本章导读 本章是 Part I 最后一章，讲注意力有限与显著性。显著性指注意力被不成比例地导向环境的某一部分，使其信息在决策中起不成比例的作用（可得性偏差是产生显著性的一种方式）。§7.1 信用卡费用 Agarwal et al. (2008)：从缴费经验中学习（上月缴费使本月缴费降 40%）又遗忘（知识每月折旧约 10%），高收入者学得快、忘得慢（图 7.1–7.3）。§7.2 对运费的不注意 Hossain & Morgan (2006)：eBay 拍卖四种"起拍价+运费"组合，更低起拍价带来更高收入（图 7.4–7.5）。§7.3 二手车市场的左位数偏差 Lacetera et al. (2012)：里程表读数的左位数偏差使价值函数在整万英里阈值处不连续（简单模型 + 图 7.6–7.9）。§7.4 显著性与税收 Chetty et al. (2009)：贴含税价使销量降 8%（DDD，图 7.10）、消费税（更显著）比销售税（不显著）更抑制啤酒消费（图 7.11–7.12）——人们对不显著的税反应不足。§7.5 金融市场中的不注意：7.5.1 困惑的投资者 Rashes (2001)（相似代码 MCI vs MCIC，图 7.13）、7.5.2 周五效应 DellaVigna & Pollet (2009)（图 7.14）、7.5.3 盈余惊喜的对比效应 Hartzmark & Shue (2018)（图 7.15）、7.5.4 鸵鸟效应 Karlsson et al. (2009)（图 7.16）。图 7.1–7.16 均已转述。

Agarwal et al. (2008)：学习与遗忘 / learning and forgetting 信用卡公司有数千亿的费用与利息收入，其中超过 60% 来自滞纳金、超限费等费用。Agarwal et al. (2008) 用以下数据研究持卡人从缴费经验中的学习与遗忘模式：某全国性发卡大行约 128,000 个信用卡账户的 2002 年 1 月至 2004 年 12 月月度数据；季度信用局评级 (FICO 分) 数据（含账户持有人详细个人信息）。作者用注意力有限与显著性来解释遗忘行为：注意力是稀缺资源，故顾客对近期发生的缴费更关注，一段时间后注意力转移、从缴费中学到的教训淡忘。结果：(1) 从过去经验中学习——上月缴的费使本月缴费降低 40%（图 7.1）；(2) 随时间遗忘——知识每月折旧约 10% 或更多（图 7.1），可能因注意力稀缺、一段时间后开始转移；(3) 高收入借款人学得快一倍、忘得慢一半（图 7.2 学得更快、图 7.3 忘得更慢），可能因其有更多注意力资源或更善于利用稀缺注意力。Credit card companies have hundreds of billions of revenue from fees and interest, of which over 60% comes from fees such as late payment fees and over-limit fees. Agarwal et al. (2008) use the following data sets to study credit card holders' learning and forgetting patterns from the experience of paying fees: about 128,000 credit card accounts' monthly data between January 2002 and December 2004 from a large U.S. bank that issues credit cards nationally; quarterly credit-bureau rating (FICO score) data reporting account holders' detailed personal information. The authors use inattention and salience to interpret the forgetting behavior: attention is a scarce resource, so customers pay more attention to the fee payment that occurred recently, and after a while attention is shifted to other things so the lesson learned from the fee payment fades away. Results: (1) people learn from past experience — a fee paid last month reduces the fee payment in the current month by 40% (Figure 7.1); (2) people forget as time passes — knowledge depreciates about 10% or more per month (Figure 7.1), potentially because attention is scarce and people start to shift it away after a while; (3) higher-income borrowers learn twice as fast and forget twice as slowly (Figure 7.2 faster learning, Figure 7.3 slower forgetting), potentially because they have more attention resources or better skills of exploiting the scarce attention.

