Output and wages with inequality averse agents

Abstract.  We analyse a two‐task work environment with risk‐neutral but inequality averse individuals. For the agent employed in task 2 effort is verifiable, while in task 1 it is not. Accordingly, agent 1 receives an incentive contract that, owing to his wealth constraint, leads to a rent that the other agent resents. We show that greater inequality aversion unambiguously decreases total output and therefore average labour productivity. More specifically, inequality aversion reduces effort, wage, and payoff of agent 1. Effects on wage and effort of agent 2 depend on whether effort levels across tasks are substitutes or complements in the firm's output function. JEL classification: D2, J3     

Contract renegotiation and options in agency problems

This article discusses the ability of an agent and a principalto achieve the first-best outcome when the agent invests inan asset that has greater value if owned by the principal thanby the agent. When contracts can be renegotiated, a well-knowndanger is that the principal can hold up the agent, underminingthe agent's investment incentives. We begin by identifying acountervailing effect: Investment by the agent can increasehis value for the asset, thus improving his bargaining positionin renegotiation. We show that option contracts will achievethe first best whenever his threat-point effect dominates theholdup effect. Otherwise, achieving the first best is difficultand, in many cases, impossible.     

The progressivity of equalization payments in federations

We investigate the conditions under which an inequality averse and additively separable welfarist central government would choose to set up a progressive equalization payments scheme in a federation with local public goods. A progressive equalization payments scheme is a list of per capita net (possibly negative) subsidies – one such net subsidy for every jurisdiction – that are decreasing with respect to jurisdictions per capita wealth. We examine this question in a setting where the case for progressivity is a priori the strongest, namely: all citizens have the same utility function, inhabitants of a given jurisdiction have the same wealth and are not able to move across jurisdictions and there is no cross-jurisdiction competition in the setting of tax rates. We show that the central government favors a progressive equalization payments scheme for all distributions of wealth and population sizes if and only if its objective function is additively separable between each jurisdiction's per capita wealth and number of inhabitants. When interpreted for a mean of order r social welfare function, and assuming the absence of congestion in the local public good, this condition is shown to be equivalent to the requirement that the individual indirect utility function be additively separable between wealth public good price and be raised at the power 1/r before its agregation by means of the mean-of-order r social welfare function. Some implications of this restriction to the case where the individual's direct utility function is additively separable are also derived.     

Subsidy design: wealth versus benefits

A government would like to subsidize an indivisible good. Consumers’ valuations of the good vary according to their wealth and benefits from the good. A subsidy scheme may be based on consumers’ wealth or benefit information. We translate a wealth-based policy to a benefit-based policy, and vice versa, and give a necessary and sufficient condition for the pair of policies to implement the same assignment: consumers choose to purchase the good under the wealth-based policy if and only if they choose to do so under the translated benefit-based policy. General taxation allows equivalent policies to require the same budget.     

On the optimal design of insurance contracts with the restriction of equity risk

This paper focuses on the optimal design of insurance contracts with the restriction of equity risk by Arrow's optimal insurance model [2] and Zhou's optimal insurance model [4]. The insured aims to maximize his/her expected utility of terminal wealth, under the constraint that the insurer wishes to control his/her risk. We establish an optimal insurance model that restrains underwriting risk and investment risk simultaneously. We solve this problem and obtain the results which improve and extend the results given by Arrow [2] and Zhou [4].     

Capital income taxation when inherited wealth is not observable

This paper extends the Atkinson-Stiglitz model of direct and indirect taxation to a dynamic setting with two unobservable characteristics: productive ability and inherited wealth. Bequests are motivated by the ‘joy of giving’. A child’s inheritance is a random variable with a probability distribution that depends on his parent’s investment in a ‘bequest technology’. Public borrowing is assumed and implies the modified golden rule. We study the optimal tax policy when two instruments are available: a non-linear (wage) income tax and a proportional tax on capital income. We show that the second instrument ought, in general, to be used but that the tax rate is not necessarily positive. However, a positive tax rate is more likely when there is a positive correlation between inherited wealth and innate ability.     

