1、信息时代的价格歧视：价格、窃取和个性化定向折扣的隐私研究
本文分析了一种价格竞争模型，其中公司之间可以以一定成本通过事后对定向消费者给予折扣的方式进行标价竞争，并解决了允许消费者是否是定向选择的隐私规制（如GDPR）。被定向的消费者会收到获取和保留的折扣优惠。均衡折扣优惠以混合策略形式存在，但每个有争议的消费者只有两家公司竞争，最终的利润类似于Bertrand竞争。当定向折扣没有限制时，公司的标价竞争类似于垄断。对于合理的需求条件，如果定向成本较高，公司和消费者福利比禁止定向更差。然而，如果需求是凸的（凹的），定向会导致更高（更低）的标价，如果标价在市场的任何一方发生足够大的偏移，市场的任何一方都可以受益。在有选择的情况下，当且仅当预期折扣超过隐私成本时消费者会选择加入。在实际可行的条件下，选择加入使所有消费者受益。
We study list price competition when firms can individually target consumer discounts (at a cost) afterwards, and we address recent privacy regulation (like the GDPR) allowing consumers to choose whether to opt-in to targeting. Targeted consumers receive poaching and retention discount offers. Equilibrium discount offers are in mixed strategies, but only two firms vie for each contested consumer and final profits on them are Bertrand-like. When targeting is unrestricted, firm list pricing resembles monopoly. For plausible demand conditions and if targeting costs are not too low, firms and consumers are worse off with unrestricted targeting than banning it. However, targeting induces higher (lower) list prices if demand is convex (concave), and either side of the market can benefit if list prices shift enough in its favour. Given the choice, consumers opt in only when expected discounts exceed privacy costs. Under empirically plausible conditions, opt-in choice makes all consumers better off.
Simon Anderson, Alicia Baik, Nathan Larson, Price Discrimination in the Information Age: Prices, Poaching, and Privacy with Personalized Targeted Discounts, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2085–2115, https://doi.org/10.1093/restud/rdac073
2、存钱、消费还是赠予？关于老年人的住房、家庭保险和储蓄模型
住房和家庭如何塑造了老年人的储蓄、消费和代际转移行为？本文使用“健康与退休研究”数据，我们发现向子女进行的代际转移是变相提高的，房屋所有者支出速度比租户慢得多，但通常在入住疗养院时出售他们的房屋，而子女提供照顾能够减缓入住疗养院的速度，并与更大的遗赠（特别是房屋）有关。为了解释这些事实，我们建立了一个关于家庭的动态、非合作模型，该模型包括不可分割的住房资产，并包括老年父母和子女之间关于父母的住房和护理安排的联合协商。该模型产生了真实的储蓄和护理选择，并匹配了转移和房产变现的时机。本文创新点是将住房作为承诺渠道：在没有长期家庭契约的情况下，住房为更高效储蓄提供了承诺机制。我们发现，这一渠道使老年时的住房拥有率提高约三分之一，家庭购房意愿增加了5-10%。这一机制还促进了非正式照顾，减缓了消费，导致遗赠增加，实证上也支持了以上影响。
How do housing and family shape the savings, spending, and inter-generational transfer behaviour of the elderly? Using the Health and Retirement Study, we document that inter-generational transfers to children are substantially backloaded, that homeowners dis-save much more slowly than renters but often sell their houses when entering a nursing home, and that care by children slows down nursing home entry and is linked to larger bequests, particularly of housing. To rationalise these facts, we develop a dynamic, non-cooperative model of the family with an indivisible housing asset and joint bargaining between elderly parents and their children over the housing and care arrangements of the parents. The model generates realistic savings and care choices and matches the timing of transfers and home liquidations. A key novelty is the housing-as-commitment channel: In the absence of long-run family contracts, housing provides a commitment device for more efficient savings. We find that this channel increases homeownership in old age by one-third and families’ willingness to pay for houses by 5–10%. This mechanism also facilitates informal care, slows down spending, and leads to larger bequests, implications that we support empirically.
