def test_read_file_from_egg():
'''
Test of utils.read_file() function, case of reading file from .egg
'''
path = os.path.join(CUR_PATH)
fname = 'default_parameters.json'
bytes_data = utils.read_file(path, fname)
assert isinstance(bytes_data, io.StringIO)
def test_read_file():
'''
Test of utils.read_file() function
'''
path = os.path.join(CUR_PATH, 'test_io_data')
fname = 'SS_fsolve_inputs.pkl'
bytes_data = utils.read_file(path, fname)
assert isinstance(bytes_data, io.TextIOWrapper)
def ss_profiles(base_ss, base_params, reform_ss=None,
reform_params=None, by_j=True, var='nssmat',
plot_data=False,
plot_title=None, path=None):
'''
Plot lifecycle profiles of given variable in the SS.
Args:
base_ss (dictionary): SS output from baseline run
base_params (OG-USA Specifications class): baseline parameters
object
reform_ss (dictionary): SS output from reform run
reform_params (OG-USA Specifications class): reform parameters
object
var (string): name of variable to plot
plot_data (bool): whether to plot data values for given variable
plot_title (string): title for plot
path (string): path to save figure to
Returns:
fig (Matplotlib plot object): plot of lifecycle profiles
'''
if reform_ss:
assert (base_params.S == reform_params.S)
assert (base_params.starting_age == reform_params.starting_age)
assert (base_params.ending_age == reform_params.ending_age)
age_vec = np.arange(base_params.starting_age,
base_params.starting_age + base_params.S)
fig1, ax1 = plt.subplots()
if by_j:
cm = plt.get_cmap('coolwarm')
ax1.set_prop_cycle(color=[cm(1. * i / 7) for i in range(7)])
for j in range(base_params.J):
plt.plot(age_vec, base_ss[var][:, j],
label='Baseline, j = ' + str(j))
if reform_ss:
plt.plot(age_vec, reform_ss[var][:, j],
label='Reform, j = ' + str(j), linestyle='--')
else:
base_var = (
base_ss[var][:, :] *
base_params.lambdas.reshape(1, base_params.J)).sum(axis=1)
plt.plot(age_vec, base_var, label='Baseline')
if reform_ss:
reform_var = (
reform_ss[var][:, :] *
reform_params.lambdas.reshape(1, reform_params.J)).sum(axis=1)
plt.plot(age_vec, reform_var, label='Reform', linestyle='--')
if plot_data:
assert var == 'nssmat'
labor_file = utils.read_file(
cur_path, "data/labor/cps_hours_by_age_hourspct.txt")
data = pd.read_csv(labor_file, header=0, delimiter='\t')
piv = data.pivot(index='age', columns='hours_pct',
values='mean_hrs')
lab_mat_basic = np.array(piv)
lab_mat_basic /= np.nanmax(lab_mat_basic)
piv2 = data.pivot(index='age', columns='hours_pct',
values='num_obs')
weights = np.array(piv2)
weights /= np.nansum(weights, axis=1).reshape(
60, 1)
weighted = np.nansum((lab_mat_basic * weights), axis=1)
weighted = np.append(weighted, np.zeros(20))
weighted[60:] = np.nan
plt.plot(age_vec, weighted, linewidth=2.0, label='Data',
linestyle=':')
plt.xlabel(r'Age')
plt.ylabel(VAR_LABELS[var])
plt.legend(loc=9, bbox_to_anchor=(0.5, -0.15), ncol=2)
if plot_title:
plt.title(plot_title, fontsize=15)
if path:
fig_path1 = os.path.join(path)
plt.savefig(fig_path1, bbox_inches="tight")
else:
return fig1
plt.close()
def get_imm_resid(totpers, min_yr, max_yr, graph=True):
'''
--------------------------------------------------------------------
Calculate immigration rates by age as a residual given population
levels in different periods, then output average calculated
immigration rate. We have to replace the first mortality rate in
this function in order to adjust the first implied immigration rate
(Source: Population data come from Annual Estimates of the Resident
Population by Single Year of Age and Sex: April 1, 2010 to July 1,
2013 (Both sexes) National Characteristics, Vintage 2013, US Census
Bureau,
http://www.census.gov/popest/data/national/asrh/2013/index.html)
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utils.read_file()
get_fert()
get_mort()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data (beg per is 1)
pop_2010 = (100,) vector, population for ages 0 to 99 in 2010
pop_2011 = (100,) vector, population for ages 0 to 99 in 2011
pop_2012 = (100,) vector, population for ages 0 to 99 in 2012
pop_2013 = (100,) vector, population for ages 0 to 99 in 2013
imm_mat = (3, 100) matrix, immigration rates computed as
residuals for each age in three successive pairs of
years
pop11vec = (3,) vector, age-1 population in first three years
pop21vec = (3,) vector, age-1 population in last three years
fert_rates = (100,) vector, fertility rates by model age
mort_rates = (100,) vector, mortality rates by model age
infmort_rate = scalar > 0, infant mortality rate from 2015 U.S. CIA
World Factbook
newbornvec = (3,) vector, total births in first three years
pop11mat = (3, 99) matrix, population of age 1 through 99 for
first three years
pop12mat = (3, 99) matrix, population of age 2 through 100 for
first three years
pop22mat = (3, 99) matrix, population of age 2 through 100 for
last three years
mort_mat = (3, 99) matrix, the first 99 mortality rates copied
into 3 rows
imm_rates_all = (100,) vector, average of three years residual
immigration rates by each age in data
imm_func = function, generated by interp1d function, takes
ages and returns the interpolated immigration rates
age_per = (E+S,) vector, age in years at each period of life
imm_rates = (E+S,) vector, immigration rates that correspond to
each period of life
RETURNS: imm_rates
--------------------------------------------------------------------
'''
cur_path = os.path.split(os.path.abspath(__file__))[0]
pop_file = utils.read_file(cur_path,
"data/demographic/pop_data.csv")
pop_data = pd.read_csv(pop_file, sep=',', thousands=',')
pop_data_samp = pop_data[(pop_data['Age'] >= min_yr - 1) &
(pop_data['Age'] <= max_yr - 1)]
pop_2010, pop_2011, pop_2012, pop_2013 = (
np.array(pop_data_samp['2010'], dtype='f'),
np.array(pop_data_samp['2011'], dtype='f'),
np.array(pop_data_samp['2012'], dtype='f'),
np.array(pop_data_samp['2013'], dtype='f'))
pop_2010_EpS = pop_rebin(pop_2010, totpers)
pop_2011_EpS = pop_rebin(pop_2011, totpers)
pop_2012_EpS = pop_rebin(pop_2012, totpers)
pop_2013_EpS = pop_rebin(pop_2013, totpers)
# Create three years of estimated immigration rates for youngest age
# individuals
imm_mat = np.zeros((3, totpers))
pop11vec = np.array([pop_2010_EpS[0], pop_2011_EpS[0],
pop_2012_EpS[0]])
pop21vec = np.array([pop_2011_EpS[0], pop_2012_EpS[0],
pop_2013_EpS[0]])
fert_rates = get_fert(totpers, min_yr, max_yr, False)
mort_rates, infmort_rate = get_mort(totpers, min_yr, max_yr, False)
newbornvec = np.dot(fert_rates, np.vstack((pop_2010_EpS,
pop_2011_EpS,
pop_2012_EpS)).T)
imm_mat[:, 0] = ((pop21vec - (1 - infmort_rate) * newbornvec) /
pop11vec)
# Estimate 3 years of immigration rates for all other-aged
# individuals
pop11mat = np.vstack((pop_2010_EpS[:-1], pop_2011_EpS[:-1],
pop_2012_EpS[:-1]))
pop12mat = np.vstack((pop_2010_EpS[1:], pop_2011_EpS[1:],
pop_2012_EpS[1:]))
pop22mat = np.vstack((pop_2011_EpS[1:], pop_2012_EpS[1:],
pop_2013_EpS[1:]))
mort_mat = np.tile(mort_rates[:-1], (3, 1))
imm_mat[:, 1:] = (pop22mat - (1 - mort_mat) * pop11mat) / pop12mat
# Final estimated immigration rates are the averages over 3 years
imm_rates = imm_mat.mean(axis=0)
age_per = np.linspace(1, totpers, totpers)
if graph:
'''
----------------------------------------------------------------
output_fldr = string, path of the OUTPUT folder from cur_path
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
fig, ax = plt.subplots()
plt.scatter(age_per, imm_rates, s=40, c='red', marker='d')
plt.plot(age_per, imm_rates)
# 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('Fitted immigration rates by age ($i_{s}$), residual',
# fontsize=20)
plt.xlabel(r'Age $s$ (model periods)')
plt.ylabel(r'Imm. rate $i_{s}$')
plt.xlim((0, totpers + 1))
# Create directory if OUTPUT directory does not already exist
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) is False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "imm_rates_orig")
plt.savefig(output_path)
# plt.show()
return imm_rates
def get_pop_objs(E, S, T, min_yr, max_yr, curr_year, GraphDiag=True):
'''
--------------------------------------------------------------------
This function produces the demographics objects to be used in the
OG-USA model package.
