def def_BoroCnst(self, BoroCnstArt):
"""
Defines the constrained portion of the consumption function as cFuncNowCnst,
an attribute of self.
Parameters
----------
BoroCnstArt : float or None
Borrowing constraint for the minimum allowable assets to end the
period with. If it is less than the natural borrowing constraint,
then it is irrelevant; BoroCnstArt=None indicates no artificial bor-
rowing constraint.
Returns
-------
None
"""
# Make temporary grids of income shocks and next period income values
ShkCount = self.TranShkValsNext.size
pLvlCount = self.pLvlGrid.size
PermShkVals_temp = np.tile(
np.reshape(self.PermShkValsNext, (1, ShkCount)), (pLvlCount, 1))
TranShkVals_temp = np.tile(
np.reshape(self.TranShkValsNext, (1, ShkCount)), (pLvlCount, 1))
pLvlNext_temp = (np.tile(
np.reshape(self.pLvlNextFunc(self.pLvlGrid), (pLvlCount, 1)),
(1, ShkCount),
) * PermShkVals_temp)
# Find the natural borrowing constraint for each persistent income level
aLvlMin_candidates = (self.mLvlMinNext(pLvlNext_temp) -
TranShkVals_temp * pLvlNext_temp) / self.Rfree
aLvlMinNow = np.max(aLvlMin_candidates, axis=1)
self.BoroCnstNat = LinearInterp(np.insert(self.pLvlGrid, 0, 0.0),
np.insert(aLvlMinNow, 0, 0.0))
# Define the minimum allowable mLvl by pLvl as the greater of the natural and artificial borrowing constraints
if self.BoroCnstArt is not None:
self.BoroCnstArt = LinearInterp(np.array([0.0, 1.0]),
np.array([0.0, self.BoroCnstArt]))
self.mLvlMinNow = UpperEnvelope(self.BoroCnstArt, self.BoroCnstNat)
else:
self.mLvlMinNow = self.BoroCnstNat
# Define the constrained consumption function as "consume all" shifted by mLvlMin
cFuncNowCnstBase = BilinearInterp(
np.array([[0.0, 0.0], [1.0, 1.0]]),
np.array([0.0, 1.0]),
np.array([0.0, 1.0]),
)
self.cFuncNowCnst = VariableLowerBoundFunc2D(cFuncNowCnstBase,
self.mLvlMinNow)
class GenIncProcessConsumerType(IndShockConsumerType):
"""
A consumer type with idiosyncratic shocks to persistent and transitory income.
His problem is defined by a sequence of income distributions, survival prob-
abilities, and persistent income growth functions, as well as time invariant
values for risk aversion, discount factor, the interest rate, the grid of
end-of-period assets, and an artificial borrowing constraint.
See init_explicit_perm_inc for a dictionary of the
keywords that should be passed to the constructor.
Parameters
----------
cycles : int
Number of times the sequence of periods should be solved.
"""
cFunc_terminal_ = BilinearInterp(np.array([[0.0, 0.0], [1.0, 1.0]]),
np.array([0.0, 1.0]), np.array([0.0,
1.0]))
solution_terminal_ = ConsumerSolution(cFunc=cFunc_terminal_,
mNrmMin=0.0,
hNrm=0.0,
MPCmin=1.0,
MPCmax=1.0)
state_vars = ['pLvl', "mLvl", 'aLvl']
def __init__(self, **kwds):
params = init_explicit_perm_inc.copy()
params.update(kwds)
# Initialize a basic ConsumerType
IndShockConsumerType.__init__(self, **params)
self.solve_one_period = make_one_period_oo_solver(
ConsGenIncProcessSolver)
# a poststate?
self.state_now['aLvl'] = None
self.state_prev['aLvl'] = None
# better way to do this...
self.state_now["mLvl"] = None
self.state_prev["mLvl"] = None
def pre_solve(self):
# AgentType.pre_solve()
self.update_solution_terminal()
def update(self):
"""
Update the income process, the assets grid, the persistent income grid,
and the terminal solution.
Parameters
----------
None
Returns
-------
None
"""
IndShockConsumerType.update(self)
self.update_pLvlNextFunc()
self.update_pLvlGrid()
def update_solution_terminal(self):
"""
Update the terminal period solution. This method should be run when a
new AgentType is created or when CRRA changes.
Parameters
----------
None
Returns
-------
None
"""
self.solution_terminal.vFunc = ValueFuncCRRA(self.cFunc_terminal_,
self.CRRA)
self.solution_terminal.vPfunc = MargValueFuncCRRA(
self.cFunc_terminal_, self.CRRA)
self.solution_terminal.vPPfunc = MargMargValueFuncCRRA(
self.cFunc_terminal_, self.CRRA)
self.solution_terminal.hNrm = 0.0 # Don't track normalized human wealth
self.solution_terminal.hLvl = lambda p: np.zeros_like(p)
# But do track absolute human wealth by persistent income
self.solution_terminal.mLvlMin = lambda p: np.zeros_like(p)
# And minimum allowable market resources by perm inc
def update_pLvlNextFunc(self):
"""
A dummy method that creates a trivial pLvlNextFunc attribute that has
no persistent income dynamics. This method should be overwritten by
subclasses in order to make (e.g.) an AR1 income process.
