Present Bias and Hyperbolic Discounting: Why Plans Change

Present bias is placing a heavy extra weight on right now, as against every other moment. Hyperbolic discounting is the name for the shape of curve that would produce it. Because that curve falls steeply at first and gently afterwards, one person can prefer patience while both options are distant and prefer impatience the moment one of them becomes immediate.

The whole mechanism rests on the difference between two shapes, and on nothing else. A curve that falls at a constant proportional rate keeps every ranking intact as time passes: what a person prefers for next March, they will still prefer when March arrives. A curve that falls steeply near the present and then flattens does not keep rankings intact, and the plan gets broken by the same person who made it, sincerely, a few weeks earlier. The reversal is a property of the shape rather than a property of the person. Good intentions therefore leave it intact, and the arrangements that beat it are structural rather than motivational. The whole demonstration runs on one person and two amounts of money.

What is discounting, before any curve is drawn?

DiscountingPlacing less weight on an amount because it arrives later rather than sooner. is simply the everyday fact that a rupee arriving later is worth less to the person receiving it than a rupee arriving now. No theory is needed to see it. A caterer taking a wedding booking offers to knock something off the bill for payment on the day of signing rather than on the day of the event. The household on the other side of the table would rather pay less now, so the offer works. A street vendor buying stock offers his supplier a smaller sum in cash today instead of a larger sum at the end of the month, and the supplier sometimes takes it.

The vendor and the caterer are both putting a number on waiting. If Rs 10,000/- today feels the same to a person as Rs 11,000/- in a month, then a month of waiting costs that person about a tenth of the amount, and that fraction is the discount for that month. Discounting is not a mistake and not a bias. Discounting is the ordinary business of comparing money that arrives at different times, and everybody does it. The bias is never in the fact of discounting; it is only ever in the shape of the discount as the delay stretches out. The shape of the discount is the only question worth asking, and the two shapes below are the two answers.

What does a constant-rate curve preserve?

Take the simplest possible answer to that question. Suppose a person takes a fixed proportion off for every month of waiting, the same proportion every month, no matter how far away the month is. Say a tenth. Then Rs 10,000/- promised in one month is worth Rs 9,000/- now, in two months Rs 8,100/-, in three months Rs 7,290/-, and so on down. A fixed proportion taken off every month is constant-rate discountingA curve that falls by the same proportion every period, which is what keeps a ranking from changing as the date approaches., and it is the shape the standard textbook assumes without ever remarking on it.

One property makes this shape special. Two options can be set against each other: Rs 10,000/- at some date, and Rs 12,000/- one month after that date. Under a constant tenth a month, the later amount is worth Rs 10,800/- when measured beside the sooner one, and that stays true wherever the pair is placed. Pushing both a year out leaves the later amount still worth exactly 8.0 per cent more than the sooner one. Under a constant rate the ranking between two options never depends on how far away they both are, so a plan made in advance is still the preferred plan when the date arrives. The person may be very patient or very impatient; either way they are consistent, and they do not surprise themselves.

What does a curve that is steeper near now destroy?

Now change one thing. Suppose the proportion taken off is large for the first month of waiting and gets smaller for each month after that. Waiting from today until next month costs a third of the amount. Waiting from month five to month six costs an eighth. The far future is discounted gently; the near future is discounted brutally. A discount that is brutal near the present and gentle far away is hyperbolic discountingA curve that falls steeply near the present and then flattens out, so distant delays cost far less per month than near ones., named for the shape of the curve, and it is the model Ainslie set out in Psychological Bulletin in 1975 after work on delayed reward.

The illustrative curve divides an amount by one plus half the number of months of delay. So Rs 10,000/- one month away is worth Rs 6,667/-, two months away Rs 5,000/-, three months away Rs 4,000/-, and six months away Rs 2,500/-. The monthly cost of waiting changes along that curve: the first month of delay takes 33.3 per cent, the second takes 25.0 per cent, the third 20.0 per cent, and by the sixth month a further month of waiting only costs 12.5 per cent. The defining property of this shape is not that it is steep but that its steepness itself changes, falling away as the delay grows, and that is exactly what a constant rate refuses to do. The changing steepness is what breaks plans. The half-per-month rule is an invented illustration chosen for round arithmetic, not a measured rate for anybody.

Present Bias vs Hyperbolic Discounting: are they two names for one thing?

Present bias and hyperbolic discounting are not the same thing, and keeping them apart is worth the effort. Present biasAn extra weight placed on right now specifically, over and above ordinary discounting of later amounts. is an observation about what people do: offered a choice between something now and something better shortly afterwards, they take the immediate one far more often than the same people take the immediate one when both options are moved back by a few months. Present bias is a finding. A finding can be recorded, counted and argued about without any curve being drawn at all.

