Inequality

Inequality

Sin Yee Koh , in International Encyclopedia of Human Geography (Second Edition), 2020

Abstract

Inequality refers to the phenomenon of unequal and/or unjust distribution of resources and opportunities among members of a given society. The term inequality may mean different things to different people and in different contexts. Moreover, inequality encompasses distinct yet overlapping economic, social, and spatial dimensions. Debates about inequality are further complicated by the disjuncture between the moral ethics of equity and social justice, on the one hand, and the normative idea of "deservingness," on the other hand. In recent years, there has been increasing awareness of inequalities that are observable within social groups, in addition to those across social groups. This awareness has led to an increasing realization that inequality is systemic and entrenched in various socioeconomic and political structures. Geographers' contributions toward the topic of inequality in this regard include highlighting the persistence of unequal and differentiated rights, interrogating global and extreme inequality, and analyzing the manifestations and causes of urban inequalities.

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Inequality

L. Osberg , in International Encyclopedia of the Social & Behavioral Sciences, 2001

2 Inequality Among Whom?

Because assessing the extent of inequality involves a comparison of resources, it is crucial to be clear about whose resources are being compared—and which resources. An analyst who looks only at inequality in family or household income is ignoring the fact that families and households differ significantly in size. On the other hand, if an analyst were to look only at the distribution of money income directly received by individual persons, the fact that many people (e.g., young children, unpaid spouses) have zero cash income of their own would tend to exaggerate measured inequality.

Because individuals without income of their own typically reside in households in which other family members do have cash income, the effective degree of sharing of income within households is crucial to inequality measurement. However, this is difficult to observe in practice, and it is often convenient for researchers to assume that all persons within a household have the same level of effective income (Phipps and Burton 1995 demonstrate that alternative assumptions can make a big difference to perceived poverty). Similarly, it is common to assume that all members of a given household have the same socioeconomic status. Effectively, such procedures amount to assuming away inequality within groups of people (in this example, coresident household members) and concentrating attention on inequality between groups.

Assuming equality within groups can be problematic (e.g., much feminist scholarship has challenged the presumption of within-family equality in consumption, status, and power). Furthermore, the larger the group is, the harder it generally becomes to maintain the presumption of within-group equality. There is much social interest in the extent of inequality between broad groups of people (e.g., occupational groups, regions, racial or ethnic groups, age cohorts, etc.). In some instances, between-group comparisons are driven by an underlying theoretical framework which defines categories of interest (e.g., bourgeoisie/proletariat). However, when within-group inequality is large relative to that between groups (as in income comparisons between age groups, where inequality among individuals of the same age is far greater than the differences in average income between people of different ages), comparisons of average group characteristics may suggest unwarranted stereotyping.

Furthermore, the term 'inequality' can be used in two subtly different conceptual senses. In some discussions—discrimination is an example—'inequality' is used to refer to differences between particular individuals or groups (e.g., person A is not equal to person B). In other instances, 'inequality' refers to differences among people in general (e.g., in country A there is more inequality than in country B). These usages need to be distinguished, since pairwise and group inequalities do not necessarily imply aggregate inequality differences. Table 1 presents a numerical example of men and women in 'Arcadia' and 'Bucolia' to make the point.

Table 1. A comparison of inequality in two hypothetical societies

Men Women
Arcadia 4 6 8 2 4 6
Bucolia 0 6 12 6 6 6

Is there more inequality in Arcadia than in Bucolia, or less? Would eliminating between group inequality imply an end to inequality? Inequality among groups of people is illustrated by comparison of men and women in Arcadia and Bucolia. In Arcadia, women have a lower average income (4) than men (6), while in Bucolia the average is the same (6). However, the equality of male and female average income in Bucolia does not imply equality of individual incomes. Inequalities in average income between groups also do not imply individual inequalities (in Arcadia, for example, two-thirds of men can be matched with women with exactly the same income while in Bucolia only one match can be found).