Parameters
----------
None
Returns
-------
None
"""
pLvlNextFuncBasic = LinearInterp(np.array([0.0, 1.0]),
np.array([0.0, 1.0]))
self.pLvlNextFunc = self.T_cycle * [pLvlNextFuncBasic]
self.add_to_time_vary("pLvlNextFunc")
def install_retirement_func(self):
"""
Installs a special pLvlNextFunc representing retirement in the correct
element of self.pLvlNextFunc. Draws on the attributes T_retire and
pLvlNextFuncRet. If T_retire is zero or pLvlNextFuncRet does not
exist, this method does nothing. Should only be called from within the
method update_pLvlNextFunc, which ensures that time is flowing forward.
Parameters
----------
None
Returns
-------
None
"""
if (not hasattr(self, "pLvlNextFuncRet")) or self.T_retire == 0:
return
t = self.T_retire
self.pLvlNextFunc[t] = self.pLvlNextFuncRet
def update_pLvlGrid(self):
"""
Update the grid of persistent income levels. Currently only works for
infinite horizon models (cycles=0) and lifecycle models (cycles=1). Not
clear what to do about cycles>1 because the distribution of persistent
income will be different within a period depending on how many cycles
have elapsed. This method uses a simulation approach to generate the
pLvlGrid at each period of the cycle, drawing on the initial distribution
of persistent income, the pLvlNextFuncs, and the attribute pLvlPctiles.
Parameters
----------
None
Returns
-------
None
"""
LivPrbAll = np.array(self.LivPrb)
# Simulate the distribution of persistent income levels by t_cycle in a lifecycle model
if self.cycles == 1:
pLvlNow = Lognormal(self.pLvlInitMean,
sigma=self.pLvlInitStd,
seed=31382).draw(self.AgentCount)
pLvlGrid = [] # empty list of time-varying persistent income grids
# Calculate distribution of persistent income in each period of lifecycle
for t in range(len(self.PermShkStd)):
if t > 0:
PermShkNow = self.PermShkDstn[t -
1].draw(N=self.AgentCount)
pLvlNow = self.pLvlNextFunc[t - 1](pLvlNow) * PermShkNow
pLvlGrid.append(
get_percentiles(pLvlNow, percentiles=self.pLvlPctiles))
# Calculate "stationary" distribution in infinite horizon (might vary across periods of cycle)
elif self.cycles == 0:
T_long = 1000 # Number of periods to simulate to get to "stationary" distribution
pLvlNow = Lognormal(mu=self.pLvlInitMean,
sigma=self.pLvlInitStd,
seed=31382).draw(self.AgentCount)
t_cycle = np.zeros(self.AgentCount, dtype=int)
for t in range(T_long):
LivPrb = LivPrbAll[
t_cycle] # Determine who dies and replace them with newborns
draws = Uniform(seed=t).draw(self.AgentCount)
who_dies = draws > LivPrb
pLvlNow[who_dies] = Lognormal(self.pLvlInitMean,
self.pLvlInitStd,
seed=t + 92615).draw(
np.sum(who_dies))
t_cycle[who_dies] = 0
for j in range(self.T_cycle): # Update persistent income
these = t_cycle == j
PermShkTemp = self.PermShkDstn[j].draw(N=np.sum(these))
pLvlNow[these] = self.pLvlNextFunc[j](
pLvlNow[these]) * PermShkTemp
t_cycle = t_cycle + 1
t_cycle[t_cycle == self.T_cycle] = 0
# We now have a "long run stationary distribution", extract percentiles
pLvlGrid = [] # empty list of time-varying persistent income grids
for t in range(self.T_cycle):
these = t_cycle == t
pLvlGrid.append(
get_percentiles(pLvlNow[these],
percentiles=self.pLvlPctiles))
# Throw an error if cycles>1
else:
assert False, "Can only handle cycles=0 or cycles=1!"
# Store the result and add attribute to time_vary
self.pLvlGrid = pLvlGrid
self.add_to_time_vary("pLvlGrid")
def sim_birth(self, which_agents):
"""
Makes new consumers for the given indices. Initialized variables include aNrm and pLvl, as
well as time variables t_age and t_cycle. Normalized assets and persistent income levels
are drawn from lognormal distributions given by aNrmInitMean and aNrmInitStd (etc).
Parameters
----------
which_agents : np.array(Bool)
Boolean array of size self.AgentCount indicating which agents should be "born".
