def setUp(self):
# Make one agent type and an economy for it to live in
self.agent = AggShockMarkovConsumerType()
self.agent.cycles = 0
self.agent.AgentCount = 1000 # Low number of simulated agents
self.agent.IncomeDstn[0] = 2 * [self.agent.IncomeDstn[0]] ## see #557
self.economy = CobbDouglasMarkovEconomy(agents=[self.agent])
class testAggShockMarkovConsumerType(unittest.TestCase):
def setUp(self):
self.agent = AggShockMarkovConsumerType()
self.agent.IncomeDstn[0] = 2*[self.agent.IncomeDstn[0]] ## see #557
self.economy = CobbDouglasMarkovEconomy(
agents = [self.agent])
def test_economy(self):
self.agent.getEconomyData(self.economy) # Makes attributes of the economy, attributes of the agent
self.economy.makeAggShkHist() # Make a simulated history of the economy
# Set tolerance level.
self.economy.tolerance = 0.5
class testAggShockMarkovConsumerType(unittest.TestCase):
def setUp(self):
# Make one agent type and an economy for it to live in
self.agent = AggShockMarkovConsumerType()
self.agent.cycles = 0
self.agent.AgentCount = 1000 # Low number of simulated agents
self.agent.IncomeDstn[0] = 2 * [self.agent.IncomeDstn[0]] ## see #557
self.economy = CobbDouglasMarkovEconomy(agents=[self.agent])
def test_agent(self):
# Have one consumer type inherit relevant objects from the economy,
# then solve their microeconomic problem
self.agent.getEconomyData(self.economy)
self.agent.solve()
self.assertAlmostEqual(
self.agent.solution[0].cFunc[0](10.0, self.economy.MSS),
2.5635896520991377)
def test_economy(self):
# Adjust the economy so that it (fake) solves quickly
self.economy.act_T = 500 # Short simulation history
self.economy.max_loops = 3 # Just quiet solving early
self.economy.verbose = False # Turn off printed messages
self.agent.getEconomyData(self.economy)
self.economy.makeAggShkHist(
) # Make a simulated history of aggregate shocks
self.economy.solve(
) # Solve for the general equilibrium of the economy
self.economy.AFunc = self.economy.dynamics.AFunc
self.assertAlmostEqual(self.economy.AFunc[0].slope, 1.0904698841958917)
self.assertAlmostEqual(self.economy.history["AaggNow"][5],
9.467758924955897)
# KS assume that 'good' and 'bad' times are of equal expected duration
# The probability of a change in the aggregate state is p_change=0.125
p_change=0.125
p_remain=1-p_change
# Now we define macro transition probabilities for AggShockMarkovConsumerType
# [i,j] is probability of being in state j next period conditional on being in state i this period.
# In both states, there is 0.875 chance of staying, 0.125 chance of switching
AggMrkvArray = \
np.array([[p_remain,p_change], # Probabilities of states 0 and 1 next period if in state 0
[p_change,p_remain]]) # Probabilities of states 0 and 1 next period if in state 1
KSAgentDictionary['MrkvArray'] = AggMrkvArray
# %%
# Create the Krusell-Smith agent as an instance of AggShockMarkovConsumerType
KSAgent = AggShockMarkovConsumerType(**KSAgentDictionary)
# %% [markdown]
# Now we need to specify the income distribution.
#
# The HARK toolkit allows for two components of labor income: Persistent (or permanent), and transitory.
#
# Using the KS notation above, a HARK consumer's income is
# \begin{eqnarray}
# y & = & w p \ell \epsilon
# \end{eqnarray}
# where $p$ is the persistent component of income. Krusell and Smith did not incorporate a persistent component of income, however, so we will simply calibrate $p=1$ for all states.