To answer the seemingly simple question of whether, overall, there is more inequality in Arcadia than in Bucolia, or less, one must compare the entire distribution of outcomes. Although there is a large middle class in Bucolia (two-thirds of the inhabitants have the same outcome (6)), there are also greater extremes (from 0 to 12). In Arcadia, middle-class incomes are more differentiated, but the extremes are not as widely separated. Hence, answering the seemingly simple question whether there is more or less inequality requires finding a way to summarize the number and size of differences in outcomes among all individuals.

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Inequality

Marcos Mendes , in Inequality, Democracy and Growth in Brazil, 2015

2.1 Introduction

In Brazil, an engineer earns seven times more than a carpenter. In the United Kingdom, this difference is 2.1 times, in the United States, no more than 1.8 and in Canada, 1.7. The curious thing is that high-income employment in Brazil has about the same remuneration as developed countries. The Brazilian engineer earns, on average, US$3700 per month, more than the Canadian (US$3000), almost equal to the British (US$3800) and a little less than the American (US$4700) (http://www.worldsalaries.org). Values expressed in US$ from 2005, corrected by purchasing power parity.

The Brazilian engineer can lead a standard of life similar to their colleagues in other countries. The situation for the carpenter, however, is much different. While they earn US$512 per month, their colleagues north of the equator receive about US$1800 in the United Kingdom and Canada and US$2500 in the United States. The Brazilian carpenter probably has a quality of life well below his foreign colleagues. This great difference in incomes between white- and blue-collar workers is a portrait of Brazilian inequality.

In the other three countries, for example, engineers and carpenters, and their respective families, often study at the same schools, use the same health services and drive the same kinds of cars. In Brazil, the engineer's son will be born in a private hospital, paid for by a private health plan, go to a private school and, most of the time, travel by car. The carpenter's son will probably be born in a public hospital, attend public school and use public transportation, all of lesser quality than his private counterpart. They live and grow up in parallel worlds. They may live in the same city, but usually go to different places in their leisure time. The engineer's son will probably do better in his studies and get a higher paying job than the carpenter's son. This inequality carries on from one generation to the next.

The central argument of this book is that this inequality in income, assets, and human capital is an important causal factor in the recent history of low economic growth in Brazil. Before exploring this idea in more detail, it is important to take a closer look at inequality around the world, the degree of inequality in Brazil and its tendency over the last few years.

The first relevant fact is that inequality persists over time. Countries that were unequal in the past tend to perpetuate inequality over time. The causes for this fact will be analyzed in Chapter 3. Figure 2.1 presents the Gini Index of income inequality for several countries, comparing inequality in the past (using the oldest available data) with current inequality (most recent available data). 1 The main message of this figure is that, for this group of countries, inequality in the past "explains" 80% of current inequality. The figure also highlights the fact that Latin American and Caribbean countries (represented by spheres) are, in general, more unequal than other nations. Brazil (triangle) is among the most unequal in the world, both past and the present.

Figure 2.1. Past Inequality versus Present Inequality: Gini Index for Selected Countries.

 (Source: Brazil Presidency of the Republic, 2012. (http://www.wider.unu.edu/research/database/en_gb/ database/). Prepared by author. Note: Brazil is represented by a triangle, other Latin American countries by a sphere and all other countries by a cross.)

The news is that Brazilian inequality has fallen consistently since 1995, with acceleration of this trend from 2001 on, as presented in Figure 2.2. For reasons analyzed in this chapter, the inertia shown in Figure 2.1 has been partially broken in recent years. However, the reduction in the Gini Index may be fading out: in 2012, for the first time since 2001, it did not decrease in relation to the previous year, signaling that inequality could be stabilizing at a still high level.

Figure 2.2. Income Inequality in Brazil: Gini Index for Household Per Capita Income (1977-2012).

