Generic Uniqueness of the Solutions to a Continuous Linear Programming Problem

Consider two continuous functions f,g mapping the interval [0,S] of the real line into R. Let f also be strictly increasing. We are interested in the set of probability distributions on the interval [0,S] that maximize the expectation of f subject to the constraint that the expectation of g be no greater than a constant. We provide a sufficient condition on the pair (f,g) for the solution to this linear programming problem to be unique and show that this sufficient condition is satisfied "generically."Linear Programming

Using Hit Rate Tests to Test for Racial Bias in Law Enforcement: Vehicle Searches in Wichita

This paper considers the use of outcomes-based tests for detecting racial bias in the context of police searches of motor vehicles. It shows that the test proposed in Knowles, Persico and Todd (2001) can also be applied in a more general environment where police officers are heterogenous in their tastes for discrimination and in their costs of search and motorists are heterogeneous in their benefits and costs from criminal behavior. We characterize the police and motorist decision problems in a game theoretic framework and establish properties of the equilibrium. We also extend the model to the case where drivers' characteristics are mutable in the sense that drivers can adapt some of their characteristics to reduce the probability of being monitored. After developing the theory that justifies the application of outcomes-based tests, we apply the tests to data on police searches of motor vehicles gathered by the Wichita Police deparment. The empirical findings are consistent with the notion that police in Wichita choose their search strategies to maximize successful searches, and not out of racial bias.

Using Hit Rates to Test for Racial Bias in Law Enforcement: Vehicle Searches in Wichita

This paper considers the use of outcomes-based tests for detecting racial bias in the context of police searches of motor vehicles. It shows that the test proposed in Knowles, Persico and Todd (2001) can also be applied in a more general environment where police officers are heterogenous in their tastes for discrimination and in their costs of search and motorists are heterogeneous in their benefits and costs from criminal behavior. We characterize the police and motorist decision problems in a game theoretic framework and establish properties of the equilibrium. We also extend of the model to the case where drivers’ characteristics are mutable in the sense that drivers can adapt some of their characteristics to reduce the probability of being monitored. After developing the theory that justifies the application of outcomes-based tests, we apply the tests to data on police searches of motor vehicles gathered by the Wichita Police department. The empirical findings are consistent with the notion that police in Wichita choose their search strategies to maximize successful searches, and not out of racial bias.Racial Profiling, Crime, Police, Wichita

Information Acquisition and Refunds for Returns

A product exhibits personal fit uncertainty when its consumers have idiosyncratic and uncertain values for it. Often a consumer can learn her long-run value quickly by obtaining the good for a trial period. Money back guarantees of satisfaction are commonly used to lower the cost to consumers of learning their values this way. Increasingly, however, consumers can instead learn about their values before they purchase by, e.g., reading product reviews or consulting experts. We study the effect on a firm’s optimal price and refund of this competing source of information. An efficient outcome would be achieved by setting the refund for a return equal to its salvage value. But a monopoly will, for some parameters, induce consumers to stay uninformed by promising a refund that is greater than the salvage value. This generates an inefficiently large number of returns, which the firm finds worthwhile in order to eliminate the information rents that consumers would obtain by becoming informed. This finding is consistent with the observation that for many products, money back guarantees are generous, as they commonly refund the entire, or almost the entire, purchase price of a product.information acquisition, refunds, money back guarantees, personal fit uncertainty

Information Acquisition and Refunds for Returns

A product exhibits personal fit uncertainty when its consumers have idiosyncratic and uncertain values for it. Often a consumer can learn her long-run value quickly by obtaining the good for a trial period. Money back guarantees of satisfaction are commonly used to lower the cost to consumers of learning their values this way. Increasingly, however, consumers can instead learn about their values before they purchase by, e.g., reading product reviews or consulting experts. We study the effect on a firm’s optimal price and refund of this competing source of information. An efficient outcome would be achieved by setting the refund for a return equal to its salvage value. But a monopoly will, for some parameters, induce consumers to stay uninformed by promising a refund that is greater than the salvage value. This generates an inefficiently large number of returns, which the firm finds worthwhile in order to eliminate the information rents that consumers would obtain by becoming informed. This finding is consistent with the observation that for many products, money back guarantees are generous, as they commonly refund the entire, or almost the entire, purchase price of a product.information acquisition, refunds, money back guarantees, personal fit uncertainty

Information Acquisition and the Excess Refund Puzzle

A buyer can learn her value for a returnable experience good by trying it out, with the option of returning the good for whatever refund the seller offers. Sellers tend to offer a “no questions asked” refund for such returns, a money back guarantee. The refund is often too generous, generating inefficiently high levels of returns. We present two versions of a model of a returnable goods market. In the Information Acquisition Model, consumers are ex ante identical and uninformed of their private values for the good. The firm then offers a generous refund in order to induce the consumers to learn their values by purchasing and trying the good out, rather than by doing costly research prior to purchasing. In the Screening Model, some consumers have negligible costs of becoming informed about their values prior to purchasing, and always do so; other consumers have prohibitive costs of acquiring pre-purchase information and always stay uninformed. The firm’s optimal screening menu may then contain only a single contract, one that specifies a generous refund, and hence a high purchase price, in order to weaken the incentive constraint of the informed consumers.information acquisition, refunds, money back guarantees, returnable experience goods

Don't Spread Yourself Too Thin: The Impact of Task Juggling on Workers' Speed of Job Completion

We show that task juggling, i.e., the spreading of effort across too many active projects, decreases the performance of workers, raising the chances of low throughput, long duration of projects and exploding backlogs. Individual speed of job completion cannot be explained only in terms of effort, ability and experience: work scheduling is a crucial "input" that cannot be omitted from the production function of individual workers. We provide a simple theoretical model to study the effects of increased task juggling on the duration of projects. Using a sample of Italian judges we show that those who are induced for exogenous reasons to work in a more parallel fashion on many trials at the same time, take longer to complete similar portfolios of cases. The exogenous variation that identifies this causal effect is constructed exploiting the lottery that assigns cases to judges together with the procedural prescription requiring judges to hold the first hearing of a case no later than 60 days from filing.individual production function, work scheduling, duration of trials

The Effect of Adolescent Experience on Labor Market Outcomes: The Case of Height

Taller workers receive a wage premium, and the disparity in wages is similar in magnitude to the race and gender gaps. We exploit the variation in an individual’s height over time to explore the ways in which height affects wages. Specifically, we show that for white males the effect of adult height is essentially eliminated when adolescent height is taken into account. We find that participation in high school sports and clubs, and to a lesser extent schooling, are channels through which teen height affects adult wages. The benefits of being a taller teen seem to accrue equally across income classes and also across broad occupation categories, suggesting that the benefits of teen height do not result from occupational sorting. Because height is heritable and because tall adults tend to have children with each other, the benefits of teen height tend to be perpetuated across generations. Finally, we use our estimates of the teen height premium to perform a simple calculation of the monetary benefits of a newly approved treatment for children that increases height.Confidence, Optimism, Behavioral Economics

The Effect of Adolescent Experience on Labor Market Outcomes: The Case of Height

Taller workers receive a wage premium. Net of differences in family background, the disparity is similar in magnitude to the race and gender gaps. We exploit variation in an individual's height over time to explore how height affects wages. Controlling for teen height essentially eliminates the effect of adult height on wages for white males. The teen height premium is not explained by differences in resources or endowments. The teen height premium is partly mediated through participation in high school sports and clubs. We estimate the monetary benefits of a medical treatment for children that increases height.