Economics - Theoretical Economics, Economics - General Economics, and Quantitative Finance - Risk Management

Abstract

An important but understudied question in economics is how people choose when facing uncertainty in the timing of events. Here we study preferences over time lotteries, in which the payment amount is certain but the payment time is uncertain. Expected discounted utility theory (EDUT) predicts decision makers to be risk-seeking over time lotteries. We explore a normative model of growth-optimality, in which decision makers maximise the long-term growth rate of their wealth. Revisiting experimental evidence on time lotteries, we find that growth-optimality accords better with the evidence than EDUT. We outline future experiments to scrutinise further the plausibility of growth-optimality.

Adamou, Alexander, Berman, Yonatan, and Peters, Ole

Subjects

Economics - General Economics

Abstract

Economic growth is measured as the rate of relative change in gross domestic product (GDP) per capita. Yet, when incomes follow random multiplicative growth, the ensemble-average (GDP per capita) growth rate is higher than the time-average growth rate achieved by each individual in the long run. This mathematical fact is the starting point of ergodicity economics. Using the atypically high ensemble-average growth rate as the principal growth measure creates an incomplete picture. Policymaking would be better informed by reporting both ensemble-average and time-average growth rates. We analyse rigorously these growth rates and describe their evolution in the United States and France over the last fifty years. The difference between the two growth rates gives rise to a natural measure of income inequality, equal to the mean logarithmic deviation. Despite being estimated as the average of individual income growth rates, the time-average growth rate is independent of income mobility.

This paper uses Bureau of Labor Statistics employment and wage data to study the distributional impact of the COVID-19 crisis on wages in the United States by mid-April. It answers whether wages of lower-wage workers decreased more than others', and to what extent. We find that the COVID-19 outbreak exacerbates existing inequalities. Workers at the bottom quintile in mid-March were three times more likely to be laid off by mid-April compared to higher-wage workers. Weekly wages of workers at the bottom quintile decreased by 6% on average between mid-February and mid-March and by 26% between mid-March and mid-April. The average decrease for higher quintiles was less than 1% between mid-February and mid-March and about 10% between mid-March and mid-April. We also find that workers aged 16-24 were hit much harder than older workers. Hispanic workers were also hurt more than other racial groups. Their wages decreased by 2-3 percentage points more than other workers' between mid-March and mid-April.

Peters, Ole, Adamou, Alexander, Kirstein, Mark, and Berman, Yonatan

Subjects

Economics - Theoretical Economics

Abstract

Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and probabilities inferred from real people's decisions (the same parameters estimated empirically). The inferred probabilities are called "decision weights." It is considered a robust experimental finding that decision weights are higher than probabilities for rare events, and (necessarily, through normalisation) lower than probabilities for common events. Typically this is presented as a cognitive bias, i.e. an error of judgement by the person. Here we point out that the same observation can be described differently: broadly speaking, probability weighting means that a decision maker has greater uncertainty about the world than the observer. We offer a plausible mechanism whereby such differences in uncertainty arise naturally: when a decision maker must estimate probabilities as frequencies in a time series while the observer knows them a priori. This suggests an alternative presentation of probability weighting as a principled response by a decision maker to uncertainties unaccounted for in an observer's model.

Adamou, Alexander T. I., Berman, Yonatan, Mavroyiannis, Diomides P., and Peters, Ole B.

Subjects

Economics - Theoretical Economics and Economics - General Economics

Abstract

An important question in economics is how people choose between different payments in the future. The classical normative model predicts that a decision maker discounts a later payment relative to an earlier one by an exponential function of the time between them. Descriptive models use non-exponential functions to fit observed behavioral phenomena, such as preference reversal. Here we propose a model of discounting, consistent with standard axioms of choice, in which decision makers maximize the growth rate of their wealth. Four specifications of the model produce four forms of discounting -- no discounting, exponential, hyperbolic, and a hybrid of exponential and hyperbolic -- two of which predict preference reversal. Our model requires no assumption of behavioral bias or payment risk.