 (Source: Barros et al., 2009. Brazil IPEA, 2012 and Brazil, Instituto de Pesquisa Econômica Aplicada (IPEA), 2013. Primary Source: Pesquisa Nacional por Amostra de Domicílios – PNAD (National Research by Sample Households) 1977-2012. Prepared by the author.)

The process of inequality reduction is not only Brazilian, having occurred in most Latin American countries. Figure 2.3 shows that 9 of the 14 regional countries had a reduction of inequality between 1995 and 2009. On average, this index fell 0.55% per year. The Brazilian reduction was a little more intense than the regional average and only came in behind Peru and Paraguay.

Figure 2.3. Yearly Average Rate of Variation of the Gini Index in Latin American Countries: 1995-2009 (% PY).

 (Source: World Bank, 2011. Prepared by the author. Note: Data used is from time periods nearest to 1995 and 2009. The years vary from between 1995 and 1997 with the final year between 2007 and 2009.)

Despite the recent reduction, Brazil remains a very unequal country. Figure 2.4 compares the Gini Index for Brazil with the 27 other countries used in Chapter 1 as a comparison group. One notes that, even with the recent improvement, Brazilian inequality (and that of Latin America) continues well above the average and among the higher rates in the group.

Figure 2.4. Gini Index in Selected Countries (different years).

 (Source: Brazil IPEA, 2012 for Brazil, World Bank, 2011 for other Latin American countries and, for the remaining countries, World Inequality Database (WIID2C). Prepared by the author.)

The recent reduction in Brazilian inequality was translated into significant income growth by the poorest. In Figure 2.5, it can be seen that, between 2001 and 2011, the per capita income of the poorest 10% grew at an average of 6.7% per year, while the richest 10% was only 1.5% per year: on average, the poorer the household, the greater the income growth.

Figure 2.5. Yearly Average Real Growth Rate of Household Per Capita Income Between 2001 and 2011 in Brazil by Income Decile (% PY).

 (Source: Brazil IPEA, 2012.)

This is certainly one of the factors that created a sense of well-being and progress in the first decade of the 21st century. In these years, a large number of people escaped poverty. As seen in Figure 2.6, in 2003, 24.4% of the population lived below the poverty line (in the concept adopted by Millennium Development Goals of US$2 per day) and, in 2011, this percentage had fallen to 10.2%. According to estimates presented by a Brazilian public think tank (IPEA), the reduction in inequality was the main source of poverty reduction: "about 52% [of this decrease in poverty] was caused by changes in income inequality, and the remainder explained by the effects of growth"(Brazil IPEA, 2012, p. 10).

Figure 2.6. Population with Per Capita Household Income Below the Poverty Line in Brazil (Millennium Development Goals Criteria) (%).

 (Source: Brazil IPEA, 2012. Prepared by the author.)

According to the same study, if it had not been for the redistribution of income, the income growth necessary to produce such reduction would have to be 6.6% per year between 2001 and 2011, instead of 2.8% per year (the average rate of growth for the period). This data shows the great power of income redistribution as a mechanism to reduce poverty in a very unequal country.

Total household income is composed of different income sources: wages, retirement paid by the public sector, benefits received from governmental social assistance programs, dividends received from investments, unemployment compensation, etc. Each of these components of total household income can be more/less concentrated in the hands of the rich than others. Therefore, it is interesting to analyze how much each income component contributes to inequality and how this contribution changes over time.

It is important to ask:

●

If income is so concentrated in Brazil, which sources of income are more concentrated than the others, and how does each of them contribute to such a high Gini Index?

●

What would be the causes for the recent reduction in inequality? If it is so time resistant (as is shown in Figure 2.1 above), what broke the historical inertia and produced this uncommon tendency to fall?

According to what was highlighted in the previous chapter, one hypothesis analyzed in this book is that the coexistence of a democratic regime with a large population of poor living in an unequal society would have induced politicians to seek votes of the poor using redistributive policies. It is therefore important to evaluate if these policies had an important role in the reduction of inequality (and poverty). Moreover, it is relevant to evaluate future prospects. Will inequality continue to fall in the coming years?