Daniel Barczyk, Sean Fahle, Matthias Kredler, Save, Spend, or Give? A Model of Housing, Family Insurance, and Savings in Old Age, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2116–2187, https://doi.org/10.1093/restud/rdac081
3、迷雾中的困惑：空气污染对痴呆症的影响
我们研究了长期累积暴露于空气中的细小颗粒物（PM2.5）是否会影响个体被诊断为阿尔茨海默病或相关痴呆症的概率。我们追踪了2001年至2013年间，年龄在六十五岁及以上的美国人的健康、居住地点和PM2.5暴露情况。《清洁空气法》推广使得个体暴露于PM2.5 的准随机变化。我们利用这些法规构建了个体十年间PM2.5 的工具变量，并使用灵活的Probit概率模型研究，该模型同时考虑了基于生存的任何潜在样本选择。我们发现，每立方米PM2.5 十年增加1微克，将使得新痴呆症诊断的概率增加2.15%。其他条件相等的情况下，我们发现女性、年龄较大的人和具有更多痴呆症临床风险因素的人的影响更大。这些影响在当前法规阈值之下仍然存在。
We study whether long-term cumulative exposure to airborne small particulate matter (PM2.5) affects the probability that an individual receives a new diagnosis of Alzheimer's disease or related dementias. We track the health, residential location, and PM2.5 exposures of Americans aged sixty-five and above from 2001 through 2013. The expansion of Clean Air Act regulations led to quasi-random variation in individuals’ subsequent exposures to PM2.5. We leverage these regulations to construct instrumental variables for individual-level decadal PM2.5 that we use within flexible probit models that also account for any potential sample selection based on survival. We find that a 1 µg/m3 increase in decadal PM2.5 increases the probability of a new dementia diagnosis by an average of 2.15 percentage points (pp). All else equal, we find larger effects for women, older people, and people with more clinical risk factors for dementia. These effects persist below current regulatory thresholds.
Kelly C Bishop, Jonathan D Ketcham, Nicolai V Kuminoff, Hazed and Confused: The Effect of Air Pollution on Dementia, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2188–2214, https://doi.org/10.1093/restud/rdac078
4、“既然你这么富有，一定非常聪明”: 才能、收益分享和金融工资溢价
过去几十年，金融部门的工资水平大幅增加。我们探讨了这种增长的两种潜在解释：（1）对人才的需求增加，（2）公司与员工分享收益。通过将瑞典工人的行政数据（包括独特的个人才能度量）与雇主的财务信息相匹配，我们没有发现金融领域的才能水平（平均水平和顶级水平）改善的证据。各种才能和教育水平的样本中都发现了相对金融工资的增长，这些因素最多可以解释增长的20%。相反，不断增加的与员工分享的金融部门利润的上升占了相对工资增长的一半。劳动力供给有限可以通过金融领域早期职业入门和社会关系的重要性来解释。我们的发现缓解了对金融领域的“人才流失”的担忧，但表明金融从业者随着工龄增加捕获的收益递增。
Financial sector wages have increased extraordinarily over the last decades. We address two potential explanations for this increase: (1) rising demand for talent and (2) firms sharing rents with their employees. Matching administrative data of Swedish workers, which include unique measures of individual talent, with financial information on their employers, we find no evidence that talent in finance improved, neither on average nor at the top. The increase in relative finance wages is present across talent and education levels, which together can explain at most 20% of it. In contrast, rising financial sector profits that are shared with employees account for up to half of the relative wage increase. The limited labour supply response may partly be explained by the importance of early-career entry and social connections in finance. Our findings alleviate concerns about “brain drain” into finance but suggest that finance workers have captured rising rents over time.
