def describeMPCdstn(SomeTypes,percentiles):
MPC_sim = np.concatenate([ThisType.MPCnow for ThisType in SomeTypes])
MPCpercentiles_quarterly = getPercentiles(MPC_sim,percentiles=percentiles)
MPCpercentiles_annual = 1.0 - (1.0 - MPCpercentiles_quarterly)**4
for j in range(len(percentiles)):
print('The ' + str(100*percentiles[j]) + 'th percentile of the MPC is ' + str(MPCpercentiles_annual[j]))
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 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 makePandemicShockProbsFigure(Agents,
spec_name,
PanShock,
UnempD,
UnempH,
UnempC,
UnempP,
UnempA1,
UnempA2,
DeepD,
DeepH,
DeepC,
DeepP,
DeepA1,
DeepA2,
show_fig=False,
for_mini=False):
'''
Make figures showing the probability of becoming unemployed and deeply
unemployed when the pandemic hits, by age, income, and education.
Parameters
----------
Agents : [AgentType]
List of types of agents in the economy. Only the first three types
will actually be used by this function, and not changed at all--
they are deepcopied and manipulated.
spec_name : str
Filename suffix for figure to be saved, or subdirectory of ./Figures/
for the figure to be saved (if for_mini is True)
PanShock : bool
This isn't used; it's here for technical reasons.
UnempD : float
Constant for highschool dropouts in the Markov-shock logit for unemployment.
UnempH : float
Constant for highschool grads in the Markov-shock logit for unemployment.
UnempC : float
Constant for college goers in the Markov-shock logit for unemployment.
UnempP : float
Coefficient on log permanent income in the Markov-shock logit for unemploment.
UnempA1 : float
Coefficient on age in the Markov-shock logit for unemployment.
UnempA2 : float
Coefficient on age squared in the Markov-shock logit for unemployment.
DeepD : float
Constant for highschool dropouts in the Markov-shock logit for deep unemployment.
DeepH : float
Constant for highschool grads in the Markov-shock logit for deep unemployment.
DeepC : float
Constant for college goers in the Markov-shock logit for deep unemployment.
DeepP : float
Coefficient on log permanent income in the Markov-shock logit for deep unemploment.
DeepA1 : float
Coefficient on age in the Markov-shock logit for deep unemployment.
DeepA2 : float
Coefficient on age squared in the Markov-shock logit for deep unemployment.
show_fig : bool
Indicator for whether the figure should be displayed to screen; default True.
for_mini : bool
Indicator for whether this call was from the MINI script, which changes the
target directory where the figure is saved.
Returns
-------
data: Dict
A dictionary with data to plot pandemic shock unemployment probablities.
'''
if for_mini:
fig_name_base = figs_dir + spec_name + '/UbyDemog'
else:
fig_name_base = figs_dir + 'UnempProbByDemog' + spec_name
BigPop = 100000
T = Agents[0].T_retire + 1
PlvlAgg_adjuster = Agents[0].PermGroFacAgg**(-np.arange(T))
Unemp0 = [UnempD, UnempH, UnempC]
Deep0 = [DeepD, DeepH, DeepC]
# Initialize an array to hold permanent income percentile data
pctiles = [0.05, 0.25, 0.5, 0.75, 0.95]
pLvlPercentiles = np.zeros((3, 5, T)) + np.nan
# Get distribution of permanent income at each age for each education level,
# as well as the probability of unemployment and deep unemployment for all
TempTypes = deepcopy(Agents)
for n in range(3):
ThisType = TempTypes[n]
e = ThisType.EducType
ThisType.AgentCount = int(EducShares[e] * BigPop)
ThisType.mortality_off = True
ThisType.T_sim = T
ThisType.initializeSim()
pLvlInit = ThisType.pLvlNow.copy()
