The Effect of School Choice on Participants: Evidence from Randomized Lotteries

School choice has become an increasingly prominent strategy for enhancing academic achievement. To evaluate the impact on participants, we exploit randomized lotteries that determine high school admission in the Chicago Public Schools. Compared to those students who lose lotteries, students who win attend high schools that are better in a number of dimensions, including peer achievement and attainment levels. Nonetheless, we find little evidence that winning a lottery provides any systematic benefit across a wide variety of traditional academic measures. Lottery winners do, however, experience improvements on a subset of nontraditional outcome measures, such as self‐reported disciplinary incidents and arrest rates.     

Lottery Games and Risky Technologies: Communications About Low-Probability/High-Consequence Events

There are strong structural similarities between risks from technological hazards and big-purse state lottery games. Risks from technological hazards are often described as low-probability, high-consequence negative events. State lotteries could be equally well characterized as low-probability, high-consequence positive events. Typical communications about state lotteries provide a virtual strategic textbook for opponents of risky technologies. The same techniques can be used to sell lottery tickets or "sell" opposition to risky technologies. Eight basic principles are enumerated.     

Random Expected Utility

We develop and analyze a model of random choice and random expected utility. A decision problem is a finite set of lotteries that describe the feasible choices. A random choice rule associates with each decision problem a probability measure over choices. A random utility function is a probability measure over von Neumann–Morgenstern utility functions. We show that a random choice rule maximizes some random utility function if and only if it is mixture continuous, monotone (the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem), extreme (lotteries that are not extreme points of the decision problem are chosen with probability 0), and linear (satisfies the independence axiom).     

Preferences for One‐Shot Resolution of Uncertainty and Allais‐Type Behavior

Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker who has recursive, nonexpected utility preferences over compound lotteries. The decision maker has preferences for one‐shot resolution of uncertainty if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic preferences for one‐shot resolution of uncertainty and static preferences that are identified with commonly observed behavior in Allais‐type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium.     

Measurement error, skewness, and risk analysis: coping with the long tail of the distribution.

Probabilistic risk analyses often construct multistage chance trees to estimate the joint probability of compound events. If random measurement error is associated with some or all of the estimates, we show that resulting estimates of joint probability may be highly skewed. Joint probability estimates based on the analysis of multistage chance trees are more likely than not to be below the true probability of adverse events, but will sometimes substantially overestimate them. In contexts such as insurance markets for environmental risks, skewed distributions of risk estimates amplify the "winner's curse" so that the estimated risk premium for low-probability events is likely to be lower than the normative value. Skewness may result even in unbiased estimators of expected value from simple lotteries, if measurement error is associated with both the probability and pay-off terms. Further, skewness may occur even if the error associated with these two estimates is symmetrically distributed. Under certain circumstances, skewed estimates of expected value may result in risk-neutral decisionmakers exhibiting a tendency to choose a certainty equivalent over a lottery of equal expected value, or vice versa. We show that when distributions of estimates of expected value are, positively skewed, under certain circumstances it will be optimal to choose lotteries with nominal values lower than the value of apparently superior certainty equivalents. Extending the previous work of Goodman (1960), we provide an exact formula for the skewness of products.     

The Effect of Raffle Odds on Signing In at a Treatment Center for Adults with Mental Illness

Abstract

This case study describes the use of a daily raffle to increase attendance in a socialization center for approximately 75 adults diagnosed with mental illness. Specifically, the relationship between signing in, which was a measure of attendance, and the odds of winning points which could be exchanged for tangible and edible items was examined. An ABACADABACAD reversal design was used to evaluate the effects of three levels of odds (25%, 50%, 75%) on signing in to the center. Results indicated that signing in increased by 14% over baseline when the raffle was in place. However, no difference between the odds conditions was evident. A cost-benefit analysis showed that the raffle was cost effective for the center.     

Cautious Expected Utility and the Certainty Effect

Many violations of the independence axiom of expected utility can be traced to subjects' attraction to risk‐free prospects. The key axiom in this paper, negative certainty independence ([Dillenberger, 2010]), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy negative certainty independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well defined sense. We show that our representation can also be derived from a “cautious” completion of an incomplete preference relation.     

