Economic Dynamics

Displaying 34 Items

Growth, Automation and the Long-Run Share of Labor

(with Dilip Mookherjee), June 2020. Supplementary Appendix. Slides.

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.

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.

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.

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 (Published version of unpublished notes from 2001.)

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.


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  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.

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 Microeconomic2 38–76, 2010.

SummaryThis 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.

SummaryThe 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.

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.


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.

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.

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.

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.

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.”

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.

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.

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.

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.

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.

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.

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.

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.