ThisType.makeShockHistory()
ThisType.history['pLvlNow'] = np.cumprod(
ThisType.history['PermShkNow'], axis=0)
ThisType.history['pLvlNow'] *= np.tile(
np.reshape(pLvlInit, (1, ThisType.AgentCount)), (T, 1))
ThisType.history['pLvlNow'] *= np.tile(
np.reshape(PlvlAgg_adjuster, (T, 1)), (1, ThisType.AgentCount))
for t in range(T):
pLvlPercentiles[n, :, t] = getPercentiles(
ThisType.history['pLvlNow'][t, :], percentiles=pctiles)
AgeArray = np.tile(np.reshape(np.arange(T) / 4 + 24, (T, 1)),
(1, ThisType.AgentCount))
AgeSqArray = np.tile(np.reshape(np.arange(T) / 4 + 24, (T, 1)),
(1, ThisType.AgentCount))
UnempX = np.exp(Unemp0[e] +
UnempP * np.log(ThisType.history['pLvlNow']) +
UnempA1 * AgeArray + UnempA2 * AgeSqArray)
DeepX = np.exp(Deep0[e] + DeepP * np.log(ThisType.history['pLvlNow']) +
DeepA1 * AgeArray + DeepA2 * AgeSqArray)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
ThisType.history['UnempPrb'] = UnempPrb
ThisType.history['DeepPrb'] = DeepPrb
UnempPrbAll = np.concatenate(
[ThisType.history['UnempPrb'] for ThisType in TempTypes], axis=1)
DeepPrbAll = np.concatenate(
[ThisType.history['DeepPrb'] for ThisType in TempTypes], axis=1)
# Get overall unemployment and deep unemployment probabilities at each age
UnempPrbMean = np.mean(UnempPrbAll, axis=1)
DeepPrbMean = np.mean(DeepPrbAll, axis=1)
data = dict()
# Plot overall unemployment probabilities in top left
plt.subplot(2, 2, 1)
dashes2 = [10, 2]
AgeVec = np.arange(T) / 4 + 24
plt.plot(AgeVec, UnempPrbMean, '-b')
plt.plot(AgeVec, DeepPrbMean, 'r', dashes=dashes2)
data['overall'] = [AgeVec, UnempPrbMean, DeepPrbMean]
plt.legend(['Unemployed', 'Deep unemp'], loc=1)
plt.ylim(0, 0.20)
plt.xticks([])
plt.ylabel('Probability')
plt.title('All education (mean)')
# Plot dropout unemployment probabilities by permanent income
e = 0
p = 0
data['dropout'] = dict()
plt.subplot(2, 2, 2)
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, ':b')
plt.plot(AgeVec, DeepPrb, ':r')
data['dropout'][p] = [AgeVec, UnempPrb, DeepPrb]
p = 4
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, ':b')
plt.plot(AgeVec, DeepPrb, ':r')
data['dropout'][p] = [AgeVec, UnempPrb, DeepPrb]
p = 2
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, '-b')
plt.plot(AgeVec, DeepPrb, 'r', dashes=dashes2)
plt.yticks([])
plt.xticks([])
plt.ylim(0, 0.20)
data['dropout'][p] = [AgeVec, UnempPrb, DeepPrb]
plt.title('Dropout')
# Plot highschool unemployment probabilities by permanent income
e = 1
p = 0
data['highschool'] = dict()
plt.subplot(2, 2, 3)
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, ':b')
plt.plot(AgeVec, DeepPrb, ':r')
data['highschool'][p] = [AgeVec, UnempPrb, DeepPrb]
p = 4
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, ':b')
plt.plot(AgeVec, DeepPrb, ':r')
data['highschool'][p] = [AgeVec, UnempPrb, DeepPrb]
p = 2
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, '-b')
plt.plot(AgeVec, DeepPrb, 'r', dashes=dashes2)
data['highschool'][p] = [AgeVec, UnempPrb, DeepPrb]
plt.ylim(0, 0.20)
plt.xlabel('Age')
plt.ylabel('Probability')
plt.title('High school')
# Plot college unemployment probabilities by permanent income
e = 2
p = 0
data['college'] = dict()
plt.subplot(2, 2, 4)
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, ':b')
plt.plot(AgeVec, DeepPrb, ':r')
data['college'][p] = [AgeVec, UnempPrb, DeepPrb]
p = 4
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, ':b')
plt.plot(AgeVec, DeepPrb, ':r')
data['college'][p] = [AgeVec, UnempPrb, DeepPrb]
p = 2
