def test_plot_population_path_save_fig(tmpdir):
E = 0
S = base_params.S
age_per_EpS = np.arange(21, S + 21)
pop_2013_pct = base_params.omega[0, :]
omega_path_lev = base_params.omega.T
omega_SSfx = base_params.omega_SS
curr_year = base_params.start_year
parameter_plots.plot_population_path(
age_per_EpS, pop_2013_pct, omega_path_lev, omega_SSfx,
curr_year, E, S, output_dir=tmpdir)
img = mpimg.imread(os.path.join(tmpdir, 'PopDistPath.png'))
assert isinstance(img, np.ndarray)
def test_plot_population_path():
E = 0
S = base_params.S
age_per_EpS = np.arange(21, S + 21)
pop_2013_pct = base_params.omega[0, :]
omega_path_lev = base_params.omega.T
omega_SSfx = base_params.omega_SS
curr_year = base_params.start_year
fig = parameter_plots.plot_population_path(
age_per_EpS, pop_2013_pct, omega_path_lev, omega_SSfx,
curr_year, E, S)
assert fig
def get_pop_objs(E, S, T, min_yr, max_yr, curr_year, GraphDiag=False):
'''
This function produces the demographics objects to be used in the
OG-USA model package.
Args:
E (int): number of model periods in which agent is not
economically active, >= 1
S (int): number of model periods in which agent is economically
active, >= 3
T (int): number of periods to be simulated in TPI, > 2*S
min_yr (int): age in years at which agents are born, >= 0
max_yr (int): age in years at which agents die with certainty,
>= 4
curr_year (int): current year for which analysis will begin,
>= 2016
GraphDiag (bool): =True if want graphical output and printed
diagnostics
Returns:
pop_dict (dict): includes:
omega_path_S (Numpy array), time path of the population
distribution from the current state to the steady-state,
size T+S x S
g_n_SS (scalar): steady-state population growth rate
omega_SS (Numpy array): normalized steady-state population
distribution, length S
surv_rates (Numpy array): survival rates that correspond to
each model period of life, length S
mort_rates (Numpy array): mortality rates that correspond to
each model period of life, length S
g_n_path (Numpy array): population growth rates over the time
path, length T + S
'''
assert curr_year >= 2019
# age_per = np.linspace(min_yr, max_yr, E+S)
fert_rates = get_fert(E + S, min_yr, max_yr, graph=False)
mort_rates, infmort_rate = get_mort(E + S, min_yr, max_yr, graph=False)
mort_rates_S = mort_rates[-S:]
imm_rates_orig = get_imm_resid(E + S, min_yr, max_yr)
OMEGA_orig = np.zeros((E + S, E + S))
OMEGA_orig[0, :] = ((1 - infmort_rate) * fert_rates + np.hstack(
(imm_rates_orig[0], np.zeros(E + S - 1))))
OMEGA_orig[1:, :-1] += np.diag(1 - mort_rates[:-1])
OMEGA_orig[1:, 1:] += np.diag(imm_rates_orig[1:])
# Solve for steady-state population growth rate and steady-state
# population distribution by age using eigenvalue and eigenvector
# decomposition
eigvalues, eigvectors = np.linalg.eig(OMEGA_orig)
g_n_SS = (eigvalues[np.isreal(eigvalues)].real).max() - 1
eigvec_raw =\
eigvectors[:,
(eigvalues[np.isreal(eigvalues)].real).argmax()].real
omega_SS_orig = eigvec_raw / eigvec_raw.sum()
# Generate time path of the nonstationary population distribution
omega_path_lev = np.zeros((E + S, T + S))
pop_data = pd.read_csv(
'https://www2.census.gov/programs-surveys/popest/technical-documentation/file-layouts/2010-2019/nc-est2019-agesex-res.csv'
