All – DEBRAJ RAY

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).

On an Apparently Innocuous Difference in Two Versions of Gini’s Coefficient of Inequality: A Symposium

with Rajiv Sethi, Sam Bowles and Wendy Carlin, forthcoming, Journal of Income Distribution (Special Issue for Peter Lambert), edited by John Creedy and S. Subramanian.

Summary: This is not so much a joint paper but a compendium of notes on a basic feature of the Gi ni coefficient. More teaching material than of research interest.

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.”

Multiple Threats to Peace

October 2010.

Summary. This paper studies costly conflict in a world of complete information, in which society can commit to divisible transfers among all potentially warring groups. The difficulty in preventing conflict arises from the possibility that there may be several conflictual divisions of society, each based on a different marker, such as class, geography, religion, or ethnicity.

An “Animal Farm” Perspective On Covid-19 and Other Diseases

with S. Subramanian, January 2021.

Summary. All communicable diseases are equal, but some appear to be more equal than others. We compare Covid-19 to other communicable diseases in poor countries.

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.

India’s Lockdown

(with S. Subramanian and Lore Vandewalle), August 2020, Centre for Economic Policy Research, Policy Brief 102, April 2020.

We discuss the modalities and wisdom of India’s lockdown as a response to the covid-19 pandemic. Here is a related video interview.

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.

Information and Enforcement in Informal Credit Markets

(with Parikshit Ghosh), Economica 83, 59–90, 2016.

Summary. We study loan enforcement in informal credit markets with multiple lenders but no sharing of credit histories, and derive the dynamics of loan size and interest rates for relational lending. In the presence of a sufficient fraction of ‘natural defaulters’, the rest of the market can be incentivized against default by micro-rationing—sharper credit limits and possibly higher interest rates that serve as gateways into new borrowing relationships. When there are too few natural defaulters in the market, this can be supplemented by macro-rationing—random exclusion of some borrowers. When information collection is endogenized, multiple equilibria may arise. (Published version of unpublished notes from 2001.)

Aspirations And The Development Treadmill

Journal of Human Development and Capabilities 17, 309–323, 2016.

Summary. I describe a positive theory of socially determined aspirations, and some implications of that theory for the study of economic inequality and social conflict. The main contribution of the theory is that it attempts to describe, in the same explanatory arc, how a change in aspirations can be inspirational in some circumstances, or a source of frustration and resentment in others. These different reactions arise from the aspirational gap: the difference between socially generated aspirations and the current socio-economic standard that the individual enjoys. Ever-accelerating economic development can cut both ways in terms of inspiration and frustration.

Anatomy of a Contract Change

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

Summary. We 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.

Poverty and Self-Control

(with Doug Bernheim and Sevin Yeltekin), Econometrica 83 (5), 1877-1911, 2015. Online Appendix. A link to the 1999 version, which only had numerical results.

Summary. Poverty can perpetuate itself by undermining the capacity for self-control. Our main result demonstrates that low initial assets can limit self-control, trapping people in poverty, while those with high initial assets can accumulate indefinitely.

Nit-Piketty

CesIfo Economic Studies 2015.

Summary. Yes, capital must displace labor, but not because r > g. This article is based on this blog post, Branko Milanovic objected here; I replied. Piketty replies to some of his critics here.

The Farsighted Stable Set

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

Summary. We 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. Sequel.

Gender Differentials in Eye Care: Access and Treatment

(with Rajshri Jayaraman and Shing-Yi Wang), Economic and Political Weekly 49 No. 25, June 21, 2014.

Summary. Two potential sources of gender bias in health care are (a) females access treatment later than males and (b) they receive differential care at the medical facility. We explore both of these for eye care at a large Indian medical facility. At presentation, women have worse diagnoses than men for indicators of symptomatic illness, such as myopia and cataract. There is no difference in treatment.

Inefficiency and the Golden Rule: Phelps-Koopmans Revisited

(with Tapan Mitra), in Sugata Marjit and Meenakshi Rajeev (eds), Emerging Issues in Economic Development: A Contemporary Theoretical Perspective: Essays in Honour of Dipankar Dasgupta & Amitava Bose, Oxford University Press, 2012.

Summary. We study the celebrated Phelps-Koopmans theorem in environments with nonconvex production technologies. We argue that a robust failure of the theorem occurs in such environments. Specifically, we prove that the Phelps-Koopmans theorem must fail whenever the net output of the aggregate production function f(x), given by f(x) − x, is increasing in any region between the golden rule and the maximum sustainable capital stock.

The Age Distribution of Missing Women in India

(with Siwan Anderson), Economic & Political Weekly 47, No. 47-48, December, 2012.

Summary. Relative to developed countries, there are far fewer women than men in India. Estimates suggest that among the stock of women who could potentially be alive today, over 25 million are “missing”. Sex selection at birth and the mistreatment of young girls are widely regarded as key explanations. We provide a decomposition of missing women by age across the states. While we do not dispute the existence of severe gender bias at young ages, our computations yield some striking findings. First, the vast majority of missing women in India are of adult age. Second, there is significant variation in the distribution of missing women by age across different states. Missing girls at birth are most pervasive in some north-western states, but excess female mortality at older ages is relatively low. In contrast, some north-eastern states have the highest excess female mortality in adulthood but the lowest number of missing women at birth.

Ethnicity and Conflict: An Empirical Study

(with Joan Esteban and Laura. Mayoral), American Economic Review 102, 1310-1342, 2012. Online Appendix.

Summary. We examine empirically the impact of ethnic divisions on conflict, by using a specification based on Esteban and Ray (2011). That theory links conflict intensity to three indices of ethnic distribution: polarization, fractionalization, and the Gini-Greenberg index. The empirical analysis verifies that these distributional measures are significant correlates of conflict. These effects persist as we introduce country-specific measures of group cohesion and of the importance of public goods, and combine them with the distributional measures exactly as described by the theory.

A Theory of Occupational Choice with Endogenous Fertility

(with Dilip Mookherjee and Silvia Prina), American Economic Journal: Microeconomics 4, 1–34, 2012.

