depreciation rate of
capital
SS_tol = scalar > 0, tolerance level for steady-state fsolve
EulDiff = Boolean, =True if want difference version of Euler
errors beta*(1+r)*u'(c2) - u'(c1), =False if want
ratio version [beta*(1+r)*u'(c2)]/[u'(c1)] - 1
maxiter_SS = integer >= 1, maximum number of iterations in outer
loop bisection method
iter_SS = integer >= 0, index of iteration number
mindist_SS = scalar > 0, minimum distance tolerance for
convergence
dist_SS = scalar > 0, distance metric for current iteration
xi_SS = scalar in (0,1], updating parameter
KL_init = (2,) vector, (K_init, L_init)
c1_options = length 1 dict, options to pass into
opt.root(c1_bSp1err,...)
cnb_args = length 8 tuple, args to pass into get_cnb_vecs()
#r_params = length 3 tuple, args to pass into get_r()
w_params = length 2 tuple, args to pass into get_w()
K_init = scalar, initial value of aggregate capital stock supplied
L_init = scalar, initial value of aggregate labor
r_init = scalar, initial value for interest rate
w_init = scalar, initial value for wage
K_d = scalar, capital demand
rpath = (S,) vector, lifetime path of interest rates
wpath = (S,) vector, lifetime path of wages
c1_args = length 10 tuple, args to pass into c1_bSp1err()
results_c1 = results object, root finder results from
opt.root(c1_bSp1err,...)
c1_new = scalar, updated value of optimal c1 given r_init and
w_init
cvec_new = (S,) vector, updated values for lifetime consumption
nvec_new = (S,) vector, updated values for lifetime labor supply
b_s_new = (S,) vector, updated values for lifetime wealth
b_splus1_new = (S,) vector, updated values for lifetime savings
(b1, b2,...bS)
b_Sp1_new = scalar, updated value for savings in last period,
should be arbitrarily close to zero
K_new = scalar, updated K given bvec_new
K_cnstr = boolean, =True if K_new <= 0
L_new = scalar, updated L given nvec_new
KL_new = (2,) vector, updated K and L given bvec_new, nvec_new
K_ss = scalar > 0, steady-state aggregate capital stock supplied
K_d_ss = scalar > 0, steady-state aggregate capital stock demanded
L_ss = scalar > 0, steady-state aggregate labor
r_ss = scalar > 0, steady-state interest rate
w_ss = scalar > 0, steady-state wage
c1_ss = scalar > 0, steady-state consumption in first period
c_ss = (S,) vector, steady-state lifetime consumption
n_ss = (S,) vector, steady-state lifetime labor supply
b_s_ss = (S,) vector, steady-state wealth enter period with
b_splus1_ss = (S,) vector, steady-state lifetime savings
(b1_ss, b2_ss, ...bS_ss) where b1_ss=0
b_Sp1_ss = scalar, steady-state savings for period after last
period of life. b_Sp1_ss approx. 0 in equilibrium
Y_params = length 2 tuple, (A, alpha)
Y_ss = scalar > 0, steady-state aggregate output (GDP)
C_ss = scalar > 0, steady-state aggregate consumption
n_err_params = length 5 tuple, args to pass into get_n_errors()
n_err_ss = (S,) vector, lifetime labor supply Euler errors
b_err_params = length 2 tuple, args to pass into get_b_errors()
b_err_ss = (S-1) vector, lifetime savings Euler errors
RCerr_ss = scalar, resource constraint error
ss_time = scalar, seconds elapsed to run steady-state comput'n
ss_output = length 14 dict, steady-state objects {n_ss, b_ss,
c_ss, b_Sp1_ss, w_ss, r_ss, K_ss, L_ss, Y_ss, C_ss,
n_err_ss, b_err_ss, RCerr_ss, ss_time}
FILES CREATED BY THIS FUNCTION:
SS_bc.png
SS_n.png
RETURNS: ss_output
--------------------------------------------------------------------
'''
start_time = time.clock()
c1_init = init_vals
(S, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec, A, alpha, delta,
r_star, SS_tol, EulDiff, hh_fsolve) = args
c1_options = {'maxiter': 500}
cnb_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
