def setUp(self):
# Create portfolio choice consumer type
self.pcct = cpm.PortfolioConsumerType()
self.pcct.cycles = 0
# Solve the model under the given parameters
self.pcct.solve()
def test_joint_dist(self):
# Create portfolio choice consumer type
self.joint_dist = cpm.PortfolioConsumerType()
self.joint_dist.IndepDstnBool = False
self.joint_dist.solve_one_period = make_one_period_oo_solver(
cpm.ConsPortfolioJointDistSolver)
# Solve model under given parameters
self.joint_dist.solve()
def test_discrete(self):
# Make example type of agent who can only choose risky share along discrete grid
init_discrete_share = cpm.init_portfolio.copy()
# PortfolioConsumerType requires vFuncBool to be True when DiscreteShareBool is True
init_discrete_share["DiscreteShareBool"] = True
init_discrete_share["vFuncBool"] = True
# Create portfolio choice consumer type
self.discrete = cpm.PortfolioConsumerType(**init_discrete_share)
# Solve model under given parameters
self.discrete.solve()
def test_sticky(self):
# Make another example type, but this one can only update their risky portfolio
# share in any particular period with 15% probability.
init_sticky_share = cpm.init_portfolio.copy()
init_sticky_share["AdjustPrb"] = 0.15
# Create portfolio choice consumer type
self.sticky = cpm.PortfolioConsumerType(**init_sticky_share)
# Solve the model under the given parameters
self.sticky.solve()
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()
def test_discrete_and_joint(self):
# Make example type of agent who can only choose risky share along
# discrete grid and income dist is correlated with risky dist
init_discrete_and_joint_share = cpm.init_portfolio.copy()
# PortfolioConsumerType requires vFuncBool to be True when DiscreteShareBool is True
init_discrete_and_joint_share["DiscreteShareBool"] = True
init_discrete_and_joint_share["vFuncBool"] = True
# Create portfolio choice consumer type
self.discrete_and_joint = cpm.PortfolioConsumerType(
**init_discrete_and_joint_share)
self.discrete_and_joint.IndepDstnBool = False
self.discrete_and_joint.solve_one_period = make_one_period_oo_solver(
cpm.ConsPortfolioJointDistSolver)
# Solve model under given parameters
self.discrete_and_joint.solve()
if __name__ == '__main__':
# Running as a script
my_file_path = os.path.abspath("../")
else:
# Running from do_ALL
my_file_path = os.path.dirname(os.path.abspath("do_ALL.py"))
my_file_path = os.path.join(my_file_path, "Code/Python/")
FigPath = os.path.join(my_file_path, "Figures/")
# %% Calibration and solution
sys.path.append(my_file_path)
# Loading the parameters from the ../Code/Calibration/params.py script
from Calibration.params import dict_portfolio, time_params
agent = cpm.PortfolioConsumerType(**dict_portfolio)
agent.solve()
# %% Run simulation and store results in a data frame
# Number of agents and periods in the simulation.
agent.AgentCount = 50 # Number of instances of the class to be simulated.
# Since agents can die, they are replaced by a new agent whenever they do.
# Number of periods to be simulated
agent.T_sim = agent.T_cycle * 50
# Set up the variables we want to keep track of.
agent.track_vars = [
'aNrmNow', 'cNrmNow', 'pLvlNow', 't_age', 'ShareNow', 'mNrmNow'
]
FigPath = os.path.join(my_file_path,"Figures/")
# %% 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
# In the discrete portfolio shares case, the user also must
# 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
# Do away with probability of death mpc_dict['LivPrb'] = [1] * dict_portfolio['T_cycle'] # Risky returns mu = 0.05 std = 0.1 # Construct the distribution approximation for integration RiskyDstnFunc = lambda count: approxLognormal(count, mu=mu, sigma=std) # Contruct function for drawing returns RiskyDrawFunc = lambda seed: drawLognormal(1, mu=mu, sigma=std, seed=seed) mpc_dict['approxRiskyDstn'] = RiskyDstnFunc mpc_dict['drawRiskyFunc'] = RiskyDrawFunc agent = cpm.PortfolioConsumerType(**mpc_dict) agent.cylces = 0 agent.solve() # %% Compute the theoretical MPC (for when there is no labor income) # First extract some parameter values that will be used crra = agent.CRRA sigma_r = std goth_r = mu + sigma_r**2 / 2 beta = agent.DiscFac # Compute E[Return factor ^(1-rho)] E_R_exp = np.exp((1 - crra) * goth_r - crra * (1 - crra) * sigma_r**2 / 2) # And the theoretical MPC
# No income shocks pf_dict['PermShkStd'] = [0] * t_cycle pf_dict['TranShkStd'] = [0] * t_cycle # Make agent live for sure until the terminal period pf_dict['T_retire'] = t_cycle pf_dict['LivPrb'] = [1] * t_cycle # Shut down income growth pf_dict['PermGroFac'] = [1] * t_cycle # Decrease grid for speed pf_dict['aXtraCount'] = 100 # %% Create both agents port_agent = cpm.PortfolioConsumerType(**pf_dict) port_agent.solve() pf_agent = cis.PerfForesightConsumerType(**pf_dict) pf_agent.solve() # %% Construct the analytical solution rho = pf_dict['CRRA'] R = pf_dict['Rfree'] Beta = pf_dict['DiscFac'] T = pf_dict['T_cycle'] + 1 thorn_r = (R * Beta)**(1 / rho) / R ht = lambda t: (1 - (1 / R)**(T - t + 1)) / (1 - 1 / R) - 1