6. Biased Beliefs
6. Biased Beliefs
本章导读 本章讲有偏信念及其纠正。§6.1 有偏信念与信息干预：6.1.1 返校决策 Jensen (2010)（多米尼加 8 年级男生感知教育回报偏低，告知真实回报使在校年限增加 0.20–0.35 年）；6.1.2 发薪日贷款 Bertrand & Morse (2011)（三种信息处理图 6.1–6.3 分别减少借款 23%/16%/12%）；6.1.3 误判的女性劳动供给社会规范 Bursztyn et al. (2018)（沙特男性低估他人支持女性工作的比例，信息干预提升妻子求职率 5.8%→16.2%）。§6.2 投射偏差 (projection bias)：定义 6.1；6.2.1 理论 Loewenstein et al. (2003)（简单投射偏差 \(\tilde u(c,s\mid s')=(1-\alpha)u(c,s)+\alpha u(c,s')\)，嵌入跨期选择与习惯形成）；6.2.2 天气对敞篷车购买的影响 Busse et al. (2015)（去季节趋势后高温仍显著提高敞篷车购买，图 6.4–6.8）。§6.3 其他有偏信念：过度自信、归因偏差、基率偏差、确认偏差、Dunning-Kruger、事后聪明、热手谬误、控制错觉、近因偏差、幸存者偏差、赌徒谬误。图 6.1–6.8 已转述（6.1、6.2 以表格重现）。
6. Biased Beliefs
Overview This chapter covers biased beliefs and their correction. §6.1 biased beliefs and information intervention: 6.1.1 returning to school Jensen (2010) (8th-grade boys in the Dominican Republic perceive a low education return; telling them the actual return raises years of schooling by 0.20–0.35); 6.1.2 payday loan Bertrand & Morse (2011) (three information treatments, Figures 6.1–6.3, reduce borrowing by 23%/16%/12%); 6.1.3 misperceived social norm in women's labor supply Bursztyn et al. (2018) (Saudi males underestimate the share of others supporting women working; information intervention raises the wives' job-application rate 5.8%→16.2%). §6.2 projection bias: Definition 6.1; 6.2.1 theory Loewenstein et al. (2003) (simple projection bias \(\tilde u(c,s\mid s')=(1-\alpha)u(c,s)+\alpha u(c,s')\), embedded in inter-temporal choice and habit formation); 6.2.2 effect of weather on convertible-car purchases Busse et al. (2015) (after removing the seasonal trend, higher temperature still significantly raises convertible purchases, Figures 6.4–6.8). §6.3 other biased beliefs: overconfidence, attribution bias, base-rate bias, confirmation bias, Dunning-Kruger, hindsight bias, hot-hand fallacy, illusion of control, recency bias, survivorship bias, gambler's fallacy. Figures 6.1–6.8 are paraphrased (6.1, 6.2 reproduced as tables).
6.1 有偏信念与信息干预 / Biased Beliefs and Information Intervention
6.1.1 返校：Jensen (2010) / Returning to School
6.1 Biased Beliefs and Information Intervention
6.1.1 Returning to School: Jensen (2010)
Jensen (2010)：感知回报而非实际回报 / perceived, not actual, return Jensen (2010) 研究多米尼加共和国 8 年级男生的就学决策，强调决定"是否返校"的是教育的感知回报而非实际回报。为估计教育的实际回报，作者用 2001 年 1 月对多米尼加全国非农村地区（占总人口三分之二）1,500 户家庭的入户调查数据：完成中学的工人平均收入比未完成者高 40%，然而只有 25%–30% 的学生完成中学。作者随后做学生调查：2001 年 4、5 月间，从 150 个家庭样本聚类中各随机抽取 15 名 8 年级男生。作者认为多米尼加学生对就学回报存在系统性偏差：学生调查显示，就读中学的平均隐含感知回报仅 9%，且 42% 的学生报告"有无中学文凭，其预期收入没有差别"。信息干预：作者在调查末尾对受访学生随机提供"实际中学回报"的信息；该干预在学校层面而非个人层面进行，因为同校学生间易于沟通。结果：获得信息干预的处理组学生平均多完成 0.20–0.35 年学业；对那些起初感知回报很低的学生，效应尤其强。Jensen (2010) studies the schooling decisions of 8th-grade boys in the Dominican Republic, emphasizing that it is the perceived return of education, not the actual return, that determines the decision of whether to return to school. To estimate the returns to education, the author uses data from a household survey in January 2001 of 1,500 households in nationwide non-rural areas (two-thirds of the total population) of the Dominican Republic: the mean earnings of workers who completed secondary school are 40% higher than those who have not, however only 25%–30% of students complete secondary school. The author then conducts a student survey by randomly selecting 15 boys from the 8th grade for each of 150 household sample clusters during April and May 2001. The author believes students have a systematic bias in their beliefs of the schooling return: the survey shows the average implied perceived return of attending secondary school is only 9%, and 42% of students report no difference in their expected earnings with and without a secondary school diploma. Information intervention: at the end of the survey the author randomly provides interviewed students with information about the actual high-schooling return; the treatment is done at the school level rather than the individual level, because students in the same school can easily communicate with each other. Result: students in the treatment group with the information intervention end up completing 0.20–0.35 more years of school on average; the effects are particularly strong for those who had a low perceived return of education to begin with.
