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utilities.py
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utilities.py
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import numpy as np
import squigglepy as sq
# from squigglepy import K, M
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import create_style_script as css
# Use custom plot style
plt.rcParams.update(css.mplstyle)
#plt.style.use('plot_style.mplstyle')
def gen_market_returns(n, mean, sd, m):
"""
Generate the market returns for each year.
Parameters:
n (int): The number of years.
mean (float): The mean market return.
sd (float): The standard deviation of market returns.
Returns:
ndarray: The market returns for each year.
"""
return [sq.norm(mean=mean, sd=sd) @ n for m in range(m)]
def gen_ar_income(n, ar_coefficients, start, sd, baseline, min_income, m):
"""
Generate m paths of n years of income following an AR(p) process with deviations from a lifecycle baseline.
Parameters:
n (int): The number of years.
ar_coefficients (list): The coefficients of the AR process.
start (float): The starting income.
sd (float): The standard deviation of the random shocks.
baseline (array): The baseline income for each year.
min_income (float): The minimum income.
m (int): The number of paths.
Returns:
ndarray: An m x n array where each row is a different path.
"""
p = len(ar_coefficients)
income = np.full((m, n), start) # initialize income array
shocks = np.zeros((m, n)) # initialize shocks array
shocks[:, :p] = np.random.normal(0, sd, (m, p)) # initialize first p shocks
for i in range(m):
for t in range(p, n):
# Calculate the new shock value based on the AR process
new_shock = np.dot(
ar_coefficients, shocks[i, t - p : t][::-1]
) + np.random.normal(0, sd)
shocks[i, t] = new_shock # update the shock for path i at year t
# Compute the income for year t
income[i, t] = max(baseline[t] + new_shock, min_income)
return income
def gen_combined_income(n, ar_coefficients, start, sd, baseline, min_income, m, years_until_retirement, retirement_income, interest_rate_cumulative):
"""
Generate m paths of n years of income, combining pre-retirement and post-retirement income.
Parameters:
n (int): The number of years.
ar_coefficients (list): The coefficients of the AR process.
start (float): The starting income.
sd (float): The standard deviation of the random shocks.
baseline (array): The baseline income for each year.
min_income (float): The minimum income.
m (int): The number of paths.
years_until_retirement (int): The number of years until retirement.
retirement_income (float): The retirement income.
interest_rate_cumulative (ndarray): The cumulative interest rate for each year.
Returns:
ndarray: An m x n array where each row is a different path.
"""
# Generate pre-retirement income
pre_retirement_income = gen_ar_income(
years_until_retirement,
ar_coefficients,
start,
sd,
baseline[:years_until_retirement],
min_income,
m,
)
# Generate post-retirement income
if n > years_until_retirement:
post_retirement_income = np.zeros((m, n - years_until_retirement))
for t in range(n - years_until_retirement):
post_retirement_income[:, t] = retirement_income * interest_rate_cumulative[:, years_until_retirement + t]
# Combine pre-retirement and post-retirement income
combined_income = np.hstack((pre_retirement_income, post_retirement_income))
else:
combined_income = pre_retirement_income
return combined_income
def gen_ar_inflation(n, ar_coefficients, sd, inflation_rate, m):
"""
Generate m paths of n years of inflation following an AR(p) process with deviations from an inflation rate baseline.
Parameters:
n (int): The number of years.
ar_coefficients (list): The coefficients of the AR process.
sd (float): The standard deviation of the random shocks.
inflation_rate (float): The baseline inflation rate for each year.
m (int): The number of paths.
Returns:
ndarray: An m x n array where each row is a different path.
"""
p = len(ar_coefficients)
inflation = np.full((m, n), inflation_rate) # initialize inflation array
shocks = np.zeros((m, n)) # initialize shocks array
shocks[:, :p] = np.random.normal(0, sd, (m, p)) # initialize first p shocks
for i in range(m):
for t in range(p, n):
# Calculate the new shock value based on the AR process
new_shock = np.dot(
ar_coefficients, shocks[i, t - p : t][::-1]
) + np.random.normal(0, sd)
shocks[i, t] = new_shock # update the shock for path i at year t
# Compute the inflation for year t
inflation[i, t] = inflation_rate + new_shock
return inflation
def financial_life_model(input_params):
"""
Simulate the financial life of an individual over a certain number of years.
