def makeConvergencePlot(DiscFac, CRRA, Rfree, PermShkStd):
# Construct finite horizon agent with baseline parameters
baseAgent_Fin = IndShockConsumerType(verbose=0, **base_params)
baseAgent_Fin.DiscFac = DiscFac
baseAgent_Fin.CRRA = CRRA
baseAgent_Fin.Rfree = Rfree
baseAgent_Fin.PermShkStd = [PermShkStd]
baseAgent_Fin.cycles = 100
baseAgent_Fin.updateIncomeProcess()
baseAgent_Fin.solve()
baseAgent_Fin.unpack('cFunc')
# figure limits
mMax = 6 # 11
mMin = 0
cMin = 0
cMax = 4 # 7
mPlotMin = 0
mLocCLabels = 5.6 # 9.6 # Defines horizontal limit of figure
mPlotTop = 3.5 # 6.5 # Defines maximum m value where functions are plotted
mPts = 1000 # Number of points at which functions are evaluated
plt.figure(figsize=(12, 8))
plt.ylim([cMin, cMax])
plt.xlim([mMin, mMax])
mBelwLabels = np.linspace(mPlotMin, mLocCLabels - 0.1,
mPts) # Range of m below loc of labels
m_FullRange = np.linspace(mPlotMin, mPlotTop, mPts) # Full plot range
c_Tm0 = m_FullRange # c_Tm0 defines the last period consumption rule (c=m)
c_Tm1 = baseAgent_Fin.cFunc[-2](
mBelwLabels
) # c_Tm1 defines the second-to-last period consumption rule
c_Tm5 = baseAgent_Fin.cFunc[-6](
mBelwLabels) # c_Tm5 defines the T-5 period consumption rule
c_Tm10 = baseAgent_Fin.cFunc[-11](
mBelwLabels) # c_Tm10 defines the T-10 period consumption rule
c_Limt = baseAgent_Fin.cFunc[0](
mBelwLabels
) # c_Limt defines limiting infinite-horizon consumption rule
plt.plot(mBelwLabels, c_Limt, label="$c(m)$")
plt.plot(mBelwLabels, c_Tm1, label="$c_{T-1}(m)$")
plt.plot(mBelwLabels, c_Tm5, label="$c_{T-5}(m)$")
plt.plot(mBelwLabels, c_Tm10, label="$c_{T-10}(m)$")
plt.plot(m_FullRange, c_Tm0, label="$c_{T}(m) = 45$ degree line")
plt.legend(fontsize='x-large')
plt.tick_params(
labelbottom=False,
labelleft=False,
left="off",
right="off",
bottom="off",
top="off",
)
plt.show()
return None
def makeTargetMfig(Rfree, DiscFac, CRRA, permShkStd, TranShkStd):
inf_hor = IndShockConsumerType(quietly=True, **base_params)
inf_hor.Rfree = Rfree
inf_hor.DiscFac = DiscFac
inf_hor.CRRA = CRRA
inf_hor.permShkStd = [permShkStd]
inf_hor.TranShkStd = [TranShkStd]
inf_hor.update_income_process()
mPlotMin = 0
mPlotMax = 250
inf_hor.aXtraMax = mPlotMax
inf_hor.solve(quietly=True, messaging_level=logging.CRITICAL)
soln = inf_hor.solution[0]
Bilt, cFunc = soln.Bilt, soln.cFunc
cPlotMin = 0, cFunc(mPlotMax)
if Bilt.GICNrm: # tattle
soln.check_GICNrm(soln, quietly=False, messaging_level=logging.WARNING)
mBelwStE = np.linspace(mPlotMin, mPlotMax, 1000)
EPermGroFac = inf_hor.PermGroFac[0]
def EmDelEq0(mVec):
return (EPermGroFac / Rfree) + (1.0 - EPermGroFac / Rfree) * mVec
cBelwStE_Best = cFunc(mBelwStE) # "best" = optimal c
cBelwStE_Sstn = EmDelEq0(mBelwStE) # "sustainable" c
mNrmStE = Bilt.mNrmStE
plt.figure(figsize=(12, 8))
plt.plot(mBelwStE, cBelwStE_Best, label="$c(m_{t})$")
plt.plot(mBelwStE,
cBelwStE_Sstn,
label="$\mathsf{E}_{t}[\Delta m_{t+1}] = 0$")