6.1.2 发薪日贷款：Bertrand 和 Morse (2011) / Payday Loan
6.1.2 Payday Loan: Bertrand and Morse (2011)
Bertrand & Morse (2011)：信息干预减少高息借款 / information intervention reduces high-cost borrowing 作者用美国某最大发薪日放贷公司 2008 年 5 月至 9 月、11 个州 77 家门店的数据，研究信息干预对使用高成本债务——发薪日贷款的影响。发薪日贷款门店提供一定额度（如 USD 350）贷款，要求在借款人下个发薪日偿还；其成本通常表现为固定费率（如每借 USD 100 收 USD 15），不随贷款期限或借款人风险变化。在被询问的 6,538 名借款人中，1,441 人同意参与研究。信息干预：对 1,441 名参与者随机给予不同信息作为不同处理（图 6.1–6.3）。处理 1 平均减少借款 USD 55（23%）；处理 2 平均减少 USD 38（16%）；处理 3 平均减少 USD 28（12%）。The authors use data from 77 stores in 11 states between May 2008 and September 2008 from one of the largest payday lending companies in the U.S. to study the effect of information intervention on the use of high-cost debt — payday loans. A payday loan store offers a certain amount (e.g. USD 350) of loan, asked to be repaid on the borrower's next payday; its cost typically comes as a fixed fee (e.g. USD 15 per USD 100 of loan) and does not vary based on the length of the loan or the borrower's risk. Of the 6,538 borrowers asked, 1,441 agreed to participate in the research program. Information intervention: the 1,441 participants are randomly offered different information as different treatments (Figures 6.1–6.3). Treatment 1 reduces borrowing on average by USD 55 (23%); Treatment 2 by USD 38 (16%); Treatment 3 by USD 28 (12%).
表 / Table — Figure 6.1 (Treatment 1)：不同类型贷款的年利率 / Annual interest rates on different types of loans
| Loan type | Median annual interest % (from government surveys) |
|---|---|
| Payday Loan | 443% |
| Installment Car Loans | 18% |
| Credit Card | 16% |
| Subprime Mortgages | 10% |
表 / Table — Figure 6.2 (Treatment 2)：借 USD 300 的费用或利息 / Fees or interest to borrow USD 300
| Repay in | Payday lender (fee USD 15 per USD 100) | Credit card (20% APR) |
|---|---|---|
| 2 weeks | USD 45 | USD 2.50 |
| 1 month | USD 90 | USD 5 |
| 2 months | USD 180 | USD 10 |
| 3 months | USD 270 | USD 15 |
图 6.3（处理 3，已转述 / Figure 6.3, Treatment 3, paraphrased） 图标式信息："在 10 个办理新发薪日贷款的典型人当中……" —— 2.5 人会还清而不续借；2 人会续借 1–2 次；1.5 人会续借 3–4 次；4 人会续借 5 次及以上。意在用"多数人反复续借"的事实纠正借款人对自身还款能力的乐观偏差。An icon-style infographic: "Out of 10 typical people taking out a new payday loan…" — 2.5 people will pay it back without renewing; 2 people will renew 1 or 2 times; 1.5 people will renew 3 or 4 times; 4 people will renew 5 or more times. It aims to correct borrowers' optimistic bias about their own repayment ability with the fact that most people renew repeatedly.
