تحرک و بی ثباتی: افزایش نابرابری درآمد در ایالات متحده Mobility and volatility: What is behind the rising income inequality in the United States

1. Introduction Since the 1970s, the inequality of household incomes in the United States has increased considerably [1–4]. This trend can be caused by changes in income mobility. For instance, if the affluent can become wealthier at a faster pace, while the growth-rate of the middle class and the poor stays constant, this will lead to the increase of income inequality. Indeed, the income share of the top 1% U.S. households doubled from 1979 to 2007 owning largely to the growth of CEO and executive compensation [5,6]. On the other hand, the surge of inequality can also be a result of rising income volatility [7,8], a measure of the instability of household income. A few studies have found that U.S. household incomes became more volatile during the preceding decades [9–13]. Yet, because these studies focus primarily on detecting the trend of volatility, the causality between volatility and inequality has received limited attention. Moreover, much of the existing research on income distribution uses cross-sectional data; these data, however, only provide snapshot information [4,14–17] and reveal little about income volatility. To clarify the impact of mobility and volatility on income disparities, a more comprehensive model that contains both factors is needed. Regarding income distribution models, Pareto’s seminal work [18] has inspired an avalanche of related studies. For example, Champernowne has constructed a stochastic model to simulate Pareto’s power law [19], and Mandelbrot has applied Lévy’s theory to develop the Pareto-Lévy law [20]. A large portion of recent effort has been spent on constructing new models that are able to replicate the income’s cumulative distributions. These include, among others, the κ-generalized distribution [21], kinetic exchange models [22,23], generalized Lotka–Volterra models [24], Boltzmann–Gibbs distribution and Yakovenko models [25–28]. These models are based on intuitive assumptions or phenomenological arguments such as multiplicative and additive randomness [26]. Although the models’ prediction exactly matches the empirical data (such as data from the U.S. Internal Revenue Service [28]), the socioeconomic meanings of these models have not been fully explored. As a result, critical socioeconomic concepts such as mobility and volatility are not reflected in these models. This limits the opportunity to apply these models to social sciences and, in particular, makes it difficult for econo-physicists to communicate with social scientists [29]. In this paper, we examine the factors of mobility and volatility embedded in the simplest model— the Fokker–Planck equation-based model [27,28]. Our results show that this equation is more than a match for empirical data; it can provide insightful knowledge about the causal dynamics of economic inequality – especially how income mobility and volatility affect inequality – and can shed light on the decline of the American Dream.