--------------------------------------------------------------------
INPUTS:
E = integer >= 1, number of model periods in which agent is
not economically active
S = integer >= 3, number of model periods in which agent is
economically active
T = integer > 2*S, number of periods to be simulated in TPI
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
curr_year = integer >= 2016, current year for which analysis will
begin
GraphDiag = boolean, =True if want graphical output and printed
diagnostics
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
get_fert()
get_mort()
get_imm_resid()
utils.read_file()
pop_rebin()
immsolve()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
age_per = (E+S,) vector, age in years at each period of life
fert_rates = (E+S,) vector, fertility rates that correspond to
each model period of life
mort_rates = (E+S,) vector, mortality rates that correspond to
each model period of life
infmort_rate = scalar > 0, infant mortality rate from 2015 U.S.
CIA World Factbook
mort_rates_S = (S,) vector, mortality rates that correspond to
each economically active model period of life
imm_rates_orig = (E+S,) vector, immigration rates by age estimated
as residuals from get_imm_resid()
OMEGA_orig = (E+S, E+S) matrix, transition matrix for
population distribution law of motion
eigvalues = (E+S,) vector, eigenvalues of OMEGA matrix
eigvectors = (E+S, E+S) matrix, matrix of eigenvectors of OMEGA
where each column is the eigenvector that goes
with the corresponding eigenvalue in eigvalues
g_n_SS_orig = scalar, steady-state population growth rate, which
is the largest real part of the eigenvalues
eigvec_raw = (E+S,) vector, nonnormalized eigenvector
corresponding to the largest real-part eigenvalue
omega_SS_orig = (E+S,) vector, steady-state population
distribution which is normalized eigvec_raw
omega_path_orig = (E+S, T) matrix, time path of the population
distribution from the current state to the steady-
state
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data, beg per=1
pop_2013 = (100,) vector, population for ages 0 to 99 in 2013
age_per_EpS = (E+S,) vector, period numbers 1 through E+S
pop_2013_EpS = (E+S,) vector, population distribution by model
periods E + S in levels
pop_2013_pct = (E+S,) vector, 2013 population distribution in
percentages
pop_curr = (E+S,) vector, current-period population
distribution in percentages
data_year = integer, most recent year in data
per = integer, index for period
pop_next = (E+S,) vector, next-period population distribution
imm_tol = scalar > 0, tolerance for fsolve in immsolve()
fixper = ?
omega_SSfx = ?
imm_objs = ?
imm_fulloutput = ?
imm_rates_adj = ?
imm_diagdict = ?
omega_path_S = ?
imm_rates_S = ?
imm_rates_S_adj = ?
RETURNS: omega_path_S.T, g_n_SS,
omega_SSfx[-S:] / omega_SSfx[-S:].sum(), 1-mort_rates_S,
mort_rates_S, g_n_path, imm_rates_mat
--------------------------------------------------------------------
'''
# 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, graph=False)
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))
cur_path = os.path.split(os.path.abspath(__file__))[0]
pop_file = utils.read_file(cur_path,
"data/demographic/pop_data.csv")
pop_data = pd.read_csv(pop_file, sep=',', thousands=',')
pop_data_samp = pop_data[(pop_data['Age'] >= min_yr - 1) &
(pop_data['Age'] <= max_yr - 1)]
pop_2013 = np.array(pop_data_samp['2013'], 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_2013_EpS = pop_rebin(pop_2013, E + S)
pop_2013_pct = pop_2013_EpS / pop_2013_EpS.sum()
# Age most recent population data to the current year of analysis
pop_curr = pop_2013_EpS.copy()
data_year = 2013
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 2013
pop_past = pop_curr # assume 2012-2013 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))
fig, ax = plt.subplots()
plt.plot(age_per_EpS, omega_SS_orig, label="Original Dist'n")
plt.plot(age_per_EpS, omega_SSfx, label="Fixed Dist'n")
# 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(
'Original steady-state population distribution vs. fixed',
fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r"Pop. dist'n $\omega_{s}$")
plt.xlim((0, E + S + 1))
plt.legend(loc='upper right')
# Create directory if OUTPUT directory does not already exist
'''
----------------------------------------------------------------
output_fldr = string, path of the OUTPUT folder from cur_path
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) is False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "OrigVsFixSSpop")
plt.savefig(output_path)
plt.show()
# 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))
fig, ax = plt.subplots()
plt.plot(age_per_EpS, imm_rates_orig, label="Original Imm. Rates")
plt.plot(age_per_EpS, imm_rates_adj, label="Adj. Imm. Rates")
# 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(
'Original immigration rates vs. adjusted',
fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r"Imm. rates $i_{s}$")
plt.xlim((0, E + S + 1))
plt.legend(loc='upper center')
# Create directory if OUTPUT directory does not already exist
output_path = os.path.join(output_dir, "OrigVsAdjImm")
plt.savefig(output_path)
plt.show()
# Plot population distributions for data_year, curr_year,
# curr_year+20, omega_SSfx, and omega_SS_orig
fig, ax = plt.subplots()
plt.plot(age_per_EpS, pop_2013_pct, label="2013 pop.")
plt.plot(age_per_EpS, (omega_path_lev[:, 0] /
omega_path_lev[:, 0].sum()),
label=str(curr_year) + " pop.")
plt.plot(age_per_EpS, (omega_path_lev[:, int(0.5 * S)] /
omega_path_lev[:, int(0.5 * S)].sum()),
label="T=" + str(int(0.5 * S)) + " pop.")
plt.plot(age_per_EpS, (omega_path_lev[:, int(S)] /
omega_path_lev[:, int(S)].sum()),
label="T=" + str(int(S)) + " pop.")
plt.plot(age_per_EpS, omega_SSfx, label="Adj. SS pop.")
# 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(
'Population distribution at points in time path',
fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r"Pop. dist'n $\omega_{s}$")
plt.xlim((0, E+S+1))
plt.legend(loc='lower left')
# Create directory if OUTPUT directory does not already exist
output_path = os.path.join(output_dir, "PopDistPath")
plt.savefig(output_path)
plt.show()
# return omega_path_S, g_n_SS, omega_SSfx, survival rates,
# mort_rates_S, and g_n_path
return (omega_path_S.T, g_n_SS, omega_SSfx[-S:] /
omega_SSfx[-S:].sum(), 1-mort_rates_S, mort_rates_S,
g_n_path, imm_rates_mat.T, omega_S_preTP)
def get_mort(totpers, min_yr, max_yr, graph=False):
'''
--------------------------------------------------------------------
This function generates a vector of mortality rates by model period
age.
