def makeMPCfig(kappa, weights):
'''
Plot the CDF of the marginal propensity to consume. A sub-function of makeCSTWresults().
Parameters
----------
kappa : np.array
Array of (annualized) marginal propensities to consume for the economy.
weights : np.array
Age-conditional weight array for the data in kappa.
Returns
-------
these_percents : np.array
Array of percentiles of the marginal propensity to consume.
kappa_percentiles : np.array
Array of MPCs corresponding to the percentiles in these_percents.
'''
these_percents = np.linspace(0.0001, 0.9999, 201)
kappa_percentiles = getPercentiles(kappa,
weights,
percentiles=these_percents)
plt.plot(kappa_percentiles, these_percents, '-k', linewidth=1.5)
plt.xlabel('Marginal propensity to consume', fontsize=14)
plt.ylabel('Cumulative probability', fontsize=14)
plt.title('CDF of the MPC', fontsize=16)
plt.show()
return (these_percents, kappa_percentiles)
def makeMPCfig(kappa,weights):
'''
Plot the CDF of the marginal propensity to consume. A sub-function of makeCSTWresults().
Parameters
----------
kappa : np.array
Array of (annualized) marginal propensities to consume for the economy.
weights : np.array
Age-conditional weight array for the data in kappa.
Returns
-------
these_percents : np.array
Array of percentiles of the marginal propensity to consume.
kappa_percentiles : np.array
Array of MPCs corresponding to the percentiles in these_percents.
'''
these_percents = np.linspace(0.0001,0.9999,201)
kappa_percentiles = getPercentiles(kappa,weights,percentiles=these_percents)
plt.plot(kappa_percentiles,these_percents,'-k',linewidth=1.5)
plt.xlabel('Marginal propensity to consume',fontsize=14)
plt.ylabel('Cumulative probability',fontsize=14)
plt.title('CDF of the MPC',fontsize=16)
plt.show()
return (these_percents,kappa_percentiles)
def makeValidationFigures(params, use_cohorts):
'''
Make several figures that compare simulated outcomes from the estimated model
to their data counterparts, for external validation.
Parameters
----------
params : np.array
Size 33 array of model parameters, like that used for estimation.
use_cohorts : bool
Indicator for whether or not to model differences across cohorts.
Returns
-------
None
'''
# Make, solve, and simulate the types
param_dict = convertVecToDict(params)
if use_cohorts:
type_list = makeMultiTypeWithCohorts(param_dict)
else:
type_list = makeMultiTypeSimple(param_dict)
for this_type in type_list:
this_type.track_vars.append('MedLvlNow')
this_type.track_vars.append('iLvlNow')
this_type.track_vars.append('HitCfloor')
this_type.CalcExpectationFuncs = True
this_type.DeleteSolution = False
multiThreadCommandsFake(type_list, ['estimationAction()'], num_jobs=5)
# Combine simulated data across all types
aLvlHist = np.concatenate(
[this_type.aLvlNow_hist for this_type in type_list], axis=1)
hLvlHist = np.concatenate(
[this_type.hLvlNow_hist for this_type in type_list], axis=1)
OOPhist = np.concatenate(
[this_type.OOPmedNow_hist for this_type in type_list], axis=1)
MortHist = np.concatenate(
[this_type.DiePrbNow_hist for this_type in type_list], axis=1)
WeightHist = np.concatenate(
[this_type.CumLivPrb_hist for this_type in type_list], axis=1)
MedHist = np.concatenate(
[this_type.MedLvlNow_hist for this_type in type_list], axis=1)
# Combine data labels across types
HealthTert = np.concatenate(
[this_type.HealthTert for this_type in type_list])
HealthQuint = np.concatenate(
[this_type.HealthQuint for this_type in type_list])
WealthQuint = np.concatenate(
[this_type.WealthQuint for this_type in type_list])
IncQuint = np.concatenate(
[this_type.IncQuintLong for this_type in type_list])
Sex = np.concatenate([this_type.SexLong for this_type in type_list])
# Combine in-data-span masking array across all types
Active = hLvlHist > 0.
InDataSpan = np.concatenate(
[this_type.InDataSpanArray for this_type in type_list], axis=1)
WeightAdj = InDataSpan * WeightHist
# For each type, calculate the probability that no health investment is purchased at each age
# and the probability the
iLvlZeroRate = np.zeros((10, 25))
HitCfloorRate = np.zeros((10, 25))
for j in range(10):
this_type = type_list[j]
iLvlZero = this_type.iLvlNow_hist == 0.
HitCfloor = this_type.HitCfloor_hist == 1.
iLvlZeroSum = np.sum(iLvlZero * this_type.CumLivPrb_hist, axis=1)
HitCfloorSum = np.sum(HitCfloor * this_type.CumLivPrb_hist, axis=1)
PopSum = np.sum(this_type.CumLivPrb_hist, axis=1)
iLvlZeroRate[j, :] = iLvlZeroSum / PopSum
HitCfloorRate[j, :] = HitCfloorSum / PopSum
# Calculate median (pseudo) bank balances for each type
bLvl_init_median = np.zeros(10)
for n in range(10):
bLvl_init_median[n] = np.median(
type_list[n].aLvlInit) + type_list[n].IncomeNow[2]
# Extract deciles of health by age from the simulated data
pctiles = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]
SimHealthPctiles = np.zeros((15, len(pctiles)))
for t in range(15):
SimHealthPctiles[t, :] = getPercentiles(hLvlHist[t, :],
weights=WeightAdj[t, :],
percentiles=pctiles)
# Plot the probability of purchasing zero health investment by age, sex, and income
colors = ['b', 'r', 'g', 'c', 'm']
AgeVec = np.linspace(67., 95., num=15)
for n in range(5):
plt.plot(AgeVec, iLvlZeroRate[n, :15], '-' + colors[n])
plt.xlabel('Age')
plt.ylabel(r'Prob[$n_{it}=0$]')
plt.title('Probability of Buying No Health Investment, Women')
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
])
plt.savefig('../Figures/ZeroInvstWomen.pdf')
plt.show()
for n in range(5):
plt.plot(AgeVec, iLvlZeroRate[n + 5, :15], '-' + colors[n])
plt.xlabel('Age')
plt.ylabel(r'Prob[$n_{it}=0$]')
plt.title('Probability of Buying No Health Investment, Men')
plt.savefig('../Figures/ZeroInvstMen.pdf')
plt.show()
# Plot the probability of hitting the consumption floor by age, sex, and income
colors = ['b', 'r', 'g', 'c', 'm']
AgeVec = np.linspace(67., 95., num=15)
for n in range(5):
plt.plot(AgeVec, HitCfloorRate[n, :15], '-' + colors[n])
plt.xlabel('Age')
plt.ylabel(r'Prob[$c_{it}={c}$]')
plt.title('Probability of Using Consumption Floor, Women')
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
])
plt.savefig('../Figures/cFloorWomen.pdf')
plt.show()
for n in range(5):
plt.plot(AgeVec, HitCfloorRate[n + 5, :15], '-' + colors[n])
plt.xlabel('Age')
plt.ylabel(r'Prob[$c_{it}={c}$]')
plt.title('Probability of Using Consumption Floor, Men')
plt.savefig('../Figures/cFloorMen.pdf')
plt.show()
# Plot health investment as a function of market resources by type, holding h and Dev fixed
B = np.linspace(1., 50., 201)
some_ones = np.ones_like(B)
hLvl = 0.6
Dev = 0.0
t = 0
Age = str(65 + 2 * t)
for i in range(5):
this_type = type_list[i]
MedShk = np.exp(this_type.MedShkMeanFunc[t](hLvl) +
Dev * this_type.MedShkStdFunc(hLvl))
I = np.maximum(
this_type.solution[t].PolicyFunc.iFunc(B, hLvl * some_ones,
MedShk * some_ones), 0.0)
plt.plot(B, I, '-' + colors[i])
plt.xlabel(r'Bank balances $b_{it}$, \$10,000 (y2000)')
plt.ylabel(r'Health investment $n_{it}$, \$10,000 (y2000)')
plt.xlim([1., 50.])
