Unambiguous Trends Combining Absolute and Relative Income Poverty: New Results and Global Application

Abstract

1. Introduction

The first and maybe the most prominent of the Millennium Development Goals was to halve extreme income poverty by 2015, taking 1990 as the reference year. An individual is considered extremely poor if their income is lower than $1.90 per day in 2011 Purchasing Power Parity (PPP) (Ferreira et al. 2016). This absolute poverty threshold reflects the poverty standards in the poorest countries, which typically capture the minimal resources necessary for nutrition and other subsistence needs. By 2015, this goal had been reached by a large margin (World Bank 2018). Over the same period, besides strong growth, many countries experienced an increase in within-country income inequality (Bourguignon 2015; Milanovic 2016). In such countries, the rising inequality may have translated into greater social exclusion of the poor because relatively deprived individuals experience difficulties in engaging in the everyday life of their society (Townsend 1979; Ravallion 2008). This evolution is captured by rising relative poverty indicators. If absolute poverty decreases while relative poverty increases, one may wonder how global income poverty has evolved over the period 1990–2015 when adopting a definition of income poverty that accounts for both its absolute and relative aspects.

There are several reasons for adopting an “overall” definition of poverty, which conflates absolute and relative poverty. First, such a definition is necessary when taking a world approach to economic poverty and exclusion. As argued by Atkinson and Bourguignon (2001), taking a world approach requires a framework that unifies the poverty measurement practices in developing countries and in developed countries. If the former rely on absolute measures typically grounded in subsistence, the latter use relative measures grounded in social participation. Second, such a definition is also necessary when being poor is interpreted as having insufficient welfare, and individual welfare depends on both own income and relative income (Ravallion 2008; Ravallion and Chen 2011). There is now ample evidence that relative income is an important determinant of subjective well-being (Clark and Oswald 1996; Luttmer 2005; Perez-Truglia 2020). More generally, if subsistence and social participation are two determinants of welfare, then welfare depends on own income and relative income. Finally, such a definition is necessary when policy makers that care for both subsistence and social inclusion, such as the World Bank (2015), need to select among policies that affect both absolute and relative poverty.¹

When absolute and relative measures show opposite trends, the direction of overall poverty change may depend on some parameters entering its definition. Most notably, the evolution of overall poverty may depend on the normative weight that captures the priority assigned to the absolutely poor. This priority measures how much more (or less) overall poverty is reduced when an additional unit of income is given to an absolutely poor individual rather than to an individual who is only relatively poor. Also, the evolution of overall poverty may depend on the exact definition of the poverty lines. Indeed, adopting a more “demanding” relative line mechanically increases the importance given to social participation in the overall measure. This dependence on such arbitrarily chosen parameters significantly limits the usefulness of overall poverty measures.

This paper shows under a rather mild normative assumption that global overall income poverty has been (at least) halved over 1990–2015, regardless of the value chosen for the priority parameter. Moreover, this result is highly robust and in particular holds for alternative specifications of the relative line. The magnitude of poverty reduction is much larger than what alternative overall poverty measures find. To reach this result, this paper makes use of a recently proposed family of overall poverty indices parametrized by the priority given to the absolutely poor (Decerf 2017). We provide a new result for this family of indices: all indices may agree on the direction of overall poverty change even in some cases for which absolute and relative measures show opposite trends. This result follows from the fact that these indices satisfy our normative assumption.

Our analysis relies on a normative assumption stating that an individual who is absolutely poor is poorer than an individual who is only relatively poor, regardless of the income standard in their respective societies. That is, an absolutely poor individual in a low-income country cannot be considered less poor than a relatively poor individual in a higher-income country whose personal income is above the absolute threshold. Under a world approach, this assumption amounts to granting a form of precedence to subsistence over social participation. Atkinson and Bourguignon (2001), and later Decerf (2017), express support for granting some form of precedence to subsistence over social participation.² Under a welfarist approach, this assumption implies that individual welfare depends on relative income, but only above the absolute threshold. This corresponds to a Maslovian view whereby individuals give precedence to their subsistence needs, at least when these needs are not minimally satisfied. We conduct an online survey in the United States, the United Kingdom, and South Africa in order to test whether our assumption collects considerable support under both of its interpretations. In all three countries, the vast majority of respondents state that (a) an individual deprived in terms of subsistence needs is poorer than an individual deprived in terms of social participation and (b) they would themselves prefer to be deprived in terms of social participation rather than deprived in terms of subsistence.³

Our normative assumption plays a key role in the possibility of making overall poverty comparisons that are independent of the value chosen for the priority parameter. We illustrate this based on an example for which absolute and relative poverty follow opposite trends. Consider an income distribution for which the absolute poverty threshold is lower than the relative poverty threshold. Assume that this distribution has only one poor individual and this individual is absolutely poor. Consider a second distribution that is obtained from the first distribution by a particular form of unequal growth: the income of all individuals increases, the income of the poor individual is lifted above the absolute threshold, but their income increases at a slower pace than the relative threshold. The poor individual is only relatively poor in the second distribution but their income is now further away from the relative threshold. Therefore, relative poverty is larger in the second distribution. Our normative assumption implies that overall poverty is unambiguously larger in the first distribution because the only poor individual is absolutely poor in the first but not in the second distribution.

This paper characterizes the conditions under which overall poverty comparisons are independent of the priority assigned to an absolutely poor individual over an only relatively poor individual. In the family of indices considered, the two extreme values of this parameter attribute zero and infinite priority to the absolutely poor, respectively. The necessary and sufficient conditions obtained are easy to use. The reason is that all family members yield poverty comparisons that lie between those yielded by the two extreme family members. Therefore, these conditions allow us to place a lower and an upper bound on the extent of overall poverty reduction.

Using World Bank data, we show empirically that when we measure global poverty, all indices in the family considered have declined by at least 50 percent from 1990 to 2015. The extent of overall poverty reduction is considerably large. This result is not entirely driven by the tremendous progress achieved by one or two populous countries such as China or India. In fact, our result holds for almost one-fourth of all countries, when taken individually. Our result is robust to five different definitions of the relative line. These alternative specifications reflect to a large extent the variety of proposals made in the literature (Atkinson and Bourguignon 2001; Chen and Ravallion 2013; Jolliffe and Prydz 2016; World Bank 2018). In particular, we consider mean- as well as median-sensitive relative poverty lines and we allow for different values for their slopes and intercepts. Our finding confirms and strengthens positive evaluations of the success achieved against global income poverty over the period 1990–2015.

