hurdle_rate insensitivity

[sternluke]

Increasing the hurdle_rate does not seem to limit the frequency or magnitude of investing as I would expect. For example, I see very similar investing behavour for hurdle_rate=0.125 and hurdle_rate=0.75

hurdle_rate=0.125 output:

hurdle_rate=0.75 output:

[jose-moran]

Automated Code Analysis (LLM-assisted)

This analysis was generated using automated code review with LLM assistance.

Root Cause Identified

The hurdle rate insensitivity is caused by the formula in compute_hurdle_adjusted_value() (productivity_investment_planner.py:151-185).

The formula computes the present value of perpetual cost savings:

hurdle_value = cost_reduction_per_period * (1 + r_h) / r_h

This produces values that are always much larger than the candidate investment:

Hurdle Rate	Discount Factor	Hurdle Value	Ratio to Investment
0.05	21.00	$5,274,962	527.5x
0.15	7.67	$1,925,780	192.6x
0.25	5.00	$1,255,943	125.6x
0.50	3.00	$753,566	75.4x
0.75	2.33	$586,107	58.6x
1.00	2.00	$502,377	50.2x

The profitability check hurdle_value > candidate_investment is always true because:

1. The perpetuity formula gives a very high present value
2. Cost reduction per period = $251,189 (for typical parameters)
3. Even at r_h=1.0, this gives hurdle_value = $502,377 vs candidate = $10,000

Proposed Fix Options

1. Use NPV instead of perpetuity PV: Compare investment cost against finite-horizon cost savings
2. Change profitability criterion: Use marginal return rate instead of absolute comparison
3. Apply the correct formula from investment_decision.md: The condition should be $(I/Y)^{1-α} ≤ φ * (1+r_h)/r_h$

Reproduction Code

import numpy as np
from macromodel.agents.firms.func.productivity_investment_planner import SimpleProductivityInvestmentPlanner

n_firms = 5
planner = SimpleProductivityInvestmentPlanner(
    n_firms=n_firms,
    hurdle_rate=0.75,  # Very high hurdle rate
    max_investment_fraction=0.1,
    investment_effectiveness=0.1,
    investment_elasticity=0.3,
    investment_propensity=0.2,
)

current_tfp = np.ones(n_firms)
current_production = np.full(n_firms, 1_000_000.0)
current_unit_costs = np.full(n_firms, 10.0)
available_cash = np.full(n_firms, 500_000.0)

total_inv, _, _ = planner.plan_productivity_investment(
    current_tfp=current_tfp,
    current_production=current_production,
    current_unit_costs=current_unit_costs,
    available_cash=available_cash,
    current_prices=np.ones(18),
    n_industries=18,
    input_usage=np.ones((n_firms, 18)),
    current_tech_multipliers=np.ones((n_firms, 18)),
    substitution_bundle_matrix=None,
)

print(f"Investment with hurdle_rate=0.75: {total_inv[0]:,.0f}")
# Output: Investment with hurdle_rate=0.75: 10,000 (same as with hurdle_rate=0.05)

[sternluke]

Unfortunately, I am still observing that is_investment_profitable() consistently returns True independent of hurdle_rate.

For hurdle_rate = 0.75:
lhs ranges from 0.1 to 0.0 while rhs = 0.7 resulting in is_investment_profitable() = True for all timesteps

For hurdle_rate = 0.125:
lhs ranges from 0.1 to 0.01 while rhs = 2.699 resulting in is_investment_profitable() = True for all timesteps

As a result extra_capital_qty outputs are the same for both hurdle_rates:

hurdle_rate = 0.125:

Timestep: 0, Year: 2014, Month:0
unconstrained_target_capital_inputs [1][16] 3.8032e+05
planned_investment [1] 9.4609e+06
weights/safe_prices [1][16] 8.1944e-04
extra_capital_qty [1][16] 7.7527e+03
BEFORE target_capital_inputs [1][16] 3.8032e+05
AFTER target_capital_inputs [1][16] 3.8807e+05

Timestep: 1, Year: 2014, Month:3
unconstrained_target_capital_inputs [1][16] 3.8032e+05
planned_investment [1] 9.3784e+06
weights/safe_prices [1][16] 8.2556e-04
extra_capital_qty [1][16] 7.8094e+03
BEFORE target_capital_inputs [1][16] 3.8032e+05
AFTER target_capital_inputs [1][16] 3.8813e+05

Timestep: 2, Year: 2014, Month:6
unconstrained_target_capital_inputs [1][16] 3.8370e+05
planned_investment [1] 9.3927e+06
weights/safe_prices [1][16] 8.2205e-04
extra_capital_qty [1][16] 7.8752e+03
BEFORE target_capital_inputs [1][16] 3.8370e+05
AFTER target_capital_inputs [1][16] 3.9157e+05

hurdle_rate = 0.75:

Timestep: 0, Year: 2014, Month:0
unconstrained_target_capital_inputs [1][16] 3.8032e+05
planned_investment [1] 9.4609e+06
weights/safe_prices [1][16] 8.1944e-04
extra_capital_qty [1][16] 7.7527e+03
BEFORE target_capital_inputs [1][16] 3.8032e+05
AFTER target_capital_inputs [1][16] 3.8807e+05

Timestep: 1, Year: 2014, Month:3
unconstrained_target_capital_inputs [1][16] 3.8032e+05
planned_investment [1] 9.3784e+06
weights/safe_prices [1][16] 8.2556e-04
extra_capital_qty [1][16] 7.8094e+03
BEFORE target_capital_inputs [1][16] 3.8032e+05
AFTER target_capital_inputs [1][16] 3.8813e+05

Timestep: 2, Year: 2014, Month:6
unconstrained_target_capital_inputs [1][16] 3.8370e+05
planned_investment [1] 9.3927e+06
weights/safe_prices [1][16] 8.2205e-04
extra_capital_qty [1][16] 7.8752e+03
BEFORE target_capital_inputs [1][16] 3.8370e+05
AFTER target_capital_inputs [1][16] 3.9157e+05