REVISING THE GLOBAL MULTIDIMENSIONAL POVERTY INDEX: EMPIRICAL INSIGHTS AND ROBUSTNESS

The global Multidimensional Poverty Index, published annually since 2010, captures acute multidimensional poverty in the developing world. In 2018, five of its ten indicators were revised with the purpose of aligning the index to the Sustainable Development Goals (SDGs) insofar as current data permit. This paper provides comprehensive analyses of the consequences of this revision from three perspectives. First, we thoroughly discuss new empirical insights for 105 countries in the developing world based on a data set including 8.78 million individual observations. Second, we analyze the robustness of country orderings to changes in key parameters, including the poverty cutoff and dimensional weights. Third, we compare the revised and the original specifications by implementing both on the same 105 national data sets. The country orderings in the revised specification are found to be robust to a range of plausible parametric alternatives. Largely, these country orderings are at least as robust as the original one.

Providing rigorous answers to these questions entails data-intensive empirical analyses.We build upon the same data that were used to produce the results of the revised global MPI in 2018.It consists of a unique data set that includes 105 strictly standardized microdata surveys (see Alkire et al., 2018), each of them being nationally representative of the population in a country located in one of the following six developing world regions as defined by UNDP: the Arab States, East Asia and the Pacific, Europe and Central Asia, Latin America and the Caribbean, South Asia, and Sub-Saharan Africa.The overall pooled sample results in 8.78 million individual observations that represent around 5.7 billion people.This corresponds to nearly 77 percent of the global population and 91 percent of the population living in the developing world.Given that levels of acute multidimensional poverty are expected to be low outside the developing world, our analysis is close to having a global scale.To the best of our knowledge, there is no analysis of the robustness of cross-country multidimensional poverty comparisons to alternative parameter values that builds on such an extensive and recent microdata.Only Alkire and Santos (2014) and Robles and Sumner, (2020) come close to such an ambitious endeavor by investigating multidimensional poverty based, however, on the 2010 specification of the global MPI.Other studies adopting alternative indices to operationalize a multidimensional approach to poverty while building on large cross-country microdata sets include Burchi et al., (2018) andWorld Bank (2018).
To tackle the first question, we perform a thorough assessment of the joint distribution of deprivations before a multidimensional poverty analysis focusing on an array of aggregate measures.Thus we align our paper with other scholarship emphasizing the practical importance of the joint distribution of deprivations to understand the many facets of poverty (e.g., Atkinson, 2003Atkinson, , 2019;;Duclos et al., 2006;Wolff and De-Shalit, 2007;Robles and Sumner, 2020).Our results suggest for instance that 81-99 percent of the population in the developing world who are deprived in one indicator experience one or more additional deprivations.To uncover heterogeneities, we also disaggregate the aggregate poverty measures by world region, rural-urban areas, and age groups.
Addressing the second question, we analyze the robustness of the revised global MPI to changes in the multidimensional poverty cutoff and the weights within a counting framework to measure multidimensional poverty (Alkire and Foster, 2011b).One way in which we do this consists of examining the effects of shifts in the specification of the global MPI on the absolute position of each country in a global poverty ordering.We build on analyses of the robustness of pairwise comparisons considering standard errors applied in Alkire andSantos (2010, 2014), Yalonetzky (2014), Santos and Villatoro (2018) and Chen et al. (2019), among others, which relies on statistical tests to assess country poverty orderings, taking them two by two.This approach assesses an array of alternative MPI specifications simultaneously and can be summarized as the proportion of orderings that are preserved across these different specifications.Essentially, this method compares the relative order between two countries.In addition to the robustness analysis of the MPI value (as in Alkire andSantos, 2010, 2014), we assess the robustness of the poverty headcount ratio.Our results suggest, for instance, that across the entire set of countries, 95 percent of country pairwise orderings by MPI are robust for a range of plausible poverty lines and almost 90 percent of country pairwise comparisons by MPI are robust across to alternative plausible weighting schemes.
According to the terms Tony Atkinson suggested (World Bank, 2017, p. 171), we assess robustness of the revised version of the global MPI to local changes in the poverty cutoff and weighting structure, as defined in the Alkire-Foster method.This implements Sen's suggestion that in a plural society, we may "have some good reason to use ranges of weights on which we may find some agreement," especially if they "yield rather similar principal guidelines" (2009, p. 243).Our aim is thus to explore how stable the global MPI is to local changes in the poverty cutoff, and the weighting vector.This constitutes novel, useful empirical evidence for policymaking, and for subsequent cross-country research based on the revised global MPI.Assessing robustness of the global MPI to general (i.e., unbounded) parametric changes, including non-additively decomposable weighting structures, or establishing first-order stochastic dominance across the whole range of parameter values is beyond the scope of this paper.Explorations in that direction can be found in Alkire et al. (2019) and Azpitarte et al. (2020).
Finally, to address the third question, we perform a detailed empirical comparison of the poverty patterns arising in light of the original and revised versions of the global MPI.Feeding the same data into both specifications of the index, we first analyze differences in the key aggregate poverty measures by world regions, as well as the deprivation rates suffered by the whole population and the subset of poor people.In addition, we perform a country pairwise comparison analysis (with hypothesis tests) to assess the robustness of relative orderings between the two versions of the index.Our results show that the recent revision results in lower deprivation headcount ratios in child mortality whereas deprivation headcount ratios for nutrition, education, and housing increase-all as theoretically expected.
This paper is structured as follows.Section 2 briefly presents the methods and data underlying the global MPI.Section 3 contains the results of the revised MPI at the global level, by world regions, rural-urban areas, and age groups.Section 4 analyses the robustness of the revised global MPI to changes in dimensional weights and the poverty cutoff.Section 5 compares the poverty figures of the original and the revised versions of the global MPI.Finally, Section 6 offers the concluding remarks.

the reviSed global mpi: methodS and data
The global MPI is arguably the most well-known application of the dual cutoff counting approach to poverty developed by Alkire and Foster (2011b;AF henceforth).Whereas the innovation of the dual cutoff approach was general and methodological, the innovation of the global MPI lies, precisely, in selection and extensive empirical application of indicators and deprivation values.Given that the defining feature of the global MPI is its indicators and weights, and given that the revision adjusted the former, it is paramount to consider how to assess the revised global MPI, as this points out exercises that could also be useful when other established measures adjust their parameters.Therefore, in this section, let us make a formal presentation of the method, which will allow us to put the main elements of the revision in a formal context, the data that we use as well as explaining our empirical methods.