Summary. Theories based on partial equilibrium reasoning alone cannot explain the widespread negative cross-sectional correlation between parental wages and fertility, without restrictive assumptions on preferences and childcare costs. We argue that incorporating a dynamic general equilibrium analysis of returns to human capital can help explain observed empirical patterns.

Apples and Oranges: Building a Better Dow

(with Rajiv Sethi), August 2012.

Summary. The Dow relies on price-weighting, which is decidedly an odd methodology. We propose a bridging process that generates convergence to a value-weighted index without compromising the historical continuity of the Dow.

On the Phelps–Koopmans Theorem

(with Tapan Mitra), Journal of Economic Theory 147, 833–849, 2012.

Summary. We examine whether the Phelps–Koopmans theorem is valid in models with nonconvex production technologies. Dedicated to the memory of David Cass: mentor, friend and an extraordinary economic theorist.

Status, Intertemporal Choice, and Risk-Taking

(with Arthur Robson), Econometrica 80, 1505–1531 (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.

Ethnicity and Conflict: Theory and Facts

(with Joan Esteban and Laura Mayoral), Science 336, 858 – 865, 2012.

Summary. Over the second half of the 20th century, conflicts within national boundaries became increasingly dominant. Many (if not most) such conflicts involved violence along ethnic lines. On the basis of recent theoretical and empirical research, we provide evidence that preexisting ethnic divisions do influence social conflict. Our analysis also points to particular channels of influence. Specifically, we show that two different measures of ethnic division—polarization and fractionalization—jointly influence conflict, the former more so when the winners enjoy a “public” prize (such as political power or religious hegemony), the latter more so when the prize is “private” (such as looted resources, government subsidies, or infrastructures).

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.

Comparing Polarization Measures

(with J. Esteban), M. Garfinkel and S. Skaperdas (eds), Oxford Handbook of the Economics of Peace and Conflict, Oxford University Press, 2011.

Summary. We review some alternative measures of unidimensional polarization, grouped into two families: polarization and bi-polarization measures. We take as a base for our analysis the set of axioms that characterize the measure of polarization developed in Esteban and Ray (Econometrica 1994) and Duclos, Esteban and Ray (Econometrica 2013),

A Model of Ethnic Conflict

(with Joan Esteban), Journal of the European Economic Association 9, 496–521, 2011.

Summar. We present a model of conflict in which discriminatory government policy or social intolerance is responsive to various forms of ethnic activism, including violence. The model allows for both financial and human contributions to conflict and allows for a variety of individual attitudes (“radicalism”) towards the cause. The main results concern the effects of within-group heterogeneity in radicalism and income, as well as the correlation between radicalism and income, in precipitating conflict.

Missing Women: Age and Disease

(with Siwan 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.

Aspirations, Segregation and Occupational Choice

(with Dilip Mookherjee and Stefan Napel), Journal of the European Economic Association 8, 139–168, 2010.

Summary. This paper examines steady states of an overlapping generations economy with a given distribution of household locations over a one-dimensional interval. The paper studies steady state configurations of skill acquisition, both with and without segregation, and studies the macroeconomic and welfare effects of segregation on aggregate economic outcomes.

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.

A Remark on Color-Blind Affirmative Action

(with Rajiv Sethi), Journal of Public Economic Theory 12, 399-406, 2010.

Summary. Elite educational institutions have turned to criteria that meet diversity goals without being formally contingent on applicant identity. Under weak and generic conditions, such color-blind affirmative action policies must be nonmonotone in student test scores.

Social Interactions And Segregation In Skill Accumulation

(with Dilip Mookherjee and Stefan Napel), Journal of the European Economic Association 8, 1–13, 2010.

Summary. This paper studies human capital investment in a spatial setting with interpersonal complementarities. A mixture of local and global social interactions affect the cost of acquiring education, and the return to human capital is determined endogenously in the market.

Poverty and Disequalization

(with Dilip Mookherjee) Journal of Globalization and Development 1, Article 3, 2010.

Summary. We study the intergenerational transmission of inequality using a model in which parents can make both financial and occupational bequests to their children. An equal steady state with high per capita skill can co-exist with unequal steady states with low per capita skill. We investigate dynamics starting from arbitrary initial conditions.

Inequality and Markets: Some Implications of Occupational Diversity

(with Dilip Mookherjee), American Economic Journal Microeconomics 2 38–76, 2010.

Summary. This paper studies income distribution in an economy with borrowing constraints. If the span of occupational investments is large, long-run wealth distributions display persistent inequality. With a “rich” set of occupations, so that training costs form an interval, the distribution is unique and the average return to education must rise with educational investment.

The Phelps–Koopmans Theorem and Potential Optimality

International Journal of Economic Theory 6 11–28, 2010.

Summary. The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false in a strong sense. Not only can there be efficient paths with capital stocks forever above and bounded away from a unique golden rule, such paths can also be optimal under the infinite discounted sum of a one-period utility function.

Costly Conflict Under Complete Information

unpublished manuscript, June 2009.

Summary. This paper studies costly conflict in a world of complete information, in which society can commit to divisible transfers among all potentially warring groups. The difficulty in preventing conflict arises from the possibility that there may be several conflictual divisions of society, each based on a different marker, such as class, geography, religion, or ethnicity. It is shown that this diversity of societal markers is particularly conducive to social instability when potential conflict is over private, divisible resources. In contrast, when conflict is over public goods, such diversity promotes social stability.

A Game-Theoretic Perspective on Coalition Formation

This book is now open access! Click the image or the title to download a free electronic copy, and if you like it, please buy the print version.

New York: Oxford University Press, 2008.

Informal Insurance in Social Networks

(with Francis Bloch and Garance Genicot), Journal of Economic Theory 143, 36-58, 2008.

Summary. This paper studies bilateral insurance schemes across networks of individuals. We investigate the structure of self-enforcing insurance networks. Network links play two distinct and possibly conflictual roles. They act as conduits for both transfers and information; affecting the scope for insurance and the severity of punishments upon noncompliance. Their interaction leads to a characterization of stable networks as suitably “sparse” networks. Thickly and thinly connected networks tend to be stable, whereas intermediate degrees of connectedness jeopardize stability.

