3. Present-Biased Preferences
3. Present-Biased Preferences
本章导读 本章讲现时偏误偏好 (present-biased preferences)，即人们对当下的看重超过未来。§3.1 引子：肥胖、吸毒过量、信用卡债务、暴力犯罪、跨期偏好的时间不一致等自控问题。§3.2 拟双曲贴现 (quasi-hyperbolic discounting)：§3.2.1 指数贴现 \(E(t)=e^{-\lambda t}\) (3.1) —— 时间一致；§3.2.2 双曲贴现 \(H(t)=\frac{1}{1+\lambda t}\) (3.2) —— 时间不一致（单期贴现率随时间下降）；§3.2.3 拟双曲（Beta-Delta）贴现 Phelps-Pollak 1968 & Laibson 1997：\(Q(t)=1\)（\(t=0\)）、\(\beta\delta^t\)（\(t\ge1\)）(3.4)，\(\beta\) 为情感/自控部分（约 0.75）、\(\delta\) 为理性/财务部分（约 1）；用 \(\beta=0.5,\delta=1\) 解释过度放纵 (overindulgence) 与拖延 (procrastination)；§3.2.4 成熟 vs 天真：\(\hat\beta=\beta\) 全成熟、\(\hat\beta=1\) 全天真、\(\hat\beta\in(\beta,1)\) 部分成熟（Rabin 三电影例：成熟者跳过第 1 周、天真者跳过第 3 周最佳电影；承诺装置/IIA 违背等支持性证据）。§3.3 相关研究：3.3.1 不再融资按揭 Keys et al. 2016（~20% 不融资、损失约 USD 11,500），3.3.2 疲劳使 \(\beta\) 下降 Dai et al. 2015（12 小时班次手卫生合规率降 8.7%，图 3.1），3.3.3 自控过度自信 DellaVigna-Malmendier 2006（健身房月卡每次 >USD 17），3.3.4 其他（Stephens 2003、Duflo 2011 化肥、O'Donoghue-Rabin 1999）。§3.4 Beta-Delta 模型的含义：做成熟者、改变当下成本-收益结构、用承诺装置、即时给予（Uber 即时支付）。图 3.1 已转述。
3. Present-Biased Preferences
Overview This chapter covers present-biased preferences, i.e. people caring more about today than the future. §3.1 motivating examples: self-control problems such as obesity, drug overdose, credit-card debt, violent crime, and the time inconsistency of inter-temporal preferences. §3.2 quasi-hyperbolic discounting: §3.2.1 exponential discounting \(E(t)=e^{-\lambda t}\) (3.1) — time consistency; §3.2.2 hyperbolic discounting \(H(t)=\frac{1}{1+\lambda t}\) (3.2) — time inconsistency (the one-period discount rate decreases over time); §3.2.3 quasi-hyperbolic (Beta-Delta) discounting Phelps-Pollak 1968 & Laibson 1997: \(Q(t)=1\) (\(t=0\)), \(\beta\delta^t\) (\(t\ge1\)) (3.4), with \(\beta\) the emotional/self-control part (about 0.75) and \(\delta\) the rational/financial part (about 1); using \(\beta=0.5,\delta=1\) to explain overindulgence and procrastination; §3.2.4 sophistication vs naïveté: \(\hat\beta=\beta\) fully sophisticated, \(\hat\beta=1\) fully naive, \(\hat\beta\in(\beta,1)\) partially sophisticated (Rabin's three-movie example: the sophisticated skip week 1, the naive skip the best week-3 movie; commitment-device / IIA-violation supporting evidence). §3.3 related studies: 3.3.1 failure to refinance mortgage Keys et al. 2016 (~20% don't refinance, loss about USD 11,500), 3.3.2 beta lower when tired Dai et al. 2015 (hand-hygiene compliance drops 8.7% over a 12-hour shift, Figure 3.1), 3.3.3 overconfidence in self-control DellaVigna-Malmendier 2006 (gym monthly fee, over USD 17 per visit), 3.3.4 others (Stephens 2003, Duflo 2011 fertilizer, O'Donoghue-Rabin 1999). §3.4 implications of the Beta-Delta model: be sophisticated, change the present cost-benefit structure, use commitment devices, give people what they want instantly (Uber instant pay). Figure 3.1 is paraphrased.