6.1.3 误判的女性劳动供给社会规范：Bursztyn et al. (2018) / Misperceived Social Norm in Women Labor Supply
6.1.3 Misperceived Social Norm in Women Labor Supply: Bursztyn et al. (2018)
Bursztyn et al. (2018)：纠正误判的社会规范 / correcting a misperceived social norm 作者用 2017 年 10 月 9 日至 13 日对沙特阿拉伯利雅得 500 名 18–35 岁男性的调查数据，研究信息干预对女性劳动供给决策的影响。沙特女性劳动供给比例很低（低于 15%）；作者认为男性对女性是否工作有话语权，故以男性为受试者。实验设计：(1) 先询问参与者自身意见，是否同意若干陈述，包括"在我看来，女性应被允许在家庭之外工作"——87% 的男性匿名表示同意；(2) 再请参与者估计他人对这些陈述的看法，并用 USD 20 的亚马逊礼品卡码激励估计准确——结果 75% 的参与者低估了同意该陈述的其他男性人数；(3) 随机抽 50% 参与者，告知"87% 的男性同意上述陈述"；(4) 最后向所有参与者提供"在礼品卡与替妻子注册一个求职 APP 之间选择"——无信息干预者中 23% 选择求职 APP，有信息干预者中 32% 选择。回访：3–5 个月后（2018/1/10–3/6）电话回访询问其妻子的劳动供给，妻子在家庭外求职的比例从 5.8% 升至 16.2%（显著）；其他结果方向一致但不显著。The authors use survey data between October 9 and October 13, 2017 of 500 Saudi males aged 18 to 35 living in Riyadh, Saudi Arabia, to study the effect of information intervention on female labor-supply decisions. The female labor-supply ratio is very low in Saudi Arabia (less than 15%); the authors believe males have the say in females' labor supply, so they chose males as subjects. Experiment design: (1) the survey first elicits participants' own opinions by asking whether they agree with several statements, including "In my opinion, women should be allowed to work outside of the home" — 87% of males anonymously agreed; (2) participants are then asked to estimate the beliefs of others on those statements, with accuracy encouraged by a USD 20 Amazon gift card code — 75% of participants underestimated the number of other males agreeing with that statement; (3) 50% of participants are randomly selected to receive the information that 87% of males agreed with the above statement; (4) finally, all participants are offered to choose between a gift card and registering their wives for a job-matching app — 23% of participants without the information intervention choose the job app, while 32% of those with it choose it. Follow-up call: after 3–5 months (01/10/2018 to 03/06/2018) participants are contacted by phone about their wives' labor supply; the percentage of wives who applied for a job outside the home increased from 5.8% to 16.2% (significant); other results have a consistent direction but are not significant.
6.2 投射偏差 / Project Bias
定义 6.1（投射偏差 / Projection Bias） 称人们具有投射偏差 (projection bias)，若他们夸大了未来偏好与当前偏好的相似程度，因为他们未能完全理解自己的行为与外生冲击会如何改变其未来偏好。People are said to have projection bias if they exaggerate the degree to which their future preferences resemble their current preferences, because they fail to completely understand how their own behaviors and exogenous shocks may affect their preferences in the future.
6.2.1 理论：Loewenstein et al. (2003) / Theory
Loewenstein et al. (2003) 提出如下简单模型来刻画投射偏差的效应。设主体在当前状态为 \(s'\) 时，对"在状态 \(s\) 下消费 \(c\)"有一个投射效用 \(\tilde u(c,s\mid s')\)，满足
6.2 Project Bias
Definition 6.1 (Projection Bias) 称人们具有投射偏差 (projection bias)，若他们夸大了未来偏好与当前偏好的相似程度，因为他们未能完全理解自己的行为与外生冲击会如何改变其未来偏好。People are said to have projection bias if they exaggerate the degree to which their future preferences resemble their current preferences, because they fail to completely understand how their own behaviors and exogenous shocks may affect their preferences in the future.
6.2.1 Theory: Loewenstein et al. (2003)
Loewenstein et al. (2003) propose the following simple model to illustrate the effect of projection bias. Suppose the agent has a projected utility \(\tilde u(c,s\mid s')\) of consuming \(c\) in state \(s\) given the current state is \(s'\), which satisfies
$$\tilde u(c,s\mid s')=(1-\alpha)\,u(c,s)+\alpha\,u(c,s')\quad\text{for }\alpha\in[0,1]$$
称为简单投射偏差。若 \(\alpha=0\)，则 \(\tilde u(c,s\mid s')=u(c,s)\)，无投射偏差；若 \(\alpha=1\)，则 \(\tilde u(c,s\mid s')=u(c,s')\)，完全投射偏差。
注 6.1 / Remark 6.1 具有投射偏差的人并非误判未来状态的概率分布；相反，他们误判的是自己在那些未来状态下的感受（偏好）。People with projection bias are not misjudging the probability distribution of future states; instead, they are misjudging how they feel (preferences) in those future states.