plt.xlim(mPlotMin, mPlotMax)
plt.ylim(cPlotMin, cFunc(mPlotMax))
plt.plot(
[mNrmStE, mNrmStE],
[0, 2.5],
color="black",
linestyle="--",
)
plt.tick_params(
# labelbottom=False,
# labelleft=False,
# left="off",
right="off",
# bottom="off",
top="off",
)
plt.text(0, 1.47, r"$c$", fontsize=26)
plt.text(3.02, 0, r"$m$", fontsize=26)
plt.text(mNrmStE - 0.05, -0.1, "m̌", fontsize=26)
plt.legend(fontsize='x-large')
plt.show()
return None
def makeTargetMfig(Rfree, DiscFac, CRRA, PermShkStd, TranShkStd):
baseAgent_Inf = IndShockConsumerType(verbose=0, cycles=0, **base_params)
baseAgent_Inf.Rfree = Rfree
baseAgent_Inf.DiscFac = DiscFac
baseAgent_Inf.CRRA = CRRA
baseAgent_Inf.PermShkStd = [PermShkStd]
baseAgent_Inf.TranShkStd = [TranShkStd]
baseAgent_Inf.updateIncomeProcess()
baseAgent_Inf.checkConditions()
mPlotMin = 0
mPlotMax = 250
baseAgent_Inf.aXtraMax = mPlotMax
baseAgent_Inf.solve()
baseAgent_Inf.unpack('cFunc')
cPlotMin = 0
cPlotMax = baseAgent_Inf.cFunc[0](mPlotMax)
if (baseAgent_Inf.GPFInd >= 1):
baseAgent_Inf.checkGICInd(verbose=3)
mBelwTrg = np.linspace(mPlotMin, mPlotMax, 1000)
EPermGroFac = baseAgent_Inf.PermGroFac[0]
EmDelEq0 = lambda m: (EPermGroFac / Rfree) + (1.0 - EPermGroFac / Rfree
) * m
cBelwTrg_Best = baseAgent_Inf.cFunc[0](mBelwTrg) # "best" = optimal c
cBelwTrg_Sstn = EmDelEq0(mBelwTrg) # "sustainable" c
mNrmTrg = baseAgent_Inf.solution[0].mNrmSS
plt.figure(figsize=(12, 8))
plt.plot(mBelwTrg, cBelwTrg_Best, label="$c(m_{t})$")
plt.plot(mBelwTrg,
cBelwTrg_Sstn,
label="$\mathsf{E}_{t}[\Delta m_{t+1}] = 0$")
plt.xlim(mPlotMin, mPlotMax)
plt.ylim(cPlotMin, cPlotMax)
plt.plot(
[mNrmTrg, mNrmTrg],
[0, 2.5],
color="black",
linestyle="--",
)
plt.tick_params(
# labelbottom=False,
# labelleft=False,
# left="off",
right="off",
# bottom="off",
top="off",
)
plt.text(0, 1.47, r"$c$", fontsize=26)
plt.text(3.02, 0, r"$m$", fontsize=26)
plt.text(mNrmTrg - 0.05, -0.1, "m̌", fontsize=26)
plt.legend(fontsize='x-large')
plt.show()
return None
def makeBoundsFigure(UnempPrb, PermShkStd, TranShkStd, DiscFac, CRRA):
baseAgent_Inf = IndShockConsumerType(verbose=0, cycles=0, **base_params)
baseAgent_Inf.UnempPrb = UnempPrb
baseAgent_Inf.PermShkStd = [PermShkStd]
baseAgent_Inf.TranShkStd = [TranShkStd]
baseAgent_Inf.DiscFac = DiscFac
baseAgent_Inf.CRRA = CRRA
baseAgent_Inf.updateIncomeProcess()
baseAgent_Inf.checkConditions()
baseAgent_Inf.solve()
baseAgent_Inf.unpack('cFunc')
# Retrieve parameters (makes code readable)
Rfree = baseAgent_Inf.Rfree
CRRA = baseAgent_Inf.CRRA
EPermGroFac = baseAgent_Inf.PermGroFac[0]
mNrmTrg = baseAgent_Inf.solution[0].mNrmSS
UnempPrb = baseAgent_Inf.UnempPrb
κ_Min = 1.0 - (Rfree**(-1.0)) * (Rfree * DiscFac)**(1.0 / CRRA)
h_inf = (1.0 / (1.0 - EPermGroFac / Rfree))
cFunc_Uncnst = lambda m: (h_inf - 1) * κ_Min + κ_Min * m
cFunc_TopBnd = lambda m: (1 - UnempPrb**(1.0 / CRRA) *
(Rfree * DiscFac)**(1.0 / CRRA) / Rfree) * m
