Julius Silver Professor, Faculty of Arts and Science, and
Professor of Economics, New York University

Co-Editor, American Economic Review
Research Associate, NBER
Part-Time Professor, University of Warwick

Department of EconomicsNYU, 19 West 4th Street
New York, NY 10012, U.S.A.

debraj.ray@nyu.edu, +1 (212)-998-8906.

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FEATURED RESEARCH
(A slightly whimsical, mainly recent collection; use navbar and search icon at top of page to look for specific research areas and papers.)

Games of Love and Hate

(with Rajiv Vohra), August 2018.

Dedicated to Tapan Mitra — advisor, colleague and dear friend. Tapanda, your sense of aesthetics, minimalism and rigor has been an inspiration to us. We hope you will find some reflection of it in these pages.

Summary. A game of love and hate is one in which a player’s payoff is a function of her own action and the payoffs of other players. For each action profile, the associated payoff profile solves an interdependent utility system, and if that solution is bounded and unique for every profile we call the game coherent. Coherent games generate a standard normal form. Our central theorem states that every Nash equilibrium of such a game is Pareto optimal.

 

 

Noisy Agents

(with Francisco Espinosa), July 2018. Supplementary Appendix.

SummaryAgents signal their type in a principal-agent model; the principal seeks to retain good agents. Types are signaled with some ambient noise. Agents can choose to add or remove additional noise at a cost. It is shown that monotone retention strategies, in which the principal keeps the agent if the signal crosses some threshold, are generically never equilibria. The main result identifies an equilibrium with a bounded retention zone, in which the principal is wary of both excessively good and excessively bad signals: she retains the agent if the signal is “moderate” and replaces him otherwise. 

Missing Unmarried Women

(with Siwan Anderson), February 2018, forthcoming, Journal of the European Economic Association.

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.

Maximality in the Farsighted Stable Set

(with Rajiv Vohra), December 2017.

SummaryThe stable set of von Neumann and Morgenstern was 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. 

Capital and Inequality in the Long Run: Automation Without Technical Progress

(with Dilip Mookherjee), December 2017.

Summary. We present a theory of long run inequality and automation driven by capital accumulation rather than technical progress. At the heart of the theory is a singularity condition that guarantees automation in the production of automated technologies. If that condition is satisfied, the functional share of capital approaches 100% in the long run.

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.

Backward Discounting

(with Nikhil Vellodi and Ruqu Wang), March 2018. Online Appendix.

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. 

Aspirations and Inequality

(with Garance Genicot) Econometrica 85, 485-519, 2017. Online Appendix2009 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.

Anatomy of a Contract Change

with Rajshri Jayaraman and Francis de Vericourt, American Economic Review 106, 316-358, 2016Online Appendix.

SummaryWe study a contract change for tea pluckers. Base wages increased while incentive piece rates were lowered or kept unchanged. Yet, in the following month, output increased by 20–80%. This response contradicts the standard model, is only partly explicable by greater supervision, and appears to be “behavioral.” But in subsequent months, the increase is comprehensively reversed. Our findings suggest that behavioral responses may be ephemeral, and should ideally be tracked over an extended period. 

The Farsighted Stable Set

(with Rajiv Vohra), Econometrica  83, 977–1011, 2015. Online Appendix.

SummaryWe propose a definition of farsighted stability in coalitional games, in the spirit of von Neumann-Morgenstern stability and its modification by Harsanyi. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single-payoff allocation. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games.

Coalition Formation

(with Rajiv Vohra),  in Handbook of Game Theory Vol 4 (H.P. Young and S. Zamir, eds), Elsevier North Holland, 2014.