The Alkire-Foster (AF) Method
Let us consider a society containing n individuals and j = 1, ⋯, d relevant indicators.Let X be a (n × d)sized matrix containing the achievement levels of these indicators.These data can be transformed into matrix g 0 containing defined binary deprivation indicators for all the individuals in each one of the indicators.If individual i falls short of the minimum achievement level in indicator j that is necessary for them to be considered non-deprived, then g 0 ij = 1.Otherwise, g 0 ij = 0.Each deprivation may have a different relative importance, which is reflected in the vector of weights w = (w 1 ⋯w d ) such that w j > 0 and ∑ d j=1 w j = 1.Each element w j reflects the relative value or importance of each deprivation to poverty.Aggregating across weighted indicators, we can obtain individual deprivation scores as c i = ∑ d j=1 w j g 0 ij , ∀i.These scores represent the number of weighted deprivations experienced by each individual.
An individual is identified as poor if their deprivation score equals or exceeds the poverty cutoff k.Formally, an individual is considered to be poor using an identification function that we define as g 0 i , w, k = (c i ≥ k), where g 0 i is the row of the deprivation matrix containing all the deprivation indicators of person i.The identification function equals 1 if the individual is poor and 0 otherwise.In this notation, we explicitly state the set of parameters that define the specification of the poverty measure.Note that the deprivation matrix reflects the definition of indicators, whereby it is easy to see that the revision modifies the identification of the poor, even though w and k remain unchanged.
After the identification step of poverty measurement, we aggregate across individuals to obtain the poverty headcount ratio as , which represents proportion of poor people.Second, the rate of multidimensional poverty intensity can be computed as is the number of poor people.Thus A represents the average number of weighted deprivations experienced by the poor.Third, the adjusted poverty headcount ratio, denoted asM 0 , combines H and A in a multiplicative form, such that This rate represents the num- ber of weighted deprivations experienced by the poor as a proportion of the number of individuals in the whole sample.The adjusted headcount ratio is the level of the MPI, so M 0 and MPI are interchangeable notations.Note that every specifica- tion of an MPI and its subindices requires a specific choice of (1) indicator defini- tions, (2) dimensional weights, and (3) a poverty cutoff.This shows how and why the revision of indicators affects these aggregate poverty measures.

The Original and the Revised Global MPI
The original and the revised versions of the global MPI share many common elements in their specifications.They both comprise three dimensions, namely health, education, and living standards, and ten indicators, two of which pertain to health, two to education, and six to living standards.Both global MPI specifications have a nested weight structure: reflecting their roughly equal importance, each dimension is given the same weight (one-third) and every indicator is given the same weight within dimensions.The poverty cutoff is k = 1 3 in both specifications, signifying that a person is identified as multidimensionally poor if they suffer deprivations in one-third or more of the weighted indicators.Both specifications are augmented by exploring two additional cross-dimensional cutoffs: severity and vulnerability.People suffering deprivations in half or more of the weighted indicators are considered severely poor.Individuals are identified as vulnerable to multidimensional poverty if their weighted deprivation score is equal to or greater than one-fifth and lower than one-third. 6 The revision of the global MPI modified five of the ten indicators.Table 1 summarizes these revisions highlighting them in bold font, and a detailed account of how the revised indicators are justified given the purpose of the global MPI can be found in Alkire and Kanagaratnam (2021). 7In the revised version, the nutrition status for children under 5 includes the union between weight-for-age (underweight) and height-for-age (stunting).The original specification was limited to only underweight.The inclusion of stunting better aligns with the Sustainable Development Goals (SDG) framework toward zero hunger. 8In addition, for 51 countries where there is nutrition data for adults, we applied the BMI-for-age measure for individuals aged 15-19 and the BMI measure for adults 20 years and older.The original specification applied the BMI measure for all individuals 15 years and older.The BMI-for-age measure better accommodates the sporadic growth experience of youth than a BMI measure.
In the revised specification, a child death is considered in the child mortality indicator only if it took place 5 years before the survey.This avoids capturing past mortality stocks and allows to better capture policy success in reducing it.The deprivation cutoff in years of schooling was revised from 5 to 6 years to reflect the international standard duration of primary schooling.The previous flooring indicator is now coupled with walls and roof, allowing for a comprehensive housing indicator.The assets indicator was expanded to include computer and animal cart and thus reflect urban and rural deprivations more adequately (Vollmer and Alkire, 2020).
The revision of the global MPI indicators means that empirical evidence of its past robustness may not apply.For instance, one can hardly anticipate a perfect overlap between children who are stunted and those who are underweight, as the former results from longer-term, sustained nutritional deprivations (Neufeld and Osendarp, 2014;World Health Organization, 2019).Additional evidence of lack 6 For the present paper, however, our definition is consistent with the UNDP-OPHI collaboration.The category of people who are not poor but close to it-i.e., who are deprived in 20-33.32percent of dimensions-was measured and reported in the 2010 HDR and that category has been called vulnerability in the HDRs ever since.
7 This paper offers an extensive documentation of the data-intensive analyses leading to the final revised version of the global MPI.It provides details of the data limitations that prevent considering alternative indicator definitions, and even alternative dimensions.Readers are referred to this paper for a detailed description of the normative and theoretical justifications of the revised deprivation cutoff definitions.
8 Specifically indicator 2.2.1 of Goal 2 of the SDGs (https://susta inabl edeve lopme nt.un.org/sdg2 of overlap between these two measures of nutrition status can be found in Stevens et al. (2012), who show that the prevalence of stunted children in 141 countries declined more rapidly in 1985-2011 than that of underweight.Similarly, restricting the death of a child only to the last 5 years preceding the survey will likely detect the recent success in reducing the global under-5 mortality rate by more than half between 1990 and 2015 (90-43 per 1000 children) (UN, 2015a).Finally, as stated in Alkire and Kanagaratnam (2021), the revision of the years of schooling indicator may seem to be a minor one in theory, yet it can entail considerable empirical consequences.In most countries, having completed 5 or 6 years of schooling is synonym of having completed primary or not, which is hardly a minor shift in the deprivation cutoff; moreover, in the developing regions, individuals aged 15 and older are estimated to have an average of 6 years of schooling, not 5 (Barro and Lee, 2013).