EulDiff)
w_params = (A, alpha, delta)
K_params = (A, alpha, delta)
r_ss = r_star
w_ss = firms.get_w(r_ss, w_params)
if hh_fsolve:
b_init = np.ones((S - 1, 1)) * 0.05
n_init = np.ones((S, 1)) * 0.4
guesses = np.append(b_init, n_init)
bn_params = (r_ss, w_ss, S, beta, sigma, l_tilde, b_ellip, upsilon,
chi_n_vec, EulDiff)
[solutions, infodict, ier, message] = \
opt.fsolve(hh.bn_solve, guesses, args=bn_params,
xtol=SS_tol, full_output=True)
euler_errors = infodict['fvec']
print('Max Euler errors: ', np.absolute(euler_errors).max())
b_splus1_ss = np.append(solutions[:S - 1], 0.0)
n_ss = solutions[S - 1:]
b_Sp1_ss = 0.0
b_s_ss = np.append(0.0, b_splus1_ss[:-1])
c_ss = hh.get_cons(r_ss, w_ss, b_s_ss, b_splus1_ss, n_ss)
else:
rpath = r_ss * np.ones(S)
wpath = w_ss * np.ones(S)
c1_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
rpath, wpath, EulDiff)
c1_options = {'maxiter': 500}
results_c1 = \
opt.root(hh.c1_bSp1err, c1_new, args=(c1_args),
method='lm', tol=SS_tol, options=(c1_options))
c1_ss = results_c1.x
cnb_args = (0.0, beta, sigma, l_tilde, b_ellip, upsilon, chi_n_vec,
EulDiff)
c_ss, n_ss, b_s_ss, b_Sp1_ss = hh.get_cnb_vecs(c1_ss, rpath, wpath,
cnb_args)
b_splus1_ss = np.append(b_s_ss[1:], b_Sp1_ss)
L_ss = aggr.get_L_s(n_ss)
K_s_ss, K_cnstr = aggr.get_K_s(b_s_ss)
K_d_ss = firms.get_K_d(r_ss, L_ss, K_params)
Y_params = (A, alpha)
Y_ss = aggr.get_Y(Y_params, K_d_ss, L_ss)
C_ss = aggr.get_C(c_ss)
n_err_args = (w_ss, c_ss, sigma, l_tilde, chi_n_vec, b_ellip, upsilon,
EulDiff)
n_err_ss = hh.get_n_errors(n_ss, n_err_args)
b_err_params = (beta, sigma)
b_err_ss = hh.get_b_errors(b_err_params, r_ss, c_ss, EulDiff)
NX_ss = Y_ss - C_ss - delta * K_s_ss
RCerr_ss = Y_ss - C_ss - delta * K_s_ss - NX_ss
ss_time = time.clock() - start_time
ss_output = {
'n_ss': n_ss,
'b_s_ss': b_s_ss,
'b_splus1_ss': b_splus1_ss,
'c_ss': c_ss,
'b_Sp1_ss': b_Sp1_ss,
'w_ss': w_ss,
'r_ss': r_ss,
'K_s_ss': K_s_ss,
'K_d_ss': K_d_ss,
'L_ss': L_ss,
'Y_ss': Y_ss,
'C_ss': C_ss,
'n_err_ss': n_err_ss,
'b_err_ss': b_err_ss,
'RCerr_ss': RCerr_ss,
'ss_time': ss_time
}
print('n_ss is: ', n_ss)
print('b_splus1_ss is: ', b_splus1_ss)
print('K_s_ss=', K_s_ss, 'K_d_ss=', K_d_ss, ', L_ss=', L_ss)
print('r_ss=', r_ss, ', w_ss=', w_ss)
print('Maximum abs. labor supply Euler error is: ',
np.absolute(n_err_ss).max())
print('Maximum abs. savings Euler error is: ', np.absolute(b_err_ss).max())
print('Resource constraint error is: ', RCerr_ss)
print('Net Exports = ', NX_ss)
print('Output and consumption: ', Y_ss, C_ss)
print('Steady-state residual savings b_Sp1 is: ', b_Sp1_ss)
# Print SS computation time
utils.print_time(ss_time, 'SS')
if graphs:
'''
----------------------------------------------------------------
cur_path = string, path name of current directory
output_fldr = string, folder in current path to save files
output_dir = string, total path of images folder
output_path = string, path of file name of figure to be saved
age_pers = (S,) vector, ages from 1 to S
----------------------------------------------------------------
'''
# Create directory if images directory does not already exist
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = 'images'
output_dir = os.path.join(cur_path, output_fldr)
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
# Plot steady-state consumption and savings distributions
age_pers = np.arange(1, S + 1)
fig, ax = plt.subplots()
plt.plot(age_pers, c_ss, marker='D', label='Consumption')
plt.plot(age_pers, b_splus1_ss, marker='D', label='Savings')
# for the minor ticks, use no labels; default NullFormatter
minorLocator = MultipleLocator(1)
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