(Source: Male and Female death probabilities Actuarial Life table,
2011 Social Security Administration,
http://www.ssa.gov/oact/STATS/table4c6.html)
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, total number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utils.read_file()
mort_rates2011.csv
OBJECTS CREATED WITHIN FUNCTION:
infmort_rate = scalar > 0, infant mortality rate from 2015 U.S.
CIA World Factbook
cur_path = string, path where function calling file resides
mort_file = string, path of mortality rate data source (.csv)
mort_data = 120 x 7 DataFrame, 2011 mortality rate data for
men and women
age_year_all = (114,) vector, ages by year for which total
mortality have positive population weight
mort_rates_all = (114,) vector, mortality rates by all ages with
positive population weight
mort_rates_mxyr = (100,) vector, truncated mortality rates by age
binsize = scalar > 0, size of each model period bin in data
years
num_sub_bins = scalar, an arbitrarily and deliberately large
number of sub-bins that each population bin will
be broken up into
len_subbins = scalar, length of a model period in data sub-bins
mort_rates_sub = (num_sub_bins*100,) vector, mortality rates by
sub-bin implied by mort_rates_mxyr
mort_rates = (totpers,) vector, mortality rates that correspond
to each period of life
i = integer >= 0, index of model period being computed
beg_sub_bin = integer >= 0, index of beginning sub-bin for
calculation of cumulative mortality rate of given
model period
end_sub_bin = integer >= 0, index of ending sub-bin + 1 for
calculation of cumulative mortality rate of given
model period
FILES CREATED BY THIS FUNCTION:
mort_rates.png
RETURNS: mort_rates, infmort_rate
--------------------------------------------------------------------
'''
# Get mortality rate by age data
infmort_rate = 0.00587 # taken from 2015 U.S. infant mortality rate
cur_path = os.path.split(os.path.abspath(__file__))[0]
mort_file = utils.read_file(
cur_path, 'data/demographic/mort_rates2011.csv')
mort_data = pd.read_csv(mort_file, sep=',', thousands=',')
age_year_all = mort_data['Age'] + 1
mort_rates_all = (
((mort_data['Male Mort. Rate'] * mort_data['Num. Male Lives']) +
(mort_data['Female Mort. Rate'] *
mort_data['Num. Female Lives'])) /
(mort_data['Num. Male Lives'] + mort_data['Num. Female Lives']))
age_year_all = age_year_all[np.isfinite(mort_rates_all)]
mort_rates_all = mort_rates_all[np.isfinite(mort_rates_all)]
# Calculate implied mortality rates in sub-bins of mort_rates_all.
mort_rates_mxyr = mort_rates_all[0:max_yr]
num_sub_bins = int(100)
len_subbins = ((np.float64((max_yr - min_yr + 1) * num_sub_bins)) /
totpers)
mort_rates_sub = np.zeros(num_sub_bins * max_yr, dtype=float)
for i in range(max_yr):
mort_rates_sub[i * num_sub_bins:(i + 1) * num_sub_bins] =\
(1 - ((1 - mort_rates_mxyr[i]) ** (1.0 / num_sub_bins)))
mort_rates = np.zeros(totpers)
end_sub_bin = 0
for i in range(totpers):
beg_sub_bin = int(end_sub_bin)
end_sub_bin = int(np.rint((i + 1) * len_subbins))
mort_rates[i] = (
1 - (1 - (mort_rates_sub[beg_sub_bin:end_sub_bin])).prod())
mort_rates[-1] = 1 # Mortality rate in last period is set to 1
if graph:
'''
----------------------------------------------------------------
age_mid_new = (totpers,) vector, midpoint age of each model
period age bin
output_fldr = string, folder in current path to save files
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
age_mid_new = (np.linspace(np.float(max_yr) / totpers, max_yr,
totpers) - (0.5 * np.float(max_yr) /
totpers))
fig, ax = plt.subplots()
plt.scatter(np.hstack([0, age_year_all]),
np.hstack([infmort_rate, mort_rates_all]),
s=20, c='blue', marker='o', label='Data')
plt.scatter(np.hstack([0, age_mid_new]),
np.hstack([infmort_rate, mort_rates]),
s=40, c='red', marker='d',
label='Model period (cumulative)')
plt.plot(np.hstack([0, age_year_all[min_yr - 1:max_yr]]),
np.hstack([infmort_rate,
mort_rates_all[min_yr - 1:max_yr]]))
plt.axvline(x=max_yr, color='red', linestyle='-', linewidth=1)
# 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('Fitted mortality rate function by age ($rho_{s}$)',
# fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Mortality rate $\rho_{s}$')
plt.xlim((min_yr-2, age_year_all.max()+2))
plt.ylim((-0.05, 1.05))
plt.legend(loc='upper left')
plt.text(-5, -0.2,
"Source: Actuarial Life table, 2011 Social Security " +
"Administration.", fontsize=9)
plt.tight_layout(rect=(0, 0.03, 1, 1))
# Create directory if OUTPUT directory does not already exist
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) is False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "mort_rates")
plt.savefig(output_path)
# plt.show()
return mort_rates, infmort_rate
def get_fert(totpers, min_yr, max_yr, graph=False):
'''
--------------------------------------------------------------------
This function generates a vector of fertility rates by model period
age that corresponds to the fertility rate data by age in years
(Source: National Vital Statistics Reports, Volume 64, Number 1,
January 15, 2015, Table 3, final 2013 data
http://www.cdc.gov/nchs/data/nvsr/nvsr64/nvsr64_01.pdf)
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, total number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utlis.read_file()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data (beg per=1)
curr_pop = (100,) vector, population for ages 0 to 99 in 2013
curr_pop_pct = (100,) vector, population (in percent) for ages 0
to 99 in 2013
fert_data = (13,) vector, fertility rates for given age bins.
We divide numbers by 2,000 because original data is
in births per 1000 women. We assume an equal number
of men. Added two zeros on the front and on the
back to make spline interpolation work right
age_midp = (13,) vector, midpoint age of age bins ranges from
original data (9, 10, 10-14, 15-17, 18-19, 20-24,
25-29, 30-34, 35-39, 40-44, 45-49, 55, 56). The
first two and last two are not data
fert_func = function, generated by interp1d function, takes
ages and returns the interpolated fertility rates
binsize = scalar > 0, size of each model period bin in data
years
num_sub_bins = scalar, an arbitrarily and deliberately large
number of sub-bins that each population bin will be
broken up into
len_subbins = scalar, length of a model period in data sub-bins
age_sub = (num_sub_bins*100,) vector, midpoint ages of each
data sub-bin
curr_pop_sub = (num_sub_bins*100,) vector, population linearly
interpolated from data in each sub-bin
fert_rates_sub = (num_sub_bins*100,) vector, fertility rates by sub-
bin interpolated from fert_func()
pred_ind = (num_sub_bins*100,) boolean vector, =True if period
is one that must be interpolated
age_pred = (num_sub_bins*100-some,) vector, midpoint age in
years corresponding to each period to be
interpolated
fert_rates = (totpers,) vector, fertility rates for each model
period of life
i = integer >= 0, index of model period being computed
beg_sub_bin = integer >= 0, index of beginning sub-bin for
calculation of average fertility rate of given
model period
end_sub_bin = integer >= 0, index of ending sub-bin + 1 for
calculation of average fertility rate of given
model period
FILES CREATED BY THIS FUNCTION:
fert_rates.png
RETURNS: fert_rates
--------------------------------------------------------------------
'''
# Get current population data (2013) for weighting
cur_path = os.path.split(os.path.abspath(__file__))[0]
pop_file = utils.read_file(cur_path,
"data/demographic/pop_data.csv")
pop_data = pd.read_csv(pop_file, sep=',', thousands=',')
pop_data_samp = pop_data[(pop_data['Age'] >= min_yr - 1) &
(pop_data['Age'] <= max_yr - 1)]
curr_pop = np.array(pop_data_samp['2013'], dtype='f')
curr_pop_pct = curr_pop / curr_pop.sum()
# Get fertility rate by age-bin data
fert_data = (np.array([0.0, 0.0, 0.3, 12.3, 47.1, 80.7, 105.5, 98.0,
49.3, 10.4, 0.8, 0.0, 0.0]) / 2000)
age_midp = np.array([9, 10, 12, 16, 18.5, 22, 27, 32, 37, 42, 47,
55, 56])
# Generate interpolation functions for fertility rates
fert_func = si.interp1d(age_midp, fert_data, kind='cubic')