Data
We use the same data that were used to produce the revised global MPI following Alkire et al. (2018) andpublished in OPHI (2018).These data are based on 105 nationally representative data sets drawn from four major sources: the Demographic and Health Surveys (DHS), the Multiple Indicator Cluster Surveys (MICS), the Pan Arab Project for Family Health (PAPFAM) surveys, and six national surveys.9Among these 105 countries, subnational disaggregation was possible for 88 countries.The vast majority of the countries (90) had surveys that were fielded between 2011 and 2016, and this represents 97 percent of the population covered in the 2018 global MPI.Details of the standardization of the indicators for each survey can be found in Alkire et al. (2018).
In 87 countries, the results were based on all 10 indicators of the global MPI.10In 17 countries, the results were based on nine indicators, while Philippines (alone) lacked two indicators.The countries lacking one indicator mainly lacked information on nutrition or child mortality, with Egypt lacking cooking fuel, Honduras lacking electricity, and China not having information on housing.To account for these special cases, weights on other indicators within the dimension of the missing indicator are equally increased such that they sum up to one-third.This procedure amounts to maintaining equal weights across the three dimensions, while making best use of the limited available information.Thus, it is aimed at preserving the theoretical rationale of the global MPI since it was conceived in 2010.

Aggregating and Disaggregating the Global MPI
When estimating the global MPI and its component indices, each one of the underlying national surveys has a specific complex survey design, by which each household is assigned a sampling weight.In each national survey, these weights are inversely proportional to the probability of selection within the specified sampling frame (ICF International, 2012;Khan and Hancioglu, 2019).Thus, they expand the sample in each country to the corresponding population size at the moment of the survey.Therefore, each national survey, in principle, can produce unbiased estimators of M 0 , H, and A for each country. 11Depending on sample design it may be possible to obtain poverty estimates for subnational regions (such as provinces, departments, or states), urban and rural areas, for instance.
Formally, as the global MPI relies on the AF method, the value of the MPI of country u = {1⋯U }, denoted as MPI X u , can be disaggregated by a set of mutually exclusive exhaustive subgroups  = 1, ⋯, m (e.g., subnational regions, urban-rural) as: where n u is the population in country u, and MPI (X u ) denotes the MPI of sub- group in country u with a population sized n u .For notational convenience, we omit the parameters of the poverty identification function in the above equation to highlight on which data a particular estimate depends.Equation (1) states that country level MPI can also be obtained as population weighted average of the dis- aggregated subgroup-specific MPIs.In turn, H can be disaggregated following the same procedure.Moreover, A can also be disaggregated in a similar way replacing the country and subgroup population sizes by the number of poor people in the corresponding levels.
Starting from the country level, the H, A, and MPI values can be aggregated into a supranational level.This could be world regions or the developing world as represented by our 105 countries.Essentially, aggregation follows a similar logic as the disaggregation procedure that we just described.For instance, the MPI value of the supranational level of interest, denoted as MPI X , can computed as: where X refers to the pooled data representing the supranational level, which has a population of size n .This means that MPI X can be obtained as population weighted average of the country level MPIs.Consequently, subgroup estimates from the different countries are related to MPI X as follows: Note that the above equation shows that MPI (X u ) can in fact be conceived as the result of a two-level disaggregation of MPI X with the appropriate population weights.
This procedure emphasizes the vital role of population weights to obtain meaningful supranational multidimensional poverty estimates.On one hand, population weighting aligns with the global MPI's core conceptual underpinning, namely Amartya Sen's people-centered approach to human development (Sen, 2009).A simple unweighted average of all country-level MPIs would assign a life in India, for instance, a much lower importance than a life in, say, the Maldives.On the other hand, a more technical way to understand the need of population weighting is to view our pooled data as one stratified sample representing the supranational region of interest.To adequately reflect this population, sampling weights must be rescaled using the country-specific ratio n u ∕n .
(1) The aggregation procedure allows us to discuss a difficult data constraint that is currently impossible to circumvent with the existing data: not all the national data sets are collected in the same time span.The survey used ranges between 2006 and 2016.Thus, the "raw" pooled data set expands to an abstract population size that hardly has a meaningful interpretation, as it is a mixture of national population sizes at different times.Therefore, if all indicators were identical, differences between world regions or countries, for instance, could be attributable to (1) different survey years or (2) different levels of measured poverty.This creates challenges in interpreting cross-regional differences.To recover the logic of our analysis, we operationalize the population weighting procedure by computing population shares in a common time period using known real population sizes.This amounts to rescaling the sampling weights for each national survey so that they add up to the population of that country in the chosen common time period.In 2018, we rescaled the weights to add up to the 2016 population size (UNDESA, 2017).This facilitates international comparisons, and it is a convention used in the global MPI reports to aggregate using a common population year (Alkire et al., 2018).As a result, if the population date post-dates the survey, and if population has grown, and if poverty is declining, this convention will overstate the number of poor persons-hence giving an incentive to countries that may have reduced poverty to update surveys regularly.The following results must be interpreted keeping this in mind.

the reviSed global mpi: what inSightS do we really gain?
Let us begin our analysis by discussing the prevalence of deprivations one by one, and the extent to which they overlap.Subsequently, we will assess the patterns of multidimensional poverty in the developing world highlighting heterogeneities between world regions, urban and rural areas, and age groups.