Returns
-------
None
"""
# Get and store states for newly born agents
N = np.sum(which_agents) # Number of new consumers to make
aNrmNow_new = Lognormal(self.aNrmInitMean,
self.aNrmInitStd,
seed=self.RNG.randint(0, 2**31 - 1)).draw(N)
self.state_now['pLvl'][which_agents] = Lognormal(
self.pLvlInitMean,
self.pLvlInitStd,
seed=self.RNG.randint(0, 2**31 - 1)).draw(N)
self.state_now['aLvl'][
which_agents] = aNrmNow_new * self.state_now['pLvl'][which_agents]
self.t_age[
which_agents] = 0 # How many periods since each agent was born
self.t_cycle[
which_agents] = 0 # Which period of the cycle each agent is currently in
def transition(self):
"""
Calculates updated values of normalized market resources
and persistent income level for each
agent. Uses pLvlNow, aLvlNow, PermShkNow, TranShkNow.
Parameters
----------
None
Returns
-------
pLvlNow
mLvlNow
"""
aLvlPrev = self.state_prev['aLvl']
RfreeNow = self.get_Rfree()
# Calculate new states: normalized market resources
# and persistent income level
pLvlNow = np.zeros_like(aLvlPrev)
for t in range(self.T_cycle):
these = t == self.t_cycle
pLvlNow[these] = (
self.pLvlNextFunc[t - 1](self.state_prev['pLvl'][these]) *
self.shocks['PermShk'][these])
#state value
bLvlNow = RfreeNow * aLvlPrev # Bank balances before labor income
# Market resources after income - state value
mLvlNow = bLvlNow + \
self.shocks['TranShk'] * \
pLvlNow
return (pLvlNow, mLvlNow)
def get_controls(self):
"""
Calculates consumption for each consumer of this type using the consumption functions.
Parameters
----------
None
Returns
-------
None
"""
cLvlNow = np.zeros(self.AgentCount) + np.nan
MPCnow = np.zeros(self.AgentCount) + np.nan
for t in range(self.T_cycle):
these = t == self.t_cycle
cLvlNow[these] = self.solution[t].cFunc(
self.state_now["mLvl"][these], self.state_now['pLvl'][these])
MPCnow[these] = self.solution[t].cFunc.derivativeX(
self.state_now["mLvl"][these], self.state_now['pLvl'][these])
self.controls["cLvl"] = cLvlNow
self.MPCnow = MPCnow
def get_poststates(self):
"""
Calculates end-of-period assets for each consumer of this type.
Identical to version in IndShockConsumerType but uses Lvl rather than Nrm variables.
Parameters
----------
None
Returns
-------
None
"""
self.state_now['aLvl'] = self.state_now["mLvl"] - self.controls["cLvl"]
# moves now to prev
AgentType.get_poststates(self)
def update_solution_terminal(self):
"""
Updates the terminal period solution and solves for optimal consumption
and labor when there is no future.
Parameters
----------
None
Returns
-------
None
"""
t = -1
TranShkGrid = self.TranShkGrid[t]
LbrCost = self.LbrCost[t]
WageRte = self.WageRte[t]
bNrmGrid = np.insert(
self.aXtraGrid, 0, 0.0
) # Add a point at b_t = 0 to make sure that bNrmGrid goes down to 0
bNrmCount = bNrmGrid.size # 201
TranShkCount = TranShkGrid.size # = (7,)
bNrmGridTerm = np.tile(
np.reshape(bNrmGrid, (bNrmCount, 1)),
(1, TranShkCount
)) # Replicated bNrmGrid for each transitory shock theta_t
TranShkGridTerm = np.tile(
TranShkGrid, (bNrmCount, 1)
) # Tile the grid of transitory shocks for the terminal solution. (201,7)
# Array of labor (leisure) values for terminal solution
LsrTerm = np.minimum(
(LbrCost / (1.0 + LbrCost)) * (bNrmGridTerm /
(WageRte * TranShkGridTerm) + 1.0),
1.0,
)
LsrTerm[0, 0] = 1.0
LbrTerm = 1.0 - LsrTerm
# Calculate market resources in terminal period, which is consumption
mNrmTerm = bNrmGridTerm + LbrTerm * WageRte * TranShkGridTerm
cNrmTerm = mNrmTerm # Consume everything we have
# Make a bilinear interpolation to represent the labor and consumption functions
LbrFunc_terminal = BilinearInterp(LbrTerm, bNrmGrid, TranShkGrid)
cFunc_terminal = BilinearInterp(cNrmTerm, bNrmGrid, TranShkGrid)
# Compute the effective consumption value using consumption value and labor value at the terminal solution
xEffTerm = LsrTerm**LbrCost * cNrmTerm
vNvrsFunc_terminal = BilinearInterp(xEffTerm, bNrmGrid, TranShkGrid)
vFunc_terminal = ValueFuncCRRA(vNvrsFunc_terminal, self.CRRA)
# Using the envelope condition at the terminal solution to estimate the marginal value function
vPterm = LsrTerm**LbrCost * CRRAutilityP(xEffTerm, gam=self.CRRA)
vPnvrsTerm = CRRAutilityP_inv(
vPterm, gam=self.CRRA
) # Evaluate the inverse of the CRRA marginal utility function at a given marginal value, vP
vPnvrsFunc_terminal = BilinearInterp(vPnvrsTerm, bNrmGrid, TranShkGrid)
vPfunc_terminal = MargValueFuncCRRA(
vPnvrsFunc_terminal, self.CRRA) # Get the Marginal Value function
bNrmMin_terminal = ConstantFunction(
0.0
) # Trivial function that return the same real output for any input
self.solution_terminal = ConsumerLaborSolution(
cFunc=cFunc_terminal,
LbrFunc=LbrFunc_terminal,
vFunc=vFunc_terminal,
vPfunc=vPfunc_terminal,
bNrmMin=bNrmMin_terminal,
)
def solveConsPortfolio(solution_next, ShockDstn, IncomeDstn, RiskyDstn, LivPrb,
DiscFac, CRRA, Rfree, PermGroFac, BoroCnstArt,
aXtraGrid, ShareGrid, vFuncBool, AdjustPrb,
DiscreteShareBool, ShareLimit, IndepDstnBool):
'''
Solve the one period problem for a portfolio-choice consumer.