作者把投射偏差嵌入跨期选择问题。标准经济学中，具有期望效用性质的决策者求解 \(\max_{\{c_t,\dots,c_T\}}\mathbb{E}_t[U_t(c_t,\dots,c_T)]=\mathbb{E}_t\big[\sum_{\tau=t}^T\delta^\tau u(c_\tau,s_\tau)\big]\)，能沿状态路径 \(\{s_t,\dots,s_T\}\) 正确预期每个未来期的期间效用。而具投射偏差者改为求解 \(\max_{\{c_t,\dots,c_T\}}\mathbb{E}_t\big[\tilde U_t(c_t,\dots,c_T\mid s_t)\big]=\mathbb{E}_t\big[\sum_{\tau=t}^T\delta^\tau\tilde u(c_\tau,s_\tau\mid s_t)\big]\)。作者也把投射偏差嵌入习惯形成问题：标准下决策者偏好 \(V_t(c_t,\dots,c_T)=\sum_{\tau=t}^T\delta^\tau v(c_\tau-s_\tau)\)，其中 \(s_t=(1-\gamma)s_{t-1}+\gamma c_{t-1}\)（\(0<\gamma\le1\)）；具投射偏差者改为求解 \(\max\tilde V_t(c_t,\dots,c_T\mid s_t)=\sum_{\tau=t}^T\delta^\tau\tilde v(c_\tau-s_\tau)\)，其中 \(\tilde v(c_\tau-s_\tau)=(1-\alpha)v(c_\tau-s_\tau)+\alpha v(c_\tau-s_t)\)、\(s_t=(1-\gamma)s_{t-1}+\gamma c_{t-1}\)。作者还作了其他扩展并证明相关命题，其旨趣与上述例子相同。
6.2.2 天气对敞篷车购买的影响：Busse et al. (2015) / Effect of Weather on Convertible Car Purchase
called a simple projection bias. If \(\alpha=0\), then \(\tilde u(c,s\mid s')=u(c,s)\) and the person has no projection bias; if \(\alpha=1\), then \(\tilde u(c,s\mid s')=u(c,s')\) and the person has full projection bias.
Remark 6.1 具有投射偏差的人并非误判未来状态的概率分布；相反，他们误判的是自己在那些未来状态下的感受（偏好）。People with projection bias are not misjudging the probability distribution of future states; instead, they are misjudging how they feel (preferences) in those future states.
The authors embed projection bias into the inter-temporal choice problem. In standard economics the decision maker with expected-utility preferences solves \(\max_{\{c_t,\dots,c_T\}}\mathbb{E}_t[U_t(c_t,\dots,c_T)]=\mathbb{E}_t\big[\sum_{\tau=t}^T\delta^\tau u(c_\tau,s_\tau)\big]\), correctly anticipating the period utility in every future period along the state path \(\{s_t,\dots,s_T\}\). An agent with projection-biased preferences instead solves \(\max_{\{c_t,\dots,c_T\}}\mathbb{E}_t\big[\tilde U_t(c_t,\dots,c_T\mid s_t)\big]=\mathbb{E}_t\big[\sum_{\tau=t}^T\delta^\tau\tilde u(c_\tau,s_\tau\mid s_t)\big]\). The authors also embed projection bias into the habit-formation problem: in standard economics the decision maker has preferences \(V_t(c_t,\dots,c_T)=\sum_{\tau=t}^T\delta^\tau v(c_\tau-s_\tau)\), where \(s_t=(1-\gamma)s_{t-1}+\gamma c_{t-1}\) (\(0<\gamma\le1\)); an agent with projection-biased preferences and habit formation instead solves \(\max\tilde V_t(c_t,\dots,c_T\mid s_t)=\sum_{\tau=t}^T\delta^\tau\tilde v(c_\tau-s_\tau)\), where \(\tilde v(c_\tau-s_\tau)=(1-\alpha)v(c_\tau-s_\tau)+\alpha v(c_\tau-s_t)\) and \(s_t=(1-\gamma)s_{t-1}+\gamma c_{t-1}\). The authors also make other extensions and prove related propositions, all of which have a taste similar to the examples above.
