def make_EndOfPrdvFuncCond(self):
"""
Construct the end-of-period value function conditional on next period's
state. NOTE: It might be possible to eliminate this method and replace
it with ConsIndShockSolver.make_EndOfPrdvFunc, but the self.X_cond
variables must be renamed.
Parameters
----------
none
Returns
-------
EndofPrdvFunc_cond : ValueFuncCRRA
The end-of-period value function conditional on a particular state
occuring in the next period.
"""
VLvlNext = (
self.PermShkVals_temp ** (1.0 - self.CRRA)
* self.PermGroFac ** (1.0 - self.CRRA)
) * self.vFuncNext(self.mNrmNext)
EndOfPrdv_cond = self.DiscFacEff * np.sum(VLvlNext * self.ShkPrbs_temp, axis=0)
EndOfPrdvNvrs_cond = self.uinv(EndOfPrdv_cond)
EndOfPrdvNvrsP_cond = self.EndOfPrdvP_cond * self.uinvP(EndOfPrdv_cond)
EndOfPrdvNvrs_cond = np.insert(EndOfPrdvNvrs_cond, 0, 0.0)
EndOfPrdvNvrsP_cond = np.insert(EndOfPrdvNvrsP_cond, 0, EndOfPrdvNvrsP_cond[0])
aNrm_temp = np.insert(self.aNrm_cond, 0, self.BoroCnstNat)
EndOfPrdvNvrsFunc_cond = CubicInterp(
aNrm_temp, EndOfPrdvNvrs_cond, EndOfPrdvNvrsP_cond
)
EndofPrdvFunc_cond = ValueFuncCRRA(EndOfPrdvNvrsFunc_cond, self.CRRA)
return EndofPrdvFunc_cond
def post_solve(self):
self.solution_fast = deepcopy(self.solution)
if self.cycles == 0:
terminal = 1
else:
terminal = self.cycles
self.solution[terminal] = self.solution_terminal_cs
for i in range(terminal):
solution = self.solution[i]
# Construct the consumption function as a linear interpolation.
cFunc = LinearInterp(solution.mNrm, solution.cNrm)
"""
Defines the value and marginal value functions for this period.
Uses the fact that for a perfect foresight CRRA utility problem,
if the MPC in period t is :math:`\kappa_{t}`, and relative risk
aversion :math:`\rho`, then the inverse value vFuncNvrs has a
constant slope of :math:`\kappa_{t}^{-\rho/(1-\rho)}` and
vFuncNvrs has value of zero at the lower bound of market resources
mNrmMin. See PerfForesightConsumerType.ipynb documentation notebook
for a brief explanation and the links below for a fuller treatment.
https://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/#vFuncAnalytical
https://www.econ2.jhu.edu/people/ccarroll/SolvingMicroDSOPs/#vFuncPF
"""
vFuncNvrs = LinearInterp(
np.array([solution.mNrmMin, solution.mNrmMin + 1.0]),
np.array([0.0, solution.vFuncNvrsSlope]),
)
vFunc = ValueFuncCRRA(vFuncNvrs, self.CRRA)
vPfunc = MargValueFuncCRRA(cFunc, self.CRRA)
consumer_solution = ConsumerSolution(
cFunc=cFunc,
vFunc=vFunc,
vPfunc=vPfunc,
mNrmMin=solution.mNrmMin,
hNrm=solution.hNrm,
MPCmin=solution.MPCmin,
MPCmax=solution.MPCmax,
)
Ex_IncNext = 1.0 # Perfect foresight income of 1
# Add mNrmStE to the solution and return it
consumer_solution.mNrmStE = _add_mNrmStENumba(
self.Rfree,
self.PermGroFac[i],
solution.mNrm,
solution.cNrm,
solution.mNrmMin,
Ex_IncNext,
_find_mNrmStE,
)
self.solution[i] = consumer_solution
def make_EndOfPrdvFuncCond(self):
"""
Construct the end-of-period value function conditional on next period's
state.
Parameters
----------
EndOfPrdvP : np.array
Array of end-of-period marginal value of assets corresponding to the
asset values in self.aNrmNow.