A Dashboard of Deprivation Indicators
An analysis of deprivation headcount ratios one at a time is the simplest way to start a description of poverty patterns in the developing world.This is akin to taking a dashboard approach to multidimensional poverty, which focuses on the marginal indicator distributions (Ravallion, 2011).These are termed uncensored headcount ratios (Alkire et al., 2015) and they correspond to the column-wise mean of the deprivation matrix g 0 .While analysing these headcount ratios, however, one must keep in mind that these figures result from an estimation performed before the identification and aggregation steps, so they do not correspond to a full-fledged poverty analysis.The focus is not on the poor population, but on the society as a whole, and the interconnections between the indicators are cast aside, for now.
Globally, the highest aggregate uncensored headcount ratios correspond to cooking fuel (44.8 percent), housing (39.6 percent), and sanitation (37.0 percent) (Figure 1).Deprivations in these indicators afflict large portions of the population, regardless if and how one gauges their poverty status, but there are stark differences between world regions.Deprivations in nine of the ten indicators are unambiguously higher in Sub-Saharan Africa.Considering 95 percent confidence intervals, the uncensored deprivation headcount ratio in this region is over twothirds in cooking fuel, housing, sanitation, and electricity.
The uncensored headcount ratios in nutrition are quite similar in South Asia and Sub-Saharan Africa-around 38 percent.Otherwise, the uncensored headcount ratios in Sub-Saharan Africa are statistically significantly highest among all world regions in all the other nine indicators.The prevalence of hardships in this region regularly emerges even through a purely monetary approach to poverty (Ravallion, 2016;World Bank, 2018).From a global perspective, the uncensored headcount ratios of nine indicators are over 10 percent.The only exception is child mortality for which we observe very low poverty headcount ratios in every region.This coheres with the low levels of under-5 mortality globally in recent years (UN, 2015b;You et al., 2015), and is also aligned with Bishai et al. (2016) who make a case for improvements in coverage of health determinants as a main driver of fast reductions in child (and maternal) mortality in the developing world.

Joint Distribution of Deprivations
The analysis of each indicator one by one provides useful insights, but considering them as separate entities overlooks their interlinkages or natural interconnections.Source: Own calculations based on country-specific microdata.People who suffer one deprivation are very likely to face other deprivations at the same time.As shown in Figure 2, at a global level, around 27 percent of the population do not suffer any deprivation and 21 percent face exactly one single deprivation.The majority of the population (52 percent) are multiply deprived; they face two or more deprivations.However, there is a high level of heterogeneity by world region around this global pattern.In South Asia, around 17 percent of people face one deprivation and roughly 16 percent of people face two or three simultaneous deprivations.This means, for instance, that multisectoral policies with unified targeting mechanisms have more chances of being effective in the battle against these joint deprivations.In Sub-Saharan Africa, however, the most likely situation is to suffer five, six, or seven simultaneous deprivations-13-15 percent of the population fall in each of these three categories.The likelihood of living deprivation-free is the lowest in this region.This depicts much larger, more complex challenges for policymaking.More actors and institutions need to align efforts in the form of multisectoral programs, which are challenging given some persistent institutional fragility (Deléchat et al., 2018;McKay and Thorbecke, 2019).However, if aligned, it may be possible to reduce deprivations synergistically.
The higher number of simultaneous deprivations experienced by individuals has important consequences for policymaking.The challenges that they raise for policymaking in South Asia and South Africa may not be faced without accepting that poverty is multidimensional and that no one-proxy will do to fully grasp the livelihood of poor people.To see this, let us consider the distribution of the number of deprivations conditional on being deprived in each indicator.Figure 3 considers 100 percent of the persons who are deprived in a given indicator such as child mortality, and plots the percentage of them who are deprived in differing numbers of other indicators simultaneously.Implicitly, indicators are here equally weighted.Taking into account the confidence intervals of these conditional frequencies, facing one single deprivation alone is never the most likely situation (Figure 3).12 Figure 3 is a graphical representation of the information presented in Table 2, which shows only the mean point estimates.We can see that the proportion of persons who are only deprived in electricity or assets are less than 1 and 2 percent, respectively.We also see that those deprived only in housing are around 4 percent,   and those deprived only in child mortality, school attendance, years of schooling, and sanitation are between 5 and 10 percent.Only in three indicators of the ten that are included in the global MPI, more than one in ten persons are only deprived in that indicator: water, cooking fuel, and nutrition.Thus, across all ten indicators, between 81 and 99 percent of the population in the developing world deprived in that indicator experience one or more additional deprivations.At the bottom of Table 2, we can also see for every one of the ten indicators, the average number of additional deprivations is between 3 (nutrition and cooking fuel) and 5 (electricity and assets).
Based on this, we argue that the global MPI is a useful way to account for the direct interlinkages across these deprivations.This index summarizes the multidimensional nature of poverty as measured by the manifestation of manifold deprivations, while accounting for their interlinkages.