# plt.title('Steady-state consumption and savings', fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Units of consumption')
plt.xlim((0, S + 1))
# plt.ylim((-1.0, 1.15 * (b_ss.max())))
plt.legend(loc='upper left')
output_path = os.path.join(output_dir, 'SS_bc')
plt.savefig(output_path)
# plt.show()
plt.close()
# Plot steady-state labor supply distributions
fig, ax = plt.subplots()
plt.plot(age_pers, n_ss, marker='D', label='Labor supply')
# for the minor ticks, use no labels; default NullFormatter
minorLocator = MultipleLocator(1)
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
# plt.title('Steady-state labor supply', fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Labor supply')
plt.xlim((0, S + 1))
# plt.ylim((-0.1, 1.15 * (n_ss.max())))
plt.legend(loc='upper right')
output_path = os.path.join(output_dir, 'SS_n')
plt.savefig(output_path)
# plt.show()
plt.close()
return ss_output
def get_SS_bsct(init_vals, args, graphs=False):
'''
--------------------------------------------------------------------
Solve for the steady-state solution of the S-period-lived agent OG
model with endogenous labor supply using the bisection method for
the outer loop
--------------------------------------------------------------------
INPUTS:
init_vals = length 3 tuple, (Kss_init, Lss_init, c1_init)
args = length 15 tuple, (J, S, lambdas, emat, beta, sigma,
l_tilde, b_ellip, upsilon, chi_n_vec, A, alpha, delta,
SS_tol, EulDiff)
graphs = boolean, =True if output steady-state graphs
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
firms.get_r()
firms.get_w()
hh.bn_solve()
hh.c1_bSp1err()
hh.get_cnb_vecs()
aggr.get_K()
aggr.get_L()
aggr.get_Y()
aggr.get_C()
hh.get_cons()
hh.get_n_errors()
hh.get_b_errors()
utils.print_time()
OBJECTS CREATED WITHIN FUNCTION:
start_time = scalar > 0, clock time at beginning of program
Kss_init = scalar > 0, initial guess for steady-state aggregate
capital stock
Lss_init = scalar > 0, initial guess for steady-state aggregate
labor
rss_init = scalar > 0, initial guess for steady-state interest
rate
wss_init = scalar > 0, initial guess for steady-state wage
c1_init = scalar > 0, initial guess for first period consumpt'n
S = integer in [3, 80], number of periods an individual
lives
beta = scalar in (0,1), discount factor for each model per
sigma = scalar > 0, coefficient of relative risk aversion
l_tilde = scalar > 0, time endowment for each agent each period
b_ellip = scalar > 0, fitted value of b for elliptical
disutility of labor
upsilon = scalar > 1, fitted value of upsilon for elliptical
disutility of labor
chi_n_vec = (S,) vector, values for chi^n_s
A = scalar > 0, total factor productivity parameter in
firms' production function
alpha = scalar in (0,1), capital share of income
delta = scalar in [0,1], model-period depreciation rate of
capital
SS_tol = scalar > 0, tolerance level for steady-state fsolve
EulDiff = Boolean, =True if want difference version of Euler
errors beta*(1+r)*u'(c2) - u'(c1), =False if want
ratio version [beta*(1+r)*u'(c2)]/[u'(c1)] - 1
hh_fsolve = boolean, =True if solve inner-loop household problem
by choosing c_1 to set final period savings b_{S+1}=0
KL_outer = boolean, =True if guess K and L in outer loop
Otherwise, guess r and w in outer loop
maxiter_SS = integer >= 1, maximum number of iterations in outer
loop bisection method
iter_SS = integer >= 0, index of iteration number
mindist_SS = scalar > 0, minimum distance tolerance for
convergence
dist_SS = scalar > 0, distance metric for current iteration
xi_SS = scalar in (0,1], updating parameter
KL_init = (2,) vector, (K_init, L_init)
c1_options = length 1 dict, options to pass into
opt.root(c1_bSp1err,...)