“Timing Is Everything” and Marital Bliss

We first show that in a marriage market, when the stability of a matching is disturbed when a new agent joins the game, natural greedy behavior defines an equilibration procedure that converges to a stable matching for the extended problem. We then consider the iterative procedure under which agents join the game sequentially, and the natural greedy procedure is applied after the entrance of each agent. It is shown that this procedure converges to a stable matching for the original (global) problem and that for each agent, if the order of all other agents is given, he/she weakly improves his/her final outcome by deferring his/her arrival time. The agent that arrives last gets his/her optimal outcome under stable matchings. Journal of Economic Literature Classification Numbers: C78, C62.     

Fiat money and the value of binding portfolio constraints

We establish necessary and sufficient conditions for the individual optimality of a consumption-portfolio plan in an infinite horizon economy where agents are uniformly impatient and fiat money is the only asset available for intertemporal transfers of wealth. Next, we show that fiat money has a positive equilibrium price if and only if for some agent the zero short sale constraint is binding and has a positive shadow price (now or in the future). As there is always an agent that is long, it follows that marginal rates of intertemporal substitution never coincide across agents. That is, monetary equilibria are never full Pareto efficient. We also give a counter-example illustrating the occurrence of monetary bubbles under incomplete markets in the absence of uniform impatience.     

Wealth constraint and contractual arrangements

Abstract .  We examine how a project owner optimally selects a project operator and motivates him to deliver an unobservable effort when potential operators are wealth constrained. We show that, when potential operators' abilities are common knowledge, an operator's share of realized profit can be increasing, invariant, or decreasing in his ability depending on the nature of production technology. However, when potential operators are privately informed about both their abilities and their effort supply, a bunching contract arises in equilibrium for a general class of production technology. In the case of bunching, all potential operators are selected equally often and awarded an equal share of realized profit. The finding provides an explanation for the relative uniformity of contract terms in many practical settings.     

On mean-variance portfolio selection under a hidden Markovian regime-switching model

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black–Scholes–Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.     

Wealth Effects, Distribution, and the Theory of Organization

We construct a general equilibrium model of firm formation in which organization is endogenous. Firms are coalitions of agents providing effort and investment capital. Effort is unobservable unless a fixed monitoring cost is paid, and borrowing is subject to a costly state verification problem. Because incentives vary with an agent's wealth, different types of agents become attractive firm members under different circumstances. When borrowing is not costly, firms essentially consist of one type of agent and are organized efficiently. But when the costly state verification problem is sufficiently severe, firm organization will depend on the distribution of wealth: with enough inequality, it will tend to be dictated by incentives of rich agents to earn high returns to wealth, even if the chosen organizational form is not a technically efficient way to provide incentives.Journal of Economic LiteratureClassification Numbers: D2, D31, J41, L2.     

SOCIAL STATUS,EDUCATION AND GOVERNMENT SPENDING IN A TWO‐SECTOR MODEL OF ENDOGENOUS GROWTH*

This paper extends the relative wealth specification of status preference to the two‐sector Uzawa (1965 )– Lucas (1988 ) model and examines the effectiveness of government spending on economic growth. It is found that the desire for relative wealth‐induced social status and/or the education component of relative wealth‐induced social status are important ingredients in determining the growth rate effects of government spending. Provided that the agent is concerned with his or her relative social position, the education‐induced social status plays a more important role than the physical‐asset‐induced social status in determining the validity of public spending on growth. If individuals do not care about their education‐driven social rewards, then an increase in government spending has no effect on the balanced growth rate regardless of the presence of the physical‐asset‐induced social status. A rise in government spending reduces the long‐run growth rate if the education‐induced social status is present.     

Production subsidies and redistribution

Who gains from stimulating output? We explore a dynamic model with production subsidies where the population is heterogeneous in one dimension: wealth. There are two channels through which production subsidies redistribute resources across the population. First, poorer agents gain from a rise in wages, since—to the extent there is an operative wealth effect in labor supply—they work harder. Second, because a current output boost will raise consumption today relative to the future, thus lowering real interest rates, poor agents gain in relative terms since their income is based less on interest income. We examine optimal redistribution from the perspective of an arbitrary consumer in the population. We show that, if this consumer has commitment at time zero to set all present and future subsidy rates, and for a class of preferences that admits aggregation in wealth, then output stimulation, and hence redistribution, will only occur at time zero; after that, subsidies are zero. A byproduct of our analysis of this environment is a median-voter theorem: with direct voting over subsidy sequences at time zero, the sequence preferred by the median-wealth consumer is the unique outcome. We also study lack of commitment, since interest-rate manipulation is associated with time inconsistency. We analyze this case formally by looking at the Markov-perfect (time-consistent) equilibrium in a game between successive identical decision makers (e.g., the median agent). Here, subsidies persist—they are constant over time—and are more distortionary than under commitment. Moreover, whereas under commitment asset inequality changes initially—in favor of the consumer who decides on policy—it does not under lack of commitment.     

