A scaling perspective on the distribution of executive compensation

Income distribution in Thailand is scale-invariant

“…For more than a century, numerous studies have investigated and confirmed that income and wealth distributions have no characteristic scale (see Jagielski et al [ 15 ] and references therein). A recent study by Sitthiyot et al [ 16 ] confirms previous empirical findings in that the distribution of average executive compensation is statistically scale-invariant or self-similar across time period, industry type, and company size. That is time period, type of industry, and company size have no effects on the distribution of average executive compensation.…”

“…Given that there has yet to be an agreement on the choice of statistical distributions to be used in order to fit the data on income and test the property of scale invariance, this study therefore employs an alternative method that is based on the Kolmogorov-Smirnov test (K-S test) introduced by Sitthiyot et al [ 16 ] which is relatively simple and does not require a priori assumption with regard to the distribution of data. To our knowledge, no study has conducted a formal test whether the distribution of income in Thailand is statistically scale-invariant across years before.…”

A simple method for estimating the Lorenz curve

“…Moreover, we conduct the Kolmogorov-Smirnov test (K-S test) to compare whether the estimated income shares by decile are different from the actual observations with the null hypothesis being no difference between the two. According to Sitthiyot et al (2020), the K-S test is commonly used to determine if two datasets differ significantly. Its advantage is that it makes no assumption about the distribution of data.…”

“…Given the limitations of the interpolation technique and no single statistical distribution that fits the entire income distribution, numerous studies have suggested a variety of parametric functional forms to directly estimate the Lorenz curve. Examples include Kakwani andPodder (1973, 1976), Kakwani (1980), Rasche et al (1980), Aggarwal (1984), Gupta (1984), Arnold (1986), Rao and Tam (1987), Villaseñor and Arnold (1989), Basmann et al (1990), Ortega et al (1991), Chotikapanich (1993), Rao (1996, 2000), Ryu and Slottje (1996), Sarabia (1997), Sarabia et al (1999Sarabia et al ( , 2001Sarabia et al ( , 2010Sarabia et al ( , 2015Sarabia et al ( , 2017, Sarabia and Pascual (2002), Rohde (2009), Helene (2010), Wang and Smyth (2015), Fellman (2018), Tanak et al (2018), Paul and Shankar (2020), and Sitthiyot et al (2020). However, many existing widely used functional forms often cited in the literature do not have a closed-form expression for the Gini index, making it computationally inconvenient to calculate since they require the valuation of the beta function, for example, Kakwani and Podder (1976), Kakwani (1980), Rasche et al (1980), andOrtega et al (1991), or the confluent hypergeometric function, for example, Rao and Tam (1987).…”

A simple method for measuring inequality

“…According to Eliazar and Sokolov (2012), the application of the Gini index has grown beyond socioeconomics and reached various disciplines of science. Examples include astrophysics-the analysis of galaxy morphology (Abraham et al, 2003); ecology-patterns of inequality between species abundances in nature and wealth in society (Scheffer et al, 2017); econophysics-wealth inequality in minority game (Ho et al, 2004); scale invariance in the distribution of executive compensation (Sitthiyot et al, 2020); engineering-the analysis of load feature in heating, ventilation, and air conditioning systems (Zhou et al, 2015); finance-the analysis of fluctuations in time intervals of financial data (Sazuka and Inoue, 2007); human geography-measuring differential accessibility to facilities between various segments of population (Cromley, 2019); informetrics-the analysis of citation (Bertoli-Barsotti and Lando, 2019); medical chemistry-the analysis of kinase inhibitors (Graczyk, 2007); population biology-heterogeneities in transmission of infectious agents (Woolhouse et al, 1997); public health-the analysis of life expectancy (De Vogli et al, 2005); the analysis of real biological harm (Sapolsky, 2018); renewable and sustainable energy-the analysis of irregularity of photovoltaic power output (Das, 2014); sustainability science-the study of land change (Rindfuss et al, 2004); transport geography-equity in accessing public transport (Delbosc and Currie, 2011); selection of tram links for priority treatments (Pavkova et al, 2016). In effect, the Gini index is applicable to any size distributions in the context of general data sets with non-negative quantities such as count, length, area, volume, mass, energy, and duration (Eliazar, 2018).…”