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Contracts, Wage Differentials and Involuntary Unemployment

Studies in Microeconomics 12(1) 10–31, 2024. Dedicated to Ashok Kotwal.

Summary. I study a simple model of labour markets with imperfect monitoring and efficiency wages that provide work incentives. Involuntary unemployment is an outcome, but it is just one particular instance of many inter-firm wage differentials that pervade the equilibrium. The goal of this paper is to study the relationship between firm size, work standards, wages paid, contractual utility for workers, and capital intensity in production. Under certain conditions: (a) larger firms pay higher wages and demand higher individual effort levels; (b) despite these opposing effects, larger firms offer a higher net contractual utility and (c) larger firms are more capital intensive, even when production functions are homothetic in capital and labour.

 

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. Supplementary Notes.

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.

Past and Future: Backward and Forward Discounting

(with Nikhil Vellodi and Ruqu Wang), Journal of the European Economic Association 22 (2), 837–875, 2024. Online Appendix. This paper has been around for many years… here is an older version with Ruqu.

Summary. We 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.

Too Good To Be True? Retention Rules for Noisy Agents

(with Francisco Espinosa), revised January 2022, forthcoming American Economic Journal: Microeconomics. Supplementary Appendix.

Summary. An agent who privately knows his type (good or bad) seeks to be retained by a principal. A principal seeks to retain good agents. Agents signal their type with some ambient noise, but can alter this noise, perhaps at some cost. Our main finding, that we examine in several extensions, is that in equilibrium,  the principal treats extreme signals in either direction with suspicion, and retains the agent if and only if the signal falls in some intermediate bounded set. In short, she follows the maxim: “if it seems too good to be true, it probably is.”  

Partially Additive Utility Representations

(with Siddharth Chatterjee and Arunava Sen, 2021).

General classes of utility representations are introduced which are partially additive. Preferences that admit such representations are characterized.

A Principal-Agent Relationship With No Advantage to Commitment

(with Francisco Espinosa and Rajiv Vohra), in Pure and Applied Functional Analysis 6, 1043-1064 (2021).

Summary. This paper explores conditions under which the ability to commit in a principal-agent relationship creates no additional benefit for the principal, over and above simultaneous interaction without commitment. A central assumption is that the principal’s payoff depends only on the payoff to the agent and her type. Dedicated to Ali Khan on the occasion of his 70th birthday.

Decoding India’s Low Covid-19 Case Fatality Rate

(with Minu Philip and S. Subramanian),  Journal of Human Development and Capabilities 22, 27-51 (2021).

Summary. India’s case fatality rate (CFR) under covid-19 is strikingly low, trending from 3% or more, to a current level of under 1.8%. The world average rate is far higher. Several observers have noted that this difference is at least partly due to India’s younger age distribution. In this paper, we use age-specific fatality rates from comparison countries, coupled with India’s distribution of covid-19 cases to “predict” what India’s CFR would be with those age-specific rates. In most cases, those predictions are lower than India’s actual performance, suggesting that India’s CFR is, if anything, too high rather than too low.

India’s Lockdown: An Interim Report

(with S. Subramanian), May 2020, Indian Economic Review, https://doi.org/10.1007/s41775-020-00094-2

Summary. The world has continued to change rapidly since the last version of this article was written on May 20, 2020. Yet, as this article goes to press, we are aware of two realities; first, that we cannot perennially chase a moving target, but second, that nothing about the fundamental trends that we have identified appear to have changed. India is firmly in the throes of a vicious pandemic that we can only hope will abate with the development of an effective vaccine. Our plea for the widespread provision of adequate health and medical facilities, adequate protection for the elderly, and transfers to those severely affected by the lockdown are absolutely unchanged in the face of the latest data. In contrast, the brutal enforcement of a lockdown with none of these accompanying measures can only worsen outcomes for the poorest and most vulnerable among the population.

A Sovereign Fund for India

(with Parikshit Ghosh), October 2019.  Forthcoming in Kaushik Basu, Maitreesh Ghatak, Kenneth Kletzer, Sudipto Mundle and Eric Verhoogen (eds), Development, Distribution, and Markets: Essays in Honour of Pranab Bardhan, Oxford University Press.

We propose that India build up a sovereign fund, to be invested in portfolios of equity, bonds and other financial assets, and managed professionally as any fund would be managed, subject to certain constraints that we describe in this paper. The proposal to access Indian corporate value consists of two parts: I. A one-time directive that will require every publicly traded Indian company to issue new shares to the government, equal to some fraction (say 10–20%) of their outstanding shares in the mar- ket. II. An ongoing obligation to transfer some given fraction (again 10–20%) of every new share issue — whether in the form of an initial public offering or an expansion of the existing share base — to the India Fund.

Aspirations and Economic Behavior

(with Garance Genicot), Annual Review of Economics 12, 715-746 (2020). [Slides from a 2023 review lecture]

This paper reviews the literature on aspirations in economics, with a particular focus on socially determined aspirations. The core theory builds on two fundamental principles: (a) aspirations can serve to inspire, but still higher aspirations can lead to frustration and resentment; and (b) aspirations are largely determined by an individual’s social environment. We discuss the implications of this framework for the study of interpersonal inequality, social conflict, fertility choices, risk taking and goal-setting.

Information Aggregation in a Financial Market with General Signal Structure

(with Youcheng Lou, Sahar Parsa, Duan Li and Shouyang Wang),  Journal of Economic Theory 183, 594–624 (2019).