Michael J Böhm, Daniel Metzger, Per Strömberg, “Since You’re So Rich, You Must Be Really Smart”: Talent, Rent Sharing, and the Finance Wage Premium, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2215–2260, https://doi.org/10.1093/restud/rdac079
5、机器人、贸易和卢迪主义：最优技术监管的充分统计量方法
从机器人的出现到贸易机会的增加，技术变革造就了赢家和输家。政府政策应该如何应对？我们提供了在次优的背景下的最优技术监管的一般理论，其中家庭之间的差异性大，对受到技术变革影响的企业子集征收线性税，对劳动收入征收非线性税。我们的第一组结果包括最优税收公式，其基于最少的结构性假设，涉及足够多的统计量，可以分析新技术（如机器人和贸易）对分配效应的影响。我们的最终结果是比较静态分析，其中包括，尽管分配方面的担忧为机器人和贸易征收非零税提供了理由，但这些税的幅度可能会随着自动化和全球化的深化以及不平等的加剧而减少。
Technological change, from the advent of robots to expanded trade opportunities, creates winners and losers. How should government policy respond? We provide a general theory of optimal technology regulation in a second-best world, with rich heterogeneity across households, linear taxes on the subset of firms affected by technological change, and a non-linear tax on labour income. Our first set of results consists of optimal tax formulas, with minimal structural assumptions, involving sufficient statistics that can be implemented using evidence on the distributional impact of new technologies, such as robots and trade. Our final results are comparative static exercises illustrating, among other things, that while distributional concerns create a rationale for non-zero taxes on robots and trade, the magnitude of these taxes may decrease as the process of automation and globalization deepens and inequality increases.
Arnaud Costinot, Iván Werning, Robots, Trade, and Luddism: A Sufficient Statistic Approach to Optimal Technology Regulation, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2261–2291, https://doi.org/10.1093/restud/rdac076
6、智商、预期和选择
我们使用行政和基于调查的微观数据研究了智力（智商）、通货膨胀预期形成和代表性男性人口的消费计划之间的关系。高智商的男性对通货膨胀的预测误差比其他男性低50％。高智商的男性随时间展现出一致的通货膨胀预期和感知。在选择方面，只有高智商的男性在预期通货膨胀较高时会增加其消费倾向，正如消费者欧拉方程所规定的那样。教育水平、收入、其他预期和社会经济地位等因素尽管很重要，但并不能解释智商不同对预期和选择的影响。已有文献尝试将有限理性的代理人纳入宏观模型，但并没有完全捕捉到我们所记录的所有事实。我们讨论了期望形成和选择的哪些方面对家庭消费的异质代理模型以及财政、货币政策传导产生重要作用。
We use administrative and survey-based micro data to study the relationship between cognitive abilities (IQ), the formation of inflation expectations, and the consumption plans of a representative male population. High-IQ men display 50 %% lower forecast errors for inflation than other men. High-IQ men, but not others, have consistent inflation expectations and perceptions over time. In terms of choice, only high-IQ men increase their consumption propensity when expecting higher inflation as the consumer Euler equation prescribes. Education levels, income, other expectations, and socio-economic status, although important, do not explain the variation in expectations and choice by IQ. Recent modelling attempts to incorporate boundedly rational agents into macro models do not fully capture all the facts we document. We discuss which dimensions of expectations formation and choice are important for heterogeneous-agents models of household consumption and for the transmission of fiscal and monetary policy.