plt.ylim([-0.01, 0.65])
#plt.legend(['Bottom quintile','Second quintile','Third quintile','Fourth quintile','Top quintile'])
plt.title('Health Investment Function at Age ' + Age + ' by Income, Women')
plt.savefig('../Figures/iFuncWomen.pdf')
plt.show()
for i in range(5):
this_type = type_list[i + 5]
MedShk = np.exp(this_type.MedShkMeanFunc[t](hLvl) +
Dev * this_type.MedShkStdFunc(hLvl))
I = np.maximum(
this_type.solution[t].PolicyFunc.iFunc(B, hLvl * some_ones,
MedShk * some_ones), 0.0)
plt.plot(B, I, '-' + colors[i])
plt.xlabel(r'Bank balances $b_{it}$, \$10,000 (y2000)')
plt.ylabel(r'Health investment $n_{it}$, \$10,000 (y2000)')
plt.xlim([1., 50.])
plt.ylim([-0.01, 0.65])
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
],
loc=4)
plt.title('Health Investment Function at Age ' + Age + ' by Income, Men')
plt.savefig('../Figures/iFuncMen.pdf')
plt.show()
# Plot PDV of total medical expenses by health at median wealth at age 69-70 by income quintile and sex
t = 2
H = np.linspace(0.0, 1.0, 201)
for n in range(5):
B = bLvl_init_median[n] * np.ones_like(H)
M = type_list[n].solution[t].TotalMedPDVfunc(B, H)
plt.plot(H, M, color=colors[n])
plt.xlim([0., 1.])
plt.ylim([0., 17])
plt.xlabel(r'Health capital $h_{it}$')
plt.ylabel('PDV total medical care, $10,000 (y2000)')
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
])
plt.title('Total Medical Expenses by Health and Income, Women')
plt.savefig('../Figures/TotalMedPDVbyIncomeWomen.pdf')
plt.show()
for n in range(5, 10):
B = bLvl_init_median[n] * np.ones_like(H)
M = type_list[n].solution[t].TotalMedPDVfunc(B, H)
plt.plot(H, M, color=colors[n - 5])
plt.xlim([0., 1.])
plt.ylim([0., 17])
plt.xlabel(r'Health capital $h_{it}$')
plt.ylabel('PDV total medical care, $10,000 (y2000)')
#plt.legend(['Bottom quintile','Second quintile','Third quintile','Fourth quintile','Top quintile'])
plt.title('Total Medical Expenses by Health and Income, Men')
plt.savefig('../Figures/TotalMedPDVbyIncomeMen.pdf')
plt.show()
# Plot PDV of OOP medical expenses by health at median wealth at age 69-70 by income quintile and sex
colors = ['b', 'r', 'g', 'c', 'm']
t = 2
H = np.linspace(0.0, 1.0, 201)
for n in range(5):
B = bLvl_init_median[n] * np.ones_like(H)
M = type_list[n].solution[t].OOPmedPDVfunc(B, H)
plt.plot(H, M, color=colors[n])
plt.xlim([0., 1.])
plt.ylim([0., 3.5])
plt.xlabel(r'Health capital $h_{it}$')
plt.ylabel('PDV OOP medical expenses, $10,000 (y2000)')
#plt.legend(['Bottom quintile','Second quintile','Third quintile','Fourth quintile','Top quintile'])
plt.title('OOP Medical Expenses by Health and Income, Women')
plt.savefig('../Figures/OOPmedPDVbyIncomeWomen.pdf')
plt.show()
for n in range(5, 10):
B = bLvl_init_median[n] * np.ones_like(H)
M = type_list[n].solution[t].OOPmedPDVfunc(B, H)
plt.plot(H, M, color=colors[n - 5])
plt.xlim([0., 1.])
plt.ylim([0., 3.5])
plt.xlabel(r'Health capital $h_{it}$')
plt.ylabel('PDV total medical care, $10,000 (y2000)')
#plt.legend(['Bottom quintile','Second quintile','Third quintile','Fourth quintile','Top quintile'])
plt.title('OOP Medical Expenses by Health and Income, Men')
plt.savefig('../Figures/OOPmedPDVbyIncomeMen.pdf')
plt.show()
# Plot life expectancy by health at median wealth at age 69-70 by income quintile and sex
colors = ['b', 'r', 'g', 'c', 'm']
t = 2
H = np.linspace(0.0, 1.0, 201)
for n in range(5):
B = bLvl_init_median[n] * np.ones_like(H)
M = type_list[n].solution[t].ExpectedLifeFunc(B, H)
plt.plot(H, M, color=colors[n])
plt.xlim([0., 1.])
plt.ylim([0., 20.])
plt.xlabel(r'Health capital $h_{it}$')
plt.ylabel('Remaining years of life expectancy')
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
])
plt.title('Life Expectancy at Age 69 by Health and Income, Women')
plt.savefig('../Figures/LifeExpectancybyIncomeWomen.pdf')
plt.show()
for n in range(5, 10):
B = bLvl_init_median[n] * np.ones_like(H)
M = type_list[n].solution[t].ExpectedLifeFunc(B, H)
plt.plot(H, M, color=colors[n - 5])
plt.xlim([0., 1.])
plt.ylim([0., 20.])
plt.xlabel(r'Health capital $h_{it}$')
plt.ylabel('Remaining years of life expectancy')
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
])
plt.title('Life Expectancy at Age 69 by Health and Income, Men')
plt.savefig('../Figures/LifeExpectancybyIncomeMen.pdf')
plt.show()
# Extract deciles of health from the HRS data
DataHealthPctiles = np.zeros((15, len(pctiles)))
for t in range(15):
these = np.logical_and(Data.AgeBoolArray[:, :, t], Data.Alive)
h_temp = Data.h_data[these]
DataHealthPctiles[t, :] = getPercentiles(h_temp, percentiles=pctiles)
# Plot deciles of health by by age
plt.plot(AgeVec, SimHealthPctiles, '-k')
plt.plot(AgeVec, DataHealthPctiles, '--k')
plt.ylim(0., 1.)
plt.ylabel('Health capital $h_{it}$')
plt.xlabel('Age')
plt.title('Simulated vs Actual Distribution of Health by Age')
plt.savefig('../Figures/HealthDistribution.pdf')
plt.show()
OOPmodFunc = lambda x: np.log(10000 * x)
# Extract many percentiles of OOP spending from the simulated data
OOP_sim = OOPhist.flatten()
Weight_temp = WeightAdj.flatten()
CDFvalsSim = np.linspace(0.0001, 0.999, 1000)
OOPsimCDF_A0 = getPercentiles(OOP_sim * 10000,
weights=Weight_temp,
percentiles=CDFvalsSim)
OOPsimCDF_B0 = getPercentiles(OOPmodFunc(OOP_sim),
weights=Weight_temp,
percentiles=CDFvalsSim)
# Extract some percentiles of OOP spending from the HRS data
these = np.logical_and(Data.Alive, np.logical_not(np.isnan(Data.m_data)))
OOP_data = Data.m_data[these]
CDFvalsData = np.linspace(0.0001, 0.999, 500)
OOPdataCDF_A0 = getPercentiles(OOP_data * 10000,
weights=None,
percentiles=CDFvalsData)
OOPdataCDF_B0 = getPercentiles(OOPmodFunc(OOP_data),
weights=None,
percentiles=CDFvalsData)
# Plot the CDF of log out-of-pocket medical spending
plt.subplot(211)
plt.title('CDF of OOP Medical Spending')
plt.plot(OOPdataCDF_B0, CDFvalsData, '-r')
plt.plot(OOPsimCDF_B0, CDFvalsSim, '-b')
plt.xlim(8., 11.5)
plt.ylim(0.85, 1.0)
plt.xticks([
np.log(3000),
np.log(6000),
np.log(12000),
np.log(24000),
np.log(48000),
np.log(96000)
], ['3000', '6000', '12000', '24000', '48000', '96000'])
# Plot the CDF of out-of-pocket medical spending
plt.subplot(212)
plt.plot(OOPdataCDF_A0, CDFvalsData, '-r')
plt.plot(OOPsimCDF_A0, CDFvalsSim, '-b')
plt.xlim(0., 3000.)