On the Salience of Ethnic Conflict

(with Joan Esteban), American Economic Review 98:5, 2185–2202, 2008. Online Appendix.

Summary. “In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillment.” — Donald Horowitz (1985).

Polarization, Fractionalization and Conflict

(with Joan Esteban), Journal of Peace Research 45, 163-182, 2008.

Summary. We provide a theoretical framework that distinguishes between the occurrence of conflict and its severity, and clarifies the role of polarization and fractionalization in each of these cases.

A Dynamic Incentive-Based Argument for Conditional Transfers

(with Dilip Mookherjee), Economic Record 84, S2–S16, 2008.

Summary. We compare the long-run (steady state) effects of replacing unconditional transfers to the poor by transfers conditional on education of children. Conditional transfers (funded by taxes on earnings of the skilled) are shown to generate higher long run output per capita and higher (utilitarian and Rawlsian) welfare.

Group Decision-Making in the Shadow of Disagreement

(with Kfir Eliaz and Ronny Razin), Journal of Economic Theory 132, 236–273, 2007.

Summary. A model of group decision-making is studied, in which one of two alternatives must be chosen. Our model is distinguished by three features: private information regarding valuations, differing intensities in preferences, and the option to declare neutrality to avoid disagreement. There is always an equilibrium in which the majority is more aggressive in pushing its alternative, thus enforcing their will via both numbers and voice. However, under general conditions an aggressive minority equilibrium inevitably makes an appearance, provided that the group is large enough. Such equilibria invariably display a “tyranny of the minority”: the increased aggression of the minority always outweighs their smaller number, leading to the minority outcome being implemented with larger probability than the majority alternative.

Introduction to Development Theory

Journal of Economic Theory 137, 1-10, 2007.

Summary. This article introduces a symposium on economic development theory, published as a special issue of the Journal of Development Economics.

Development Economics

The New Palgrave Dictionary of Economics, edited by Lawrence Blume and Steven Durlauf, 2007.

Summary. Entry for the New Palgrave.

Coalition Formation with Binding Agreements

(with Kyle Hyndman), Review of Economic Studies 74, 1125–1147, 2007.

Summary. We study coalition formation in “real time”, a situation in which coalition formation is intertwined with the ongoing receipt of payoffs. Agreements are assumed to be permanently binding: They can only be altered with the full consent of existing signatories. For characteristic function games we prove that equilibrium processes—whether or not these are history dependent—must converge to efficient absorbing states. For three-player games with externalities each player has enough veto power that a general efficiency result can be established. However, there exist four-player games in which all Markov equilibria are inefficient from every initial condition, despite the ability to write permanently binding agreements. Online Appendix.

Inequality and Inefficiency in Joint Projects

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

Summary. A 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.

Reciprocity in Groups and the Limits to Social Capital

(with Francis Bloch and Garance Genicot), American Economic Review 97 (Papers and Proceedings), 65–69, 2007.

Summary. Based on our earlier work on risk sharing in groups and networks (Garance Genicot and Debraj Ray, 2003, 2005 and Francis Bloch, Garance Genicot and Debraj Ray, 2006), this paper proposes a simple model of mutual help in groups and networks. We argue that, if social capital can promote cooperation among groups of individuals, it can also hurt it. When groups of individuals can jointly deviate from a social norm, the fact that they have built strong ties among themselves may in fact make deviations easier, and weaken cooperation in society as a whole.

Beyond Nandigram: Industrialisation in West Bengal

(with Abhijit Vinayak Banerjee, Pranab Bardhan, Kaushik Basu, Mrinal Datta Chaudhuri, Maitreesh Ghatak, Ashok Sanjay Guha, Mukul Majumdar and Dilip Mookherjee), Economic and Political Weekly Commentary, April 2007.

Summary. If we are to learn the right lessons from the tragedy of Nandigram, then we must ensure that the government is involved in the land acquisition process and that we correctly deal with three sets of issues: the size and form of compensation, the eligibility for compensation and the credibility of the process.

An Extension of a Measure of Polarization, With an Application to the Income Distribution of Five OECD Countries

(with Joan Esteban and Carlos Gradín), Journal of Economic Inequality 5, 1–19, 2007.

Summary. We introduce an extension of the Esteban and Ray [Econometrica, 62:819–851 1994] measure of polarization that can be applied to density functions. As a by-product we also derive the Wolfson [Am. Econ. Rev., 84:353–358 1994] measure as a special case. This derivation has the virtue of casting both measures in the context of a (statistically) unified framework. We study the polarization of the distribution of household income for five OECD countries (LIS database): US, UK, Canada, Germany and Sweden.

Contracts and Externalities: How Things Fall Apart

(with Garance Genicot), Journal of Economic Theory 131, 71-100, 2006.

Summary. A single principal interacts with several agents, offering them contracts. The outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.

Bargaining Power and Enforcement in Credit Markets

(with Garance Genicot), Journal of Development Economics 79, 398-412, 2006.

Summary. In a credit market with enforcement constraints, we study the effects of a change in the outside options of a potential defaulter on the terms of the credit contract, as well as on borrower payoffs. The results crucially depend on the allocation of “bargaining power” between the borrower and the lender. We prove that there is a crucial threshold of relative weights such that if the borrower has power that exceeds this threshold, her expected utility must go up whenever her outside options come down. But if the borrower has less power than this threshold, her expected payoff must come down with her outside options. These disparate findings within a single model permit us to interpret existing literature on credit markets in a unified way.

A Decision-Theoretic Basis for Choice Shifts in Groups

(with Kfir Eliaz and Ronny Razin), American Economic Review 96, 1321-1332, 2006.

Summary. The phenomenon of choice shifts in group decision-making has received much attention in the social psychology literature. Faced with a choice between a “safe” and “risky” decision, group members appear to move to one extreme or the other, relative to the choices each member might have made on her own. Both risky and cautious shifts have been identified in different situations. This paper demonstrates that from an individual decision-making perspective, choice shifts may be viewed as a systematic violation of expected utility theory. We propose a model in which a well-known failure of expected utility — captured by the Allais paradox — is equivalent to a particular configuration of choice shifts. Thus, our results imply a connection between two well-known behavioral regularities, one in individual decision theory and another in the social psychology of groups.