cFunc_BotBnd = lambda m: (1 - (Rfree * DiscFac)**(1.0 / CRRA) / Rfree) * m
# Plot the consumption function and its bounds
cMaxLabel = r"c̅$(m) = (m-1+h)κ̲$" # Use unicode kludge
cMinLabel = r"c̲$(m)= (1-\Phi_{R})m = κ̲ m$"
mPlotMax = 25
mPlotMin = 0
# mKnk is point where the two upper bounds meet
mKnk = ((h_inf - 1) * κ_Min) / (
(1 - UnempPrb**(1.0 / CRRA) *
(Rfree * DiscFac)**(1.0 / CRRA) / Rfree) - κ_Min)
mBelwKnkPts = 300
mAbveKnkPts = 700
mBelwKnk = np.linspace(mPlotMin, mKnk, mBelwKnkPts)
mAbveKnk = np.linspace(mKnk, mPlotMax, mAbveKnkPts)
mFullPts = np.linspace(mPlotMin, mPlotMax, mBelwKnkPts + mAbveKnkPts)
plt.figure(figsize=(12, 8))
plt.plot(mFullPts, baseAgent_Inf.cFunc[0](mFullPts), label=r'$c(m)$')
plt.plot(mBelwKnk, cFunc_Uncnst(mBelwKnk), label=cMaxLabel, linestyle="--")
plt.plot(
mAbveKnk,
cFunc_Uncnst(mAbveKnk),
label=
r'Upper Bound $ = $ Min $[\overline{\overline{c}}(m),\overline{c}(m)]$',
linewidth=2.5,
color='black')
plt.plot(mBelwKnk, cFunc_TopBnd(mBelwKnk), linewidth=2.5, color='black')
plt.plot(mAbveKnk,
cFunc_TopBnd(mAbveKnk),
linestyle="--",
label=r"$\overline{\overline{c}}(m) = κ̅m = (1 - ℘^{1/ρ}Φᵣ)m$")
plt.plot(mBelwKnk, cFunc_BotBnd(mBelwKnk), color='red', linewidth=2.5)
plt.plot(mAbveKnk,
cFunc_BotBnd(mAbveKnk),
color='red',
label=cMinLabel,
linewidth=2.5)
plt.tick_params(labelbottom=False,
labelleft=False,
left='off',
right='off',
bottom='off',
top='off')
plt.xlim(mPlotMin, mPlotMax)
plt.ylim(mPlotMin, 1.12 * cFunc_Uncnst(mPlotMax))
plt.text(mPlotMin,
1.12 * cFunc_Uncnst(mPlotMax) + 0.05,
"$c$",
fontsize=22)
plt.text(mPlotMax + 0.1, mPlotMin, "$m$", fontsize=22)
plt.legend(fontsize='x-large')
plt.show()
return None
# + {"cell_marker": "\"\"\"", "cell_type": "markdown"}
# The next step is to change the values of parameters as we want.
#
# To see all the parameters used in the model, along with their default values, see $\texttt{ConsumerParameters.py}$
#
# Parameter values are stored as attributes of the $\texttt{ConsumerType}$ the values are used for. For example, the risk-free interest rate $\texttt{Rfree}$ is stored as $\texttt{BaselineExample.Rfree}$. Because we created $\texttt{BaselineExample}$ using the default parameters values at the moment $\texttt{BaselineExample.Rfree}$ is set to the default value of $\texttt{Rfree}$ (which, at the time this demo was written, was 1.03). Therefore, to change the risk-free interest rate used in $\texttt{BaselineExample}$ to (say) 1.02, all we need to do is:
#
# -
# Change the Default Riskfree Interest Rate
BaselineExample.Rfree = 1.02
# +
## Change some parameter values
BaselineExample.Rfree = 1.02 #change the risk-free interest rate
BaselineExample.CRRA = 2. # change the coefficient of relative risk aversion
BaselineExample.BoroCnstArt = -.3 # change the artificial borrowing constraint
BaselineExample.DiscFac = .5 #chosen so that target debt-to-permanent-income_ratio is about .1
