Feedback Mechanisms,Judgment Bias,and Trust Formation in Online Auctions*

Online markets, like eBay, Amazon, and others rely on electronic reputation or feedback systems to curtail adverse selection and moral hazard risks and promote trust among participants in the marketplace. These systems are based on the idea that providing information about a trader's past behavior (performance on previous market transactions) allows market participants to form judgments regarding the trustworthiness of potential interlocutors in the marketplace. It is often assumed, however, that traders correctly process the data presented by these systems when updating their initial beliefs. In this article, we demonstrate that this assumption does not hold. Using a controlled laboratory experiment simulating an online auction site with 127 participants acting as buyers, we find that participants interpret seller feedback information in a biased (non‐Bayesian) fashion, overemphasizing the compositional strength (i.e., the proportion of positive ratings) of the reputational information and underemphasizing the weight (predictive validity) of the evidence as represented by the total number of transactions rated. Significantly, we also find that the degree to which buyers misweigh seller feedback information is moderated by the presentation format of the feedback system as well as attitudinal and psychological attributes of the buyer. Specifically, we find that buyers process feedback data presented in an Amazon‐like format—a format that more prominently emphasizes the strength dimension of feedback information—in a more biased (less‐Bayesian) manner than identical ratings data presented using an eBay‐like format. We further find that participants with greater institution‐based trust (i.e., structural assurance) and prior online shopping experience interpreted feedback data in a more biased (less‐Bayesian) manner. The implications of these findings for both research and practice are discussed.     

Tenable Strategy Blocks and Settled Equilibria

When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set‐valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal‐form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal‐form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff‐equivalent equilibrium, a property that other related concepts have not satisfied.     

Tight Revenue Bounds With Possibilistic Beliefs and Level‐k Rationality

Mechanism design enables a social planner to obtain a desired outcome by leveraging the players' rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes. In this paper, we prove this fundamental intuition for players with possibilistic beliefs, a model long considered in epistemic game theory. Specifically, • We define a sequence of monotonically increasing revenue benchmarks for single‐good auctions, G⁰≤G¹≤G²≤⋯, where each Gⁱ is defined over the players' beliefs and G⁰ is the second‐highest valuation (i.e., the revenue benchmark achieved by the second‐price mechanism). • We (1) construct a single, interim individually rational, auction mechanism that, without any clue about the rationality level of the players, guarantees revenue G^k if all players have rationality levels ≥k+1, and (2) prove that no such mechanism can guarantee revenue even close to G^k when at least two players are at most level‐k rational.     

Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff‐relevant consequences as a function of actions. We introduce the notion of a Berk–Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback–Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self‐confirming equilibrium constitute special cases where players have correctly specified models. We provide a learning foundation for Berk–Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.     

Sign Restrictions,Structural Vector Autoregressions,and Useful Prior Information

This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just‐identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n‐variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse‐response functions that are implicit in the traditional sign‐restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just‐identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market.     

Random Choice and Private Information

We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter's perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent's beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well‐calibrated or rational.     

Utilitarian Preferences With Multiple Priors

This paper proposes a method for aggregating individual preferences in the context of uncertainty. Individuals are assumed to abide by Savage's model of Subjective Expected Utility, in which everyone has his/her own utility and subjective probability. Disagreement on probabilities among individuals gives rise to uncertainty at the societal level, and thus society may entertain a set of probabilities rather than only one. We assume that social preference admits a Maxmin Expected Utility representation. In this context, two Pareto‐type conditions are shown to be equivalent to social utility being a weighted average of individual utilities and the social set of priors containing only weighted averages of individual priors. Thus, society respects consensus among individuals' beliefs and does not add ambiguity beyond disagreement on beliefs. We also deal with the case in which society does not rule out any individual belief.     