)
pop_data = (pop_data[pop_data['SEX'] == 0][[
'AGE', 'POPESTIMATE2016', 'POPESTIMATE2017', 'POPESTIMATE2018',
'POPESTIMATE2019'
]])
pop_data.rename(columns={
'AGE': 'Age',
'POPESTIMATE2016': '2016',
'POPESTIMATE2017': '2017',
'POPESTIMATE2018': '2018',
'POPESTIMATE2019': '2019'
},
inplace=True)
pop_data_samp = pop_data[(pop_data['Age'] >= min_yr - 1)
& (pop_data['Age'] <= max_yr - 1)]
pop_2019 = np.array(pop_data_samp['2019'], dtype='f')
# Generate the current population distribution given that E+S might
# be less than max_yr-min_yr+1
age_per_EpS = np.arange(1, E + S + 1)
pop_2019_EpS = pop_rebin(pop_2019, E + S)
pop_2019_pct = pop_2019_EpS / pop_2019_EpS.sum()
# Age most recent population data to the current year of analysis
pop_curr = pop_2019_EpS.copy()
data_year = 2019
pop_next = np.dot(OMEGA_orig, pop_curr)
g_n_curr = (
(pop_next[-S:].sum() - pop_curr[-S:].sum()) / pop_curr[-S:].sum()
) # g_n in 2019
pop_past = pop_curr # assume 2018-2019 pop
# Age the data to the current year
for per in range(curr_year - data_year):
pop_next = np.dot(OMEGA_orig, pop_curr)
g_n_curr = ((pop_next[-S:].sum() - pop_curr[-S:].sum()) /
pop_curr[-S:].sum())
pop_past = pop_curr
pop_curr = pop_next
# Generate time path of the population distribution
omega_path_lev[:, 0] = pop_curr.copy()
for per in range(1, T + S):
pop_next = np.dot(OMEGA_orig, pop_curr)
omega_path_lev[:, per] = pop_next.copy()
pop_curr = pop_next.copy()
# Force the population distribution after 1.5*S periods to be the
# steady-state distribution by adjusting immigration rates, holding
# constant mortality, fertility, and SS growth rates
imm_tol = 1e-14
fixper = int(1.5 * S)
omega_SSfx = (omega_path_lev[:, fixper] / omega_path_lev[:, fixper].sum())
imm_objs = (fert_rates, mort_rates, infmort_rate,
omega_path_lev[:, fixper], g_n_SS)
imm_fulloutput = opt.fsolve(immsolve,
imm_rates_orig,
args=(imm_objs),
full_output=True,
xtol=imm_tol)
imm_rates_adj = imm_fulloutput[0]
imm_diagdict = imm_fulloutput[1]
omega_path_S = (omega_path_lev[-S:, :] /
np.tile(omega_path_lev[-S:, :].sum(axis=0), (S, 1)))
omega_path_S[:, fixper:] = \
np.tile(omega_path_S[:, fixper].reshape((S, 1)),
(1, T + S - fixper))
g_n_path = np.zeros(T + S)
g_n_path[0] = g_n_curr.copy()
g_n_path[1:] = ((omega_path_lev[-S:, 1:].sum(axis=0) -
omega_path_lev[-S:, :-1].sum(axis=0)) /
omega_path_lev[-S:, :-1].sum(axis=0))
g_n_path[fixper + 1:] = g_n_SS
omega_S_preTP = (pop_past.copy()[-S:]) / (pop_past.copy()[-S:].sum())
imm_rates_mat = np.hstack(
(np.tile(np.reshape(imm_rates_orig[E:], (S, 1)), (1, fixper)),
np.tile(np.reshape(imm_rates_adj[E:], (S, 1)), (1, T + S - fixper))))
if GraphDiag:
# Check whether original SS population distribution is close to
# the period-T population distribution
omegaSSmaxdif = np.absolute(omega_SS_orig -
(omega_path_lev[:, T] /
omega_path_lev[:, T].sum())).max()
if omegaSSmaxdif > 0.0003:
print('POP. WARNING: Max. abs. dist. between original SS ' +
"pop. dist'n and period-T pop. dist'n is greater than" +
' 0.0003. It is ' + str(omegaSSmaxdif) + '.')
else:
print('POP. SUCCESS: orig. SS pop. dist is very close to ' +
"period-T pop. dist'n. The maximum absolute " +
'difference is ' + str(omegaSSmaxdif) + '.')