Alternative measures find much less overall poverty reduction than our lower bound estimate. The reason is that these alternative measures behave as relative measures as soon as the relative threshold is larger than the absolute threshold, i.e., as soon as the income standard reaches a certain value. Beyond that point, alternative measures violate our normative assumption and therefore need not record any progress when economic growth lifts individuals out of absolute poverty. For the set of countries whose relative threshold is larger than the absolute threshold, we show that all our measures find a rate of poverty reduction that is on average several times higher than the one found using the most well-known alternative measure. For some cases, such as urban China from 1996, the alternative measure increases while the entire family of measures that we consider declines.

Our empirical analysis has an additional implication for the literature on global poverty measurement. Our results further suggest that the selection of poverty indices, which has been largely neglected in the literature, affects the magnitude of overall poverty reduction at least as much as the selection of poverty lines. Specifically, similar differences in trends emerge when we compare our results with those obtained from standard indices to measure overall poverty than when we change the lines keeping the index constant.

The rest of the paper is organized as follows. First, we present the theory. Second, we present the survey providing support for our normative assumption. Third, we present the data and the empirical analysis. Lastly, we provide some concluding comments.

2. Absolute, Relative and Overall Poverty Measures

In this theoretical section, we present the basic framework, introduce the four families of poverty measures that we use, and study the conditions under which the family of overall measures that satisfy our assumption yields unambiguous comparisons.

2.1. Basic Framework

Let an income distribution y ≔ (y₁, …, y_n) be a list of nonnegative incomes sorted in nondecreasing order, with |$n \in \mathbb {N}$|⁠. The set of such income distributions is denoted by Y. Let |$\bar{y}$| denote the income standard in distribution y, e.g., mean or median income in y. The income standard is homogeneous of degree 1. We consider two different poverty statuses, each identified by a specific poverty line.

The absolute poverty line is defined by a poverty threshold |$z_a \in \mathbb {R}_{++}$|⁠, which does not depend on the income standard. An individual i is deemed absolutely poor if y_i < z_a. We interpret z_a as the minimal income level that allows purchase of the goods necessary to satisfy basic needs (e.g., food, clothes, or shelter). The number of absolutely poor individuals in distribution y is denoted by q_a(y).

The relative poverty line is defined by a threshold function |$z_r:\mathbb {R}_{+}\rightarrow \mathbb {R}_{+}$| defined as |$z_r(\bar{y})=b+s\bar{y}$|⁠, where s ∈ (0, 1) is the slope of the relative line and b ≥ 0 is its intercept. Strongly relative poverty lines have b = 0 and weakly relative lines have b > 0 (Ravallion and Chen 2011). Typically, the slope takes the value s = 0.5. An individual i is deemed relatively poor if |$y_i\lt z_r(\bar{y})$|⁠. We interpret the relative threshold |$z_r(\bar{y})$| as the minimal amount necessary to engage in the everyday life of a society whose income standard is |$\bar{y}$|⁠. The number of relatively poor individuals in distribution y is denoted by q_r(y).

A poverty measure is a function P: Y → [0, 1] that ranks all income distributions using a fixed (set of) poverty line(s). If for two distributions x, y ∈ Y we have P(x) > P(y), then x has more poverty than y. We say that P measures absolute (resp. relative) poverty if P identifies the poor using only the absolute (resp. relative) line. We say that P measures overall poverty if P identifies the poor using both the absolute and the relative line. In this latter case, the number of individuals who are poor is denoted by q(y) = max {q_a(y), q_r(y)} and the number of individuals who are only relatively poor is q(y) − q_a(y). Since income distributions are sorted, if i ≤ q_a(y) then individual i is absolutely poor and if q_a(y) + 1 ≤ i ≤ q(y) then individual i is only relatively poor.

2.2. Four Families of Additive Poverty Measures

We consider four families of additive poverty measures: one family of absolute measures, one family of relative measures, and two families of overall measures, which combine absolute and relative poverty. Only one of the two families of overall measures satisfies our normative assumption. All measures considered are additive, which implies that poverty is measured as the average poverty contribution of all individuals in a distribution.

2.3. Disagreement between Absolute and Relative Measures

In this section we discuss the implications of our normative assumption for overall poverty comparisons of two distributions for which absolute measures disagree with relative measures. We say that there is a disagreement between absolute and relative measures on two distributions when these measures draw opposite evaluations of the distributions, i.e., either A_α(x) > A_α(y) and R_α(x) < R_α(y), or A_α(x) < A_α(y) and R_α(x) > R_α(y).

We present our analysis using a stylized example for which the absolute threshold is set at $1.90 a day (i.e., the extreme poverty threshold of the World Bank) and the relative threshold is set at half mean income.⁶ Consider the distributions x and y shown in table 1. Both distributions feature three individuals. Individual 1 is absolutely poor, individual 2 is only relatively poor, and individual 3 is nonpoor. Distribution y is obtained from x by a particular form of “unequal growth.” The income of each individual i is larger in y than in x, which yields a mean income in y ($10) twice as large as the mean income in x ($5). Yet, the income growth from x to y is not equi-proportional. The income of the nonpoor individual 3 is more than doubled while the incomes of the poor individuals 1 and 2 grow at a slower pace. When considering gap-sensitive poverty measures (α > 0), there is disagreement between absolute and relative measures over these two distributions that have different income standards: A_α(x) > A_α(y) and R_α(x) < R_α(y).⁷ They disagree because they provide different comparisons of individual situations across distributions having different income standards. In our framework, the situation of any individual i is defined by their bundle|$(y_i,\bar{y})$|⁠. Each additive poverty measure implicitly defines a complete ranking of individual bundles, summarized by its iso-poverty map (IPM). An iso-poverty map is a collection of iso-poverty curves, which are defined as the set of all individual bundles associated to a given value of poverty contribution.