Francesco D’Acunto, Daniel Hoang, Maritta Paloviita, Michael Weber, IQ, Expectations, and Choice, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2292–2325, https://doi.org/10.1093/restud/rdac075
7、从邻居那里了解变化状态
代理人使用私人信号和其邻居前期对状态的估计来了解一个变化状态。本文中，贝叶斯性质代理人使用具有时间不变权重的加权作为邻居的估计值来实现均衡解。因此，这些动态与网络学习的可解释DeGroot模型相似，但这些动态是平衡结果，而不是行为假设。我们研究了随着邻域规模的增大，信息聚合是否是接近最优的。这个问题的一个关键条件是信号的多样性：每个个体的邻居都有私人信号，这些信号不仅包含独立的信息，而且具有足够不同的分布。如果信号的多样性不存在（例如私人信号是独立同分布的），学习在所有网络中都是次优的，而在某些网络中低效率。本文发现学习的社会影响对个人的信号质量更为敏感，而对一个人的邻居数量不敏感，这一特征与具有外生更新性质的标准模型相反。
Agents learn about a changing state using private signals and their neighbours’ past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbours’ estimates simply by taking weighted sums with time-invariant weights. The dynamics thus parallel those of the tractable DeGroot model of learning in networks, but arise as an equilibrium outcome rather than a behavioural assumption. We examine whether information aggregation is nearly optimal as neighbourhoods grow large. A key condition for this is signal diversity: each individual’s neighbours have private signals that not only contain independent information, but also have sufficiently different distributions. Without signal diversity—e.g. if private signals are i.i.d.—learning is suboptimal in all networks and highly inefficient in some. Turning to social influence, we find it is much more sensitive to one’s signal quality than to one’s number of neighbours, in contrast to standard models with exogenous updating rules.
Krishna Dasaratha, Benjamin Golub, Nir Hak, Learning from Neighbours about a Changing State, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2326–2369, https://doi.org/10.1093/restud/rdac077
8、竞赛中的最优反馈
我们分析了一种最优动态竞赛模型，其中在设计者通过粗略的二进制信号 --- 泊松成功来监测努力程度。设计者目标是给定固定奖励的情况下，尽可能在最短的时间内激励参赛者付出努力最大化。设计者有很多竞赛可以选择，其中包括终止竞赛和调整奖励分配规则以及参赛者的实时反馈。每个最大化努力的竞赛（同时最大化总期望成功）都有一个依赖历史的终止规则，一个可以让代理充分了解他们自己成功程度的反馈政策，和一个奖励分配规则（可以期望地获得固定的奖金份额）。任何可以在最短时间内达到这一目标的竞赛都必须是我们所说的第二次机会：一旦到达预定数量的成功，竞赛进入一个倒计时阶段，在这个阶段，参赛者被给予最后一次成功的机会。
We obtain optimal dynamic contests for environments where the designer monitors effort through coarse, binary signals—Poisson successes—and aims to elicit maximum effort, ideally in the least amount of time possible, given a fixed prize. The designer has a vast set of contests to choose from, featuring termination and prize-allocation rules together with real-time feedback for the contestants. Every effort-maximizing contest (which also maximizes total expected successes) has a history-dependent termination rule, a feedback policy that keeps agents fully apprised of their own success, and a prize-allocation rule that grants them, in expectation, a time-invariant share of the prize if they succeed. Any contest that achieves this effort in the shortest possible time must in addition be what we call second chance: once a pre-specified number of successes arrive, the contest enters a countdown phase where contestants are given one last chance to succeed.
Jeffrey C Ely, George Georgiadis, Sina Khorasani, Luis Rayo, Optimal Feedback in Contests, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2370–2394, https://doi.org/10.1093/restud/rdac074
9、流动性与汇率关系的实证研究
我们发现有力的实证证据表明，政府债券的流动性收益与标准经济基本面结合起来，可以很好地解释名义汇率波动。我们发现有力的证据表明，流动性收益的变化在解释所有G10国家的汇率变动方面具有重要意义，而且我们强调美元也符合此模型。我们展示了这些关系是如何在具有流动性回报的新凯恩斯两国模型中产生的。此外，我们还发现主权违约风险和货币互换市场摩擦也起到了一定的作用。
We find strong empirical evidence that the liquidity yield on government bonds in combination with standard economic fundamentals can well account for nominal exchange rate movements. We find impressive evidence that changes in the liquidity yield are significant in explaining exchange rate changes for all the G10 countries, and we stress that the US dollar is not special in this relationship. We show how these relationships arise out of a canonical two-country New Keynesian model with liquidity returns. Additionally, we find a role for sovereign default risk and currency swap market frictions.