Summary. This chapter surveys a sizable and growing literature on coalition formation. We refer to theories in which one or more groups of agents (“coalitions”) deliberately get together to jointly determine within-group actions, while interacting noncooperatively across groups. The chapter describes a variety of solution concepts, using an umbrella model that adopts an explicit real-time approach. Players band together, perhaps disband later and re-form in shifting alliances, all the while receiving payoffs at each date according to the coalition structure prevailing at the time. We use this model to nest two broad approaches to coalition formation, one based on cooperative game theory, the other based on noncooperative bargaining. Three themes that receive explicit emphasis are agent farsightedness, the description of equilibrium coalition structures, and the efficiency implications of the various theories.

Implications of an Economic Theory of Conflict: Hindu-Muslim Violence in India

(with Anirban Mitra), Journal of Political Economy 122, 719-765, 2014.

Summary. We model intergroup conflict driven by economic changes within groups. We show that if group incomes are low, increasing group incomes raises violence against that group and lowers violence generated by it. We then apply the model to data on Hindu-Muslim violence in India. Our main result is that an increase in per capita Muslim expenditures generates a large and significant increase in future religious conflict. An increase in Hindu expenditures has a negative or no effect. These findings speak to the origins of Hindu-Muslim violence in post-Independence India. Online Appendix.

Status, Intertemporal Choice, and Risk-Taking

(with Arthur Robson), Econometrica  801505–1531 (2012). Online Appendix.

Summary. This paper studies endogenous risk-taking by embedding a concern for status (relative consumption) into an otherwise conventional model of economic growth. We prove that if the intertemporal production function is strictly concave, an equilibrium must converge to a unique steady state in which there is recurrent endogenous risk taking.

Linking Conflict to Inequality and Polarization

(with Joan Esteban), American Economic Review 101, 1345–1374, 2011.

Summary. In this paper we study a behavioral model of conflict that provides a basis for choosing certain indices of dispersion as indicators for conflict. We show that a suitable monotone transform of the equilibrium level of conflict can be proxied by a linear function of the Gini coefficient, the Herfindahl-Hirschman fractionalization index, and a specific measure of polarization due to Esteban and Ray.

Missing Women: Age and Disease

(with S. Anderson)Review of Economic Studies 77, 1262-1300, 2010. Online Appendix,

Summary. Relative to developed countries and some parts of the developing world, most notably sub-Saharan Africa, there are far fewer women than men in India and China. It has been argued that as many as a 100 million women could be missing. The possibility of gender bias at birth and the mistreatment of young girls are widely regarded as key explanations. We provide a decomposition of these missing women by age and cause of death. While we do not dispute the existence of severe gender bias at young ages, our computations yield some striking new findings: (1) the vast majority of missing women in India and a significant proportion of those in China are of adult age; (2) as a proportion of the total female population, the number of missing women is largest in sub-Saharan Africa, and the absolute numbers are comparable to those for India and China; (3) almost all the missing women stem from disease-by-disease comparisons and not from the changing composition of disease, as described by the epidemiological transition.

Uneven Growth: A Framework for Research in Development Economics

Journal of Economic Perspectives 24 (3), Summer, 45-60, 2010.

Summary. In many developing countries, economic growth has been fundamentally uneven. This article takes the reality of “uneven growth” seriously, and uses it as an organizing device for a research program in Development Economics.

Inequality and Inefficiency in Joint Projects

(with Jean-Marie Baland and Olivier Dagnelie), Economic Journal 117, 922-935, 2007.

SummaryA group of agents voluntarily participates in a joint project, in which efforts are not perfectly substitutable. The output is divided according to some given vector of shares. A share vector is unimprovable if no other share vector yields a higher sum of payoffs. We describe unimprovable share vectors.

On the Dynamics of Inequality

Economic Theory 29, 291–306, 2006.

Summary. The dynamics of inequality are studied in a model of human capital accumulation with credit constraints. This model admits a multiplicity of steady state skill ratios that exhibit varying degrees of inequality across households. The main result studies nonstationary equilibrium paths, and shows that an equilibrium sequence of skill ratios must converge monotonically to the smallest steady state that exceeds the initial ratio for that sequence. This paper, in honor of Mukul Majumdar, publishes notes from 1990, which contain a different proof of the main result.