# Calculate average fertility rate in each age bin using trapezoid
# method with a large number of points in each bin.
binsize = (max_yr - min_yr + 1) / totpers
num_sub_bins = float(10000)
len_subbins = (np.float64(100 * num_sub_bins)) / totpers
age_sub = (np.linspace(np.float64(binsize) / num_sub_bins,
np.float64(max_yr),
int(num_sub_bins*max_yr)) - 0.5 *
np.float64(binsize) / num_sub_bins)
curr_pop_sub = np.repeat(np.float64(curr_pop_pct) / num_sub_bins,
num_sub_bins)
fert_rates_sub = np.zeros(curr_pop_sub.shape)
pred_ind = (age_sub > age_midp[0]) * (age_sub < age_midp[-1])
age_pred = age_sub[pred_ind]
fert_rates_sub[pred_ind] = np.float64(fert_func(age_pred))
fert_rates = np.zeros(totpers)
end_sub_bin = 0
for i in range(totpers):
beg_sub_bin = int(end_sub_bin)
end_sub_bin = int(np.rint((i + 1) * len_subbins))
fert_rates[i] = ((
curr_pop_sub[beg_sub_bin:end_sub_bin] *
fert_rates_sub[beg_sub_bin:end_sub_bin]).sum() /
curr_pop_sub[beg_sub_bin:end_sub_bin].sum())
if graph:
'''
----------------------------------------------------------------
age_fine_pred = (300,) vector, equally spaced support of ages
between the minimum and maximum interpolating
ages
fert_fine_pred = (300,) vector, interpolated fertility rates
based on age_fine_pred
age_fine = (300+some,) vector of ages including leading
and trailing zeros
fert_fine = (300+some,) vector of fertility rates including
leading and trailing zeros
age_mid_new = (totpers,) vector, midpoint age of each model
period age bin
output_fldr = string, folder in current path to save files
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
# Generate finer age vector and fertility rate vector for
# graphing cubic spline interpolating function
age_fine_pred = np.linspace(age_midp[0], age_midp[-1], 300)
fert_fine_pred = fert_func(age_fine_pred)
age_fine = np.hstack((min_yr, age_fine_pred, max_yr))
fert_fine = np.hstack((0, fert_fine_pred, 0))
age_mid_new = (np.linspace(np.float(max_yr) / totpers, max_yr,
totpers) - (0.5 * np.float(max_yr) /
totpers))
fig, ax = plt.subplots()
plt.scatter(age_midp, fert_data, s=70, c='blue', marker='o',
label='Data')
plt.scatter(age_mid_new, fert_rates, s=40, c='red', marker='d',
label='Model period (integrated)')
plt.plot(age_fine, fert_fine, label='Cubic spline')
# 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('Fitted fertility rate function by age ($f_{s}$)',
# fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Fertility rate $f_{s}$')
plt.xlim((min_yr - 1, max_yr + 1))
plt.ylim((-0.15 * (fert_fine_pred.max()),
1.15 * (fert_fine_pred.max())))
plt.legend(loc='upper right')
plt.text(-5, -0.018,
"Source: National Vital Statistics Reports, " +
"Volume 64, Number 1, January 15, 2015.", fontsize=9)
plt.tight_layout(rect=(0, 0.03, 1, 1))
# Create directory if OUTPUT directory does not already exist
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) is False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "fert_rates")
plt.savefig(output_path)
return fert_rates
def get_pop_objs(E, S, T, min_yr, max_yr, curr_year, GraphDiag=True):
'''
--------------------------------------------------------------------
This function produces the demographics objects to be used in the
OG-USA model package.
--------------------------------------------------------------------
INPUTS:
E = integer >= 1, number of model periods in which agent is
not economically active
S = integer >= 3, number of model periods in which agent is
economically active
T = integer > 2*S, number of periods to be simulated in TPI
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
curr_year = integer >= 2016, current year for which analysis will
begin
GraphDiag = boolean, =True if want graphical output and printed
diagnostics
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
get_fert()
get_mort()
get_imm_resid()
utils.read_file()
pop_rebin()
immsolve()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
age_per = (E+S,) vector, age in years at each period of life
fert_rates = (E+S,) vector, fertility rates that correspond to
each model period of life
mort_rates = (E+S,) vector, mortality rates that correspond to
each model period of life
infmort_rate = scalar > 0, infant mortality rate from 2015 U.S.
CIA World Factbook
mort_rates_S = (S,) vector, mortality rates that correspond to
each economically active model period of life
imm_rates_orig = (E+S,) vector, immigration rates by age estimated
as residuals from get_imm_resid()
OMEGA_orig = (E+S, E+S) matrix, transition matrix for
population distribution law of motion
eigvalues = (E+S,) vector, eigenvalues of OMEGA matrix
eigvectors = (E+S, E+S) matrix, matrix of eigenvectors of OMEGA
where each column is the eigenvector that goes
with the corresponding eigenvalue in eigvalues
g_n_SS_orig = scalar, steady-state population growth rate, which
is the largest real part of the eigenvalues
eigvec_raw = (E+S,) vector, nonnormalized eigenvector
corresponding to the largest real-part eigenvalue
omega_SS_orig = (E+S,) vector, steady-state population
distribution which is normalized eigvec_raw
omega_path_orig = (E+S, T) matrix, time path of the population
distribution from the current state to the steady-
state
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data, beg per=1
pop_2013 = (100,) vector, population for ages 0 to 99 in 2013
age_per_EpS = (E+S,) vector, period numbers 1 through E+S
pop_2013_EpS = (E+S,) vector, population distribution by model
periods E + S in levels
pop_2013_pct = (E+S,) vector, 2013 population distribution in
percentages
pop_curr = (E+S,) vector, current-period population
distribution in percentages
data_year = integer, most recent year in data
per = integer, index for period
pop_next = (E+S,) vector, next-period population distribution
imm_tol = scalar > 0, tolerance for fsolve in immsolve()
fixper = ?
omega_SSfx = ?
imm_objs = ?
imm_fulloutput = ?
imm_rates_adj = ?
imm_diagdict = ?
omega_path_S = ?
imm_rates_S = ?
imm_rates_S_adj = ?