# Plot the adjusted steady-state population distribution versus
# the original population distribution. The difference should be
# small
omegaSSvTmaxdiff = np.absolute(omega_SS_orig - omega_SSfx).max()
if omegaSSvTmaxdiff > 0.0003:
print('POP. WARNING: The maximimum absolute difference ' +
'between any two corresponding points in the original' +
' and adjusted steady-state population ' +
'distributions is' + str(omegaSSvTmaxdiff) + ', ' +
'which is greater than 0.0003.')
else:
print('POP. SUCCESS: The maximum absolute difference ' +
'between any two corresponding points in the original' +
' and adjusted steady-state population ' +
'distributions is ' + str(omegaSSvTmaxdiff))
# Print whether or not the adjusted immigration rates solved the
# zero condition
immtol_solved = \
np.absolute(imm_diagdict['fvec'].max()) < imm_tol
if immtol_solved:
print('POP. SUCCESS: Adjusted immigration rates solved ' +
'with maximum absolute error of ' +
str(np.absolute(imm_diagdict['fvec'].max())) +
', which is less than the tolerance of ' + str(imm_tol))
else:
print('POP. WARNING: Adjusted immigration rates did not ' +
'solve. Maximum absolute error of ' +
str(np.absolute(imm_diagdict['fvec'].max())) +
' is greater than the tolerance of ' + str(imm_tol))
# Test whether the steady-state growth rates implied by the
# adjusted OMEGA matrix equals the steady-state growth rate of
# the original OMEGA matrix
OMEGA2 = np.zeros((E + S, E + S))
OMEGA2[0, :] = ((1 - infmort_rate) * fert_rates + np.hstack(
(imm_rates_adj[0], np.zeros(E + S - 1))))
OMEGA2[1:, :-1] += np.diag(1 - mort_rates[:-1])
OMEGA2[1:, 1:] += np.diag(imm_rates_adj[1:])
eigvalues2, eigvectors2 = np.linalg.eig(OMEGA2)
g_n_SS_adj = (eigvalues[np.isreal(eigvalues2)].real).max() - 1
if np.max(np.absolute(g_n_SS_adj - g_n_SS)) > 10**(-8):
print('FAILURE: The steady-state population growth rate' +
' from adjusted OMEGA is different (diff is ' +
str(g_n_SS_adj - g_n_SS) + ') than the steady-' +
'state population growth rate from the original' + ' OMEGA.')
elif np.max(np.absolute(g_n_SS_adj - g_n_SS)) <= 10**(-8):
print('SUCCESS: The steady-state population growth rate' +
' from adjusted OMEGA is close to (diff is ' +
str(g_n_SS_adj - g_n_SS) + ') the steady-' +
'state population growth rate from the original' + ' OMEGA.')
# Do another test of the adjusted immigration rates. Create the
# new OMEGA matrix implied by the new immigration rates. Plug in
# the adjusted steady-state population distribution. Hit is with
# the new OMEGA transition matrix and it should return the new
# steady-state population distribution
omega_new = np.dot(OMEGA2, omega_SSfx)
omega_errs = np.absolute(omega_new - omega_SSfx)
print('The maximum absolute difference between the adjusted ' +
'steady-state population distribution and the ' +
'distribution generated by hitting the adjusted OMEGA ' +
'transition matrix is ' + str(omega_errs.max()))
# Plot the original immigration rates versus the adjusted
# immigration rates
immratesmaxdiff = \
np.absolute(imm_rates_orig - imm_rates_adj).max()
print('The maximum absolute distance between any two points ' +
'of the original immigration rates and adjusted ' +
'immigration rates is ' + str(immratesmaxdiff))
# plots
pp.plot_omega_fixed(age_per_EpS,
omega_SS_orig,
omega_SSfx,
E,
S,
output_dir=OUTPUT_DIR)
pp.plot_imm_fixed(age_per_EpS,
imm_rates_orig,
imm_rates_adj,
E,
S,
output_dir=OUTPUT_DIR)
pp.plot_population_path(age_per_EpS,
pop_2019_pct,
omega_path_lev,
omega_SSfx,
curr_year,
E,
S,
output_dir=OUTPUT_DIR)
# return omega_path_S, g_n_SS, omega_SSfx, survival rates,
# mort_rates_S, and g_n_path
pop_dict = {
'omega': omega_path_S.T,
'g_n_SS': g_n_SS,
'omega_SS': omega_SSfx[-S:] / omega_SSfx[-S:].sum(),
'surv_rate': 1 - mort_rates_S,
'rho': mort_rates_S,
'g_n': g_n_path,
'imm_rates': imm_rates_mat.T,
'omega_S_preTP': omega_S_preTP
}
return pop_dict