Any iso-poverty curve of A_α and R_α is the set of bundles associated to a given value of normalized income. For A_α, the normalized income only depends on own income, and all iso-poverty curves are flat lines, as illustrated by the IPM represented in fig. 1(a) for the case α > 0. For R_α, the normalized income is own income divided by the relative poverty threshold, which increases with the income standard. As a result, all iso-poverty curves are homothetic to the relative line, as illustrated by its IPM represented in fig. 1(b) for the case α > 0.⁸

Figure 1.

Distribution x Has Higher Absolute Poverty but Lower Relative Poverty than y

Source: Authors’ own elaboration.

Note: The graphs plot the iso-poverty maps (IPM) of absolute and relative measures for the case α > 0. The solid lines are iso-poverty curves. These lines reveal how different bundles |$(y_i, \bar{y})$| are implicitly compared across distributions with different income standards.

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There is more absolute poverty in x than in y because for the absolutely poor individual 1 we have x₁ < y₁. Hence, individual 1’s normalized income (with respect to the absolute threshold) is smaller in x than in y. Therefore, individual 1 is on a lower iso-poverty curve of A_α in x than in y. In contrast, there is less relative poverty in x than in y because the incomes of individuals 1 and 2 do not grow as fast as the income standard. This implies that their normalized incomes (with respect to the relative threshold) are larger in x than in y. Therefore, individuals 1 and 2 are on a higher iso-poverty curve of R_α in x than in y.

We turn now to overall poverty measures. There is less overall poverty as measured by O_α in x than in y when α > 0. The reason is easily understood by looking at the IPM of O_α, which is illustrated in fig. 2(a) for the case α > 0.⁹ This IPM is defined by the function d_ar, which computes the normalized income with respect to the largest poverty threshold. As a result, this IPM corresponds to the IPM of absolute measures in very-low-income countries (z_a > z_r) and corresponds to the IPM of relative measures in higher-income countries (z_a < z_r). When comparing distributions x and y, measure O_α agrees with R_α because both distributions have a mean income large enough for the relative threshold to be larger than the absolute threshold.

Figure 2.

Under Our Normative Assumption (P^λ), Distribution x Has Larger Overall Poverty than y

Source: Authors’ own elaboration.

Note: The graphs plot the iso-poverty maps (IPM) of O_α with α > 0 and P^λ with λ ∈ (0, 1). The solid lines are iso-poverty curves. These lines reveal how different bundles |$(y_i, \bar{y})$| are implicitly compared across distributions with different income standards.

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Importantly, the IPM of O_α reveals that this overall measure violates our normative assumption. As illustrated using fig. 2(a), its iso-poverty curves cross the absolute threshold. When α > 0, the contribution to O_α of individual 1 in x is smaller than the contribution to O_α of individual 2 in y, even if the former is absolutely poor and the latter is not.¹⁰

In contrast, there is more overall poverty as measured by P^λ in x than in y, for all values of λ. The reason is easily understood by looking at the interpersonal comparisons inherent in P^λ. All measures P^λ are associated to the same IPM, which is illustrated in fig. 2(b).¹¹ First, as for measure A_α, all the iso-poverty curves below the absolute threshold are flat. The reason is that the poverty contribution of an absolutely poor individual only depends on their individual income. Thus, the contribution to P^λ of individual 1 is larger in x than in y. Importantly, this also implies that no iso-poverty curve “crosses” the absolute threshold. That is, no iso-poverty curve has some of its bundles below the absolute threshold and some of its bundles above the absolute threshold. Hence, an absolutely poor individual always contributes more to P^λ than an individual who is only relatively poor.¹² This shows that measure P^λ satisfies our normative assumption. Second, the IPM reveals that the contribution to P^λ of individual 2 is also larger in x than in y.¹³ At any bundle above the absolute threshold, the slope of the iso-poverty curve associated to P^λ is less steep than the slope of the iso-poverty curve associated to R_α. Iso-poverty curves associated to P^λ make a trade-off between the absolute and relative aspects of income, while iso-poverty curves associated to R_α only capture the relative aspect.

This stylized example shows that overall poverty comparisons depend on the interpersonal comparisons made across societies with different income standards. Our normative assumption constrains these interpersonal comparisons by giving some precedence to absolutely poor individuals. Unlike O_α, the overall measure P^λ satisfies this assumption.

2.4. Unambiguous Overall Comparisons with P ^λ

In this section we characterize the conditions under which we can draw overall poverty comparisons with P^λ that are independent of the priority parameter λ. As we show below, it is possible to draw such unambiguous comparisons with P^λ even for some pairs of distributions for which A_α and R_α disagree.

Figure 3 graphically illustrates the impact of parameter λ on the shape of the contribution function at a fixed level of income standard. As the graph for λ = 1 reveals, P¹ gives infinite priority to the absolutely poor because the contribution of the only relatively poor is constant in own income. Then, the graph for λ = 0 shows that P⁰ gives infinite priority to the only relatively poor because the contribution of the absolutely poor is constant in own income.

Figure 3.

Contribution to P ^λ as a Function of Income y_i, at a Fixed Income Standard |$\bar{y}$|

Source: Authors’ own elaboration.

Note: The graph plots individual i’s poverty contribution |$1- d^\lambda (y_i,\bar{y})$| as a function of y_i at a given income standard |$\bar{y}$|⁠, for a generic value of λ ∈ (0, 1), and for the two extreme cases λ = 1 and λ = 0.

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In general, when there is disagreement between absolute and relative measures, the overall poverty comparison with P^λ depends on the value taken by parameter λ. We provide an illustrative example in the supplementary online appendix. However, there are pairs of distributions for which A_α and R_α disagree but the overall poverty comparison with P^λ is unambiguous. This is illustrated with the stylized example given in table 1. In that example, the unambiguous comparison follows from the fact that all poor individuals are on a higher iso-poverty curve of P^λ in y than in x. Thus, regardless of the value given to parameter λ, there is more overall poverty (as measured by P^λ) in x than in y. Proposition 1 formalizes the possibility of making unambiguous overall comparisons with P^λ even when absolute and relative measures disagree.

Note that it is not necessary that all bundles move onto higher iso-poverty curves in order to have an overall poverty comparison that does not depend on the priority parameter.¹⁵

The necessary and sufficient condition under which an overall poverty comparison does not depend on the value chosen for λ follows from Proposition 2.

