Wealthy Agents Research Articles

Asymptotic linearity of consumption functions and computational efficiency

We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying, or loosely speaking, behaves like a power function for wealthy agents. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of wealth. Our results are useful for obtaining good initial guesses when numerically computing consumption functions, and provide a theoretical justification for linearly extrapolating consumption functions outside the grid.

Wealth and the principal–agent matching

AbstractI study the role the agent's wealth plays in the principal–agent matching with moral hazard and limited liability. I consider wealth and talent as the agent's type and size as the firm's (principal's) type. Wealthier agents match with bigger firms, when talent is homogeneous among them, whereas for equally wealthy agents, more talented agents will match with bigger firms. I describe economic conditions over types such that pairs of higher types will write contracts in which the agent gets more than the limited liability rents. Finally, I write conditions on wealth for assortative matching in talent to hold.

Do toddlers prefer that agents help similar or dissimilar needy agents?

AbstractRecent research revealed rich socio‐cognitive abilities in toddlerhood. The current study investigates whether 21‐month‐olds expect that wealthy agents help agents needing food or shelter. By using the violation of expectation (VoE) implicit paradigm, toddlers' expectations on helping behaviors were explored upon the arrival of agents that need food (food condition) and shelter (shelter condition) in a within‐subjects design. Two experiments were carried out, wherein, in one, the wealthy and needy agents were morphologically similar (Experiment 1), in the other one, the wealthy agents were morphologically different from needy agents (Experiment 2). The results showed that when needy agents are morphologically similar to wealthy agents, toddlers looked longer at the event that displayed the wealthy agents help needy agents only in food condition. When needy agents were morphologically different from wealthy agents, toddlers looked longer at the event that showed wealthy agents help needy agents in both food and shelter conditions. These findings demonstrate an interplay between similarity and helping behaviors in association with biological needs, and shed light on possible evolutionary mechanisms underlying prosociality.

Stock Return Uncertainty and Life Insurance

Knightian uncertainty embedded in stock returns causes rising demand for life insurance, as the uncertainty averse agent seeks alternative investment channels. Life insurance demand of middle-aged agent is more sensitive to the uncertainty. Stock return uncertainty reduces the agent’s total wealth and subsequently the propensity of wealthy agent serving as an insurance seller. Rising demand and falling supply of life insurance imply that life insurance is more expensive in the presence of stock return uncertainty. Sensitivity of life insurance demand to the mortality rate and key stock return characteristics also changes with the uncertainty.

Wealth-relative effects in cooperation games

This paper investigates cooperation games in which poor agents do not benefit from cooperation with wealthy agents. They instead benefit from considering wealth relative to decision payoffs of fitness or wealth. Of concern is the effect of cooperation on participants, their rational self-interest and choices, and not the evolution of cooperation directly. The accumulation of fitness or wealth has been shown in the literature to lead to different optimal strategies for wealthy and poor players in Chicken games. The effect could have important explanatory power if it were more broadly applicable. First we empirically compare two published results, one involving the temptation parameter vs. degree of cooperation in Prisoner's Dilemma, and the other a surprising result from a public goods game with participants from different cultures, networks and wealth in which a fixed rather than relative payoff scheme was used. Using the temptation data to calibrate the public goods behavior suggests wealth factors can provide an explanation for the results. Second we show using simulation that adding a survival threshold to a wealth or fitness accumulating Iterated Prisoner's Dilemma produces a wealth relative effect. We clarify previous results to show the poor must avoid survival risk, regardless of whether this is associated with cooperation or defection. We do this by introducing the Farmer's Game, a simulation of Iterated Prisoner's Dilemma with wealth accumulation and a survival threshold. This is used to evaluate the Tit-for-Tat strategy and four variants. Equilibrium payoffs keep the game scaled to social relevance, with a fraction of all payoffs externalized as a turn cost parameter. Findings include poor performance of Tit-for-Tat near the survival threshold, superior performance of low risk strategies for both poor and wealthy players, dependence of survival of the poor near the threshold on Tit-for-Tat forgiveness, unexpected optimization of forgiveness without encountering a social dilemma, improved performance of a diverse mix of strategies, and a more abrupt threshold of social catastrophe for the better performing mix. Lastly we compare cooperating and non-cooperating societies using the simulation and discover disturbing connections between cooperation and familiar non-egalitarian wealth distribution patterns.