Returns
-------
none
"""
def v_lvl_next(shocks, a_nrm):
return (shocks[0]**(1.0 - self.CRRA) *
self.PermGroFac**(1.0 - self.CRRA)) * self.vFuncNext(
self.m_nrm_next(shocks, a_nrm))
EndOfPrdv_cond = self.DiscFacEff * calc_expectation(
self.IncShkDstn, v_lvl_next, self.aNrmNow)
EndOfPrdvNvrs = self.uinv(
EndOfPrdv_cond) # value transformed through inverse utility
EndOfPrdvNvrsP = self.EndOfPrdvP_cond * self.uinvP(EndOfPrdv_cond)
EndOfPrdvNvrs = np.insert(EndOfPrdvNvrs, 0, 0.0)
EndOfPrdvNvrsP = np.insert(
EndOfPrdvNvrsP, 0, EndOfPrdvNvrsP[0]
) # This is a very good approximation, vNvrsPP = 0 at the asset minimum
aNrm_temp = np.insert(self.aNrmNow, 0, self.BoroCnstNat)
EndOfPrdvNvrsFunc = CubicInterp(aNrm_temp, EndOfPrdvNvrs,
EndOfPrdvNvrsP)
EndOfPrdvFunc_dond = ValueFuncCRRA(EndOfPrdvNvrsFunc, self.CRRA)
return EndOfPrdvFunc_dond
def update_solution_terminal(self):
"""
Solves the terminal period of the portfolio choice problem. The solution is
trivial, as usual: consume all market resources, and put nothing in the risky
asset (because you have nothing anyway).
Parameters
----------
None
Returns
-------
None
"""
# Consume all market resources: c_T = m_T
cFuncAdj_terminal = IdentityFunction()
cFuncFxd_terminal = IdentityFunction(i_dim=0, n_dims=2)
# Risky share is irrelevant-- no end-of-period assets; set to zero
ShareFuncAdj_terminal = ConstantFunction(0.0)
ShareFuncFxd_terminal = IdentityFunction(i_dim=1, n_dims=2)
# Value function is simply utility from consuming market resources
vFuncAdj_terminal = ValueFuncCRRA(cFuncAdj_terminal, self.CRRA)
vFuncFxd_terminal = ValueFuncCRRA(cFuncFxd_terminal, self.CRRA)
# Marginal value of market resources is marg utility at the consumption function
vPfuncAdj_terminal = MargValueFuncCRRA(cFuncAdj_terminal, self.CRRA)
dvdmFuncFxd_terminal = MargValueFuncCRRA(cFuncFxd_terminal, self.CRRA)
dvdsFuncFxd_terminal = ConstantFunction(
0.0) # No future, no marg value of Share
# Construct the terminal period solution
self.solution_terminal = PortfolioSolution(
cFuncAdj=cFuncAdj_terminal,
ShareFuncAdj=ShareFuncAdj_terminal,
vFuncAdj=vFuncAdj_terminal,
vPfuncAdj=vPfuncAdj_terminal,
cFuncFxd=cFuncFxd_terminal,
ShareFuncFxd=ShareFuncFxd_terminal,
vFuncFxd=vFuncFxd_terminal,
dvdmFuncFxd=dvdmFuncFxd_terminal,
dvdsFuncFxd=dvdsFuncFxd_terminal,
)
def make_vFunc(self, solution):
"""
Construct the value function for each current state.
Parameters
----------
solution : ConsumerSolution
The solution to the single period consumption-saving problem. Must
have a consumption function cFunc (using cubic or linear splines) as
a list with elements corresponding to the current Markov state. E.g.
solution.cFunc[0] is the consumption function when in the i=0 Markov
state this period.
Returns
-------
vFuncNow : [ValueFuncCRRA]
A list of value functions (defined over normalized market resources
m) for each current period Markov state.