3.1 引子 / Motivating Examples
在商业实践或日常生活中，我们常处于必须做跨期 (inter-temporal) 决策的情境，但实际做出的决策往往与标准经济模型的预测不符。以下例子表明人们存在某种自控问题（如过度放纵）：
- 肥胖：成人肥胖率极高。1962 年美国 20 岁以上成人肥胖率为 23%，到 2019 年升至 36.5%。
- 吸毒过量：1999–2019 年美国超过 770,000 人死于吸毒过量；仅 2017 一年就有逾 70,000 人。
- 信用卡债务：截至 2020 年 1 月，41.2% 的美国家庭有某种信用卡债；结转余额家庭的平均信用卡债约为 USD 9,333。
- 暴力犯罪：按 FBI 数据，美国每 10 万人有 368.9 起暴力犯罪（仅含报案）；按 BJS（司法统计局）数据，每 10 万人有 2,320 起（含报案与未报案）。
- 时间不一致：在实验室让人们在两套方案中选择。情境一：方案 A——一周后得 USD 100；方案 B——立即得 USD 95。人们常选 B，不愿多等一周。情境二：方案 C——两周后得 USD 100；方案 D——一周后得 USD 95。人们常选 C，宁愿多等一周。
这些例子表明人们偏好中可能存在某种偏差，使他们对今天的看重超过未来。下文先介绍 Beta-Delta 模型（解释此偏差的候选模型），再介绍相关文献与含义。
3.2 拟双曲贴现 / Quasi-Hyperbolic Discounting
3.2.1 指数贴现：时间一致性 / Exponential Discounting: Time Consistency
标准经济学总假设：无论起点在哪个时间，相同时间间隔的两期之间贴现率相同。这种贴现率对应一个指数贴现因子作为贴现函数。记从 \(t\) 期之后到现在的指数贴现因子为 \(E(t)\)：
3.1 Motivating Examples
In business practice or daily life, we often find ourselves in situations where we have to make an inter-temporal decision; however, the decisions we actually make always turn out not to be the ones predicted by standard economic models. The following examples show that people display certain kinds of self-control problems (e.g. overindulgence):
- Obesity: the adult obesity rate is enormously high. In 1962 the obesity rate was 23% among U.S. adults of age 20 or older, but the number increases to 36.5% in 2019.
- Drug overdose: in the U.S., over 770,000 people died from drug overdoses from 1999 to 2019; in the single year of 2017, over 70,000 died from it.
- Credit-card debt: as of January 2020, 41.2% of U.S. households carry some sort of credit-card debt; the average credit-card debt for a balance-carrying household is around USD 9,333.
- Violent crimes: by FBI data there are 368.9 violent crimes (only reported crimes) per 100,000 people in the U.S.; by BJS (Bureau of Justice Statistics) data there are 2,320 violent crimes (including both reported and unreported) per 100,000 people.
- Time inconsistency: in a lab setting people are asked about two schedules. Setting one: Schedule A — get USD 100 in one week; Schedule B — get USD 95 right away. People often choose Schedule B, and they don't want to wait one more week. Setting two: Schedule C — get USD 100 in two weeks; Schedule D — get USD 95 in one week. People often choose Schedule C, and they would rather wait one more week.
These examples indicate that there might be some bias in people's preferences such that they care more about today than the future. Below we first discuss the Beta-Delta model (a candidate model that explains such bias), then some related studies, and finally some implications.
3.2 Quasi-Hyperbolic Discounting
3.2.1 Exponential Discounting: Time Consistency
In standard economics it is always assumed that the discount rate is the same between any two periods of the same time interval, regardless of the specific time point at the beginning. Such a discount rate corresponds to an exponential discount factor as the discount function. Denote the exponential discount factor from \(t\) periods later to now by \(E(t)\):
$$E(t)=e^{-\lambda t}\quad\text{with }\lambda\in(0,1)\text{ for }t\ge0\tag{3.1}$$
(3.1) 满足时间一致性，因为对任意 \(\tau\)，\(\dfrac{E(t_0+t)}{E(t_0)}=\dfrac{E(t_0+\tau+t)}{E(t_0+\tau)}=e^{-\lambda t}\)。
3.2.2 双曲贴现：时间不一致性 / Hyperbolic Discounting: Time Inconsistency
把从 \(t\) 期之后到现在的贴现因子取为下式时，称为双曲贴现因子：
(3.1) satisfies time consistency because for all \(\tau\), \(\dfrac{E(t_0+t)}{E(t_0)}=\dfrac{E(t_0+\tau+t)}{E(t_0+\tau)}=e^{-\lambda t}\).
3.2.2 Hyperbolic Discounting: Time Inconsistency
The following discount factor \(H(t)\), from \(t\) periods later to now, is called a hyperbolic discount factor:
$$H(t)=\frac{1}{1+\lambda t}\tag{3.2}$$
(3.2) 蕴含时间不一致：为示例取 \(\lambda=1\)，考虑从第 \(T\) 期到第 \(T+1\) 期的贴现：
(3.2) implies time inconsistency: for illustration take \(\lambda=1\) and consider the discount from period \(T\) to period \(T+1\):
$$\frac{H(T+1)}{H(T)}=\frac{\frac{1}{1+T+1}}{\frac{1}{1+T}}=1-\frac{1}{2+T}\tag{3.3}$$
(3.3) 关于 \(T\) 递减。故单期贴现率随时间下降（时间不一致），当 \(T\to\infty\) 时趋于零贴现。
3.2.3 拟双曲贴现：Phelps 和 Pollak (1968) 与 Laibson (1997) / Quasi-Hyperbolic Discounting
Phelps & Pollak (1968) 与 Laibson (1997) 给出 (3.2) 双曲贴现的一个近似，称为拟双曲贴现因子，它保留了相同的时间不一致性。记从 \(t\) 期之后到现在的拟双曲贴现因子为 \(Q(t)\)：
(3.3) decreases in \(T\). So the one-period discount rate decreases over time (time inconsistency), and finally goes to zero-discount when \(T\to\infty\).