图 7.1–7.3（已转述 / Figures 7.1–7.3, paraphrased） 图 7.1（\(k\) 月前所缴费用对当前缴费的影响）：横轴为"\(k\)（几个月前）"，纵轴为"给定 \(k\) 月前缴过费时当前的平均缴费"；滞纳金、超限费、预借现金费三条线均从低（约 0.4）随 \(k\) 增大而回升至约 1.2——刚缴过费时本月缴费大幅下降（学习），但随月份推移效应衰减（遗忘）。图 7.2（高收入者学得更快）：横轴账户存续月数、纵轴缴费频率，低/中/高收入三条递减曲线，高收入曲线下降最快（学习最快）。图 7.3（高收入者忘得更慢）：横轴"几月前缴费"、纵轴"缴费频率的下降量"，高收入曲线的回升最慢（遗忘最慢）。Figure 7.1 (impact of fees paid \(k\) months ago on fees paid now): the horizontal axis is "\(k\) (months ago)", the vertical axis "mean fees paid now given a fee paid \(k\) months ago"; the late-fee, over-limit-fee, and cash-advance-fee lines all rise from low (about 0.4) back up to about 1.2 as \(k\) grows — a recently paid fee sharply lowers this month's payment (learning), but the effect decays over months (forgetting). Figure 7.2 (higher income learns faster): the horizontal axis account tenure in months, the vertical axis fee frequency, with low/middle/high-income decreasing curves, the high-income curve falling fastest (learning fastest). Figure 7.3 (higher income forgets slower): the horizontal axis "months ago fee paid", the vertical axis "reduction in fee frequency", with the high-income curve recovering slowest (forgetting slowest).

Hossain & Morgan (2006)：起拍价 vs 运费 / opening bid vs shipping 作者运行 80 场 eBay 拍卖：对十种 CD 各拍四件（2001 年 11 月）、对十种 Xbox 游戏各拍四件（2002 年 3 月）。同款的四件被随机分入以下四种处理：A：起拍价 USD 4.00、运费 USD 0.00；B：起拍价 USD 0.01、运费 USD 3.99；C：起拍价 USD 6.00、运费 USD 2.00；D：起拍价 USD 2.00、运费 USD 6.00。其中 A、B 为低保留价组（起拍价 + 运费 = USD 4.00，图 7.4），C、D 为高保留价组（起拍价 + 运费 = USD 8.00，图 7.5）。结果：总体而言，更低的起拍价带来更高的拍卖收入，即便总保留价（起拍价 + 运费）相同。一个可能解释是竞拍者主要盯着起拍价、而对运费给予不足的注意；不过心理账户等替代解释也无法排除。The authors ran 80 eBay auctions: four pieces of each of ten CDs (November 2001) and four pieces of each of ten Xbox games (March 2002). The four pieces of the same item are randomly assigned to one of the following four treatments: A: set the opening bid at USD 4.00 and shipping cost at USD 0.00; B: opening bid USD 0.01 and shipping USD 3.99; C: opening bid USD 6.00 and shipping USD 2.00; D: opening bid USD 2.00 and shipping USD 6.00. Here A and B form the low-reserve group (opening bid + shipping = USD 4.00, Figure 7.4), and C and D the high-reserve group (opening bid + shipping = USD 8.00, Figure 7.5). Results: in general, a lower opening bid leads to higher revenue from the auction, even though the total reserve price (opening bid plus shipping) is the same. One possible explanation is that bidders mainly focus on the opening bid price and pay insufficient attention to the shipping cost; though alternative explanations such as mental accounts cannot be ruled out.