"""
vFuncNow = [] # Initialize an empty list of value functions
# Loop over each current period state and construct the value function
for i in range(self.StateCount):
# Make state-conditional grids of market resources and consumption
mNrmMin = self.mNrmMin_list[i]
mGrid = mNrmMin + self.aXtraGrid
cGrid = solution.cFunc[i](mGrid)
aGrid = mGrid - cGrid
# Calculate end-of-period value at each gridpoint
EndOfPrdv_all = np.zeros((self.StateCount, self.aXtraGrid.size))
for j in range(self.StateCount):
if self.possible_transitions[i, j]:
EndOfPrdv_all[j, :] = self.EndOfPrdvFunc_list[j](aGrid)
EndOfPrdv = np.dot(self.MrkvArray[i, :], EndOfPrdv_all)
# Calculate (normalized) value and marginal value at each gridpoint
vNrmNow = self.u(cGrid) + EndOfPrdv
vPnow = self.uP(cGrid)
# Make a "decurved" value function with the inverse utility function
vNvrs = self.uinv(vNrmNow) # value transformed through inverse utility
vNvrsP = vPnow * self.uinvP(vNrmNow)
mNrm_temp = np.insert(mGrid, 0, mNrmMin) # add the lower bound
vNvrs = np.insert(vNvrs, 0, 0.0)
vNvrsP = np.insert(
vNvrsP, 0, self.MPCmaxEff[i] ** (-self.CRRA / (1.0 - self.CRRA))
)
MPCminNvrs = self.MPCminNow[i] ** (-self.CRRA / (1.0 - self.CRRA))
vNvrsFunc_i = CubicInterp(
mNrm_temp, vNvrs, vNvrsP, MPCminNvrs * self.hNrmNow[i], MPCminNvrs
)
# "Recurve" the decurved value function and add it to the list
vFunc_i = ValueFuncCRRA(vNvrsFunc_i, self.CRRA)
vFuncNow.append(vFunc_i)
return vFuncNow
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.
"""
self.solution_terminal_cs = ConsumerSolution(
cFunc=self.cFunc_terminal_,
vFunc=ValueFuncCRRA(self.cFunc_terminal_, self.CRRA),
vPfunc=MargValueFuncCRRA(self.cFunc_terminal_, self.CRRA),
vPPfunc=MargMargValueFuncCRRA(self.cFunc_terminal_, self.CRRA),
mNrmMin=0.0,
hNrm=0.0,
MPCmin=1.0,
MPCmax=1.0,
)
def make_vFunc(self, solution):
"""
Make the beginning-of-period value function (unconditional on the shock).
Parameters
----------
solution : ConsumerSolution
The solution to this single period problem, which must include the
consumption function.
Returns
-------
vFuncNow : ValueFuncCRRA
A representation of the value function for this period, defined over
normalized market resources m: v = vFuncNow(m).
"""
# Compute expected value and marginal value on a grid of market resources,
# accounting for all of the discrete preference shocks
PrefShkCount = self.PrefShkVals.size
mNrm_temp = self.mNrmMinNow + self.aXtraGrid
vNrmNow = np.zeros_like(mNrm_temp)
vPnow = np.zeros_like(mNrm_temp)
for j in range(PrefShkCount):
this_shock = self.PrefShkVals[j]
this_prob = self.PrefShkPrbs[j]
cNrmNow = solution.cFunc(mNrm_temp,
this_shock * np.ones_like(mNrm_temp))
aNrmNow = mNrm_temp - cNrmNow
vNrmNow += this_prob * (this_shock * self.u(cNrmNow) +
self.EndOfPrdvFunc(aNrmNow))
vPnow += this_prob * this_shock * self.uP(cNrmNow)
# Construct the beginning-of-period value function
vNvrs = self.uinv(vNrmNow) # value transformed through inverse utility
vNvrsP = vPnow * self.uinvP(vNrmNow)
mNrm_temp = np.insert(mNrm_temp, 0, self.mNrmMinNow)
vNvrs = np.insert(vNvrs, 0, 0.0)
vNvrsP = np.insert(vNvrsP, 0,
self.MPCmaxEff**(-self.CRRA / (1.0 - self.CRRA)))
MPCminNvrs = self.MPCminNow**(-self.CRRA / (1.0 - self.CRRA))
vNvrsFuncNow = CubicInterp(mNrm_temp, vNvrs, vNvrsP,
MPCminNvrs * self.hNrmNow, MPCminNvrs)
vFuncNow = ValueFuncCRRA(vNvrsFuncNow, self.CRRA)
return vFuncNow
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)
def make_vFunc(self, solution):
"""
Creates the value function for this period, defined over market resources
m and persistent income p. self must have the attribute EndOfPrdvFunc in
order to execute.