3.2.3 Quasi-Hyperbolic Discounting: Phelps and Pollak (1968) and Laibson (1997)
Phelps & Pollak (1968) and Laibson (1997) propose an approximation to the hyperbolic discount function in (3.2) with the time-inconsistency property, called a quasi-hyperbolic discount factor, which is constructed to share the same time-inconsistency property. Denote the quasi-hyperbolic discount factor from \(t\) periods later to now by \(Q(t)\):
$$Q(t)=\begin{cases}1 & \text{if } t=0\\ \beta\delta^t & \text{if } t=1,2,\dots\end{cases}\quad\text{for }\beta\in(0,1)\text{ and }\delta\in(0,1)\tag{3.4}$$
注意 (3.4) 中的 \(\delta\) 等价于 (3.1) 中的 \(e^{-\lambda}\)。(3.4) 蕴含时间不一致：从第 \(0\) 期到第 \(T\) 期的贴现 \(\dfrac{Q(T)}{Q(0)}=\beta\delta^T\) (3.5)；从第 \(t\) 期到第 \(t+T\) 期的贴现 \(\dfrac{Q(T+t)}{Q(t)}=\dfrac{\beta\delta^{T+t}}{\beta\delta^t}=\delta^T\) (3.6)。比较 (3.5)、(3.6)：\(\dfrac{Q(T)}{Q(0)}<\dfrac{Q(T+t)}{Q(t)}\)，呈时间不一致——贴现率随时间上升（即对未来各期之间不大贴现），与 (3.2) 双曲贴现一致。
Note that the \(\delta\) in (3.4) is equivalent to \(e^{-\lambda}\) in (3.1). (3.4) implies time inconsistency: the discount from period \(0\) to period \(T\) is \(\dfrac{Q(T)}{Q(0)}=\beta\delta^T\) (3.5); the discount from period \(t\) to period \(t+T\) is \(\dfrac{Q(T+t)}{Q(t)}=\dfrac{\beta\delta^{T+t}}{\beta\delta^t}=\delta^T\) (3.6). Comparing (3.5) and (3.6): \(\dfrac{Q(T)}{Q(0)}<\dfrac{Q(T+t)}{Q(t)}\), which displays time inconsistency — the discount rate is increasing over time (i.e. not discounting much between future periods), the same as the hyperbolic discount factor in (3.2).
理解 \(\beta\) 与 \(\delta\) / Understanding \(\beta\) and \(\delta\) \(\beta\) 捕捉贴现的情感部分：\(\beta<1\) 意味主体对未来效用的看重低于即时效用；一些研究估计 \(\beta\approx0.75\)。\(\delta\) 捕捉贴现的理性 / 财务部分：它来自标准指数贴现因子；对短时间间隔通常假设 \(\delta\approx1\)（如 \(\delta=0.96\)）。\(\beta\) captures the emotional part of the discounting: \(\beta<1\) means the agent cares less about future utility than instant utility; some studies estimate \(\beta\approx0.75\). \(\delta\) captures the rational / financial part of the discounting: it comes from the standard exponential discount factor; for short time intervals it's typical to assume \(\delta\approx1\) (e.g. \(\delta=0.96\)).
例：\(\beta=0.5,\delta=1\) 解释过度放纵与拖延 / Example: \(\beta=0.5,\delta=1\) explains overindulgence and procrastination 过度放纵 (overindulgence)：设吃蛋糕在当天产生 \(10\) 效用、次日产生 $-15$ 效用。今天会吃吗？会，因为今天吃产生 \(10-0.5\times15=2.5>0\)。会选择"今天决定明天吃"吗？不会，因为明天吃、以今天评估产生 \(0.5\times(10-15)=-2.5<0\)。所以拟双曲贴现下，主体会做"对今天只略好、对未来很坏"的事——即过度放纵。拖延 (procrastination)：设慢跑在当天产生 $-6$ 效用、次日产生 \(8\) 效用。今天会去慢跑吗？不会，因为今天慢跑产生 \(-6+0.5\times8=-2<0\)。会选择"今天决定明天去慢跑"吗？会，因为明天慢跑、以今天评估产生 \(0.5\times(-6+8)=1>0\)。但真到了明天，会去吗？不会，因为明天慢跑仍产生 \(-6+0.5\times8=-2<0\)。所以主体不会做"对今天只略坏、对未来很好"的事——明知该做却从不今天做、寄望明天，而明天永不到来，这正是拖延。Overindulgence: suppose eating a cake generates \(10\) utils on the day of eating and $-15$ utils on the following day. Will the agent eat the cake today? Yes, because eating it today generates \(10-0.5\times15=2.5>0\). Will the agent choose today to eat the cake tomorrow? No, because eating it tomorrow, evaluated on today, generates \(0.5\times(10-15)=-2.5<0\). So under quasi-hyperbolic discounting the agent will do things that are only slightly good for today and very bad for the future — overindulgence. Procrastination: suppose jogging generates $-6$ utils on the day of jogging and \(8\) utils on the following day. Will the agent go jogging today? No, because jogging today generates \(-6+0.5\times8=-2<0\). Will the agent choose today to go jogging tomorrow? Yes, because jogging tomorrow, evaluated on today, generates \(0.5\times(-6+8)=1>0\). But when it actually comes to tomorrow, will the agent really go jogging? No, because again jogging tomorrow generates \(-6+0.5\times8=-2<0\). So the agent will not do things that are only slightly bad for today but very good for the future — they know they should do it but never do it today and hope to do it tomorrow, which never happens; this is procrastination.
