A sender persuades a receiver to accept a project by disclosing information about a payoff‐relevant quality. The receiver has private information about the quality, referred to as his type. We show that the sender‐optimal mechanism takes the form of nested intervals: each type accepts on an interval of qualities and a more optimistic type's interval contains a less optimistic type's interval. This nested‐interval structure offers a simple algorithm to solve for the optimal disclosure and connects our problem to the monopoly screening problem. The mechanism is optimal even if the sender conditions the disclosure mechanism on the receiver's reported type.
This paper develops a dynamic model of rational behavior under uncertainty, in which the agent maximizes the stream of future τ ‐quantile utilities, for τ ∈ (0,1). That is, the agent has a quantile utility preference instead of the standard expected utility. Quantile preferences have useful advantages, including the ability to capture heterogeneity and allowing the separation between risk aversion and elasticity of intertemporal substitution. Although quantiles do not share some of the helpful properties of expectations, such as linearity and the law of iterated expectations, we are able to establish all the standard results in dynamic models. Namely, we show that the quantile preferences are dynamically consistent, the corresponding dynamic problem yields a value function, via a fixed point argument, this value function is concave and differentiable, and the principle of optimality holds. Additionally, we derive the corresponding Euler equation, which is well suited for using well‐known quantile regression methods for estimating and testing the economic model. In this way, the parameters of the model can be interpreted as structural objects. Therefore, the proposed methods provide microeconomic foundations for quantile regression methods. To illustrate the developments, we construct an intertemporal consumption model and estimate the discount factor and elasticity of intertemporal substitution parameters across the quantiles. The results provide evidence of heterogeneity in these parameters.
This paper shows that bargainers may reach delayed agreements even in environments where there is no uncertainty about payoffs or feasible actions. Under such conditions, delay may arise when bargainers face direct forms of strategic uncertainty—that is, uncertainty about the opponent's play. The paper restricts the nature of this uncertainty in two important ways. First, it assumes on‐path strategic certainty : Bargainers face uncertainty only after surprise moves. Second, it assumes Battigalli and Siniscalchi's (2002) rationality and common strong belief of rationality (RCSBR)—a requirement that bargainers are “strategically sophisticated.” The main result characterizes the set of outcomes consistent with on‐path strategic certainty and RCSBR. It shows that these assumptions allow for delayed agreement, despite the fact that the bargaining environment is one of complete information. The source of delay is second‐order optimism : Bargainers do not put forward “good” offers early in the negotiation process because they fear that doing so will cause the other party to become more optimistic about her future prospects.
We study the problem of measuring group differences in choices when the dimensionality of the choice set is large. We show that standard approaches suffer from a severe finite‐sample bias, and we propose an estimator that applies recent advances in machine learning to address this bias. We apply this method to measure trends in the partisanship of congressional speech from 1873 to 2016, defining partisanship to be the ease with which an observer could infer a congressperson's party from a single utterance. Our estimates imply that partisanship is far greater in recent years than in the past, and that it increased sharply in the early 1990s after remaining low and relatively constant over the preceding century.
We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.
We introduce a new solution concept for models of coalition formation, called the myopic stable set (MSS). The MSS is defined for a general class of social environments and allows for an infinite state space. An MSS exists and, under minor continuity assumptions, it is also unique. The MSS generalizes and unifies various results from more specific applications. It coincides with the coalition structure core in coalition function form games when this set is nonempty; with the set of stable matchings in the Gale-Shapley matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria in pseudo-potential games and finite supermodular games. We also characterize the MSS for the class of proper simple games.
I develop a search‐and‐bargaining model of endogenous intermediation in over‐the‐counter markets. Unlike the existing work, my model allows for rich investor heterogeneity in three simultaneous dimensions: preferences, inventories, and meeting rates. By comparing trading‐volume patterns that arise in my model and are observed in practice, I argue that the heterogeneity in meeting rates is the main driver of intermediation patterns. I find that investors with higher meeting rates (i.e., fast investors) are less averse to holding inventories and more attracted to cash earnings, which makes the model corroborate a number of stylized facts that do not emerge from existing models: (i) fast investors provide intermediation by charging aspeed premium, and (ii) fast investors hold more extreme inventories. Then, I use the model to study the effect of trading frictions on the supply and price of liquidity. On social welfare, I show that the interaction of meeting rate heterogeneity with optimal inventory management makes the equilibrium inefficient. I provide a financial transaction tax/subsidy scheme that corrects this inefficiency, in which fast investors cross‐subsidize slow investors.
We show that even in the absence of data on individual decisions, the distribution of individual attitudes towards risk can be identified from the aggregate conditions that characterize equilibrium on markets for risky assets. Taking parimutuel horse races as a textbook model of contingent markets, we allow for heterogeneous bettors with very general risk preferences, including non-expected utility. Under a standard single-crossing condition on preferences, we identify the distribution of preferences among the population of bettors and we derive testable implications. We estimate the model on data from U.S. races. Specifications based on expected utility fit the data very poorly. Our results stress the crucial importance of nonlinear probability weighting. They also suggest that several dimensions of heterogeneity may be at work.
This paper considers inference on fixed effects in a linear regression model estimated from network data. An important special case of our setup is the two‐way regression model. This is a workhorse technique in the analysis of matched data sets, such as employer–employee or student–teacher panel data. We formalize how the structure of the network affects the accuracy with which the fixed effects can be estimated. This allows us to derive sufficient conditions on the network for consistent estimation and asymptotically valid inference to be possible. Estimation of moments is also considered. We allow for general networks and our setup covers both the dense and the sparse case. We provide numerical results for the estimation of teacher value‐added models and regressions with occupational dummies.
We can often predict the behavior of those closest to us more accurately than that of complete strangers, yet we routinely engage in strategic situations with both: our social network impacts our strategic knowledge. Peer‐confirming equilibrium describes the behavioral consequences of this intuition in a noncooperative game. We augment a game with a network to represent strategic information: if two players are linked in the network, they have correct conjectures about each others' strategies. In peer‐confirming equilibrium, there is common belief that players (i) behave rationally and (ii) correctly anticipate neighbors' play. In simultaneous‐move games, adding links to the network always restricts the set of outcomes. In dynamic games, the outcome set may vary non‐monotonically with the network because the actions of well‐connected players help poorly‐connected players coordinate. This solution concept provides a useful language for studying public good provision, highlights a new channel through which central individuals facilitate coordination, and delineates possible sources of miscoordination in protests and coups.