Charles Engel, Steve Pak Yeung Wu, Liquidity and Exchange Rates: An Empirical Investigation, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2395–2438, https://doi.org/10.1093/restud/rdac072
10、宏观经济稳定的失业保险
本文研究了具有不完全市场一般均衡、搜索摩擦和名义僵化的性质的失业保险。如果失业者的边际消费倾向高于就业者，或者如果代理商出于未来收入风险的考虑而进行预防性储蓄，那么失业保险的提高将提高消费的总需求。失业保险会提高产出和就业，除非货币政策提高了名义利率进而对产出和就业产生扰动影响。在对2008年至2014年美国经济的分析中，失业保险福利增加使得当期产出乘数约为1。如果没有这些增加，失业率可能会高出多达0.4个百分点。
I study unemployment insurance (UI) in general equilibrium with incomplete markets, search frictions, and nominal rigidities. An increase in generosity raises the aggregate demand for consumption if the unemployed have a higher marginal propensity to consume than the employed or if agents precautionary save in light of future income risk. This raises output and employment unless monetary policy raises the nominal interest rate. In an analysis of the U.S. economy over 2008–2014, UI benefit extensions had a contemporaneous output multiplier around 1. The unemployment rate would have been as much as 0.4 pp higher absent these extensions.
Rohan Kekre, Unemployment Insurance in Macroeconomic Stabilization, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2439–2480, https://doi.org/10.1093/restud/rdac080
11、美国各州职业许可的福利分析
我们评估了职业许可对工人和消费者的福利效应。我们估计了一个劳动力市场均衡模型，其中许可限制了劳动力供应，但也通过工人质量和选择影响劳动力需求。美国各州之间颁布了不同的职业许可，我们发现职业许可提高了工资和工时，但降低了就业。本文估计发现职业剩余的平均福利损失为12%，工人和消费者分别承担70%和30%的负担，更高的支付意愿抵消了消费者更高价格的80%，更高的工资为工人弥补了占职业特定人力资本的强制性投资成本的60%，职业许可似乎在更常见的职业中具有更有利的福利效应。
We assess the welfare consequences of occupational licensing for workers and consumers. We estimate a model of labour market equilibrium in which licensing restricts labour supply but also affects labour demand via worker quality and selection. On the margin of occupations licensed differently between U.S. states, we find that licensing raises wages and hours but reduces employment. We estimate an average welfare loss of 12% of occupational surplus. Workers and consumers respectively bear 70% and 30% of the incidence. Higher willingness to pay offsets 80% of higher prices for consumers, and higher wages compensate workers for 60% of the cost of mandated investment in occupation-specific human capital. Welfare effects appear more favourable in occupations in which licensing is more common.
Morris M Kleiner, Evan J Soltas, A Welfare Analysis of Occupational Licensing in U.S. States, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2481–2516, https://doi.org/10.1093/restud/rdad015
12、稳健实施的网络解决方案：相同但未知分布的情况
本文研究了稳健机制设计，其中代理人普遍认为其他代理人的类型是同分布的，但没有假定实际分布形式是共同知识，也不知道设计者知道与否。首先，我们对这些假设下的所有激励兼容转移进行了刻画。其次，本文描述了通过直接机制实现全面执行的条件，这些条件只引出与支付相关的信息，并分析了在可能的情况下实现该目标的转移方案。完全实施的结果表明，问题可以被转化为设计一个具有策略外部性的网络，其受适当的约束限制，这些约束又是由激励兼容性要求决定的。
We study robust mechanism design in environments in which agents commonly believe that others’ types are identically distributed, but we do not assume that the actual distribution is common knowledge, nor that it is known to the designer. First, we characterize all incentive compatible transfers under these assumptions. Second, we characterize the conditions under which full implementation is possible via direct mechanisms, that only elicit payoff relevant information, and the transfer schemes which achieve it whenever possible. The full implementation results obtain from showing that the problem can be transformed into one of designing a network of strategic externalities, subject to suitable constraints which are dictated by the incentive compatibility requirements.