6.2.2 Effect of Weather on Convertible Car Purchase: Busse et al. (2015)
Busse et al. (2015)：天气引发的投射偏差 / weather-induced projection bias 作者用美国 20% 新车经销商 2001 年 1 月 1 日至 2008 年 12 月 31 日的汽车交易数据，研究天气对敞篷车销量的影响。总体直觉：温暖宜人的日子里人们倾向把当下的感受与偏好投射到未来，从而更可能买敞篷车；但这是非理性的，因为敞篷车是耐用品、要在许多不同状态的时期里使用，其在未来各期与各状态（冬夏）下的效用并不相同，而人们似乎忽略了这种效用差异。第一，作者发现敞篷车销量有强烈的季节性（图 6.4）；但仅有季节性不足以证明投射偏差，因为完全理性的顾客也可能等到暖天才买以降低存储成本。第二，作者剔除季节趋势，看敞篷车购买与气温各自的残差（图 6.5 气温残差、图 6.6 敞篷车销量残差），发现两个残差之间显著正相关（图 6.7，t 统计量 7.6）——即在季节效应之外，更高气温也倾向提高敞篷车购买。此外，作者还发现购买敞篷车的概率与高温值之间的关系（图 6.8）：控制季节趋势后，气温越高、购买敞篷车的概率越高。图 6.5 与 6.8 的证据支持顾客存在投射偏差偏好这一潜在解释。The authors use automobile transactions data of 20% of all new car dealerships in the U.S. from January 1, 2001 to December 31, 2008 to study the effect of weather on convertible-car sales. The overall intuition: on warm nice days people tend to project this feeling and preferences into the future, which makes them more likely to buy a convertible car; but this behavior is irrational, because a convertible car is a durable good to be used in many periods of different states, and its utility won't be the same across all future periods and states (winter and summer), yet people seem to ignore this utility difference. First, the authors find convertible-car sales have a strong seasonality pattern (Figure 6.4); but this seasonal pattern alone is not enough to justify the projection-bias story, because perfectly rational customers might wait until warm days to buy convertibles to reduce storage cost. Second, the authors remove the seasonal trend and look at the residuals of both convertible-car purchases and weather temperature (Figure 6.5 temperature residual, Figure 6.6 convertible-sales residual), and find a significantly positive correlation between the two residuals (Figure 6.7, t-stat 7.6) — i.e. higher temperature (in addition to the seasonal effect) tends to increase the purchase of convertible cars. Moreover, the authors find a relation between the probability of purchasing convertible cars and the high-temperature value (Figure 6.8): after controlling for the seasonal trend, higher temperature leads to a higher probability of purchasing convertible cars. The evidence in Figures 6.5 and 6.8 supports the potential explanation of projection-bias preferences of customers.
图 6.4–6.8（已转述 / Figures 6.4–6.8, paraphrased） 图 6.4（敞篷车销量比例的季节趋势）：横轴 2001–2008 各月，纵轴"敞篷车占售出车辆百分比"，呈明显的年周期波动（夏高冬低）。图 6.5（芝加哥气温残差）与图 6.6（芝加哥敞篷车销量残差）：各自去季节后的残差散点，围绕 0 上下波动。图 6.7（两残差的相关）：横轴气温残差、纵轴敞篷车销量百分比残差，散点带正斜率拟合线，t 统计量 7.6——去季节后高温仍提高敞篷车购买。图 6.8（购买敞篷车的概率与高温）：横轴高温区间（25–30、…、>100 华氏度），纵轴"相对 65–70 度基准的购买概率点效应"（带 95% 置信区间），随温度上升而单调上升。Figure 6.4 (seasonal trend in percentage of convertibles sold): the horizontal axis is months 2001–2008, the vertical axis "convertible percentage of vehicles sold", showing a clear annual cycle (high in summer, low in winter). Figure 6.5 (Chicago temperature residual) and Figure 6.6 (Chicago convertible-sales residual): deseasonalized residual scatters, each fluctuating around 0. Figure 6.7 (correlation between the two residuals): the horizontal axis is the temperature residual, the vertical axis the convertible-sales-percentage residual, a scatter with a positive-slope fitted line, t-stat 7.6 — higher temperature still raises convertible purchases after deseasonalizing. Figure 6.8 (probability of buying a convertible vs. high temperature): the horizontal axis is the high-temperature bin (25–30, …, >100 Fahrenheit), the vertical axis "percentage-point effect on the purchase probability relative to the 65–70 degree baseline" (with 95% confidence intervals), rising monotonically with temperature.