Summary. We study a financial market with asymmetric, multidimensional trader signals that have general correlation structure. Each of a continuum of traders belongs to one of finitely many “information groups.” There is a multidimensional aggregate signal for each group. Each trader observes an idiosyncratic signal about the fundamental, built from this group signal. Correlations across group signals are arbitrary. Several existing models serve as special cases, and new applications become possible. We establish existence and regularity of linear equilibrium, and demonstrate that the equilibrium price aggregates information perfectly as noise trade vanishes. Combines and extends results in Parsa and Ray (2017) and Lou, Li and Wang (2017), both mimeo. Online Appendix.

Games of Love and Hate

(with Rajiv Vohra), Journal of Political Economy 128, 1789-1825 (2020).

Dedicated to Tapan Mitra — advisor, colleague and dear friend, whose sense of aesthetics, minimalism and rigor has been an inspiration to us. Tapan Mitra died on February 3, 2019.

Summary. A strategic situation with payoff-based externalities is one in which a player’s payoff is a function of her own action and the payoffs of other players. Every action profile therefore induces an interdependent utility system. A strategic situation is continuous if each such utility system is continuous. If each utility system is bounded, with a unique payoff solution for every action profile, we call the strategic situation coherent, and if the same condition also applies to every subset of players, we call the situation sub-coherent. A coherent, sub-coherent and continuous situation generates a standard normal form, referred to as a game of love and hate. Our central theorem states that every equilibrium of a game of love and hate is Pareto optimal, in sharp contrast to the general prevalence of inefficient equilibria in the presence of externalities. While externalities are restricted to flow only through payoffs there are no other constraints: they could be positive or negative, or of varying sign. We further show that our coherence, sub-coherence and continuity requirements are tight.

Maximality in the Farsighted Stable Set

(with Rajiv Vohra)   Econometrica 87(5), 1763–1779 Online Appendix.

Summary. The stable set of von Neumann and Morgenstern can be extended to cover farsighted coalitional deviations, as proposed by Harsanyi (1974), and more recently reformulated by Ray and Vohra (2015). However,  while coalitional deviations improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable, and easily verifiable, properties is unaffected by the imposition of this stringent maximality requirement. 

Hindu-Muslim Violence in India: A Postscript from the 21st Century

(with Anirban Mitra), in Advances in the Economics of Religion (J-P Carvalho, S. Iyer and J. Rubin, eds.) Volume 158, International Economic Association Series, Palgrave Macmillan (2019).

Summary.  We revisit and extend the core issues studied in Mitra and Ray (2014). The main reason behind this retrospection is to check if the robust empirical patterns recorded there persist once we consider a longer time frame extending into the 21st century. We make three observations: (i) There is a clear economic component to violence, roughly along the lines of our earlier paper; (ii)  There is a new aspect which is assuming salience now — namely, a strong political component which is manifesting itself through the presence of BJP legislators; (iii) Ahmedabad exemplifies the ascendancy of this political component. 

Missing Unmarried Women

(with Siwan Anderson), Journal of the European Economic Association 2019 17(5), 1585–1616; jvy027, https://doi.org/10.1093/jeea/jvy027

Summary. We provide systematic estimates of the excess female mortality faced by older unmarried women in developing regions. We place these estimates in the context of the missing women phenomenon. There are approximately 1.5 million missing women between the ages of 30 and 60 years old each year. We find that 35% of these missing women of adult age can be attributed to not being married. These estimates vary by region. India has the largest proportion of missing adult women who are without a husband, followed by the countries in East Africa. By contrast, China has almost no missing unmarried women. We show that 70% of missing unmarried women are of reproductive age and that it is the relatively high mortality rates of these young unmarried women (compared to their married counterparts) that drive this phenomenon.

Hedonistic Altruism and Welfare Economics

August 2013, revised February 2018.

Summary. When future generations enter hedonistically into current welfare, a social planner should overweight the future relative to the individual, even if every individual has the same discount factor.

Certified Random: A New Order for Co-Authorship

(with Arthur Robson), American Economic Review 108, 489–520 (2018).

Summary. Certified random order (a) distributes the gain from first authorship evenly over the alphabet, (b) allows either author to signal when contributions are extremely unequal, (c) will invade an environment where alphabetical order is dominant, (d) is robust to deviations, (e) may be ex-ante more efficient than alphabetical order, and (f) is no more complex than the existing alphabetical system modified by occasional reversal of name order.

Conflict and Development

(with Joan Esteban) Annual Reviews of Economics  9, 263-293, 2017.

Summary. In this review, we examine the links between economic development and social conflict. By economic development, we refer broadly to aggregate changes in per capita income and wealth or in the distribution of that wealth. By social conflict, we refer to within-country unrest, ranging from peaceful demonstrations, processions, and strikes to violent riots and civil war. We organize our review by critically examining three common perceptions: that conflict declines with ongoing economic growth; that conflict is principally organized along economic differences rather than similarities; and that conflict, most especially in developing countries, is driven by ethnic motives.

Aspirations and Inequality

(with Garance Genicot) Econometrica 85, 485-519, 2017. Online Appendix. 2009 version.

Summary. This paper develops a theory of socially determined aspirations, and the interaction of those aspirations with growth and inequality. The interaction is bidirectional: economy-wide outcomes determine individual aspirations, which in turn determine investment incentives and social outcomes. Thus aspirations, income, and the distribution of income evolve jointly.

Kenneth Arrow

El Trimestre Económico 84. 761-769, 2017.

Summary. A translation into Spanish of my post on the event of Kenneth Arrow’s death. The original post is available here.