The Global MPI, Its Components, and Related Measures
The overall incidence of multidimensional poverty in the developing world is around 23.2 percent, and the average poor person experiences around 49.5 percent of the weighted deprivations.The population-weighted average value of the global MPI is 0.115.To delve deeper, we present the regional heterogeneities (see Table 3).
It is statistically unambiguous that Sub-Saharan Africa followed by South Asia have the largest proportions of their population living in poverty (57.7 percent and 31.3 percent, respectively).However, there is no direct relationship between the incidence and the intensity of poverty.In Sub-Saharan Africa and in the Arab States, we find that the average poor person experiences more than half of the weighted deprivations (54.9 percent and 50.8 percent, respectively).Balancing incidence and intensity, and including 95 percent confidence intervals, the adjusted headcount ratio depicts a clear regional poverty ordering with Sub-Saharan Africa (0.317) as the poorest region, followed by South Asia (0.143) and the Arab States (0.098).
When it comes to severe multidimensional poverty, Sub-Saharan Africa is the most affected region, with 35.3 percent of this population facing this condition.The region is also home to the largest number of severe poor-342 million people.The incidence of severe poverty in South Asia is 11.5 percent (200 million), whereas in the Arab States it is around 10 percent (see Table 4).
So far, we have focused on people who are poor, with varying intensity, by the global MPI.We also want to stress that South Asia has the largest incidence of vulnerability to poverty in the developing world (18.9 percent, see Table 3).It is also noticeable that a large proportion of the population are vulnerable to poverty in Sub-Saharan Africa (17.3 percent), which confirms the marked challenges for policymaking in this region.On average, three of every four persons in Sub-Saharan Africa are either poor or vulnerable to multidimensional poverty.
After identifying the part of the population suffering multidimensional poverty across various poverty cutoffs, naturally the question arises as to how they are poor.For this, we take a step further with respect to our previous analysis of uncensored headcount ratios and identify the proportion of the population who   are poor and deprived in each indicator.These proportions are called the censored headcount ratios (Alkire et al., 2015).They are denoted as h j , j = 1⋯10 and they can be computed as the mean of corresponding column of matrix g 0 : Unlike their uncensored counterparts, the censored headcount ratios depend on the poverty cutoff and thus they focus on the proportion of people who are poor and deprived in each indicator.
Compared to South Asia and Sub-Saharan Africa, the censored headcount ratios are low in East Asia and the Pacific, Europe and Central Asia, and Latin America and the Caribbean (see Figure 4).In contrast, the censored headcount ratios in Sub-Saharan Africa are highest for every single indicator, followed by those in South Asia.
There are some stark differences between the uncensored and censored headcount ratios in different regions.These differences denote that some deprivations are prevalent across the population, but are not necessarily a condition of the poor, because people deprived in those indicators are not deprived in at least one-third of the weighted indicators overall.This may be due to nonsampling measurement issues, preferences, data issues, or pervasive singleton deprivations.Empirically, the indicators that are most often censored are nutrition, water, housing, and cooking fuel in East Asia and the Pacific; sanitation in Latin America and the Caribbean; and sanitation, housing, and cooking fuel in South Asia.
So far, our assessment of the revised global MPI results has focused on proportions of the population.However, the actual number of people suffering poverty and deprivation is also important.Whereas South Asia and Sub-Saharan Africa are home to the largest number of poor people (546 and 560 million, respectively), the number of people vulnerable to poverty is highest in South Asia and East Asia and the Pacific (330 and 313 million, respectively) (see Figure 5).Although according to point estimates there are more MPI-poor people in Sub-Saharan Africa than in South Asia, if we consider the standard error of these estimates, the number of MPI-poor people in these regions is actually undistinguishable. 13In contrast, the number of people suffering severe multidimensional poverty (defined as those deprived in 50 percent or more of the weighted indicators) is unambiguously highest in Sub-Saharan Africa (342 million), followed by South Asia (200 million).

Poverty in Selected Population Subgroups
We will close out this section by scrutinizing two key disaggregations of the global MPI values at the country level, which can then be aggregated into the regional level using the appropriate population weights.The first one distinguishes 13 To check that this important result is robust to the year selected for the known population size (2016) to exactly reproduce the results in (OPHI, 2018), we also compared the number of poor people in Sub-Saharan Africa and South Asia taking (a) 2015 and (b) the country-varying survey year for the known population sizes.In both cases, we confirm that the estimated number of poor people in both regions are statistically undistinguishable.Taking 2015 population sizes and 95 percent confidence levels, the number of poor people in sub-Saharan Africa is between 314 and 380 million, whereas that in South Asia is between 346 and 362 million.Taking the country-varying survey year population sizes, these bounds are 313-379 million people in sub-Saharan Africa and 346-364 million people in South Asia.urban and rural poverty14 (see Table 5), and the second disaggregates by age groups (see Table 6), to show the share of people in different age cohorts who live in MPI poor households.
For policy purposes, it is useful to compare the poverty measures of each subgroup with the global aggregate.We find that some 36 percent of the global rural population are MPI poor.In contrast, only 8 percent of the global urban population are MPI poor.The subgroup disaggregation also shows that only in two world regions, namely South Asia and Sub-Saharan Africa, poverty exceeds the global average.In South Asia and Sub-Saharan Africa, 41 percent and 73 percent of the rural population, respectively, are MPI poor.In fact, the Sub-Saharan Africa figure is around two times that of the average in the developing world.
In terms of age group, we find that a higher share of younger children lives in MPI poor households.In 105 countries covered by the global MPI, some 38 percent of the children under 10 percent and 28 percent of children between 10 and 17 years are MPI poor.This finding is in line with other studies (World Bank, 2018).Source: Own calculations based on country-specific microdata.

robUStneSS oF the reviSed global mpi
As we mentioned earlier, one particular MPI specification underlies all the results that we have discussed so far.When the MPI was first released in 2010, there was some skepticism about its robustness to alternative parametrizations in the academic and policy-making spheres (see Ferreira 2011 for a discussion on this matter).However, this index was found to be robust to changes in (1) the dimensional weights and (2) the poverty cutoff in Alkire andSantos (2010, 2014), and Alkire et al. (2015).For comparative purposes, we evaluate the robustness of the revised index to the same parameters as the 2014 paper.For the same reason, similar alternative parametrizations are chosen to perform a meaningful comparative local robustness analysis of the original and revised versions of the global MPI.

