The Dynamics of Inequality

The past forty years have seen a rapid rise in top income inequality in the United States. While there is a large number of existing theories of the Pareto tail of the long‐run income distributions, almost none of these address the fast rise in top inequality observed in the data. We show that standard theories, which build on a random growth mechanism, generate transition dynamics that are too slow relative to those observed in the data. We then suggest two parsimonious deviations from the canonical model that can explain such changes: “scale dependence” that may arise from changes in skill prices, and “type dependence,” that is, the presence of some “high‐growth types.” These deviations are consistent with theories in which the increase in top income inequality is driven by the rise of “superstar” entrepreneurs or managers.     

Altruism in Networks

We provide the first analysis of altruism in networks. Agents are embedded in a fixed network and care about the well‐being of their network neighbors. Depending on incomes, they may provide financial support to their poorer friends. We study the Nash equilibria of the resulting game of transfers. We show that equilibria maximize a concave potential function. We establish existence, uniqueness of equilibrium consumption, and generic uniqueness of equilibrium transfers. We characterize the geometry of the network of transfers and highlight the key role played by transfer intermediaries. We then study comparative statics. A positive income shock to an individual benefits all. For small changes in incomes, agents in a component of the network of transfers act as if they were organized in an income‐pooling community. A decrease in income inequality or expansion of the altruism network may increase consumption inequality.     

Parenting With Style: Altruism and Paternalism in Intergenerational Preference Transmission

We develop a theory of parent‐child relations that rationalizes the choice between alternative parenting styles (as set out in Baumrind, 1967). Parents maximize an objective function that combines Beckerian altruism and paternalism towards children. They can affect their children's choices via two channels: either by influencing children's preferences or by imposing direct restrictions on their choice sets. Different parenting styles (authoritarian, authoritative, and permissive) emerge as equilibrium outcomes and are affected both by parental preferences and by the socioeconomic environment. Parenting style, in turn, feeds back into the children's welfare and economic success. The theory is consistent with the decline of authoritarian parenting observed in industrialized countries and with the greater prevalence of more permissive parenting in countries characterized by low inequality.     

Aspirations and Inequality

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. When capital stocks lie in some compact set, steady state distributions must exhibit inequality and are typically clustered around local poles. When sustained growth is possible, initial histories matter. Either there is convergence to an equal distribution (with growth) or there is perennial relative divergence across clusters, with within‐cluster convergence. A central feature that drives these results is that aspirations that are moderately above an individual's current standard of living tend to encourage investment, while still higher aspirations may lead to frustration.     

The Role of Automatic Stabilizers in the U.S. Business Cycle

Most countries have automatic rules in their tax‐and‐transfer systems that are partly intended to stabilize economic fluctuations. This paper measures their effect on the dynamics of the business cycle. We put forward a model that merges the standard incomplete‐markets model of consumption and inequality with the new Keynesian model of nominal rigidities and business cycles, and that includes most of the main potential stabilizers in the U.S. data and the theoretical channels by which they may work. We find that the conventional argument that stabilizing disposable income will stabilize aggregate demand plays a negligible role in the dynamics of the business cycle, whereas tax‐and‐transfer programs that affect inequality and social insurance can have a larger effect on aggregate volatility. However, as currently designed, the set of stabilizers in place in the United States has had little effect on the volatility of aggregate output fluctuations or on their welfare costs despite stabilizing aggregate consumption. The stabilizers have a more important role when monetary policy is constrained by the zero lower bound, and they affect welfare significantly through the provision of social insurance.     

Generalized Instrumental Variable Models

This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can arise when there are multiple sources of heterogeneity, censored or discrete endogenous variables, or inequality restrictions on functions of observed and unobserved variables. The models generalize the class of incomplete instrumental variable (IV) models in which unobserved variables are single‐valued functions of observed variables. Thus the models are referred to as generalized IV (GIV) models, but there are important cases in which instrumental variable restrictions play no significant role. Building on a definition of observational equivalence for incomplete models the development uses results from random set theory that guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case‐by‐case proofs of sharpness. The use of random sets defined on the space of unobserved variables allows identification analysis under mean and quantile independence restrictions on the distributions of unobserved variables conditional on exogenous variables as well as under a full independence restriction. The results are used to develop sharp bounds on the distribution of valuations in an incomplete model of English auctions, improving on the pointwise bounds available until now. Application of many of the results of the paper requires no familiarity with random set theory.     