UnempX = np.exp(Unemp0[e] + UnempP * np.log(pLvlPercentiles[e, p, :]) +
UnempA1 * AgeVec + UnempA2 * AgeVec**2)
DeepX = np.exp(Deep0[e] + DeepP * np.log(pLvlPercentiles[e, p, :]) +
DeepA1 * AgeVec + DeepA2 * AgeVec**2)
denom = (1. + UnempX + DeepX)
UnempPrb = UnempX / denom
DeepPrb = DeepX / denom
plt.plot(AgeVec, UnempPrb, '-b')
plt.plot(AgeVec, DeepPrb, 'r', dashes=dashes2)
data['college'][p] = [AgeVec, UnempPrb, DeepPrb]
plt.ylim(0, 0.20)
plt.xlabel('Age')
plt.yticks([])
plt.title('College')
# Save the figure and display it to screen
plt.suptitle('Unemployment probability after pandemic shock')
plt.savefig(fig_name_base + '.pdf', bbox_inches='tight')
if not for_mini:
plt.savefig(fig_name_base + '.png', bbox_inches='tight')
plt.savefig(fig_name_base + '.svg', bbox_inches='tight')
if show_fig:
plt.show()
else:
plt.clf()
plt.close()
return data
def runExperiment(Agents, PanShock, StimMax, StimCut0, StimCut1, BonusUnemp,
BonusDeep, T_ahead, UnempD, UnempH, UnempC, UnempP, UnempA1,
UnempA2, DeepD, DeepH, DeepC, DeepP, DeepA1, DeepA2,
Dspell_pcvd, Dspell_real, Lspell_pcvd, Lspell_real,
L_shared):
'''
Conduct a fiscal policy experiment by announcing a fiscal stimulus T periods
ahead of when checks will actually arrive. The stimulus is in response to a
global health crisis that shocks many consumers into unemployment, and others
into "deep" unemployment that they think will last several quarters.
Parameters
----------
Agents : [AgentType]
List of agent types in the economy.
PanShock : bool
Indicator for whether the pandemic actually hits.
StimMax : float
Maximum stimulus check a household can receive, denominated in $1000.
StimCut0 : float or None
Permanent income threshold where stimulus check begins to phase out.
Can only be None if StimCut1 is also None.
StimCut1 : float or None
Permanent income threshold where stimulus check is completely phased out.
None means that the same stimulus check is given to everyone.
BonusUnemp : float
One time "bonus benefit" given to regular unemployed people at t=0.
BonusDeep : float
One time "bonus benefit" given to deeply unemployed people at t=0.
T_ahead : int
Number of quarters after announcement that the stimulus checks will arrive.
UnempD : float
Constant for highschool dropouts in the Markov-shock logit for unemployment.
UnempH : float
Constant for highschool grads in the Markov-shock logit for unemployment.
UnempC : float
Constant for college goers in the Markov-shock logit for unemployment.
UnempP : float
Coefficient on log permanent income in the Markov-shock logit for unemploment.
UnempA1 : float
Coefficient on age in the Markov-shock logit for unemployment.
UnempA2 : float
Coefficient on age squared in the Markov-shock logit for unemployment.
DeepD : float
Constant for highschool dropouts in the Markov-shock logit for deep unemployment.
DeepH : float
Constant for highschool grads in the Markov-shock logit for deep unemployment.
DeepC : float
Constant for college goers in the Markov-shock logit for deep unemployment.
DeepP : float
Coefficient on log permanent income in the Markov-shock logit for deep unemploment.
DeepA1 : float
Coefficient on age in the Markov-shock logit for deep unemployment.
DeepA2 : float
Coefficient on age squared in the Markov-shock logit for deep unemployment.
Dspell_pcvd : float
Perceived average duration of a "deep unemployment" spell.
Dspell_real : float
Actual average duration of a "deep unemployment" spell.
Lspell_pcvd : float
Perceived average duration of the marginal utility-reducing lockdown.