An Empirical Equilibrium Model of a Decentralized Asset Market

I estimate a search‐and‐bargaining model of a decentralized market to quantify the effects of trading frictions on asset allocations, asset prices, and welfare, and to quantify the effects of intermediaries that facilitate trade. Using business‐aircraft data, I find that, relative to the Walrasian benchmark, 18.3 percent of the assets are misallocated; prices are 19.2 percent lower; and the aggregate welfare losses equal 23.9 percent. Dealers play an important role in reducing trading frictions: In a market with no dealers, a larger fraction of assets would be misallocated, and prices would be higher. However, dealers reduce aggregate welfare because their operations are costly, and they impose a negative externality by decreasing the number of agents' direct transactions.     

The Political Economy of Moral Conflict: An Empirical Study of Learning and Law Enforcement Under Prohibition

The U.S. Prohibition experience shows a remarkable policy reversal. In only 14 years, a drastic shift in public opinion required two constitutional amendments. I develop and estimate a model of endogenous law enforcement, determined by beliefs about the Prohibition‐crime nexus and alcohol‐related moral views. In turn, the policy outcomes shape subsequent learning about Prohibition enforcement costs. I estimate the model through maximum likelihood on Prohibition Era city‐level data on police enforcement, crime, and alcohol‐related legislation. The model can account for the variation in public opinion changes, and the heterogeneous responses of law enforcement and violence across cities. Results show that a 15% increase in the homicide rate can be attributed to Prohibition enforcement. The subsequent learning‐driven adjustment of local law enforcement allowed for the alcohol market to rebound to 60% of its pre‐Prohibition size. I conclude with counterfactual exercises exploring the welfare implications of policy learning, prior beliefs, preference polarization, and alternative political environments. Results illustrate the importance of incorporating the endogenous nature of law enforcement into our understanding of policy failure and policy success.     

Communication With Unknown Perspectives

Consider a group of individuals with unobservable perspectives (subjective prior beliefs) about a sequence of states. In each period, each individual receives private information about the current state and forms an opinion (a posterior belief). She also chooses a target individual and observes the target's opinion. This choice involves a trade‐off between well‐informed targets, whose signals are precise, and well‐understood targets, whose perspectives are well known. Opinions are informative about the target's perspective, so observed individuals become better understood over time. We identify a simple condition under which long‐run behavior is history independent. When this fails, each individual restricts attention to a small set of experts and observes the most informed among these. A broad range of observational patterns can arise with positive probability, including opinion leadership and information segregation. In an application to areas of expertise, we show how these mechanisms generate own field bias and large field dominance.     

Nonparametric Welfare Analysis for Discrete Choice

We consider empirical measurement of equivalent variation (EV) and compensating variation (CV) resulting from price change of a discrete good using individual‐level data when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV and CV can be expressed as simple closed‐form functionals of conditional choice probabilities under essentially unrestricted preference distributions. These results hold even when the distribution and dimension of unobserved heterogeneity are neither known nor identified, and utilities are neither quasilinear nor parametrically specified. The welfare distributions take simple forms that are easy to compute in applications. In particular, average EV for a price rise equals the change in average Marshallian consumer surplus and is smaller than average CV for a normal good. These nonparametric point‐identification results fail for ordered choice if the unit price is identical for all alternatives, thereby providing a connection to Hausman–Newey's (2014) partial identification results for the limiting case of continuous choice.     

Promotion,Turnover, and Compensation in the Executive Labor Market

This paper develops a generalized Roy model with human capital accumulation, moral hazard, and career concerns. We identify and estimate the model with a large panel that matches data on publicly listed firms to information on their executives. The structural estimates obtained are used to decompose the firm‐size pay gap. We find that although total compensation and incentive pay increase with firm size, certainty‐equivalent pay decreases with firm size. In larger firms, and for more highly ranked executives, weaker signal quality about effort results in higher risk premiums. This risk premium accounts for roughly 80 percent of the firm‐size gap in total compensation. Larger firms are also willing to pay more than smaller ones to attract executives. Finally, the estimated coefficients on human capital accumulation from formal education and experience gained from different firms are individually significant, but their collective effect on firm‐size pay differentials nets out.     

A Polynomial Optimization Approach to Principal–Agent Problems

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.     

