def setUp(self):
# Parameters from Mehra and Prescott (1985):
Avg = 1.08 # equity premium
Std = 0.20 # standard deviation of rate-of-return shocks
RiskyDstnFunc = cpm.RiskyDstnFactory(
RiskyAvg=Avg, RiskyStd=Std) # Generates nodes for integration
RiskyDrawFunc = cpm.LogNormalRiskyDstnDraw(
RiskyAvg=Avg, RiskyStd=Std
) # Function to generate draws from a lognormal distribution
init_portfolio = copy.copy(
param.init_idiosyncratic_shocks
) # Default parameter values for inf horiz model - including labor income with transitory and permanent shocks
init_portfolio['approxRiskyDstn'] = RiskyDstnFunc
init_portfolio['drawRiskyFunc'] = RiskyDrawFunc
init_portfolio[
'RiskyCount'] = 2 # Number of points in the approximation; 2 points is minimum
init_portfolio[
'RiskyShareCount'] = 25 # How many discrete points to allow for portfolio share
init_portfolio[
'Rfree'] = 1.0 # Riskfree return factor (interest rate is zero)
init_portfolio['CRRA'] = 6.0 # Relative risk aversion
# Uninteresting technical parameters:
init_portfolio['aXtraMax'] = 100
init_portfolio['aXtraCount'] = 50
init_portfolio[
'BoroCnstArt'] = 0.0 # important for theoretical reasons
init_portfolio[
'DiscFac'] = 0.92 # Make them impatient even wrt a riskfree return of 1.08
# Create portfolio choice consumer type
self.pcct = cpm.PortfolioConsumerType(**init_portfolio)
# %% {"code_folding": []}
# Solve the model under the given parameters
self.pcct.solve()
# %% Calibration and solution
# Import parameters from external file
sys.path.append(os.path.realpath('../'))
# Loading the parameters from the ../Code/Calibration/params.py script
from Calibration.params import dict_portfolio, time_params, det_income, Mu, Rfree, Std, norm_factor
# Create new dictionary
merton_dict = copy(dict_portfolio)
# Adjust certain parameters to align with Merton-Samuleson
# Log normal returns (Overwriting Noramal returns defined in params)
mu = Mu + Rfree
RiskyDstnFunc = cpm.RiskyDstnFactory(RiskyAvg=mu, RiskyStd=Std) # Generates nodes for integration
RiskyDrawFunc = cpm.LogNormalRiskyDstnDraw(RiskyAvg=mu, RiskyStd=Std) # Generates draws from the "true" distribution
# Make agent inifitely lived. Following parameter examples from ConsumptionSaving Notebook
merton_dict['approxRiskyDstn'] = RiskyDstnFunc
merton_dict['drawRiskyFunc'] = RiskyDrawFunc
agent = cpm.PortfolioConsumerType(**merton_dict)
agent.solve()
# %%
aMin = 0 # Minimum ratio of assets to income to plot
aMax = 1e5 # Maximum ratio of assets to income to plot
aPts = 1000 # Number of points to plot
# Campbell-Viceira (2002) approximation to optimal portfolio share in Merton-Samuelson (1969) model
# input a function that *draws* from the distribution in drawRiskyFunc
#
# Other assumptions:
# * distributions are time constant
# * probability of being allowed to reoptimize is time constant
# * If p < 1, you must specify the PortfolioSet discretely
#
# %% {"code_folding": []}
# Set up the model
# Parameters from Mehra and Prescott (1985):
Avg = 1.08 # equity premium
Std = 0.20 # standard deviation of rate-of-return shocks
RiskyDstnFunc = cpm.RiskyDstnFactory(RiskyAvg=Avg, RiskyStd=Std) # Generates nodes for integration
RiskyDrawFunc = cpm.LogNormalRiskyDstnDraw(RiskyAvg=Avg, RiskyStd=Std) # Generates draws from a lognormal distribution
init_portfolio = copy.copy(param.init_idiosyncratic_shocks) # Default parameter values for inf horiz model
init_portfolio['approxRiskyDstn'] = RiskyDstnFunc
init_portfolio['drawRiskyFunc'] = RiskyDrawFunc
init_portfolio['RiskyCount'] = 2 # Number of points in the approximation; 2 points is minimum
init_portfolio['RiskyShareCount'] = 25 # How many discrete points to allow in the share approximation
init_portfolio['Rfree'] = 1.0 # Riskfree return factor is 1 (interest rate is zero)
init_portfolio['CRRA'] = 6.0 # Relative risk aversion
# Uninteresting technical parameters:
init_portfolio['aXtraMax'] = 100
init_portfolio['aXtraCount'] = 50
init_portfolio['BoroCnstArt'] = 0.0 # important for theoretical reasons
# init_portfolio['vFuncBool'] = True # We do not need value function for purposes here