Proposition 2 directly implies that checking whether an overall poverty comparison is independent of λ only requires computing P^λ for the two extreme values of λ.

The easy-to-use conditions obtained in Proposition 2 are the consequence of the linear expression of P^λ. We discuss in the supplementary online appendix the implications of considering hierarchical indices based on nonlinear expressions.

Note also that the conditions obtained in Proposition 2 are logically unrelated to first-order stochastic dominance (Atkinson 1987). More precisely, it is neither necessary nor sufficient that distribution y first-order stochastically dominates distribution x in order to conclude that y has unambiguously less P^λ-poverty than x. Footnote 15 provides an example showing that first-order stochastic dominance is not necessary. To see that first-order stochastic dominance is not sufficient, consider two distributions related by stochastic dominance that each have only one poor individual, who is only relatively poor. It can be that the poor individual in the distribution with higher income standard lies on a lower iso-poverty curve of P^λ than the poor individual living in the distribution with lower income standard, even if the latter has a strictly smaller income. In that case, the distribution that first-order stochastically dominates the other has unambiguously more P^λ-poverty.

3. Support for Normative Assumption

3.1. Survey Design

To test whether our normative assumption receives support from the general population, we conducted an online survey in the United States, the United Kingdom, and South Africa. In each country, we collected data from a sample of 385 respondents representative of the national population in terms of region, age, and gender, resulting in a total sample of 1,155. Survey responses were collected between March 25 and April 17, 2021 using Qualtrics.

Respondents were faced with two hypothetical scenarios: a simple and a more complex one. In each of these scenarios there are two individuals (a and b) living in two different countries (A and B). Person a is absolutely poor while Person b is only relatively poor, and they are respectively described as not having enough income to satisfy their basic needs or to participate in the everyday activities of their country. We asked respondents to rank these two individuals according to their degree of poverty.¹⁶ In the simple scenario, we additionally asked respondents which situation they would prefer for themselves.¹⁷

The simple and complex scenarios differ in several respects. First, in the simple scenario we explicitly mention it if an individual does not have enough income to either satisfy their basic needs or participate in the everyday activities of their country. In the complex scenario, instead respondents have to identify the poverty status from individual income levels and poverty thresholds. Second, in the simple scenario Person a is not relatively poor, while in the complex scenario Person a is both absolute and relatively poor.

3.2. Results

Table 2 displays the distribution of responses by their ranking of poverty types for both scenarios. Columns 1 and 2 display the results for the simple and complex scenarios respectively including all responses. We observe that in both scenarios almost 60 percent of respondents believe that the absolutely poor individual is poorer than the relatively poor individual. In both cases, this share is three times larger than for any other option.

In Column 3 we focus on those respondents who provided consistent answers across the simple and complex questions. We classify a response as consistent if the respondent selects a similar choice in both scenarios: either the same person (a or b) as poorer, both individuals as equally poor, or none as poor. These responses are probably of higher quality than the inconsistent ones. For instance, consistent respondents are likely to have put more effort into selecting their answers or to have higher cognitive skills. Our results indicate that consistent respondents are slightly more educated than inconsistent ones.¹⁸ When we focus on consistent respondents, we observe that more than 80 percent of them believe that the absolutely poor individual is poorer than the relatively poor one in both scenarios.

In each country surveyed, the majority of respondents gives support to our normative assumption. Specifically, in each country more than 50 percent (70 percent) of all (consistent) respondents believe that the absolutely poor individual is poorer, and the share of respondents who choose any other option is at least half of this. The main difference across countries is that there is slightly higher support for our normative assumption in the United States and the United Kingdom than in South Africa (see tables S6.1, S6.3, and S6.5 in the supplementary online appendix).

So far, we have analyzed the opinions about the severity of different types of poverty. We turn now to preferences. For the simple scenario, we asked respondents whether they would prefer to be the only absolutely poor person, the only relatively poor person, or whether they would be indifferent. Almost 80 percent of all respondents state that they would prefer to be only relatively poor over only absolutely poor. This share goes up to 86 percent among consistent respondents (see table 3). These results are similar across countries (see tables S6.2, S6.4, and S6.6 in the supplementary online appendix). Taking all the results from the survey together, we can conclude that they give substantial support to our normative assumption.

4. Data and Parameters

4.1. Poverty Data

Our source of data is PovcalNet,¹⁹ an online tool of the World Bank whose main goal is to replicate the Bank’s poverty estimations. PovcalNet offers income or consumption data from more than 160 countries in the world from 1981 to 2015. We use data from 1990 until 2015. We estimate poverty for each reference year defined by the World Bank, these being designed to perform multicountry aggregations since surveys are conducted in different years across countries.²⁰ We take 1990 as our base year because it was the reference year used for the objective of halving global extreme poverty by 2015 (one of the United Nations’ Millennium Development Goals). We include all countries that have information in both 1990 and 2015.²¹ The final sample includes 160 countries, among which 3 have data for rural and urban areas separately. This gives a total of 163 units of analysis.

One of the main advantages of PovcalNet is that it provides poverty estimates that are internationally comparable. In order to allow for cross-country comparisons, the World Bank translates the survey data using the 2011 PPP exchange rates for household consumption from the International Comparison Program.

4.2. Poverty Lines

Estimating poverty with P^λ requires selecting both an absolute line (z_a) and a relative line (z_r). We consider several pairs of poverty lines (see next section), but we mostly focus on our preferred pair of lines. In our main pair of lines, the absolute threshold is set at $1.90 per person per day, in 2011 PPP. This has been the official extreme poverty threshold of the World Bank since 2015 (Ferreira et al. 2016). Our main relative threshold, in turn, is set at half mean income in each country. Selecting a relative line that is mean sensitive instead of median sensitive is a conservative assumption. This choice magnifies the relative component of our overall poverty measures because mean income is significantly larger than median income in most countries. Also, many countries saw their mean income increase faster than their median income over 1990–2015. Therefore, if the reduction in absolute poverty more than compensates the increase in relative poverty under a mean-sensitive line, it is very likely also to hold when changing the income standard to median income. Finally, a slope equal to 0.5 is standard for mean-sensitive relative lines.²²

5. Empirical Results

We present three sets of results. First, we show that global overall poverty measured by P^λ has been at least halved over the period 1990–2015, independently of the value chosen for the priority parameter. Second, we show that this result is robust to using alternative population weights and alternative poverty lines. Finally, we compare our results to those obtained by alternative standard measures in terms of the magnitude of poverty change.