RETURNS: omega_path_S.T, g_n_SS,
omega_SSfx[-S:] / omega_SSfx[-S:].sum(), 1-mort_rates_S,
mort_rates_S, g_n_path, imm_rates_mat
--------------------------------------------------------------------
'''
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, graph=False)
#imm_rates_orig = np.zeros(E+S)
imm_rates_S = imm_rates_orig[-S:]
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))
cur_path = os.path.split(os.path.abspath(__file__))[0]
pop_file = utils.read_file(cur_path,
"data/demographic/pop_data.csv")
pop_data = pd.read_table(pop_file, sep=',', thousands=',')
pop_data_samp = pop_data[(pop_data['Age']>=min_yr-1) &
(pop_data['Age']<=max_yr-1)]
age_year_all = pop_data_samp['Age'] + 1
pop_2013 = np.array(pop_data_samp['2013'], 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_2013_EpS = pop_rebin(pop_2013, E+S)
pop_2013_pct = pop_2013_EpS / pop_2013_EpS.sum()
# Age most recent population data to the current year of analysis
pop_curr = pop_2013_EpS.copy()
data_year = 2013
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 2013
pop_past = pop_curr # assume 2012-2013 pop
for per in range(curr_year - data_year): # Age the data to
# the current 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
curr_dict = {"pop_" + str(curr_year) + "_pct":
pop_curr.copy() / pop_curr.sum()}
# 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_rates_adj = np.zeros(E+S)
imm_rates_S_adj = imm_rates_adj[-S:]
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))))
# omega_diffs_orig = (omega_path_S[1:,1:] -
# (1/(1+np.tile(np.reshape(g_n_path[1:],(1,T+S-1)),(S-1,1))))*(1-np.tile(np.reshape(mort_rates_S[:-1],(S-1,1)),(1,T+S-1)))*omega_path_S[:-1,:-1] -
# (1/(1+np.tile(np.reshape(g_n_path[1:],(1,T+S-1)),(S-1,1))))*np.tile(np.reshape(imm_rates_orig[E+1:],(S-1,1)),(1,T+S-1))*omega_path_S[1:,:-1])
# omega_diffs_adj = (omega_path_S[1:,1:] -
# (1/(1+np.tile(np.reshape(g_n_path[1:],(1,T+S-1)),(S-1,1))))*(1-np.tile(np.reshape(mort_rates_S[:-1],(S-1,1)),(1,T+S-1)))*omega_path_S[:-1,:-1] -
# (1/(1+np.tile(np.reshape(g_n_path[1:],(1,T+S-1)),(S-1,1))))*np.tile(np.reshape(imm_rates_adj[E+1:],(S-1,1)),(1,T+S-1))*omega_path_S[1:,:-1])
# omega_diffs_mixed = (omega_path_S[1:,1:] -
# (1/(1+np.tile(np.reshape(g_n_path[1:],(1,T+S-1)),(S-1,1))))*(1-np.tile(np.reshape(mort_rates_S[:-1],(S-1,1)),(1,T+S-1)))*omega_path_S[:-1,:-1] -
# (1/(1+np.tile(np.reshape(g_n_path[1:],(1,T+S-1)),(S-1,1))))*imm_rates_mat[1:,:-1]*omega_path_S[1:,:-1])
# np.savetxt('omega_diffs_orig.csv', omega_diffs_orig, delimiter=',')
# np.savetxt('omega_diffs_adj.csv', omega_diffs_adj, delimiter=',')
# np.savetxt('omega_diffs_mixed.csv', omega_diffs_mixed, delimiter=',')
if GraphDiag == True:
# 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))
fig, ax = plt.subplots()
plt.plot(age_per_EpS, omega_SS_orig, label="Original Dist'n")
plt.plot(age_per_EpS, omega_SSfx, label="Fixed Dist'n")
# 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(
'Original steady-state population distribution vs. fixed',
fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r"Pop. dist'n $\omega_{s}$")
plt.xlim((0, E+S+1))
plt.legend(loc='upper right')
# Create directory if OUTPUT directory does not already exist
'''
----------------------------------------------------------------
output_fldr = string, path of the OUTPUT folder from cur_path
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
cur_path = os.path.split(os.path.abspath(__file__))[0]
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) == False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "OrigVsFixSSpop")
plt.savefig(output_path)
plt.show()
# 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 == True:
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))
fig, ax = plt.subplots()
plt.plot(age_per_EpS, imm_rates_orig, label="Original Imm. Rates")
plt.plot(age_per_EpS, imm_rates_adj, label="Adj. Imm. Rates")
# 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(
'Original immigration rates vs. adjusted',
fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r"Imm. rates $i_{s}$")
plt.xlim((0, E+S+1))
plt.legend(loc='upper center')
# Create directory if OUTPUT directory does not already exist
output_path = os.path.join(output_dir, "OrigVsAdjImm")
plt.savefig(output_path)
plt.show()
# Plot population distributions for data_year, curr_year,
# curr_year+20, omega_SSfx, and omega_SS_orig
fig, ax = plt.subplots()
plt.plot(age_per_EpS, pop_2013_pct, label="2013 pop.")
plt.plot(age_per_EpS,
(omega_path_lev[:, 0] / omega_path_lev[:, 0].sum()),
label=str(curr_year)+" pop.")
plt.plot(age_per_EpS, (omega_path_lev[:, int(0.5 * S)] /
omega_path_lev[:, int(0.5 * S)].sum()),
label="T="+str(int(0.5 * S))+" pop.")
plt.plot(age_per_EpS, (omega_path_lev[:, int(S)] /
omega_path_lev[:, int(S)].sum()),
label="T="+str(int(S))+" pop.")
plt.plot(age_per_EpS, omega_SSfx, label="Adj. SS pop.")
# 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(
'Population distribution at points in time path',
fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r"Pop. dist'n $\omega_{s}$")
plt.xlim((0, E+S+1))
plt.legend(loc='lower left')
# Create directory if OUTPUT directory does not already exist
output_path = os.path.join(output_dir, "PopDistPath")
plt.savefig(output_path)
plt.show()
# return omega_path_S, g_n_SS, omega_SSfx, survival rates,
# mort_rates_S, and g_n_path
return (omega_path_S.T, g_n_SS,
omega_SSfx[-S:] / omega_SSfx[-S:].sum(), 1-mort_rates_S,
mort_rates_S, g_n_path, imm_rates_mat.T, omega_S_preTP)
def get_imm_resid(totpers, min_yr, max_yr, graph=True):
'''
--------------------------------------------------------------------
Calculate immigration rates by age as a residual given population
levels in different periods, then output average calculated
immigration rate. We have to replace the first mortality rate in
this function in order to adjust the first implied immigration rate
(Source: Population data come from Annual Estimates of the Resident
Population by Single Year of Age and Sex: April 1, 2010 to July 1,
2013 (Both sexes) National Characteristics, Vintage 2013, US Census
Bureau,
http://www.census.gov/popest/data/national/asrh/2013/index.html)
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utils.read_file()
get_fert()
get_mort()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data (beg per is 1)
pop_2010 = (100,) vector, population for ages 0 to 99 in 2010
pop_2011 = (100,) vector, population for ages 0 to 99 in 2011
pop_2012 = (100,) vector, population for ages 0 to 99 in 2012
pop_2013 = (100,) vector, population for ages 0 to 99 in 2013
imm_mat = (3, 100) matrix, immigration rates computed as
residuals for each age in three successive pairs of
years
pop11vec = (3,) vector, age-1 population in first three years
pop21vec = (3,) vector, age-1 population in last three years
fert_rates = (100,) vector, fertility rates by model age
mort_rates = (100,) vector, mortality rates by model age