Impatience versus Incentives

This paper studies the dynamics of long‐term contracts in repeated principal–agent relationships with an impatient agent. Despite the absence of exogenous uncertainty, Pareto‐optimal dynamic contracts generically oscillate between favoring the principal and favoring the agent.     

Implementation With Contingent Contracts

We study dominant strategy incentive compatibility in a mechanism design setting with contingent contracts where the payoff of each agent is observed by the principal and can be contracted upon. Our main focus is on the class of linear contracts (one of the most commonly used contingent contracts) which consist of a transfer and a flat rate of profit sharing. We characterize outcomes implementable by linear contracts and provide a foundation for them by showing that, in finite type spaces, every social choice function that can be implemented using a more general nonlinear contingent contract can also be implemented using a linear contract. We then qualitatively describe the set of implementable outcomes. We show that a general class of social welfare criteria can be implemented. This class contains social choice functions (such as the Rawlsian) which cannot be implemented using (uncontingent) transfers. Under additional conditions, we show that only social choice functions in this class are implementable.     

A Theory of Macroprudential Policies in the Presence of Nominal Rigidities

We propose a theory of monetary policy and macroprudential interventions in financial markets. We focus on economies with nominal rigidities in goods and labor markets and subject to constraints on monetary policy, such as the zero lower bound or fixed exchange rates. We identify an aggregate demand externality that can be corrected by macroprudential interventions in financial markets. Ex post, the distribution of wealth across agents affects aggregate demand and output. Ex ante, however, these effects are not internalized in private financial decisions. We provide a simple formula for the required financial interventions that depends on a small number of measurable sufficient statistics. We also characterize optimal monetary policy. We extend our framework to incorporate pecuniary externalities, providing a unified approach to both externalities. Finally, we provide a number of applications which illustrate the relevance of our theory.     

Dual‐Donor Organ Exchange

Owing to the worldwide shortage of deceased‐donor organs for transplantation, living donations have become a significant source of transplant organs. However, not all willing donors can donate to their intended recipients because of medical incompatibilities. These incompatibilities can be overcome by an exchange of donors between patients. For kidneys, such exchanges have become widespread in the last decade with the introduction of optimization and market design techniques to kidney exchange. A small but growing number of liver exchanges have also been conducted. Over the last two decades, a number of transplantation procedures emerged where organs from two living donors are transplanted to a single patient. Prominent examples include dual‐graft liver transplantation, lobar lung transplantation, and simultaneous liver‐kidney transplantation. Exchange, however, has been neither practiced nor introduced in this context. We introduce dual‐donor organ exchange as a novel transplantation modality, and through simulations show that living‐donor transplants can be significantly increased through such exchanges. We also provide a simple theoretical model for dual‐donor organ exchange and introduce optimal exchange mechanisms under various logistical constraints.     

Random Choice and Private Information

We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter's perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent's beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well‐calibrated or rational.     

Political Economy of Redistribution

It is often argued that additional constraints on redistribution such as granting veto power to more players in society better protects property from expropriation. We use a model of multilateral bargaining to demonstrate that this intuition may be flawed. Increasing the number of veto players or raising the supermajority requirement for redistribution may reduce protection on the equilibrium path. The reason is the existence of two distinct mechanisms of property protection. One is formal constraints that allow individuals or groups to block any redistribution that is not in their favor. The other occurs in equilibrium where players without such powers protect each other from redistribution. Players without formal veto power anticipate that the expropriation of other similar players will ultimately hurt them and thus combine their influence to prevent redistributions. In a stable allocation, the society exhibits a “class” structure with class members having equal wealth and strategically protecting each other from redistribution.     

Cautious Expected Utility and the Certainty Effect

Many violations of the independence axiom of expected utility can be traced to subjects' attraction to risk‐free prospects. The key axiom in this paper, negative certainty independence ([Dillenberger, 2010]), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy negative certainty independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well defined sense. We show that our representation can also be derived from a “cautious” completion of an incomplete preference relation.     