Inequality, Lobbying, and Resource Allocation

(with J. Esteban), American Economic Review 96, 257–279 (2006). Supplementary Notes.

Summary. This paper describes how wealth inequality may distort public resource allocation. A government seeks to allocate limited resources to productive sectors, but sectoral productivity is privately known by agents with vested interests in those sectors. They lobby the government for preferential treatment. The government—even if it honestly seeks to maximize economic efficiency—may be confounded by the possibility that both high wealth and true economic desirability create loud lobbies. Broadly speaking, both poorer economies and unequal economies display greater public misallocation. The paper warns against the conventional wisdom that this is so because such governments are more “corrupt.”

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.

Polarization: Concepts, Measurement, Estimation

(with Jean-Yves Duclos and Joan Esteban), in C. Barrett (ed), The Social Economics of Poverty: Identities, Groups, Communities and Networks, London: Routledge, 2006.

Satisficing and Selection in Electoral Competition

(with Jon Bendor and Dilip Mookherjee), Quarterly Journal of Political Science 1, 171–200, 2006.

Summary. We model political parties as adaptive decision makers who compete in a sequence of elections. The key assumptions are that winners satisfice (the winning party in period t keeps its platform in t + 1) while losers search. Under fairly mild assumptions about losers’ search rules, we show that the sequence of winning platforms is absorbed into the top cycle of the (finite) set of feasible platforms with probability one.

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.

Farsighted Network Formation

(with Bhaskar Dutta and Sayantan Ghosal), Journal of Economic Theory 122, 143 – 164, 2005.

Summary. This paper studies a model of dynamic network formation when individuals are farsighted: players evaluate the desirability of a “current” move in terms of its consequences on the entire discounted stream of payoffs. We define a concept of equilibrium which takes into account farsighted behavior of agents and allows for limited cooperation amongst agents.

Informal Insurance, Enforcement Constraints, and Group Formation

(with Garance Genicot), in G. Demange and M. Wooders (eds), Network and Group Formation, Cambridge: Cambridge University Press, 2005.

Summary. This paper, largely based on Genicot and Ray (2003), discusses group formation in the context of informal insurance arrangements with enforcement constraints.

Polarization: Concepts, Measurement, Estimation

(with Jean-Yves Duclos and Joan Esteban), Econometrica 72, 1737–1772, 2004.

Summary. We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fits into what we call the “identity-alienation” framework, and simultaneously satisfies a set of axioms. Here is a link to a somewhat expanded version, which was published in C. Barrett (ed), The Social Economics of Poverty: Identities, Groups, Communities and Networks, London: Routledge (2005).

Robert Rosenthal

(with Roy Radner), Journal of Economic Theory y 112, 365–368, 2003.

Summary. Robert Rosenthal died on February 25, 2002, of a sudden heart attack. He was just 58, in the prime of his professional life. He is missed and loved by the many friends, colleagues and students who knew him. Publications of Bob Rosenthal.

Persistent Inequality

(with Dilip Mookherjee), Review of Economic Studies 70, 369-393, 2003.

Summary. When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state.

Group Formation in Risk-Sharing Arrangements

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

Summary. We 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.

Coalition Formation as a Dynamic Process

(with Hideo Konishi), Journal of Economic Theory 110, 1–41, 2003.

Summary. We study coalition formation as an ongoing, dynamic process, with payoffs generated as coalitions form, disintegrate, or regroup.

Contractual Structure and Wealth Accumulation

(with Dilip Mookherjee), American Economic Review 92, 818–849, 2002. Online Appendix.

Summary. Can historical wealth distributions affect long-run output and inequality despite “rational” saving, convex technology and no externalities? We consider a model of equilibrium short-period financial contracts, where poor agents face credit constraints owing to moral hazard and limited liability. If agents have no bargaining power, poor agents have no incentive to save: poverty traps emerge and agents are polarized into two classes, with no interclass mobility. If instead agents have all the bargaining power, strong saving incentives are generated: the wealth of poor and rich agents alike drift upward indefinitely and “history” does not matter eventually.

Strategy for Economic Reform in West Bengal

(with Abhijit Banerjee, Pranab Bardhan, Kaushik Basu, Mrinal Datta Chaudhuri, Maitreesh Ghatak, Ashok Sanjay Guha, Mukul Majumdar and Dilip Mookherjee), Economic and Political Weekly Special Article, October 12, 2002

Summary. During the last two decades West Bengal has led the rest of the country with regard to agricultural performance and implementation of panchayat institutions. But these developments have begun to level out. This paper reviews performance of these different sectors, discusses possible explanatory factors, and makes a number of suggestions for policy reforms.

Is Equality Stable?

(with Dilip Mookherjee), American Economic Review (Papers and Proceedings) 92, 253–259, 2002.

Summary. We explore the view, further developed in our other work, that inequality is an inevitable consequence of the market mechanism.

The Time Structure of Self-Enforcing Agreements

Econometrica 70, 547–582, 2002.

Summary. A principal and an agent enter into a sequence of agreements. The principal faces an interim participation constraint at each date, but can commit to the current agreement; in contrast, the agent has the opportunity to renege on the current agreement. We show that every constrained efficient sequence must, after a finite number of dates, exhibit a continuation that maximizes the agent’s payoff over all such sequences.

Reinforcement Learning in Repeated Interaction Games

(with Jon Bendor and Dilip Mookherjee), Advances in Theoretical Economics 1, Issue 1, Article 3. Additional notes on extending the model to the probabilistic choice framework of Luce.

Summary. We study long run implications of reinforcement learning when two players repeatedly interact with one another over multiple rounds to play a finite action game. Within each round, the players play the game many successive times with a fixed set of aspirations used to evaluate payoff experiences as successes or failures. The probability weight on successful actions is increased, while failures result in players trying alternative actions in subsequent rounds. The learning rule is supplemented by small amounts of inertia and random perturbations to the states of players. Aspirations are adjusted across successive rounds on the basis of the discrepancy between the average payoff and aspirations in the most recently concluded round. We define and characterize pure steady states of this model, and establish convergence to these under appropriate conditions.

