Contracts with Interdependent Preferences

(with Marek Weretka), March 2024.

Summary.  This paper studies contracting between a principal and multiple agents. The setup is classical except for the assumption that agents have interdependent preferences. We characterize cost effective contracts, and relate the direction of co-movement in rewards — “joint liability” (positive) or “tournaments” (negative) — to the assumed structure of preference interdependence. We identify two asymmetries. First, the optimal contract leans towards joint liability rather than tournaments, especially in larger teams, in a sense made precise in the paper. Second, when the mechanism-design problem is augmented by robustness constraints designed to eliminate multiple equilibria, the principal may prefer teams linked via adversarial rather than altruistic preferences.

Nash Bargaining with Coalitional Threats

(with Rajiv Vohra). March 2024.

Summary. We axiomatically characterize bargaining outcomes in the presence of coalitional threats. As in Nash’s solution, these involve the product of payoffs net of disagreement points, but coalitional threats appear as conventional constraints, and are not netted out from payoffs as disagreement points are. This basic property is implied by a new “expansion axiom”  that is automatically satisfied in the standard bargaining problem. We then endogenize coalitional threats using internal consistency. For games with convex feasible sets of payoffs, the internally consistent solution coincides with one in which the only threat from each coalition is the use of their “standard” Nash solution, unconstrained by subcoalitions. For transferable-utility games, this observation uncovers a connection between the coalitional bargaining solution and the egalitarian solution of Dutta and Ray (1989, 1991).

Measuring Upward Mobility

(with Garance Genicot). This version February 2023. Forthcoming, American Economic Review. [Slides]

Summary. We develop a measure of upward mobility that distills central features of the relative and absolute approaches to measuring mobility. The former is embodied in the Growth Progressivity axiom: transfers of instantaneous growth rates from relatively rich to poor individuals increases upward mobility. The absolute approach is embodied in the Growth Alignment axiom: mobility increases with higher growth for all individuals. These axioms, along with standard auxiliary restrictions, identify a simple one-parameter family of upward mobility measures, linear in individual growth rates and exhibiting geometrically declining weights on baseline incomes. A serendipitous implication of our measure is that it does not rely on panel data, which greatly expands our analytical scope to data-poor settings.

Backward Discounting

(with Nikhil Vellodi and Ruqu Wang), November 2022, forthcoming, Journal of the European Economic Association. Online Appendix. This paper has been around for a while… here is an older version with Ruqu.

SummaryWe study a model of time preferences in which agents discount both past and future payoffs to obtain their lifetime felicity. Agents derive utility from their current lifetime felicity, as well the anticipated felicity of a distinguished future self. These postulates permit an agent to anticipate future regret in current decisions, and generate a set of novel testable implications in line with empirical evidence. 

The Social Equilibrium of Relational Arrangements

(with Parikshit Ghosh),  forthcoming, Journal of Institutional and Theoretical Economics, Special Issue on Relational Contracts.

Summary. Building on Ghosh and Ray (1996), we study norms within partnerships that exhibit gradually increasing cooperation, thus serving to deter deviations. But socially beneficial gradualism may be undermined by partners renegotiating to greater cooperation from the outset. We show that incomplete information regard- ing partner patience ameliorates this tension even as it adds to the anonymity of the environment.

Signaling and Discrimination in Collaborative Projects

with Paula Onuchic, American Economic Review 113 (1), 210-252 (2023).

Summary. We propose a model of collaborative work in pairs. Each potential partner draws an idea from a distribution that depends on their unobserved ability. The partners then choose to combine their ideas, or work separately. These decisions are based on the intrinsic value of their projects, but also on signaling payoffs, which depend on the public’s assessment of individual contributions to joint work. We study this equilibrium interaction, and argue equilibria with symmetric collaborative strategies are often fragile, in a sense made precise in the paper. In such cases, asymmetric equilibria exist: upon observing a collaborative outcome, the public ascribes higher credit to one of the partners based on payoff-irrelevant “identities.”

Growth, Automation and the Long-Run Share of Labor

(with Dilip Mookherjee), Review of Economic Dynamics 46, 1-26, https://doi.org/10.1016/j.red.2021.09.003 (2022).. Supplementary Appendix.

Summary. We describe a minimal set of sufficient conditions for progressive automation and for the labor share of income to converge to zero in the long run: (i) an asymmetry between physical and human capital: individual claims on the former can be reproduced linearly, while human capital consists of embodied skills; (ii) the technical feasibility of sectoral automation; (ii) a self-replication condition on the production function for robot services; (iv) asymptotic homotheticity (more generally neutrality) of demand, and (v) a minimal degree of patience or intergenerational altruism among a fraction of households. However, human labor is displaced gradually, and real wages could rise indefinitely. Technical progress is not needed for our results, but our findings extend to endogenous technical progress even if such progress is not biased ex ante in favor of automation.

Groups in Conflict: Private and Public Prizes

(with Laura Mayoral),  Journal of Development Economics 154, https://doi.org/10.1016/j.jdeveco.2021.102759 (2022).

 Supplementary Appendix.

Summary. This paper studies costly conflict over private and public goods. Oil is an example of the former, political and civil rights an example of the latter. Our theory predicts that groups in conflict are likely to be small when the prize is private, and large when the prize is public. We examine these implications empirically by constructing a global dataset at the ethnic group level and studying conflict along ethnic lines. Our theoretical predictions find significant confirmation in this setting, and the analysis sheds new light on group size and collective action in the context of violent conflict.

Conveying Value Via Categories

(with Paula Onuchic), October 2019, revised December 2022. Forthcoming, Theoretical Economics.

A sender is about to come into possession of an object of heterogeneous quality. Prior to knowing that quality, she commits to a categorization. That is, she partitions the set of qualities into  subsets — some possibly singletons — and verifiably commits to reveal the element in which the quality belongs. The categories  must be monotone. Our main results fully describe the profit-maximizing categorization  for any pair of priors over object quality held by sender and receiver. We apply these results to the design of educational grades.