def calculateLorenzDifference(sim_wealth, weights, percentiles, target_levels):
'''
Calculates the sum of squared differences between the simulatedLorenz curve
at the specified percentile levels and the target Lorenz levels.
Parameters
----------
sim_wealth : numpy.array
Array with simulated wealth values.
weights : numpy.array
List of weights for each row of sim_wealth.
percentiles : [float]
Points in the distribution of wealth to match.
target_levels : np.array
Actual U.S. Lorenz curve levels at the specified percentiles.
Returns
-------
distance : float
Sum of squared distances between simulated and target Lorenz curves.
'''
sim_lorenz = getLorenzShares(sim_wealth,
weights=weights,
percentiles=percentiles)
distance = sum((100 * sim_lorenz - 100 * target_levels)**2)
return distance
def makeLorenzFig(real_wealth, real_weights, sim_wealth, sim_weights):
'''
Produces a Lorenz curve for the distribution of wealth, comparing simulated
to actual data. A sub-function of makeCSTWresults().
Parameters
----------
real_wealth : np.array
Data on household wealth.
real_weights : np.array
Weighting array of the same size as real_wealth.
sim_wealth : np.array
Simulated wealth holdings of many households.
sim_weights :np.array
Weighting array of the same size as sim_wealth.
Returns
-------
these_percents : np.array
An array of percentiles of households, by wealth.
real_lorenz : np.array
Lorenz shares for real_wealth corresponding to these_percents.
sim_lorenz : np.array
Lorenz shares for sim_wealth corresponding to these_percents.
'''
these_percents = np.linspace(0.0001, 0.9999, 201)
real_lorenz = getLorenzShares(real_wealth,
weights=real_weights,
percentiles=these_percents)
sim_lorenz = getLorenzShares(sim_wealth,
weights=sim_weights,
percentiles=these_percents)
plt.plot(100 * these_percents, real_lorenz, '-k', linewidth=1.5)
plt.plot(100 * these_percents, sim_lorenz, '--k', linewidth=1.5)
plt.xlabel('Wealth percentile', fontsize=14)
plt.ylabel('Cumulative wealth ownership', fontsize=14)
plt.title('Simulated vs Actual Lorenz Curves', fontsize=16)
plt.legend(('Actual', 'Simulated'), loc=2, fontsize=12)
plt.ylim(-0.01, 1)
plt.show()
return (these_percents, real_lorenz, sim_lorenz)
def makeLorenzFig(real_wealth,real_weights,sim_wealth,sim_weights):
'''
Produces a Lorenz curve for the distribution of wealth, comparing simulated
to actual data. A sub-function of makeCSTWresults().
Parameters
----------
real_wealth : np.array
Data on household wealth.
real_weights : np.array
Weighting array of the same size as real_wealth.
sim_wealth : np.array
Simulated wealth holdings of many households.
sim_weights :np.array
Weighting array of the same size as sim_wealth.
Returns
-------
these_percents : np.array
An array of percentiles of households, by wealth.
real_lorenz : np.array
Lorenz shares for real_wealth corresponding to these_percents.
sim_lorenz : np.array
Lorenz shares for sim_wealth corresponding to these_percents.
'''
these_percents = np.linspace(0.0001,0.9999,201)
real_lorenz = getLorenzShares(real_wealth,weights=real_weights,percentiles=these_percents)
sim_lorenz = getLorenzShares(sim_wealth,weights=sim_weights,percentiles=these_percents)
plt.plot(100*these_percents,real_lorenz,'-k',linewidth=1.5)
plt.plot(100*these_percents,sim_lorenz,'--k',linewidth=1.5)
plt.xlabel('Wealth percentile',fontsize=14)
plt.ylabel('Cumulative wealth ownership',fontsize=14)
plt.title('Simulated vs Actual Lorenz Curves',fontsize=16)
plt.legend(('Actual','Simulated'),loc=2,fontsize=12)
plt.ylim(-0.01,1)
plt.show()
return (these_percents,real_lorenz,sim_lorenz)
def calculateLorenzDifference(sim_wealth,weights,percentiles,target_levels):
'''
Calculates the sum of squared differences between the simulatedLorenz curve
at the specified percentile levels and the target Lorenz levels.
Parameters
----------
sim_wealth : numpy.array
Array with simulated wealth values.
weights : numpy.array
List of weights for each row of sim_wealth.
percentiles : [float]
Points in the distribution of wealth to match.
target_levels : np.array
Actual U.S. Lorenz curve levels at the specified percentiles.
Returns
-------
distance : float
Sum of squared distances between simulated and target Lorenz curves.