infmort_rate = scalar > 0, infant mortality rate from 2015 U.S. CIA
World Factbook
newbornvec = (3,) vector, total births in first three years
pop11mat = (3, 99) matrix, population of age 1 through 99 for
first three years
pop12mat = (3, 99) matrix, population of age 2 through 100 for
first three years
pop22mat = (3, 99) matrix, population of age 2 through 100 for
last three years
mort_mat = (3, 99) matrix, the first 99 mortality rates copied
into 3 rows
imm_rates_all = (100,) vector, average of three years residual
immigration rates by each age in data
imm_func = function, generated by interp1d function, takes
ages and returns the interpolated immigration rates
age_per = (E+S,) vector, age in years at each period of life
imm_rates = (E+S,) vector, immigration rates that correspond to
each period of life
RETURNS: imm_rates
--------------------------------------------------------------------
'''
cur_path = os.path.split(os.path.abspath(__file__))[0]
pop_file = utils.read_file(cur_path,
"data/demographic/pop_data.csv")
pop_data = pd.read_table(pop_file, sep=',', thousands=',')
pop_data_samp = pop_data[(pop_data['Age']>=min_yr-1) &
(pop_data['Age']<=max_yr-1)]
age_year_all = pop_data_samp['Age'] + 1
pop_2010, pop_2011, pop_2012, pop_2013 = (
np.array(pop_data_samp['2010'], dtype='f'),
np.array(pop_data_samp['2011'], dtype='f'),
np.array(pop_data_samp['2012'], dtype='f'),
np.array(pop_data_samp['2013'], dtype='f'))
pop_2010_EpS = pop_rebin(pop_2010, totpers)
pop_2011_EpS = pop_rebin(pop_2011, totpers)
pop_2012_EpS = pop_rebin(pop_2012, totpers)
pop_2013_EpS = pop_rebin(pop_2013, totpers)
# Create three years of estimated immigration rates for youngest age
# individuals
imm_mat = np.zeros((3, totpers))
pop11vec = np.array([pop_2010_EpS[0], pop_2011_EpS[0],
pop_2012_EpS[0]])
pop21vec = np.array([pop_2011_EpS[0], pop_2012_EpS[0],
pop_2013_EpS[0]])
fert_rates = get_fert(totpers, min_yr, max_yr, False)
mort_rates, infmort_rate = get_mort(totpers, min_yr, max_yr, False)
newbornvec = np.dot(fert_rates,
np.vstack((pop_2010_EpS, pop_2011_EpS, pop_2012_EpS)).T)
imm_mat[:, 0] = ((pop21vec - (1 - infmort_rate) * newbornvec) /
pop11vec)
# Estimate 3 years of immigration rates for all other-aged
# individuals
pop11mat = np.vstack((pop_2010_EpS[:-1], pop_2011_EpS[:-1],
pop_2012_EpS[:-1]))
pop12mat = np.vstack((pop_2010_EpS[1:], pop_2011_EpS[1:],
pop_2012_EpS[1:]))
pop22mat = np.vstack((pop_2011_EpS[1:], pop_2012_EpS[1:],
pop_2013_EpS[1:]))
mort_mat = np.tile(mort_rates[:-1], (3, 1))
imm_mat[:, 1:] = (pop22mat - (1 - mort_mat) * pop11mat) / pop12mat
# Final estimated immigration rates are the averages over 3 years
imm_rates = imm_mat.mean(axis=0)
age_per = np.linspace(1, totpers, totpers)
if graph == True:
'''
----------------------------------------------------------------
output_fldr = string, path of the OUTPUT folder from cur_path
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
fig, ax = plt.subplots()
plt.scatter(age_per, imm_rates, s=40, c='red', marker='d')
plt.plot(age_per, imm_rates)
# 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('Fitted immigration rates by age ($i_{s}$), residual',
# fontsize=20)
plt.xlabel(r'Age $s$ (model periods)')
plt.ylabel(r'Imm. rate $i_{s}$')
plt.xlim((0, totpers+1))
# Create directory if OUTPUT directory does not already exist
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) == False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "imm_rates_orig")
plt.savefig(output_path)
# plt.show()
return imm_rates
def get_fert(totpers, min_yr, max_yr, graph=False):
'''
--------------------------------------------------------------------
This function generates a vector of fertility rates by model period
age that corresponds to the fertility rate data by age in years
(Source: National Vital Statistics Reports, Volume 64, Number 1,
January 15, 2015, Table 3, final 2013 data
http://www.cdc.gov/nchs/data/nvsr/nvsr64/nvsr64_01.pdf)
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, total number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utlis.read_file()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data (beg per=1)
curr_pop = (100,) vector, population for ages 0 to 99 in 2013
curr_pop_pct = (100,) vector, population (in percent) for ages 0
to 99 in 2013
fert_data = (13,) vector, fertility rates for given age bins.
We divide numbers by 2,000 because original data is
in births per 1000 women. We assume an equal number
of men. Added two zeros on the front and on the
back to make spline interpolation work right
age_midp = (13,) vector, midpoint age of age bins ranges from
original data (9, 10, 10-14, 15-17, 18-19, 20-24,
25-29, 30-34, 35-39, 40-44, 45-49, 55, 56). The
first two and last two are not data
fert_func = function, generated by interp1d function, takes
ages and returns the interpolated fertility rates
binsize = scalar > 0, size of each model period bin in data
years
num_sub_bins = scalar, an arbitrarily and deliberately large
number of sub-bins that each population bin will be
broken up into
len_subbins = scalar, length of a model period in data sub-bins
age_sub = (num_sub_bins*100,) vector, midpoint ages of each
data sub-bin
curr_pop_sub = (num_sub_bins*100,) vector, population linearly
interpolated from data in each sub-bin
fert_rates_sub = (num_sub_bins*100,) vector, fertility rates by sub-
bin interpolated from fert_func()
pred_ind = (num_sub_bins*100,) boolean vector, =True if period
is one that must be interpolated
age_pred = (num_sub_bins*100-some,) vector, midpoint age in
years corresponding to each period to be
interpolated
fert_rates = (totpers,) vector, fertility rates for each model
period of life
i = integer >= 0, index of model period being computed
beg_sub_bin = integer >= 0, index of beginning sub-bin for
calculation of average fertility rate of given
model period
end_sub_bin = integer >= 0, index of ending sub-bin + 1 for
calculation of average fertility rate of given
model period
FILES CREATED BY THIS FUNCTION:
fert_rates.png
RETURNS: fert_rates
--------------------------------------------------------------------
'''
# Get current population data (2013) for weighting
cur_path = os.path.split(os.path.abspath(__file__))[0]
pop_file = utils.read_file(cur_path,
"data/demographic/pop_data.csv")
pop_data = pd.read_table(pop_file, sep=',', thousands=',')
pop_data_samp = pop_data[(pop_data['Age']>=min_yr-1) &
(pop_data['Age']<=max_yr-1)]
age_year_all = pop_data_samp['Age'] + 1
curr_pop = np.array(pop_data_samp['2013'], dtype='f')
curr_pop_pct = curr_pop / curr_pop.sum()
# Get fertility rate by age-bin data
fert_data = (np.array([0.0, 0.0, 0.3, 12.3, 47.1, 80.7, 105.5, 98.0,
49.3, 10.4, 0.8, 0.0, 0.0]) / 2000)
age_midp = np.array([9, 10, 12, 16, 18.5, 22, 27, 32, 37, 42, 47,
55, 56])
# Generate interpolation functions for fertility rates
fert_func = si.interp1d(age_midp, fert_data, kind='cubic')