5.1. Evolution of Overall Poverty by P^λ

We start by analyzing the change in poverty between 1990 and 2015 in a small set of countries (see table 4).²³ These countries were selected for illustrative purposes. Except Pakistan, they have all experienced a decrease in absolute poverty (by both A₀ and A₁) and an increase in relative poverty (by both R₀ and R₁). Altogether, these countries cover more than 46 percent of the sample population size over every year from 1990 to 2015. In particular, China, India, Indonesia, and Pakistan are the top four most populous countries in the developing world.

Table 4 displays the values of mean income per capita, inequality, and poverty as measured by various indices in 2015 relative to 1990 for each country. Consider for instance the row corresponding to urban China. We observe that urban China has experienced a sharp increase both in mean income per capita and inequality as measured by the Gini index over this period (see Columns 1 and 2). The former led to a sharp decrease in absolute poverty as measured by A₀ and A₁ (see Columns 4 and 5). In turn, the increase in inequality led to an increase in relative poverty as measured by R₀ and R₁ (see Columns 6 and 7). This shows that, when taking α = 0 or α = 1, the absolute measures disagree with the relative measures on the evolution of poverty in urban China (as indicated in Column 8). However, the overall poverty measures P¹ (equivalent to A₁) and P⁰ have both declined over 1990–2015 (see Columns 3 and 4). As both P¹ and P⁰ have decreased, from Corollary 1 we can conclude that overall poverty measured by P^λ has been reduced in urban China, independently of the value chosen for the priority parameter (as indicated in the last column). In this sense, the decrease in absolute poverty more than compensates the increase in relative poverty. Moreover, as both P¹ and P⁰ have been at least halved over the period, we can conclude from Corollary 2 that P^λ has been (at least) halved in urban China, independently of the value chosen for the priority parameter.

The evolution of poverty in urban China is not an exception as many countries, especially in the developing world, experienced both a strong growth and an increase in within-country inequality over the period (Anand and Segal 2008; Ravallion 2014; Bourguignon 2015; Milanovic 2016). Several other cases presented in table 4, namely Bangladesh, rural China, rural and urban India, and rural and urban Indonesia, experience a similar evolution: the absolute measures disagree with the relative measures but overall poverty measured by P^λ is unambiguously reduced. In four out of these six cases, we can conclude that P^λ has been unambiguously halved. In the remaining cases, i.e., urban India and urban Indonesia, whether P^λ has been halved or not depends on the priority parameter (P⁰ has not been halved over the period) but the reduction is at least 48 percent for any λ. The last two countries in the table provide examples of alternative trends in poverty. In Pakistan, there was no increase in relative poverty but the strong decrease in absolute poverty has led overall poverty measured by P^λ to be divided by a factor at least larger than 5. In Jamaica, however, the decrease in absolute poverty was not large enough to offset the increase in relative poverty, leading to a slight increase in P^λ when the priority given to absolutely poor individuals is sufficiently low (as revealed by P⁰).

We turn now to the evolution of global poverty. To keep the exposition simple, for the absolute and relative measures we focus on the head-count ratios A₀ and R₀ and, whenever relevant, we mention whether the results also hold (qualitatively) for α = 1. Figure 4 shows the evolution of global poverty (relative to 1990) by P^λ, A₀, and R₀ (see also the last row of table 4). The absolute measure A₀ disagrees with the relative measure R₀: A₀ has declined by 72 percent while R₀ has increased by 7 percent.²⁴ The overall poverty measure P¹, which gives infinite priority to absolutely poor individuals, has declined by 76 percent. Finally, the overall poverty measure P⁰, which gives infinite priority to relatively poor individuals, has declined by 59 percent. Thus, there is an unambiguous reduction in global poverty measured by P^λ. Moreover, P⁰ provides the lower bound for this overall poverty reduction, which is larger than 50 percent. By Corollary 2, we can conclude that P^λ has been halved over the period, independently of the priority assigned to the absolutely poor.

Figure 4.

Evolution of Global Poverty Relative to 1990

Source: Authors’ calculations based on data from PovcalNet, 1990–2015.

Note: The graph plots the evolution of global poverty as measured by different indices for all reference years until 2015 relative to 1990.

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The trends in global poverty are similar to those observed in the developing world, which concentrates most of the reduction in absolute poverty over this period (see fig. S6.1 in the supplementary online appendix). If we look at the evolution of poverty by regions,²⁵ we observe that the decline in P^λ is mostly driven by (populous) regions with large initial poverty. These are mainly East Asia and Pacific, South Asia, and Sub-Saharan Africa, which respectively explain 53, 23, and 19 percent of global P¹ in 1990 and 47, 26, and 14 percent of global P⁰ in 1990. Figure S3.2 in the supplementary online appendix show the evolution of poverty in these three regions (we present the remaining regions in fig S6.2 in the supplementary online appendix). All regions except North America have experienced an unambiguous decline in P^λ over 1990–2015. Moreover, P^λ has been unambiguously halved in East Asia and Pacific, and South Asia.

5.2. Robustness

In this section we study the robustness of our results in two different ways. First, we study robustness to population weights and verify that the results are not fully driven by a few major countries. Second, we study whether our results are robust to alternative definitions of the poverty lines.

5.2.1. Robustness to Population Weights

One potential concern about our analysis is whether the reduction in P^λ is completely driven by the evolution of poverty in one or two large countries. In order to assess this, we perform two robustness checks. First, we exclude China and India from the sample. Second, we fully ignore population weights and compute the number of countries for which we can conclude that P^λ has decreased (resp. has been halved) regardless of the priority parameter.

China and India represent together almost 40 percent of our sample population size. Also, they have both experienced a strong reduction in P^λ for all λ. We first analyze whether the global decline in P^λ also holds when we exclude these two countries. Figure 5 shows that even when these large economies are removed, both P⁰ and P¹ have significantly decreased. When removing China and India, absolute poverty measured by A₀ decreases by 46 percent (instead of 72 percent) and overall poverty measured by P^λ decreases by at least 36 percent (instead of 59 percent) (see table S3.1 in the supplementary online appendix).²⁶ Hence, these two countries alone do not completely drive our result.