Parameters
----------
solution : ConsumerSolution
The solution to this single period problem, which must include the
consumption function.
Returns
-------
vFuncNow : ValueFuncCRRA
A representation of the value function for this period, defined over
market resources m and persistent income p: v = vFuncNow(m,p).
"""
mSize = self.aXtraGrid.size
pSize = self.pLvlGrid.size
# Compute expected value and marginal value on a grid of market resources
pLvl_temp = np.tile(self.pLvlGrid,
(mSize, 1)) # Tile pLvl across m values
mLvl_temp = (np.tile(self.mLvlMinNow(self.pLvlGrid), (mSize, 1)) +
np.tile(np.reshape(self.aXtraGrid, (mSize, 1)),
(1, pSize)) * pLvl_temp)
cLvlNow = solution.cFunc(mLvl_temp, pLvl_temp)
aLvlNow = mLvl_temp - cLvlNow
vNow = self.u(cLvlNow) + self.EndOfPrdvFunc(aLvlNow, pLvl_temp)
vPnow = self.uP(cLvlNow)
# Calculate pseudo-inverse value and its first derivative (wrt mLvl)
vNvrs = self.uinv(vNow) # value transformed through inverse utility
vNvrsP = vPnow * self.uinvP(vNow)
# Add data at the lower bound of m
mLvl_temp = np.concatenate((np.reshape(self.mLvlMinNow(self.pLvlGrid),
(1, pSize)), mLvl_temp),
axis=0)
vNvrs = np.concatenate((np.zeros((1, pSize)), vNvrs), axis=0)
vNvrsP = np.concatenate((np.reshape(vNvrsP[0, :],
(1, vNvrsP.shape[1])), vNvrsP),
axis=0)
# Add data at the lower bound of p
MPCminNvrs = self.MPCminNow**(-self.CRRA / (1.0 - self.CRRA))
m_temp = np.reshape(mLvl_temp[:, 0], (mSize + 1, 1))
mLvl_temp = np.concatenate((m_temp, mLvl_temp), axis=1)
vNvrs = np.concatenate((MPCminNvrs * m_temp, vNvrs), axis=1)
vNvrsP = np.concatenate((MPCminNvrs * np.ones((mSize + 1, 1)), vNvrsP),
axis=1)
# Construct the pseudo-inverse value function
vNvrsFunc_list = []
for j in range(pSize + 1):
pLvl = np.insert(self.pLvlGrid, 0, 0.0)[j]
vNvrsFunc_list.append(
CubicInterp(
mLvl_temp[:, j] - self.mLvlMinNow(pLvl),
vNvrs[:, j],
vNvrsP[:, j],
MPCminNvrs * self.hLvlNow(pLvl),
MPCminNvrs,
))
vNvrsFuncBase = LinearInterpOnInterp1D(
vNvrsFunc_list, np.insert(self.pLvlGrid, 0,
0.0)) # Value function "shifted"
vNvrsFuncNow = VariableLowerBoundFunc2D(vNvrsFuncBase, self.mLvlMinNow)
# "Re-curve" the pseudo-inverse value function into the value function
vFuncNow = ValueFuncCRRA(vNvrsFuncNow, self.CRRA)
return vFuncNow
def make_EndOfPrdvFunc(self, EndOfPrdvP):
"""
Construct the end-of-period value function for this period, storing it
as an attribute of self for use by other methods.
Parameters
----------
EndOfPrdvP : np.array
Array of end-of-period marginal value of assets corresponding to the
asset values in self.aLvlNow x self.pLvlGrid.