3.2.4 拟双曲贴现下的成熟与天真 / Sophistication and Naïveté
3.2.4 Sophistication and Naïveté under Quasi-Hyperbolic Discounting
使用拟双曲贴现的主体也许并未完全意识到自己的 \(\beta\)。设 \(\hat\beta\) 为主体以为自己拥有的 beta（但贴现时实际仍按真实 \(\beta\) 行事）。定义：完全成熟 (fully sophisticated)——\(\hat\beta=\beta\)，即完全意识到自己的自控问题；完全天真 (fully naive)——\(\hat\beta=1\)，即完全没意识到自控问题；部分成熟 (partially sophisticated)——\(\hat\beta\in(\beta,1)\)，部分意识到自控问题。
An agent using quasi-hyperbolic discounting might not be fully aware of the \(\beta\) he or she has. Let \(\hat\beta\) be the beta the agent thinks he or she has (but actually they still act by the true \(\beta\) when discounting). Define: fully sophisticated — \(\hat\beta=\beta\), i.e. the agent is fully aware of his or her self-control problem; fully naive — \(\hat\beta=1\), i.e. the agent is fully unaware of his or her self-control problem; partially sophisticated — \(\hat\beta\in(\beta,1)\), i.e. the agent is partially aware of his or her self-control problem.
例：重访拖延 + Rabin 的三电影例 / Example: revisiting procrastination + Rabin's three-movie example 重访拖延（§3.2.3）：若主体完全成熟，则今天不会相信明天能去慢跑——因为他知道真实 \(\beta=0.5\)，能预料到明天来临时会感到慢跑的负效用，故知道未来也不会去。若主体完全天真，则今天会天真地相信明天能去慢跑；然而真到明天，他会改变主意。Rabin 的三电影例：一周三场电影：第 1 周中庸电影 (\(3\) 效用)、第 2 周好电影 (\(5\) 效用)、第 3 周 Johnny Depp 电影 (\(8\) 效用)。设主体拟双曲贴现 \(\beta=0.5,\delta=1\)，且必须恰好放弃一场电影、那一周得 \(0\) 效用。完全成熟者跳过第 1 周：第 1 周时主体知道，若看了第 1 周中庸电影，则第 2 周一定也会看好电影（因 \(\underbrace{5}_{\text{Week 2}}>\underbrace{4=0.5\times8}_{\text{Week 3}}\)），故第 1 周总贴现效用为 \(\underbrace{3}_{\text{Week 1}}+\underbrace{0.5\times5}_{\text{Week 2}}=5.5\)；但若第 1 周跳过中庸电影，则第 1 周总贴现效用为 \(0.5\times(\underbrace{5+8}_{\text{Week 2 and 3}})=6.5>5.5\)。故完全成熟者第 1 周跳过中庸电影。完全天真者跳过第 3 周：第 1 周时主体决定跳过第 2 周好电影，因为 \(\underbrace{3}_{\text{Week 1}}>\underbrace{2.5=0.5\times5}_{\text{Week 2}}\) 且 \(\underbrace{0.5\times8=4}_{\text{Week 3}}>\underbrace{2.5=0.5\times5}_{\text{Week 2}}\)，故第 1 周看电影；然而真到第 2 周，主体改变主意、决定跳过第 3 周，因为 \(\underbrace{5}_{\text{Week 2}}>\underbrace{4=0.5\times8}_{\text{Week 3}}\)。故完全天真者最终跳过了第 3 周最好的 Johnny Depp 电影。Revisiting procrastination (§3.2.3): if the agent is fully sophisticated, then today he won't believe he can go jogging tomorrow — because he knows his actual \(\beta=0.5\) and can anticipate the negative utility of jogging he will feel when tomorrow arrives, so he knows he won't be able to go jogging in the future. If the agent is fully naive, then today he will naively believe that tomorrow he can go jogging; however, when tomorrow really comes, he will change his mind. Rabin's three-movie example: three movies in a week — week 1 mediocre movie (\(3\) utils), week 2 good movie (\(5\) utils), week 3 Johnny Depp movie (\(8\) utils). Suppose the agent has quasi-hyperbolic discounting \(\beta=0.5,\delta=1\) and must give up exactly one movie, receiving \(0\) util that week. The fully sophisticated skip week 1: in week 1 the agent knows that if he sees the mediocre movie in week 1, then in week 2 he will surely also see the good movie (since \(\underbrace{5}_{\text{Week 2}}>\underbrace{4=0.5\times8}_{\text{Week 3}}\)), so the total discounted utility in week 1 is \(\underbrace{3}_{\text{Week 1}}+\underbrace{0.5\times5}_{\text{Week 2}}=5.5\); but if he skips the mediocre movie in week 1, the total discounted utility in week 1 is \(0.5\times(\underbrace{5+8}_{\text{Week 2 and 3}})=6.5>5.5\). So the fully sophisticated agent skips the mediocre movie in week 1. The fully naive skip week 3: in week 1 the agent decides to skip the good movie in week 2 because \(\underbrace{3}_{\text{Week 1}}>\underbrace{2.5=0.5\times5}_{\text{Week 2}}\) and \(\underbrace{0.5\times8=4}_{\text{Week 3}}>\underbrace{2.5=0.5\times5}_{\text{Week 2}}\), so he watches the movie in week 1; however, when it's actually week 2 the agent changes his mind and decides to skip week 3 because \(\underbrace{5}_{\text{Week 2}}>\underbrace{4=0.5\times8}_{\text{Week 3}}\). So the fully naive agent ends up skipping the best Johnny Depp movie in week 3.
