Hector Chade

Matching with noise and the acceptance curse

Abstract This paper explores matching with both search and information frictions. Specifically, everyone observes only a noisy signal of the true type of any potential mate. In this context, matching decisions must incorporate not only information about a partners attribute conveyed by the noisy signal, but also—as in the winners curse in auction theory—information about a partners type contained in his or her acceptance decision. We show that there exists an equilibrium exhibiting a stochastic positive assorting of types, generalizing [Becker, J. Polit. Economy 81 (1973) 813–846]. In equilibrium, selection is adverse: being accepted reduces an agents estimate of a potential partners type, a phenomenon that we call the acceptance curse effect.

Two-Sided Search and Perfect Segregation with Fixed Search Costs

This paper studies a two-sided search model with the following characteristics: there is a continuum of agents with different types in each population, match utility is nontransferable, and there is a fixed search cost that agents incur in each period. When utility functions are additively separable in types and strictly increasing in the partners type, there exists a unique matching equilibrium that exhibits perfect segregation as in Smith (1997) and Burdett and Coles (1997); i.e., agents form clusters and mate only within them. The role of additive separability and fixed search costs is discussed and contrasted with the discounted case, and an intuitive explanation for the different results obtained in the literature is provided. Also, a simple suffcient condition on the match utility function and the density of types allow us to characterize the duration of the search for each type of agent.

Informed Principal, Moral Hazard, and the Value of a More Informative Technology

We analyze a principal-agent model with moral hazard in which the principal has private information about the technology. We characterize Perfect Bayesian Equilibria of the contracting game that possess the following properties: (i) a principal with a more informative technology ends up earning less profits than a principal with a less informative one does; (ii) compared to the complete information case, the actions implemented by the privately informed principal can be distorted; (iii) the agent can end up being better off when the principal has private information.

Repeated Games with Present-Biased Preferences

We study infinitely repeated games with perfect monitoring, where players have [beta]-[delta] preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in [beta] or [delta]. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor.

Optimal insurance with adverse selection

We solve the principal-agent problem of a monopolist insurer selling to an agent whose riskiness (loss chance) is private information, a problem introduced in Stiglitzs (1977) seminal paper. For an \emph{arbitrary} type distribution, we prove several properties of optimal menus, such as efficiency at the top and downward distortions elsewhere. We show that these results extend beyond the insurance problem we emphasize. We also prove that the principal always prefers an agent facing a larger loss, and a poorer one if the agents risk aversion decreases with wealth. For the standard case of a continuum of types and a smooth density, we show that, under the mild assumptions of a log-concave density and decreasing absolute risk aversion, the optimal premium is \emph{backwards-S shaped} in the amount of coverage, first concave, then convex. This curvature result implies that quantity discounts are consistent with adverse selection in insurance, contrary to the conventional wisdom from competitive models.

Information Acquisition, Moral Hazard, and Rewarding for Bad News

This paper analyzes a principal-agent problem with moral hazard where a principal searches for an opportunity of uncertain return, and hires an agent to evaluate available options. The agent’s effort affects the informativeness of a signal about an option’s return. Based on the information provided by the agent, the principal decides whether to exercise the option at hand. We derive properties of the optimal contract in both static and dynamic versions of the problem. We show that sometimes the agent is rewarded for delivering ‘bad news’ about the quality of an option. We characterize distortions (relative to the first best) on the implemented effort level and optimal stopping decision. We show that for some parameter values the principal commits to an ex-post suboptimal stochastic decision to exercise an option.

Optimal insurance with adverse selection: Optimal insurance with adverse selection

I model job‐search monitoring in the optimal unemployment insurance framework, in which job‐search effort is the workers private information. In the model, monitoring provides costly information upon which the government conditions unemployment benefits. Using a simple one‐period model with two effort levels, I show analytically that the monitoring precision increases and the utility spread decreases if and only if the inverse of the workers utility in consumption has a convex derivative. The quantitative analysis that follows extends the model by allowing a continuous effort and separations from employment. That analysis highlights two conflicting economic forces affecting the optimal precision of monitoring with respect to the generosity of the welfare system: higher promised utility is associated not only with a higher cost of moral hazard, but also with lower effort and lower value of employment. The result is an inverse U‐shaped precision profile with respect to promised utility. Unemployment insurance optimal contracts moral hazard job‐search monitoring D82 E24 J64 J65

Delegated information acquisition with moral hazard

We analyze a principal–agent problem with moral hazard where a principal searches for an opportunity of uncertain return, and hires an agent to evaluate available options. The agents effort affects the informativeness of a signal about an options return. Based on the information provided by the agent, the principal decides whether to exercise the option at hand. We derive properties of the optimal contract in both static and dynamic versions of the problem. We show that there are intermediate values of the prior probability that the option is of high quality at which positive effort cannot be sustained. We also show that if the prior is below a threshold, then the agent is rewarded for delivering ‘bad news’ about the options quality. We derive distortions (relative to the first best) on the implemented effort level and optimal stopping decision. For some parameter values, it is optimal for the principal to commit to an ex-post suboptimal stochastic decision to exercise an option.

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the sellers incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyers rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price.

Coverage Denied: Excluding Bad Risks, Inefficiency, and Pooling in Insurance

Models of insurance with adverse selection predict that only the best risks — those least likely to suffer a loss — are uninsured, a prediction at odds with coverage denials for pre-existing conditions. They also typically assume that insurance pro- vision is costless: the only cost is claims payment. We introduce costly insurance provision into a standard monopoly insurance model with adverse selection. We show that with loading or a fixed cost of claims processing, the insurer denies coverage only to those likely to be the worst risks. We also show that loading overturns three classic textbook properties of monopoly pricing models: no one is pooled with the highest consumer type; the highest type gets an efficient contract; and all other types get contracts distorted downwards from their efficient contracts. Indeed all types can be pooled on a single contract. Finally we show that both loading and a fixed claims cost do not affect qualitative properties of (Rothschild-Stiglitz) competitive equilibrium (when it exists), so these costs generate potentially testable implications of competitive vs monopoly insurance: for example, no competitive equilibrium can be pooling.