plt.ylim(0.0, 0.9)
plt.xlabel('Out-of-pocket medical expenses, biannual')
plt.ylabel('Cumulative distribution')
plt.legend(['HRS data', 'Model'], loc=4)
plt.savefig('../Figures/OOPdistribution.pdf')
plt.show()
# Calculate the serial correlation of log OOP medical spending in simulated data
Med_sim = np.log(10000 * OOPhist + 1.)
serial_corr_sim = np.zeros(15)
serial_corr_sim_inc = np.zeros((15, 5))
for t in range(15):
these = np.logical_and(WeightAdj[t + 1, :] > 0., WeightAdj[t + 1, :] <
1.) # Alive but not the first simulated period
Med_t = Med_sim[t + 1, these]
Med_tm1 = Med_sim[t, these]
weight_reg = WeightAdj[t + 1, these]
const_reg = np.ones_like(Med_t)
regressors = np.transpose(np.vstack([const_reg, Med_tm1]))
temp_model = WLS(Med_t, regressors, weights=weight_reg)
temp_results = temp_model.fit()
serial_corr_sim[t] = temp_results.rsquared
for i in range(5):
those = np.logical_and(these, IncQuint == i + 1)
Med_t = Med_sim[t + 1, those]
Med_tm1 = Med_sim[t, those]
weight_reg = WeightAdj[t + 1, those]
const_reg = np.ones_like(Med_t)
regressors = np.transpose(np.vstack([const_reg, Med_tm1]))
temp_model = WLS(Med_t, regressors, weights=weight_reg)
temp_results = temp_model.fit()
serial_corr_sim_inc[t, i] = temp_results.rsquared
# Calculate the serial correlation of log OOP medical spending in HRS data
DataExists = np.logical_and(np.logical_not(np.isnan(Data.m_data[:-1, :])),
np.logical_not(np.isnan(Data.m_data[1:, :])))
BothAlive = np.logical_and(Data.Alive[:-1, :], Data.Alive[1:, :])
Usable = np.logical_and(DataExists, BothAlive)
serial_corr_data = np.zeros(15)
serial_corr_data_inc = np.zeros((15, 5))
Med_data = np.log(10000 * Data.m_data + 1.)
for t in range(15):
these = np.logical_and(Usable, Data.AgeBoolArray[:-1, :, t])
Med_t = Med_data[1:, :][these]
Med_tm1 = Med_data[:-1, :][these]
const_reg = np.ones_like(Med_t)
regressors = np.transpose(np.vstack([const_reg, Med_tm1]))
temp_model = OLS(Med_t, regressors)
temp_results = temp_model.fit()
serial_corr_data[t] = temp_results.rsquared
for i in range(5):
those = np.logical_and(these, Data.IncQuintBoolArray[:-1, :, i])
Med_t = Med_data[1:, :][those]
Med_tm1 = Med_data[:-1, :][those]
const_reg = np.ones_like(Med_t)
regressors = np.transpose(np.vstack([const_reg, Med_tm1]))
temp_model = OLS(Med_t, regressors)
temp_results = temp_model.fit()
serial_corr_data_inc[t, i] = temp_results.rsquared
# Make a plot of serial correlation of OOP medical expenses
plt.subplot(3, 2, 1)
plt.plot(AgeVec, serial_corr_data, '-r')
plt.plot(AgeVec, serial_corr_sim, '-b')
plt.ylim(0, 0.5)
plt.xticks([])
plt.text(75, 0.4, 'All individuals')
plt.subplot(3, 2, 2)
plt.plot(AgeVec, serial_corr_data_inc[:, 0], '-r')
plt.plot(AgeVec, serial_corr_sim_inc[:, 0], '-b')
plt.ylim(0, 0.5)
plt.xticks([])
plt.yticks([])
plt.text(70, 0.4, 'Bottom income quintile')
plt.subplot(3, 2, 3)
plt.plot(AgeVec, serial_corr_data_inc[:, 1], '-r')
plt.plot(AgeVec, serial_corr_sim_inc[:, 1], '-b')
plt.ylim(0, 0.5)
plt.xticks([])
plt.text(67, 0.4, 'Second income quintile')
plt.ylabel('$R^2$ of regression of $\log(OOP_{t})$ on $\log(OOP_{t-1})$')
plt.subplot(3, 2, 4)
plt.plot(AgeVec, serial_corr_data_inc[:, 2], '-r')
plt.plot(AgeVec, serial_corr_sim_inc[:, 2], '-b')
plt.ylim(0, 0.5)
plt.xticks([])
plt.yticks([])
plt.text(70, 0.4, 'Third income quintile')
plt.subplot(3, 2, 5)
plt.plot(AgeVec, serial_corr_data_inc[:, 3], '-r')
plt.plot(AgeVec, serial_corr_sim_inc[:, 3], '-b')
plt.ylim(0, 0.5)
plt.xlabel('Age')
plt.text(70, 0.4, 'Fourth income quintile')
plt.subplot(3, 2, 6)
plt.plot(AgeVec, serial_corr_data_inc[:, 4], '-r')
plt.plot(AgeVec, serial_corr_sim_inc[:, 4], '-b')
plt.ylim(0, 0.5)
plt.xlabel('Age')
plt.yticks([])
plt.text(70, 0.4, 'Top income quintile')
plt.savefig('../Figures/SerialCorrOOP.pdf')
plt.show()
# Make a plot of serial correlation of OOP medical expenses
plt.plot(AgeVec + 2, serial_corr_data, '-r')
plt.plot(AgeVec + 2, serial_corr_sim, '-b')
plt.xlabel('Age')
plt.ylabel('$R^2$ of regression of $\log(OOP_{t})$ on $\log(OOP_{t-1})$')
plt.legend(['HRS data', 'Model'], loc=1)
plt.show()
# Calculate mortality probability by age and income quintile in simulated data
MortByIncAge_data = Data.MortByIncAge
MortByIncAge_sim = np.zeros((5, 15))
MortByAge_sim = np.zeros(15)
for t in range(15):
THESE = np.logical_and(Active[t, :], InDataSpan[t, :])
Weight = WeightHist[t + 1, THESE]
WeightSum = np.sum(Weight)
Mort = MortHist[t + 1, THESE]
MortByAge_sim[t] = np.dot(Mort, Weight) / WeightSum
for i in range(5):
right_inc = IncQuint == i + 1
these = np.logical_and(THESE, right_inc)
Mort = MortHist[t + 1, these]
Weight = WeightHist[t + 1, these]
WeightSum = np.sum(Weight)
MortByIncAge_sim[i, t] = np.dot(Mort, Weight) / WeightSum
# Plot mortality probability by age and income quintile
income_colors = ['b', 'r', 'g', 'm', 'c']
for i in range(5):
plt.plot(AgeVec, MortByIncAge_sim[i, :] - MortByAge_sim,
'-' + income_colors[i])
for i in range(5):
plt.plot(AgeVec, MortByIncAge_data[i, :] - MortByAge_sim,
'.' + income_colors[i])
plt.xlabel('Age')
plt.ylabel('Relative death probability (biannual)')
plt.title('Death Probability by Income Quintile')
plt.legend([
'Bottom quintile', 'Second quintile', 'Third quintile',
'Fourth quintile', 'Top quintile'
],
loc=2)
plt.savefig('../Figures/MortByIncAge.pdf')
plt.show()
# Plot the 99% confidence band of the health production function
mean = np.array([-2.13369276099, 1.71842956397])
covar = np.array([[0.02248322, 0.01628292], [0.01628308, 0.01564192]])
dstn = multivariate_normal(mean, covar)
N = 10000
M = 201
draws = dstn.rvs(10000)
MedVec = np.linspace(0., 1.5, M)
func_data = np.zeros((N, M))
def makeHealthProdFunc(LogSlope, LogCurve):
LogJerk = 15.6
tempw = np.exp(LogJerk)
HealthProd0 = 1. - tempw
tempx = np.exp(
LogSlope) # Slope of health production function at iLvl=0
HealthProd2 = np.exp(LogJerk - LogCurve)
HealthProdFunc = lambda i: tempx / HealthProd0 * (
(i * HealthProd2**(
(1. - HealthProd0) / HealthProd0) + HealthProd2**
(1. / HealthProd0))**HealthProd0 - HealthProd2)
return HealthProdFunc
for n in range(N):
f = makeHealthProdFunc(draws[n, 0], draws[n, 1])
func_data[n, :] = f(MedVec)
f = makeHealthProdFunc(Params.test_param_vec[25],
Params.test_param_vec[26])
CI_array = np.zeros((M, 2))
for m in range(M):
CI_array[m, :] = getPercentiles(func_data[:, m],
percentiles=[0.025, 0.975])
health_prod = f(MedVec)
plt.plot(MedVec, health_prod, '-r')
plt.plot(MedVec, CI_array[:, 0], '--k', linewidth=0.5)
plt.plot(MedVec, CI_array[:, 1], '--k', linewidth=0.5)
plt.xlim([-0.005, 1.5])
plt.ylim([0., None])
plt.xlabel('Health investment $n_{it}$, \$10,000 (y2000)')
plt.ylabel('Health produced ')
plt.title('Estimated Health Production Function')
plt.legend([
'Estimated health production function',
'Pointwise 95% confidence bounds'
],
loc=4)
plt.savefig('../Figures/HealthProdFunc.pdf')
plt.show()
def FagerengObjFunc(center, spread, verbose=False):
'''
Objective function for the quick and dirty structural estimation to fit
Fagereng, Holm, and Natvik's Table 9 results with a basic infinite horizon
consumption-saving model (with permanent and transitory income shocks).