Parameters:
input_params (tuple): A tuple containing the following inputs:
m (int): The number of paths to simulate.
years (int): The number of years to simulate.
cash_start (float): The initial cash.
market_start (float): The initial market wealth.
income_start (float): The initial income.
life_cycle_income (float): The baseline lifecycle income.
min_income (float): The minimum level of income.
min_cash (float): The minimum level of cash.
min_market (float): The minimum level of market wealth.
inflation_rate (float): The inflation rate.
ar_income_coefficients (list): The coefficients of the AR process for income.
ar_income_sd (float): The standard deviation of the AR process for income.
ar_inflation_coefficients (list): The coefficients of the AR process for inflation.
ar_inflation_sd (float): The standard deviation of the AR process for inflation.
r (float): The constant risk-free interest rate.
proportion_dissavings_from_cash (float): The proportion of dissavings that comes from cash.
beta (float): The discount factor.
alpha (float): The coefficient of relative risk aversion.
Returns:
dict: A dictionary containing the simulated paths of income, inflation, cash, market, wealth, consumption, savings and non_financial_wealth.
"""
# Unpack parameters
m = input_params["m"]
years = input_params["years"]
# income_start = input_params["income_start"]
life_cycle_income = input_params["life_cycle_income"]
min_income = input_params["min_income"]
inflation_rate = input_params["inflation_rate"]
ar_income_coefficients = input_params["ar_income_coefficients"]
ar_income_sd = input_params["ar_income_sd"]
ar_inflation_coefficients = input_params["ar_inflation_coefficients"]
ar_inflation_sd = input_params["ar_inflation_sd"]
r = input_params["r"]
years_until_retirement = input_params["years_until_retirement"]
years_until_death = input_params["years_until_death"]
retirement_income = input_params["retirement_income"]
wealth_fraction_consumed_after_retirement = input_params["wealth_fraction_consumed_after_retirement"]
# Preallocate arrays
income = np.zeros((m, years))
inflation = np.zeros((m, years))
cash = np.zeros((m, years))
market = np.zeros((m, years))
financial_wealth = cash + market
consumption = np.zeros((m, years))
savings = np.zeros((m, years))
non_financial_wealth = np.zeros((m, years))
total_wealth = financial_wealth + non_financial_wealth
inflation = gen_ar_inflation(
years,
ar_inflation_coefficients,
ar_inflation_sd,
inflation_rate,
m,
)
market_returns = gen_market_returns(years, 0.05, 0.15, m)
# Derived parameters
# marginal_propensity_to_consume = r / (1 + r)
cumulative_inflation = np.cumprod(1 + inflation, axis=1)
real_interest_rate = r - inflation
interest_rate_cumulative = np.cumprod(1 + (r - np.zeros((m, years))), axis=1)
market_returns = market_returns / cumulative_inflation
# Generate income, inflation, and market returns paths
income = gen_combined_income(
years,
ar_income_coefficients,
life_cycle_income[0],
ar_income_sd,
life_cycle_income,
min_income,
m,
years_until_retirement,
retirement_income,
interest_rate_cumulative
)
income = np.maximum(income, min_income) / cumulative_inflation
for i in range(m):
# Set initial conditions
non_financial_wealth[i, 0] = income[i, 0:].sum()
financial_wealth[i, 0] = input_params["cash_start"] + input_params["market_start"]
total_wealth[i, 0] = financial_wealth[i, 0] + non_financial_wealth[i, 0]
remaining_total_wealth_annualized = (total_wealth[i, 0] - income[i, 0]) / years
consumption[i, 0] = (
input_params["income_fraction_consumed"] * income[i, 0]
+ input_params["wealth_fraction_consumed_before_retirement"] * remaining_total_wealth_annualized
)
savings[i, 0] = income[i, 0] - consumption[i, 0]
cash[i, 0] = input_params["cash_start"] + savings[i, 0]
market[i, 0] = input_params["market_start"] * (1 + market_returns[i, 0])