#
# For each of the two aggregate states we need to specify:
# * The _proportion_ of consumers in the $e$ and the $u$ states
# * The level of persistent/permanent productivity $p$ (always 1)
def setUp(self):
self.agent = AggShockMarkovConsumerType()
self.agent.IncomeDstn[0] = 2 * [self.agent.IncomeDstn[0]] ## see #557
self.economy = CobbDouglasMarkovEconomy(agents=[self.agent])
AggShockExample.unpack('cFunc')
m_grid = np.linspace(0, 10, 200)
AggShockExample.unpack('cFunc')
for M in AggShockExample.Mgrid.tolist():
mMin = AggShockExample.solution[0].mNrmMin(M)
c_at_this_M = AggShockExample.cFunc[0](m_grid + mMin,
M * np.ones_like(m_grid))
plt.plot(m_grid + mMin, c_at_this_M)
plt.ylim(0.0, None)
plt.show()
# ### Example Implementations of AggShockMarkovConsumerType
if solve_markov_micro or solve_markov_market or solve_krusell_smith:
# Make a Markov aggregate shocks consumer type
AggShockMrkvExample = AggShockMarkovConsumerType()
AggShockMrkvExample.IncomeDstn[0] = 2 * [AggShockMrkvExample.IncomeDstn[0]]
AggShockMrkvExample.cycles = 0
# Make a Cobb-Douglas economy for the agents
MrkvEconomyExample = CobbDouglasMarkovEconomy(agents=[AggShockMrkvExample])
MrkvEconomyExample.DampingFac = 0.2 # Turn down damping
MrkvEconomyExample.makeAggShkHist(
) # Simulate a history of aggregate shocks
AggShockMrkvExample.getEconomyData(
MrkvEconomyExample
) # Have the consumers inherit relevant objects from the economy
if solve_markov_micro:
# Solve the microeconomic model for the Markov aggregate shocks example type (and display results)
t_start = process_time()
def consExample(filename):
KSAgentDictionary = {
"CRRA" : 3.0, # Coefficient of relative risk aversion
"DiscFac" : 0.99, # Intertemporal discount factor
"LivPrb" : [1.0], # Survival probability
"AgentCount" : 1000, # Number of agents of this type (only matters for simulation)
"aNrmInitMean" : 0.0, # Mean of log initial assets (only matters for simulation)
"aNrmInitStd" : 0.0, # Standard deviation of log initial assets (only for simulation)
"pLvlInitMean" : 0.0, # Mean of log initial permanent income (only matters for simulation)
"pLvlInitStd" : 0.0, # Standard deviation of log initial permanent income (only matters for simulation)
"PermGroFacAgg" : 1.0, # Aggregate permanent income growth factor (only matters for simulation)
"T_age" : None, # Age after which simulated agents are automatically killed
"T_cycle" : 1, # Number of periods in the cycle for this agent type
#
# Parameters for constructing the "assets above minimum" grid
"aXtraMin" : 0.001, # Minimum end-of-period "assets above minimum" value
"aXtraMax" : 20, # Maximum end-of-period "assets above minimum" value
"aXtraExtra" : [None], # Some other value of "assets above minimum" to add to the grid
"aXtraNestFac" : 3, # Exponential nesting factor when constructing "assets above minimum" grid
"aXtraCount" : 24, # Number of points in the grid of "assets above minimum"
#
# Parameters describing the income process
"PermShkCount" : 1, # Number of points in discrete approximation to permanent income shocks - no shocks of this kind!
"TranShkCount" : 1, # Number of points in discrete approximation to transitory income shocks - no shocks of this kind!
"PermShkStd" : [0.], # Standard deviation of log permanent income shocks - no shocks of this kind!
"TranShkStd" : [0.], # Standard deviation of log transitory income shocks - no shocks of this kind!
"UnempPrb" : 0.0, # Probability of unemployment while working - no shocks of this kind!
"UnempPrbRet" : 0.0, # Probability of "unemployment" while retired - no shocks of this kind!
"IncUnemp" : 0.0, # Unemployment benefits replacement rate
"IncUnempRet" : 0.0, # "Unemployment" benefits when retired
"tax_rate" : 0.0, # Flat income tax rate
"T_retire" : 0, # Period of retirement (0 --> no retirement)
"BoroCnstArt" : 0.0, # Artificial borrowing constraint; imposed minimum level of end-of period assets
"cycles" : 0, # Consumer is infinitely lived
"PermGroFac" : [1.0], # Permanent income growth factor
#
# New Parameters that we need now
'MgridBase': np.array([0.1, 0.3, 0.6,
0.8, 0.9, 0.98,
1.0, 1.02, 1.1,
1.2, 1.6, 2.0,
3.0]), # Grid of capital-to-labor-ratios (factors)
'MrkvArray': np.array([[0.875, 0.125],
[0.125, 0.875]]),# Transition probabilities for macroecon. [i,j] is probability of being in state j next
# period conditional on being in state i this period.
'PermShkAggStd' : [0.0, 0.0], # Standard deviation of log aggregate permanent shocks by state. No continous shocks in a state.
'TranShkAggStd' : [0.0, 0.0], # Standard deviation of log aggregate transitory shocks by state. No continuous shocks in a state.