cnb_args = length 8 tuple, args to pass into get_cnb_vecs()
r_params = length 3 tuple, args to pass into get_r()
w_params = length 2 tuple, args to pass into get_w()
K_init = scalar, initial value of aggregate capital stock
L_init = scalar, initial value of aggregate labor
r_init = scalar, initial value for interest rate
w_init = scalar, initial value for wage
rpath = (S,) vector, lifetime path of interest rates
wpath = (S,) vector, lifetime path of wages
c1_args = length 10 tuple, args to pass into c1_bSp1err()
results_c1 = results object, root finder results from
opt.root(c1_bSp1err,...)
c1_new = scalar, updated value of optimal c1 given r_init and
w_init
cvec_new = (S,) vector, updated values for lifetime consumption
nvec_new = (S,) vector, updated values for lifetime labor supply
bvec_new = (S,) vector, updated values for lifetime savings
(b1, b2,...bS)
b_Sp1_new = scalar, updated value for savings in last period,
should be arbitrarily close to zero
K_new = scalar, updated K given bvec_new
K_cnstr = boolean, =True if K_new <= 0
L_new = scalar, updated L given nvec_new
KL_new = (2,) vector, updated K and L given bvec_new, nvec_new
K_ss = scalar > 0, steady-state aggregate capital stock
L_ss = scalar > 0, steady-state aggregate labor
r_ss = scalar > 0, steady-state interest rate
w_ss = scalar > 0, steady-state wage
c1_ss = scalar > 0, steady-state consumption in first period
c_ss = (S,) vector, steady-state lifetime consumption
n_ss = (S,) vector, steady-state lifetime labor supply
b_ss = (S,) vector, steady-state lifetime savings
(b1_ss, b2_ss, ...bS_ss) where b1_ss=0
b_Sp1_ss = scalar, steady-state savings for period after last
period of life. b_Sp1_ss approx. 0 in equilibrium
Y_params = length 2 tuple, (A, alpha)
Y_ss = scalar > 0, steady-state aggregate output (GDP)
C_ss = scalar > 0, steady-state aggregate consumption
n_err_params = length 5 tuple, args to pass into get_n_errors()
n_err_ss = (S,) vector, lifetime labor supply Euler errors
b_err_params = length 2 tuple, args to pass into get_b_errors()
b_err_ss = (S-1) vector, lifetime savings Euler errors
RCerr_ss = scalar, resource constraint error
ss_time = scalar, seconds elapsed to run steady-state comput'n
ss_output = length 14 dict, steady-state objects {n_ss, b_ss,
c_ss, b_Sp1_ss, w_ss, r_ss, K_ss, L_ss, Y_ss, C_ss,
n_err_ss, b_err_ss, RCerr_ss, ss_time}
FILES CREATED BY THIS FUNCTION:
SS_bc.png
SS_n.png
RETURNS: ss_output
--------------------------------------------------------------------
'''
start_time = time.clock()
Kss_init, Lss_init, c1_init = init_vals
(J, S, lambdas, emat, beta, sigma, l_tilde, b_ellip, upsilon,
chi_n_vec, A, alpha, delta, SS_tol, EulDiff) = args
maxiter_SS = 200
iter_SS = 0
mindist_SS = 1e-12
dist_SS = 10
xi_SS = 0.2
KL_init = np.array([Kss_init, Lss_init])
c1_options = {'maxiter': 500}
r_params = (A, alpha, delta)
w_params = (A, alpha)
while (iter_SS < maxiter_SS) and (dist_SS >= mindist_SS):
iter_SS += 1
K_init, L_init = KL_init
r_init = firms.get_r(r_params, K_init, L_init)
w_init = firms.get_w(w_params, K_init, L_init)
rpath = r_init * np.ones(S)
wpath = w_init * np.ones(S)
cmat = np.zeros((S, J))
nmat = np.zeros((S, J))
bmat = np.zeros((S, J))
b_Sp1_vec = np.zeros(J)
for j in range(J):
c1_args = (0.0, emat[:, j], beta, sigma, l_tilde, b_ellip,