Aspirations, Poverty and Economic Change

in Abhijit Banerjee, Roland Benabou and Dilip Mookherjee, What Have We Learned About Poverty?, Oxford University Press, 2006.

Summary. Introduces the idea of aspirations as a socially determined reference point. The paper argues that reachable aspirations serve to inspire, while still higher aspirations could lead to frustration.

Group Formation in Risk-Sharing Arrangements

 (with Garance Genicot), Review of Economic Studies 70, 87-113, 2003.

SummaryWe study informal insurance within communities, explicitly recognizing the possibility that subgroups of individuals may destabilize insurance arrangements among the larger group. We therefore consider self-enforcing risk-sharing agreements that are robust not only to single-person deviations but also to potential deviations by subgroups. Variant on an Example in the paper. A conjecture related to the paper.

Conflict and Distribution

(with Joan Esteban), Journal of Economic Theory 87, 379-415, 1999.

Summary. We develop a behavioral model that links the level and pattern of social conflict to the society-wide distribution of individual characteristics. The model can be applied to groups that differ in characteristics such as wealth, ethnicity, religion, and political ideology. We settle questions of existence and uniqueness of conflict equilibrium. Conflict is seen to be closely connected with the bimodality of the underlying distribution of characteristics. However, in general, the conflictdistribution relationship is nonlinear and surprisingly complex. Our results on conflict patterns also throw light on the phenomena of extremism and moderation.

A Theory of Endogenous Coalition Structures

(with Rajiv Vohra), Games and Economic Behavior 26, 286–336, 1999.

Summary. Consider an environment with widespread externalities, and suppose that binding agreements can be written. We study coalition formation in such a setting. Our analysis proceeds by defining on a partition function an extensive-form bargaining game. We establish the existence of a stationary subgame perfect equilibrium. Our main results are concerned with the characterization of equilibrium coalition structures. We develop an algorithm that generates such a  structure. Our characterization results are especially sharp for symmetric partition functions.

Egalitarianism and Incentives

(with Kaoru Ueda), Journal of Economic Theory 71, 324-348, 1996.

Summary. A group of agents is collectively engaged in a joint productive activity. Each agent supplies an observable input, and output is then collectively shared among the members according a social welfare function. However, individual actions are taken on a selfish basis, and the collective decision is only made after inputs are chosen. This leads to inefficiency. The aim of this paper is to show formally that, contrary to popular belief, the degree of inefficiency decreases in the extent of egalitarianism embodied in the social welfare function.

On the Measurement of Polarization

(with Joan Esteban), Econometrica  62, 819–851, 1994.

Summary. This paper is concerned with the conceptualization and measurement of polarization. Suppose that a population is grouped into significantly-sized “clusters’,” such that each cluster is “similar” in terms of the attributes of its members, but different clusters have “dissimilar” attributes. In that case we would say that the society is “polarized.” We study these intuitive criteria carefully, and provide a theory of measurement.

Wages and Involuntary Unemployment in the Slack Season of a Village Economy

(with Anindita Mukherjee), Journal of Development Economics 37, 227-264, 1992.

Summary. We model slack season wages in a village economy, in the presence of involuntary unemployment. Our model draws its inspiration from sociological notions of ‘everyday peasant resistance’.  A continuum of equilibrium wage configurations is obtained. These configurations, barring one, involve wages exceeding reservation wages, despite the presence of involuntary unemployment.

A Concept of Egalitarianism Under Participation Constraints

(with Bhaskar Dutta), Econometrica 57, 615-635, 1989.

Summary. We introduce a new solution concept for transferable-utility games in characteristic function form, when individuals collectively believe in equality as a desirable social goal, although in their private actions they behave selfishly. This latter consideration implies that an “egalitarian solution” must satisfy core-like participation constraints, while the former implies that such a solution is also a Lorenz-maximal element of the constrained set. Despite the well-known fact that the Lorenz ordering is incomplete, we show that the egalitarian solution is unique whenever it exists.