支持性证据 / Supporting evidence （脚注：此处提到的证据中，"带天真/成熟的现时偏误偏好"只是若干替代解释之一。）承诺装置的采用支持（至少部分）成熟的现时偏误偏好的存在：承诺装置把某些选择从选择集中拿走，对时间一致的主体是弱占优劣策略；完全天真的现时偏误主体也不会采用承诺装置（理由同时间一致者——他们相信自己未来并无现时偏误）。有人采用承诺装置后却仍失败支持"非完全成熟"主体的存在：若完全成熟则不会失败、若完全天真则一开始就不会采用，部分成熟则会采用但可能失败（但也有竞争性故事，如对抗承诺装置的诱惑存在不确定性，使即便完全成熟者也难以完美预测）。IIA（无关备选独立性）被违背支持现时偏误（至少时间不一致）主体的存在：设三期，第 1 期有一个坏选择、第 2 期有一个不太坏的选择。完全天真主体会在第 3 期选好选择（若加入第 3 期好选择，完全天真者第 1 期可能以为会等到第 2、3 期；但第 2 期来临时变得不耐烦、选了不太坏的）。于是第 3 期的好选择是"从未被选中的无关选择"，却改变了天真者在坏与不太坏之间的选择。完全成熟主体：三期，第 1 期坏、第 2 期不太坏、第 3 期好；成熟者第 1 期可能预料到第 2 期会选不太坏的（完全意识到第 2 期的不耐烦），于是在第 1 期比较"不太坏"与"坏"时可能选坏选择。于是第 2 期不太坏的选择是"从未被选中的无关选择"，却改变了成熟者在坏与好之间的选择。(Footnote: among the evidence mentioned here, "present-biased preferences with naïveté and sophistication" is just one of the alternative explanations.) The take-up of commitment devices supports the existence of (at least partially) sophisticated present-biased preferences: a commitment device takes certain choices out of the choice set, which is a weakly dominated strategy for time-consistent agents; and fully naive present-biased agents won't take up the commitment device for the same reason as time-consistent agents — they believe they are not present biased in future periods. The fact that some people take up a commitment device and then fail supports the existence of not-fully-sophisticated agents: if fully sophisticated they won't fail, if fully naive they won't pick up the device in the first place, and the partially sophisticated will pick it up but may fail on it (but there are competing stories, e.g. uncertainty in temptations against the commitment device, which makes it impossible even for a fully sophisticated agent to make perfect predictions). The fact that Independence of Irrelevant Alternatives is violated supports the existence of present-biased (at least time-inconsistent) agents: suppose three periods, with a bad choice in period 1 and a not-so-bad choice in period 2. A fully naive agent chooses the good choice in period 3 (if we add a good choice in period 3, a fully naive agent in period 1 may think he will wait in period 2 until period 3; however when period 2 really comes the fully naive agent becomes impatient and just takes up the not-so-bad choice). In this way, period 3's good choice is an irrelevant choice that never got chosen, but it still changes the fully naive agent's choice between bad and not-so-bad. A fully sophisticated agent: three periods, bad in period 1, not-so-bad in period 2, good in period 3; the sophisticated agent in period 1 may think he will take the not-so-good choice in period 2 (being fully aware of his impatience in period 2), so when comparing not-so-bad and bad choices in period 1 it's possible the agent will choose the bad choice in period 1. In this way, period 2's not-so-bad choice is an irrelevant choice that never got chosen, but it still changes the fully sophisticated agent's choice between bad and good choices.