Parameters
----------
solution_next : PortfolioSolution
Solution to next period's problem.
ShockDstn : [np.array]
List with four arrays: discrete probabilities, permanent income shocks,
transitory income shocks, and risky returns. This is only used if the
input IndepDstnBool is False, indicating that income and return distributions
can't be assumed to be independent.
IncomeDstn : [np.array]
List with three arrays: discrete probabilities, permanent income shocks,
and transitory income shocks. This is only used if the input IndepDsntBool
is True, indicating that income and return distributions are independent.
RiskyDstn : [np.array]
List with two arrays: discrete probabilities and risky asset returns. This
is only used if the input IndepDstnBool is True, indicating that income
and return distributions are independent.
LivPrb : float
Survival probability; likelihood of being alive at the beginning of
the succeeding period.
DiscFac : float
Intertemporal discount factor for future utility.
CRRA : float
Coefficient of relative risk aversion.
Rfree : float
Risk free interest factor on end-of-period assets.
PermGroFac : float
Expected permanent income growth factor at the end of this period.
BoroCnstArt: float or None
Borrowing constraint for the minimum allowable assets to end the
period with. In this model, it is *required* to be zero.
aXtraGrid: np.array
Array of "extra" end-of-period asset values-- assets above the
absolute minimum acceptable level.
ShareGrid : np.array
Array of risky portfolio shares on which to define the interpolation
of the consumption function when Share is fixed.
vFuncBool: boolean
An indicator for whether the value function should be computed and
included in the reported solution.
AdjustPrb : float
Probability that the agent will be able to update his portfolio share.
DiscreteShareBool : bool
Indicator for whether risky portfolio share should be optimized on the
continuous [0,1] interval using the FOC (False), or instead only selected
from the discrete set of values in ShareGrid (True). If True, then
vFuncBool must also be True.
ShareLimit : float
Limiting lower bound of risky portfolio share as mNrm approaches infinity.
IndepDstnBool : bool
Indicator for whether the income and risky return distributions are in-
dependent of each other, which can speed up the expectations step.
Returns
-------
solution_now : PortfolioSolution
The solution to the single period consumption-saving with portfolio choice
problem. Includes two consumption and risky share functions: one for when
the agent can adjust his portfolio share (Adj) and when he can't (Fxd).
'''
# Make sure the individual is liquidity constrained. Allowing a consumer to
# borrow *and* invest in an asset with unbounded (negative) returns is a bad mix.
if BoroCnstArt != 0.0:
raise ValueError('PortfolioConsumerType must have BoroCnstArt=0.0!')
# Make sure that if risky portfolio share is optimized only discretely, then
# the value function is also constructed (else this task would be impossible).
if (DiscreteShareBool and (not vFuncBool)):
raise ValueError(
'PortfolioConsumerType requires vFuncBool to be True when DiscreteShareBool is True!'
)
# Define temporary functions for utility and its derivative and inverse
u = lambda x: utility(x, CRRA)
uP = lambda x: utilityP(x, CRRA)
uPinv = lambda x: utilityP_inv(x, CRRA)
n = lambda x: utility_inv(x, CRRA)
nP = lambda x: utility_invP(x, CRRA)
# Unpack next period's solution
vPfuncAdj_next = solution_next.vPfuncAdj
dvdmFuncFxd_next = solution_next.dvdmFuncFxd
dvdsFuncFxd_next = solution_next.dvdsFuncFxd
vFuncAdj_next = solution_next.vFuncAdj
vFuncFxd_next = solution_next.vFuncFxd
# Major method fork: (in)dependent risky asset return and income distributions
if IndepDstnBool: # If the distributions ARE independent...
# Unpack the shock distribution
IncPrbs_next = IncomeDstn.pmf
PermShks_next = IncomeDstn.X[0]
TranShks_next = IncomeDstn.X[1]
Rprbs_next = RiskyDstn.pmf
Risky_next = RiskyDstn.X
zero_bound = (
np.min(TranShks_next) == 0.