Shifting the Poverty Cutoff
Let us first visually describe some robustness patterns by assessing the H and MPI complementary cumulative distribution functions (CDF) over different pov- erty cutoffs k.In Figure 6, we can see that H and MPI for Sub-Saharan Africa are the highest, and conversely, they are the lowest in Europe and Central Asia.These are powerful results in that they hold true over the entire set of possible poverty cutoffs.
In an inspection of the pattern of MPI levels, one can identify three groups of world regions.Sub-Saharan Africa is undoubtedly the poorest region, followed by South Asia and the Arab States as regions with middle MPI levels.East Asia and the Pacific, Latin America and the Caribbean, and Europe and Central Asia are the least poor world regions.
In a general way, results that hold true over the entire range of k are the exception.As both H and MPI are monotonic decreasing functions of k, differ- ent population sub sets are effectively identified as multidimensionally poor by adopting distinct kvalues.Each one of these subsets regroups people who expe- rience joint deprivations to different extents and with varying intensity.Their livelihoods are different, and the types of policies required to improve their situation should build upon these differences to be effective.Thus, we argue that if changes arise due to shifts in k, they have a meaningful interpretation and they may usefully point toward distinct poverty analyses and policy actions against different patterns and intensities of joint deprivations.We reiterate that instead of delving deeper into a general robustness analysis of H and MPI distributions, it may be more informative to focus on local robustness within a relevant neighborhood of k (World Bank, 2017, p.171).One useful way to establish this neigh- borhood is to build upon the difference made between the poor population, those living in severe poverty, and those who are vulnerable to poverty.Let us recall that the multidimensionally poor people were identified with the cutoff k = 1 3 , the severely multidimensionally poor people with k = 1 2 (which is a subset of the former group), and people who are vulnerable to multidimensional poverty are identified if 1 3 > c i ≥ 1 5 .These definitions implicitly define the range k ∈ 1 5 ; 1 2 as the relevant range in which to assess the local robustness of H and MPI around the baseline cutoff k = 1 3 .Restricting our visual analysis of Figure 6 to k ∈ 1 5 ; 1 2 , we find that the H and MPI distributions of South Asia are the second highest in the developing world, followed by the Arab States.We cannot establish clear differences between East Asia and the Pacific and Latin America and the Caribbean, as their complementary CDF cross each other.For kvalues close to 1 5 (i.e., vulnerability), Latin America and the Caribbean tend to be less poor by H and the MPI.This means that the likelihood of being vulnerable to poverty is lower in this region.However, this relative advantage is not preserved for kvalues closer to 1 2 (severe poverty), meaning that the likelihood of suffering severe poverty tends to be similar in both regions.
To start describing the robustness of H and MPI to changes in kvalues within the relevant neighbourhood, let us discuss the extent to which the absolute country poverty orderings shift. 15We focus on rank changes corresponding to shifts in the position of each country in the poverty ordering.In Figure 7, we plot the country rank by H (panel a) and MPI (panel b) for different kvalues against the rank at the baseline (k=1/3). 16The closer the points are to the diagonal, the closer the country rank under the alternative kvalue is to the rank at the baseline.We can clearly see that MPI orderings are more stable than H orderings, and that this is particularly true for the least poor countries (upper-right side of the plots).The median Euclidean distance of country ranks by H is 3.74, whereas it is 2.89 for rankings by the MPI .Thus the adjustment of H by the average intensity of the poor (A) to yield the MPI endows the latter with a higher absolute country rank stability.Partly, this is a consequence of the monotonic nature of H (decreasing) and A (increasing) with respect to k, which attenuates the responsiveness of MPI with respect to k shifts compared to H.However, more than a purely technical result, we also argue that this points to the practical superiority of MPI compared to H as for international poverty comparisons. 15We choose the country as the unit of analysis of our formal robustness tests to align with a standard strand of literature adopting the country poverty orderings as the object of sensitivity analysis for internationally comparable measures (see, e.g., Noorbakhsh, 1998 andPermanyer, 2011 for the HDI; Foster et al., 2013 for the HDI, the Index of Economic Freedom (IEF), and the Environmental Performance Index (EPI); Alkire and Santos, 2014 for the previous version of the global MPI). 16All the rankings for each k value consider ties detected by hypothesis tests comparing the values of H and MPI for the different countries.Going beyond single-country descriptions, let us now focus on country pairwise comparisons following the approach of Alkire and Santos (2010) and Alkire et al. (2015).We evaluate the extent to which the ordering between pairs of countries established at the baseline specification is preserved if the poverty cutoff shifts across the relevant range 1 5 ; 1 2 , i.e., several different MPI specifications simultaneously.Establishing the order of two countries in terms of their poverty relies on statistical hypothesis testing to take sampling error into account.Therefore, we can distinguish three possible outcomes: poverty is significantly higher in one country, the other country, or they are not significantly different from each other.We consider a pairwise comparison to be robust if the pairwise poverty order is preserved across all alternative specifications.One way to summarize the results of these hypotheses tests is to compute the proportion of robust pairwise country orderings of all possible pairwise comparisons, denoted as R pwc .In a variant of this approach we only consider those pairwise comparisons, which we found to be significantly different under baseline, denoted R * pwc .The motivation for this is that significant differences between countries are of particular interest to policy makers. 17These figures are presented in Table 7.
It is important to consider how to interpret all analyses of pairwise comparisons in what follows.As should be self-evident, it is not possible to assess the extent of robustness across world regions based on the percent of pairwise comparisons alone.Such assessments must consider, in addition, the number of countries being compared, as well as their mean poverty level and the dispersion around it.We thus interpret our results keeping this in mind and take an empirical approach.Further research may develop refined methods, which explicitly address these issues.
First, for the pairwise comparisons between the entire set of countries ("Developing world" line in Table 7), nearly 95 percent of country pairwise orderings by H and MPI are found to entail significant differences at the baseline.Moreover, we find R * pwc of around 94 percent for the entire developing world.Alkire and Santos (2014) found a slightly higher rate (95.7 percent) in a comparable robustness analysis of the 2010 version of the MPI.However, they considered k = 1 5 and k = 2 5 as alternative poverty cutoffs; therefore, finding a similar robustness rate when the upper-limit alternative cutoff is pushed to k = 1 2 depicts a higher level of robustness of the revised index.
In an analysis by world regions, we find that the overall robustness figures mask stark differences between world regions.R * pwc by MPI is above 90 percent for every world region except for Europe and Central Asia and South Asia, where it is just over 66 percent and 80 percent, respectively, although as mentioned above this is not decisive because of the lower number of countries.Overall, the robustness of H as measured by the proportion of robust pairwise comparisons that are significant at the baseline is lower compared to the MPI (see Table 7).
Having compact summary measures of robustness is undeniably useful, but to be clear, two elements need to be taken into account to meaningfully interpret the ratios presented in Table 7 (see Alkire and Santos, 2014).The first is that regions with a high number of countries (such as Sub-Saharan Africa) may tend to show higher robustness due to the larger number of comparisons that are possible.The second element is that regions where the differences between countries in terms of H and MPI are high will tend to show a higher stability because the common range between poverty levels is wider.Our results should be interpreted taking this into account.Note for instance, that Europe and Central Asia is the least poor region in the developing world (with simple mean incidence of 2.38 percent and MPI value 17 The formalization of the ratio is explained in Appendix A.  of 0.009), and it is also the region where the levels of H and MPI are relatively less dispersed (with standard deviations of 3.19 percent and 0.013, respectively).
The overall low levels of inequality across countries in this region make it difficult to arrive at a stable pairwise ordering by H and MPI.We stress that is not neces- sarily a negative result, as it reflects the fact that poverty levels in this region are "clustered" in the lower extreme, depicting a favorable state of affairs in terms of poverty and inequality between countries.

