Our friend and frequent collaborator Prof. Michael McAleer loved to enumerate lists and to give practical advice. Here, we present a review of 10 ways to derive the well-known Gini coefficient based on entropy measures. In fact, Mike was a collaborator on some of this work, as will be discussed in the paper. All are useful ways to combine two powerful tools, entropy measures and Gini coefficients to examine inequality in income distribution functions (IDFs) and can be applied to distributions of other random variables. Others have shown that a Gini coefficient can be derived from the first moment of an observed share function. Ryu and Slottje demonstrated that by projecting the observed share function with other moments and functions different approximated share functions can be derived. By doing so, more information can be conveyed about the underlying IDF that generated the observed Gini value. In the spirit of Prof. Michael McAleer, we present 10 different ways to utilize entropy functions to generate Gini coefficient measures.

This paper examines the relationship between political dominance and economic inequality in the U.S. for the years 1947-2017. Conventional wisdom suggests that when Democrats control Congress and the Presidency, they will pursue policy goals that are inequality reducing through government actions. Republican controlled Congresses and presidencies are presumed to pursue economic growth and limited government intervention policies. However, are these beliefs true? Economic inequality is a broad term with various interpretations. In this paper we adopt a different approach. We consider the distribution of utility that individuals possess, while understanding that of course this depends in part on their income levels. We do find that Democratic presidential administrations correlate with lowering economic inequality and when Republican presidents hold the White House this correlates with increasing levels of economic inequality. However, we find that dominance by a given party in Congress has a negligible impact.

The Gini coefficient is generally used to measure and summarize inequality over the entire income distribution function (IDF). Unfortunately, it is widely held that the Gini does not detect changes in the tails of the IDF particularly well. This paper introduces a new inequality measure that summarizes inequality well over the middle of the IDF and the tails simultaneously. We adopt an unconventional approach to measure inequality, as will be explained below, that better captures the level of inequality across the entire empirical distribution function, including in the extreme values at the tails.

This paper introduces a new perspective on Rawls’s Difference Principle. We link two distinctive approaches to analysing the social welfare implications of alternative policy actions; the utilitarian approach and the Rawlsian distributive justice approach, together in a cohesive way. While there is a large optimal tax literature, that literature generally treats the decision maker as a utilitarian. This paper adds a different dimension in that we compare and contrast what would happen if a Rawlsian government (RG), had as its objective function maximizing the utility of the poorest social group and compare that economic state to one where a utilitarian government (UG) existed that had as its principle objective maximizing the total utility of its entire society but subject to the constraint of a targeted level of inequality, using the maximum entropy method to capture the distribution of individual ability. Each government chooses tax parameters to achieve their respective goals under balanced budget constraints. Individuals in both regimes have different capabilities and maximize utility through suitable labor/leisure choices. The exercise shows that Gini coefficients are lower but hours worked increase under both RG and UG regimes even if people are allowed to work while they receive welfare payments. There are, however, differences in the total utility and inequality levels achieved under the different regimes.

This paper introduces a new Maximum Entropy based inequality measure that is related to Basmann’s class of weighted geometric mean (WGM) measures, but with the added feature that the new measure is flexible enough to describe other characteristics of an observed income distribution function (IDF), a feature that other well-known measures do not possess. As an application, using Current Population Survey (CPS) data, we apply the new measure to Blinder and Esaki’s (1978) aggregate macro-modeling approach to examine US income inequality trends from 1947 to 2014. Increases in the unemployment rate and decreases in inflation rates and in the growth rate in gross domestic product (GDP) were found to deepen income inequality; rising inequality is a recent trend many policymakers have been watching with concern.

There is a vast literature on the selection of an appropriate index of income inequality and on what desirable properties such a measure (or index) should contain. The Gini index is, of course, the most popular. There is a concurrent literature on the use of hypothetical statistical distributions to approximate and describe an observed distribution of incomes. Pareto and others observed early on that incomes tend to be heavily right-tailed in their distribution. These asymmetries led to approximating the observed income distributions with extreme value hypothetical statistical distributions, such as the Pareto distribution. But these income distribution functions (IDFs) continue to be described with a single index (such as the Gini) that poorly detects the extreme values present in the underlying empirical IDF. This paper introduces a new inequality measure to supplement, but not to replace, the Gini that measures more accurately the inherent asymmetries and extreme values that are present in observed income distributions. The new measure is based on a third-order term of a Legendre polynomial from the logarithm of a share function (or Lorenz curve). We advocate using the two measures together to provide a better description of inequality inherent in empirical income distributions with extreme values.

Bentham (1789) introduced utility as the pursuit of happiness, with happiness defined in his philosophical view as existing if pleasure predominated over pain. This paper is the first to derive and compare the relative frequency distributions of income and utility in Bentham's classical sense. A utility-based Gini coefficient is formulated from a utility distribution derived from the better known income distribution. A utility-based Lorenz curve is defined as the accumulated sum of pain and pleasure, as Bentham defined them. A utility-based polarization index is created as the ratio of accumulated pain to accumulated pleasure. If raw income data are unavailable, an income distribution can still be estimated from a summary inequality statistic such as the Gini coefficient using the maximum entropy method. In this study, a measure of true income inequality, utility inequality, and the pain suffered by the poorest group are quantified and estimated using National Tax Service data from Korea.

Measuring an individual's human capital at a point in time as the present actuarial value of expected net lifetime earnings has a lengthy history. Calculating such measures requires accurate estimates of worklife expectancy. Here, worklife estimates for men and women in the USA categorized by educational attainment, race, marital status, parental status and current labour force status are presented. Race has a much larger impact on the worklife expectancy of men than women. Education is associated with larger worklife differentials for women. The association between marriage and worklife expectancy is significant, but of opposite sign, for men and women: married women (men) have a lower (higher) worklife expectancy than single women (men). Parenthood is associated with a reduction in the worklife expectancy of women; the association is smaller and varies from positive for some education/marital status groups to negative for others for men.