Parameters
----------
center : float
Center of the uniform distribution of discount factors.
spread : float
Width of the uniform distribution of discount factors.
verbose : bool
When True, print to screen MPC table for these parameters. When False,
print (center, spread, distance).
Returns
-------
distance : float
Euclidean distance between simulated MPCs and (adjusted) Table 9 MPCs.
'''
# Give our consumer types the requested discount factor distribution
beta_set = approxUniform(N=TypeCount,
bot=center - spread,
top=center + spread)[1]
for j in range(TypeCount):
EstTypeList[j](DiscFac=beta_set[j])
# Solve and simulate all consumer types, then gather their wealth levels
multiThreadCommands(
EstTypeList,
['solve()', 'initializeSim()', 'simulate()', 'unpackcFunc()'])
WealthNow = np.concatenate([ThisType.aLvlNow for ThisType in EstTypeList])
# Get wealth quartile cutoffs and distribute them to each consumer type
quartile_cuts = getPercentiles(WealthNow, percentiles=[0.25, 0.50, 0.75])
for ThisType in EstTypeList:
WealthQ = np.zeros(ThisType.AgentCount, dtype=int)
for n in range(3):
WealthQ[ThisType.aLvlNow > quartile_cuts[n]] += 1
ThisType(WealthQ=WealthQ)
# Keep track of MPC sets in lists of lists of arrays
MPC_set_list = [[[], [], [], []], [[], [], [], []], [[], [], [], []],
[[], [], [], []]]
# Calculate the MPC for each of the four lottery sizes for all agents
for ThisType in EstTypeList:
ThisType.simulate(1)
c_base = ThisType.cNrmNow
MPC_this_type = np.zeros((ThisType.AgentCount, 4))
for k in range(4): # Get MPC for all agents of this type
Llvl = lottery_size[k]
Lnrm = Llvl / ThisType.pLvlNow
if do_secant:
SplurgeNrm = Splurge / ThisType.pLvlNow
mAdj = ThisType.mNrmNow + Lnrm - SplurgeNrm
cAdj = ThisType.cFunc[0](mAdj) + SplurgeNrm
MPC_this_type[:, k] = (cAdj - c_base) / Lnrm
else:
mAdj = ThisType.mNrmNow + Lnrm
MPC_this_type[:, k] = cAdj = ThisType.cFunc[0].derivative(mAdj)
# Sort the MPCs into the proper MPC sets
for q in range(4):
these = ThisType.WealthQ == q
for k in range(4):
MPC_set_list[k][q].append(MPC_this_type[these, k])
# Calculate average within each MPC set
simulated_MPC_means = np.zeros((4, 4))
for k in range(4):
for q in range(4):
MPC_array = np.concatenate(MPC_set_list[k][q])
simulated_MPC_means[k, q] = np.mean(MPC_array)
# Calculate Euclidean distance between simulated MPC averages and Table 9 targets
diff = simulated_MPC_means - MPC_target
if drop_corner:
diff[0, 0] = 0.0
distance = np.sqrt(np.sum((diff)**2))
if verbose:
print(simulated_MPC_means)
else:
print(center, spread, distance)
return distance
def calcStats(self, aLvlNow, pLvlNow, MPCnow, TranShkNow, EmpNow, t_age,
LorenzBool, ManyStatsBool):
'''
Calculate various statistics about the current population in the economy.
Parameters
----------
aLvlNow : [np.array]
Arrays with end-of-period assets, listed by each ConsumerType in self.agents.
pLvlNow : [np.array]
Arrays with permanent income levels, listed by each ConsumerType in self.agents.
MPCnow : [np.array]
Arrays with marginal propensity to consume, listed by each ConsumerType in self.agents.
TranShkNow : [np.array]
Arrays with transitory income shocks, listed by each ConsumerType in self.agents.
EmpNow : [np.array]
Arrays with employment states: True if employed, False otherwise.
t_age : [np.array]
Arrays with periods elapsed since model entry, listed by each ConsumerType in self.agents.
LorenzBool: bool
Indicator for whether the Lorenz target points should be calculated. Usually False,
only True when DiscFac has been identified for a particular nabla.
ManyStatsBool: bool
Indicator for whether a lot of statistics for tables should be calculated. Usually False,
only True when parameters have been estimated and we want values for tables.