Shifting the Weighting Structure
Let us now focus on a robustness analysis to changes in the dimensional weights.In a strict sense, there is an infinite combination of alternative weights, and we reiterate that a full robustness evaluation is beyond the scope of this paper (see Alkire et al., 2019 for such analysis).Following Alkire and Santos (2014), we consider three sets of plausible weights that could make sense in the practical academic and policy-making spheres, while also being easy to comprehend widely.They consist of considering, in turn, one dimension to be twice as important as the other two.Effectively, these alternative weights are computed based on different arrangements of the trio (25 percent, 25 percent, and 50 percent) (see Foster et al., 2013).These weighting structures cover a parsimonious, yet meaningful subset of alternative options-they are local changes in these parameters (World Bank, 2017, p. 171).Documenting that H and MPI are sta- ble poverty measures within a subset of relevant, plausible range of parameters constitutes important evidence of their usefulness for policymaking, and for subsequent cross-country research building upon them.Not all possible parameter values are practically relevant, thus the analysis that we offer here is not aimed to be a general robustness analysis in the sense of the World Bank (2017), nor can it be directly extended to non-additively separable weighting structures (see Alkire et al., (2019) and Azpitarte et al., (2020) for research in this direction).
Let us first conduct a robustness analysis of each country's absolute positions in the poverty orderings by H and MPI. Figure 8 depicts the absolute rank shifts due to changes in the weight structure and it is interpreted in the same way as Figure 7.This time, however, we do not observe a dissimilar response of H and MPI to changes in the weight structure.Largely, we can see that the absolute country ranks by H and MPI are preserved under alternative weight structures.The average Euclidian distance with respect to each country's mean rank is 36.08 for H and 35.80 for MPI.This corroborates that absolute rank shifts by both H and MPI are similar in magni- tude.Furthermore, we do not observe distinct rank shift patterns arising from giving a 50 percent weight to any particular dimension, nor do we detect a clear relationship between rank shifts and the country rank at the baseline.These results are important in that they confirm that the absolute country orderings by the global MPI aggregate poverty figures are robust to differing views regarding the relative importance of each dimension in the index.
Let us now turn to a country pairwise comparisons analysis.Following the same approach introduced above, we now assess the robustness of the baseline measure of pairwise poverty orderings across the four weighting structures simultaneously.alternative weighting structures.A directly comparable analysis was conducted in Alkire and Santos (2014) for the 2010 global MPI specification, where they found a rate of 88.9 percent.We can thus affirm that the country ordering by the 2018 specification of this index is no less stable as the original one to changes in the dimensional weights.

