Suspicious Discontinuities (2020)

If you spent any time browsing personal finance communities late last year, you likely encountered a strange phenomenon: individuals desperately seeking ways to lose money before December 31st.

One popular strategy involved purchasing put options that were almost certain to expire worthless. By doing this, the buyer could effectively manufacture a financial loss.

The "Subsidy Cliff"

The motivation behind this behavior often stems from the U.S. health insurance system. Specifically, there is a rigid income ceiling for receiving subsidies. For a single person, this cutoff is ** $48,560** (though it scales for families, e.g.,$ 100,400 for a household of four).

While variables like age, geography, and plan type can shift the numbers, a person crossing this threshold might see their annual insurance premiums jump by approximately $7,200.

The Mathematical Incentive

Consider an individual earning $55,000. Their financial situation looks like this:

$\text{Effective Income} = \$55,000 - \text{Losses}$

If they can reduce their reported income by $\$ 6,440 $to fall under the$ $48,560 $limit, they save$ $7,200$ in premiums. This results in a net gain.

Scenario	Gross Income	Loss Strategy	Subsidy Status	Net Financial Position
A	$55,000	None	$\text{No Subsidy}$	Base
B	$55,000	$-\$ 6,440$	$\text{Subsidized}$	$\text{Base} - \$ 6,440 + $7,200 = \text{Base} + $760$

Consequently, the system creates a ~~incentive to earn more~~ disincentive to increase earnings.

Systemic Discontinuities

Tax and benefit policies are riddled with these "sharp edges." Other examples include:

TANF (Temporary Assistance for Needy Families) limits.
Medicaid eligibility thresholds.
CHIP (Children's Health Insurance Program):
- Limits for free coverage.
- Limits for reduced-cost coverage.

While TANF and Medicaid generally target low-income brackets, CHIP thresholds often extend into the middle class. Regardless of the bracket, the result is the same: a "suspicious discontinuity" where losing money becomes the rational choice.

The Ethics of Tax Avoidance

Regarding the legitimacy of these maneuvers, one might recall the perspective of Judge Learned Hand:

"Anyone may arrange his affairs so that his taxes shall be as low as possible; he is not bound to choose that pattern which best pays the treasury."

The courts have consistently maintained that minimizing tax liability is not "sinister." Whether rich or poor, no citizen is legally obligated to pay more than the minimum required by law.

However, from a systemic view, a policy that encourages citizens to transfer wealth to wealthy options traders just to keep their insurance is objectively sub-optimal.

Proposed Solution: Smoothing

The fix is straightforward: replace hard thresholds with slow phase-outs.

Analogies in Technology

Queue Management

In hardware or software, a "naive queue" exhibits similar discontinuous behavior. This can lead to unfair outcomes, particularly for "bursty" workloads. A workload with low average bandwidth but high peaks might suffer more packet drops than a steady, high-bandwidth stream.

To solve this, engineers use Random Early Detection (RED). Instead of waiting for the queue to be 100% full, the system drops packets based on a probability tied to the current queue depth.

def random_early_drop(queue_fullness):
    # Instead of: if fullness == 1.0: drop()
    # We use a probability curve:
    drop_probability = calculate_prob(queue_fullness)
    if random.random() < drop_probability:
        return "DROP"
    return "KEEP"

Link Aggregators

A similar logic applies to sites like Reddit or Hacker News. There is a massive discontinuity in traffic between a post that is "on the front page" and one that is not. It is essentially a queue where $N$ votes trigger a massive surge, while $N-1$ votes result in relative obscurity.

Education and the Pell Grant

Universities often use Pell Grant eligibility as a proxy to measure their commitment to low-income students. This has created a perverse set of incentives:

The Admission Gap: Students below the Pell threshold see a higher admission probability; those above it see a lower one.
The Internal Paradox:
- Among non-qualifiers, the poorest are hit hardest.
- Among qualifiers, the wealthiest benefit the most.

Gaming the Admissions Process

Savvy parents have noticed this discontinuity. To increase their child's chances of admission to a selective college, they may employ the same tactics used for ACA subsidies:

Contribute to a traditional IRA instead of a Roth IRA.
Intentionally lose money on options trading.

By artificially depressing their income below the Pell Grant threshold, they "buy" a higher probability of admission.

Election Statistics

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