Paper # Author Title
We explore model misspecification in an observational learning framework. Individuals learn from private and public signals and the actions of others. An agent's type specifies her model of the world. Misspecified types have incorrect beliefs about the signal distribution, how other agents draw inference and/or others' payoffs. We establish that the correctly specified model is robust in that agents with approximately correct models almost surely learn the true state asymptotically. We develop a simple criterion to identify the asymptotic learning outcomes that arise when misspecification is more severe. Depending on the nature of the misspecification, learning may be correct, incorrect or beliefs may not converge. Different types may asymptotically disagree, despite observing the same sequence of information. This framework captures behavioral biases such as confirmation bias, false consensus effect, partisan bias and correlation neglect, as well as models of inference such as level-k and cognitive hierarchy. Download Paper
This paper formalizes the optimal design of randomized controlled trials (RCTs) in the presence of interference between units, where an individual's outcome depends on the behavior and outcomes of others in her group. We focus on randomized saturation (RS) designs, which are two-stage RCTs that first randomize the treatment saturation of a group, then randomize individual treatment assignment. Our main contributions are to map the potential outcomes framework with partial interference to a regression model with clustered errors, calculate the statistical power of different RS designs, and derive analytical insights for how to optimally design an RS experiment. We show that the power to detect average treatment effects declines precisely with the ability to identify novel treatment and spillover estimands, such as how effects vary with the intensity of treatment. We provide software that assists researchers in designing RS experiments. Download Paper
This paper studies how persistence can be used to create incentives in a continuous-time stochastic game in which a long-run player interacts with a se- quence of short-run players. Observation of the long-run player's actions are distorted by a Brownian motion and the actions of both players impact future payoffs through a state variable. For example, a firm or worker provides customers with a product, and the quality of this product depends on both current and past investment choices by the firm. I derive general conditions under which a Markov equilibrium emerges as the unique perfect public equilibrium, and char- acterize the equilibrium payoff and actions in this equilibrium, for any discount rate. I develop an application of persistent product quality to illustrate how per- sistence creates effective intertemporal incentives in a setting where traditional channels fail, and explore how the structure of persistence impacts equilibrium behavior. This demonstrates the power of the continuous-time setting to deliver sharp insights and a tractable equilibrium characterization for a rich class of dynamic games. Download Paper
A firm employs workers to obtain costly unverifiable information - for example, categorizing the content of images. Workers are monitored by comparing their messages. The optimal contract under limited liability exhibits three key features: (i) the monitoring technology depends crucially on the commitment power of the firm - virtual monitoring, or monitoring with arbitrarily small probability, is optimal when the firm can commit to truthfully reveal messages from other workers, while monitoring with strictly positive probability is optimal when the firm can hide messages (partial commitment), (ii) bundling multiple tasks reduces worker rents and monitoring inefficiencies; and (iii) the optimal contract is approximately efficient under full but not partial commitment. We conclude with an application to crowdsourcing platforms, and characterize the optimal contract for tasks found on these platforms. Download Paper
This paper demonstrates that a misspecified model of information processing interferes with long-run learning and allows inefficient choices to persist in the face of contradictory public information. I consider an observational learning environment where agents observe a private signal about a hidden state, and some agents observe the actions of their predecessors. Prior actions aggregate multiple sources of correlated information about the state, and agents face an inferential challenge to distinguish between new and redundant information. When individuals significantly overestimate the amount of new information, beliefs about the state become entrenched and incorrect learning may occur. When individuals sufficiently overestimate the amount of redundant information, beliefs are fragile and learning is incomplete. Learning is complete when agents have an approximately correct model of inference, establishing that the correct model is robust to perturbation. These results have important implications for timing, frequency and strength of policy interventions to facilitate learning. Download Paper
This paper formalizes the design of experiments intended specifically to study spillover effects. By first randomizing the intensity of treatment within clusters and then randomly assigning individual treatment conditional on this cluster-level intensity, a novel set of treatment effects can be identified. We develop a formal framework for consistent estimation of these effects, and provide explicit expressions for power calculations. We show that the power to detect average treatment effects declines precisely with the quantity that identifies the novel treatment effects. A demonstration of the technique is provided using a cash transfer program in Malawi. Download Paper
This paper studies a class of continuous-time stochastic games in which the actions of a long-run player have a persistent effect on payoffs. For example, the quality of a firm's product depends on past as well as current effort, or the level of a policy instrument depends on a government's past choices. The long-run player faces a population of small players, and its actions are imperfectly observed. I establish the existence of Markov equilibria, characterize the Perfect Public Equilibria (PPE) pay-offset as the convex hull of the Markov Equilibria payoff set, and identify conditions for the uniqueness of a Markov equilibrium in the class of all PPE. The existence proof is constructive: it characterizes the explicit form of Markov equilibria payoffs and actions, for any discount rate. Action persistence creates a crucial new channel to generate intertemporal incentives in a setting where traditional channels fail, and can provide permanent non-trivial incentives in many settings. These results offer a novel framework for thinking about reputational dynamics of firms, governments, and other long-run agents. Download Paper
This paper formalizes the design of experiments intended specifically to study spillover effects. By first randomizing the intensity of treatment within clusters and then randomly assigning individual treatment conditional on this cluster-level intensity, a novel set of treatment effects can be identified. We develop a formal framework for consistent estimation of these effects, and provide explicit expressions for power calculations. We show that the power to detect average treatment effects declines precisely with the quantity that identifies the novel treatment effects. A demonstration of the technique is provided using a cash transfer program in Malawi. Download Paper
This paper demonstrates that a misspecified model of information processing interferes with long-run learning and offers an explanation for why individuals may continue to choose an inefficient action, despite sufficient public information to learn the true state. I consider a social learning environment where agents draw inference from private signals, public signals and the actions of their predecessors, and sufficient public information exists to achieve asymptotically efficient learning. Prior actions aggregate multiple sources of information; agents face an inferential challenge to distinguish new information from redundant information. I show that when individuals significantly overestimate the amount of new information contained in prior actions, beliefs about the unknown state become entrenched and incorrect learning may occur. On the other hand, when individuals sufficiently overestimate the amount of redundant information, beliefs are fragile and learning is incomplete. When agents have an approximately correct model of inference, learning is complete - the model with no information-processing bias is robust to perturbation. Download Paper
This paper formalizes the design of experiments intended specifically to study spillover effects. By first randomizing the intensity of treatment within clusters and then randomly assigning individual treatment conditional on this cluster-level intensity, a novel set of treatment effects can be identified. We develop a formal framework for consistent estimation of these effects, and provide explicit expressions for power calculations. We show that the power to detect average treatment effects declines precisely with the quantity that identifies the novel treatment effects. A demonstration of the technique is provided using a cash transfer program in Malawi. Download Paper