Returns
-------
none
"""
vLvlNext = self.vFuncNext(
self.mLvlNext,
self.pLvlNext) # value in many possible future states
EndOfPrdv = self.DiscFacEff * np.sum(
vLvlNext * self.ShkPrbs_temp,
axis=0) # expected value, averaging across states
EndOfPrdvNvrs = self.uinv(
EndOfPrdv) # value transformed through inverse utility
EndOfPrdvNvrsP = EndOfPrdvP * self.uinvP(EndOfPrdv)
# Add points at mLvl=zero
EndOfPrdvNvrs = np.concatenate((np.zeros(
(self.pLvlGrid.size, 1)), EndOfPrdvNvrs),
axis=1)
if hasattr(self, "MedShkDstn"):
EndOfPrdvNvrsP = np.concatenate((np.zeros(
(self.pLvlGrid.size, 1)), EndOfPrdvNvrsP),
axis=1)
else:
EndOfPrdvNvrsP = np.concatenate(
(
np.reshape(EndOfPrdvNvrsP[:, 0], (self.pLvlGrid.size, 1)),
EndOfPrdvNvrsP,
),
axis=1,
)
# This is a very good approximation, vNvrsPP = 0 at the asset minimum
aLvl_temp = np.concatenate(
(
np.reshape(self.BoroCnstNat(self.pLvlGrid),
(self.pLvlGrid.size, 1)),
self.aLvlNow,
),
axis=1,
)
# Make an end-of-period value function for each persistent income level in the grid
EndOfPrdvNvrsFunc_list = []
for p in range(self.pLvlGrid.size):
EndOfPrdvNvrsFunc_list.append(
CubicInterp(
aLvl_temp[p, :] - self.BoroCnstNat(self.pLvlGrid[p]),
EndOfPrdvNvrs[p, :],
EndOfPrdvNvrsP[p, :],
))
EndOfPrdvNvrsFuncBase = LinearInterpOnInterp1D(EndOfPrdvNvrsFunc_list,
self.pLvlGrid)
# Re-adjust the combined end-of-period value function to account for the natural borrowing constraint shifter
EndOfPrdvNvrsFunc = VariableLowerBoundFunc2D(EndOfPrdvNvrsFuncBase,
self.BoroCnstNat)
self.EndOfPrdvFunc = ValueFuncCRRA(EndOfPrdvNvrsFunc, self.CRRA)
def solveConsPortfolio(
solution_next,
ShockDstn,
IncShkDstn,
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.
IncShkDstn : distribution.Distribution
Discrete distribution of 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
TranShks_next = IncShkDstn.X[1]
Risky_next = RiskyDstn.X
# Flag for whether the natural borrowing constraint is zero
zero_bound = np.min(TranShks_next) == 0.0
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:
# Add an asset point at exactly zero
aNrmGrid = np.insert(aXtraGrid, 0, 0.0)
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
# Make tiled arrays to calculate future realizations of mNrm and Share when integrating over IncShkDstn
bNrm_tiled, Share_tiled = np.meshgrid(bNrmGrid,
ShareGrid,
indexing="ij")
# Calculate future realizations of market resources
def m_nrm_next(shocks, b_nrm):
return b_nrm / (shocks[0] * PermGroFac) + shocks[1]
# Evaluate realizations of marginal value of market resources next period
def dvdb_dist(shocks, b_nrm, Share_next):
mNrm_next = m_nrm_next(shocks, b_nrm)
dvdmAdj_next = vPfuncAdj_next(mNrm_next)
if AdjustPrb < 1.0:
dvdmFxd_next = dvdmFuncFxd_next(mNrm_next, Share_next)
# Combine by adjustment probability
dvdm_next = AdjustPrb * dvdmAdj_next + (
1.0 - AdjustPrb) * dvdmFxd_next
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
dvdm_next = dvdmAdj_next
return (shocks[0] * PermGroFac)**(-CRRA) * dvdm_next
# Evaluate realizations of marginal value of risky share next period
def dvds_dist(shocks, b_nrm, Share_next):
mNrm_next = m_nrm_next(shocks, b_nrm)