图 7.4、7.5（拍卖收入，已转述 / Figures 7.4, 7.5, paraphrased） 两图各为两张表（(a) 十种 CD、(b) 十种 Xbox 游戏），逐一列出"低运费处理"与"高运费处理"两种设定下的平均收入及百分比差异。图 7.4（低保留价组，起拍价+运费=USD 4.00）与图 7.5（高保留价组，=USD 8.00）均显示：把更多保留价放进运费（高起拍价、低运费 vs 低起拍价、高运费）时，低起拍价 + 高运费那一档反而带来更高的平均收入——多数商品的百分比差异为正，印证竞拍者忽视运费。Each figure is two tables ((a) ten CDs, (b) ten Xbox games), listing for each item the average revenue and percentage difference under the "low-shipping treatment" vs "high-shipping treatment". Both Figure 7.4 (low-reserve group, opening bid + shipping = USD 4.00) and Figure 7.5 (high-reserve group, = USD 8.00) show that when more of the reserve price is loaded into shipping (high opening bid + low shipping vs low opening bid + high shipping), the low-opening-bid + high-shipping option yields higher average revenue — most items show a positive percentage difference, confirming that bidders neglect shipping cost.

Lacetera et al. (2012)：里程表的左位数偏差 / left-digit bias in odometer readings 作者用美国某最大批发二手车拍卖运营商 2002 年 1 月至 2008 年 9 月的数据，研究里程表读数的左位数偏差对市场价格的影响。左位数偏差指顾客对价格中更靠左的数字给予更多注意，这被用于营销中的"99 美分定价"——例如售价常定为 USD 3.99 而非 USD 4.00 以促进销售。The authors use data from one of the largest operators of wholesale used-car auctions in the U.S. from January 2002 to September 2008 to study the effect of left-digit bias in odometer readings on market prices. Left-digit bias means customers pay more attention to the more left digits in prices, which is used in marketing as 99-cent pricing — e.g. product prices are always set as USD 3.99 rather than USD 4.00 to facilitate sales.

简单模型 / Simple model 作者先讨论如下简单模型：The authors start by discussing the following simple model:

$$\tilde m=d_H 10^H+\sum_{j=1}^{\infty}\Big[\prod_{k=1}^{j}(1-\theta_k)\Big]d_{H-j}10^{H-j}$$

其中 \(\tilde m\) 是成本的感知值，\(H\) 标记最左位数字、\(H-j\) 标记从左数第 \(j\) 位，\(d_{H-j}\in\{0,1,\dots,9\}\) 是从左数第 \(j\) 位上的数字，\(\theta_k\in[0,1]\) 是从左数第 \(k\) 位相对第 \(k-1\) 位的递减权重。基本思想是：主体对越靠右的数字注意越少，使右侧数字的取值越发"不透明"。这与 DellaVigna (2009) 的简单模型一致：对价值 \(V=v+o\) 的商品（\(v\) 为可见成分、\(o\) 为不透明成分），感知值为 \(\hat V=v+(1-\theta)o\)，\(\theta\in[0,1]\) 表示不注意程度——\(\theta=0\) 为完全注意的标准情形，\(\theta=1\) 为完全不注意。where \(\tilde m\) is the perceived value of the cost, \(H\) indexes the leftmost digit and \(H-j\) the \(j\)th digit from the left, \(d_{H-j}\in\{0,1,\dots,9\}\) is the number on the \(j\)th digit from the left, and \(\theta_k\in[0,1]\) is the reducing weight assigned to the \(k\)th digit relative to the \(k-1\)th digit from the left. The basic idea is that agents pay less and less attention to the digits on the right, which makes the right-digit values more opaque. This is consistent with the simple model in DellaVigna (2009): for a good with value \(V=v+o\) where \(v\) is the visible component and \(o\) the opaque component, the perceived value is \(\hat V=v+(1-\theta)o\) for \(\theta\in[0,1]\), where \(\theta\) denotes the degree of inattention — \(\theta=0\) is the standard case of full attention, and \(\theta=1\) is complete inattention.