) # Flag for whether the natural borrowing constraint is zero
RiskyMax = np.max(Risky_next)
# bNrm represents R*a, balances after asset return shocks but before income.
# This just uses the highest risky return as a rough shifter for the aXtraGrid.
if zero_bound:
aNrmGrid = aXtraGrid
bNrmGrid = np.insert(RiskyMax * aXtraGrid, 0,
np.min(Risky_next) * aXtraGrid[0])
else:
aNrmGrid = np.insert(aXtraGrid, 0,
0.0) # Add an asset point at exactly zero
bNrmGrid = RiskyMax * np.insert(aXtraGrid, 0, 0.0)
# Get grid and shock sizes, for easier indexing
aNrm_N = aNrmGrid.size
bNrm_N = bNrmGrid.size
Share_N = ShareGrid.size
Income_N = IncPrbs_next.size
Risky_N = Rprbs_next.size
# Make tiled arrays to calculate future realizations of mNrm and Share when integrating over IncomeDstn
bNrm_tiled = np.tile(np.reshape(bNrmGrid, (bNrm_N, 1, 1)),
(1, Share_N, Income_N))
Share_tiled = np.tile(np.reshape(ShareGrid, (1, Share_N, 1)),
(bNrm_N, 1, Income_N))
IncPrbs_tiled = np.tile(np.reshape(IncPrbs_next, (1, 1, Income_N)),
(bNrm_N, Share_N, 1))
PermShks_tiled = np.tile(np.reshape(PermShks_next, (1, 1, Income_N)),
(bNrm_N, Share_N, 1))
TranShks_tiled = np.tile(np.reshape(TranShks_next, (1, 1, Income_N)),
(bNrm_N, Share_N, 1))
# Calculate future realizations of market resources
mNrm_next = bNrm_tiled / (PermShks_tiled * PermGroFac) + TranShks_tiled
Share_next = Share_tiled
# Evaluate realizations of marginal value of market resources next period
dvdmAdj_next = vPfuncAdj_next(mNrm_next)
if AdjustPrb < 1.:
dvdmFxd_next = dvdmFuncFxd_next(mNrm_next, Share_next)
dvdm_next = AdjustPrb * dvdmAdj_next + (
1. -
AdjustPrb) * dvdmFxd_next # Combine by adjustment probability
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
dvdm_next = dvdmAdj_next
# Evaluate realizations of marginal value of risky share next period
dvdsAdj_next = np.zeros_like(
mNrm_next) # No marginal value of Share if it's a free choice!
if AdjustPrb < 1.:
dvdsFxd_next = dvdsFuncFxd_next(mNrm_next, Share_next)
dvds_next = AdjustPrb * dvdsAdj_next + (
1. -
AdjustPrb) * dvdsFxd_next # Combine by adjustment probability
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
dvds_next = dvdsAdj_next
# If the value function has been requested, evaluate realizations of value
if vFuncBool:
vAdj_next = vFuncAdj_next(mNrm_next)
if AdjustPrb < 1.:
vFxd_next = vFuncFxd_next(mNrm_next, Share_next)
v_next = AdjustPrb * vAdj_next + (1. - AdjustPrb) * vFxd_next
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
v_next = vAdj_next
else:
v_next = np.zeros_like(dvdm_next) # Trivial array
# Calculate intermediate marginal value of bank balances by taking expectations over income shocks
temp_fac_A = uP(PermShks_tiled *
PermGroFac) # Will use this in a couple places
dvdb_intermed = np.sum(IncPrbs_tiled * temp_fac_A * dvdm_next, axis=2)
dvdbNvrs_intermed = uPinv(dvdb_intermed)
dvdbNvrsFunc_intermed = BilinearInterp(dvdbNvrs_intermed, bNrmGrid,
ShareGrid)
dvdbFunc_intermed = MargValueFunc2D(dvdbNvrsFunc_intermed, CRRA)
# Calculate intermediate value by taking expectations over income shocks
temp_fac_B = (PermShks_tiled * PermGroFac)**(1. - CRRA
) # Will use this below
if vFuncBool:
v_intermed = np.sum(IncPrbs_tiled * temp_fac_B * v_next, axis=2)
vNvrs_intermed = n(v_intermed)
vNvrsFunc_intermed = BilinearInterp(vNvrs_intermed, bNrmGrid,
ShareGrid)
vFunc_intermed = ValueFunc2D(vNvrsFunc_intermed, CRRA)
# Calculate intermediate marginal value of risky portfolio share by taking expectations
dvds_intermed = np.sum(IncPrbs_tiled * temp_fac_B * dvds_next, axis=2)
