employed_income_dist = [
np.ones(1),
np.ones(1),
np.ones(1),
] # Income distribution when employed
unemployed_income_dist = [
np.ones(1),
np.ones(1),
np.zeros(1),
] # Income distribution when permanently unemployed
MarkovType.IncomeDstn = [[employed_income_dist, unemployed_income_dist]
] # set the income distribution in each state
MarkovType.cycles = 0
# %%
# Solve the "Markov TBS" model
t_start = process_time()
MarkovType.solve()
t_end = process_time()
MarkovType.unpackcFunc()
# %%
print('Solving the same model "the long way" took ' + str(t_end - t_start) +
" seconds.")
# plotFuncs([ExampleType.solution[0].cFunc,ExampleType.solution[0].cFunc_U],0,m_upper)
plotFuncs(MarkovType.cFunc[0], 0, m_upper)
diffFunc = lambda m: ExampleType.solution[0].cFunc(m) - MarkovType.cFunc[0][0](
m)
print("Difference between the (employed) consumption functions:")
plotFuncs(diffFunc, 0, m_upper)
def setUp(self):
# Set up and solve TBS
base_primitives = {'UnempPrb': .015,
'DiscFac': 0.9,
'Rfree': 1.1,
'PermGroFac': 1.05,
'CRRA': .95}
TBSType = TractableConsumerType(**base_primitives)
TBSType.solve()
# Set up and solve Markov
MrkvArray = [np.array([[1.0-base_primitives['UnempPrb'], base_primitives['UnempPrb']],[0.0, 1.0]])]
Markov_primitives = {"CRRA": base_primitives['CRRA'],
"Rfree": np.array(2*[base_primitives['Rfree']]),
"PermGroFac": [np.array(2*[base_primitives['PermGroFac'] /
(1.0-base_primitives['UnempPrb'])])],
"BoroCnstArt": None,
"PermShkStd": [0.0],
"PermShkCount": 1,
"TranShkStd": [0.0],
"TranShkCount": 1,
"T_total": 1,
"UnempPrb": 0.0,
"UnempPrbRet": 0.0,
"T_retire": 0,
"IncUnemp": 0.0,
"IncUnempRet": 0.0,
"aXtraMin": 0.001,
"aXtraMax": TBSType.mUpperBnd,
"aXtraCount": 48,
"aXtraExtra": [None],
"aXtraNestFac": 3,
"LivPrb":[np.array([1.0,1.0]),],
"DiscFac": base_primitives['DiscFac'],
'Nagents': 1,
'psi_seed': 0,
'xi_seed': 0,
'unemp_seed': 0,
'tax_rate': 0.0,
'vFuncBool': False,
'CubicBool': True,
'MrkvArray': MrkvArray,
'T_cycle':1
}
MarkovType = MarkovConsumerType(**Markov_primitives)
MarkovType.cycles = 0
employed_income_dist = DiscreteDistribution(np.ones(1),
[np.ones(1),
np.ones(1)])
unemployed_income_dist = DiscreteDistribution(np.ones(1),
[np.ones(1),
np.zeros(1)])
MarkovType.IncomeDstn = [[employed_income_dist,
unemployed_income_dist]]
MarkovType.solve()
MarkovType.unpackcFunc()
self.TBSType = TBSType
self.MarkovType = MarkovType
def main():
# Import the HARK library. The assumption is that this code is in a folder
# contained in the HARK folder. Also import the ConsumptionSavingModel
import numpy as np # numeric Python
from HARK.utilities import plotFuncs # basic plotting tools
from HARK.ConsumptionSaving.ConsMarkovModel import MarkovConsumerType # An alternative, much longer way to solve the TBS model
from time import clock # timing utility
do_simulation = True
# Define the model primitives
base_primitives = {
'UnempPrb': .00625, # Probability of becoming unemployed
'DiscFac': 0.975, # Intertemporal discount factor
'Rfree': 1.01, # Risk-free interest factor on assets
'PermGroFac': 1.0025, # Permanent income growth factor (uncompensated)
'CRRA': 1.0
} # Coefficient of relative risk aversion
# Define a dictionary to be used in case of simulation
simulation_values = {
'aLvlInitMean': 0.0, # Mean of log initial assets for new agents
'aLvlInitStd': 1.0, # Stdev of log initial assets for new agents
'AgentCount': 10000, # Number of agents to simulate
'T_sim': 120, # Number of periods to simulate
'T_cycle': 1
} # Number of periods in the cycle
# Make and solve a tractable consumer type
ExampleType = TractableConsumerType(**base_primitives)
t_start = clock()
ExampleType.solve()
t_end = clock()
print('Solving a tractable consumption-savings model took ' +
str(t_end - t_start) + ' seconds.')