Returns
-------
None
'''
# Combine inputs into single arrays
aLvl = np.hstack(aLvlNow)
pLvl = np.hstack(pLvlNow)
age = np.hstack(t_age)
TranShk = np.hstack(TranShkNow)
Emp = np.hstack(EmpNow)
# Calculate the capital to income ratio in the economy
CohortWeight = self.PopGroFac**(-age)
CapAgg = np.sum(aLvl * CohortWeight)
IncAgg = np.sum(pLvl * TranShk * CohortWeight)
KtoYnow = CapAgg / IncAgg
self.KtoYnow = KtoYnow
# Store Lorenz data if requested
self.LorenzLong = np.nan
if LorenzBool:
order = np.argsort(aLvl)
aLvl = aLvl[order]
CohortWeight = CohortWeight[order]
wealth_shares = getLorenzShares(aLvl,
weights=CohortWeight,
percentiles=self.LorenzPercentiles,
presorted=True)
self.Lorenz = wealth_shares
if ManyStatsBool:
self.LorenzLong = getLorenzShares(aLvl,
weights=CohortWeight,
percentiles=np.arange(
0.01, 1.0, 0.01),
presorted=True)
else:
self.Lorenz = np.nan # Store nothing if we don't want Lorenz data
# Calculate a whole bunch of statistics if requested
if ManyStatsBool:
# Reshape other inputs
MPC = np.hstack(MPCnow)
# Sort other data items if aLvl and CohortWeight were sorted
if LorenzBool:
pLvl = pLvl[order]
MPC = MPC[order]
TranShk = TranShk[order]
age = age[order]
Emp = Emp[order]
aNrm = aLvl / pLvl # Normalized assets (wealth ratio)
IncLvl = TranShk * pLvl # Labor income this period
# Calculate overall population MPC and by subpopulations
#MPCsixmonths = 1.0 - 0.25*((1.0 - MPC) + (1.0 - MPC)**2 + (1.0 - MPC)**3 + (1.0 - MPC)**4)
MPCsixmonths = 1.0 - (1.0 - MPC)**2
self.MPCall = np.sum(
MPCsixmonths * CohortWeight) / np.sum(CohortWeight)
employed = Emp
unemployed = np.logical_not(employed)
if self.T_retire > 0: # Adjust for the lifecycle model, where agents might be retired instead
unemployed = np.logical_and(unemployed, age < self.T_retire)
employed = np.logical_and(employed, age < self.T_retire)
retired = age >= self.T_retire
else:
retired = np.zeros_like(unemployed, dtype=bool)
self.MPCunemployed = np.sum(
MPCsixmonths[unemployed] * CohortWeight[unemployed]) / np.sum(
CohortWeight[unemployed])
self.MPCemployed = np.sum(
MPCsixmonths[employed] * CohortWeight[employed]) / np.sum(
CohortWeight[employed])
self.MPCretired = np.sum(
MPCsixmonths[retired] * CohortWeight[retired]) / np.sum(
CohortWeight[retired])
self.MPCbyWealthRatio = calcSubpopAvg(MPCsixmonths, aNrm,
self.cutoffs, CohortWeight)
self.MPCbyIncome = calcSubpopAvg(MPCsixmonths, IncLvl,
self.cutoffs, CohortWeight)
# Calculate the wealth quintile distribution of "hand to mouth" consumers
quintile_cuts = getPercentiles(aLvl,
weights=CohortWeight,
percentiles=[0.2, 0.4, 0.6, 0.8])
wealth_quintiles = np.ones(aLvl.size, dtype=int)
wealth_quintiles[aLvl > quintile_cuts[0]] = 2
wealth_quintiles[aLvl > quintile_cuts[1]] = 3
wealth_quintiles[aLvl > quintile_cuts[2]] = 4
wealth_quintiles[aLvl > quintile_cuts[3]] = 5
MPC_cutoff = getPercentiles(
MPCsixmonths, weights=CohortWeight, percentiles=[
2.0 / 3.0
]) # Looking at consumers with MPCs in the top 1/3
these = MPCsixmonths > MPC_cutoff
in_top_third_MPC = wealth_quintiles[these]
temp_weights = CohortWeight[these]
hand_to_mouth_total = np.sum(temp_weights)
hand_to_mouth_pct = []
for q in range(1, 6):
hand_to_mouth_pct.append(
np.sum(temp_weights[in_top_third_MPC == q]) /
hand_to_mouth_total)
self.HandToMouthPct = np.array(hand_to_mouth_pct)
else: # If we don't want these stats, just put empty values in history
self.MPCall = np.nan
self.MPCunemployed = np.nan
self.MPCemployed = np.nan
self.MPCretired = np.nan
self.MPCbyWealthRatio = np.nan
self.MPCbyIncome = np.nan
self.HandToMouthPct = np.nan
def makeCSTWstats(DiscFac,
nabla,
this_type_list,
age_weight,
lorenz_distance=0.0,
save_name=None):
'''
Displays (and saves) a bunch of statistics. Separate from makeCSTWresults()
for compatibility with the aggregate shock model.
Parameters
----------
DiscFac : float
Center of the uniform distribution of discount factors
nabla : float
Width of the uniform distribution of discount factors
this_type_list : [cstwMPCagent]
List of agent types in the economy.
age_weight : np.array
Age-conditional array of weights for the wealth data.
lorenz_distance : float
Distance between simulated and actual Lorenz curves, for display.
save_name : string
Name to save the calculated results, for later use in producing figures
and tables, etc.
Returns
-------
none
'''
sim_length = this_type_list[0].sim_periods
sim_wealth = (np.vstack(
(this_type.W_history for this_type in this_type_list))).flatten()
sim_wealth_short = (np.vstack(
(this_type.W_history[0:sim_length, :]
for this_type in this_type_list))).flatten()
sim_kappa = (np.vstack(
(this_type.kappa_history for this_type in this_type_list))).flatten()
sim_income = (np.vstack((this_type.pHist[0:sim_length, :] *
np.asarray(this_type.TranShkHist[0:sim_length, :])
for this_type in this_type_list))).flatten()
sim_ratio = (np.vstack((this_type.W_history[0:sim_length, :] /
this_type.pHist[0:sim_length, :]
for this_type in this_type_list))).flatten()
if Params.do_lifecycle:
sim_unemp = (np.vstack((np.vstack((
this_type.IncUnemp == this_type.TranShkHist[0:Params.working_T, :],
np.zeros((Params.retired_T + 1, this_type_list[0].Nagents),
dtype=bool)))
for this_type in this_type_list))).flatten()
sim_emp = (np.vstack((np.vstack(
(this_type.IncUnemp !=
this_type.TranShkHist[0:Params.working_T, :],
np.zeros((Params.retired_T + 1, this_type_list[0].Nagents),
dtype=bool)))
for this_type in this_type_list))).flatten()
sim_ret = (np.vstack((np.vstack(
(np.zeros((Params.working_T, this_type_list[0].Nagents),
dtype=bool),
np.ones((Params.retired_T + 1, this_type_list[0].Nagents),
dtype=bool)))
for this_type in this_type_list))).flatten()
else:
sim_unemp = np.vstack(
(this_type.IncUnemp == this_type.TranShkHist[0:sim_length, :]
for this_type in this_type_list)).flatten()
sim_emp = np.vstack(
(this_type.IncUnemp != this_type.TranShkHist[0:sim_length, :]
for this_type in this_type_list)).flatten()
sim_ret = np.zeros(sim_emp.size, dtype=bool)
sim_weight_all = np.tile(np.repeat(age_weight, this_type_list[0].Nagents),
Params.pref_type_count)
if Params.do_beta_dist and Params.do_lifecycle:
kappa_mean_by_age_type = (np.mean(np.vstack(
(this_type.kappa_history for this_type in this_type_list)),
axis=1)).reshape(
(Params.pref_type_count * 3,
DropoutType.T_total + 1))
kappa_mean_by_age_pref = np.zeros(
(Params.pref_type_count, DropoutType.T_total + 1)) + np.nan
for j in range(Params.pref_type_count):
kappa_mean_by_age_pref[
j, ] = Params.d_pct * kappa_mean_by_age_type[
3 * j + 0, ] + Params.h_pct * kappa_mean_by_age_type[
3 * j + 1, ] + Params.c_pct * kappa_mean_by_age_type[
3 * j + 2, ]
kappa_mean_by_age = np.mean(kappa_mean_by_age_pref, axis=0)
kappa_lo_beta_by_age = kappa_mean_by_age_pref[0, :]
kappa_hi_beta_by_age = kappa_mean_by_age_pref[Params.pref_type_count -
1, :]
lorenz_fig_data = makeLorenzFig(Params.SCF_wealth, Params.SCF_weights,