# No marginal value of Share if it's a free choice!
dvdsAdj_next = np.zeros_like(mNrm_next)
if AdjustPrb < 1.0:
dvdsFxd_next = dvdsFuncFxd_next(mNrm_next, Share_next)
# Combine by adjustment probability
dvds_next = AdjustPrb * dvdsAdj_next + (
1.0 - AdjustPrb) * dvdsFxd_next
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
dvds_next = dvdsAdj_next
return (shocks[0] * PermGroFac)**(1.0 - CRRA) * dvds_next
# If the value function has been requested, evaluate realizations of value
def v_intermed_dist(shocks, b_nrm, Share_next):
mNrm_next = m_nrm_next(shocks, b_nrm)
vAdj_next = vFuncAdj_next(mNrm_next)
if AdjustPrb < 1.0:
vFxd_next = vFuncFxd_next(mNrm_next, Share_next)
# Combine by adjustment probability
v_next = AdjustPrb * vAdj_next + (1.0 - AdjustPrb) * vFxd_next
else: # Don't bother evaluating if there's no chance that portfolio share is fixed
v_next = vAdj_next
return (shocks[0] * PermGroFac)**(1.0 - CRRA) * v_next
# Calculate intermediate marginal value of bank balances by taking expectations over income shocks
dvdb_intermed = calc_expectation(IncShkDstn, dvdb_dist, bNrm_tiled,
Share_tiled)
# calc_expectation returns one additional "empty" dimension, remove it
# this line can be deleted when calc_expectation is fixed
dvdb_intermed = dvdb_intermed[:, :, 0]
dvdbNvrs_intermed = uPinv(dvdb_intermed)
dvdbNvrsFunc_intermed = BilinearInterp(dvdbNvrs_intermed, bNrmGrid,
ShareGrid)
dvdbFunc_intermed = MargValueFuncCRRA(dvdbNvrsFunc_intermed, CRRA)
# Calculate intermediate value by taking expectations over income shocks
if vFuncBool:
v_intermed = calc_expectation(IncShkDstn, v_intermed_dist,
bNrm_tiled, Share_tiled)
# calc_expectation returns one additional "empty" dimension, remove it
# this line can be deleted when calc_expectation is fixed
v_intermed = v_intermed[:, :, 0]
vNvrs_intermed = n(v_intermed)
vNvrsFunc_intermed = BilinearInterp(vNvrs_intermed, bNrmGrid,
ShareGrid)
vFunc_intermed = ValueFuncCRRA(vNvrsFunc_intermed, CRRA)
# Calculate intermediate marginal value of risky portfolio share by taking expectations
dvds_intermed = calc_expectation(IncShkDstn, dvds_dist, bNrm_tiled,
Share_tiled)
# calc_expectation returns one additional "empty" dimension, remove it
# this line can be deleted when calc_expectation is fixed
dvds_intermed = dvds_intermed[:, :, 0]
dvdsFunc_intermed = BilinearInterp(dvds_intermed, bNrmGrid, ShareGrid)
# Make tiled arrays to calculate future realizations of bNrm and Share when integrating over RiskyDstn
aNrm_tiled, Share_tiled = np.meshgrid(aNrmGrid,
ShareGrid,
indexing="ij")
# Evaluate realizations of value and marginal value after asset returns are realized
def EndOfPrddvda_dist(shock, a_nrm, Share_next):
# Calculate future realizations of bank balances bNrm
Rxs = shock - Rfree
Rport = Rfree + Share_next * Rxs
b_nrm_next = Rport * a_nrm
return Rport * dvdbFunc_intermed(b_nrm_next, Share_next)
def EndOfPrdv_dist(shock, a_nrm, Share_next):
# Calculate future realizations of bank balances bNrm
Rxs = shock - Rfree
Rport = Rfree + Share_next * Rxs
b_nrm_next = Rport * a_nrm
return vFunc_intermed(b_nrm_next, Share_next)
def EndOfPrddvds_dist(shock, a_nrm, Share_next):
# Calculate future realizations of bank balances bNrm
Rxs = shock - Rfree
Rport = Rfree + Share_next * Rxs
b_nrm_next = Rport * a_nrm
return Rxs * a_nrm * dvdbFunc_intermed(
b_nrm_next, Share_next) + dvdsFunc_intermed(
b_nrm_next, Share_next)
# Calculate end-of-period marginal value of assets by taking expectations
EndOfPrddvda = (DiscFac * LivPrb * calc_expectation(
RiskyDstn, EndOfPrddvda_dist, aNrm_tiled, Share_tiled))
