Wealth Dynamics Research Articles

Multi-Scale Economic Dynamics: The Micro-Macro Wealth Dynamics and the Two-Level Imbalances of the Euro Crisis

In this paper, we introduce a system of ordinary differential equations (ODE) to model the micro-macro wealth dynamics of interactions between international enterprise competitiveness and the macroeconomic growth as an open system. The novelty of the approach is to postulate predator-prey interplay between domestic and non-domestic companies and link this interplay to GDP growth to construct a micro-macro wealth dynamic model. By analyzing the market share data of the retail industry of 13 largest Eurozone nations as a system, our model suggests that the predator-prey relation exists and non-domestic companies have a negative contribution to GDP growth. Such dynamics reveals two levels of imbalances: company competitiveness and national economic growth.

Rational Inattention and Dynamics of Consumption and Wealth in General Equilibriumm

This paper derives the general equilibrium effects of rational inattention (or RI; Sims 2003, 010) in a model of incomplete income insurance (Huggett 1993, Wang 2003). We first show that, under the assumption of CARA utility with Gaussian shocks, the permanent income hypothesis (PIH) arises in steady state equilibrium due to a balancing of precautionary savings and impatience. We explore how the introduction of RI can help the model fit the joint equilibrium dynamics of consumption, income, and wealth. We then contrast RI with habit formation and show that the two models make very different general equilibrium predictions, and that RI is closer to the data. We finally show that the equilibrium welfare costs of incomplete information due to RI are relatively low within the CARA-Gaussian setting.

Rational inattention and the dynamics of consumption and wealth in general equilibrium

We propose a recursive utility version of a basic Huggett (1993) model to study the implications of rational inattention (or RI, Sims, 2003, 2010) for the cross-sectional dispersion of consumption and wealth (relative to income) in general equilibrium. We find that incorporating RI can significantly improve the model's predictions in both dimensions in general equilibrium. In addition, we find that intertemporal substitution plays an important role in determining the two key dispersion moments via affecting the degree of optimal attention in equilibrium. Finally, we show that alternative models that rely on habit formation, incomplete information about current income, or borrowing constraints are not consistent with the facts we document.

Income and Wealth Inequality in America, 1949–2016

This paper introduces a new long-run data set based on archival data from historical waves of the Survey of Consumer Finances. Studying the joint distribution of household income and wealth, we expose the central importance of portfolio composition and asset prices for wealth dynamics in postwar America. Asset prices shift the wealth distribution because of systematic differences in household portfolios along the wealth distribution. Middle-class portfolios are dominated by housing, while rich households predominantly own business equity. Differential changes in equity and house prices shaped wealth dynamics in postwar America and decoupled the income and wealth distribution over extended periods.

Wealth dynamics in a sentiment-driven market

We study dynamics of a simulated world with stock and money, driven by the externally given processes which we refer to as sentiments. The considered sentiments influence the buy/sell stock trading attitude, the perceived price uncertainty, and the trading intensity of all or a part of the market participants. We study how the wealth of market participants evolves in time in such an environment. We discuss the opposite perspective in which the parameters of the sentiment processes can be inferred a posteriori from the observed market behavior.

Global Inequality Dynamics: New Findings from WID.world

This paper presents new findings on global inequality dynamics from the World Wealth and Income Database (WID.world), with particular emphasis on the contrast between the trends observed in the United States, China, France, and the United Kingdom. We observe rising top income and wealth shares in nearly all countries in recent decades. But the magnitude of the increase varies substantially, thereby suggesting that different country-specific policies and institutions matter considerably. Long-run wealth inequality dynamics appear to be highly unstable. We stress the need for more democratic transparency on income and wealth dynamics and better access to administrative and financial data.

Welfare Impacts of Index Insurance in the Presence of a Poverty Trap

This paper evaluates the welfare impacts of an index-based livestock insurance designed to compensate for satellite-based predicted livestock mortality in northern Kenya, where previous work has established the presence of poverty traps. We simulate household wealth dynamics based on rich panel and experimental data. The bifurcated livestock dynamics associated with the poverty trap gives rise to insurance valuation that is highly nonlinear in herd size. Estimated willingness to pay among vulnerable groups who most need insurance is, on average, lower than commercially viable rates. Targeted premium subsidization nonetheless appears to offer more cost-effective poverty reduction than need-based direct transfers.