Figure 5.

Evolution of Global Poverty excluding China and India Relative to 1990

Source: Authors’ calculations based on data from PovcalNet, 1990–2015.

Note: The graph plots the evolution of global poverty excluding China and India as measured by different indices for all reference years until 2015 relative to 1990.

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Second, we study the robustness of our results to ignoring population weights. Figure 6 displays the ratios of P⁰, P¹, and R₀ in 2015 relative to 1990 for each country in our sample.²⁷ Countries are ordered in descending order of the value of P⁰ in 2015 relative to 1990. We can easily observe that except for a few countries at the top of the graph, most countries experience a decrease in P⁰. Moreover, most of them also experience a decrease in P¹, the other extreme member of our family. These two observations together imply that P^λ is reduced in many countries, independently of the priority parameter.

Figure 6.

Poverty in 2015 Relative to 1990 by Country: P⁰, P¹, and R₀

Source: Authors’ calculations based on data from PovcalNet, 1990 and 2015.

Note: The graph plots the values of P⁰, P¹, and R₀ in 2015 relative to 1990 for each country in the sample. For visualization purposes, values larger than 2.5 are not displayed. We exclude countries with at least two values larger than 2.5. This concerns Bulgaria, Croatia, Czech Republic, Latvia, Luxembourg, Montenegro, Romania, and Slovak Republic. The following countries are displayed but have one value larger than 2.5: Austria, Djibouti, Finland, Georgia, Germany, Italy, Lithuania, North Macedonia, Serbia, Sweden, Taiwan, China, United Arab Emirates, United States, Yemen, and Zimbabwe. Finally, note that there are several countries in the graph for which R₀ in 1990 is the same as in 2015, and hence the ratio 2015/1990 equals 1. For these countries, PovcalNet has survey data for only one year over the whole period. Thus, to extrapolate the distribution across years they assume equi-proportionate growth. This implies that when R₀ is defined using a strongly relative line, it does not change over time. This affects the following countries: Kiribati, Lebanon, Suriname, Syrian Arab Republic, Turkmenistan, Tuvalu, United Arab Emirates, and Vanuatu.

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More precisely, we can compute the fraction of countries for which P^λ has been reduced and the fraction for which it has been halved, independently of the priority parameter. To do so, we perform all within-country pairwise poverty comparisons between 1990 and 2015. For each pairwise comparison, we first identify whether there is disagreement between A₀ and R₀. We observe that A₀ and R₀ have evolved in opposite directions in almost 30 percent of the cases. Results are similar when we compare A₁ and R₁ (35 percent of disagreements) (see table S3.2 in the supplementary online appendix). Moreover, we observe that P^λ has unambiguously declined in 67 percent of countries and has been unambiguously halved in 23 percent of countries (see table S3.3 in the supplementary online appendix).

5.2.2. Robustness to Poverty Lines

We show here that our results still hold for alternative pairs of poverty lines. Table 5 displays the specific combinations of absolute and relative lines that we use. The first five pairs of lines (pairs 1 to 5 in table 5) all use different relative lines but the same absolute line. The first alternative relative line is similar to our main relative line but is based on median income instead of mean income. The second alternative relative line is also based on median income and has the same gradient as the previous one but in addition it has an intercept of $1. This line, called the societal poverty line, has been estimated by Jolliffe and Prydz (2017) from regressions of 699 national poverty thresholds against median income. A recent report from the World Bank estimates societal poverty, which corresponds to the head-count ratio below the societal poverty line (World Bank 2018). The third alternative relative line has an intercept of $0.40 and a relative gradient of 50 percent of the mean national income. This line has been estimated from regressions of national poverty thresholds by Ravallion and Chen (2017) (see their fig. 5, panel b). As some authors consider relative lines with a smaller slope parameter (see for instance Atkinson and Bourguignon 2001), our pair 5 has a slope of 0.33 and an intercept of $1. Finally, our sixth combination of lines sets the absolute line at 3.2 PPP$ a day and uses the relative line of our main specification (pair 1). The absolute threshold of $3.20 a day corresponds to the lower-middle-income international poverty line suggested by the World Bank (see Jolliffe and Prydz 2016).

For all pairs of lines, we observe a continuous decrease in overall measure P⁰ over 1990–2015 (see fig. 7). Considering all pairs, the decline in P⁰ between 1990 and 2015 ranges from 47 percent to 66 percent (see Column 1 of table 5). Even considering the most conservative pair of lines (pair 6), P⁰ decreases by almost 50 percent between 1990 and 2015.²⁸ This shows that our main result is robust to using alternative relative lines and almost robust to all pair of lines.

Figure 7.

Evolution of P⁰ Relative to 1990 by Line

Source: Authors’ calculations based on data from PovcalNet, 1990–2015.

Note: The graph plots the evolution of P⁰ relative to 1990 for all pairs of poverty lines as defined in table 5.

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Table S6.7 in the supplementary online appendix replicates table 4 for the same selection of countries using the most conservative pair of lines. All selected countries except Jamaica (as for the first pair of lines) have experienced a substantial decrease in overall poverty measured by either P⁰ or P¹ with this alternative pair. Moreover, for all of the selected countries the decrease in P^λ is independent of the priority parameter.

Finally, considering all countries in our sample individually for our most conservative pair of lines, we observe that P^λ has unambiguously declined in 72 percent of them. Moreover, P^λ has been unambiguously halved in 20 percent of them (see table S6.8 in the supplementary online appendix). Again, this shows that even for alternative pairs our results are not fully driven by a small number of large countries.

5.3. Comparison of Overall Poverty Measures

5.3.1. Impact of Index versus Impact of Poverty Line

The literature on global poverty measurement has paid more attention to the definition of the poverty lines than to the selection of the poverty index. We can compare the reduction of poverty between 1990 and 2015 across overall poverty measures and all the pairs of poverty lines considered. To quantify this comparison, we compute two mean variances. First, we compute the variance in poverty reduction between the main overall poverty measures (P⁰, O₀, and O₁) for each pair of lines and we take the average across pairs (between-index variance). Second, we compute the variance in poverty reduction between pairs of lines for each index and we take the average across indices (within-index variance).²⁹ We conservatively ignore P¹ first, even if including it would only increase the variance between indices, because it is formally equivalent to A₁, a purely absolute index. Table 6 shows that the between- and within-index standard deviations are quite similar: 0.063 and 0.070 respectively.³⁰ This comparison suggests that in this case the selection of poverty indices affects the magnitude of overall poverty reduction as much as the selection of poverty lines.