Lspell_real : float
Actual average duration of the marginal utility-reducing lockdown. If
L_shared is True, it represents that *exact* duration of the lockdown,
which should be an integer.
L_shared : bool
Indicator for whether the "lockdown" being lifted is a common/shared event
across all agents (True) versus whether it's an idiosyncratic shock (False).
Returns
-------
TBD
'''
PlvlAgg_adjuster = Agents[0].PlvlAgg_base
T = Agents[0].T_sim
# Adjust fiscal stimulus parameters by the level of aggregate productivity,
# which is 96 years more advanced than you would expect because reasons.
# Multiply unemployment benefits by 0.8 to reflect fact that labor force participation rate is 0.8.
StimMax *= PlvlAgg_adjuster
BonusUnemp *= PlvlAgg_adjuster * 0.8
BonusDeep *= PlvlAgg_adjuster * 0.8
if StimCut0 is not None:
StimCut0 *= PlvlAgg_adjuster
if StimCut1 is not None:
StimCut1 *= PlvlAgg_adjuster
# Make dictionaries of parameters to give to the agents
experiment_dict_D = {
'PanShock': PanShock,
'T_advance': T_ahead + 1,
'StimMax': StimMax,
'StimCut0': StimCut0,
'StimCut1': StimCut1,
'BonusUnemp': BonusUnemp,
'BonusDeep': BonusDeep,
'UnempParam0': UnempD,
'UnempParam1': UnempP,
'UnempParam2': UnempA1,
'UnempParam3': UnempA2,
'DeepParam0': DeepD,
'DeepParam1': DeepP,
'DeepParam2': DeepA1,
'DeepParam3': DeepA2,
'Dspell_pcvd': Dspell_pcvd,
'Dspell_real': Dspell_real,
'Lspell_pcvd': Lspell_pcvd,
'Lspell_real': Lspell_real,
'L_shared': L_shared
}
experiment_dict_H = experiment_dict_D.copy()
experiment_dict_H['UnempParam0'] = UnempH
experiment_dict_H['DeepParam0'] = DeepH
experiment_dict_C = experiment_dict_D.copy()
experiment_dict_C['UnempParam0'] = UnempC
experiment_dict_C['DeepParam0'] = DeepC
experiment_dicts = [
experiment_dict_D, experiment_dict_H, experiment_dict_C
]
# Begin the experiment by resetting each type's state to the baseline values
PopCount = 0
for ThisType in Agents:
ThisType.read_shocks = True
e = ThisType.EducType
ThisType(**experiment_dicts[e])
PopCount += ThisType.AgentCount
# Update the perceived and actual Markov arrays, solve and re-draw shocks if
# warranted, then impose the pandemic shock and the stimulus, and finally
# simulate the model for three years.
experiment_commands = [
'updateMrkvArray()', 'solveIfChanged()', 'makeShocksIfChanged()',
'initializeSim()', 'hitWithPandemicShock()', 'announceStimulus()',
'simulate()'
]
multiThreadCommandsFake(Agents, experiment_commands)
# Extract simulated consumption, labor income, and weight data
cNrm_all = np.concatenate(
[ThisType.history['cNrmNow'] for ThisType in Agents], axis=1)
lLvl_all = np.concatenate(
[ThisType.history['lLvlNow'] for ThisType in Agents], axis=1)
Mrkv_hist = np.concatenate(
[ThisType.history['MrkvNow'] for ThisType in Agents], axis=1)
t_cycle_hist = np.concatenate(
[ThisType.history['t_cycle'] for ThisType in Agents], axis=1)
u_all = np.concatenate([ThisType.history['uNow'] for ThisType in Agents],
axis=1)
w_all = np.concatenate([ThisType.history['wNow'] for ThisType in Agents],
axis=1)
pLvl_all = np.concatenate(
[ThisType.history['pLvlNow'] for ThisType in Agents], axis=1)
Weight_all = np.concatenate(
[ThisType.history['Weight'] for ThisType in Agents], axis=1)
pLvl_all /= PlvlAgg_adjuster
lLvl_all /= PlvlAgg_adjuster
cLvl_all = cNrm_all * pLvl_all
# Get initial Markov states
Mrkv_init = np.concatenate(
[ThisType.history['MrkvNow'][0, :] for ThisType in Agents])
Age_init = np.concatenate([ThisType.age_base for ThisType in Agents])
WorkingAge = Age_init <= 163
Employed = np.logical_and(np.logical_or(Mrkv_init == 0, Mrkv_init == 3),
WorkingAge)
Unemployed = np.logical_and(np.logical_or(Mrkv_init == 1, Mrkv_init == 4),
WorkingAge)
DeepUnemp = np.logical_and(np.logical_or(Mrkv_init == 2, Mrkv_init == 5),
WorkingAge)
MrkvTags = (np.vstack([Employed, Unemployed, DeepUnemp, WorkingAge]))