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Inequality Analysis: Overview

Guillermina Jasso , in International Encyclopedia of the Social & Behavioral Sciences (Second Edition), 2015

Abstract

Inequality is pervasive in the social life, and understanding it is a central task for the social sciences. This article provides an overview of inequality analysis, discussing the framework with its questions and building blocks and surveying the twin branches of theoretical inequality analysis and empirical inequality analysis, the latter only briefly given that dozens of other articles discuss empirical studies of inequality. Substantively, this article identifies two main types of inequality – inequality between persons and inequality between subgroups – and highlights the fundamental questions concerning the determinants and consequences of inequality. Methodologically, it summarizes the major tools for measuring both kinds of inequality, including both scalar measures and whole-distribution approaches. To illustrate theoretical inequality analysis, the article reviews recent examples of a priori explorations, including mechanisms for altering inequality.

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The External Benefits of Education

W.W. McMahon , in International Encyclopedia of Education (Third Edition), 2010

Reduced inequality and lower poverty

Inequality in the distribution of income is increasing dramatically in the United States and in other OECD countries. It is related to inequality earlier in access to education as shown by Psacharopoulos. More recent studies also show that remarkable increases in earnings inequality in the United States, United Kingdom, and OECD since 1980 is linked with human capital skills in dealing with new technology (Faggio et al., 2008).

Reducing high-school dropout rates also reduces inequality (Levin, 2006: 9). In higher education, Leslie and Brinkman (1988) conclude that increased access in the United States reduces inequality except in states where the tax systems are regressive as in Florida and Mississippi. In the OECD countries, however, higher education contributes to greater inequality as shown in Table 1 . Admissions are restrictive in many European universities, 2-year associate degrees are far less widespread, and need-based aid is less available. Therefore, although increased access to higher education reduces inequality in most states in the United States, it probably does not in Europe because of policies related to less need-based aid and proportionally fewer in associate degree programs.

Poverty is reduced, however, by economic growth, increased high-school completion, and increased access to higher education. The value of this direct effect is estimated to be $3110 per year for completion of college degrees in Table 1 .

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Inequality, Poverty, and Opportunity

Kui-Wai Li , in Redefining Capitalism in Global Economic Development, 2017

Abstract

A prime issue in capitalism is income inequality. This chapter argued that income inequality could be the "best" form of inequality as it can be adjusted and improved through policies, while other forms of inequality could be life-long. Inter-personal and intra-personal inequality is analyzed to examine the inevitability of inequality, but the more important issue is the improvability of inequality. Poverty could be a more relevant topic than inequality, and a conceptual difference is made between the stock and flow of poverty. While policies concentrated on the stock issue, it is the flow that would lighten the level of poverty. Indeed, ultimately, it is the generation of economic opportunity that could improve inequality and reduce poverty.

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Statistical Inequalities

H.M. Mahmoud , J.L. Gastwirth , in International Encyclopedia of Education (Third Edition), 2010

Inequalities for Moments

So far, the common inequalities for the probability of an event have been described and they all involve moments. It is useful to have inequalities for the moments themselves. We shall very briefly sketch the most salient ones. These inequalities appear more often in advanced topics and measure-theoretic proofs, where a careful argument is usually made about the existence of the moments involved. In the following, the moments are assumed to exist and are finite.

Jensen's Inequality

This inequality states that for any random variable X and convex function ϕ,

ϕ ( E [ X ] ) ≤ E [ ϕ ( X ) ] .

A standard use of this inequality assures that the variance

Var [ X ] = E [ X 2 ] − ( E [ X ] ) 2

is non-negative. This follows from convexity of the function ϕ(u) = u 2.