dvdsFunc_intermed = BilinearInterp(dvds_intermed, bNrmGrid, ShareGrid)
# Make tiled arrays to calculate future realizations of bNrm and Share when integrating over RiskyDstn
aNrm_tiled = np.tile(np.reshape(aNrmGrid, (aNrm_N, 1, 1)),
(1, Share_N, Risky_N))
Share_tiled = np.tile(np.reshape(ShareGrid, (1, Share_N, 1)),
(aNrm_N, 1, Risky_N))
Rprbs_tiled = np.tile(np.reshape(Rprbs_next, (1, 1, Risky_N)),
(aNrm_N, Share_N, 1))
Risky_tiled = np.tile(np.reshape(Risky_next, (1, 1, Risky_N)),
(aNrm_N, Share_N, 1))
# Calculate future realizations of bank balances bNrm
Share_next = Share_tiled
Rxs = Risky_tiled - Rfree
Rport = Rfree + Share_next * Rxs
bNrm_next = Rport * aNrm_tiled
# Evaluate realizations of value and marginal value after asset returns are realized
dvdb_next = dvdbFunc_intermed(bNrm_next, Share_next)
dvds_next = dvdsFunc_intermed(bNrm_next, Share_next)
if vFuncBool:
v_next = vFunc_intermed(bNrm_next, Share_next)
else:
v_next = np.zeros_like(dvdb_next)
# Calculate end-of-period marginal value of assets by taking expectations
EndOfPrddvda = DiscFac * LivPrb * np.sum(
Rprbs_tiled * Rport * dvdb_next, axis=2)
EndOfPrddvdaNvrs = uPinv(EndOfPrddvda)
# Calculate end-of-period value by taking expectations
if vFuncBool:
EndOfPrdv = DiscFac * LivPrb * np.sum(Rprbs_tiled * v_next, axis=2)
EndOfPrdvNvrs = n(EndOfPrdv)
# Calculate end-of-period marginal value of risky portfolio share by taking expectations
EndOfPrddvds = DiscFac * LivPrb * np.sum(
Rprbs_tiled * (Rxs * aNrm_tiled * dvdb_next + dvds_next), axis=2)
else: # If the distributions are NOT independent...
# Unpack the shock distribution
ShockPrbs_next = ShockDstn[0]
PermShks_next = ShockDstn[1]
TranShks_next = ShockDstn[2]
Risky_next = ShockDstn[3]
zero_bound = (
np.min(TranShks_next) == 0.
) # Flag for whether the natural borrowing constraint is zero
# Make tiled arrays to calculate future realizations of mNrm and Share; dimension order: mNrm, Share, shock
if zero_bound:
aNrmGrid = aXtraGrid
else:
aNrmGrid = np.insert(aXtraGrid, 0,
0.0) # Add an asset point at exactly zero
aNrm_N = aNrmGrid.size
Share_N = ShareGrid.size
Shock_N = ShockPrbs_next.size
aNrm_tiled = np.tile(np.reshape(aNrmGrid, (aNrm_N, 1, 1)),
(1, Share_N, Shock_N))
Share_tiled = np.tile(np.reshape(ShareGrid, (1, Share_N, 1)),
(aNrm_N, 1, Shock_N))
ShockPrbs_tiled = np.tile(np.reshape(ShockPrbs_next, (1, 1, Shock_N)),
(aNrm_N, Share_N, 1))
PermShks_tiled = np.tile(np.reshape(PermShks_next, (1, 1, Shock_N)),
(aNrm_N, Share_N, 1))
TranShks_tiled = np.tile(np.reshape(TranShks_next, (1, 1, Shock_N)),
(aNrm_N, Share_N, 1))
Risky_tiled = np.tile(np.reshape(Risky_next, (1, 1, Shock_N)),
(aNrm_N, Share_N, 1))
# Calculate future realizations of market resources
Rport = (1. - Share_tiled) * Rfree + Share_tiled * Risky_tiled
mNrm_next = Rport * aNrm_tiled / (PermShks_tiled *
PermGroFac) + TranShks_tiled
Share_next = Share_tiled
# Evaluate realizations of marginal value of market resources next period
dvdmAdj_next = vPfuncAdj_next(mNrm_next)
if AdjustPrb < 1.:
dvdmFxd_next = dvdmFuncFxd_next(mNrm_next, Share_next)
dvdm_next = AdjustPrb * dvdmAdj_next + (
1. -
AdjustPrb) * dvdmFxd_next # Combine by adjustment probability
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
dvdm_next = dvdmAdj_next
# Evaluate realizations of marginal value of risky share next period
dvdsAdj_next = np.zeros_like(
mNrm_next) # No marginal value of Share if it's a free choice!