预测与结果 / Prediction and results 预测（图 7.6 预测的不连续价值函数）：里程与市场价值之间的关系呈分段直线，在整万英里阈值处跳变——两阈值间斜率约为 \(-\alpha(1-\theta)\)（部分感知里程增加），跨过阈值处出现约 \(\alpha\theta\cdot10{,}000\) 的不连续下跌（更新后的左位数重新捕获稀缺注意力，使顾客在过阈值后立刻自我修正）。结果：实际价值函数确实在阈值附近呈不连续（图 7.7 原始价格）；作者控制品牌、车型、年款、车身等可观测量后，对残差价格重画图形，模式更干净（图 7.8 残差价格）。经销商（批发市场买家）所表现的左位数偏差，本质上源于零售买家（即经销商的下游顾客）的此种偏差——经销商知道顾客有此偏差，故据此行事（图 7.9 批发价与零售价）。Prediction (Figure 7.6, predicted discontinuous value function): the relationship between mileage and market value is a piecewise line that jumps at round 10,000-mile thresholds — between two thresholds the slope is about \(-\alpha(1-\theta)\) (partial perception of the mileage increase), and at the threshold there is a discontinuous drop of about \(\alpha\theta\cdot10{,}000\) (the updated left digit recaptures the scarce attention, so customers correct themselves right after passing the threshold). Results: the actual value function indeed displays discontinuous patterns around thresholds (Figure 7.7, raw prices); after the authors control for observables such as make, model, model year and body effects and redo the graph for the residual price, the pattern is even cleaner (Figure 7.8, residual prices). The left-digit bias displayed by dealers (buyers in the wholesale market) is basically a result of such bias displayed by retail buyers, who are the customers of the wholesale-market buyers — dealers know their customers have such bias, so they act accordingly (Figure 7.9, wholesale price and retail price).

图 7.6–7.9（已转述 / Figures 7.6–7.9, paraphrased） 图 7.6（预测）：价值随里程整体下行的折线，在 40,000、50,000、… 等整万处出现台阶式下跌；标注两段斜率 \(-\alpha\) 与 \(-\alpha(1-\theta)\)、不连续幅度 \(\alpha\theta\,10{,}000\)。图 7.7（实际原始价格）：横轴里程（取整到最近 500），纵轴平均售价，整体下行并在整万英里竖线处出现锯齿/台阶。图 7.8（残差价格）：去除车型等效应后的残差价格更平滑地下行，台阶式不连续更清晰。图 7.9（批发价与零售价）：零售价（上）与批发价（下）两条线并行下行，二者都在整万英里处出现同向的不连续——零售端的偏差传导到批发端。Figure 7.6 (prediction): a downward-sloping piecewise line of value vs mileage with step drops at round 10,000s like 40,000, 50,000, …; annotated with the two slopes \(-\alpha\) and \(-\alpha(1-\theta)\) and the discontinuity magnitude \(\alpha\theta\,10{,}000\). Figure 7.7 (actual raw prices): the horizontal axis mileage (rounded to nearest 500), the vertical axis average sales price, declining overall with sawtooth/step drops at the round-10,000-mile vertical lines. Figure 7.8 (residual prices): after removing model effects, the residual price declines more smoothly with clearer step discontinuities. Figure 7.9 (wholesale and retail price): the retail-price (upper) and wholesale-price (lower) lines decline in parallel, both with same-direction discontinuities at round 10,000 miles — the retail-side bias is transmitted to the wholesale side.

Chetty et al. (2009)：对不显著的税反应不足 / under-reacting to non-salient taxes 作者用以下数据表明消费者对不显著的税反应不足。田野实验数据：2006 年 2 月 22 日至 3 月 15 日，一家处理门店与两家控制门店关于洗护用品的每周扫描仪数据；处理组 13 个品类、控制组 95 个品类，分析在品类层面进行（同品类内所有产品求和）。观测数据：1970–2003 年美国各州层面消费税（included in posted prices，更显著）与销售税（added at register，不显著）的变化数据，以及各州年度总啤酒消费数据；好处在于酒精同时受两种州级税（消费税更显著、销售税不显著），二者在样本期内变动都很大（脚注：样本期内销售税有 153 次立法变动、消费税有 131 次），故可利用两种税效应之差（潜在由显著性导致）。The authors use the following data sets to show consumers under-react to non-salient taxes. Field experiment data: scanner data of weekly information on toiletry products sold at one treatment store and two control stores from February 22, 2006 to March 15, 2006; 13 product categories in the treatment group and 95 in the control group, with the analysis conducted at the category level (summing all products within the same category). Observational data: state-level changes in excise tax (included in posted prices, thus more salient) and sales tax (added at the register, thus less salient) from 1970 to 2003 in the U.S., plus annual state-level total beer consumption; the benefit is that alcohol is subject to two state-level taxes (excise more salient, sales less salient), both of which vary a lot in the sample period (footnote: during the sample period there are 153 legislated changes to the sales tax and 131 to the excise tax), so the authors can exploit the difference in the effects of the two taxes potentially caused by salience.