5.3.2. Comparison of P^λ with the Atkinson–Bourguignon Measures

In this section we compare the results on overall poverty change obtained by P^λ with the alternative approach most commonly used in the literature. Despite the normative appeal of our approach, its empirical relevance largely depends on the extent to which poverty change estimates differ from those obtained using standard measures. The dominant practice in evaluating global overall poverty is to estimate the evolution of the Atkinson–Bourguignon overall poverty measure O₀, i.e., the head-count ratio below the upper contour of the absolute and relative lines. This is, for instance, the approach followed by Chen and Ravallion (2013), Jolliffe and Prydz (2017), and Ravallion and Chen (2017). Thus, we focus our comparative analysis on O₀, and we briefly comment on the comparison with O₁.

If we look again at table 5, we can compare our estimation of overall poverty reduction (P^λ) with that estimated by O₀. The main takeaway is that, for all pair of lines, the poverty reduction estimated by O₀ does not lie inside our two bounds (P¹ and P⁰). Even our most conservative estimation (associated with P⁰) finds more poverty reduction than O₀, and this is true for the entire period (see fig. S3.3 in the supplementary online appendix).³¹ Importantly, this underestimation³² is not merely the result of O₀ being insensitive to the depth of poverty (i.e., the gap with respect to the poverty threshold). Indeed, we can alternatively compare our estimates with that obtained using O₁, i.e., the poverty-gap ratio below the upper contour of the absolute and relative lines, a standard gap-sensitive measure. Interestingly, we observe that, except for pair 6 whose absolute threshold is larger, O₁ also finds less poverty reduction than P⁰.

We can better quantify to what extent O₀ underestimates the decline in poverty. In order to do so, in fig. 8 we plot the (negative) growth rate of P⁰ relative to the (negative) growth rate of O₀ over three-year periods for the entire sample.³³ We plot each ratio at the end of each three-year period. For instance, the dot in 1993 represents the growth rate of P⁰ over 1990–1993 relative to the growth rate of O₀ over the same period. As the ratio of growth rates between P⁰ and O₀ depends on the pair of poverty lines, we focus on our main pair of lines (pair 1) and we briefly comment on the results for the alternative pairs. We observe that the ratio of growth rates is always larger than 1 and tends to increase over time, reaching more than 2 by the end of the period. Given that both P⁰ and O₀ decrease in each three-year period, this means that P⁰ decreases systematically more than O₀. More precisely, the rate of decline in global poverty by P⁰ is between 8 percent and 106 percent larger than that by O₀ (see table S3.5 in the supplementary online appendix). We find similar patterns for the alternative pairs of lines (see fig. S3.4 in the supplementary online appendix). For all alternative pairs, the ratio of growth rates is mostly above 1 and increasing over time. In the last period, P⁰ decreases 30 percent more than O₀ for the most conservative pair of lines and at least 50 percent more for the remaining pairs.

Figure 8.

Ratio of Growth Rates: P ⁰ over O₀. Three-Year Periods. Pair of Lines 1

Source: Authors’ calculations based on data from PovcalNet, 1990–2015.

Note: The graphs plot the ratio of growth rates between P⁰ and O₀ over three-year periods. Panel (a) includes all countries in the sample. Both P⁰ and O₀ decrease in all periods for this sample. Hence, a ratio above (below) 1 implies that P⁰ decreases more (less) than O₀. Panel (b) restricts the sample to countries with z_a < z_r. For this restricted sample, both P⁰ and O₀ decrease in all periods except 1990–1993, when they both increase. Hence, in 1993 a ratio above (below) 1 implies that P⁰ increases more (less) than O₀.

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These numbers show that the underestimation of poverty is economically relevant. Moreover, they are a lower bound on the underestimation as any other index in our family yields an even larger rate of poverty reduction relative to O₀. Specifically, the other extreme of our family, P¹, yields a rate of poverty reduction between 1.3 and 3.2 times larger than O₀ (see table S3.5 in the supplementary online appendix).³⁴

The key reason that O₀ finds less poverty reduction than P⁰ is that O₀ violates our normative assumption. The measure O₀ implicitly considers that all poor individuals are equally poor, regardless of whether they are absolutely poor or only relatively poor. Growth reduces O₀ when a poor individual exits poverty, but it does not record any progress when an absolutely poor individual crosses the absolute threshold and becomes only relatively poor. In contrast, the hierarchical measures P^λ do record such progress.

As we mentioned, the underestimation of the decline in poverty increases over time. This is because our normative assumption only plays a role in countries for which the relative threshold is larger than the absolute threshold, and the share of countries for which this is the case increases over time. Specifically, O₀ and P⁰ (as well as A₀) take the same value in low-income countries where no individual is only relatively poor (when z_a > z_r), as revealed by equations (3) and (4) with α = 0 and λ = 0 respectively.³⁵ Indeed, absolutely poor individuals all contribute 1 to both O₀ and P⁰. Thus, our normative assumption does not play a role in such countries. The measures O₀ and P⁰ register the same progress with growth until these countries grow sufficiently for relative poverty to matter. Now, as soon as the relative threshold becomes larger than the absolute threshold (z_a < z_r), some poor individuals exit absolute poverty and become only relatively poor. Then our assumption kicks in and P⁰ takes a smaller value than O₀. The reason is that, if individuals who are only relatively poor contribute 1 to O₀, they contribute less than 1 to P⁰. Therefore, P⁰ records more progress than O₀ when evaluating growth.