Hyperbolic discounting is a model. The model is a proposed shape for the curve, and its virtue is that it would produce that finding automatically. The two are related the way a footprint is related to a boot. Present bias names the behaviour; hyperbolic discounting is one candidate explanation of it, and evidence for the behaviour is not by itself evidence for that particular curve. Other shapes produce reversals too, and a person could produce the same pattern for reasons that have nothing to do with a curve, such as not believing the later payment will actually arrive.

Laibson brought the shape into finance in Golden Eggs and Hyperbolic Discounting in the Quarterly Journal of Economics in 1997, working through what it implies for saving and for arrangements that are hard to undo. O'Donoghue and Rabin, in Doing It Now or Later in the American Economic Review in 1999, gave the preferences their working name and drew the distinction that matters most in practice. The distinction is whether a person knows their own future self will reverse. Somebody who knows it will set things up in advance. Somebody who does not know it keeps making plans and keeps being surprised.

Time Inconsistency: why does the same person make and then break the same plan?

Time inconsistencyPreferring one option while it is at a distance and the other one when the moment actually arrives, with nothing having changed in between. is what a steeper-near-now curve produces, and it is worth being precise about what has to be true for it to count. Nothing new is learned. No amount changes. No fact about either option changes. The gap between the two options stays exactly the same. All that happens is that the clock runs forward and both options come closer. And the ranking flips.

The household version is easier to feel than to derive. Take it first. In January somebody decides that the coming Diwali bonus will go straight into savings rather than into a new television. The January decision is sincere, taken with a clear head, about money that is ten months away. In October the bonus arrives, the shop is a five minute walk away, and the television is bought. Nothing about the household changed in those ten months. The television did not get better and the savings did not get worse. The only thing that moved was the distance to the money.

Time inconsistency is the signature of the shape, and it is detectable precisely because nothing except distance moved between the two answers. The absence of any other movement is what separates it from an ordinary change of mind. A person who reads something in October that changes their view of what savings are for has not been inconsistent; they have updated. A person who reverses on identical information, purely because the moment arrived, has produced time inconsistency.

Where exactly does the crossover sit in this example?

The reversal can be computed rather than described, and computing it is what turns an impression into a finding. Here is the pair, held fixed throughout: Rs 10,000/- at some delay, against Rs 12,000/- one month later than that. The curve divides an amount by one plus half the number of months of delay. Now push both options into the future together, one month at a time, and work out what each is worth today.

The crossoverThe delay at which two options are valued equally, so that the preference between them flips on either side of it. is not approximate and it is not a region. Set the two values equal and solve. The sooner option is Rs 10,000/- divided by one plus half the delay; the later is Rs 12,000/- divided by one and a half plus half the delay. Cross multiplying gives 15,000 plus 5,000 times the delay on one side and 12,000 plus 6,000 times the delay on the other, so 3,000 equals 1,000 times the delay, and the delay is exactly three months. At that point both come to Rs 4,000/-. Nothing about either amount changed and nothing about the one month between them changed: only the distance to both moved, and that alone reversed the preference.

What does the reversal look like in the decision log?

The Palash decision log is an invented record of 240 decisions taken by 60 investors over eight quarters, and Meera Sundaram is one of those investors. Rs 25,000/- a month leaves her account by standing instructionAn arrangement set up once that moves a fixed amount on a fixed date afterwards, without anybody deciding again each time., an arrangement she set up on a day when the transfers were all in the future. A standing instruction is the pure case of a plan made at a distance. Every one of those monthly transfers was chosen once, by a person for whom every single transfer was months away.

Now count what happened when the moments arrived. Of the 240 logged decisions, 96 were purchases, 84 were sales, 36 were switches and 24 were pauses of a standing instruction. The four counts sum to 240 exactly. So 24 decisions out of 240, being 10.0 per cent, were somebody stopping an arrangement they had previously set up to run without them. A standing instruction exists precisely so that the later decision never has to be taken. A pause is that decision being taken anyway, and it is the clearest artefact of this mechanism the log contains. One record of 60 people over eight quarters is not evidence that any rule works. A count that small describes those 60 investors and cannot be read as the rate at which people in general reopen an arrangement.

Why is this not simply impatience?

The impatience reading is the one most often made, and it is the one that matters most to correct. Impatience is a setting. An impatient person discounts everything heavily, and the crucial word is everything: near and far alike, at the same proportional rate. Their curve is steep, but it is steep in a constant way. An impatient person plans to take the money now, and when the day comes they take the money now. Their ranking never depended on how far away the pair was, so there is no reversal, no surprise and no broken plan.