策略 1：田野实验（DDD）/ Strategy 1: field experiment (DDD) 美国多数零售店的销售税（约 7.375%）只在收银台加收、不含在标价中，故不显著。作者在处理门店里把含税价印在税前价正下方，覆盖三个应税品类约 750 种产品：化妆品、护发配件、除臭剂（选这三类因为：非超市销量领头羊，可限制销售损失；价格较高，使销售税额大到足以引起注意；价格弹性高，使需求反应可被检测）。作者用三重差分 (DDD) 方法，发现处理组（贴含税价）的销量与总收入在实验期相对两个控制组下降 8%（图 7.10；约 \(\frac{-2.14-0.06}{26.48}=8.31\%\)）。两个控制组：一是处理店内与处理品同货架的其他产品；二是邻近城市两家不贴含税价的门店。批评：需求下降可能由霍桑效应 (Hawthorne effect) 引起（脚注：霍桑效应指个体因意识到被观察而改变行为，又称观察者效应）——怪异价签的短期干预可能让人故意避免购买处理品。In most U.S. retail stores the sales tax (about 7.375%) is applied only at the register and not included in posted prices, so it is less salient. The authors post the tax-inclusive price right below the pretax price on price tags for about 750 products in three taxable groups: cosmetics, hair-care accessories, deodorants (picked because they are not sales leaders in the supermarket so as to limit losses in sales; have relatively high prices so the sales-tax value is large enough to cause attention; and exhibit high price elasticities so the demand response is detectable). Using a difference-in-differences-in-differences (DDD) approach, the authors find the quantity sold and total revenue of the treated group (with posted tax-inclusive prices) fall by 8% during the experiment relative to the two control groups (Figure 7.10; about \(\frac{-2.14-0.06}{26.48}=8.31\%\)). The two control groups: one is the other products on the same aisle as the treatment products in the treatment store; the other is two stores in nearby cities without posting tax-inclusive prices. Critique: the reduced demand might be caused by the Hawthorne effect (footnote: the Hawthorne effect means individuals may change behaviors in response to awareness of being observed, also called the observer effect) — the short-run intervention of weird price tags might make people intentionally avoid buying the treatment products.

策略 2：观测数据（消费税 vs 销售税）/ Strategy 2: observational data (excise vs sales tax) 为补充策略 1 并回应霍桑效应的批评，作者做观测分析。啤酒同时受消费税（更显著）与销售税（不显著），两者在样本期都有大量变动，作者利用州级税收政策变动检验消费者是否对不显著的税反应不足。回归结果（图 7.11）：消费税（更显著）对消费有显著负效应，而销售税（不显著）对消费的效应不显著；该模式在各设定下稳健。图形结果（图 7.12）：7.12a 消费税变化对啤酒消费有显著负效应、7.12b 销售税变化效应不显著。综合两种分析，结论是：人们对不显著的税反应不足。To complement Strategy 1 and answer the Hawthorne-effect critique, the authors conduct an observational analysis. Beer is subject to both an excise tax (more salient) and a sales tax (less salient), both of which vary a lot in the sample period, so the authors exploit state-level tax-policy variations to see if consumers under-react to less-salient taxes. Regression result (Figure 7.11): the excise tax (more salient) has a significant negative effect on consumption, while the sales tax (less salient) has a non-significant effect; the pattern is robust across specifications. Graph result (Figure 7.12): 7.12a the excise-tax change has a significant negative effect on beer consumption, while 7.12b the sales-tax change has a non-significant effect. Combining the two analyses, the conclusion is that people under-react to taxes that are not salient.