Tossed and turned: Wealth dynamics of U.S. households 2007-2009

For many years, the cross-sectional Survey of Consumer Finances (SCF) has shown relatively weak or inconsistent changes in the shape of the distribution of net worth, despite many shifts in income and other economic factors. In 2009, households that had taken part in the 2007 SCF were re-interviewed to obtain information on the changes in their financial condition over the period of the intervening financial crisis. Looked at as a second cross section, the 2009 data show a pattern of wealth distribution very similar in shape to what had been seen in the earlier cross sections. Between the two years, however, there was considerable variation in the relative positions of households within the wealth distribution. This paper presents data on the changed situation of households and it decomposes the observed wealth changes in terms of underlying portfolio shifts. It is generally recognized that changes in the value of residential real estate, corporate equities and private businesses were important sources of wealth losses. Although the data presented here confirm that picture, they also show a great deal of heterogeneity below the aggregate level. The observed stability of the pseudo-cross-sectional wealth shares in the panel despite the underlying turmoil is largely a consequence of changes in values of businesses and equities among comparatively wealthy households offsetting changes in the value of housing assets among other households.

The other, other half: Changes in the finances of the least wealthy 50 percent, 2007-2009

In discussions of household wealth, it is not surprising that discussion often tends to focus on the upper half of the wealth distribution: According to the 2007 Survey of Consumer Finances (SCF), that group held 97.5 percent of all directly owned household wealth. This paper investigates the wealth dynamics of the lower half of the distribution using data from the 2007– 2009 SCF panel to examine the degree of distributional mobility among this group, the demographic characteristics associated with such change and the role of initial portfolio allocation. It also provides information from earlier SCFs and the 2010 SCF to put the results in perspective. The analysis and conclusions set forth are those of the author and do not indicate concurrence by other members of the research staff or the Board of Governors. The author is grateful for the contributions of Jesse Bricker, Brian Bucks, Gerhard Fries, Traci Mach, Kevin Moore and other Federal Reserve colleagues; Catherine Haggerty, Micah Sjoblom and other NORC central office and field staff; and Susan Boehmer, Barry Johnson, David Paris and other staff at the Statistics of Income Division of the IRS. Above all, the author is grateful to the respondents to the SCF for their generosity in sharing their personal information in the interest of research. The author is solely responsible for any errors of commission or omission in this paper.

Drawing down Retirement Wealth: Interactions between Social Security Wealth and Private Retirement Savings

Individual financial planning for retirement in the US is increasingly important, given the trend away from employer-provided defined benefit (DB) plans, the rising Social Security (SS) Full Retirement Age (FRA), and retiring baby boomers. A key financial decision that Americans make is how to draw on their retirement wealth across various sources, including both privately saved retirement funds and SS benefits. For SS retirement benefits, the main decision is at what age to claim, with claiming before the FRA resulting in lower monthly benefits, and claiming later leading to higher benefits. The terms of this tradeoff have changed in recent years: since 2003, the FRA has risen from 65 and will gradually increase to 67 by 2027, representing a drop in the present value of SS benefits. Meanwhile, defined contribution (DC) plans have gained in popularity, presenting retirees with more control over their private retirement wealth. The changing dynamics of both SS wealth and the private retirement decision space underscore the need for examining how individuals make decisions across their entire portfolio of retirement wealth. We use HRS survey data matched to SS administrative data to study how households integrate SS benefits into their general retirement income plans. We find starkly different non-SS retirement asset decumulation patterns across individuals who claim at different ages, with those claiming before the FRA drawing down pension and IRA wealth faster than those who claim at or after the FRA. However, the earliest claimants, those who claim SS retirement benefits exactly at age 62, are a highly heterogeneous group, consisting of both low-income, high expected mortality individuals as well as individuals with high pension holdings. We further find that this earliest claimant group is more likely to have retired and begun decumulating non-SS retirement assets even before age 62; however, this group’s median and average assets are not substantially lower than later claimants. An analysis of claiming behavior by non-SS retirement wealth holdings shows that individuals with more retirement savings were overwhelmingly likely to claim between the ages of 62 and the FRA. On the other hand, those with the least retirement savings are more likely to either claim SS benefits as early as possible, either in the form of disability benefits or retirement benefits, or they would delay claiming SS retirement benefits until after the FRA. Moreover, birth cohorts facing higher FRAs tend to delay claiming SS retirement benefits on average; however, those most affected by this reduction in SS wealth – those with few other retirement assets – are the least reactive. Finally, households that do delay claiming as the FRA rises also tend to delay retirement and drawing down their non-SS retirement assets, indicating complementarity between SS and non-SS decumulation decisions and strong spillovers from changes in both SS and private retirement policy.