upsilon, chi_n_vec, rpath, wpath, EulDiff)
results_c1 = \
opt.root(hh.c1_bSp1err, c1_init, args=(c1_args),
method='lm', tol=SS_tol, options=(c1_options))
c1 = results_c1.x
cnb_args = (0.0, emat[:, j], beta, sigma, l_tilde, b_ellip,
upsilon, chi_n_vec, EulDiff)
cmat[:, j], nmat[:, j], bmat[:, j], b_Sp1_vec[j] = \
hh.get_cnb_vecs(c1, rpath, wpath, cnb_args)
K_new, K_cnstr = aggr.get_K(bmat, lambdas)
L_new = aggr.get_L(nmat, emat, lambdas)
KL_new = np.array([K_new, L_new])
dist_SS = ((KL_new - KL_init) ** 2).sum()
KL_init = xi_SS * KL_new + (1 - xi_SS) * KL_init
print('SS Iteration=', iter_SS, ', SS Distance=',
'%10.4e' % (dist_SS), ',K:', '%10.4e' % (K_new),
'L:', '%10.4e' % (L_new))
K_ss, L_ss = KL_init
r_ss = firms.get_r(r_params, K_ss, L_ss)
w_ss = firms.get_w(w_params, K_ss, L_ss)
c_ss = cmat
n_ss = nmat
b_ss = bmat
b_Sp1_ss = b_Sp1_vec
Y_params = (A, alpha)
Y_ss = aggr.get_Y(Y_params, K_ss, L_ss)
C_ss = aggr.get_C(c_ss, lambdas)
n_err_ss = np.zeros((S, J))
b_err_ss = np.zeros((S - 1, J))
for j in range(J):
n_err_params = (emat[:, j], sigma, l_tilde, chi_n_vec, b_ellip,
upsilon)
n_err_ss[:, j] = hh.get_n_errors(n_err_params, w_ss, c_ss[:, j],
n_ss[:, j], EulDiff)
b_err_params = (beta, sigma)
b_err_ss[:, j] = hh.get_b_errors(b_err_params, r_ss, c_ss[:, j],
EulDiff)
RCerr_ss = Y_ss - C_ss - delta * K_ss
ss_time = time.clock() - start_time
ss_output = {
'n_ss': n_ss, 'b_ss': b_ss, 'c_ss': c_ss, 'b_Sp1_ss': b_Sp1_ss,
'w_ss': w_ss, 'r_ss': r_ss, 'K_ss': K_ss, 'L_ss': L_ss,
'Y_ss': Y_ss, 'C_ss': C_ss, 'n_err_ss': n_err_ss,
'b_err_ss': b_err_ss, 'RCerr_ss': RCerr_ss, 'ss_time': ss_time}
print('K_ss=', K_ss, ', L_ss=', L_ss)
print('r_ss=', r_ss, ', w_ss=', w_ss)
print('Maximum abs. labor supply Euler error is: ',
np.absolute(n_err_ss).max())
print('Maximum abs. savings Euler error is: ',
np.absolute(b_err_ss).max())
print('Resource constraint error is: ', RCerr_ss)
print('Max. absolute SS residual savings b_Sp1_j is: ',
np.absolute(b_Sp1_ss).max())
# Print SS computation time
utils.print_time(ss_time, 'SS')
if graphs:
'''
----------------------------------------------------------------
cur_path = string, path name of current directory
output_fldr = string, folder in current path to save files
output_dir = string, total path of images folder
output_path = string, path of file name of figure to be saved
sgrid = (S,) vector, ages from 1 to S
lamcumsum = (J,) vector, cumulative sum of lambdas vector
jmidgrid = (J,) vector, midpoints of ability percentile bins
smat = (J, S) matrix, sgrid copied down J rows
jmat = (J, S) matrix, jmidgrid copied across S columns
----------------------------------------------------------------
'''
# Create directory if images directory does not already exist
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = 'images'
output_dir = os.path.join(cur_path, output_fldr)
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
# Plot 3D steady-state consumption distribution
sgrid = np.arange(1, S + 1)
lamcumsum = lambdas.cumsum()
jmidgrid = 0.5 * lamcumsum + 0.5 * (lamcumsum - lambdas)
smat, jmat = np.meshgrid(sgrid, jmidgrid)
cmap_c = cm.get_cmap('summer')
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel(r'age-$s$')
ax.set_ylabel(r'ability-$j$')
ax.set_zlabel(r'indiv. consumption $c_{j,s}$')