if AdjustPrb < 1.:
dvdsFxd_next = dvdsFuncFxd_next(mNrm_next, Share_next)
dvds_next = AdjustPrb * dvdsAdj_next + (
1. -
AdjustPrb) * dvdsFxd_next # Combine by adjustment probability
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
dvds_next = dvdsAdj_next
# If the value function has been requested, evaluate realizations of value
if vFuncBool:
vAdj_next = vFuncAdj_next(mNrm_next)
if AdjustPrb < 1.:
vFxd_next = vFuncFxd_next(mNrm_next, Share_next)
v_next = AdjustPrb * vAdj_next + (1. - AdjustPrb) * vFxd_next
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
v_next = vAdj_next
else:
v_next = np.zeros_like(dvdm_next) # Trivial array
# Calculate end-of-period marginal value of assets by taking expectations
temp_fac_A = uP(PermShks_tiled *
PermGroFac) # Will use this in a couple places
EndOfPrddvda = DiscFac * LivPrb * np.sum(
ShockPrbs_tiled * Rport * temp_fac_A * dvdm_next, axis=2)
EndOfPrddvdaNvrs = uPinv(EndOfPrddvda)
# Calculate end-of-period value by taking expectations
temp_fac_B = (PermShks_tiled * PermGroFac)**(1. - CRRA
) # Will use this below
if vFuncBool:
EndOfPrdv = DiscFac * LivPrb * np.sum(
ShockPrbs_tiled * temp_fac_B * v_next, axis=2)
EndOfPrdvNvrs = n(EndOfPrdv)
# Calculate end-of-period marginal value of risky portfolio share by taking expectations
Rxs = Risky_tiled - Rfree
EndOfPrddvds = DiscFac * LivPrb * np.sum(
ShockPrbs_tiled * (Rxs * aNrm_tiled * temp_fac_A * dvdm_next +
temp_fac_B * dvds_next),
axis=2)
# Major method fork: discrete vs continuous choice of risky portfolio share
if DiscreteShareBool: # Optimization of Share on the discrete set ShareGrid
opt_idx = np.argmax(EndOfPrdv, axis=1)
Share_now = ShareGrid[
opt_idx] # Best portfolio share is one with highest value
cNrmAdj_now = EndOfPrddvdaNvrs[np.arange(
aNrm_N), opt_idx] # Take cNrm at that index as well
if not zero_bound:
Share_now[
0] = 1. # aNrm=0, so there's no way to "optimize" the portfolio
cNrmAdj_now[0] = EndOfPrddvdaNvrs[
0, -1] # Consumption when aNrm=0 does not depend on Share
else: # Optimization of Share on continuous interval [0,1]
# For values of aNrm at which the agent wants to put more than 100% into risky asset, constrain them
FOC_s = EndOfPrddvds
Share_now = np.zeros_like(
aNrmGrid) # Initialize to putting everything in safe asset
cNrmAdj_now = np.zeros_like(aNrmGrid)
constrained = FOC_s[:,
-1] > 0. # If agent wants to put more than 100% into risky asset, he is constrained
Share_now[constrained] = 1.0
if not zero_bound:
Share_now[
0] = 1. # aNrm=0, so there's no way to "optimize" the portfolio
cNrmAdj_now[0] = EndOfPrddvdaNvrs[
0, -1] # Consumption when aNrm=0 does not depend on Share
cNrmAdj_now[constrained] = EndOfPrddvdaNvrs[
constrained, -1] # Get consumption when share-constrained
# For each value of aNrm, find the value of Share such that FOC-Share == 0.
# This loop can probably be eliminated, but it's such a small step that it won't speed things up much.
crossing = np.logical_and(FOC_s[:, 1:] <= 0., FOC_s[:, :-1] >= 0.)
for j in range(aNrm_N):
if Share_now[j] == 0.:
try:
idx = np.argwhere(crossing[j, :])[0][0]
bot_s = ShareGrid[idx]
top_s = ShareGrid[idx + 1]
bot_f = FOC_s[j, idx]
top_f = FOC_s[j, idx + 1]
bot_c = EndOfPrddvdaNvrs[j, idx]
top_c = EndOfPrddvdaNvrs[j, idx + 1]
alpha = 1. - top_f / (top_f - bot_f)
Share_now[j] = (1. - alpha) * bot_s + alpha * top_s
cNrmAdj_now[j] = (1. - alpha) * bot_c + alpha * top_c
except:
print('No optimal controls found for a=' +
str(aNrmGrid[j]))
# Calculate the endogenous mNrm gridpoints when the agent adjusts his portfolio
mNrmAdj_now = aNrmGrid + cNrmAdj_now
# Construct the risky share function when the agent can adjust
if DiscreteShareBool:
mNrmAdj_mid = (mNrmAdj_now[1:] + mNrmAdj_now[:-1]) / 2
mNrmAdj_plus = mNrmAdj_mid * (1. + 1e-12)
mNrmAdj_comb = (np.transpose(np.vstack(
(mNrmAdj_mid, mNrmAdj_plus)))).flatten()
mNrmAdj_comb = np.append(np.insert(mNrmAdj_comb, 0, 0.0),
mNrmAdj_now[-1])
Share_comb = (np.transpose(np.vstack(