sim_wealth, sim_weight_all)
mpc_fig_data = makeMPCfig(sim_kappa, sim_weight_all)
kappa_all = calcWeightedAvg(
np.vstack((this_type.kappa_history for this_type in this_type_list)),
np.tile(age_weight / float(Params.pref_type_count),
Params.pref_type_count))
kappa_unemp = np.sum(
sim_kappa[sim_unemp] * sim_weight_all[sim_unemp]) / np.sum(
sim_weight_all[sim_unemp])
kappa_emp = np.sum(sim_kappa[sim_emp] * sim_weight_all[sim_emp]) / np.sum(
sim_weight_all[sim_emp])
kappa_ret = np.sum(sim_kappa[sim_ret] * sim_weight_all[sim_ret]) / np.sum(
sim_weight_all[sim_ret])
my_cutoffs = [(0.99, 1), (0.9, 1), (0.8, 1), (0.6, 0.8), (0.4, 0.6),
(0.2, 0.4), (0.0, 0.2)]
kappa_by_ratio_groups = calcSubpopAvg(sim_kappa, sim_ratio, my_cutoffs,
sim_weight_all)
kappa_by_income_groups = calcSubpopAvg(sim_kappa, sim_income, my_cutoffs,
sim_weight_all)
quintile_points = getPercentiles(sim_wealth_short,
weights=sim_weight_all,
percentiles=[0.2, 0.4, 0.6, 0.8])
wealth_quintiles = np.ones(sim_wealth_short.size, dtype=int)
wealth_quintiles[sim_wealth_short > quintile_points[0]] = 2
wealth_quintiles[sim_wealth_short > quintile_points[1]] = 3
wealth_quintiles[sim_wealth_short > quintile_points[2]] = 4
wealth_quintiles[sim_wealth_short > quintile_points[3]] = 5
MPC_cutoff = getPercentiles(sim_kappa,
weights=sim_weight_all,
percentiles=[2.0 / 3.0])
these_quintiles = wealth_quintiles[sim_kappa > MPC_cutoff]
these_weights = sim_weight_all[sim_kappa > MPC_cutoff]
hand_to_mouth_total = np.sum(these_weights)
hand_to_mouth_pct = []
for q in range(5):
hand_to_mouth_pct.append(
np.sum(these_weights[these_quintiles == (q + 1)]) /
hand_to_mouth_total)
results_string = 'Estimate is DiscFac=' + str(DiscFac) + ', nabla=' + str(
nabla) + '\n'
results_string += 'Lorenz distance is ' + str(lorenz_distance) + '\n'
results_string += 'Average MPC for all consumers is ' + mystr(
kappa_all) + '\n'
results_string += 'Average MPC in the top percentile of W/Y is ' + mystr(
kappa_by_ratio_groups[0]) + '\n'
results_string += 'Average MPC in the top decile of W/Y is ' + mystr(
kappa_by_ratio_groups[1]) + '\n'
results_string += 'Average MPC in the top quintile of W/Y is ' + mystr(
kappa_by_ratio_groups[2]) + '\n'
results_string += 'Average MPC in the second quintile of W/Y is ' + mystr(
kappa_by_ratio_groups[3]) + '\n'
results_string += 'Average MPC in the middle quintile of W/Y is ' + mystr(
kappa_by_ratio_groups[4]) + '\n'
results_string += 'Average MPC in the fourth quintile of W/Y is ' + mystr(
kappa_by_ratio_groups[5]) + '\n'
results_string += 'Average MPC in the bottom quintile of W/Y is ' + mystr(
kappa_by_ratio_groups[6]) + '\n'
results_string += 'Average MPC in the top percentile of y is ' + mystr(
kappa_by_income_groups[0]) + '\n'
results_string += 'Average MPC in the top decile of y is ' + mystr(
kappa_by_income_groups[1]) + '\n'
results_string += 'Average MPC in the top quintile of y is ' + mystr(
kappa_by_income_groups[2]) + '\n'
results_string += 'Average MPC in the second quintile of y is ' + mystr(
kappa_by_income_groups[3]) + '\n'
results_string += 'Average MPC in the middle quintile of y is ' + mystr(
kappa_by_income_groups[4]) + '\n'
results_string += 'Average MPC in the fourth quintile of y is ' + mystr(
kappa_by_income_groups[5]) + '\n'
results_string += 'Average MPC in the bottom quintile of y is ' + mystr(
kappa_by_income_groups[6]) + '\n'
results_string += 'Average MPC for the employed is ' + mystr(
kappa_emp) + '\n'
results_string += 'Average MPC for the unemployed is ' + mystr(
kappa_unemp) + '\n'
results_string += 'Average MPC for the retired is ' + mystr(
kappa_ret) + '\n'
results_string += 'Of the population with the 1/3 highest MPCs...' + '\n'
results_string += mystr(
hand_to_mouth_pct[0] *
100) + '% are in the bottom wealth quintile,' + '\n'
results_string += mystr(
hand_to_mouth_pct[1] *
100) + '% are in the second wealth quintile,' + '\n'
results_string += mystr(hand_to_mouth_pct[2] *
100) + '% are in the third wealth quintile,' + '\n'
results_string += mystr(
hand_to_mouth_pct[3] *
100) + '% are in the fourth wealth quintile,' + '\n'
results_string += 'and ' + mystr(
hand_to_mouth_pct[4] *
100) + '% are in the top wealth quintile.' + '\n'
print(results_string)
if save_name is not None:
with open('./Results/' + save_name + 'LorenzFig.txt', 'w') as f:
my_writer = csv.writer(
f,
delimiter='\t',
)
for j in range(len(lorenz_fig_data[0])):
my_writer.writerow([
lorenz_fig_data[0][j], lorenz_fig_data[1][j],
lorenz_fig_data[2][j]
])
f.close()
with open('./Results/' + save_name + 'MPCfig.txt', 'w') as f:
my_writer = csv.writer(f, delimiter='\t')
for j in range(len(mpc_fig_data[0])):
my_writer.writerow([lorenz_fig_data[0][j], mpc_fig_data[1][j]])
f.close()
if Params.do_beta_dist and Params.do_lifecycle:
with open('./Results/' + save_name + 'KappaByAge.txt', 'w') as f:
my_writer = csv.writer(f, delimiter='\t')
for j in range(len(kappa_mean_by_age)):
my_writer.writerow([
kappa_mean_by_age[j], kappa_lo_beta_by_age[j],
kappa_hi_beta_by_age[j]
])
f.close()
with open('./Results/' + save_name + 'Results.txt', 'w') as f:
f.write(results_string)
f.close()
# Make a boolean array of usable observations (for non-mortality moments)
BelowCohort16 = np.tile(np.reshape(cohort_data,(1,obs)),(8,1)) < 16
Alive = h_data > 0.
NotInit = np.logical_not(InitBoolArray)
Useable = np.logical_and(BelowCohort16,np.logical_and(Alive,NotInit))
# Calculate health quintiles at data entry by age (and overwrite old health tertile info)
health_tertile_cuts = np.zeros((2,15))
health_quintile_cuts = np.zeros((4,15))
health_tert_data = np.zeros_like(health_tert_data_alt,dtype=int)
health_quint_data = np.zeros_like(health_tert_data_alt,dtype=int)
for a in range(15):
these = np.logical_and(Alive,AgeBoolArray[:,:,a])
health_temp = h_data[these]
health_quintile_cuts[:,a] = getPercentiles(health_temp,percentiles=[0.2,0.4,0.6,0.8])
health_tertile_cuts[:,a] = getPercentiles(health_temp,percentiles=[0.333,0.666])
those = BornBoolArray[a,:]
h_init_temp = h_init[those]
health_quint_data[those] = np.searchsorted(health_quintile_cuts[:,a],h_init_temp) + 1
health_tert_data[those] = np.searchsorted(health_tertile_cuts[:,a],h_init_temp) + 1
# Make data objects for the health production pre-estimation
UseableAlt = np.logical_and(BelowCohort16,Alive)
inc_quint_data_rep = np.tile(np.reshape(inc_quint_data,(1,obs)),(8,1))
wealth_quint_data_rep = np.tile(np.reshape(wealth_quint_data,(1,obs)),(8,1))
sex_data_rep = np.tile(np.reshape(sex_data,(1,obs)),(8,1))
WealthArraysBySexIncAge = []
HealthArraysBySexIncAge = []
WealthQuintArraysBySexIncAge = []
for s in range(2):
def makeCSTWstats(DiscFac,nabla,this_type_list,age_weight,lorenz_distance=0.0,save_name=None):
'''
Displays (and saves) a bunch of statistics. Separate from makeCSTWresults()
for compatibility with the aggregate shock model.