The Value of Connections: Network Effects on Stock Market Participation

We introduce an equilibrium model of the stock market participation rate with a social network. We study how information sharing through a network affects the decision to enter the stock market and how social connectivity interacts with individual income and financial literacy to create heterogeneity in stock market participation levels. We analyze how the equilibrium participation level depends on the intensity of social interactions, and provide an algorithm for finding the equilibrium stock market participation level. We test the predictions from the model using Facebook county-level connectivity data. We find the model with social networks outperforms standard models without networks in predicting heterogeneity of equilibrium stock market participation over the income distribution, explaining non-participation among wealthy agents.

A Model of Optimizing Political Expenditures to Buy Government Power

This research develops a model of optimal political expenditures that is integrated with a theory of voters maximizing their personal utility at the ballot box and that shows how money inevitably controls government leaders. The paper also demonstrates theoretically why many businesses do not make such investments despite returns on the expended political capital tending to be abnormally high. Recent worldwide events reported in the press are utilized to illustrate the general applicability of the model to the many varying ways wealthy agents control government, as well as indicate how the model variables can be estimated from actual polling results.

Risk, uncertainty, and the dynamics of inequality

The dynamics of wealth inequality are studied in a continuous-time Blanchard/Yaari model. Investment returns are idiosyncratic and subject to Knightian uncertainty. In response, agents formulate robust portfolio policies. These policies are nonhomothetic; wealthy agents invest a higher fraction of their wealth in uncertain assets yielding higher mean returns. This produces a feedback mechanism that amplifies inequality. It also produces an accelerated rate of convergence, which helps resolve a puzzle recently identified by Gabaix et al. (2016). An empirically plausible increase in uncertainty can account for about half of the recent increase in top wealth shares.

Agent-based model of the effect of globalization on inequality and class mobility

We consider a variant of the Bouchaud–Mézard model for wealth distribution in a society which incorporates the interaction radius between the agents, to model the extent of globalization in a society. The wealth distribution depends critically on the extent of this interaction. When interaction is relatively local, a small cluster of individuals emerges which accumulate most of the society’s wealth. In this regime, the society is highly stratified with little or no class mobility. As the interaction is increased, the number of wealthy agents decreases, but the overall inequality rises as the freed-up wealth is transferred to the remaining wealthy agents. However when the interaction exceeds a certain critical threshold, the society becomes highly mobile resulting in a much lower economic inequality (low Gini index). This is consistent with the Kuznets upside-down U shaped inequality curve hypothesis.

Wealth and the Principal-Agent Matching

I study the role the agent's wealth plays in the principal-agent matching with moral hazard and limited liability. I consider wealth and talent as the agent's type, and size as the firm's (principal's) type. Because utility is not perfectly transferable in this setup, I use generalized increasing differences and find that wealthier agents match with bigger firms, when talent is homogeneous among them, whereas for equally wealthy agents, more talented agents will match with bigger firms. I describe economic conditions over types such that pairs of higher types will write contracts in which the agent obtains more than the information rents, through a higher bonus, increasing the expected surplus. Finally, I provide an example in which wealth is distributed among agents in such a way that it reverses the standard result of positive assortative matching between talent and firm size.