3.3 文献中的相关研究 / Related Studies in the Literature
3.3.1 不再融资按揭：Keys et al. (2016) / Failure to Refinance Mortgage: Keys et al. (2016)
3.3 Related Studies in the Literature
3.3.1 Failure to Refinance Mortgage: Keys et al. (2016)
Keys et al. (2016)：不再融资按揭 / failure to refinance 用 2010 年 12 月在册的 150 万笔美国全国单户住宅按揭样本研究家庭再融资决策。作者发现：当利率下降时，约 20% 的家庭在"无约束且再融资最优"的情况下仍不去再融资以利用更低利率。文章显示：对中位数家庭，不再融资的损失约为 USD 11,500。一个可能解释是家庭具有 Beta-Delta 贴现因子，对"今天做再融资文书工作的成本"赋予过高权重、对"未来储蓄"赋予过低权重。Keys et al. (2016) 的调查支持该解释：在不再融资的家庭中，有 32 户通过电话联系并愿意接受调查；25% 的家庭根本没打开 NHS（芝加哥邻里住房服务）寄来的再融资要约信；在打开信的 75% 中，约 33% 说本打算打电话给贷款专员但太忙、约 33% 说觉得再融资省的钱不够多；在那 32 户中，有 12 户表示乐意让贷款专员打电话来讨论再融资。很可能这些家庭过于在意"现在打电话、做文书工作"、而低估了未来储蓄。作者无法排除注意力不足与信息缺乏等其他解释，但现时偏误仍是候选故事之一。Studies household mortgage refinancing decisions using a U.S. national sample of 1.5 million single-family residential mortgages that were active in December 2010. The authors find that when the interest rate decreases, around 20% of households fail to refinance their mortgage when they are unconstrained to refinance and it's optimal to do so to take advantage of the lower rates. The paper shows that the loss of not refinancing to the median household is about USD 11,500. One possible explanation is that households have a Beta-Delta discount factor, which places too much weight on today's cost of doing the paperwork for refinancing and too little weight on future savings. The survey by Keys et al. (2016) supports this: of the non-refinancing households, 32 were reached by phone and willing to take the survey; 25% of households didn't open the refinancing-offer letter from NHS (Neighborhood Housing Services of Chicago); of the 75% who did open the letter, about 33% said they were planning to call the loan officer but were too busy, and about 33% said they didn't think the savings from refinancing would be high enough; among the 32 households, 12 said they would be happy to have the loan officer call them to discuss the refinancing. It is likely that households care too much about making the call and doing the paperwork right away, and under-evaluate future savings. The authors could not rule out other explanations such as inattention and lack of information, but present-biased explanation is still one of the candidate stories.
3.3.2 疲劳使 \(\beta\) 下降：Dai et al. (2015) / Beta Becomes Lower When Tired
3.3.2 Beta Becomes Lower When Tired: Dai et al. (2015)
Dai et al. (2015)：疲劳降低自控 / fatigue lowers self-control 用 35 家不同医院、4,157 名医护人员、超过 1,370 万次手卫生机会的数据，研究手卫生标准流程的合规率。作者发现：经回归，合规率从 12 小时工作班次的开始到结束下降了 8.7 个百分点（图 3.1）；在更高工作强度下下降更严重；班次之间更长的休息会提高下一班次的合规率。尽管该文未明确讨论现时偏误贴现模型，结果仍提示如下合理故事：医护人员在班次中工作越久越疲劳；疲劳导致可用精力下降，故若他们用 (3.4) 的拟双曲贴现，则随疲劳加深 \(\beta\) 趋于下降；于是医护人员对"未来遵守手卫生政策的收益"越来越不在意、对"现在洗手的成本"越来越在意；因此越疲劳合规率越低。Uses a data set of 4,157 caregivers working in 35 different hospitals with over 13.7 million hand-hygiene opportunities to study the compliance rate of the hand-hygiene standard process. The authors find: by regression, the compliance rate drops by 8.7 percent from the beginning to the end of a 12-hour work shift (Figure 3.1); the decline is aggravated in higher work intensity; longer breaks between shifts increase the compliance rate in the following shift. Although the present-biased discount model is not explicitly discussed in this paper, the results still suggest the following plausible story: caregivers become tired as they work longer in the work shift; the fatigue leads to less available energy, so if they have the quasi-hyperbolic discount factor in (3.4), their \(\beta\) tends to drop as fatigue develops; so the caregivers care increasingly less about the future benefit of being compliant to the hand-hygiene policy, and increasingly more about the current cost of washing hands; therefore they display a lower compliance rate as they become tired.
图 3.1（手卫生合规率，已转述 / Figure 3.1, paraphrased） 横轴为"自班次开始的经过小时数"（0–1, 1–2, …, 11–12），纵轴为"平均手卫生合规率 (%)"。曲线从班次开始约 42%–43% 整体下行到班次结束约 34%–35%，呈阶梯式下降，直观展现合规率随工时（疲劳）累积而降低。The horizontal axis is "elapsed hours since the start of the shift" (0–1, 1–2, …, 11–12) and the vertical axis is "average hand-hygiene compliance rate (%)". The curve trends downward overall from about 42%–43% at the start of the shift to about 34%–35% at the end, declining in a stepwise manner, visually showing that the compliance rate falls as work hours (fatigue) accumulate.