图 7.10–7.12（已转述 / Figures 7.10–7.12, paraphrased） 图 7.10（贴含税价的 DDD 效应）：分"处理店 / 控制店"两栏，列出处理品类与控制品类在"基线期 / 实验期"的平均销量及其差分，逐级求差得到 DDD 估计约 $-2.20$（对应约 8% 的下降）。图 7.11（两种税差异效应的回归估计）：被解释变量为人均啤酒消费对数变化，"消费税变化"系数显著为负、"销售税变化"系数不显著（接近 0），并列基线/经济周期/酒类法规等设定。图 7.12（税变与啤酒消费变化）：7.12a 横轴消费税变化对数、纵轴人均消费变化对数，散点带显著负斜率拟合线；7.12b 横轴销售税变化对数，散点拟合线近乎水平、不显著。Figure 7.10 (DDD effect of posting tax-inclusive prices): with "treatment store / control store" panels, listing the average quantity sold of treated vs control categories in "baseline / experiment" periods and their differences, the step-by-step differencing yielding a DDD estimate of about $-2.20$ (corresponding to about an 8% drop). Figure 7.11 (regression estimates of differential effects of the two taxes): with the dependent variable the change in log per-capita beer consumption, the "excise-tax change" coefficient is significantly negative while the "sales-tax change" coefficient is non-significant (close to 0), across baseline/business-cycle/alcohol-regulation specifications. Figure 7.12 (tax change and beer consumption change): 7.12a the horizontal axis log excise-tax change, the vertical axis log per-capita consumption change, scatter with a significant negative-slope fitted line; 7.12b the horizontal axis log sales-tax change, the fitted line nearly horizontal and non-significant.

7.5.1 困惑且不注意的投资者：Rashes (2001) / Confused and Inattentive Investors Rashes (2001) 聚焦一对代码极相似但基本面无关的股票（MCI vs MCIC），表明这两只本应不相关的股票却出人意料地相互高度相关——说明存在一些不注意、困惑的人混淆了两个代码而错误交易。MCI 是 MCI Communications（一家大型电信公司，1997 年被 Worldcom 收购前）的代码；MCIC 是 Massmutual Corporate Investors（一只主要投资长期公司债的封闭式基金，从不持有电信公司证券）的代码。有趣的是，MCI 与 MCIC 高度相关，但 MCI 与可比电信公司（AT&T，代码"T"）或与市场（NYSE 综合指数，代码"NYSE"）相关性都不强（图 7.13，含两个样本期的日成交量相关系数矩阵）。Rashes (2001) focuses on a pair of stocks that have very similar tickers but are fundamentally unrelated (MCI vs MCIC), and shows that these two supposedly uncorrelated stocks are surprisingly highly correlated with each other — suggesting there exist some inattentive and confused people who mess up differentiating between the two tickers and trade them wrongly. MCI was the ticker for MCI Communications (a large telecommunication company until it was acquired by Worldcom in 1997); MCIC was the ticker for Massmutual Corporate Investors (a closed-end mutual fund primarily invested in long-term corporate debt that never held securities of any telecom company). Interestingly, MCI and MCIC are highly correlated, but MCI doesn't have strong correlation with comparable telecom firms (AT&T with ticker "T") or with the market (NYSE Composite Index with ticker "NYSE") (Figure 7.13, daily-volume correlation coefficient matrices for two sample periods).