Incentives and Income Distribution in Tenancy Relationships

I analyze a problem of partnership formation between heterogeneous principals and agents, where each partnership is subject to a moral-hazard problem. In a Walrasian equilibrium of the economy, wealthier agents work in more productive lands following a positively assortative matching pattern, since higher wealth has greater marginal effect in high-productivity lands. Consequently, the matches that consist of less wealthy agents are not able to implement the efficient effort and contracts. Agents' share of the match output is in general nonmonotone with respect to initial wealth. If wealth is more unequally distributed than land quality, then the equilibrium share (of the agents) is a monotonically increasing function of wealth.

Fokker–Planck description of wealth dynamics and the origin of Pareto's law

The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B. M. Boghosian, Phys. Rev. E89, 042804 (2014)], it was shown that this results in a Fokker–Planck equation governing the distribution of wealth. With the addition of a mechanism for wealth redistribution, it was further shown that this model results in stationary wealth distributions that are very similar in form to Pareto's well-known law. In this paper, a much simpler derivation of that Fokker–Planck equation is presented.

Wealth distribution and collective knowledge: a Boltzmann approach

We introduce and discuss a nonlinear kinetic equation of Boltzmann type that describes the influence of knowledge in the evolution of wealth in a system of agents that interact through the binary trades, an equation first introduced by Cordier et al. (2005 J. Stat. Phys. 120, 253-277 (doi:10.1007/S10955-005-5456-0)). The trades, which include both saving propensity and the risks of the market, are here modified in the risk and saving parameters, which now are assumed to depend on the personal degree of knowledge. The numerical simulations show that the presence of knowledge has the potential to produce a class of wealthy agents and to account for a larger proportion of wealth inequality.

The Information Rat Race

Information is a valuable good that requires scarce inputs, such as human talent, to produce. Competition among investors for these inputs creates an equilibrium channel that has not yet been modeled explicitly. This paper studies the dynamic implications of this channel for information choice, risk-taking, and welfare. We study a dynamic portfolio choice problem with heterogeneous agents and endogenous information choice. Our central assumption is that investors compete for information in a market for information inputs. This creates a feedback loop in which relatively wealthy agents acquire more information, obtain superior portfolio performance, and get comparatively even wealthier. Two dynamic effects arise: First, interim losers anticipate their inability to acquire future information and take on more risk in an attempt to catch up with interim winners, while interim winners take on less risk to protect their lead. Second, acquiring information is a strategic complement. In addition, we perform a welfare analysis and discuss the model’s implications for capital income inequality and delegated portfolio management.

Preschool children involve a third party in a dyadic sharing situation based on fairness

To investigate whether preschool children would involve third parties in dyadic sharing situations, we created unequal sharing situations in which one agent had no resources and a child participant and a third-party individual had unequal resources. We analyzed children’s tendency to share with the indigent agent and to involve the wealthy agent, whereas the indigent agent elicited sharing from them by means of progressive levels of request. The results showed that 5-year-olds involved the third party to a greater extent than 3.5-year-olds when they had fewer resources than the third party (Experiment 1). Yet, when 5-year-olds had the largest amount of resources, they were less likely to involve a third party but more likely to share themselves (Experiment 2). This study provides the first evidence that the tendency to involve third-party individuals in resource allocation situations develops at the preschool age and that it is based on fairness considerations.

Choosing Agents and Monitoring Consumption: A Note on Wealth as a Corruption‐Controlling Device

There are a large number of cases where corruption has been discovered when investigating levels of consumption that appear to be hard to justify. The informativeness of an agent's level of consumption depends on his legal income and initial level of wealth, as conspicuous consumption by wealthy agents leads to little updating of the principal's belief about their honesty. This introduces a tendency to prefer poor agents as they are easier to monitor. More generally, we describe the basic problem of choosing agents and monitoring consumption with the aim of reducing corruption, and discuss features of the practical applications. Castrated slaves, called eunuchs, were employed by Sultans to guard their harems. This solution to a particularly distressing principal-agent problem is one instance of a general strategy that can be called 'choosing agents'. In this strategy, the principal selects an agent, to whom he is about to delegate a task, based on an observable characteristic. In the standard agency model it is clear that the agent's degree of risk aversion can be costly to the principal. Perhaps because of the difficulty in observing risk aversion, few economists have emphasised the potential benefits of using particular types of agents. An exception is Schelling (1960), who discusses the use of agents with a low personal cost of conflict and mentions the strategic advantages of delegating authority 'to a military commander of known motivation'. A subsequent paper by Vickers (1985) emphasises the potential value of hiring a manager who is committed to maximise the company's sales instead of profits. Similarly, Rogoff (1985) analyses the benefits of delegating the conduct of monetary policy to a conservative central banker in a setting where there is time inconsistency, while Rotemberg and Saloner (2000)