'PermGroFacAgg' : 1.0
}
# Economy Dictionary
KSEconomyDictionary = {
'PermShkAggCount': 1,
'TranShkAggCount': 1,
'PermShkAggStd' : [0.0, 0.0],
'TranShkAggStd' : [0.0, 0.0],
'DeprFac' : 0.025, # Depreciation factor
'CapShare' : 0.36, # Share of capital income in cobb-douglas production function
'DiscFac' : 0.99,
'CRRA' : 3.0,
'PermGroFacAgg' : [1.0, 1.0],
'AggregateL' : 1.0, # Fix aggregate labor supply at 1.0 - makes interpretation of z easier
'act_T' : 1200, # Number of periods for economy to run in simulation
'intercept_prev' : [0.0, 0.0], # Make some initial guesses at linear savings rule intercepts for each state
'slope_prev' : [1.0, 1.0], # Make some initial guesses at linear savings rule slopes for each state
'MrkvArray' : np.array([ [0.875, 0.125],
[0.125, 0.875]]), # Transition probabilities
'MrkvNow_init' : 0 # Pick a state to start in (we pick the first state)
}
### Representative Agent
# Create the Krusell-Smith agent as an instance of AggShockMarkovConsumerType
KSAgent = AggShockMarkovConsumerType(**KSAgentDictionary)
# Construct the income distribution for the Krusell-Smith agent
prb_eg = 0.96 # Probability of employment in the good state
prb_ug = 1 - prb_eg # Probability of unemployment in the good state
prb_eb = 0.90 # Probability of employment in the bad state
prb_ub = 1 - prb_eb # Probability of unemployment in the bad state
p_ind = 1 # Persistent component of income is always 1
ell_ug = ell_ub = 0 # Labor supply is zero for unemployed consumers in either agg state
ell_eg = 1.0/prb_eg # Labor supply for employed consumer in good state
ell_eb = 1.0/prb_eb # 1=pe_g*ell_ge+pu_b*ell_gu=pe_b*ell_be+pu_b*ell_gu
# IncomeDstn is a list of lists, one for each aggregate Markov state
# Each contains three arrays of floats, representing a discrete approximation to the income process.
# Order:
# state probabilities
# idiosyncratic persistent income level by state (KS have no persistent shocks p_ind is always 1.0)
# idiosyncratic transitory income level by state
KSAgent.IncomeDstn[0] = [
[np.array([prb_eg,prb_ug]), np.array([p_ind,p_ind]), np.array([ell_eg,ell_ug])], # Agg state good
[np.array([prb_eb,prb_ub]), np.array([p_ind,p_ind]), np.array([ell_eb,ell_ub])] # Agg state bad
]
KSEconomy = CobbDouglasMarkovEconomy(agents = [KSAgent], **KSEconomyDictionary) # Combine production and consumption sides into an "Economy"
# Calibrate the magnitude of the aggregate shocks
Tran_g = 1.01 # Productivity z in the good aggregate state
Tran_b = 0.99 # and the bad state
# Aggregate productivity shock distribution by state.
# First element is probabilities of different outcomes, given the state you are in.
# Second element is agg permanent shocks (here we don't have any, so just they are just 1.).
# Third element is agg transitory shocks, which are calibrated the same as in Krusell Smith.
KSAggShkDstn = [
[np.array([1.0]),np.array([1.0]),np.array([Tran_g])], # Aggregate good
[np.array([1.0]),np.array([1.0]),np.array([Tran_b])] # Aggregate bad
]
KSEconomy.AggShkDstn = KSAggShkDstn
# Construct the economy, make an initial history, then solve
KSAgent.getEconomyData(KSEconomy) # Makes attributes of the economy, attributes of the agent
KSEconomy.makeAggShkHist() # Make a simulated history of the economy
# Tolerance level
KSEconomy.tolerance = 0.01
# Solve the economy using the market method.
KSEconomy.solve()
### Plots
print('Consumption function at each aggregate market resources gridpoint (in general equilibrium):')
m_grid = np.linspace(0,20,200)
c_m = KSAgent.solution[0].cFunc[0](m_grid,10.0*np.ones_like(m_grid))
f = plt.figure()
plt.plot(m_grid,c_m, color = '#4a69bd', linewidth = 2.5)
plt.ylabel(r'$c(y)$', labelpad = 15, rotation = 0)
plt.ylim([-0.15, 2.15])
plt.yticks([0 + 0.25 * k for k in range(9)], [r'${:.1f}$'.format(0 + 0.25 * k) if k % 2 == 0 else '' for k in range(9)])
plt.xlabel(r'$y$')
plt.xlim([-1, 21])
plt.xticks([0 + 2.5 * k for k in range(9)], [r'${:.0f}$'.format(0 + 2.5 * k) if k % 2 == 0 else '' for k in range(9)])
plt.show()
f.savefig(filename, bbox_inches='tight')
