Abstract: We study reputation formation where a long-run player repeatedly observes private signals and takes actions. Short-run players observe the long-run player's past actions but not her past signals. The long-run player can thus develop a reputation for playing a distribution over actions, but not necessarily for playing a particular mapping from signals to actions. Nonetheless, we show that the long-run player can secure her Stackelberg payoff if distinct commitment types are statistically distinguishable and the Stackelberg strategy is confound-defeating. This property holds if and only if the Stackelberg strategy is the unique solution to an optimal transport problem. If the long-run player's payoff is supermodular in one-dimensional signals and actions, she secures the Stackelberg payoff if and only if the Stackelberg strategy is monotone.  An application of our results provides a reputational foundation for a class of Bayesian persuasion solutions when the sender has a small lying cost. Our results extend to the case where distinct commitment types may be indistinguishable but the Stackelberg type is salient under the prior.

Abstract: I study dynamic contracting when a principal (Sender) with private information motivates an agent (Receiver) who has an inalienable decision right. Sender privately observes a payoff-relevant Markovian state and can use both payments (augment with transfers the ex-post value of any action) and persuasion (augment with information the ex-ante value of any action) to incentivize Receiver. For any cost of transfers, any rate of future discounting, and any Markov transition of the state, optimal transfers are dynamically backloaded—payments occur only after Sender has committed to fully reveal the state at all future continuation histories. I next characterize the value of optimal persuasion and transfers when either players are both myopic or become arbitrarily patient. Finally, I show in rideshare problems the optimal contract is a loyalty program that provides drivers a statically optimal amount of information until promotion at some stopping time after which the state is revealed.

(Updated) Abstract: I study reputation formation in repeated games where player actions endogenously determine the probability the game permanently ends. Permanent exit can render reputation useless even to a patient long-lived player whose actions are perfectly mon- itored, in stark contrast to canonical commitment payoff theorems. However, I identify tight conditions for the long-run player to attain their Stackelberg payoff in the unique Markovian equilibria. Along the way, I highlight the role of Markovian strategies in pinning down the value of reputation formation. I apply my results to repeated global games with exit, and obtain new predictions about regime survival and a dynamic foundation for risk dominant selection.

Abstract: We study persuasion games—environments where Receiver contracts their action on Sender’s choice of experiment and the realized signals about some state—and identify which predictions can be made absent knowledge about the prior. To do so, we char- acterize robust mechanisms: those which induce the same allocation rules (mappings from the state to actions) for all priors. These mechanisms take a simple form: they (1) incentivize fully revealing experiments, (2) depend only on the induced posterior, and (3) maximally punish pooling deviations. This characterization uncovers a tight rela- tionship between ordinal preference uncertainty and prior-independent predictions— allocation rules are robust if and only if the sender has a state-independent least favorite action. This, in turn, implies all (and only) ordinally monotone allocation rules are ro- bust in binary action problems. We then apply our model to school choice and uncover a novel informational justification for deferred acceptance when school preferences de- pend on students’ unknown ability. Finally, in general good allocation settings, we show all efficient allocations are robust, even when agent preferences feature state-dependent outside options and allocation externalities.

Abstract: What is the optimal order in which a researcher should submit their papers to journals of differing quality? I analyze a sequential search model without recall where the researcher's expected value from journal submission depends on the history of past submissions. Acceptances immediately terminate the search process and deliver some payoff, while rejections carry information about the paper's quality, affecting the researcher's belief in acceptance probability over future journals. When journal feedback does not change the paper's quality, the researcher's optimal strategy is monotone in their acceptance payoff. Submission costs distort the researcher's effective acceptance payoff, but maintain monotone optimality. If journals give feedback which can affect the paper's quality, such as through referee reports, the search order can change drastically depending on the agent's prior belief about their paper's quality. However, I identify a set of assortatively matched conditions on feedback such that monotone strategies remain optimal whenever the agent's prior is sufficiently optimistic.

Description: We study monopoly problems where consumers interact independently with each monopolist but may have correlated types. We identify conditions under which information landlords---type profiles which collect the lions' share of the information rents---arise, and rank correlation structures by their distributions of information rents. We then study the role (excise) taxation can have on the distribution of surplus, and characterize the equity-efficiency tradeoff induces by policies that tax and subsidize across goods which may be differentially unequal. 

These are notes loosely based on the MMSS course Math 385-0 from the fall of 2020, taught by Julian Gold. I have modified them to include some measure-theoretic basics based in part on Probability with Martingales by David Williams. If you find any [inevitable] mistakes or typos, please send me an email. Thanks to Julian for teaching a great class. 

These are my personal notes for Economics 411-1, 411-2, and 411-3,  Macroeconomics, taught at Northwestern University during the 2020-2021 school year by Professors Larry Christiano (-1), Martin Eichenbaum (-2), Guido Lorenzoni (-2) and Matthias Doepke (-3). This sequence was intended as the first-year core in macroeconomic theory and tools for PhD students. These notes are meant to serve as an individual study guide prior to exams, and as refreshers in later courses and years. As these notes are meant to serve as my own study guides prior to exams and as refreshers in later courses or years, I have condensed much of the material to keep the notes at around 100 pages. When appropriate, intuition is emphasized, though some calculations and exposition are omitted. Topics covered include dynamic programming, recursive equilibrium, growth, financial economics (-1), business cycles, asset pricing, the New Keynesian model and monetary policy (-2), and market incompleteness and search models (-3).

These are notes that I used to lead discussion from for Statistics 383-0, an accelerated undergraduate class for probability, during the winter quarter of the 2022-2023 school year. Examples with numbers are from the notes prepared by the professor, Thomas Severini, while others are ones prepared by myself or that I picked up through my own classes and compiled here. Topics covered include basic probability spaces, the law of large numbers and central limit theorems, and some applications (such as the δ method and confidence intervals). 

These were notes for a lecture I gave on September 22, 2022 for the Undergraduate Economics Society that aimed to help familiarize incoming economics major students with the calculus used in their intermediate courses.