Asset Prices and Wealth Dynamics in a Financial Market with Endogenous Liquidation Risk

Within a financial market where a risk-free bond and a long-lived risky asset are exchanged by investors with heterogeneous trading rules, we assume that the investors most exposed to the risky asset are subject to joint liquidation needs. The latter encompass a risk whenever the market impact of traders subject to them is large enough, due to a fire-sale phenomenon. Our aim is to provide conditions for the transformation of liquidation needs into liquidation risk, and to characterize the resulting asset price dynamics. We find that when the average position of traders subject to liquidation needs is lower than the position of the other traders, the former vanish and asset prices are driven solely by the dividend process. Whether liquidation risk becomes systemic or its impact is mitigated by the position of other traders, depends on the relative wealth dynamics. We provide conditions on agents positions under which the liquidation risk is always systemic because the aggressive traders dominate, as well as conditions under which the size of the liquidation risk is endogenously determined because all traders survive and the relative wealth dynamics is a mean reverting process.

Buffer-Stock Saving and Households' Response to Income Shocks

We use the Italian Survey of Household Income and Wealth, a rather unique dataset with a long time dimension of panel information on consumption, income and wealth, to structurally estimate a buffer-stock saving model. We exploit the information contained in the joint dynamics of income, consumption and wealth to quantify the degree of insurance against income risk. The estimated model implies that Italian households can insure between 89 and 95 percent of a transitory and between 7 and 9 percent of a permanent income shock. Compared to existing empirical estimates for the same dataset, our findings suggest that Italian households do not have access to significant insurance beyond self-insurance.

Game Options in an Imperfect Market with Default

We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer in [Game Options, Finance. Stoch., 4 (2000), pp. 443--463] in the case of a perfect market model to the case of an imperfect market with default, when the imperfections are taken into account via the nonlinearity of the wealth dynamics. We introduce the seller's price of the game option as the infimum of the initial wealths which allow the seller to be superhedged. We prove that this price coincides with the value function of an associated generalized Dynkin game, recently introduced in [R. Dumitrescu, M.-C. Quenez, and A. Sulem, Elect. J. Probab., 21 (2016), 64], expressed with a nonlinear expectation induced by a nonlinear backward SDE with default jump. We, moreover, study the existence of superhedging strategies. We then address the case of ambiguity on the model---for example ambiguity on the default probability---and characterize the robust seller's price of a ga...

The Dynamics of Wealth Inequality and the Effect of Income Distribution.

The rapid increase of wealth inequality in the past few decades is one of the most disturbing social and economic issues of our time. Studying its origin and underlying mechanisms is essential for policy aiming to control and even reverse this trend. In that context, controlling the distribution of income, using income tax or other macroeconomic policy instruments, is generally perceived as effective for regulating the wealth distribution. We provide a theoretical tool, based on the realistic modeling of wealth inequality dynamics, to describe the effects of personal savings and income distribution on wealth inequality. Our theoretical approach incorporates coupled equations, solved using iterated maps to model the dynamics of wealth and income inequality. Notably, using the appropriate historical parameter values we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. It is found that the effect of personal savings on wealth inequality is substantial, and its major decrease in the past 30 years can be associated with the current wealth inequality surge. In addition, the effect of increasing income tax, though naturally contributing to lowering income inequality, might contribute to a mild increase in wealth inequality and vice versa. Plausible changes in income tax are found to have an insignificant effect on wealth inequality, in practice. In addition, controlling the income inequality, by progressive taxation, for example, is found to have a very small effect on wealth inequality in the short run. The results imply, therefore, that controlling income inequality is an impractical tool for regulating wealth inequality.