7.5.2 周五效应：DellaVigna 和 Pollet (2009) / Friday Effect on Reactions to Earnings Announcements DellaVigna & Pollet (2009) 研究投资者的有限注意，表明在周五（最可能出现不注意）发布的盈余公告有 15% 更低的即时反应、70% 更高的延迟反应、8% 更低的成交量。例如，若公告在周五发布，则下一交易日（周一）的成交量显著更低，可能因为人们的注意力在周末过后没有充分重新聚焦到公告上（图 7.14）。样本期 1985 年 1 月至 2006 年 6 月；每只股票的异常成交量定义为某日的对数成交量除以第 −20 到 −11 期（10 个交易日）的平均对数成交量。DellaVigna & Pollet (2009) study the limited attention of investors and show that earnings announcements on Friday (most likely to have inattention) have a 15% lower immediate response, 70% higher delayed response, and 8% lower trading volume. For example, the trading volume becomes significantly lower on the next trading day (Monday) if the announcement is made on Friday, probably because people's attention is not sufficiently refocused back on the announcement after the break of the weekend (Figure 7.14). The sample period is January 1985 to June 2006; the abnormal volume for each stock is defined by the log volume on the day divided by the average log volume for the period −20 to −11 (10 trading days).

7.5.3 盈余惊喜感知中的对比效应：Hartzmark 和 Shue (2018) / Contrast Effect in Perception of Earnings Surprises Hartzmark & Shue (2018) 表明投资者会把当前信号与前一个信号对比，使昨日（上一季度）的盈余惊喜反向影响今日（本季度）盈余惊喜被感知的方式。例如，若昨日盈余惊喜很负面，则今日无论惊喜如何都显得更好；若昨日惊喜很正面，则今日惊喜总显得更差。由对比效应（脚注：对比效应指人们基于与其他对象的比较作判断，可能因比较对象不同而得出不同判断），可预期昨日盈余惊喜与今日对今日惊喜的收益反应之间存在负相关——这正是 Hartzmark & Shue (2018) 主要发现所示（图 7.15）。这与有限注意相关：人们仅靠前一次惊喜来判断当前惊喜，反映其注意有限、在判断时未纳入足够因素。Hartzmark & Shue (2018) show that investors contrast the current signal with the previous signal in a way that yesterday's (previous quarter's) earnings surprise inversely influences how today's (current quarter's) earnings surprise is perceived. For example, if yesterday's earnings surprise is very negative, then whatever today's surprise is, it will seem to be better; if yesterday's surprise is very positive, today's surprise will always look worse. By the contrast effect (footnote: the contrast effect means people make a judgment based on comparing an object with other objects, which may lead to different judgments based on what the comparison objects are), one expects a negative correlation between yesterday's earnings surprise and today's return reaction to today's surprise — which is exactly the case shown by the main finding of Hartzmark & Shue (2018) (Figure 7.15). This is related to limited attention because people merely focus on the previous surprise to judge the current one, reflecting that they have limited attention and don't take in enough factors in making the judgment.

7.5.4 鸵鸟效应与对损失的注意回避：Karlsson et al. (2009) / Ostrich Effect and Reluctance to Pay Attention to Losses Karlsson et al. (2009) 研究瑞典股市股权投资中的鸵鸟效应（脚注：鸵鸟效应指人们回避了解对自己不利的负面信息、佯装该信息不存在），发现当收益更低时投资者更少登录其账户。这表明投资者在信息可能对自己有害时有意转移注意力，在某些情形下造成有效注意力的有限（图 7.16）。样本期 2002 年 1 月 7 日至 2004 年 10 月 13 日；omxspi 为斯德哥尔摩全股指数水平；look-ups 为瑞典溢价养老金投资者每日账户登录数减去每日账户再平衡数。图中两条线不是水平本身，而是两个回归的残差，即 (7.1) 的 \(e_{\text{look-ups},t}\) 与 (7.2) 的 \(e_{\text{omxspi},t}\)：Karlsson et al. (2009) study the ostrich effect (footnote: the ostrich effect means people avoid learning adverse information that is bad for them and just pretend the information doesn't exist) in equity investment in the Swedish market, and find that investors log in less frequently when the return is lower. This is evidence that investors intentionally divert away their attention when the information is potentially harmful to them, which causes limited effective attention in some cases (Figure 7.16). The sample period is January 7, 2002 to October 13, 2004; omxspi is the level of the Stockholm All Shares stock index; look-ups is the daily number of Swedish Premium Pension investor account logins minus the daily number of account rebalancing. The two lines in the figure are not the levels themselves but the residuals of two regressions, i.e. \(e_{\text{look-ups},t}\) in (7.1) and \(e_{\text{omxspi},t}\) in (7.2):