# Calculate an alternate version of labor and transfer income that removes all
# transitory shocks except unemployment.
yAlt_all = pLvl_all.copy()
Checks = np.zeros_like(yAlt_all)
Checks[T_ahead, :] = np.concatenate(
[ThisType.StimLvl for ThisType in Agents], axis=0)
yAlt_all[u_all.astype(bool)] *= Agents[0].IncUnemp
if (hasattr(Agents[0], 'ContUnempBenefits')
and Agents[0].ContUnempBenefits):
yAlt_all[np.logical_and(
Mrkv_hist == 4,
t_cycle_hist <= 163)] += BonusUnemp / PlvlAgg_adjuster
yAlt_all[np.logical_and(
Mrkv_hist == 5,
t_cycle_hist <= 163)] += BonusDeep / PlvlAgg_adjuster
else:
yAlt_all[0, Unemployed] += BonusUnemp / PlvlAgg_adjuster
yAlt_all[0, DeepUnemp] += BonusDeep / PlvlAgg_adjuster
yAlt_all += Checks / PlvlAgg_adjuster
laborandtransferLvl_all = yAlt_all
# Partition the working age agents by the initial permanent income
pLvl_init = np.concatenate(
[ThisType.history['pLvlNow'][0, :] for ThisType in Agents])
Weight_init = np.concatenate(
[ThisType.history['Weight'][0, :] for ThisType in Agents]) * WorkingAge
quintile_cuts = getPercentiles(pLvl_init, Weight_init,
[0.2, 0.4, 0.6, 0.8])
inc_quint = np.zeros(PopCount)
for q in range(4):
inc_quint += pLvl_init >= quintile_cuts[q]
which_inc_quint = np.zeros((5, PopCount), dtype=bool)
for q in range(5):
which_inc_quint[q, :] = inc_quint == q
which_inc_quint[:, np.logical_not(WorkingAge)] = False
# Calculate the time series of mean consumption in each quarter
C = np.sum(cLvl_all * Weight_all, axis=1) / np.sum(Weight_all, axis=1)
# Calculate unemployment rate each quarter
U = np.sum(u_all * Weight_all, axis=1) / np.sum(w_all * Weight_all, axis=1)
# Calculate mean consumption *among the working age* by initial Markov state
with warnings.catch_warnings():
warnings.simplefilter(
"ignore"
) # Ignore divide by zero warning when no one is deeply unemployed
C_by_mrkv = np.zeros((4, T))
C_by_mrkv[0, :] = np.sum(cLvl_all * Weight_all * Employed,
axis=1) / np.sum(Weight_all * Employed,
axis=1)
C_by_mrkv[1, :] = np.sum(cLvl_all * Weight_all * Unemployed,
axis=1) / np.sum(Weight_all * Unemployed,
axis=1)
C_by_mrkv[2, :] = np.sum(cLvl_all * Weight_all * DeepUnemp,
axis=1) / np.sum(Weight_all * DeepUnemp,
axis=1)
C_by_mrkv[3, :] = np.sum(cLvl_all * Weight_all * WorkingAge,
axis=1) / np.sum(Weight_all * WorkingAge,
axis=1)
# Calculate mean consumption *among the working age* by income quintile
C_by_inc = np.zeros((5, T))
LT_by_inc = np.zeros((5, T))
for q in range(5):
C_by_inc[q, :] = np.sum(cLvl_all * Weight_all * which_inc_quint[q, :],
axis=1) / np.sum(
Weight_all * which_inc_quint[q, :], axis=1)
LT_by_inc[q, :] = np.sum(
laborandtransferLvl_all * Weight_all * which_inc_quint[q, :],
axis=1) / np.sum(Weight_all * which_inc_quint[q, :], axis=1)
return C, C_by_mrkv, C_by_inc, cLvl_all, Weight_all, MrkvTags, U, laborandtransferLvl_all, LT_by_inc
# ## Calculating the Lorenz Distance at Targets
#
# Now we want to construct a function that calculates the Euclidean distance between simulated and actual Lorenz curves at the four percentiles of interest: 20, 40, 60, and 80.