# i.e. BaselineExample.solution[0].cFunc(.9) ROUGHLY = 1.
## There is one more parameter value we need to change. This one is more complicated than the rest.
## We could solve the problem for a consumer with an infinite horizon of periods that (ex-ante)
## are all identical. We could also solve the problem for a consumer with a fininite lifecycle,
## or for a consumer who faces an infinite horizon of periods that cycle (e.g., a ski instructor
## facing an infinite series of winters, with lots of income, and summers, with very little income.)
## The way to differentiate is through the "cycles" attribute, which indicates how often the
## sequence of periods needs to be solved. The default value is 1, for a consumer with a finite
## lifecycle that is only experienced 1 time. A consumer who lived that life twice in a row, and
## then died, would have cycles = 2. But neither is what we want. Here, we need to set cycles = 0,
## to tell HARK that we are solving the model for an infinite horizon consumer.
def makeBoundsFigure(UnempPrb, permShkStd, TranShkStd, DiscFac, CRRA):
inf_hor = IndShockConsumerType(quietly=True,
messaging_level=logging.CRITICAL,
**base_params)
inf_hor.UnempPrb = UnempPrb
inf_hor.permShkStd = [permShkStd]
inf_hor.TranShkStd = [TranShkStd]
inf_hor.DiscFac = DiscFac
inf_hor.CRRA = CRRA
inf_hor.update_income_process()
inf_hor.solve(quietly=True, messaging_level=logging.CRITICAL)
soln = inf_hor.solution[0]
Bilt, Pars = soln.Bilt, soln.Pars
cFunc = soln.cFunc
mPlotMin, mPlotMax = 0, 25
inf_hor.aXtraMax = mPlotMax
# Retrieve parameters (makes code more readable)
Rfree, EPermGroFac = Pars.Rfree, Pars.PermGroFac
κ_Min = 1.0 - (Rfree**(-1.0)) * (Rfree * DiscFac)**(1.0 / CRRA)
h_inf = (1.0 / (1.0 - EPermGroFac / Rfree))
def cFunc_Uncnst(mVec):
return (h_inf - 1) * κ_Min + κ_Min * mVec
def cFunc_TopBnd(mVec):
return (1 - UnempPrb**(1.0 / CRRA) *
(Rfree * DiscFac)**(1.0 / CRRA) / Rfree) * mVec
def cFunc_BotBnd(mVec):
return (1 - (Rfree * DiscFac)**(1.0 / CRRA) / Rfree) * mVec
# Plot the consumption function and its bounds
cPlotMaxLabel = r"c̅$(m) = (m-1+h)κ̲$" # Use unicode kludge
cPlotMinLabel = r"c̲$(m)= (1-\Phi_{R})m = κ̲ m$"
# mKnk is point where the two upper bounds meet
mKnk = ((h_inf - 1) * κ_Min) / (
(1 - UnempPrb**(1.0 / CRRA) *
(Rfree * DiscFac)**(1.0 / CRRA) / Rfree) - κ_Min)
mBelwKnkPts, mAbveKnkPts = 50, 100
mBelwKnk = np.linspace(mPlotMin, mKnk, mBelwKnkPts)
mAbveKnk = np.linspace(mKnk, mPlotMax, mAbveKnkPts)
mFullPts = np.linspace(mPlotMin, mPlotMax, mBelwKnkPts + mAbveKnkPts)
plt.figure(figsize=(12, 8))
plt.plot(mFullPts, cFunc(mFullPts), label=r'$c(m)$')
plt.plot(mBelwKnk,
cFunc_Uncnst(mBelwKnk),
label=cPlotMaxLabel,
linestyle="--")
plt.plot(
mAbveKnk,
cFunc_Uncnst(mAbveKnk),
label=
r'Upper Bound $ = $ Min $[\overline{\overline{c}}(m),\overline{c}(m)]$',
linewidth=2.5,
color='black')
plt.plot(mBelwKnk, cFunc_TopBnd(mBelwKnk), linewidth=2.5, color='black')
plt.plot(mAbveKnk,
cFunc_TopBnd(mAbveKnk),
linestyle="--",
label=r"$\overline{\overline{c}}(m) = κ̅m = (1 - ℘^{1/ρ}Φᵣ)m$")
plt.plot(mBelwKnk, cFunc_BotBnd(mBelwKnk), color='red', linewidth=2.5)
plt.plot(mAbveKnk,
cFunc_BotBnd(mAbveKnk),
color='red',
label=cPlotMinLabel,
linewidth=2.5)
plt.tick_params(labelbottom=False,
labelleft=False,
left='off',
right='off',
bottom='off',
top='off')
plt.xlim(mPlotMin, mPlotMax)
plt.ylim(mPlotMin, 1.12 * cFunc_Uncnst(mPlotMax))
plt.text(mPlotMin,
1.12 * cFunc_Uncnst(mPlotMax) + 0.05,
"$c$",
fontsize=22)
plt.text(mPlotMax + 0.1, mPlotMin, "$m$", fontsize=22)
plt.legend(fontsize='x-large')
plt.show()
return None
