Since the early 2000s, research by Thomas Piketty, Emmanuel Saez, and their coauthors has revolutionized our understanding of income and wealth inequality. In this paper, I highlight some of the key empirical facts from this research and comment on how they relate to macroeconomics and to economic theory more generally. One of the key links between data and theory is the Pareto distribution. The paper describes simple mechanisms that give rise to Pareto distributions for income and wealth and considers the economic forces that influence top inequality over time and across countries. For example, it is in this context that the role of the famous r – g expression is best understood.

http://www-leland.stanford.edu/~chadj/piketty.pdf

Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality

Historical evolution of global inequality in carbon emissions and footprints versus redistributive scenarios

The rise in economic disparity presents significant risks to global social order and the resilience of local communities. However, existing measurement science for economic disparity (e.g., the Gini coefficient) does not explicitly consider a probability distribution with information, deficiencies, and uncertainties associated with the underlying income distribution. This article introduces the quantification of Shannon entropy for income inequality across scales, including national-, subnational-, and city-level data. The probabilistic principles of Shannon entropy provide a new interpretation for uncertainty and risk related to economic disparity. Entropy and information-based conflict rise as world incomes converge. High-entropy instances can resemble both happy and prosperous societies as well as a socialist-communist social structure. Low entropy signals high-risk tipping points for anomaly and conflict detection with higher confidence. Finally, spatial-temporal entropy maps for U.S. cities offer a city risk profiling framework. The results show polarization of household incomes within and across Baltimore, Washington, DC, and San Francisco. Entropy produces reliable results at significantly reduced computational costs than Gini coefficients.

Shannon Entropy for Quantifying Uncertainty and Risk in Economic Disparity

Econophysics has been used to study a range of economic and financial systems. This book uses the econophysical perspective to focus on the income distributive dynamics of economic systems. It focuses on the empirical characterization and dynamics of income distribution and its related quantities from the epistemological and practical perspectives of contemporary physics. Several income distribution functions are presented which fit income data and results obtained by statistical physicists on the income distribution problem. The book discusses two separate research traditions: the statistical physics approach, and the approach based on non-linear trade cycle models of macroeconomic dynamics. Several models of distributive dynamics based on the latter approach are presented, connecting the studies by physicists on distributive dynamics with the recent literature by economists on income inequality. As econophysics is such an interdisciplinary field, this book will be of interest to physicists, economists, statisticians and applied mathematicians.

Income Distribution Dynamics of Economic Systems: An Econophysical Approach

The key parameter that characterizes the transmissibility of a disease is the reproduction number R. If it exceeds 1, the number of incident cases will inevitably grow over time, and a large epidemic is possible. To prevent the expansion of an epidemic, R must be reduced to a level below 1. To estimate the reproduction number, the probability distribution function of the generation interval of an infectious disease is required to be available; however, this distribution is often unknown. In this paper, given the incomplete information for the generation interval, we propose a maximum entropy method to estimate the reproduction number. Based on this method, given the mean value and variance of the generation interval, we first determine its probability distribution function and in turn estimate the real-time values of the reproduction number of COVID-19 in China and the United States. By applying these estimated reproduction numbers into the susceptible-infectious-removed epidemic model, we simulate the evolutionary tracks of the epidemics in China and the United States, both of which are in accordance with that of the real incident cases.

/pdf/maximum-entropy-method-for-estimating-the-reproduction-12bp4yfa76.pdf

Maximum entropy method for estimating the reproduction number: An investigation for COVID-19 in China and the United States

Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior. We analyze datasets of household income from 67 countries, ranging from Europe to Latin America, North America and Asia. For all of the countries, we find a surprisingly uniform rule: income distribution for the great majority of populations (low and middle income classes) follows an exponential law. To explain this empirical observation, we propose a theoretical model within the standard framework of modern economics and show that free competition and Rawls’ fairness are the underlying mechanisms producing the exponential pattern. The free parameters of the exponential distribution in our model have an explicit economic interpretation and direct relevance to policy measures intended to alleviate income inequality.

Exponential structure of income inequality: evidence from 67 countries

Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior. We analyze datasets of household income from 60 countries, ranging from Europe to Latin America, North America and Asia. For all of the countries, we find a surprisingly universal rule: Income distribution for the great majority of populations (low and middle income classes) follows an exponential law. To explain this empirical observation, we propose a theoretical model within the standard framework of modern economics and show that free competition and Rawls fairness are the underlying mechanisms producing the exponential pattern. The free parameters of the exponential distribution in our model have an explicit economic interpretation and direct relevance to policy measures intended to alleviate income inequality.

Universal Exponential Structure of Income Inequality: Evidence from 60 Countries

Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior We analyze datasets of household income from 67 countries, ranging from Europe to Latin America, North America and Asia For all of the countries, we find a surprisingly uniform rule: Income distribution for the great majority of populations (low and middle income classes) follows an exponential law To explain this empirical observation, we propose a theoretical model within the standard framework of modern economics and show that free competition and Rawls' fairness are the underlying mechanisms producing the exponential pattern The free parameters of the exponential distribution in our model have an explicit economic interpretation and direct relevance to policy measures intended to alleviate income inequality

Exponential Structure of Income Inequality: Evidence from 67 Countries

Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior. We analyze datasets of household income from 67 countries, ranging from Europe to Latin America, North America and Asia. For all of the countries, we find a surprisingly uniform rule: Income distribution for the great majority of populations (low and middle income classes) follows an exponential law. To explain this empirical observation, we propose a theoretical model within the standard framework of modern economics and show that free competition and Rawls' fairness are the underlying mechanisms producing the exponential pattern. The free parameters of the exponential distribution in our model have an explicit economic interpretation and direct relevance to policy measures intended to alleviate income inequality.

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Exponential structure of income inequality: evidence from 67 countries

Universal Exponential Structure of Income Inequality: Evidence from 60 Countries

Exponential Structure of Income Inequality: Evidence from 67 Countries

Exponential Structure of Income Inequality: Evidence from 67 Countries