The Use of the Performance Diagnostic Checklist to Guide Intervention Selection in an Independently Owned Coffee Shop

Abstract

The utility of the Performance Diagnostic Checklist (PDC) (Austin, 2000) as an assessment tool to design an intervention for increasing maintenance tasks in an independently owned coffee shop was examined. The PDC, which was administered to four employees, identified a lack of appropriate antecedents and consequences as areas in need of intervention. Based on the results of the PDC, task clarification and a lottery were implemented in a multiple baseline across tasks design to increase employees' completion of maintenance tasks. The results for task group 1 yielded baseline and intervention means of 44% and 86%, respectively. The results for task group 2 yielded baseline and intervention means of 32% and 67%, respectively. A social validity measure indicated that employees thought that the appearance of the shop had improved, believed the changes helped to improve customer satisfaction, and claimed that the new procedures made their job easier. Overall, results suggest that the PDC can be an effective assessment tool for identifying and subsequently targeting specific areas of improvement within an organization.     

Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi‐experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery‐generated randomization integral to such designs from non‐random preferences and priorities remains open. This paper develops easily‐implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.     

Customer Feedback to the Main Office

Graphic feedback of the percentages of well-stocked vendor boxes was presented to circulation directors of newspapers. Feedback and state-administered lottery tickets were also presented to the delivery agents responsible for stocking the vendor boxes. This intervention package was presented in a multiple baseline design, and it was found effective in improving the availability of these newspapers to potential customers. Implications for customer service and customer feedback mechanisms are discussed.     

Ellsberg Revisited: An Experimental Study

An extension to Ellsberg's experiment demonstrates that attitudes to ambiguity and compound objective lotteries are tightly associated. The sample is decomposed into three main groups: subjective expected utility subjects, who reduce compound objective lotteries and are ambiguity neutral, and two groups that exhibit different forms of association between preferences over compound lotteries and ambiguity, corresponding to alternative theoretical models that account for ambiguity averse or seeking behavior.     

Generalized Utilitarianism and Harsanyi's Impartial Observer Theorem

Harsanyi's impartial observer must consider two types of lotteries: imaginary identity lotteries (“accidents of birth”) that she faces as herself and the real outcome lotteries (“life chances”) to be faced by the individuals she imagines becoming. If we maintain a distinction between identity and outcome lotteries, then Harsanyi‐like axioms yield generalized utilitarianism, and allow us to accommodate concerns about different individuals' risk attitudes and concerns about fairness. Requiring an impartial observer to be indifferent as to which individual should face similar risks restricts her social welfare function, but still allows her to accommodate fairness. Requiring an impartial observer to be indifferent between identity and outcome lotteries, however, forces her to ignore both fairness and different risk attitudes, and yields a new axiomatization of Harsanyi's utilitarianism.     

Consistent Probabilistic Social Choice

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non‐probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (1984). Fishburn's function returns so‐called maximal lotteries, that is, lotteries that correspond to optimal mixed strategies in the symmetric zero‐sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.     

我国彩票市场的价格体系与供需分析

为分析彩票的供需函数,建立了彩票市场的价格体系,该体系包括彩票的销售价格、预期价值和有效价格.基于此,以有效价格作为价格变量,研究了彩票的供给函数与需求函数.根据统计学的期望值原理,通过计算彩票的预期价值得到供给函数,彩票的供给曲线呈现先降后升的特点.通过回归分析估计彩票的需求函数,它是一个减函数.最后,选取我国双色球乐透型彩票进行了实证研究,估计出双色球彩票的供需函数,进行了彩票市场的均衡分析和弹性分析,并基于分析结果给出了我国发展彩票业的对策.     