ax.plot_surface(smat, jmat, c_ss.T, rstride=1,
cstride=6, cmap=cmap_c)
output_path = os.path.join(output_dir, 'c_ss_3D')
plt.savefig(output_path)
# plt.show()
plt.close()
# Plot 2D steady-state consumption distribution
minorLocator = MultipleLocator(1)
fig, ax = plt.subplots()
linestyles = np.array(["-", "--", "-.", ":"])
markers = np.array(["x", "v", "o", "d", ">", "|"])
pct_lb = 0
for j in range(J):
this_label = (str(int(np.rint(pct_lb))) + " - " +
str(int(np.rint(pct_lb + 100 * lambdas[j]))) +
"%")
pct_lb += 100 * lambdas[j]
if j <= 3:
ax.plot(sgrid, c_ss[:, j], label=this_label,
linestyle=linestyles[j], color='black')
elif j > 3:
ax.plot(sgrid, c_ss[:, j], label=this_label,
marker=markers[j - 4], color='black')
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_xlabel(r'age-$s$')
ax.set_ylabel(r'indiv. consumption $c_{j,s}$')
output_path = os.path.join(output_dir, 'c_ss_2D')
plt.savefig(output_path)
# plt.show()
plt.close()
# Plot 3D steady-state labor supply distribution
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel(r'age-$s$')
ax.set_ylabel(r'ability-$j$')
ax.set_zlabel(r'labor supply $n_{j,s}$')
ax.plot_surface(smat, jmat, n_ss.T, rstride=1,
cstride=6, cmap=cmap_c)
output_path = os.path.join(output_dir, 'n_ss_3D')
plt.savefig(output_path)
# plt.show()
plt.close()
# Plot 2D steady-state labor supply distribution
minorLocator = MultipleLocator(1)
fig, ax = plt.subplots()
linestyles = np.array(["-", "--", "-.", ":"])
markers = np.array(["x", "v", "o", "d", ">", "|"])
pct_lb = 0
for j in range(J):
this_label = (str(int(np.rint(pct_lb))) + " - " +
str(int(np.rint(pct_lb + 100 * lambdas[j]))) +
"%")
pct_lb += 100 * lambdas[j]
if j <= 3:
ax.plot(sgrid, n_ss[:, j], label=this_label,
linestyle=linestyles[j], color='black')
elif j > 3:
ax.plot(sgrid, n_ss[:, j], label=this_label,
marker=markers[j - 4], color='black')
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_xlabel(r'age-$s$')
ax.set_ylabel(r'labor supply $n_{j,s}$')
output_path = os.path.join(output_dir, 'n_ss_2D')
plt.savefig(output_path)
# plt.show()
plt.close()
# Plot 3D steady-state savings/wealth distribution
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlabel(r'age-$s$')
ax.set_ylabel(r'ability-$j$')
ax.set_zlabel(r'indiv. savings $b_{j,s}$')
ax.plot_surface(smat, jmat, b_ss.T, rstride=1,
cstride=6, cmap=cmap_c)
output_path = os.path.join(output_dir, 'b_ss_3D')
plt.savefig(output_path)
# plt.show()
plt.close()
# Plot 2D steady-state savings/wealth distribution
fig, ax = plt.subplots()
linestyles = np.array(["-", "--", "-.", ":"])
markers = np.array(["x", "v", "o", "d", ">", "|"])
pct_lb = 0
for j in range(J):
this_label = (str(int(np.rint(pct_lb))) + " - " +
str(int(np.rint(pct_lb + 100 * lambdas[j]))) +
"%")
pct_lb += 100 * lambdas[j]
if j <= 3:
ax.plot(sgrid, b_ss[:, j], label=this_label,
linestyle=linestyles[j], color='black')
elif j > 3:
ax.plot(sgrid, b_ss[:, j], label=this_label,
marker=markers[j - 4], color='black')
ax.xaxis.set_minor_locator(minorLocator)
plt.grid(b=True, which='major', color='0.65', linestyle='-')
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
ax.set_xlabel(r'age-$s$')
ax.set_ylabel(r'indiv. savings $b_{j,s}$')
output_path = os.path.join(output_dir, 'b_ss_2D')
plt.savefig(output_path)
# plt.show()
plt.close()
return ss_output