3.3.3 自控的过度自信：DellaVigna 和 Malmendier (2006) / Overconfidence in Self-Control
3.3.3 Overconfidence in Self-Control: DellaVigna and Malmendier (2006)
DellaVigna & Malmendier (2006)：健身房会员 / gym membership 用新英格兰三家健身俱乐部、7,752 名会员的合约选择与到场决策数据（1997 年 4 月至 2000 年 7 月，其中一家含 2 月）。作者发现：付统一月费（不限次月度到场）的会员每月只来 4.3 次，相当于每次到场花费超过 USD 17（远比 USD 10 的按次付费更贵）；选择月度计划而非年度计划的会员据推测偏好"可随时取消"的灵活性，然而这些月度合约会员在一年内继续续约的概率比年度合约会员高 17%。这些发现的可能解释包括主体对其未来自控的过度自信。Uses a data set of three health clubs in New England with the contract choice and club attendance decisions of 7,752 members (April 1997 to July 2000, and February for one club). The authors find: members who paid a flat monthly fee (unlimited monthly attendance) only visited 4.3 times per month, which cost them over USD 17 per visit (much more expensive than the USD 10 pay-as-you-go); members who enrolled in monthly plans rather than yearly plans presumably preferred the flexibility of being able to cancel membership, however these monthly-contract members are 17% more likely to continue their enrollment over one year than yearly-contract members. The possible explanations of these findings include the agent's overconfidence in their future self-control.
3.3.4 其他研究 / Other Studies
3.3.4 Other Studies
其他研究 / Other studies Stephens Jr (2003) 讨论购买周期中的证据，即即时消费在收到收入时上升；Huffman & Barenstein (2005) 把该行为解释为拟双曲贴现引起的不耐烦。Duflo et al. (2011) 用肯尼亚数据表明：尽管化肥号称有 70% 的投资回报率，农民仍不愿支付小额即时成本去买化肥（拖延行为）；小额、限时的补贴能显著提高农民对化肥的使用，因为对有现时偏误偏好的农民来说，成本的下降非常重要。O'Donoghue and Rabin (1999) 是一篇理论论文：讨论主体必须恰好做一次某活动的情形，主体类型包括时间一致、天真现时偏误、成熟现时偏误，活动可分为"产生即时成本"或"产生即时回报"两类。他们证明：天真现时偏误主体会拖延即时成本类活动、并对即时回报类活动预先操作（做得太早）；成熟现时偏误主体在即时成本类活动上更少拖延、但在即时回报类活动上更多预先操作。其要旨是把每类主体的福利与"时间一致偏好"基准对比以确定相对福利得失（这是该领域相当标准的做法）：对即时成本类活动，小的现时偏误（小 \(\beta\)）会严重损害天真现时偏误主体；对即时回报类活动，小的现时偏误（小 \(\beta\)）会严重损害成熟现时偏误主体。Stephens Jr (2003) discusses the evidence in the purchasing cycle, i.e. instantaneous consumption increases upon receiving income; Huffman and Barenstein (2005) interpret this behavior by impatience caused by quasi-hyperbolic discounting. Duflo et al. (2011) use Kenya data to show that farmers don't want to pay a small instant cost to buy fertilizer despite the claimed 70% ROI (a procrastination behavior); small time-limited subsidies significantly increase farmers' usage of fertilizer because the reduction in cost is very important to a farmer with present-biased preferences. O'Donoghue and Rabin (1999) is a theoretical paper: it discusses a setting where agents must do an activity exactly once; the agents include those with time-consistent discounting, naive present-biased and sophisticated present-biased preferences, and the activities can be classified as incurring either immediate costs or immediate rewards. They show that naive present-biased agents procrastinate on immediate-cost activities and preoperate (do something too soon) on immediate-reward activities; sophisticated present-biased agents are less procrastinating on immediate-cost activities but more preoperating on immediate-reward activities. The punchline is to compare the welfare of each type of agent against the baseline of time-consistent preferences to determine the relative welfare gain or loss (a fairly standard practice in this field): for immediate-cost activities, a small present bias (small \(\beta\)) can severely harm naive present-biased agents; for immediate-reward activities, a small present bias (small \(\beta\)) can severely harm sophisticated present-biased agents.
3.4 Beta-Delta 模型的含义 / Implications of Beta-Delta Model
在一个人们具有现时偏误偏好的世界里，有几件事可以帮助我们改善生活。
3.4 Implications of Beta-Delta Model
There are several things we can do to improve our lives in a world where people have present-biased preferences.