In general, O_α tends to find less poverty reduction than P^λ because the former violates our assumption. This is easily understood when z_r is strongly relative. In that case, any equi-proportionate growth in a country with z_a < z_r leaves O_α unchanged. This behavior of O_α is debatable as such growth typically allows some part of the population to escape absolute poverty. In contrast, this growth reduces P^λ because this measure implicitly considers that being only relatively poor is a form of poverty that is less severe. The same point is more subtly made when z_r is weakly relative and the growth is not equi-proportionate, even if it remains valid. Our assumption implies less steep iso-poverty curves for P^λ than for O_α (see fig. 2). Therefore, if a given growth process moves the bundle of a poor individual onto a higher iso-poverty curve of O_α (which implies less poverty), then it also moves their bundle onto a higher iso-poverty curve of P^λ. However, the converse is not true. A growth process that lifts the bundle of an absolutely poor individual above z_a, which automatically puts it on a higher iso-poverty curve of P^λ (which implies less poverty), could simultaneously put their bundle on a lower iso-poverty curve of O_α (which implies more poverty).

We illustrate the differential effect of economic growth on P⁰ and O₀ with the case of urban China. Figure 9 displays the evolution of poverty in urban China by P⁰ and O₀ using the first pair of lines. For the period 1990–1996, urban China has a low income standard and we have z_a > z_r.³⁶ Therefore, both O₀ and P⁰ register the same progress over 1990–1996 (a reduction by almost 60 percent). After 1996, as the income standard is larger and we have z_a < z_r, our assumption kicks in and the two measures start diverging. The unequal growth taking place in urban China after 1996 increases O₀ while it reduces P⁰ (which registers progress as more and more individuals cross the absolute threshold). Hence, after 1996, the progress in poverty reduction according to P⁰ is much larger than that recorded by O₀. Note that we observe a larger reduction in P⁰ compared to O₀ for all alternative pairs of lines (see fig. S3.5 in the supplementary online appendix). In each case, as soon as z_a < z_r, P⁰ and O₀ diverge and P⁰ decreases more.

Figure 9.

Evolution of Poverty by P ⁰ and O₀ Relative to 1990 for Urban China. Pair of lines 1

Source: Authors’ calculations based on data from PovcalNet, 1990–2015.

Note: The graph plots the evolution of P⁰ and O₀ relative to 1990 in urban China for the first pair of lines. It includes all single years until 2015. The vertical line indicates in which year z_r surpasses z_a.

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This mechanism has clear implications for our analysis. The estimations presented so far (based on fig. 8) include all countries in the sample for every reference year, even those for which z_a > z_r. For the first pair of lines, the share of the world’s population living in a country with z_a > z_r amounts to 57 percent in 1990 and 24 percent in 2015 (see table S3.4 in the supplementary online appendix). This increase in the share of population living in a country with z_a < z_r explains why the underestimation of poverty reduction increases over time. To account for this, in fig. 8 we compute the growth rate of P⁰ relative to O₀ excluding those countries with z_a > z_r in each three-year period. Note that the sample obtained consists of different countries in each three-year period. The underestimation of poverty reduction for this moving sample is striking. The decrease in P⁰ is for the most part more than twice the decrease in O₀, and it gets up to 12 times larger. For this restricted sample, P⁰ also finds considerably more poverty reduction than O₁ in each period.³⁷ This conveys an important message for the evaluation of poverty reduction in the future. When most countries have z_a < z_r, we can expect that using O₀ will underestimate the rate of poverty reduction by a large extent.

6. Concluding Remarks

The approaches of Atkinson and Bourguignon (2001) and Ravallion and Chen (2011) provide two different reasons to evaluate the evolution of income poverty using overall measures, which combine the absolute and relative aspects of income poverty (Ravallion 2020). Decerf (2017) proposes a normative assumption whose adoption leads to a refinement of the standard overall poverty measures. We discuss the meaning of this assumption under these two approaches and provide some survey evidence that this assumption may collect broad support. More importantly, we show that this assumption has important theoretical and empirical implications for overall poverty comparisons. On the one hand, overall measures that satisfy this assumption may provide comparisons that are independent of the priority assigned to absolutely poor individuals, even when absolute measures disagree with relative measures. On the other hand, these measures record significantly more overall poverty reduction than mainstream measures over 1990–2015 because many absolutely poor individuals became only relatively poor over that period. Mainstream overall measures record slower progress because they need not record an improvement when absolutely poor individuals become only relatively poor as their country grows. Altogether, provided one endorses this assumption, our findings confirm and strengthen positive evaluations of the success achieved against income poverty over the period covered by the Millennium Development Goals.

We acknowledge that the results of our online survey provide limited evidence on the support that our normative assumption may gather. First, the scope of the survey was rather small as only three countries were surveyed and the number of observations per country was limited. Second, online surveys are but one method to evaluate this support. It would be interesting to investigate whether lab experiments or revealed preference methods yield similar results to those of our survey.

Our theoretical results provide a ready-to-use method able to assess the trend of overall income poverty independently of the value selected for the priority parameter. This method can be readily applied in different contexts where both basic subsistence needs and social participation needs are deemed relevant.

Footnotes

Notes

Benoit Decerf is a Research Economist in the Development Research Group of the World Bank; his email address is [email protected]. Mery Ferrando (corresponding author) is an Assistant Professor in the Economics Department of Tilburg University, The Netherlands; her email address is [email protected]. The authors thank the editor and three anonymous referees for helpful comments and suggestions. This article supersedes our earlier ECINEQ working paper entitled “Income Poverty Has Been Halved in the Developing World, Even When Accounting for Relative Poverty.” The authors are grateful to Francisco Ferreira, François Maniquet, and Martin Ravallion, as well as participants at the Workshop on Poverty, Inequality and Gender - CRED, ECINEQ 2019, IARIW-WB Conference 2019, the 2nd LIS/LWS Users Conference, the Public Economics Workshop at Delhi School of Economics and seminars at the World Bank, the Université catholique de Louvain, KU Leuven, and Tilburg University for valuable comments. The authors also thank Kristof Bosmans and Janet Gornick for useful discussions on earlier versions of this paper. François Woitrin and Hans-Peter Hiddink provided excellent data assistance. Funding from the Fond National de la Recherche Scientifique (Belgium, mandats d’aspirant FC 95720 & 99238) and partial funding from the European Research Council under the EU’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 269831 are gratefully acknowledged. This project was also financially supported by the Excellence of Science (EOS) Research project of FNRS O020918F. The online survey reported in this study was pre-registered and is available in the AsPredicted Registry (#61776). All remaining errors are our own. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they represent. A supplementary online appendix is available with this article at The World Bank Economic Review website.

References