non_financial_wealth[i, 0] = income[i, 0:].sum()
financial_wealth[i, 0] = cash[i, 0] + market[i, 0]
total_wealth[i, 0] = financial_wealth[i, 0] + non_financial_wealth[i, 0]
for t in range(1, years):
# Adjust cash and market wealth before considering income and consumption
if cash[i, t - 1] < input_params["min_cash_threshold"]:
transfer_to_cash = min(input_params["min_cash_threshold"] - cash[i, t - 1], market[i, t - 1])
cash[i, t - 1] += transfer_to_cash
market[i, t - 1] -= transfer_to_cash
elif cash[i, t - 1] > input_params["max_cash_threshold"]:
transfer_to_market = cash[i, t - 1] - input_params["max_cash_threshold"]
cash[i, t - 1] -= transfer_to_market
market[i, t - 1] += transfer_to_market
non_financial_wealth[i, t] = income[
i, t:
].sum() # Sum of future income is the non-financial wealth
total_wealth[i, t] = (
financial_wealth[i, t - 1] + non_financial_wealth[i, t]
) # Total wealth is sum of financial and non-financial wealth
remaining_total_wealth_annualized = (total_wealth[i, t - 1] - income[i, t]) / (years - t)
# Compute desired consumption
if t < years_until_retirement:
consumption_from_income = input_params["income_fraction_consumed"] * income[i, t]
consumption_from_wealth = input_params["wealth_fraction_consumed_before_retirement"] * remaining_total_wealth_annualized
else:
consumption_from_income = retirement_income
consumption_from_wealth = wealth_fraction_consumed_after_retirement * remaining_total_wealth_annualized
desired_consumption = consumption_from_income + consumption_from_wealth
# Get total savings at time t
total_savings = cash[i, t - 1] + market[i, t - 1]
# If desired consumption is greater than total savings, adjust consumption
if desired_consumption > total_savings:
# Cannot consume more than total savings
consumption[i, t] = total_savings
else:
consumption[i, t] = desired_consumption
# Compute savings and allocate them to cash and market
#if t < years_until_retirement:
savings[i, t] = income[i, t] - consumption[i, t]
if cash[i, t - 1] < input_params["max_cash_threshold"]:
savings_to_cash = min(savings[i, t], input_params["max_cash_threshold"] - cash[i, t - 1])
savings_to_market = max(0, savings[i, t] - savings_to_cash)
else:
savings_to_cash = 0
savings_to_market = savings[i, t]
#else:
# savings[i, t] = 0
# Update cash and market wealth
cash[i, t] = cash[i, t - 1] * (1 + r) + savings_to_cash
market[i, t] = market[i, t - 1] * (1 + market_returns[i, t]) + savings_to_market
# Compute dissavings and adjust cash and market wealth
dissavings = max(0, - savings[i, t])
if cash[i, t] > input_params["min_cash_threshold"]:
dissavings_from_cash = min(dissavings, cash[i, t] - input_params["min_cash_threshold"])
dissavings_from_market = max(0, dissavings - dissavings_from_cash)
else:
dissavings_from_cash = 0
dissavings_from_market = dissavings
cash[i, t] = max(0, cash[i, t] - dissavings_from_cash)
market[i, t] = max(0, market[i, t] - dissavings_from_market)
# Compute financial wealth
financial_wealth[i, t] = cash[i, t] + market[i, t]
model_output = {
"income": income,
"inflation": inflation,
"cash": cash,
"market": market,
"financial_wealth": financial_wealth,
"consumption": consumption,
"savings": savings,
"non_financial_wealth": non_financial_wealth,
"total_wealth": total_wealth,
}
return model_output
def plot_model_output(
model_output,
variables=None,
alpha=0.03,
mean_line_alpha=1,
#line_color="red",
mean_line_width=2,
#background_color="black"
show_grid=True, # new option to control grid lines
grid_alpha=0.1, # option to control the transparency of grid lines
grid_style='dashed', # option to control the style of grid lines
plot_credibility_interval=True,
credibility_intervals=[0.5, 0.8, 0.95] # list of quantiles for intervals
):
"""
This function plots the output of the financial life model.