Wealth effects and agency costs

We analyze how the agent's initial wealth affects the principal's expected profits in the standard principal–agent model with moral hazard.We show that if the principal prefers a poorer agent for all specifications of action sets, probability distributions, and disutility of effort, then the agent's utility of income must exhibit a coefficient of absolute prudence less than three times the coefficient of absolute risk aversion for all levels of income, thus strengthening the sufficiency result of Thiele and Wambach (1999). Also, we prove that there is no condition on the agent's utility of income alone that will make the principal prefer richer agents. Moreover, we show that, for an interesting class of problems, the principal prefers a relatively poorer agent if agent's wealth is sufficiently large. Finally, we discuss how alternative ways of modeling the agent's outside option affects the principal's preferences for agent's wealth.     

The age-dependent value of time: a life cycle analysis

A life cycle framework is developed to examine how the value of time (VOT) changes as one ages. We consider two risk-sharing schemes, the Tonti scheme under which wealth is actuarially insured, and the Robinson Crusoe scheme under which insurance institution is entirely absent. For the first time in the literature, we characterize the condition, in terms of key parameters for valuating VOT, under which VOT may increase, decline, or even display more complicated profiles, as one ages. Our analysis reveals the crucial role played by the relative magnitude of the market interest rate to other parameters (including the parameter of time preference, the age-specific mortality and the wage growth rate) in determining the age profile of VOT, and the difference in VOT that is caused by the insurance scheme.      

The growth of relative wealth and the Kelly criterion

We propose an evolutionary framework for optimal portfolio growth theory in which investors subject to environmental pressures allocate their wealth between two assets. By considering both absolute wealth and relative wealth between investors, we show that different investor behaviors survive in different environments. When investors maximize their relative wealth, the Kelly criterion is optimal only under certain conditions, which are identified. The initial relative wealth plays a critical role in determining the deviation of optimal behavior from the Kelly criterion regardless of whether the investor is myopic across a single time period or maximizing wealth over an infinite horizon. We relate these results to population genetics, and discuss testable consequences of these findings using experimental evolution.     

International Adjustment With Habit-Forming Consumption: A Diagrammatic Exposition*

This paper presents a simple diagrammatic analysis of an open economy's external adjustment process under habit-forming individual preferences. the exposition focuses on the consumption side and alms to make transparent the linkage among wealth, past consumption experience, and current consumption. an extension of the standard representative-agent model to a growing economy of overlapping generations completes the paper. Under habit formation an agent's consumption exhibits a form of hysteresis, in that his current consumption depends on his past consumption experience as well as initial assets. In the overlapping-generations model aggregate hysteresis disappears in the long run.     

Does Inequality Foster Corruption?

In this paper, we investigate how inequality affects corruption in the presence of an imperfect credit market. We favor an explanation based on a multimarket framework where corruption in one market (or sector) arises because of imperfections exacerbated by inequality in related markets. We demonstrate that even when an individual's ability to pay bribes and benefit from engaging in corruption are not affected by wealth level, greater (wealth) inequality will lead to an increase in corruption.     

The probability of nontrivial common knowledge

We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme consistent with his cognitive capacity. Assuming that agentsʼ partitions are independently distributed, we prove that the asymptotic probability of nontrivial common knowledge undergoes a phase transition. Regardless of the number of agents, when their cognitive capacity is sufficiently large, the probability goes to one; and when it is small, it goes to zero. Our proofs rely on a graph-theoretic characterization of common knowledge that has independent interest.     

On the moral hazard problem without the first-order approach

We study the moral hazard problem without the first-order approach or other common structure. We present sufficient conditions under which the shadow value of simultaneously tightening the minimum payment and individual rationality constraints has a simple and intuitive expression. We then show how this expression can be used to perform comparative statics exercises in which we study (i) the effect of a change in the agent?s wealth on the well-being of the principal; and (ii) the effects of the outside option and minimum payment on the effort level optimally implemented.