Parameters
----------
DiscFac : float
Center of the uniform distribution of discount factors
nabla : float
Width of the uniform distribution of discount factors
this_type_list : [cstwMPCagent]
List of agent types in the economy.
age_weight : np.array
Age-conditional array of weights for the wealth data.
lorenz_distance : float
Distance between simulated and actual Lorenz curves, for display.
save_name : string
Name to save the calculated results, for later use in producing figures
and tables, etc.
Returns
-------
none
'''
sim_length = this_type_list[0].sim_periods
sim_wealth = (np.vstack((this_type.W_history for this_type in this_type_list))).flatten()
sim_wealth_short = (np.vstack((this_type.W_history[0:sim_length,:] for this_type in this_type_list))).flatten()
sim_kappa = (np.vstack((this_type.kappa_history for this_type in this_type_list))).flatten()
sim_income = (np.vstack((this_type.pHist[0:sim_length,:]*np.asarray(this_type.TranShkHist[0:sim_length,:]) for this_type in this_type_list))).flatten()
sim_ratio = (np.vstack((this_type.W_history[0:sim_length,:]/this_type.pHist[0:sim_length,:] for this_type in this_type_list))).flatten()
if Params.do_lifecycle:
sim_unemp = (np.vstack((np.vstack((this_type.IncUnemp == this_type.TranShkHist[0:Params.working_T,:],np.zeros((Params.retired_T+1,this_type_list[0].Nagents),dtype=bool))) for this_type in this_type_list))).flatten()
sim_emp = (np.vstack((np.vstack((this_type.IncUnemp != this_type.TranShkHist[0:Params.working_T,:],np.zeros((Params.retired_T+1,this_type_list[0].Nagents),dtype=bool))) for this_type in this_type_list))).flatten()
sim_ret = (np.vstack((np.vstack((np.zeros((Params.working_T,this_type_list[0].Nagents),dtype=bool),np.ones((Params.retired_T+1,this_type_list[0].Nagents),dtype=bool))) for this_type in this_type_list))).flatten()
else:
sim_unemp = np.vstack((this_type.IncUnemp == this_type.TranShkHist[0:sim_length,:] for this_type in this_type_list)).flatten()
sim_emp = np.vstack((this_type.IncUnemp != this_type.TranShkHist[0:sim_length,:] for this_type in this_type_list)).flatten()
sim_ret = np.zeros(sim_emp.size,dtype=bool)
sim_weight_all = np.tile(np.repeat(age_weight,this_type_list[0].Nagents),Params.pref_type_count)
if Params.do_beta_dist and Params.do_lifecycle:
kappa_mean_by_age_type = (np.mean(np.vstack((this_type.kappa_history for this_type in this_type_list)),axis=1)).reshape((Params.pref_type_count*3,DropoutType.T_total+1))
kappa_mean_by_age_pref = np.zeros((Params.pref_type_count,DropoutType.T_total+1)) + np.nan
for j in range(Params.pref_type_count):
kappa_mean_by_age_pref[j,] = Params.d_pct*kappa_mean_by_age_type[3*j+0,] + Params.h_pct*kappa_mean_by_age_type[3*j+1,] + Params.c_pct*kappa_mean_by_age_type[3*j+2,]
kappa_mean_by_age = np.mean(kappa_mean_by_age_pref,axis=0)
kappa_lo_beta_by_age = kappa_mean_by_age_pref[0,:]
kappa_hi_beta_by_age = kappa_mean_by_age_pref[Params.pref_type_count-1,:]
lorenz_fig_data = makeLorenzFig(Params.SCF_wealth,Params.SCF_weights,sim_wealth,sim_weight_all)
mpc_fig_data = makeMPCfig(sim_kappa,sim_weight_all)
kappa_all = calcWeightedAvg(np.vstack((this_type.kappa_history for this_type in this_type_list)),np.tile(age_weight/float(Params.pref_type_count),Params.pref_type_count))
kappa_unemp = np.sum(sim_kappa[sim_unemp]*sim_weight_all[sim_unemp])/np.sum(sim_weight_all[sim_unemp])
kappa_emp = np.sum(sim_kappa[sim_emp]*sim_weight_all[sim_emp])/np.sum(sim_weight_all[sim_emp])
kappa_ret = np.sum(sim_kappa[sim_ret]*sim_weight_all[sim_ret])/np.sum(sim_weight_all[sim_ret])
my_cutoffs = [(0.99,1),(0.9,1),(0.8,1),(0.6,0.8),(0.4,0.6),(0.2,0.4),(0.0,0.2)]
kappa_by_ratio_groups = calcSubpopAvg(sim_kappa,sim_ratio,my_cutoffs,sim_weight_all)
kappa_by_income_groups = calcSubpopAvg(sim_kappa,sim_income,my_cutoffs,sim_weight_all)
quintile_points = getPercentiles(sim_wealth_short,weights=sim_weight_all,percentiles=[0.2, 0.4, 0.6, 0.8])
wealth_quintiles = np.ones(sim_wealth_short.size,dtype=int)
wealth_quintiles[sim_wealth_short > quintile_points[0]] = 2
wealth_quintiles[sim_wealth_short > quintile_points[1]] = 3
wealth_quintiles[sim_wealth_short > quintile_points[2]] = 4
wealth_quintiles[sim_wealth_short > quintile_points[3]] = 5
MPC_cutoff = getPercentiles(sim_kappa,weights=sim_weight_all,percentiles=[2.0/3.0])
these_quintiles = wealth_quintiles[sim_kappa > MPC_cutoff]
these_weights = sim_weight_all[sim_kappa > MPC_cutoff]
hand_to_mouth_total = np.sum(these_weights)
hand_to_mouth_pct = []
for q in range(5):
hand_to_mouth_pct.append(np.sum(these_weights[these_quintiles == (q+1)])/hand_to_mouth_total)
results_string = 'Estimate is DiscFac=' + str(DiscFac) + ', nabla=' + str(nabla) + '\n'
results_string += 'Lorenz distance is ' + str(lorenz_distance) + '\n'
results_string += 'Average MPC for all consumers is ' + mystr(kappa_all) + '\n'
results_string += 'Average MPC in the top percentile of W/Y is ' + mystr(kappa_by_ratio_groups[0]) + '\n'
results_string += 'Average MPC in the top decile of W/Y is ' + mystr(kappa_by_ratio_groups[1]) + '\n'
results_string += 'Average MPC in the top quintile of W/Y is ' + mystr(kappa_by_ratio_groups[2]) + '\n'
results_string += 'Average MPC in the second quintile of W/Y is ' + mystr(kappa_by_ratio_groups[3]) + '\n'
results_string += 'Average MPC in the middle quintile of W/Y is ' + mystr(kappa_by_ratio_groups[4]) + '\n'
results_string += 'Average MPC in the fourth quintile of W/Y is ' + mystr(kappa_by_ratio_groups[5]) + '\n'
results_string += 'Average MPC in the bottom quintile of W/Y is ' + mystr(kappa_by_ratio_groups[6]) + '\n'
results_string += 'Average MPC in the top percentile of y is ' + mystr(kappa_by_income_groups[0]) + '\n'
results_string += 'Average MPC in the top decile of y is ' + mystr(kappa_by_income_groups[1]) + '\n'
results_string += 'Average MPC in the top quintile of y is ' + mystr(kappa_by_income_groups[2]) + '\n'
results_string += 'Average MPC in the second quintile of y is ' + mystr(kappa_by_income_groups[3]) + '\n'
results_string += 'Average MPC in the middle quintile of y is ' + mystr(kappa_by_income_groups[4]) + '\n'
results_string += 'Average MPC in the fourth quintile of y is ' + mystr(kappa_by_income_groups[5]) + '\n'
results_string += 'Average MPC in the bottom quintile of y is ' + mystr(kappa_by_income_groups[6]) + '\n'