(Share_now, Share_now)))).flatten()
ShareFuncAdj_now = LinearInterp(mNrmAdj_comb, Share_comb)
else:
if zero_bound:
Share_lower_bound = ShareLimit
else:
Share_lower_bound = 1.0
Share_now = np.insert(Share_now, 0, Share_lower_bound)
ShareFuncAdj_now = LinearInterp(np.insert(mNrmAdj_now, 0, 0.0),
Share_now,
intercept_limit=ShareLimit,
slope_limit=0.0)
# Construct the consumption function when the agent can adjust
cNrmAdj_now = np.insert(cNrmAdj_now, 0, 0.0)
cFuncAdj_now = LinearInterp(np.insert(mNrmAdj_now, 0, 0.0), cNrmAdj_now)
# Construct the marginal value (of mNrm) function when the agent can adjust
vPfuncAdj_now = MargValueFunc(cFuncAdj_now, CRRA)
# Construct the consumption function when the agent *can't* adjust the risky share, as well
# as the marginal value of Share function
cFuncFxd_by_Share = []
dvdsFuncFxd_by_Share = []
for j in range(Share_N):
cNrmFxd_temp = EndOfPrddvdaNvrs[:, j]
mNrmFxd_temp = aNrmGrid + cNrmFxd_temp
cFuncFxd_by_Share.append(
LinearInterp(np.insert(mNrmFxd_temp, 0, 0.0),
np.insert(cNrmFxd_temp, 0, 0.0)))
dvdsFuncFxd_by_Share.append(
LinearInterp(np.insert(mNrmFxd_temp, 0, 0.0),
np.insert(EndOfPrddvds[:, j], 0, EndOfPrddvds[0, j])))
cFuncFxd_now = LinearInterpOnInterp1D(cFuncFxd_by_Share, ShareGrid)
dvdsFuncFxd_now = LinearInterpOnInterp1D(dvdsFuncFxd_by_Share, ShareGrid)
# The share function when the agent can't adjust his portfolio is trivial
ShareFuncFxd_now = IdentityFunction(i_dim=1, n_dims=2)
# Construct the marginal value of mNrm function when the agent can't adjust his share
dvdmFuncFxd_now = MargValueFunc2D(cFuncFxd_now, CRRA)
# If the value function has been requested, construct it now
if vFuncBool:
# First, make an end-of-period value function over aNrm and Share
EndOfPrdvNvrsFunc = BilinearInterp(EndOfPrdvNvrs, aNrmGrid, ShareGrid)
EndOfPrdvFunc = ValueFunc2D(EndOfPrdvNvrsFunc, CRRA)
# Construct the value function when the agent can adjust his portfolio
mNrm_temp = aXtraGrid # Just use aXtraGrid as our grid of mNrm values
cNrm_temp = cFuncAdj_now(mNrm_temp)
aNrm_temp = mNrm_temp - cNrm_temp
Share_temp = ShareFuncAdj_now(mNrm_temp)
v_temp = u(cNrm_temp) + EndOfPrdvFunc(aNrm_temp, Share_temp)
vNvrs_temp = n(v_temp)
vNvrsP_temp = uP(cNrm_temp) * nP(v_temp)
vNvrsFuncAdj = CubicInterp(
np.insert(mNrm_temp, 0, 0.0), # x_list
np.insert(vNvrs_temp, 0, 0.0), # f_list
np.insert(vNvrsP_temp, 0, vNvrsP_temp[0])) # dfdx_list
vFuncAdj_now = ValueFunc(
vNvrsFuncAdj, CRRA) # Re-curve the pseudo-inverse value function
# Construct the value function when the agent *can't* adjust his portfolio
mNrm_temp = np.tile(np.reshape(aXtraGrid, (aXtraGrid.size, 1)),
(1, Share_N))
Share_temp = np.tile(np.reshape(ShareGrid, (1, Share_N)),
(aXtraGrid.size, 1))
cNrm_temp = cFuncFxd_now(mNrm_temp, Share_temp)
aNrm_temp = mNrm_temp - cNrm_temp
v_temp = u(cNrm_temp) + EndOfPrdvFunc(aNrm_temp, Share_temp)
vNvrs_temp = n(v_temp)
vNvrsP_temp = uP(cNrm_temp) * nP(v_temp)
vNvrsFuncFxd_by_Share = []
for j in range(Share_N):
vNvrsFuncFxd_by_Share.append(
CubicInterp(
np.insert(mNrm_temp[:, 0], 0, 0.0), # x_list
np.insert(vNvrs_temp[:, j], 0, 0.0), # f_list
np.insert(vNvrsP_temp[:, j], 0,
vNvrsP_temp[j, 0]))) #dfdx_list
vNvrsFuncFxd = LinearInterpOnInterp1D(vNvrsFuncFxd_by_Share, ShareGrid)
vFuncFxd_now = ValueFunc2D(vNvrsFuncFxd, CRRA)
else: # If vFuncBool is False, fill in dummy values
vFuncAdj_now = None
vFuncFxd_now = None
# Create and return this period's solution
return PortfolioSolution(cFuncAdj=cFuncAdj_now,
ShareFuncAdj=ShareFuncAdj_now,
vPfuncAdj=vPfuncAdj_now,
vFuncAdj=vFuncAdj_now,
cFuncFxd=cFuncFxd_now,
ShareFuncFxd=ShareFuncFxd_now,
dvdmFuncFxd=dvdmFuncFxd_now,
dvdsFuncFxd=dvdsFuncFxd_now,
vFuncFxd=vFuncFxd_now)
def test_same_length(self):
bilinear = BilinearInterp(self.f_array, self.x_array, self.y_array)
self.assertEqual(bilinear(2, 2), 4.0)
bilinear = BilinearInterp(self.f_array, self.x_array, self.y_array_t)
self.assertEqual(bilinear(2, 2), 4.0)