6.3 其他有偏信念 / Other Biased Beliefs
6.3 Other Biased Beliefs
心理学信念偏误清单 / Catalog of psychological belief biases 过度自信 (Overconfidence)：人们有时高估自身能力与预测准确度。归因偏差 (Attribution bias)：评价自己与他人行为时的系统性错误——通常把自己的好行为归于内在属性、把他人的好行为归于外在属性；对坏行为则总把自己的归于外在借口、把他人的归于内在属性。基率偏差 (Base-rate bias)：人们不会用贝叶斯法则正确计算概率。确认偏差 (Confirmation bias)：人们倾向搜寻并深刻记住与自己先验信念相符的信息。Dunning-Kruger 效应：人们总倾向高估自身能力（虚幻的优越感），并不能认识到自己能力的不足。事后聪明偏差 (Hindsight bias)：人们倾向把已发生的事件视为比其发生前实际更可预测。热手谬误 (Hot hand fallacy)：相信曾有成功结果的人更可能取得下一次成功。控制错觉 (Illusion of control)：人们倾向高估自己控制事物的能力。近因偏差 (Recency bias)：人们倾向对最近发生的事件赋予更高权重。幸存者偏差 (Survivorship bias)：人们倾向不把缺失的失败者与样本中存在的幸存者合并估计，而只关注幸存者的可得数据。赌徒谬误 (Gambler's fallacy)：错误地相信，若某随机事件过去发生过多次，则其未来发生的概率会更低（或更高）。Overconfidence: people sometimes overestimate their abilities and the accuracy of their predictions. Attribution bias: the systematic errors people make when evaluating the behaviors of their own and others — they typically attribute their own good behaviors to intrinsic properties and others' good behaviors to extrinsic properties; for bad behaviors they always attribute their own to extrinsic excuses and attribute others' to intrinsic properties. Base-rate bias: people don't use Bayes' rule to calculate probabilities correctly. Confirmation bias: people tend to search for and deeply remember information that confirms their own prior beliefs. Dunning-Kruger effect: people always tend to over-evaluate their own abilities (illusory superiority) and fail to recognize their lack of ability. Hindsight bias: people tend to perceive events that have already happened as more predictable than they actually were before the events took place. Hot-hand fallacy: the belief that people who have had successful outcomes are more likely to make the next successful outcome. Illusion of control: people tend to overestimate their ability to control things. Recency bias: people tend to put higher weights on events that happened most recently. Survivorship bias: people tend to not combine the absent failures with the survivors existing in the observed sample for estimation, and typically just focus on the available data on survivors. Gambler's fallacy: the wrong belief that the probability of a random event is lower (or higher) in the future if it happens several times in the past.
参考文献 / References
- Bertrand, M., & Morse, A. (2011). Information Disclosure, Cognitive Biases, and Payday Borrowing. Journal of Finance, 66(6), 1865–1893.
- Bursztyn, L., González, A. L., & Yanagizawa-Drott, D. (2018). Misperceived Social Norms: Female Labor Force Participation in Saudi Arabia. NBER.
- Busse, M. R., Pope, D. G., Pope, J. C., & Silva-Risso, J. (2015). The Psychological Effect of Weather on Car Purchases. Quarterly Journal of Economics, 130(1), 371–414.
- Jensen, R. (2010). The (Perceived) Returns to Education and the Demand for Schooling. Quarterly Journal of Economics, 125(2), 515–548.
- Loewenstein, G., O'Donoghue, T., & Rabin, M. (2003). Projection Bias in Predicting Future Utility. Quarterly Journal of Economics, 118(4), 1209–1248.
References
- Bertrand, M., & Morse, A. (2011). Information Disclosure, Cognitive Biases, and Payday Borrowing. Journal of Finance, 66(6), 1865–1893.
- Bursztyn, L., González, A. L., & Yanagizawa-Drott, D. (2018). Misperceived Social Norms: Female Labor Force Participation in Saudi Arabia. NBER.
- Busse, M. R., Pope, D. G., Pope, J. C., & Silva-Risso, J. (2015). The Psychological Effect of Weather on Car Purchases. Quarterly Journal of Economics, 130(1), 371–414.
- Jensen, R. (2010). The (Perceived) Returns to Education and the Demand for Schooling. Quarterly Journal of Economics, 125(2), 515–548.
- Loewenstein, G., O'Donoghue, T., & Rabin, M. (2003). Projection Bias in Predicting Future Utility. Quarterly Journal of Economics, 118(4), 1209–1248.