# Plot the consumption function and whatnot
m_upper = 1.5 * ExampleType.mTarg
conFunc_PF = lambda m: ExampleType.h * ExampleType.PFMPC + ExampleType.PFMPC * m
#plotFuncs([ExampleType.solution[0].cFunc,ExampleType.mSSfunc,ExampleType.cSSfunc],0,m_upper)
plotFuncs([ExampleType.solution[0].cFunc, ExampleType.solution[0].cFunc_U],
0, m_upper)
if do_simulation:
ExampleType(**
simulation_values) # Set attributes needed for simulation
ExampleType.track_vars = ['mLvlNow']
ExampleType.makeShockHistory()
ExampleType.initializeSim()
ExampleType.simulate()
# Now solve the same model using backward induction rather than the analytic method of TBS.
# The TBS model is equivalent to a Markov model with two states, one of them absorbing (permanent unemployment).
MrkvArray = np.array(
[[1.0 - base_primitives['UnempPrb'], base_primitives['UnempPrb']],
[0.0,
1.0]]) # Define the two state, absorbing unemployment Markov array
init_consumer_objects = {
"CRRA":
base_primitives['CRRA'],
"Rfree":
np.array(2 * [base_primitives['Rfree']
]), # Interest factor (same in both states)
"PermGroFac": [
np.array(2 * [
base_primitives['PermGroFac'] /
(1.0 - base_primitives['UnempPrb'])
])
], # Unemployment-compensated permanent growth factor
"BoroCnstArt":
None, # Artificial borrowing constraint
"PermShkStd": [0.0], # Permanent shock standard deviation
"PermShkCount":
1, # Number of shocks in discrete permanent shock distribution
"TranShkStd": [0.0], # Transitory shock standard deviation
"TranShkCount":
1, # Number of shocks in discrete permanent shock distribution
"T_cycle":
1, # Number of periods in cycle
"UnempPrb":
0.0, # Unemployment probability (not used, as the unemployment here is *permanent*, not transitory)
"UnempPrbRet":
0.0, # Unemployment probability when retired (irrelevant here)
"T_retire":
0, # Age at retirement (turned off)
"IncUnemp":
0.0, # Income when unemployed (irrelevant)
"IncUnempRet":
0.0, # Income when unemployed and retired (irrelevant)
"aXtraMin":
0.001, # Minimum value of assets above minimum in grid
"aXtraMax":
ExampleType.mUpperBnd, # Maximum value of assets above minimum in grid
"aXtraCount":
48, # Number of points in assets grid
"aXtraExtra": [None], # Additional points to include in assets grid
"aXtraNestFac":
3, # Degree of exponential nesting when constructing assets grid
"LivPrb": [np.array([1.0, 1.0])], # Survival probability
"DiscFac":
base_primitives['DiscFac'], # Intertemporal discount factor
'AgentCount':
1, # Number of agents in a simulation (irrelevant)
'tax_rate':
0.0, # Tax rate on labor income (irrelevant)
'vFuncBool':
False, # Whether to calculate the value function
'CubicBool':
True, # Whether to use cubic splines (False --> linear splines)
'MrkvArray': [MrkvArray] # State transition probabilities
}
MarkovType = MarkovConsumerType(
**init_consumer_objects) # Make a basic consumer type
employed_income_dist = [np.ones(1), np.ones(1),
np.ones(1)] # Income distribution when employed
unemployed_income_dist = [
np.ones(1), np.ones(1), np.zeros(1)
] # Income distribution when permanently unemployed
MarkovType.IncomeDstn = [[employed_income_dist, unemployed_income_dist]
] # set the income distribution in each state
MarkovType.cycles = 0
# Solve the "Markov TBS" model
t_start = clock()
MarkovType.solve()
t_end = clock()
MarkovType.unpackcFunc()
print('Solving the same model "the long way" took ' +
str(t_end - t_start) + ' seconds.')
#plotFuncs([ExampleType.solution[0].cFunc,ExampleType.solution[0].cFunc_U],0,m_upper)
plotFuncs(MarkovType.cFunc[0], 0, m_upper)
diffFunc = lambda m: ExampleType.solution[0].cFunc(m) - MarkovType.cFunc[
0][0](m)
print('Difference between the (employed) consumption functions:')
plotFuncs(diffFunc, 0, m_upper)