Hölder's Inequality

Suppose p, q > 0, such that 1 p + 1 q = 1 . For two random variables X and Y, we have,

E [ | X Y | ] ≤ ( E [ | X | p ] ) 1 / p ( E [ | X | p ] ) 1 / q .

The quantity E X P 1 / p is called the pth norm of X, and is often denoted by (it has all the properties of distance function in the space X p of random variables). Hölder's inequality can then be expressed in the notation

E XY ≤ X p Y q .

The special case p = q = 2 is known as the Cauchy–Schwarz inequality.

Minkowski's Inequality

Hölder's inequality takes a multiplicative form. It is used in the proof of a moments inequality in additive form, called Minkowski's inequality. This inequality generalizes the triangle inequality. For p ≥ 1,

X + Y p ≤ X p + Y p .

Lyapunov's Inequality

Lyapunov's inequality follows immediately from Hölder's. For any 0 < r < s,

X r ≤ X s

It is usually employed in arguments used to show that specific moment exists. Once it is known that sth moment exists (i.e., it as finite) for some s > 0, all lower order moments exist. For instance, if one knows that the fourth moment exists, one is assured of the existence of the first three moments. A typical application is when the second moment exists. In this case, the first moment (the mean) also exists.

Concluding Remarks

We discussed the most common types of inequalities for the probabilities of random variables. There are other families of inequalities that apply to sums of independent random variables. Kolmogorov's inequality stands out as an epitome of the members of the family (see Billingsley, 1995). Another type of inequalities uses the moment-generating function to bound probabilities. Two important inequalities from this class are Chernoff's and Hoeffding's inequalities (see Chernoff, 1952; Hoeffding, 1963).

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Handbook of Income Distribution

Ravi Kanbur , in Handbook of Income Distribution, 2015

Abstract

To what extent can increasing inequality be explained by globalization? And if there is a connection, what if anything can and should be done about it? This chapter begins with an overview of how conventional trade theory has fared in predicting changes in inequality and how it has needed to be extended and expanded when, contrary to some received wisdom, greater global integration is associated with increasing inequality in developed and developing countries. From there, the chapter goes well beyond these concerns to take in the effects of crises on inequality, globalization and gender inequality, openness and spatial inequality, and the effect of international migration on inequality. Finally, reviews of the latest developments in the design of national and global policy to address the challenges of globalization and inequality are presented. The literature reviewed is lively and flourishing. Having animated the economic analysis and policy discourse for the past half century, the globalization–inequality nexus seems set to continue in this vein in the coming decades.

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Earnings Inequality

Andreas Peichl , Nico Pestel , in International Encyclopedia of the Social & Behavioral Sciences (Second Edition), 2015

Abstract

Inequality has increased considerably in many Western countries over the past decades. When dealing with economic inequality as a research subject the question "inequality of what among whom?" arises. Analyses of inequality are typically concerned with the distribution of wages, earnings, or income and have been made by different strands in the literature, mainly in public and in labor economics. We summarize these strands with a special focus on earnings, which itself is the product of hourly wages and labor supply in terms of hours and weeks worked. In addition to inequality in labor market outcomes, we pay special attention to equality of opportunity.

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Data Bases and Statistical Systems: Environment and Urban Studies

Erika Nóra Regös , in International Encyclopedia of the Social & Behavioral Sciences (Second Edition), 2015

Inequality-Adjusted Human Development Index

The Inequality-adjusted Human Development Index (IHDI) was introduced by UNDP in their Human Development Report 2010. It was created to measure the level of human development of people in a society that accounts for inequality. Under perfect equality the IHDI is equal to the HDI. However it falls below the HDI when inequality rises. In other words, the IHDI can be seen as the actual level of human development (taking into account inequality), while the HDI can be viewed as an index of the potential human development that could be achieved if there is no inequality. The index has been applied to 132 countries so far. (For more information and data available see their Web site at: http://hdr.undp.org/en/statistics/ihdi.)

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