Collective Action and the Group Size Paradox

(with Joan Esteban), American Political Science Review 95, 663–672, 2001.

Summary. According to the Olson paradox, larger groups may be less successful than smaller groups in furthering their interests. We address the issue in a model with three distinctive features: explicit intergroup interaction, collective prizes with a varying mix of public and private characteristics, and nonlinear lobbying costs. The interplay of these features leads to new results. When the cost of lobbying has the elasticity of a quadratic function, or higher, larger groups are more effective no matter how private the prize. With smaller elasticities, a threshold degree of publicness is enough to overturn the Olson argument, and this threshold tends to zero as the elasticity approaches the value for a quadratic function.

Coalitional Power and Public Goods

(with Rajiv Vohra), Journal of Political Economy 109, 1355-1384, 2001.

Summary. We study the provision of public goods when all agents have complete information and can write binding agreements. The focus is on coalition formation as a potential source of inefficiency.

Economic Development: Comment on Hoff and Stiglitz

in G. Meier and J. Stiglitz (eds), Frontiers of Development Economics, World Bank and Oxford University Press, 478-485, 2001.

Social Decision Rules are Not Immune to Conflict

(with Joan Esteban), Economics of Governance 2, 59–67, 2001.

Summary. Why is rent-seeking so endemic in societies? Might it not be possible to design a Pareto-improving social decision rule that sidesteps the inefficient waste of resources resulting from conflict? We assume that a benevolent planner knows the effectiveness of each rent-seeker, that the cost of expending resources is isoelastic, and that it is the same across all players. But she does not know the precise value of this elasticity. We show that this minimal lack of information leads to the impossibility of a Pareto-improving social decision rule, as long as there are at least four agents.

Contemporary Macroeconomics

(co-edited with Amitava Bose and Abhirup Sarkar), Oxford University Press, 2001.

Aspiration-Based Reinforcement Learning in Repeated Interaction Games: An Overview

(with Jon Bendor and Dilip Mookherjee), International Game Theory Review 3, 159–174, 2001.

Summary. In models of aspiration-based reinforcement learning, agents adapt by comparing payoffs achieved from actions chosen in the past with an aspiration level. Though such models are well-established in behavioural psychology, only recently have they begun to receive attention in game theory and its applications to economics and politics. This paper provides an informal overview of a range of such theories applied to repeated interaction games.

Inequality, Control Rights, and Rent Seeking: Sugar Cooperatives in Maharashtra

(with Abhijit Banerjee, Dilip Mookherjee and Kaivan Munshi), Journal of Political Economy 109, 138-190, 2001.

Summary. This paper presents a theory of rent seeking within farmer cooperatives in which inequality of asset ownership affects relative control rights of different groups of members. . Predictions concerning the effect of the distribution of local landownership on sugarcane price, capacity levels, and participation rates of different classes of farmers are confirmed by data from nearly 100 sugar cooperatives in the Indian state of Maharashtra over the period 1971–93.

Credit Rationing in Developing Countries: An Overview of the Theory

(with Parikshit Ghosh and Debraj Ray), Chapter 11 in Readings in the Theory of Economic Development, edited by Dilip Mookherjee and Debraj Ray, London: Blackwell, 383–301l, 2000.

Summary. This paper surveys the theoretical development literature on credit markets.

What’s New in Development Economics?

The American Economist 44, 3-16, 2000.

Summary. This essay is meant to describe the current frontiers of development economics, as I see them. I might as well throw my hands up at the beginning and say there are too many frontiers. In recent years, the subject has made excellent use of economic theory, econometric methods, sociology, anthropology, political science and demography and has burgeoned into one of the liveliest areas of research in all the social sciences.

Readings in the Theory of Economic Development

(co-edited with Dilip Mookherjee), London: Blackwell, 2000.

Wealth Constraints, Lobbying and the Efficiency of Public Allocation

(with Joan Esteban), European Economic Review 44, 694-705, 2000.

Summary. We formalize a model in which individuals lobby before the government in order to bene”t from some productivity-enhancing government action (infrastructures, direct subsidies, permissions, in short). The government honestly tries to allocate these permissions to the agents that will make the best use of them, as revealed by the intensity of their lobbying. If the marginal cost of resources varies with wealth, the amount of information transmitted through lobbying will depend on the degree of inequality. In this paper, we summarize the main approach and examine the special case of equal wealth. We show that the nature of signaling equilibria is critically a!ected by per-capita wealth.

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.

Development Economics

Princeton University Press, 1998.

History and Coordination Failure

(with Alicia Adserà), Journal of Economic Growth 3, 267–276, 1998.

Summary. An extensive literature discusses the existence of a virtuous circle of expectations that might lead communities to Pareto-superior states among multiple potential equilibria. It is generally accepted that such multiplicity stems fundamentally from the presence of positive agglomeration externalities. We examine a two-sector model in this class, and look for intertemporal perfect foresight equilibria. It turns out that under some plausible conditions, positive externalities must coexist with external diseconomies elsewhere in the model, for there to exist equilibria that break free of historical initial conditions. Our main distinguishing assumption is that the positive agglomeration externalities appear with a time lag(that can be made vanishingly small). Then, in the absence of external diseconomies elsewhere, the long-run behaviour of the economy resembles that predicted by myopic adjustment. This finding is independent of the degree of forward-looking behavior exhibited by the agents.

Evolving Aspirations and Cooperation

(with Rajeeva Karandikar, Dilip Mookherjee, and Fernando Vega-Redondo), Journal of Economic Theory 80, 292-331, 1998.

Summary. A 2×2 game is played repeatedly by two satisficing players. The game considered includes the Prisoner’s Dilemma, as well as games of coordination and common interest. Each player has an aspiration at each date, and takes an action. The action is switched at the subsequent period only if the achieved payoff falls below aspirations; the switching probability depends on the shortfall. Aspirations are periodically updated according to payoff experience, but are occasionally subject to trembles. For sufficiently slow updating of aspirations and small tremble probability, it is shown that both players must ultimately cooperate most of the time.