How Portfolios Evolve after Retirement: Evidence from Australia

Households in many countries reach retirement with lump sums of financial wealth accumulated in defined contribution retirement plans. Retired households need to manage risks and generate income from their savings. We study the dynamics of retirement wealth and portfolio allocation using the three wealth waves of the Household, Income and Labour Dynamics in Australia panel survey. The average retired household maintained or accumulated wealth in 2002–2006 and decumulated in 2006–2010 consistent with trends in financial asset prices. At older ages, households prefer portfolios with less risk and more liquidity, while maintaining ownership of the family home. The probability of households exhausting financial assets increased over the sample, but households who depleted financial wealth did not liquidate their housing wealth at higher rates than other households. In contrast to the USA, the overall effect of health shocks on the wealth of retired Australian households is minimal, but financial shocks have large effects.

Credit constraints, growth and inequality dynamics

This paper examines how credit constraints affect the dynamics of wealth and thereby the dynamics of capital and output growth. We develop standard Ak growth models that display transitional dynamics, contrary to general belief, once the complete credit markets assumption is relaxed. The mechanism is that credit constraints make individual productivity differences persist, which in turn leads to the persistence of income inequality. The dynamics of inequality is jointly determined with the dynamics of aggregate capital. The economy thus passes through a transitional period of inequality, individual and aggregate capital dynamics before it converges to a long-run balanced growth path. The application of the model to the analysis of intergenerational mobility and inequality dynamics suggests substantial economic and policy significance. In particular, introducing credit constraints to the Barro Ak model, public investment could have an indirect impact on growth via its effect on inequality and mobility.

Induced uncertainty, market price of risk, and the dynamics of consumption and wealth

In this paper we examine the implications of model uncertainty or robustness (RB) for consumption and saving and the market price of uncertainty under limited information-processing capacity (rational inattention or RI). First, we show that RI by itself creates an additional demand for robustness that leads to higher “induced uncertainty” facing consumers. Second, if we allow capacity to be elastic, RB increases the optimal level of attention. Third, we explore how the induced uncertainty composed of (i) model uncertainty due to RB and (ii) state uncertainty due to RI, affects consumption and wealth dynamics, the market price of uncertainty, and the welfare losses due to incomplete information. We find that induced uncertainty can better explain the observed consumption-income volatility and market price of uncertainty – low attention increases the effect of model misspecification.

Buffer-Stock Saving and Households' Response to Income Shocks

We use the Italian Survey of Household Income and Wealth, a rather unique dataset with a long time dimension of panel information on consumption, income and wealth, to structurally estimate a buffer-stock saving model. We exploit the information contained in the joint dynamics of income, consumption and wealth to quantify the degree of insurance against income risk. The estimated model implies that Italian households can insure between 89 and 95 percent of a transitory and between 7 and 9 percent of a permanent income shock. Compared to existing empirical estimates for the same dataset, our findings suggest that Italian households do not have access to significant insurance beyond self-insurance.

Das House-Kapital: A Theory of Wealth-to-Income Ratios

This paper provides a novel macroeconomic model that is specifically designed to investigate the evolution of housing wealth. To capture the importance of land as an input factor for housing production and for the evolution of wealth in a growing economy, the analysis builds on three premises: (1) the overall land endowment is fixed; (2) the production of new houses requires land as an essential input, whereas replacement investment does not; (3) land employed for real estate development must be permanently withdrawn from alternative uses. The calibrated model replicates the historical evolution of housing wealth after Word War II remarkably accurately and accounts for the close connection of house prices to land prices in the data. It suggests a considerable further increase in housing wealth, relative to income, that is associated with a future surge in land prices and house prices. The model also provides new insights into the dynamics of non-residential wealth. JEL-Codes: E100, E200, O400.

Nursing Home Choice, Family Bargaining and Optimal Policy in a Hotelling Economy

The family plays a central role in decisions relative to the provision of long term care (LTC). We develop a model of family bargaining to study the impact of the distribution of bargaining power within the family on the choices of nursing homes, and on the location and prices chosen by nursing homes in a Hotelling economy. We show that, if the dependent parent only cares about the distance, whereas his child cares also about the price, the mark up rate of nursing homes is increasing in the bargaining power of the dependent parent. We contrast the laissez-faire with the social optimum, and we show how the social optimum can be decentralized in a first-best setting and in a second-best setting (i.e. when the government cannot force location). Finally, we explore the robustness of our results to considering families with more than one child, and to introducing a wealth accumulation motive within a dynamic OLG model, which allows us to study the joint dynamics of wealth and nursing home prices. We show that a higher capital stock raises the price of nursing homes through higher mark up rates.