Intermediatebehavioral
Time Inconsistency: Why We Procrastinate
Overview
We plan to diet tomorrow, save next month, quit next year — and then don't. Time inconsistency is the gap between plans and actions: preferences reverse as the future becomes the present. Standard exponential discounting can't produce this; hyperbolic (present-biased) discounting can. This lesson explains the models, the evidence across saving/health/work, the welfare puzzles, and the commitment-device industry built to fight our future selves.
Learning objectives
- Define time inconsistency and preference reversals
- Contrast exponential vs. hyperbolic (β-δ) discounting
- Identify present bias in saving, health, and work
- Explain sophistication vs. naïveté about self-control
- Evaluate commitment devices and policy responses
The phenomenon
Prefer 110 tomorrow, but prefer 100 in 30 days? That's a preference reversal — the same 1-day wait, different choice depending on immediacy. We do this constantly: the dieter plans salad (future self) but eats cake (present self); the student plans to start the paper early; the smoker plans to quit Monday. Exponential discounting (constant rate) can never reverse like this — it discounts every delay proportionally. Something in us discounts the immediate future extra-steeply: present bias. The planner and the doer disagree, and the doer wins.
The signature test: the same trade-off decided differently when it's 'now vs. soon' versus 'later vs. later still.' Exponential discounters never reverse; humans routinely do.
The β-δ model
Laibson's quasi-hyperbolic model captures it simply: utility = u(now) + β·[δ·u(tomorrow) + δ²·u(day after) + ...]. The β (< 1) is present bias — an extra discount applied to everything not immediate. When β=1, it's standard exponential. This one parameter generates procrastination (costs now, benefits later get deferred), preproperation (doing pleasant things too early — the mirror bias), and demand for commitment. Sophisticates know their β<1 and seek commitment; naïfs think β=1 (tomorrow they'll be disciplined) and repeatedly fail. Partial naïveté — thinking you're more disciplined than you are — is the empirically common case, and the cruelest.
δ is ordinary patience (how you trade off two future dates); β is present bias (the extra penalty on anything not now). Two parameters, a world of self-control problems.
Evidence: saving, health, work
Saving: 401(k) non-participation despite matching money (free money refused — inertia plus present bias); 'save more tomorrow' schemes succeed by moving saving to the future. Health: gym memberships bought and unused (overestimating future attendance — naïveté); smoking, overeating, and missed medication all fit present bias. Work: students' deadline bunching (Ariely-Wertenbach: self-set deadlines help, but externally imposed help more); procrastination on filing, appointments, and admin. The pattern is domain-general: costs now/benefits later get deferred; benefits now/costs later get grabbed. Present bias is among behavioral economics' most replicated findings.
Sophisticates buy commitment; naïfs buy gym memberships they'll never use. Overconfidence about future self-control is what makes present bias expensive — the bias about the bias.
Commitment devices
The market for self-binding: Save More Tomorrow (commit future raises to savings — exploits naïveté benignly), deposit contracts (forfeit money if you fail — stickK.com), deadlines and penalties, automatic transfers (pay yourself first), website blockers, and 'temptation bundling' (only watch the show at the gym). What works: devices that are voluntary (sophisticates opt in), costly to break, and timely. What doesn't: relying on willpower, or commitments the naïve won't adopt. Policy versions: cooling-off periods, auto-enrollment, sin taxes (the sophisticated smoker may welcome cigarette taxes as commitment). The commitment industry exists because the demand for self-control is real and the supply of willpower isn't.
Benartzi-Thaler's scheme: commit future pay raises to savings. Joins present bias (future saving feels cheap) with loss aversion (never cut take-home pay) — savings rates tripled in trials.
Welfare puzzles
If preferences reverse, which self counts? The planner who wants to save or the doer who wants to spend? Behavioral welfare economics wrestles: Bernheim-Rangel count only 'true' (long-run) preferences; others use the planner's. Policy implications fork: sin taxes look like helpful commitment devices if the planner's welfare counts, paternalistic overreach if the doer's does. And there's a dark side: sophisticated firms exploit naïveté — gym contracts, credit-card teaser rates, subscription traps are commitment devices in reverse, monetizing present bias. Regulating 'behavioral exploitation' while preserving helpful commitment is the frontier policy challenge.
Key points
- Time inconsistency: preferences reverse as the future becomes present — plans say salad, actions say cake.
- The β-δ model: present bias (β<1) adds extra discounting to everything non-immediate; sophistication vs. naïveté about it matters enormously.
- Evidence spans saving (Save More Tomorrow), health (unused gym memberships), and work (deadline bunching).
- Commitment devices — deposits, deadlines, auto-transfers, temptation bundling — are the constructive response.
- Welfare puzzle: which self's preferences count? And firms exploit naïveté (subscription traps) — the policy frontier.
Common misconceptions
✓ Truth: It's a predictable preference structure (present bias), not a character flaw. Smart, motivated people procrastinate exactly as the model predicts — the planner/doer conflict is structural.
✓ Truth: Willpower is the scarcest input. The evidence favors design — commitment devices, defaults, automation — over exhortations to try harder.
✓ Truth: They help sophisticates — people wise enough to know their future self-control limits. Seeking commitment is a sign of self-knowledge, not weakness.
Practice questions
Q1. Time inconsistency is demonstrated by preference reversals such as:
- Preferring $100 today over $110 tomorrow but $110 in 31 days over $100 in 30 days
- Always choosing the larger amount
- Never saving
- Always procrastinating equally
The same one-day wait decided differently when immediate vs. distant — impossible under exponential discounting, natural under present bias (β-δ).
Q2. In the β-δ model, the β parameter captures:
- Ordinary patience about future trade-offs
- Present bias — the extra discount applied to everything not immediate
- Risk aversion
- Altruism
β<1 penalizes all future outcomes relative to now; δ handles ordinary time preference between future dates. Present bias is the distinctively behavioral parameter.
Q3. Save More Tomorrow works by:
- Forcing people to save
- Letting workers commit future raises to savings — future saving feels cheap to present-biased selves, and take-home pay never falls (loss aversion)
- Paying high interest
- Banning withdrawals
The design is present-bias-aware: commit now, save later (cheap to the present self), timed to raises so nominal pay never drops. Savings rates roughly tripled.
Click a question to reveal the answer and explanation.
Frequently asked questions
What is hyperbolic discounting?
Discounting where the implied discount rate falls with delay — steep for near delays, shallow for far ones. It generates preference reversals; the β-δ model is its tractable approximation.
What's the difference between sophisticates and naïfs?
Sophisticates know they'll be tempted and seek commitment; naïfs believe tomorrow they'll be disciplined and don't. Partial naïveté — overestimating future self-control — is most common and most costly.
Does present bias explain the retirement-savings crisis?
Largely: procrastination on enrollment, under-saving despite matching funds, and cash-outs all fit β-δ. Auto-enrollment and Save More Tomorrow are present-bias-aware fixes that work.
Are sin taxes paternalistic?
If smokers are time-inconsistent, cigarette taxes function as commitment devices sophisticates would endorse — 'asymmetric paternalism.' If smokers are rational, they're just distortionary. The welfare judgment hinges on which model is right.