The Impatience

The person who resolves to save next month may be quite sincere, and so may the person who spends when next month arrives. The difficulty is that they are the same person. No new need has appeared, no promised income has vanished; the sacrifice has simply moved from the future into the present, and its weight has changed. This is a different problem from the preference for earlier enjoyment examined in The Agio. Someone can be strongly impatient and still carry out every plan, provided the terms of the comparison remain consistent as the dates approach. Present bias names the additional pull of immediacy, the force by which a future decision looks acceptable until it becomes today's decision. It makes the rate within the person less settled than the rate written on a loan. A contract can promise exactly what the next year will cost. The borrower may have a harder time promising what next year's self will be willing to do. The question of impatience therefore returns at the end of this volume in a changed form: whose valuation of waiting does the price of time answer when the same person values it differently as time passes?

Exponential discounting supplies the benchmark because it preserves the relative weights of future dates as the present advances. If each additional period multiplies a reward's value by the same factor, then moving two rewards equally closer removes a common discount from both. Their ranking need not change merely because the calendar has turned. A person can prefer a smaller reward sooner, or a larger reward later; either preference can survive the journey toward the dates at which the rewards arrive. Consistency here is a property of the comparison, not proof of wisdom, generosity or foresight. It also assumes that the relevant circumstances, information and preferences over the goods themselves have not changed. Hunger, sickness or news about a threatened payment can properly alter a choice. The puzzle begins after those explanations are held aside: the earlier plan is overturned by proximity alone. That departure from the exponential benchmark is one reason a single constant discount rate can describe some intertemporal choices poorly.¹ The benchmark remains valuable because it makes the departure intelligible. It shows that impatience and inconsistency are different dimensions of conduct, even though ordinary language often gives them the same reproachful name.

Hyperbolic discounting gives the near future a steeper discount than the distant future. In the simple form D(t) = 1/(1 + kt), with a positive k, an additional delay takes a larger proportional bite near the present than far away. The curve can therefore reverse the ranking of a smaller, earlier benefit and a larger, later one as both approach. Laibson's tractable version separates the special pull of now from the continuing discount applied afterward: today's utility receives weight one, while utility t periods ahead receives βδ^t. With β below one, the first step into the future carries an extra reduction; subsequent steps are discounted at the steady factor δ.² This is quasi-hyperbolic discounting, not the exact hyperbola. Its usefulness is that two forces can be inspected separately. A person can be fairly patient about the distance between two future dates and still be reluctant to cross the boundary from today to tomorrow. The annual interest rate on a savings account does not have two such parameters, and neither behavioral parameter can simply be read from that account's quoted yield.

A small calculation shows what the extra weight on the present can do. Imagine two certain, isolated benefits, measured directly in utility: one hundred units tomorrow or one hundred and twenty the following day. Let β be 0.8 and δ be 0.99, and hold everything else fixed. Seen today, the earlier benefit has weight-adjusted value 79.2, while the later one has value about 94.09; the person plans to wait. When tomorrow becomes today, the same comparison is one hundred now against 95.04 for waiting another day, and the plan reverses.³ No market price has moved, and no new information explains the change. The earlier benefit has acquired the privilege of being immediate. The numbers are constructed to display the mechanism, not to diagnose a reader or estimate a population. They also explain why the promise to become prudent next month can renew itself indefinitely. From each present, the future contains a patient person willing to bear the cost; when that person's appointed day arrives, he discovers that he too has a present to defend.

Someone who anticipates the reversal can try to alter the choices that will be available when it occurs. Money can be placed where it takes time to retrieve, a commitment can be made before the temptation arrives, or a rule can settle a decision that would otherwise be reopened each day. Laibson's model gives this thought an economic form through an asset that cannot be turned into immediately spendable funds. Its delay can help the earlier self protect a future use against a later impulse. Yet the protection has a cost: the same barrier that frustrates an impulse can obstruct an urgent need. The model's deterministic setting does not supply a verdict on that tradeoff in an uncertain life.⁴ Awareness matters too. A person who predicts the change can seek protection; one who expects future resolve to be stronger than it will be may fail to prepare. The institutional question is consequently more demanding than whether a choice should be made easy or difficult. It is whether the arrangement serves a purpose the person can understand and endorse, whether its terms remain visible, and whether the restriction is proportionate to the problem it is intended to solve. A costly exit may protect a chosen commitment or merely protect the seller's receipts. The fact of friction does not tell us which.

An urgent preference for money now cannot by itself establish present bias. The earlier payment may prevent a missed rent bill, replace expensive borrowing, or arrive with greater certainty than the later promise. Money received at one date can also finance consumption at another, so a choice between payments is not automatically a choice between dated pleasures. Frederick, Loewenstein and O’Donoghue emphasize these identification problems: opportunities to reallocate consumption, the curvature of utility, uncertainty and expected changes in purchasing power can all enter the observed comparison.⁵ This returns the argument to the older distinction between weakness and want. A person unable to wait because a necessity is due today has a constraint, whether or not he also has a self-control problem. Calling his borrowing impatience does not measure the separate contributions of the two. And where a seller can profit from an anticipated reversal, the proper inquiry concerns the transaction: what was understood, which future conduct was expected, what alternatives existed, and how the terms used those expectations. A behavioral label is not evidence enough to condemn a bargain; neither does a signature prove that a bargain served a stable preference untroubled by time. The economic description must be as exact as the moral question it is asked to support.

The divided preference leaves the volume with a question that no observed rate can answer on its own. The earlier self wanted to save; the later self wanted to spend. To call one choice the person's true interest requires a reason for privileging that perspective, such as a considered long-term purpose, an informed commitment or an account of welfare that can survive the change of date. The market can attach a price to either decision without settling that reason. Nor can the descriptive psychology of one person's reversals settle the ethical weight owed to future generations, which The Discount has already placed before us. What it does establish is the need to ask whose decision a contract supports across time. A useful institution can help a person carry an intention forward; a profitable one can depend on its failure. Impatience is therefore part of the explanation of interest, but never a complete certificate for it. The final plate will turn from the rates within a person to the rates across maturities, where the market's own many tomorrows take visible form.