The person with present bias behaves nothing like that. The present-biased person may be perfectly patient on average. Asked in March about a choice falling in December, they choose the larger later amount with conviction, and they mean it. Patience does not run out in December. One of the options has become immediate, the steep near end of their curve now applies to it and not to the other one, and the ranking turns over. Impatience and present bias are indistinguishable when the question is asked once, and completely distinguishable when it is asked twice at two different distances. The difference is testable, and asking the same question at two distances is the only reliable way to tell them apart.

What arrangements work against it, and why do they follow from the shape?

Once the reversal is accepted as coming from the shape of the curve rather than from a shortage of resolve, the design question answers itself. If the near end of the curve is steep, then any decision taken when the money is immediately available will be taken by that steep end. So an arrangement that works does not help the person win the later decision. An arrangement that works removes the later decision, leaving nothing there to be lost. Removing the decision is what a commitmentAn arrangement made in advance that removes or raises the cost of a decision that would otherwise be taken later. arrangement is, and every version of it shares that one property.

Three shapes recur. An arrangement made once and running by itself. Carrying out the plan then requires nothing, and stopping it requires an action. A setting where the patient outcome happens unless somebody actively escapes it. The effort then sits on the side of the reversal rather than on the side of the plan. And an arrangement that is genuinely awkward to reverse. The moment of temptation then runs into friction the distant self installed on purpose. Every arrangement that beats this mechanism works by letting the distant self decide once, rather than by helping the present self decide well repeatedly. Thaler and Sunstein set out the general design principle in Nudge in 2008, and Laibson's 1997 paper is where the case for hard-to-undo arrangements is worked through against exactly this curve.

Two honest cautions belong with the design. First, the shape of the curve explains why arrangements of this kind work at all, and which arrangement suits a particular household is a matter of suitability and appropriateness rather than of the curve. Second, the same friction that protects a plan also blocks a genuine change of mind, and a person whose circumstances really have changed now has to fight the arrangement they built. The cost is real, it is the price of the design, and pretending otherwise would misrepresent how these arrangements behave.

When is a preference for now entirely reasonable?

Wanting money sooner is often exactly right, and several perfectly good reasons produce it. A later payment might not arrive at all, and a discount for that risk is not a bias but an assessment. A household two months from an unavoidable expense has a genuine use for money now that money in six months cannot serve. Somebody paying interest at a high rate on borrowing is losing real money every month they wait.

None of these is present bias, and the test separates them cleanly. A reason that is genuinely about the situation applies whenever the question is asked. Present bias appears only when one of the options has become immediate, and vanishes when both are moved back. The same question put to somebody at two distances settles it: if the reason is real, the answer holds. If the answer flips while the reason has not changed at all, the distance did the work. The rate of discount anybody ought to apply to anything is a question of valuation rather than of behaviour.

What does present bias not explain?

A named mechanism earns trust by refusing the cases it does not cover, and this one covers less than it is usually asked to. Present bias does not explain a decision that was never revisited. Nothing reverses if nobody reopens anything, and a plan quietly left running is a different situation entirely. Present bias does not explain a change of mind that followed new information either. Updating on evidence is what a careful decision looks like, and reversing on identical evidence is not.

Present bias also does not explain the direction of a mistake in any general sense. Present bias predicts a reversal toward whichever option becomes immediate, and that is all. If somebody consistently prefers the immediate option at every distance, that is a steep constant curve and not this mechanism. The claim made here is narrow: a ranking flips as distance to both options shrinks, with everything else held still, and any explanation that needs something else to have changed is an explanation of something other than present bias.

How does somebody actually use this when reading a decision record?

Devika Rao, the adviser at the invented Palash Advisory Services Private Limited, reads the log rather than the person. She looks for a pair of entries: a choice recorded at a distance and a contrary choice recorded when the moment arrived, with nothing in between that would justify the change. The impatient person and the present-biased person both produce a single entry showing somebody taking money now, so one entry tells her almost nothing. Two entries at two distances tell her a great deal, and that is why the date on an entry matters as much as its content.

A person deciding alone can run the same check without an adviser, and it costs nothing. Write down the choice before the moment arrives, with the date. When the moment comes and the choice goes the other way, the written line is there to be read. Writing the distant decision down binds nobody. The value of writing it down is that it makes the reversal visible instead of leaving it feeling like an ordinary change of mind. Across quarters five to eight the 20 investors who adopted a written checklist recorded a reason on 34 of their 41 decisions, being 82.9 per cent, against 19 of 63, being 30.2 per cent, for the other 40. Eight quarters and 60 invented people could not establish that a written checklist changes anybody's returns.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited and the Palash decision log are invented.
Educational material. Not advice on any investment, tax, budget or market position.