Equilibrium Binding Agreements

(with Rajiv Vohra), Journal of Economic Theory 73, 30-78, 1997.

Summary. We study equilibrium binding agreements, the coalition structures that form under such agreements, and the efficiency of the outcomes that result. We analyze such agreements in a context where the payoff to each player depends on the actions of all other players. Thus a game in strategic form is a natural starting point. Unlike the device of a characteristic function, explicit attention is paid to the behavior of the complementary set of players when a coalition blocks a proposed agreement. A solution concept and its applications are discussed.

Game-Theoretical Applications to Economics and Operations Research

(edited with Bhaskar Dutta, Jan Potters, T. Parthasarathy, T. Raghavan, and Arunava Sen), Kluwer Academic Publishers, 1997. Proceedings of a conference in game theory at the Indian Statistical Institute, New Delhi.

Vertical Linkages between Formal and Informal Financial Institutions

(with Maria Floro), Review of Development Economics 1, 34-56, 1997.

Summary. The paper investigates vertical linkages between formal and informal financial institutions. Specifically, it studies a policy that expands formal credit to informal lenders, in the hope that this will improve loan terms for borrowers who are shut out of the formal sector. Special attention is paid to the Philippines. It is argued that the effects of stronger vertical links depend on the form of lender competition. In particular, if the relationship between lenders is one of strategic cooperation (sustained by threats of reprisal in a repeated setting), an expansion of formal credit may worsen the terms faced by informal borrowers.

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.

Cooperation in Community Interaction without Information Flows

(with Parikshit Ghosh), Review of Economic Studies 63, 491–519, 1996.

Summary. We study cooperative behavior in communities where the flow of information regarding past conduct is limited or missing. Players are initially randomly matched with no knowledge of each other’s past actions; they endogenously decide whether or not to continue
the repeated relationship. We define social equilibrium in such communities. Such equilibria
are characterized by an initial testing phase, followed by cooperation if the test is successful. It is precisely the presence of myopic types that permit cooperation, by raising barriers to entry into new relationships.

Labor Tying

(with Anindita Mukherjee), Journal of Development Economics 47, 207-239, 1995.

Summary. The co-existence of seasonal fluctuations in income and imperfect credit markets suggests that tied contracts should dominate rural labor markets. However, empirical observation from India suggests that this is far from being the case, and indeed, that there is a declining trend in labor tying. In our model, casual labor markets are always active despite the presence of seasonality, and a variety of implications are derived that link economic growth, changing information flows, and the decline of labor tying over time.

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.

Internally-Negotiation-Proof Equilibrium Sets: Limit Behavior for Low Discounting

Games and Economic Behavior 6, 162-177, 1994.

Summary. Recent literature in the theory of dynamic games addresses renegotiatioin-proof equilibria, For repeated games, I analyze the limit of renegotiation-proof equilibrium sets as discounting vanishes. The main result states that such limit sets must either be singletons or belong to the Pareto frontier of the convex hull of the feasible set of the stage game payoffs.

A Non-Cooperative Theory of Coalitional Bargaining

(with Kalyan Chatterjee, Bhaskar Dutta and Kunal Sengupta), Review of Economic Studies 60, 463-477, 1993.

Summary. We explore a sequential-offers model of n-person coalitional bargaining with transferable utility and with time discounting. Our focus is on stationary equilibria of the resulting non-cooperative game. Efficient stationary equilibria converge to a point in the core as the discount factor approaches 1. For strictly convex games, this is the egalitarian solution of Dutta and Ray (Econometrica 1989).

Labor Markets, Adaptive Mechanisms and Nutritional Status

Essays in Honour of K.N. Raj, P. Bardhan, M. Datta-Chaudhuri and T.N. Krishnan, Oxford University Press, 1992.

Summary. Studies the interplay of casual labor markets and long-run nutritional status.

Dynamic Equilibria With Unemployment Due to Undernourishment

(with Peter Streufert), Economic Theory 3, 61-85, 1993.

Summary. We describe steady states of a dynamic model with unemployment due to undernourishment. For many aggregate land stocks, there is a continuum of steady states, We suggest that certain land reforms can reduce unemployment.

Quantity Controls

(with Arunava Sen), in B. Dutta (ed), Welfare Economics and India, Oxford University Press, 1993.

Summary. We explore the role and necessity of quantity controls in decentralizing Pareto-optimal allocations in a market setting.

Monetary Equilibrium in the Overlapping Generations Model With Productive Capital

(with Amitava Bose), Economic Theory 3, 697-716, 1993.

Summary. We study perfect foresight competitive equilibrium in an overlapping generations model with productive capital and a fixed nominal stock of money. We obtain almost-complete characterizations of (a) the existence of a monetary equilibrium from an arbitrary initial capital stock, and (b) the existence of an efficient monetary equilibrium from an arbitrary initial capital stock,

Efficient Monetary Equilibrium in the Overlapping Generations Model

(with Joan Esteban and Tapan Mitra), Journal of Economic Theory 64, 372–389, 1993.

Summary. This paper characterizes equilibria with public debt in the overlapping generations model in which (a) money has a positive price and (b) the resulting intertemporal allocation is efficient. We identify a necessary and sufficient condition for (a) and (b), which states, loosely speaking, that the public debt must not grow “too fast.”

Theoretical Issues in Development Economics

(edited with Bhaskar Dutta, Shubhashis Gangopadhyay and Dilip Mookherjee), Oxford University Press, 1992.

Game Theory and Economic Applications

Proceedings, New Delhi (edited with Bhaskar Dutta, Dilip Mookherjee, T. Parthasarathy, S. Raghavan, and Stef Tijs), Springer Verlag, 1992.

Summary. Brings together the proceedings of a conference on Game Theory at the Indian Statistical Institute, New Delhi.

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.

On the Economic Theory of Quantity Controls

(with Arunava Sen), in K. Basu and P. Nayak (eds.), Economic Theory and Development, Oxford University Press, 1992.