# %% [markdown]
# ## The Distribution Of the Marginal Propensity to Consume
#
# For many macroeconomic purposes, the distribution of the MPC $\kappa$ is more important than the distribution of wealth. Ours is a quarterly model, and MPC's are typically reported on an annual basis; we can compute an approximate MPC from the quraterly ones as $\kappa_{Y} \approx 1.0 - (1.0 - \kappa_{Q})^4$
#
# In the cell below, we retrieve the MPCs from our simulated consumers and show that the 10th percentile in the MPC distribution is only about 6 percent, while at the 90th percentile it is almost 0.5
# %%
# Retrieve the MPC's
percentiles = np.linspace(0.1, 0.9, 9)
MPC_sim = np.concatenate([ThisType.MPCnow for ThisType in MyTypes])
MPCpercentiles_quarterly = getPercentiles(MPC_sim, percentiles=percentiles)
MPCpercentiles_annual = 1.0 - (1.0 - MPCpercentiles_quarterly)**4
print('The MPC at the 10th percentile of the distribution is ' +
str(decfmt2(MPCpercentiles_annual[0])))
print('The MPC at the 50th percentile of the distribution is ' +
str(decfmt2(MPCpercentiles_annual[4])))
print('The MPC at the 90th percentile of the distribution is ' +
str(decfmt2(MPCpercentiles_annual[-1])))
# %% [markdown]
# ## Adding Very Impatient Households
#
# Now that we have some tools for examining both microeconomic (the MPC across the population) and macroeconomic (the distribution and overall level of wealth) outcomes from our model, we are all set to conduct our experiment.
#
# In this exercise, we are going to add very impatient households to the economy in a very direct way: by replacing the *most impatient consumer type* with an *even more impatient type*. Specifically, we will have these agents have a discount factor of $\beta = 0.80$ at a quarterly frequency, which corresponds to $\beta \approx 0.41$ annual.
def calcStats(self, aLvlNow, pLvlNow, MPCnow, lIncomeLvl, 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.
lIncomeLvl : [np.array]
Arrays with labor income levels, 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)
IncLvl = np.hstack(lIncomeLvl)
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(IncLvl * 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]
IncLvl = IncLvl[order]
age = age[order]
Emp = Emp[order]
aNrm = aLvl / pLvl # Normalized assets (wealth ratio)
# Calculate overall population MPC and by subpopulations
# MPC_cf_BPP is the MPC that is comparable with the empirical estimation method
MPC_cf_BPP = 1.0 - 0.25 * ((1.0 - MPC) + (1.0 - MPC)**2 +
(1.0 - MPC)**3 + (1.0 - MPC)**4)
self.MPCall = np.sum(
MPC_cf_BPP * CohortWeight) / np.sum(CohortWeight)
employed = Emp
unemployed = np.logical_not(employed)
self.MPCbyWealthRatio = calcSubpopAvg(MPC_cf_BPP, aNrm,
self.cutoffs, CohortWeight)
self.MPCbyIncome = calcSubpopAvg(MPC_cf_BPP, 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(
MPC_cf_BPP, weights=CohortWeight, percentiles=[
2.0 / 3.0
]) # Looking at consumers with MPCs in the top 1/3
these = MPC_cf_BPP > 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()