Mariann Ollár, Antonio Penta, A Network Solution to Robust Implementation: The Case of Identical but Unknown Distributions, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2517–2554, https://doi.org/10.1093/restud/rdac084
13、更可靠的平行趋势方法
本文提出了一种用于双重差分和事件研究设计的稳健推断工具，其中平行趋势假设可能被违背。本文不要求平行趋势条件完全成立，而是对事后违背平行趋势与事前趋势的差异（“前趋势”）施加了限制。在这些限制下，感兴趣的因果参数部分得到了确定。我们介绍了两种方法，其可以保证在施加的限制下获得统一有效的推断，并得出新颖的结果，表明它们在我们的情境中具有良好性质。我们通过两个经济学案例，说明了识别平行趋势是否可能被违背的方法。我们还强调了我们的方法如何用于进行敏感性分析，以展示在对平行趋势假设可能违背的各种限制下可以得出什么因果结论。
This paper proposes tools for robust inference in difference-in-differences and event-study designs where the parallel trends assumption may be violated. Instead of requiring that parallel trends holds exactly, we impose restrictions on how different the post-treatment violations of parallel trends can be from the pre-treatment differences in trends (“pre-trends”). The causal parameter of interest is partially identified under these restrictions. We introduce two approaches that guarantee uniformly valid inference under the imposed restrictions, and we derive novel results showing that they have desirable power properties in our context. We illustrate how economic knowledge can inform the restrictions on the possible violations of parallel trends in two economic applications. We also highlight how our approach can be used to conduct sensitivity analyses showing what causal conclusions can be drawn under various restrictions on the possible violations of the parallel trends assumption.
Ashesh Rambachan, Jonathan Roth, A More Credible Approach to Parallel Trends, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2555–2591, https://doi.org/10.1093/restud/rdad018
14、生产法与成本溢价
根据成本溢价的生产法估计，任何灵活的投入都应该溢价。本文使用智利、哥伦比亚、印度、印度尼西亚、美国和南欧的制造业数据集，以及一家美国主要零售商的门店级数据来分析，发现使用劳动和原材料估算的成本溢价具有相同的分布的假说不成立。对于每个数据集，使用劳动估算的成本溢价与使用原材料估算的成本溢价呈负相关，使用劳动估算的成本溢价呈现更大的分散度，并具有相反的时间趋势。本文还发现使用能源和非能源原材料估算的成本溢价存在明显差异。企业之间的非中性生产率差异可以解释这些发现。
Under the production approach to markup estimation, any flexible input should recover the markup. I test this implication using manufacturing datasets from Chile, Colombia, India, Indonesia, the U.S., and Southern Europe, as well as store-level data from a major U.S. retailer, and overwhelmingly reject that markups estimated using labour and materials have the same distribution. For every dataset, markups estimated using labour are negatively correlated with markups estimated using materials, exhibit greater dispersion, and have opposite time trends. I continue to find stark differences in markups estimated using energy and non-energy raw materials. Non-neutral productivity differences across firms can explain these findings.