Detailed information about the distribution of estates left at death has commonly served as the basis for the estimation of wealth distributions among the living via the mortality multiplier method. The application of detailed mortality rates by demographics and other determinants of mortality is crucial for obtaining an unbiased representation of the wealth distribution of the living. Yet, in this paper we suggest that a simplified mortality multiplier method, derived using average mortality rates and aggregate tabulations by estate size, may be sufficient to derive compelling estimates of wealth concentration. We show that the application of homogeneous multipliers leads to estimates that are close in level and trend to the concentration of wealth derived in the existing literature with the detailed mortality multiplier method for a variety of countries. The use of mortality rates graduated by estate size does not confute this finding. We also derive the general formal conditions for the similarity between the distributions of wealth of the living and estates at death and discuss the main caveats. These findings may unlock a wide array of aggregate estate tabulations, previously thought to be unusable, for estimating historical trends of wealth concentration. (Stone Center on Socio-Economic Inequality Working Paper Series)

We model the joint log-income distribution of parents and children and derive analytic expressions for canonical relative and absolute intergenerational mobility measures. We find that both types of mobility measures can be expressed as a function of the other.

Berman, Yonatan, Milanovic, Branko, and Stone Center

SocArXiv, 2020.

Abstract

Homoploutia describes the situation in which the same people (homo) are wealthy (ploutia) in the space of capital and labor income in some country. It can be quantified by the share of capital-income rich who are also labor-income rich. In this paper we combine several datasets covering different time periods to document the evolution of homoploutia in the United States from 1950 to 2020. We find that homoploutia was low after World War II, has increased by the early 1960s, and then decreased until the mid-1980s. Since 1985 it has been sharply increasing: In 1985, about 17% of adults in the top decile of capital-income earners were also in the top decile of labor-income earners. In 2018 this indicator was about 30%. This makes the traditional division to capitalists and laborers less relevant today. It makes periods characterized by high interpersonal inequality, high capital-income ratio and high capital share of income in the past fundamentally different from the current situation. High homoploutia has far-reaching implications for social mobility and equality of opportunity. We also study how homoploutia is related to total income inequality. We find that rising homoploutia accounts for about 20% of the increase in total income inequality in the United States since 1986. (Stone Center Working Paper Series)

Stone Center, Adamou, Alexander, Berman, Yonatan, and Peters, Ole

SocArXiv, 2020.

Abstract

Economic growth is measured as the rate of relative change in gross domestic product (GDP) per capita. Yet, when incomes follow random multiplicative growth, the ensemble-average (GDP per capita) growth rate is higher than the time-average growth rate achieved by each individual in the long run. This mathematical fact is the starting point of ergodicity economics. Using the atypically high ensemble-average growth rate as the principal growth measure creates an incomplete picture. Policymaking would be better informed by reporting both ensemble-average and time-average growth rates. We analyse rigorously these growth rates and describe their evolution in the United States and France over the last fifty years. The difference between the two growth rates gives rise to a natural measure of income inequality, equal to the mean logarithmic deviation. Despite being estimated as the average of individual income growth rates, the time-average growth rate is independent of income mobility. (Stone Center on Socio-Economic Inequality Working Paper)

This paper combines cross-sectional and longitudinal income data to present the evolution of absolute intergenerational income mobility in ten developed economies in the 20th century. Absolute mobility decreased during the second half of the 20th century in all these countries. Increasing income inequality and decreasing growth rates have contributed to the decrease. Yet, growth is the dominant contributor in most countries. We show that detailed panel data are unnecessary for estimating absolute mobility over the long run. (Stone Center on Socio-Economic Inequality Working Paper)

Berman, Yonatan, Peters, Ole, and Adamou, Alexander

Subjects

Quantitative Finance - Economics and Quantitative Finance - General Finance

Abstract

Studies of wealth inequality often assume that an observed wealth distribution reflects a system in equilibrium. This constraint is rarely tested empirically. We introduce a simple model that allows equilibrium but does not assume it. To geometric Brownian motion (GBM) we add reallocation: all individuals contribute in proportion to their wealth and receive equal shares of the amount collected. We fit the reallocation rate parameter required for the model to reproduce observed wealth inequality in the United States from 1917 to 2012. We find that this rate was positive until the 1980s, after which it became negative and of increasing magnitude. With negative reallocation, the system cannot equilibrate. Even with the positive reallocation rates observed, equilibration is too slow to be practically relevant. Therefore, studies which assume equilibrium must be treated skeptically. By design they are unable to detect the dramatic conditions found here when data are analysed without this constraint. Comment: 6 pages, 4 figures

This paper combines historical cross-sectional and longitudinal income and wealth data in the United States to present the evolution of absolute intragenerational mobility from the 1960s onward. That is, the fraction of families with higher income or wealth over a given period. We find that the rates of absolute mobility over periods of two to four years are largely confined within 45%-55%. This occurs over all the phases of the business cycle. Absolute mobility is higher for lower percentiles, also during periods of increasing inequality. These results stem from the importance of the changes in the composition of income and wealth percentiles even over short time periods. We offer a simplified model to mathematically describe these findings.