Robust Contracts in Continuous Time

We study a continuous‐time contracting problem under hidden action, where the principal has ambiguous beliefs about the project cash flows. The principal designs a robust contract that maximizes his utility under the worst‐case scenario subject to the agent's incentive and participation constraints. Robustness generates endogenous belief heterogeneity and induces a tradeoff between incentives and ambiguity sharing so that the incentive constraint does not always bind. We implement the optimal contract by cash reserves, debt, and equity. In addition to receiving ordinary dividends when cash reserves reach a threshold, outside equity holders also receive special dividends or inject cash in the cash reserves to hedge against model uncertainty and smooth dividends. The equity premium and the credit yield spread generated by ambiguity aversion are state dependent and high for distressed firms with low cash reserves.     

A Comment on “Can Relaxation of Beliefs Rationalize the Winner's Curse?: An Experimental Study”

Ivanov, Levin, and Niederle (2010) use a common‐value second‐price auction experiment to reject beliefs‐based explanations for the winner's curse. ILN's conclusion, however, stems from the misuse of theoretical arguments. Beliefs‐based models are even compatible with some observations from ILN's experiment.     

A Dynamic Model of Demand for Houses and Neighborhoods

This paper develops a dynamic model of neighborhood choice along with a computationally light multi‐step estimator. The proposed empirical framework captures observed and unobserved preference heterogeneity across households and locations in a flexible way. We estimate the model using a newly assembled data set that matches demographic information from mortgage applications to the universe of housing transactions in the San Francisco Bay Area from 1994 to 2004. The results provide the first estimates of the marginal willingness to pay for several non‐marketed amenities—neighborhood air pollution, violent crime, and racial composition—in a dynamic framework. Comparing these estimates with those from a static version of the model highlights several important biases that arise when dynamic considerations are ignored.     

Forced Coexistence and Economic Development: Evidence From Native American Reservations

Studying Native American reservations, and their historical formation, I find that their forced integration of autonomous polities into a system of shared governance had large negative long‐run consequences, even though the affected people were ethnically and linguistically homogenous. Reservations that combined multiple sub‐tribal bands when they were formed are 30% poorer today, even when conditioning on pre‐reservation political traditions. The results hold with tribe fixed effects, identifying only off within‐tribe variation across reservations. I also provide estimates from an instrumental variable strategy based on historical mining rushes that led to exogenously more centralized reservations. Data on the timing of economic divergence and on contemporary political conflict suggest that the primary mechanism runs from persistent social divisions through the quality of local governance to the local economic environment.     

Mechanism Design With Ambiguous Communication Devices

This paper considers mechanism design problems in environments with ambiguity‐sensitive individuals. The novel idea is to introduce ambiguity in mechanisms so as to exploit the ambiguity sensitivity of individuals. Deliberate engineering of ambiguity, through ambiguous mediated communication, can allow (partial) implementation of social choice functions that are not incentive compatible with respect to prior beliefs. We provide a complete characterization of social choice functions partially implementable by ambiguous mechanisms.     

Identifying Equilibrium Models of Labor Market Sorting

We assess the empirical content of equilibrium models of labor market sorting based on unobserved (to economists) characteristics. In particular, we show theoretically that all parameters of the classic model of sorting based on absolute advantage in Becker, 1973 with search frictions can be nonparametrically identified using only matched employer–employee data on wages and labor market transitions. In particular, these data are sufficient to nonparametrically estimate the output of any individual worker with any given firm. Our identification proof is constructive and we provide computational algorithms that implement our identification strategy given the limitations of the available data sets. Finally, we add on‐the‐job search to the model, extend the identification strategy, and apply it to a large German matched employer–employee data set to describe detailed patterns of sorting and properties of the production function.     

The Economics of Counterfeiting

We develop a strategic theory of counterfeiting as a multi‐market large game. Bad guys choose whether to counterfeit, and what quality to produce. Opposing them is a continuum of good guys who select a costly verification effort. In equilibrium, counterfeiters produce better quality at higher notes, but verifiers try sufficiently harder that verification still improves. We develop a graphical framework for deducing comparative statics. Passed and counterfeiting rates vanish for low and high notes. Our predictions are consistent with time series and cross‐sectional patterns in a unique data set assembled largely from the Secret Service.