'''
sim_lorenz = getLorenzShares(sim_wealth,weights=weights,percentiles=percentiles)
distance = sum((100*sim_lorenz-100*target_levels)**2)
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
MrkvArray[t + 1, 0] = 1.0
w, v = np.linalg.eig(np.transpose(MrkvArray))
idx = (np.abs(w - 1.0)).argmin()
x = v[:, idx].astype(float)
AgeDstn = (x / np.sum(x))
return AgeDstn
# Set targets for K/Y and the Lorenz curve based on the data
if Params.do_liquid:
lorenz_target = np.array([0.0, 0.004, 0.025, 0.117])
KY_target = 6.60
else: # This is hacky until I can find the liquid wealth data and import it
lorenz_target = getLorenzShares(Params.SCF_wealth,
weights=Params.SCF_weights,
percentiles=Params.percentiles_to_match)
lorenz_long_data = np.hstack(
(np.array(0.0),
getLorenzShares(Params.SCF_wealth,
weights=Params.SCF_weights,
percentiles=np.arange(0.01, 1.0,
0.01).tolist()), np.array(1.0)))
#lorenz_target = np.array([-0.002, 0.01, 0.053,0.171])
KY_target = 10.26
# Make AgentTypes for estimation
if Params.do_lifecycle:
DropoutType = cstwMPCagent(**Params.init_dropout)
DropoutType.AgeDstn = calcStationaryAgeDstn(DropoutType.LivPrb, True)
HighschoolType = deepcopy(DropoutType)
j += 1
# Only run below this line if module is run rather than imported:
if __name__ == "__main__":
# =================================================================
# ====== Make the list of consumer types for estimation ===========
#==================================================================
# Set target Lorenz points and K/Y ratio (MOVE THIS TO SetupParams)
if Params.do_liquid:
lorenz_target = np.array([0.0, 0.004, 0.025, 0.117])
KY_target = 6.60
else: # This is hacky until I can find the liquid wealth data and import it
lorenz_target = getLorenzShares(
Params.SCF_wealth,
weights=Params.SCF_weights,
percentiles=Params.percentiles_to_match)
#lorenz_target = np.array([-0.002, 0.01, 0.053,0.171])
KY_target = 10.26
# Make a vector of initial wealth-to-permanent income ratios
a_init = drawDiscrete(N=Params.sim_pop_size,
P=Params.a0_probs,
X=Params.a0_values,
seed=Params.a0_seed)
# Make the list of types for this run, whether infinite or lifecycle
if Params.do_lifecycle:
# Make cohort scaling array
cohort_scale = Params.TFP_growth**(-np.arange(Params.total_T + 1))
cohort_scale_array = np.tile(
this_type.update()
j += 1
# Only run below this line if module is run rather than imported:
if __name__ == "__main__":
# =================================================================
# ====== Make the list of consumer types for estimation ===========
#==================================================================
# Set target Lorenz points and K/Y ratio (MOVE THIS TO SetupParams)
if Params.do_liquid:
lorenz_target = np.array([0.0, 0.004, 0.025,0.117])
KY_target = 6.60
else: # This is hacky until I can find the liquid wealth data and import it
lorenz_target = getLorenzShares(Params.SCF_wealth,weights=Params.SCF_weights,percentiles=Params.percentiles_to_match)
#lorenz_target = np.array([-0.002, 0.01, 0.053,0.171])
KY_target = 10.26
# Make a vector of initial wealth-to-permanent income ratios
a_init = drawDiscrete(N=Params.sim_pop_size,P=Params.a0_probs,X=Params.a0_values,seed=Params.a0_seed)
# Make the list of types for this run, whether infinite or lifecycle
if Params.do_lifecycle:
# Make cohort scaling array
cohort_scale = Params.TFP_growth**(-np.arange(Params.total_T+1))
cohort_scale_array = np.tile(np.reshape(cohort_scale,(Params.total_T+1,1)),(1,Params.sim_pop_size))
# Make base consumer types for each education level
DropoutType = cstwMPCagent(**Params.init_dropout)
DropoutType.a_init = a_init
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
MrkvArray[t,t+1] = LivPrb[t]
MrkvArray[t+1,0] = 1.0
w, v = np.linalg.eig(np.transpose(MrkvArray))
idx = (np.abs(w-1.0)).argmin()
x = v[:,idx].astype(float)
AgeDstn = (x/np.sum(x))
return AgeDstn
# Set targets for K/Y and the Lorenz curve based on the data
if Params.do_liquid:
lorenz_target = np.array([0.0, 0.004, 0.025,0.117])
KY_target = 6.60
else: # This is hacky until I can find the liquid wealth data and import it
lorenz_target = getLorenzShares(Params.SCF_wealth,weights=Params.SCF_weights,percentiles=Params.percentiles_to_match)
lorenz_long_data = np.hstack((np.array(0.0),getLorenzShares(Params.SCF_wealth,weights=Params.SCF_weights,percentiles=np.arange(0.01,1.0,0.01).tolist()),np.array(1.0)))
#lorenz_target = np.array([-0.002, 0.01, 0.053,0.171])
KY_target = 10.26
# Make AgentTypes for estimation
if Params.do_lifecycle:
DropoutType = cstwMPCagent(**Params.init_dropout)
DropoutType.AgeDstn = calcStationaryAgeDstn(DropoutType.LivPrb,True)
HighschoolType = deepcopy(DropoutType)
HighschoolType(**Params.adj_highschool)
HighschoolType.AgeDstn = calcStationaryAgeDstn(HighschoolType.LivPrb,True)
CollegeType = deepcopy(DropoutType)
CollegeType(**Params.adj_college)
CollegeType.AgeDstn = calcStationaryAgeDstn(CollegeType.LivPrb,True)
DropoutType.update()