Sales contests, promotion decisions and heterogeneous risk

AbstractThis paper examines a general model of sales contests in which agents have heterogeneous attitudes toward risk. It shows that agents that are less risk averse have a higher probability of success. A corollary to this result shows that when absolute risk aversion is decreasing in wealth, wealthier agents have a higher probability of promotion. The same wealth effect makes it possible for more risk averse agents to take greater risks in a multi‐round promotion tournament. Next, a stability analysis shows that these equilibria are attractors under a best response dynamic. While it is well‐known that sales contests can be an effective incentive device for eliciting effort from employees, this research suggests the added benefit that when used as a basis for promotion decisions, sales contests act to filter the hardest working agents to the top of the corporate hierarchy. Copyright © 2008 John Wiley & Sons, Ltd.

Increasing returns to savings and wealth inequality

In this paper I present an explanation to the fact that in the data wealth is substantially more concentrated than income. Starting from the observation that the composition of households' portfolios changes towards a larger share of high-yield assets as the level of net worth increases, I first use data on historical asset returns and portfolio composition by wealth level to construct an empirical return function. I then augment an Overlapping Generation version of the standard neoclassical growth model with idiosyncratic labor income risk and missing insurance markets to allow for returns on savings to be increasing in the level of accumulated assets. The quantitative properties of the model are examined and show that an empirically plausible difference between the return faced by poor and wealthy agents is able to generate a substantial increase in wealth inequality compared to the basic model, enough to match the Gini index and all but the top 1 percentile of the US distribution of wealth.

A Note on Wealth as a Corruption-Controlling Device

In the standard hazard model, withholding of effort by the agent is not observable to the principal. We argue that this assumption has to be changed in applications that study corruption. The overwhelming majority of cases where corrupt politicians have been punished involve the detection of consumption levels that appear to be too high. The informativeness of an agent's level of consumption depends on his initial level of wealth as conspicuous consumption of luxuries by wealthy agents leads to little updating of the principal's belief about their honesty. This introduces a tendency to choose poor agents as they are easier to monitor. More generally, we show that, even if agents have similar preferences, there are contractual advantages to selecting particular types. We describe the basic problem of choosing agents and monitoring consumption, and discuss a number of features of the practical applications. We show that selecting rich politicians may not help fight corruption and that the political class will exhibit lower variance in consumption than the population. In settings were formal contracts matter, we show that monitoring consumption introduces a tendency towards low powered incentive schemes (and more generally low wages) and that the measure of moral costs that is often employed in the literature can be derived (not assumed).

Beneficial Inequality in the Provision of Municipal Services: Why Rich Neighborhoods Should Get Plowed First

This paper provides an explanation for the common observation that higher income neighborhoods typically receive better public services compared with lower income neighborhoods. Intuitively, one might expect that lower income groups, which usually form the voting majority of cities, would object to an unfair allocation of this nature. Wealthy individuals, however, have the option of moving to the suburbs. As we learn from the tax competition literature, mobile factors are generally able to command a premium. Since institutional constraints prevent regressive taxation and public goods are by definition consumed in equal quantity by all agents, only public services remain as an instrument for municipalities to use to keep wealthy agents in their tax base. We show that both rich and poor agents benefit from this differential access to public services and explore how factors like the ratio of rich to poor and the differences between their incomes affect the equilibrium allocation.