# calc_expectation returns one additional "empty" dimension, remove it
# this line can be deleted when calc_expectation is fixed
EndOfPrddvda = EndOfPrddvda[:, :, 0]
EndOfPrddvdaNvrs = uPinv(EndOfPrddvda)
# Calculate end-of-period value by taking expectations
if vFuncBool:
EndOfPrdv = (DiscFac * LivPrb * calc_expectation(
RiskyDstn, EndOfPrdv_dist, aNrm_tiled, Share_tiled))
# calc_expectation returns one additional "empty" dimension, remove it
# this line can be deleted when calc_expectation is fixed
EndOfPrdv = EndOfPrdv[:, :, 0]
EndOfPrdvNvrs = n(EndOfPrdv)
# Calculate end-of-period marginal value of risky portfolio share by taking expectations
EndOfPrddvds = (DiscFac * LivPrb * calc_expectation(
RiskyDstn, EndOfPrddvds_dist, aNrm_tiled, Share_tiled))
# calc_expectation returns one additional "empty" dimension, remove it
# this line can be deleted when calc_expectation is fixed
EndOfPrddvds = EndOfPrddvds[:, :, 0]
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]
# Flag for whether the natural borrowing constraint is zero
zero_bound = np.min(TranShks_next) == 0.0
# Make tiled arrays to calculate future realizations of mNrm and Share; dimension order: mNrm, Share, shock
if zero_bound:
aNrmGrid = aXtraGrid
else:
# Add an asset point at exactly zero
aNrmGrid = np.insert(aXtraGrid, 0, 0.0)
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 = (1.0 - 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 < 1.0:
dvdmFxd_next = dvdmFuncFxd_next(mNrm_next, Share_next)
# Combine by adjustment probability
dvdm_next = AdjustPrb * dvdmAdj_next + (1.0 -
AdjustPrb) * dvdmFxd_next
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
# No marginal value of Share if it's a free choice!
dvdsAdj_next = np.zeros_like(mNrm_next)
if AdjustPrb < 1.0:
dvdsFxd_next = dvdsFuncFxd_next(mNrm_next, Share_next)
# Combine by adjustment probability
dvds_next = AdjustPrb * dvdsAdj_next + (1.0 -
AdjustPrb) * dvdsFxd_next
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 < 1.0:
vFxd_next = vFuncFxd_next(mNrm_next, Share_next)
v_next = AdjustPrb * vAdj_next + (1.0 - 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
# Will use this below
temp_fac_B = (PermShks_tiled * PermGroFac)**(1.0 - CRRA)
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
# Take cNrm at that index as well
cNrmAdj_now = EndOfPrddvdaNvrs[np.arange(aNrm_N), opt_idx]
if not zero_bound:
Share_now[
0] = 1.0 # aNrm=0, so there's no way to "optimize" the portfolio
# Consumption when aNrm=0 does not depend on Share
cNrmAdj_now[0] = EndOfPrddvdaNvrs[0, -1]
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
# Initialize to putting everything in safe asset
Share_now = np.zeros_like(aNrmGrid)
cNrmAdj_now = np.zeros_like(aNrmGrid)
# If agent wants to put more than 100% into risky asset, he is constrained
constrained_top = FOC_s[:, -1] > 0.0
# Likewise if he wants to put less than 0% into risky asset
constrained_bot = FOC_s[:, 0] < 0.0
Share_now[constrained_top] = 1.0
if not zero_bound:
Share_now[
0] = 1.0 # aNrm=0, so there's no way to "optimize" the portfolio
# Consumption when aNrm=0 does not depend on Share
cNrmAdj_now[0] = EndOfPrddvdaNvrs[0, -1]
# Mark as constrained so that there is no attempt at optimization
constrained_top[0] = True
# Get consumption when share-constrained
cNrmAdj_now[constrained_top] = EndOfPrddvdaNvrs[constrained_top, -1]
cNrmAdj_now[constrained_bot] = EndOfPrddvdaNvrs[constrained_bot, 0]
# 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:] <= 0.0, FOC_s[:, :-1] >= 0.0)
for j in range(aNrm_N):
if not (constrained_top[j] or constrained_bot[j]):
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 = 1.0 - top_f / (top_f - bot_f)