谁在市场中赌博？基金博彩行为研究

本文研究了A股市场共同基金对彩票型股票的偏好。以2003-2018年的股票型基金和混合型基金为研究对象,本文发现,A股市场共同基金股票组合中平均持有约3.49%的彩票型股票,年轻、从业经验短、学历低的基金经理持有的彩票型股票更多;收益率越低、资金净流入越少、业绩排名下降幅度越大,即业绩压力越大的基金持有的彩票型股票越多。基金对彩票型股票的偏好在年末、投资者情绪更乐观时、预期市场收益偏度更高时更强。基金持有彩票型股票损害而非改善其业绩,且持有彩票型股票的基金在其他类型股票上的投资表现也相对较差,表明基金在彩票型股票上并无选股能力,更多因为博彩心理而持有此类股票,是否持有彩票型股票可作为基金整体投资能力的判别指标。     

How to prevent leadership hubris? Comparing competitive selections,lotteries, and their combination

Hubris is a tendency of leaders to hold an overly confident view of their own capabilities and to abuse power for their own selfish goals, sometimes with disastrous consequences for organizations. A major reason for hubris is the rigorous selection process leaders typically undergo. This study proposes a governance mechanism used successfully in history to tackle hubris: partly random selections, which combine competitive selections by competence with lotteries. A frequently voiced concern about the use of lotteries is that it takes no account of the competence of the leader chosen. We propose that partly random selections can mitigate the disadvantages of both competitive selections alone and lotteries alone and reduce hubris in leaders. We conduct a test of this governance mechanism by means of a computerized laboratory experiment. Our results show that partly random selections significantly reduce the hubris of group leaders.     

MONEY PUMPS IN THE MARKET

Agents who employ non‐rational choice procedures are often vulnerable to exploitation, in the sense that a profit‐seeking trader can offer them a harmful transaction which they will nevertheless accept. We examine the vulnerability of a procedure for deciding whether to buy a lottery: observe another agent who already bought it and buy the lottery if that agent's experience was positive. We show that the exploitation of such agents can be embedded in an inter‐temporal market mechanism, in the form of speculative trade in an asset of no intrinsic value. (JEL: D84)     

The Payback of Effective Innovation Programs: Empirical Evidence from Firms that Have Won Innovation Awards

Despite the widely held belief of the importance of innovation, the connection between innovation and firm performance is empirically inconclusive, partially owing to the limitations of existing innovation measures, which tend to ignore the effectiveness of innovation programs. In this study, we use the winning of innovation awards as a proxy for the effective execution of innovation. We conducted event‐study analyses based on data from more than 1000 publicly traded firms that won innovation awards between 1998 and 2003. Our statistical tests provide strong evidence that the performance of award‐winning firms is significantly higher as compared with several sets of control firms. Over an 8‐year period, starting from 4 years before to 3 years after the year of winning the first innovation award, the test sample's mean (median) change in return on assets is nearly 33% (24%) higher than that of a control sample. The evidence also suggests that effective innovation programs can increase firms' revenue, cost efficiency, and market valuation. Over the period, the control‐adjusted mean (median) change in sales, cost per dollar of sales, and Tobin's Q are 39.28% (20.71%), −5.52% (−3.80%), and 23.70% (3.16%), respectively. Panel data regression analysis provides additional insights on the performance impact of effective innovation programs. The results show that award winners are not only financially more successful but also enjoy an indirect benefit through better R&D execution, which increases firm profitability in both the short term and long term.     

RISK AVERSION AND EXPECTED UTILITY THEORY: AN EXPERIMENT WITH LARGE AND SMALL STAKES

We employ a novel data set to estimate a structural econometric model of the decisions under risk of players in a game show where lotteries present payoffs in excess of half a million dollars. The decisions under risk of players in the presence of large payoffs allow us to estimate the parameters of the curvature of the von Neumann–Morgenstern utility function—not only locally, as in previous studies in the literature, but also globally. Our estimates of relative risk aversion indicate that a constant relative risk aversion parameter of about 1 captures the average of the sample population. We also find that individuals are practically risk neutral at small stakes and risk averse at large stakes—a necessary condition, according to Rabin’s calibration theorem, for expected utility to provide a unified account of individuals’ attitudes toward risk. Finally, we show that for lotteries characterized by substantial stakes, nonexpected utility theories fit the data equally as well as expected utility theory.     

On Monotone Recursive Preferences

We explore the set of preferences defined over temporal lotteries in an infinite horizon setting. We provide utility representations for all preferences that are both recursive and monotone. Our results indicate that the class of monotone recursive preferences includes Uzawa–Epstein preferences and risk‐sensitive preferences, but leaves aside several of the recursive models suggested by Epstein and Zin (1989) and Weil (1990). Our representation result is derived in great generality using Lundberg's (1982, 1985) work on functional equations.