Parameters:
- model_output: A dictionary where keys are labels and values are np.array of time series data.
- variables: A list of variables to plot. If None, all variables are plotted. Default is None.
- alpha: Transparency for individual paths. Default is 0.2.
- mean_line_alpha: Transparency for mean path. Default is 1 (no transparency).
- mean_line_color: Color for mean path. Default is 'red'.
- mean_line_width: Line width for mean path. Default is 2.
- show_grid: Boolean indicating whether to show grid lines or not. Default is False.
- grid_alpha: Transparency for grid lines. Default is 0.1.
- grid_style: Style for grid lines. Default is 'dashed'.
Returns:
- Nothing, but it shows a matplotlib plot.
"""
# Filter variables
if variables is not None:
model_output = {k: v for k, v in model_output.items() if k in variables}
# Create a figure and a set of subplots
ncols=1
nrows=len(model_output.keys())
fig, axs = plt.subplots(
nrows=nrows,
ncols=ncols,
figsize=(6 * ncols, 3 * nrows)
)
# Check if axs is an instance of Axes
if isinstance(axs, np.ndarray):
axs_iter = axs.flatten()
else:
axs_iter = np.array([axs])
# This will remove top/right box/border around the subplots
for ax in axs_iter:
for spine in ["top", "right"]:
ax.spines[spine].set_visible(False)
# Format y axis as currency
formatter = ticker.FormatStrFormatter("$%1.0f")
formatter = ticker.FuncFormatter(lambda x, pos: "${:,.0f}".format(x))
# Flatten the axs array and iterate over it and the items in the dictionary at the same time
for ax, (key, value) in zip(axs_iter, model_output.items()):
# Transpose the data
value = np.transpose(value)
# Plot mean path
ax.plot(
value.mean(axis=1),
color=css.primary_color,
alpha=mean_line_alpha,
linewidth=mean_line_width,
)
# Plot credibility intervals or individual paths
if plot_credibility_interval:
sorted_values = np.sort(value, axis=1) # sort values for each time step
for i in range(len(credibility_intervals)-1, -1, -1): # iterate over intervals in reverse order
lower_quantile = (1-credibility_intervals[i]) / 2 # calculate lower quantile
upper_quantile = 1 - lower_quantile # calculate upper quantile
ax.fill_between(
range(value.shape[0]), # x values (time steps)
np.quantile(sorted_values, lower_quantile, axis=1), # lower y values (lower quantile)
np.quantile(sorted_values, upper_quantile, axis=1), # upper y values (upper quantile)
color=css.primary_color,
alpha=0.3 * (i + 1) / len(credibility_intervals), # transparency
label=f'{int(credibility_intervals[i]*100)}% credibility interval' # label for legend
)
ax.legend() # show legend
else:
ax.plot(
value,
color=css.primary_color,
alpha=alpha
)
ax.set_title(key.replace("_", " ").title()) # prettify title
ax.yaxis.set_major_formatter(formatter) # format y axis with comma separator
if show_grid: # condition to plot grid lines if show_grid is True
ax.grid(color=css.primary_color, linestyle=grid_style, linewidth=0.5, alpha=grid_alpha)
#ax.set_facecolor(background_color) # set background color
if np.min(value) >= 0:
ax.set_ylim(bottom=0)
try:
if len(model_output.keys()) % 2 != 0:
fig.delaxes(axs[-1, -1])
except:
pass
# Hide x labels and tick labels for top plots and y ticks for right plots.
# for ax in axs.flat:
# ax.label_outer()
try:
for ax in axs[-1, :]:
ax.set_xlabel("Years from present")
except:
try:
for i in range(len(axs_iter)):
axs[i].set_xlabel("Years from present")
except:
axs.set_xlabel("Years from present")
try:
for ax in axs[:, -0]:
ax.set_ylabel("2023 USD")
except:
try:
axs[0].set_ylabel("2023 USD")
except:
axs.set_ylabel("2023 USD")
plt.tight_layout()
# plt.show()
return fig