Devesh Raval, Testing the Production Approach to Markup Estimation, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2592–2611, https://doi.org/10.1093/restud/rdad002
15、 不止一分钱的价值：左位数偏误和公司定价
公司商品定价经常以0.99为结尾，这是因为存在左位数偏误——即消费者倾向于认为4.99美元比5.00美元便宜很多。本文对美国二十五家连锁店销售的3500种产品的零售扫描数据的分析为这一解释提供了有力支持。文章从结构上估计了左位数偏误的幅度，并发现消费者对0. 99结尾的价格再增加一分钱的反应相当于增加了二十分之多。接下来，本文提出了一个关于左位数偏误需求的最优定价模型，并使用这一模型和其他定价过程来估计零售商在定价决策时感知到的左位数偏误水平。尽管所有零售商都通过使用.99结尾的价格来应对左位数偏误，但他们的行为始终与他们所面临的需求背道而驰。公司定价的方式就好像偏误要小得多，他们的定价更符合启发式和经验法则，而不是根据需求结构的最优化。本文计算出，由于对左位数偏误的粗略反应，零售商放弃了1%至4%的潜在毛利润。
Firms arguably price at ninety-nine-ending prices because of left-digit bias—the tendency of consumers to perceive a $4.99 as much lower than a $5.00. Analysis of retail scanner data on 3500 products sold by twenty-five U.S. chains provides robust support for this explanation. I structurally estimate the magnitude of left-digit bias and find that consumers respond to a one-cent increase from a ninety-nine-ending price as if it were more than a twenty-cent increase. Next, I solve a portable model of optimal pricing given left-digit biased demand. I use this model and other pricing procedures to estimate the level of left-digit bias retailers perceive when making their pricing decisions. While all retailers respond to left-digit bias by using ninety-nine-ending prices, their behaviour is consistently at odds with the demand they face. Firms price as if the bias were much smaller than it is, and their pricing is more consistent with heuristics and rule-of-thumb than with optimization given the structure of demand. I calculate that retailers forgo 1–4% of potential gross profits due to this coarse response to left-digit bias.
Avner Strulov-Shlain, More Than a Penny’s Worth: Left-Digit Bias and Firm Pricing, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2612–2645, https://doi.org/10.1093/restud/rdac082
16、分层树用于自适应随机化的随机对照试验
本文提出了一种两阶段随机对照试验的自适应随机化程序。该方法使用第一阶段实验的数据，以确定如何分层第二阶段的实验，其中目标是最小化平均处理效应的估计方差。我们考虑从一类分层随机化程序中进行选择，我们称之为分层树：这些程序的分层可以表示为决策树，不同的分层具有不同的处理分配概率。通过使用第一阶段来估计分层树，我们同时选择用于分层的协变量，如何在这些协变量上进行分层，以及这些分层内的分配概率。我们的主要结果表明，使用适当的估计量进行这种随机化程序将导致渐近方差在分层树类中是最小的。此外，我们的结果能够适应分层块随机化等多种分层内分配机制。在模拟研究中，该方法配合适当的交叉验证程序可以改进分层的即兴选择。最后，我们应用该方法到Karlan和Wood（2017年，《行为与实验经济学杂志》，第66卷，第1-8页）实验的第一阶段的研究中来估计分层树。
This paper proposes an adaptive randomisation procedure for two-stage randomised controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimise the variance of an estimator for the average treatment effect. We consider selection from a class of stratified randomisation procedures which we call stratification trees: these are procedures whose strata can be represented as decision trees, with differing treatment assignment probabilities across strata. By using the first wave to estimate a stratification tree, we simultaneously select which covariates to use for stratification, how to stratify over these covariates, and the assignment probabilities within these strata. Our main result shows that using this randomisation procedure with an appropriate estimator results in an asymptotic variance which is minimal in the class of stratification trees. Moreover, our results are able to accommodate a large class of assignment mechanisms within strata, including stratified block randomisation. In a simulation study, we find that our method, paired with an appropriate cross-validation procedure, can improve on ad-hoc choices of stratification. We conclude by applying our method to the study in Karlan and Wood (2017, Journal of Behavioral and Experimental Economics, vol. 66, 1–8), where we estimate stratification trees using the first wave of their experiment.
Max Tabord-Meehan, Stratification Trees for Adaptive Randomisation in Randomised Controlled Trials, The Review of Economic Studies, Volume 90, Issue 5, October 2023, Pages 2646–2673, https://doi.org/10.1093/restud/rdac083