Summary. We study when quantity controls are needed for decentralization of Pareto-optima.

Learning-by-Doing and Industrial Competition

(with Dilip Mookherjee), in B. Dutta et al. (eds.), Theoretical Issues in Economic Development, Oxford University Press, 1992.

Profitability and Concentration

(with Bhaskar Dutta, Shubhashis Gangopadhyay and Kunal Sengupta), in B. Dutta et al (eds.), Theoretical Issues in Economic Development, Oxford University Press.

On Decentralization Under Increasing Returns

(with Tapan Mitra), in M. Majumdar (ed.), Decentralization and Economic Growth, Westview Press, 1992.

Summary. In a model of economic growth with nonconvex technology, we characterize infinite-horizon optimality in terms of short-run optimality and a transversality condition.

Adapting to Undernourishment: The Biological Evidence and Its Implications

(with Partha Dasgupta), in J. Drèze and A.K. Sen (eds.), The Political Economy of Hunger, Clarendon Press, Oxford, 1991.

Summary. We critically survey the clinical literature on the possibility of adaptation to a state of undernutrition, as proposed by P. V. Sukhatme and others.

Why Does Asset Inequality Affect Unemployment? A Study of the Demand Composition Problem

(with Jean-Marie Baland), Journal of Development Economics 35, 69-92, 1991.

Summary. This paper is devoted to a general equilibrium analysis of the relationship between the inequality in asset holdings and the aggregate levels of output and employment in a developing economy. Since luxuries and basic goods compete for the use of the same scarce resources, unemployment is conceived as a mechanism whereby the market demand for basic goods can be limited to a sufficiently low level so that the high demand for luxuries can be met. The ambiguous effects of capital accumulation on employment are also examined.

On the Competitive Pressure Induced by the Diffusion of Innovations

(with Dilip Mookherjee), Journal of Economic Theory 54, 124-147, 1991.

Summary. We consider the decision of a dominant firm to adopt a sequence of potential cost-reducing innovations, where the latest technology adopted diffuses to a competitive fringe at an exogenous rate. With price competition on the product market, the leader optimally spaces apart the adoption dates of successive innovations, so the industry is characterized by cycles of alternating innovation and diffusion. These results may, however, be reversed in the case of quantity competition.

Collusive Market Structure Under Learning-by-Doing and Increasing Returns

(with Dilip Mookherjee), Review of Economic Studies 58, 993-1009, 1991.

Summary. Learning-by-doing and increasing returns are often perceived to have similar implications for market structure and conduct. We analyze this assertion in the context of an infinite-horizon, price-setting game.

Constrained Egalitarian Allocations

(with Bhaskar Dutta), Games and Economic Behavior 3, 403-422, 1991.

Summary. This paper proposes a constrained egalitarian solution concept for TU games which combines commitment for egalitarianism and promotion of individual interests in a consistent manner. The paper shows that the set of constrained egalitarian allocations is nonempty for weakly superadditive games. The solution is “almost” unique if the desirability relation between players is complete.

The Economics of Orchards: An Exercise in Point-Input, Flow-Output Capital Theory

(with Tapan Mitra and Rahul Roy), Journal of Economic Theory 53, 12-50, 1991.

Summary. This paper is concerned with the qualitative properties of optimal intertemporal programs in a model of point-input flow-output capital theory, when future utilities are discounted. Under a mild condition on the flow-output vector, we establish that optimal programs for every discount factor and every initial state (other than a unique stationary optimal state) will exhibit non-convergence.

Excess Capacity and Entry Deterrence

(with S. Gangopadhyay and K. Sengupta), Revista Española de Economía 8, 91-111,1991.

El Aprendizaje en el Trabajo y la Estructura Industrial del Mercado: Un Panorama

(with Dilip Mookherjee), El Trimestre Económico 58, 139-162 .l, 1991.

Summary. Follow-up on Mookherjee and Ray (Review of Economic Studies 1991). The article continues to discuss learning by doing and the possibility of collusive behavior among firms. An English version of this article appears as “Learning-by-Doing and Industrial Competition,” in B. Dutta et al. (eds.), Theoretical Issues in Economic Development, Oxford University Press, 1992.

Increasing Returns, Economic Growth and Decentralization

(with Mukul Majumdar), in B. Dutta, S. Gangopadhyay, D. Mookherjee and D. Ray (eds), Economic Theory and Policy: Essays in Honor of Dipak Banerjee, Oxford University Press, 1990.

Summary. We discuss quantity controls that can be used for decentralization of competitive economies with non-convex production sets.

Economic Theory and Policy: Essays in Honor of Dipak Banerjee,

(edited with Bhaskar Dutta, Shubhashis Gangopadhyay and Dilip Mookherjee), New Delhi: Oxford University Press, 1990.

Collective Dynamic Consistency in Repeated Games

Games and Economic Behavior 1, 295-326, 1989

We formalize the notion of collective dynamic consistency for noncooperative repeated games. Intuitively, we require that an equilibrium not prescribe any course of action in any subgame that players would jointly wish to renegotiate, given the restriction that any alternative must itself be invulnerable to subsequent deviations and renegotiation. While the appropriate definition of collective dynamic consistency is clear for finitely repeated games, serious conceptual difficulties arise when games are infinitely repeated.

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.

Repeated Principal-Agent Games with Eviction

(with Bhaskar Dutta and Kunal Sengupta), in P. Bardhan (ed.), The Economic Theory of Agrarian Institutions, Clarendon Press, Oxford (1989).

Summary. We study repeated principal-agent problems in which the agent can be evicted and replaced by another identical agent. Thus current output, which is perfectly observed, can be used for incentives as well as efficiency wages. We describe conditions under which eviction threats will be used in equilibrium, in addition to output-based incentives.

Interlinkages and the Pattern of Competition

(with Kunal Sengupta), in P. Bardhan (ed.) The Economic Theory of Agrarian Institutions, Clarendon Press, Oxford, 1989.

Summary. This paper provides a broad set of conditions interlinked contracts will not be observed. These conditions are given to throw better light on the circumstances in which interlinkage will indeed be observed.