Share_now[j] = (1.0 - alpha) * bot_s + alpha * top_s
cNrmAdj_now[j] = (1.0 - alpha) * bot_c + alpha * top_c
# Calculate the endogenous mNrm gridpoints when the agent adjusts his portfolio
mNrmAdj_now = aNrmGrid + cNrmAdj_now
# This is a point at which (a,c,share) have consistent length. Take the
# snapshot for storing the grid and values in the solution.
save_points = {
"a": deepcopy(aNrmGrid),
"eop_dvda_adj": uP(cNrmAdj_now),
"share_adj": deepcopy(Share_now),
"share_grid": deepcopy(ShareGrid),
"eop_dvda_fxd": uP(EndOfPrddvda),
}
# 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 * (1.0 + 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 = MargValueFuncCRRA(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 = MargValueFuncCRRA(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 = ValueFuncCRRA(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
)
# Re-curve the pseudo-inverse value function
vFuncAdj_now = ValueFuncCRRA(vNvrsFuncAdj, CRRA)
# 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 = ValueFuncCRRA(vNvrsFuncFxd, CRRA)
else: # If vFuncBool is False, fill in dummy values
vFuncAdj_now = None
vFuncFxd_now = None
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,
aGrid=save_points["a"],
Share_adj=save_points["share_adj"],
EndOfPrddvda_adj=save_points["eop_dvda_adj"],
ShareGrid=save_points["share_grid"],
EndOfPrddvda_fxd=save_points["eop_dvda_fxd"],
AdjPrb=AdjustPrb,
)
def post_solve(self):
self.solution_fast = deepcopy(self.solution)
if self.cycles == 0:
cycles = 1
else:
cycles = self.cycles
self.solution[-1] = self.solution_terminal_cs
for i in range(cycles):
for j in range(self.T_cycle):
solution = self.solution[i * self.T_cycle + j]
# Define the borrowing constraint (limiting consumption function)
cFuncNowCnst = LinearInterp(
np.array([solution.mNrmMin, solution.mNrmMin + 1]),
np.array([0.0, 1.0]),
)
"""
Constructs a basic solution for this period, including the consumption
function and marginal value function.
"""
if self.CubicBool:
# Makes a cubic spline interpolation of the unconstrained consumption
# function for this period.
cFuncNowUnc = CubicInterp(
solution.mNrm,
solution.cNrm,
solution.MPC,
solution.cFuncLimitIntercept,
solution.cFuncLimitSlope,
)
else:
# Makes a linear interpolation to represent the (unconstrained) consumption function.
# Construct the unconstrained consumption function
cFuncNowUnc = LinearInterp(
solution.mNrm,
solution.cNrm,
solution.cFuncLimitIntercept,
solution.cFuncLimitSlope,
)
# Combine the constrained and unconstrained functions into the true consumption function
cFuncNow = LowerEnvelope(cFuncNowUnc, cFuncNowCnst)
# Make the marginal value function and the marginal marginal value function
vPfuncNow = MargValueFuncCRRA(cFuncNow, self.CRRA)
# Pack up the solution and return it
consumer_solution = ConsumerSolution(
cFunc=cFuncNow,
vPfunc=vPfuncNow,
mNrmMin=solution.mNrmMin,
hNrm=solution.hNrm,
MPCmin=solution.MPCmin,
MPCmax=solution.MPCmax,
)
if self.vFuncBool:
vNvrsFuncNow = CubicInterp(
solution.mNrmGrid,
solution.vNvrs,
solution.vNvrsP,
solution.MPCminNvrs * solution.hNrm,
solution.MPCminNvrs,
)
vFuncNow = ValueFuncCRRA(vNvrsFuncNow, self.CRRA)
consumer_solution.vFunc = vFuncNow
if self.CubicBool or self.vFuncBool:
_searchFunc = (
_find_mNrmStECubic if self.CubicBool else _find_mNrmStELinear
)
# Add mNrmStE to the solution and return it
consumer_solution.mNrmStE = _add_mNrmStEIndNumba(
self.PermGroFac[j],
self.Rfree,
solution.Ex_IncNext,
solution.mNrmMin,
solution.mNrm,
solution.cNrm,
solution.MPC,
solution.MPCmin,
solution.hNrm,
_searchFunc,
)
self.solution[i * self.T_cycle + j] = consumer_solution
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,
)