四点含义 / Four implications (1) 努力做成熟者：尽量意识到自己的 \(\beta\)，以免天真地相信自己会去做那些实际上永远不会做的事。例如，永远不要把工作带回家，因为在家庭时间里 \(\beta\) 非常小，计划在那些时间工作毫无意义。(2) 改变当下的成本-收益结构：既然我们看重当下多于未来，若真想开始做某事，就该想办法给当下增加更多收益；换言之，把想做的事（无拖延）的收益前置，把不想沉溺的事的成本前置。(3) 善用承诺装置：承诺装置能帮我们避免落入拖延或过度放纵；但人们对承诺装置的采用率相当低。需谨慎：承诺装置可能是双刃剑——有时我们会对自己太过乐观，而承诺去做对未来不切实际的事。(4) 即时给予人们想要的：Uber 通常按周付司机工资，但在引入即时支付机制后，司机乐意每次提取当日收入时支付 USD 0.50，并且供给了多得多的驾驶时长（注：此例也无法排除前景理论解释——窄框定使司机分开评估每日收入，其加总效用高于同额聚合的每周收入）。此例表明：我们应充分意识到人们的现时偏误偏好，把他们想要的好处立刻给到，以最大化他们对此的感知收益、或服务于其他目的。(1) Try to be sophisticated: be aware of our own \(\beta\) as much as possible so that we won't naively believe in being able to do the things we would never actually do. For example, never bring work home, because the \(\beta\) is very small during family hours, so it's meaningless to plan on working during those hours. (2) Change the cost-benefit structure at present: since we care about the present more than the future, we should really manage to add more benefit to the present if we really want to start doing that thing; in other words, move the benefits upfront for the things we really want to do (without procrastination), and move the costs upfront for the things we don't want to be indulged in. (3) Make use of the commitment device: a commitment device could help us avoid being trapped in procrastination or overindulgence; however, people's take-up rate of commitment devices is quite low. Be cautious that using a commitment device could be a double-edged sword, because sometimes we might feel too good about ourselves and commit to something unrealistic for us in the future. (4) Give people what they want instantly: Uber usually pays drivers on a weekly basis, but after it introduced a new instant-payment mechanism, drivers would love to pay USD 0.50 every time they withdraw their daily income, and they even supply much more hours driving (note: this example cannot rule out the prospect-theory explanation either — narrow framing makes drivers evaluate daily income separately, which adds up to much higher utility than the same amount aggregated as weekly income). This example shows that we should be fully aware of people's present-biased preferences and give them the benefit they want right away to maximize their perceived benefit of it, or for the use of some other purposes.
参考文献 / References
- Dai, H., Milkman, K. L., Hofmann, D. A., & Staats, B. R. (2015). The Impact of Time at Work and Time off from Work on Rule Compliance: The Case of Hand Hygiene in Health Care. Journal of Applied Psychology, 100(3), 846.
- DellaVigna, S., & Malmendier, U. (2006). Paying Not to Go to the Gym. American Economic Review, 96(3), 694–719.
- Duflo, E., Kremer, M., & Robinson, J. (2011). Nudging Farmers to Use Fertilizer: Theory and Experimental Evidence from Kenya. American Economic Review, 101(6), 2350–90.
- Huffman, D., & Barenstein, M. (2005). A Monthly Struggle for Self-control? Hyperbolic Discounting, Mental Accounting, and the Fall in Consumption between Paydays. IZA Discussion Paper 1430.
- Keys, B. J., Pope, D. G., & Pope, J. C. (2016). Failure to Refinance. Journal of Financial Economics, 122(3), 482–499.
- Laibson, D. (1997). Golden Eggs and Hyperbolic Discounting. Quarterly Journal of Economics, 112(2), 443–478.
- O'Donoghue, T., & Rabin, M. (1999). Doing It Now or Later. American Economic Review, 89(1), 103–124.
- Phelps, E. S., & Pollak, R. A. (1968). On Second-best National Saving and Game-equilibrium Growth. Review of Economic Studies, 35(2), 185–199.
- Stephens Jr, M. (2003). "3rd of tha Month": Do Social Security Recipients Smooth Consumption between Checks? American Economic Review, 93(1), 406–422.
References
- Dai, H., Milkman, K. L., Hofmann, D. A., & Staats, B. R. (2015). The Impact of Time at Work and Time off from Work on Rule Compliance: The Case of Hand Hygiene in Health Care. Journal of Applied Psychology, 100(3), 846.
- DellaVigna, S., & Malmendier, U. (2006). Paying Not to Go to the Gym. American Economic Review, 96(3), 694–719.
- Duflo, E., Kremer, M., & Robinson, J. (2011). Nudging Farmers to Use Fertilizer: Theory and Experimental Evidence from Kenya. American Economic Review, 101(6), 2350–90.
- Huffman, D., & Barenstein, M. (2005). A Monthly Struggle for Self-control? Hyperbolic Discounting, Mental Accounting, and the Fall in Consumption between Paydays. IZA Discussion Paper 1430.
- Keys, B. J., Pope, D. G., & Pope, J. C. (2016). Failure to Refinance. Journal of Financial Economics, 122(3), 482–499.
- Laibson, D. (1997). Golden Eggs and Hyperbolic Discounting. Quarterly Journal of Economics, 112(2), 443–478.
- O'Donoghue, T., & Rabin, M. (1999). Doing It Now or Later. American Economic Review, 89(1), 103–124.
- Phelps, E. S., & Pollak, R. A. (1968). On Second-best National Saving and Game-equilibrium Growth. Review of Economic Studies, 35(2), 185–199.
- Stephens Jr, M. (2003). "3rd of tha Month": Do Social Security Recipients Smooth Consumption between Checks? American Economic Review, 93(1), 406–422.