Abstract: I study a principal-agent model in which a principal hires an agent to collect information about an unknown continuous state. The agent acquires a signal whose distribution is centered around the state, controlling the signal’s precision at a cost. The principal observes neither the precision nor the signal, but rather, using transfers that can depend on the state, incentivizes the agent to choose high precision and report the signal truthfully. I identify a sufficient and necessary condition on the agent’s information structure which ensures that there exists an optimal transfer with a simple cutoff structure: the agent receives a fixed prize when his prediction is close enough to the state and receives nothing otherwise. This condition is mild and applies to all signal distributions commonly used in the literature.

Abstract: We propose a new method for estimating selection models where the outcome equation is nonparametric and nonseparable in error terms. We show that, given the selection rule and the observed selected outcome distribution, the potential outcome distribution can be characterized as the fixed point of an operator, and we prove that this operator is a functional contraction. We propose a two-step semiparametric maximum likelihood estimator to jointly estimate the selection model and the potential outcome distribution. The consistency and asymptotic normality of the estimator are established. Our approach performs well in Monte Carlo simulations and is applicable in a variety of empirical settings where only a selected sample of outcomes is observed. Examples include consumer demand models with only transaction prices, auctions with incomplete bid data, and Roy models with data on accepted wages.

Abstract: This paper studies competition under information heterogeneity in selection markets and examines the impact of public information regulations aimed at reducing information asymmetries between competing firms. We develop a novel model and introduce new empirical strategies to analyze imperfect competition in markets where firms have heterogeneous information about consumers, vary in cost structures, and offer differentiated products. Using data from the Italian auto insurance market, we find substantial differences in the precision of risk ratings across insurers, and those with less accurate risk-rating algorithms tend to have more efficient cost structures. We assess the equilibrium effects of giving firms equal access to aggregated risk information from a centralized bureau. This policy significantly reduces prices by increasing competition, leading to a 15.7% boost in consumer surplus, almost reaching the efficiency benchmark where firms have full knowledge of consumers’ true risk. Aggregating information through the bureau favors low-risk consumers and reduces average costs by 12 euros per contract through more efficient insurer-insuree matching.