Moral Hazard in High Office and the Dynamics of Aristocracy

Both aristocratic privileges and constitutional constraints in traditional monarchies can be derived from a ruler's incentive to minimize expected costs of moral‐hazard rents for high officials. We consider a dynamic moral‐hazard model of governors serving a sovereign prince, who must deter them from rebellion and hidden corruption which could cause costly crises. To minimize costs, a governor's rewards for good performance should be deferred up to the maximal credit that the prince can be trusted to pay. In the long run, we find that high officials can become an entrenched aristocracy with low turnover and large claims on the ruler. Dismissals for bad performance should be randomized to avoid inciting rebellions, but the prince can profit from reselling vacant offices, and so his decisions to dismiss high officials require institutionalized monitoring. A soft budget constraint that forgives losses for low‐credit governors can become efficient when costs of corruption are low.     

Progressive Learning

We study a dynamic principal–agent relationship with adverse selection and limited commitment. We show that when the relationship is subject to productivity shocks, the principal may be able to improve her value over time by progressively learning the agent's private information. She may even achieve her first‐best payoff in the long run. The relationship may also exhibit path dependence, with early shocks determining the principal's long‐run value. These findings contrast sharply with the results of the ratchet effect literature, in which the principal persistently obtains low payoffs, giving up substantial informational rents to the agent.     

Insurer Competition in Health Care Markets

The impact of insurer competition on welfare, negotiated provider prices, and premiums in the U.S. private health care industry is theoretically ambiguous. Reduced competition may increase the premiums charged by insurers and their payments made to hospitals. However, it may also strengthen insurers' bargaining leverage when negotiating with hospitals, thereby generating offsetting cost decreases. To understand and measure this trade‐off, we estimate a model of employer‐insurer and hospital‐insurer bargaining over premiums and reimbursements, household demand for insurance, and individual demand for hospitals using detailed California admissions, claims, and enrollment data. We simulate the removal of both large and small insurers from consumers' choice sets. Although consumer welfare decreases and premiums typically increase, we find that premiums can fall upon the removal of a small insurer if an employer imposes effective premium constraints through negotiations with the remaining insurers. We also document substantial heterogeneity in hospital price adjustments upon the removal of an insurer, with renegotiated price increases and decreases of as much as 10% across markets.     

Poverty and Self‐Control

We argue that poverty can perpetuate itself by undermining the capacity for self‐control. In line with a distinguished psychological literature, we consider modes of self‐control that involve the self‐imposed use of contingent punishments and rewards. We study settings in which consumers with quasi‐hyperbolic preferences confront an otherwise standard intertemporal allocation problem with credit constraints. Our main result demonstrates that low initial assets can limit self‐control, trapping people in poverty, while individuals with high initial assets can accumulate indefinitely. Thus, even temporary policies that initiate accumulation among the poor may be effective. We examine implications concerning the effect of access to credit on saving, the demand for commitment devices, the design of financial accounts to promote accumulation, and the variation of the marginal propensity to consume across income from different sources. We also explore the nature of optimal self‐control, demonstrating that it has a simple and behaviorally plausible structure that is immune to self‐renegotiation.     

A Polynomial Optimization Approach to Principal–Agent Problems

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.     

Robustness and Separation in Multidimensional Screening

A principal wishes to screen an agent along several dimensions of private information simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principal's problem, in which she knows the marginal distribution of each component of the agent's type, but does not know the joint distribution. Any mechanism is evaluated by its worst‐case expected profit, over all joint distributions consistent with the known marginals. We show that the optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single crossing) on the structure of preferences within each component. The proof technique involves a generalization of the concept of virtual values to arbitrary screening problems. Sample applications include monopoly pricing and a stylized dynamic taxation model.     

Dynamic Logit With Choice Aversion

We characterize a generalization of discounted logistic choice that incorporates a parameter to capture different views the agent might have about the costs and benefits of larger choice sets. The discounted logit model used in the empirical literature is the special case that displays a “preference for flexibility” in the sense that the agent always prefers to add additional items to a menu. Other cases display varying levels of “choice aversion,” where the agent prefers to remove items from a menu if their ex ante value is below a threshold. We show that higher choice aversion, as measured by dislike of bigger menus, also corresponds to an increased preference for putting off decisions as late as possible.