$$\text{look-ups}_t=\alpha_0+\sum_{i=T,W,R,F}\alpha_{1,i}\text{Day}_{i,t}+\alpha_2\text{Trend}_t+\alpha_3\text{Transactions}_t+e_{\text{look-ups},t}\tag{7.1}$$

$$\text{omxspi}_t=\beta_0+\sum_{i=T,W,R,F}\beta_{1,i}\text{Day}_{i,t}+\beta_2\text{Trend}_t+e_{\text{omxspi},t}\tag{7.2}$$

其中 \(\text{Day}_{i,t}\) 是星期几的虚拟变量（周二、三、四、五），\(\text{Trend}_t\) 为线性时间趋势，\(\text{Transactions}_t\) 为瑞典养老金投资者当日交易总数。由图 7.16 可清楚看到：当市场表现（出乎意料地）糟糕时，人们倾向更少登录账户、从账户表现上转移注意力。关于行为金融的更详细讨论见 Part II。where \(\text{Day}_{i,t}\) is the dummy variable for days of the week (Tuesday, Wednesday, Thursday, Friday), \(\text{Trend}_t\) is a linear time trend, and \(\text{Transactions}_t\) is the daily total number of Swedish pension investor transactions. From Figure 7.16 we can clearly see that when market performance is (unexpectedly) bad, people tend to log in less frequently and divert their attention away from their account performance. See more detailed discussion on behavioral finance in Part II.

图 7.13–7.16（已转述 / Figures 7.13–7.16, paraphrased） 图 7.13（日成交量相关系数矩阵）：两面板（样本期 A、B）给出 MCI、MCIC、T、NYSE 两两相关；MCI–MCIC 相关高（约 0.5），而 MCI–T、MCI–NYSE 相关很低（接近 0）。图 7.14（盈余公告前后平均异常成交量）：横轴为相对公告日的交易日数，柱形显示公告后成交量上升，但"周五公告"组的即时上升明显弱于"非周五"组。图 7.15（盈余公告收益反应中的对比效应）：横轴为昨日盈余惊喜、纵轴为今日对今日惊喜的收益反应 \(\%[t,t+1]\)，呈明显负斜率（带置信带）。图 7.16（标准化残差指数水平与登录数）：横轴 2002–2004 日期，两条线为指数水平残差与登录数残差；指数残差走低（市场意外变差）时登录数残差也走低——印证鸵鸟效应。Figure 7.13 (daily-volume correlation coefficient matrices): two panels (sample periods A, B) give pairwise correlations of MCI, MCIC, T, NYSE; MCI–MCIC correlation is high (about 0.5), while MCI–T and MCI–NYSE correlations are very low (close to 0). Figure 7.14 (average abnormal volume around earnings announcement date): the horizontal axis is trading days relative to the announcement date; the bars show volume rising after the announcement, but the immediate rise for the "Friday announcement" group is clearly weaker than the "non-Friday" group. Figure 7.15 (contrast effects in return reactions to earnings announcements): the horizontal axis is yesterday's earnings surprise, the vertical axis today's return reaction to today's surprise \(\%[t,t+1]\), with a clear negative slope (with confidence bands). Figure 7.16 (standardized residual index level and look-ups): the horizontal axis is dates 2002–2004, the two lines are the index-level residual and the look-ups residual; when the index residual goes low (the market unexpectedly worsens) the look-ups residual also goes low — confirming the ostrich effect.