results_string += 'Average MPC for the employed is ' + mystr(kappa_emp) + '\n'
results_string += 'Average MPC for the unemployed is ' + mystr(kappa_unemp) + '\n'
results_string += 'Average MPC for the retired is ' + mystr(kappa_ret) + '\n'
results_string += 'Of the population with the 1/3 highest MPCs...' + '\n'
results_string += mystr(hand_to_mouth_pct[0]*100) + '% are in the bottom wealth quintile,' + '\n'
results_string += mystr(hand_to_mouth_pct[1]*100) + '% are in the second wealth quintile,' + '\n'
results_string += mystr(hand_to_mouth_pct[2]*100) + '% are in the third wealth quintile,' + '\n'
results_string += mystr(hand_to_mouth_pct[3]*100) + '% are in the fourth wealth quintile,' + '\n'
results_string += 'and ' + mystr(hand_to_mouth_pct[4]*100) + '% are in the top wealth quintile.' + '\n'
print(results_string)
if save_name is not None:
with open('./Results/' + save_name + 'LorenzFig.txt','w') as f:
my_writer = csv.writer(f, delimiter='\t',)
for j in range(len(lorenz_fig_data[0])):
my_writer.writerow([lorenz_fig_data[0][j], lorenz_fig_data[1][j], lorenz_fig_data[2][j]])
f.close()
with open('./Results/' + save_name + 'MPCfig.txt','w') as f:
my_writer = csv.writer(f, delimiter='\t')
for j in range(len(mpc_fig_data[0])):
my_writer.writerow([lorenz_fig_data[0][j], mpc_fig_data[1][j]])
f.close()
if Params.do_beta_dist and Params.do_lifecycle:
with open('./Results/' + save_name + 'KappaByAge.txt','w') as f:
my_writer = csv.writer(f, delimiter='\t')
for j in range(len(kappa_mean_by_age)):
my_writer.writerow([kappa_mean_by_age[j], kappa_lo_beta_by_age[j], kappa_hi_beta_by_age[j]])
f.close()
with open('./Results/' + save_name + 'Results.txt','w') as f:
f.write(results_string)
f.close()
def calcStats(self,aLvlNow,pLvlNow,MPCnow,TranShkNow,EmpNow,t_age,LorenzBool,ManyStatsBool):
'''
Calculate various statistics about the current population in the economy.
Parameters
----------
aLvlNow : [np.array]
Arrays with end-of-period assets, listed by each ConsumerType in self.agents.
pLvlNow : [np.array]
Arrays with permanent income levels, listed by each ConsumerType in self.agents.
MPCnow : [np.array]
Arrays with marginal propensity to consume, listed by each ConsumerType in self.agents.
TranShkNow : [np.array]
Arrays with transitory income shocks, listed by each ConsumerType in self.agents.
EmpNow : [np.array]
Arrays with employment states: True if employed, False otherwise.
t_age : [np.array]
Arrays with periods elapsed since model entry, listed by each ConsumerType in self.agents.
LorenzBool: bool
Indicator for whether the Lorenz target points should be calculated. Usually False,
only True when DiscFac has been identified for a particular nabla.
ManyStatsBool: bool
Indicator for whether a lot of statistics for tables should be calculated. Usually False,
only True when parameters have been estimated and we want values for tables.
Returns
-------
None
'''
# Combine inputs into single arrays
aLvl = np.hstack(aLvlNow)
pLvl = np.hstack(pLvlNow)
age = np.hstack(t_age)
TranShk = np.hstack(TranShkNow)
Emp = np.hstack(EmpNow)
# Calculate the capital to income ratio in the economy
CohortWeight = self.PopGroFac**(-age)
CapAgg = np.sum(aLvl*CohortWeight)
IncAgg = np.sum(pLvl*TranShk*CohortWeight)
KtoYnow = CapAgg/IncAgg
self.KtoYnow = KtoYnow
# Store Lorenz data if requested
self.LorenzLong = np.nan
if LorenzBool:
order = np.argsort(aLvl)
aLvl = aLvl[order]
CohortWeight = CohortWeight[order]
wealth_shares = getLorenzShares(aLvl,weights=CohortWeight,percentiles=self.LorenzPercentiles,presorted=True)
self.Lorenz = wealth_shares
if ManyStatsBool:
self.LorenzLong = getLorenzShares(aLvl,weights=CohortWeight,percentiles=np.arange(0.01,1.0,0.01),presorted=True)
else:
self.Lorenz = np.nan # Store nothing if we don't want Lorenz data
# Calculate a whole bunch of statistics if requested
if ManyStatsBool:
# Reshape other inputs
MPC = np.hstack(MPCnow)
# Sort other data items if aLvl and CohortWeight were sorted
if LorenzBool:
pLvl = pLvl[order]
MPC = MPC[order]
TranShk = TranShk[order]
age = age[order]
Emp = Emp[order]
aNrm = aLvl/pLvl # Normalized assets (wealth ratio)
IncLvl = TranShk*pLvl # Labor income this period
# Calculate overall population MPC and by subpopulations
MPCannual = 1.0 - (1.0 - MPC)**4
self.MPCall = np.sum(MPCannual*CohortWeight)/np.sum(CohortWeight)
employed = Emp
unemployed = np.logical_not(employed)
if self.T_retire > 0: # Adjust for the lifecycle model, where agents might be retired instead
unemployed = np.logical_and(unemployed,age < self.T_retire)
employed = np.logical_and(employed,age < self.T_retire)
retired = age >= self.T_retire
else:
retired = np.zeros_like(unemployed,dtype=bool)
self.MPCunemployed = np.sum(MPCannual[unemployed]*CohortWeight[unemployed])/np.sum(CohortWeight[unemployed])
self.MPCemployed = np.sum(MPCannual[employed]*CohortWeight[employed])/np.sum(CohortWeight[employed])
self.MPCretired = np.sum(MPCannual[retired]*CohortWeight[retired])/np.sum(CohortWeight[retired])
self.MPCbyWealthRatio = calcSubpopAvg(MPCannual,aNrm,self.cutoffs,CohortWeight)
self.MPCbyIncome = calcSubpopAvg(MPCannual,IncLvl,self.cutoffs,CohortWeight)
# Calculate the wealth quintile distribution of "hand to mouth" consumers
quintile_cuts = getPercentiles(aLvl,weights=CohortWeight,percentiles=[0.2, 0.4, 0.6, 0.8])
wealth_quintiles = np.ones(aLvl.size,dtype=int)
wealth_quintiles[aLvl > quintile_cuts[0]] = 2
wealth_quintiles[aLvl > quintile_cuts[1]] = 3
wealth_quintiles[aLvl > quintile_cuts[2]] = 4
wealth_quintiles[aLvl > quintile_cuts[3]] = 5
MPC_cutoff = getPercentiles(MPCannual,weights=CohortWeight,percentiles=[2.0/3.0]) # Looking at consumers with MPCs in the top 1/3
these = MPCannual > MPC_cutoff
in_top_third_MPC = wealth_quintiles[these]
temp_weights = CohortWeight[these]
hand_to_mouth_total = np.sum(temp_weights)
hand_to_mouth_pct = []
for q in range(1,6):
hand_to_mouth_pct.append(np.sum(temp_weights[in_top_third_MPC == q])/hand_to_mouth_total)
self.HandToMouthPct = np.array(hand_to_mouth_pct)
else: # If we don't want these stats, just put empty values in history
self.MPCall = np.nan
self.MPCunemployed = np.nan
self.MPCemployed = np.nan
self.MPCretired = np.nan
self.MPCbyWealthRatio = np.nan
self.MPCbyIncome = np.nan
self.HandToMouthPct = np.nan