# Calculate average fertility rate in each age bin using trapezoid
# method with a large number of points in each bin.
binsize = (max_yr - min_yr + 1) / totpers
num_sub_bins = float(10000)
len_subbins = (np.float64(100 * num_sub_bins)) / totpers
age_sub = (np.linspace(np.float64(binsize) / num_sub_bins,
np.float64(max_yr), int(num_sub_bins*max_yr)) -
0.5 * np.float64(binsize) / num_sub_bins)
curr_pop_sub = np.repeat(np.float64(curr_pop_pct) /
num_sub_bins, num_sub_bins)
fert_rates_sub = np.zeros(curr_pop_sub.shape)
pred_ind = (age_sub > age_midp[0]) * (age_sub < age_midp[-1])
age_pred = age_sub[pred_ind]
fert_rates_sub[pred_ind] = np.float64(fert_func(age_pred))
fert_rates = np.zeros(totpers)
end_sub_bin = 0
for i in range(totpers):
beg_sub_bin = int(end_sub_bin)
end_sub_bin = int(np.rint((i + 1) * len_subbins))
fert_rates[i] = ((curr_pop_sub[beg_sub_bin:end_sub_bin] *
fert_rates_sub[beg_sub_bin:end_sub_bin]).sum() /
curr_pop_sub[beg_sub_bin:end_sub_bin].sum())
if graph == True:
'''
----------------------------------------------------------------
age_fine_pred = (300,) vector, equally spaced support of ages
between the minimum and maximum interpolating
ages
fert_fine_pred = (300,) vector, interpolated fertility rates
based on age_fine_pred
age_fine = (300+some,) vector of ages including leading
and trailing zeros
fert_fine = (300+some,) vector of fertility rates including
leading and trailing zeros
age_mid_new = (totpers,) vector, midpoint age of each model
period age bin
output_fldr = string, folder in current path to save files
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
# Generate finer age vector and fertility rate vector for
# graphing cubic spline interpolating function
age_fine_pred = np.linspace(age_midp[0], age_midp[-1], 300)
fert_fine_pred = fert_func(age_fine_pred)
age_fine = np.hstack((min_yr, age_fine_pred, max_yr))
fert_fine = np.hstack((0, fert_fine_pred, 0))
age_mid_new = (np.linspace(np.float(max_yr) /
totpers, max_yr, totpers) -
(0.5 * np.float(max_yr) / totpers))
fig, ax = plt.subplots()
plt.scatter(age_midp, fert_data, s=70, c='blue', marker='o',
label='Data')
plt.scatter(age_mid_new, fert_rates, s=40, c='red', marker='d',
label='Model period (integrated)')
plt.plot(age_fine, fert_fine, label='Cubic spline')
# 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('Fitted fertility rate function by age ($f_{s}$)',
# fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Fertility rate $f_{s}$')
plt.xlim((min_yr-1, max_yr+1))
plt.ylim((-0.15*(fert_fine_pred.max()),
1.15*(fert_fine_pred.max())))
plt.legend(loc='upper right')
plt.text(-5, -0.018,
"Source: National Vital Statistics Reports, Volume 64, Number 1, January 15, 2015.",
fontsize=9)
plt.tight_layout(rect=(0, 0.03, 1, 1))
# Create directory if OUTPUT directory does not already exist
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) == False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "fert_rates")
plt.savefig(output_path)
# plt.show()
return fert_rates
def get_mort(totpers, min_yr, max_yr, graph=False):
'''
--------------------------------------------------------------------
This function generates a vector of mortality rates by model period
age.
(Source: Male and Female death probabilities Actuarial Life table,
2011 Social Security Administration,
http://www.ssa.gov/oact/STATS/table4c6.html)
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, total number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utils.read_file()
mort_rates2011.csv
OBJECTS CREATED WITHIN FUNCTION:
infmort_rate = scalar > 0, infant mortality rate from 2015 U.S.
CIA World Factbook
cur_path = string, path where function calling file resides
mort_file = string, path of mortality rate data source (.csv)
mort_data = 120 x 7 DataFrame, 2011 mortality rate data for
men and women
age_year_all = (114,) vector, ages by year for which total
mortality have positive population weight
mort_rates_all = (114,) vector, mortality rates by all ages with
positive population weight
mort_rates_mxyr = (100,) vector, truncated mortality rates by age
binsize = scalar > 0, size of each model period bin in data
years
num_sub_bins = scalar, an arbitrarily and deliberately large
number of sub-bins that each population bin will
be broken up into
len_subbins = scalar, length of a model period in data sub-bins
mort_rates_sub = (num_sub_bins*100,) vector, mortality rates by
sub-bin implied by mort_rates_mxyr
mort_rates = (totpers,) vector, mortality rates that correspond
to each period of life
i = integer >= 0, index of model period being computed
beg_sub_bin = integer >= 0, index of beginning sub-bin for
calculation of cumulative mortality rate of given
model period
end_sub_bin = integer >= 0, index of ending sub-bin + 1 for
calculation of cumulative mortality rate of given
model period
FILES CREATED BY THIS FUNCTION:
mort_rates.png
RETURNS: mort_rates, infmort_rate
--------------------------------------------------------------------
'''
# Get mortality rate by age data
infmort_rate = 0.00587 # taken from 2015 U.S. infant mortality rate
cur_path = os.path.split(os.path.abspath(__file__))[0]
mort_file = utils.read_file(cur_path,
'data/demographic/mort_rates2011.csv')
mort_data = pd.read_table(mort_file, sep=',', thousands=',')
age_year_all = mort_data['Age'] + 1
mort_rates_all = (((mort_data['Male Mort. Rate'] *
mort_data['Num. Male Lives']) + (mort_data['Female Mort. Rate']
* mort_data['Num. Female Lives'])) /
(mort_data['Num. Male Lives'] + mort_data['Num. Female Lives']))
age_year_all = age_year_all[np.isfinite(mort_rates_all)]
mort_rates_all = mort_rates_all[np.isfinite(mort_rates_all)]
# Calculate implied mortality rates in sub-bins of mort_rates_all.
mort_rates_mxyr = mort_rates_all[0:max_yr]
binsize = (max_yr - min_yr + 1) / totpers
num_sub_bins = int(100)
len_subbins = ((np.float64((max_yr - min_yr + 1) * num_sub_bins)) /
totpers)
mort_rates_sub = np.zeros(num_sub_bins * max_yr, dtype=float)
for i in range(max_yr):
mort_rates_sub[i*num_sub_bins:(i+1)*num_sub_bins] =\
(1 - ((1 - mort_rates_mxyr[i]) ** (1.0 / num_sub_bins)))
mort_rates = np.zeros(totpers)
end_sub_bin = 0
for i in range(totpers):
beg_sub_bin = int(end_sub_bin)
end_sub_bin = int(np.rint((i + 1) * len_subbins))
mort_rates[i] = (1 - (1 - (mort_rates_sub[beg_sub_bin:end_sub_bin])).prod())
mort_rates[-1] = 1 # Mortality rate in last period is set to 1
if graph == True:
'''
----------------------------------------------------------------
age_mid_new = (totpers,) vector, midpoint age of each model
period age bin
output_fldr = string, folder in current path to save files
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
age_mid_new = (np.linspace(np.float(max_yr) /
totpers, max_yr, totpers) -
(0.5 * np.float(max_yr) / totpers))
fig, ax = plt.subplots()
plt.scatter(np.hstack([0, age_year_all]),
np.hstack([infmort_rate, mort_rates_all]),
s=20, c='blue', marker='o', label='Data')
plt.scatter(np.hstack([0, age_mid_new]),
np.hstack([infmort_rate, mort_rates]),
s=40, c='red', marker='d', label='Model period (cumulative)')
plt.plot(np.hstack([0, age_year_all[min_yr-1:max_yr]]),
np.hstack([infmort_rate, mort_rates_all[min_yr-1:max_yr]]))
plt.axvline(x=max_yr, color='red', linestyle='-', linewidth=1)
# 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('Fitted mortality rate function by age ($rho_{s}$)',
# fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Mortality rate $\rho_{s}$')
plt.xlim((min_yr-2, age_year_all.max()+2))
plt.ylim((-0.05, 1.05))
plt.legend(loc='upper left')
plt.text(-5, -0.2,
"Source: Actuarial Life table, 2011 Social Security Administration.",
fontsize=9)
plt.tight_layout(rect=(0, 0.03, 1, 1))
# Create directory if OUTPUT directory does not already exist
output_fldr = "OUTPUT/Demographics"
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) == False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, "mort_rates")
plt.savefig(output_path)
# plt.show()
return mort_rates, infmort_rate
def get_fert(totpers, min_yr, max_yr, graph=False):
'''
--------------------------------------------------------------------
This function generates a vector of fertility rates by model period
age that corresponds to the fertility rate data by age in years
--------------------------------------------------------------------
INPUTS:
totpers = integer >= 3, total number of agent life periods (E+S)
min_yr = integer >= 0, age in years at which agents are born,
minimum age
max_yr = integer >= 4, age in years at which agents die with
certainty, maximum age
graph = boolean, =True if want graphical output
OTHER FUNCTIONS AND FILES CALLED BY THIS FUNCTION:
utlis.read_file()
pop_data.csv
OBJECTS CREATED WITHIN FUNCTION:
cur_path = string, path in which calling file resides
pop_file = string, path of population data source csv file
pop_data = 101 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 100
pop_data_samp = 100 x 5 DataFrame, Age, Pop2010, Pop2011, Pop2012,
Pop2013, for ages 0 to 99
age_year_all = (100,) vector, ages by year from data (beg per=1)
curr_pop = (100,) vector, population for ages 0 to 99 in 2013
curr_pop_pct = (100,) vector, population (in percent) for ages 0
to 99 in 2013
fert_data = (13,) vector, fertility rates for given age bins.