A Consistent Bargaining Set

(with Bhaskar Dutta, Kunal Sengupta and Rajiv Vohra), Journal of Economic Theory 49, 93-112, 1989.

Summary. Both the core and the bargaining set fail to satisfy a natural requirement of consistency. In excluding imputations to which there exist objections, the core does not assess the “credibility” of such objections. The bargaining set goes a step further. Only objections which have no counter-objections are considered justified. However, the credibility of counter-objections is not similarly assessed. We formulate a notion of a consistent bargaining set in which each objection in a “chain” of objections is tested in precisely the same way as its predecessor. Various properties of the consistent bargaining set are also analyzed.

Credible Coalitions and the Core

International Journal of Game Theory 18, 185-187, 1989.

Summary. A problem with the concept of the core is that it does not explicitly capture the credibility of blocking coalitions, This notion is defined, and the concept of a modified core introduced, consisting of allocations not blocked by any credible coalition. The core and modified core are then shown to be identical. The concept of credibility is thus implicit in the definition of the core.

Markov-Perfect Equilibrium in Altruistic Growth Economies With Production Uncertainty

(with Doug Bernheim), Journal of Economic Theory 47, 195-202, 1989.

Summary. This paper concerns the existence of Markov perfect equilibria in altruistic growth economies. Previous work on deterministic models has established existence only under extremely restrictive conditions. We show that the introduction of production uncertainly yields an existence theorem for aggregative infinite horizon models with very general forms of altruism.

Economic Growth With Intergenerational Altruism

(with Doug Bernheim), Review of Economic Studies 54, 227-243, 1987.

Summary. We consider the properties of equilibrium behavior in an aggregative growth model with intergenerational altruism. Various positive properties such as the cyclicity of equilibrium programs, and the convergence of equilibrium stocks to a steady state, are analyzed. Among other normative properties, it is established that under certain natural conditions, Nash equilibrium programs are efficient and “modified Pareto optimal”, in a sense made clear in the paper, but never Pareto optimal in the traditional sense.

Inequality as a Determinant of Malnutrition and Unemployment, II. Policy

(with Partha Dasgupta), Economic Journal 97, 177-188, 1987.

Summary. This is the second part of a two-part article which develops a theory of involuntary unemployment and the incidence of undernourishment, relates these in turn to the production and distribution of income, and ultimately to the distribution of productive assets. In this part, we study policy options such as land reform.

Nonpaternalistic Intergenerational Altruism

Journal of Economic Theory 41, 112-132, 1987.

Summary. The paper develops a concept of equilibrium behaviour in a model of nonpaternalistic intergenerational altruism. When each generation’s utility depends on that of at least two successors, equilibria may be inefficient.

Inequality as a Determinant of Malnutrition and Unemployment, I. Theory

(with Partha Dasgupta), Economic Journal 96, 1011-1034, 1986.

Summary. This is the first part of a two-part article which develops a theory of involuntary unemployment and the incidence of undernourishment, relates these in turn to the production and distribution of income, and ultimately to the distribution of productive assets. In this part, we study the general equilibrium of such a framework and describe its properties.

On the Existence of Markov-Consistent Plans Under Uncertainty

(with Doug Bernheim), Review of Economic Studies 53, 877-882, 1986.

An Economic Theory of Malnutrition

(with Partha Dasgupta), in I.S. Gulati and M. Shroff (eds.), Economic Theory and Underdevelopment: Essays in Honour of I.G. Patel, 1986.

Summary. An initial, sketchy version of the Dasgupta-Ray papers on involntary unemployment and undernutrition.

Intertemporal Borrowing to Sustain Exogenous Consumption Standards under Uncertainty

Journal of Economic Theory 33, 72-87, 1984.

Summary. Consider an agent who is attempting to maintain a given consumption level over time. in the face of a stochastic technology. He is permitted to borrow and lend at given rates of interest. The main results are: (i) if the borrowing rate of interest exceeds the lending rate. the expected net indebtedness of the agent must grow unboundedly large, unless the consumption target is attainable with at most one loan, and (ii) the probabilities of the two events: becoming increasingly indebted, and accumulating unbounded wealth, sum to unity.

Survival, Growth and Technical Progress in a Small Resource-Importing Economy

International Economic Review 25, 275-295, 1984.

Summary. This paper studies a small open economy with steadily rising prices of an imported resource. Consider any consumption plan, such as one that involves a minimum consumption (“survival”) or growth at some arithmetic or proportional rate. For any such plan, a criterion is provided, involving the plan itself, the resource price path, and the technology, which will permit a “planner” to deduce whether this plan is feasible. Choice among these plans requires, of course, a sharper ethical criterion.

Dynamic Optimization on a Non-Convex Feasible Set: Some General Results for Non-Smooth Technologies

(with Tapan Mitra), Zeitschrift für Nationalökonomie / Journal of Economics, 44, 151-175, 1984.

Summary. This paper studies a model of intertemporal accumulation with a non-convex technology that could also have kinks.

Altruistic Growth Economies. 2. Properties of Bequest Equilibria

(with Doug Bernheim), IMSSS Technical Report, Stanford University, 1983.

Summary. We describe an economy with intergenerational altruism, and study the properties of bequest equilibrium in Markov strategies.

Altruistic Growth Economies. 1. Existence of Bequest Equilibria

(with Doug Bernheim), IMSSS Technical Report, Stanford University, 1983.

Summary. We describe an economy with intergenerational altruism, and establish the existence of a bequest equilibrium in Markov strategies.

Efficient and Optimal Programs When Investment is Irreversible: A Duality Theory

(with Tapan Mitra), Journal of Mathematical Economics 11, 81-113, 1983.

Summary. We formulate a duality theory of efficient and optimal programs in intertemporal models with irreversible investment.

Feasible Alternatives Under Deteriorating Terms of Trade

(with Mukul Majumdar and Tapan Mitra), Journal of International Economics 13, 105-134, 1982.

Summary. The paper presents a dynamic general equilibrium model of a small open economy which employs an essential imported input in production. We describe necessary and sufficient conditions on the technology and the rate of decline of the terms of trade that ensure survival.