We divide numbers by 2,000 because original data is
in births per 1000 women. We assume an equal number
of men. Added two zeros on the front and on the
back to make spline interpolation work right
age_midp = (13,) vector, midpoint age of age bins ranges from
original data (9, 10, 10-14, 15-17, 18-19, 20-24,
25-29, 30-34, 35-39, 40-44, 45-49, 55, 56). The
first two and last two are not data
fert_func = function, generated by interp1d function, takes
ages and returns the interpolated fertility rates
binsize = scalar > 0, size of each model period bin in data
years
num_sub_bins = scalar, an arbitrarily and deliberately large
number of sub-bins that each population bin will be
broken up into
len_subbins = scalar, length of a model period in data sub-bins
age_sub = (num_sub_bins*100,) vector, midpoint ages of each
data sub-bin
curr_pop_sub = (num_sub_bins*100,) vector, population linearly
interpolated from data in each sub-bin
fert_rates_sub = (num_sub_bins*100,) vector, fertility rates by sub-
bin interpolated from fert_func()
pred_ind = (num_sub_bins*100,) boolean vector, =True if period
is one that must be interpolated
age_pred = (num_sub_bins*100-some,) vector, midpoint age in
years corresponding to each period to be
interpolated
fert_rates = (totpers,) vector, fertility rates for each model
period of life
i = integer >= 0, index of model period being computed
beg_sub_bin = integer >= 0, index of beginning sub-bin for
calculation of average fertility rate of given
model period
end_sub_bin = integer >= 0, index of ending sub-bin + 1 for
calculation of average fertility rate of given
model period
FILES CREATED BY THIS FUNCTION:
fert_rates.png
RETURNS: fert_rates
--------------------------------------------------------------------
'''
# Get current population data for weighting
pop_file = utils.read_file(cur_path, pop_dir)
pop_data = pd.read_csv(pop_file,
sep=r'\s+',
usecols=['Year', 'Age', 'Total'])
pop_data = select_pop_data(pop_data)
pop_data_samp = pop_data[(pop_data['Age'] >= min_yr - 1)
& (pop_data['Age'] <= max_yr - 1)]
curr_pop = np.array(pop_data_samp[pop_data_samp['Year'] == 2014]['Total'],
dtype='f')
curr_pop_pct = curr_pop / curr_pop.sum(
) # pct population of that age group within same year
# Get fertility rate by age-bin data
fert_data = pd.read_csv(fert_dir, sep=',\s*',\
usecols=['Year1', 'Age', 'ASFR', 'AgeDef',\
'Collection', 'RefCode'])
fert_data = select_fert_data(fert_data)
fert_list = []
for i in range(14, 51):
age = fert_data[fert_data['Age'] == i]
data = age[age['Year'].isin(range(1990, 2015))]
fert_list.append(data['Values'].mean())
fert_data = fert_data[fert_data['Year'] == 1995]
fert_data['Values'] = fert_list
fert_data['Values'] = fert_data['Values'] / 2
# Generate interpolation functions for fertility rates
fert_func = si.splrep(fert_data['Age'], fert_data['Values'])
#### AGE BIN CREATION
# Calculate average fertility rate in each age bin using trapezoid
# method with a large number of points in each bin.
binsize = (max_yr - min_yr +
1) / totpers # creating different generations (I believe?)
num_sub_bins = float(10000)
len_subbins = (np.float64(100 * num_sub_bins)) / totpers
# 100 (lifetime year) / totpers gives us size of bins. To get length of subbin shouldnt we dividing by num_sub_bins ????
age_sub = (
np.linspace(
np.float64(binsize) /
num_sub_bins, # gives us the first subbin (len subbin)
np.float64(max_yr), # gives us end point
int(num_sub_bins * max_yr)) - 0.5 * #
np.float64(binsize) / num_sub_bins)
# gives us mid age of all subbins
### POPULATION CREATION
ages = np.linspace(min_yr, max_yr, curr_pop_pct.shape[0])
pop_func = si.splrep(ages, curr_pop_pct)
new_bins = np.linspace(min_yr, max_yr,\
num_sub_bins * max_yr)
curr_pop_sub = si.splev(new_bins, pop_func)
curr_pop_sub = curr_pop_sub / curr_pop_sub.sum()
fert_rates_sub = np.zeros(curr_pop_sub.shape)
pred_ind = (age_sub > fert_data['Age'].iloc[0]) * (
age_sub < fert_data['Age'].iloc[-1]
) # makes sure it is inside valid range
age_pred = age_sub[
pred_ind] #gets age_sub in the valid range by applying pred_ind
fert_rates_sub[pred_ind] = np.float64(si.splev(age_pred, fert_func))
fert_rates_sub[fert_rates_sub < 0] = 0
fert_rates = np.zeros(totpers)
end_sub_bin = 0
for i in range(totpers):
beg_sub_bin = int(end_sub_bin)
end_sub_bin = int(np.rint((i + 1) * len_subbins))
fert_rates[i] = ((curr_pop_sub[beg_sub_bin:end_sub_bin] *
fert_rates_sub[beg_sub_bin:end_sub_bin]).sum() /
curr_pop_sub[beg_sub_bin:end_sub_bin].sum())
fert_rates = np.nan_to_num(fert_rates)
if graph:
'''
----------------------------------------------------------------
age_fine_pred = (300,) vector, equally spaced support of ages
between the minimum and maximum interpolating
ages
fert_fine_pred = (300,) vector, interpolated fertility rates
based on age_fine_pred
age_fine = (300+some,) vector of ages including leading
and trailing zeros
fert_fine = (300+some,) vector of fertility rates including
leading and trailing zeros
age_mid_new = (totpers,) vector, midpoint age of each model
period age bin
output_fldr = string, folder in current path to save files
output_dir = string, total path of OUTPUT folder
output_path = string, path of file name of figure to be saved
----------------------------------------------------------------
'''
# Generate finer age vector and fertility rate vector for
# graphing cubic spline interpolating function
age_fine_pred = np.linspace(age_midp[0], age_midp[-1], 300)
fert_fine_pred = fert_func(age_fine_pred)
age_fine = np.hstack((min_yr, age_fine_pred, max_yr))
fert_fine = np.hstack((0, fert_fine_pred, 0))
age_mid_new = (
np.linspace(np.float(max_yr) / totpers, max_yr, totpers) -
(0.5 * np.float(max_yr) / totpers))
fig, ax = plt.subplots()
plt.scatter(age_midp,
fert_data,
s=70,
c='blue',
marker='o',
label='Data')
plt.scatter(age_mid_new,
fert_rates,
s=40,
c='red',
marker='d',
label='Model period (integrated)')
plt.plot(age_fine, fert_fine, label='Cubic spline')
# 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('Fitted fertility rate function by age ($f_{s}$)',
# fontsize=20)
plt.xlabel(r'Age $s$')
plt.ylabel(r'Fertility rate $f_{s}$')
plt.xlim((min_yr - 1, max_yr + 1))
plt.ylim(
(-0.15 * (fert_fine_pred.max()), 1.15 * (fert_fine_pred.max())))
plt.legend(loc='upper right')
plt.text(-5,
-0.018,
'Source: National Vital Statistics Reports, ' +
'Volume 64, Number 1, January 15, 2015.',
fontsize=9)
plt.tight_layout(rect=(0, 0.03, 1, 1))
# Create directory if OUTPUT directory does not already exist
output_fldr = 'OUTPUT/Demographics'
output_dir = os.path.join(cur_path, output_fldr)
if os.access(output_dir, os.F_OK) is False:
os.makedirs(output_dir)
output_path = os.path.join(output_dir, 'fert_rates')
plt.savefig(output_path)
return fert_rates