the reviSed and original global mpi: an empirical compariSon
To empirically evaluate the consequences of the revision, we produced estimates for the original version with the exact same data used for the estimation of the revised version.In that sense, our figures do not actually reflect the original MPI values reported in 2010 (UNDP, 2010; Alkire and Santos, 2014), but rather a set of counterfactual estimations that are useful only for evaluative purposes.We compare actual (revised specification) and counterfactual (original specification) figures in three ways.First, we focus on differences between aggregate MPI figures, then we assess differences in indicator deprivation headcount ratios, and finally, we perform a country pairwise comparison analysis between the 2010 and 2018 indicator specifications using the 2018 data sets.
In a nutshell, we find that the range of the overall, global proportion of people who live in multidimensional poverty (H) is very similar after the revision.With 95 percent confidence intervals, the level of H level ranges between 22.6 and 23.9 percent in the revised specification and 23.4 and 24.7 percent in the original one.In that sense, the differences induced by the revision are certainly small, yet given the large sample at hand (and the ensuing small standard errors for our estimates); hypothesis tests on the difference of H between both specifications show that the difference, although small, is statistically significant (see Table 9).Importantly, however, even this strict way of assessing robustness finds a non-statistically significant difference for the proportion of poor people in Sub-Saharan Africa, the poorest region in the world.This is also true for Europe and Central Asia if we take a 5 percent significance level.The similar range of poverty incidence in these regions directly implies a similarly stable nature of the number of people identified as poor in both specifications.
Turning now to the intensity of poverty, A, we find that it has significantly shifted in every region due to the revision.It ranges between 49.3 and 49.7 percent, in the revised specification, and between 45.3 and 45.9 percent in the original one.The biggest intensity shift is found in Europe and Central Asia (+15.3 percentage points), followed by Latin America and the Caribbean (+10.4 pp).
Finally, the MPI levels for the whole developing world range between 0.112 and 0.119 in the revised specification and 0.116 and 0.123 in the original one.The level of the index is around the same range after the revision, although the statistically significant shifts in A (and in H for some regions) yields statistically signifi- cant differences for the MPI as well (see Table 9).
To gain a more in-depth insight about changes in the intensity of poverty, let us present a disaggregated analysis by indicator.Not only will we present how the revision modified the prevalence of deprivations among the poor (censored headcount ratios), but also among the entire population (uncensored headcount ratios).
The deprivation headcount ratios corresponding to four of the five revised indicators have significantly increased in the revised specification.The only   exception is the assets indicator, for which censored and uncensored headcount ratios remained unchanged, despite the inclusion of two items-computer and animal cart in the revision.This result is aligned with Vollmer and Alkire (2020) who found that these two items have relatively low difficulty and discrimination parameters in an Item-Response Theory analysis.This reflects that they are likely to be associated with the other items included in the assets indicator.
The censored and uncensored deprivations in child mortality are dramatically lower in the revised global MPI-by around 10 percentage points (see Figure 9).This is because the revised indicator only considers deaths occurred during the last 5 years preceding the survey-as opposed to the household ever having suffered the death of a child in the original version of the global MPI.The lower headcount ratios observed in the revised index are more accurate as well as policy salient.This is in line with the success in reducing the global under-5 mortality rate by more than half between 1990 and 2015 (90-43 per 1,000 children) (UN, 2015a).Similarly, You et al. (2015) have estimated that around 94 million children would die before they are 5 years old by 2030 if each country maintains their observed mortality rate in 2015.However, they also estimate that more than one-fourth of these could be prevented if each country manages to keep the 2000-2015 average annual reduction pace between 2016 and 2030.Conversely, the censored and uncensored deprivation headcount ratios corresponding to nutrition, education, and housing are all higher in the new version of the MPI-by around 4 pp., 3 pp., and 8 pp., respectively.In the revision, these indicators have been assigned more demanding deprivation cutoffs, which better align with the international standards evinced in the SDG indicators.
In a more detailed cross-country analysis, we find that the MPI distribution across the 105 considered countries has remained largely unchanged.As depicted in the quantile-quantile plot in Figure 10, the shape of both MPI structures' distributions is similar.Their corresponding quantiles match closely, and no systematic differences can be detected across the entire observed range of MPI values.Such a close distributional resemblance probably translates into a highly robust country ordering by the MPI (Alkire et al., 2015).To explore this, we performed a pairwise comparison analysis where the alternative specification is defined as the original definition of indicators.
Taking into account both significant and non-significant poverty orderings at the baseline (i.e., the revised specification), 93.02 percent of the possible country pairwise comparisons are identical in both MPI versions (4,982 of 5,356).This rate can be interpreted a summary figure of the overall robustness of the MPI to the revision.To gauge the robustness of strict poverty orderings only, we can focus on 86.07 percent of the possible pairwise comparisons (4,610 of 5,356) that are found to be strict in the 2018 MPI specification.Practically, all of them (99.15 percent) are identical in the 2010 specification (4,571 of 4,610).In our view, this is a quite powerful result showing that MPI revision manages to better identify deprivations, while maintaining country poverty orderings largely unchanged.

conclUding remarkS
In 2018, the definitions of five of the ten global MPI indicators were revised.The motivation for the revision was to align the global MPI closer to the 2030 development agenda, and this was made possible by improvement and expansion in indicator availability in surveys.This is the first paper to provide comprehensive analyses of the poverty pattern in the developing regions of the world using the revised global MPI.The empirical assessment is focused on three aspects.First, we assess the extent to which people experience overlapping deprivations across indicators and provide insights on the state of multidimensional poverty across world regions, and by their urban-rural locations and age groups.Second, we test the robustness of the revised global MPI to changes in poverty cutoffs and dimensional weights.Third, we extend the robustness analyses by comparing the poverty patterns and country poverty ranking between the original and revised global MPI.
Our results show that the recent revision results in lower uncensored deprivation rates in child mortality, whereas rates for nutrition, education, and housing increaseall as theoretically expected.We also find this to translate into a higher intensity of poverty, whereas the headcount ratio somewhat decreases, leading the MPI to barely change.Moreover, our results also indicate that 81-99 percent of the population in the developing world who are deprived in one indicator experience one or more additional deprivations.This striking finding confirms the interlinkages across deprivations and the need to view them jointly.However, joint distributions vary: the proportion of persons who are only deprived in one indicator, or in two, three, or up to nine additional indicators, varies greatly across the ten considered indicators.
The global MPI identification strategy censors the deprivations of non-poor persons.Exploration of the patterns by indicator across all major world regions and using different poverty cutoffs reveal stark regional differences in terms of the prevalence of indicators and extent of censoring.This underscores the value added of a counting approach in bringing different patterns of interlinkages across deprivations into a common framework.
Across the entire set of countries, 94-95 percent of country pairwise orderings by H and MPI are robust for poverty lines from 20 to 50 percent, and almost 90 per- cent of country pairwise comparisons for MPI (88 percent for H) are robust across the weighting scheme of 25-50 percent per dimension.Comparing these results to the original MPI, we find that revised global MPI country orderings across a plausible set of poverty cutoffs and weights are no less stable than the original MPI.
Estimating the global MPI is not short of challenges.One sustained challenge is basing the estimates on a more recent data.For the revised global MPI data applied in this paper, the most recent surveys that were available for Azerbaijan, Djibouti, Somalia, and Uzbekistan were carried out in 2006; and in Vanuatu it was 2007.We recognize that the population in these countries is small, as such, unlikely to change the global poverty pattern presented in this paper.However, poverty measurement must strive to capture people's most recent lived experience.The second challenge is the limited indicator availability within the surveys used.We had hoped to augment the revised global MPI with additional dimensions such as on work, security, to name a few.This proved challenging as data related to these dimensions at a global scale is non-existing.These remain as missing dimensions.We recognize that quantity and quality of internationally comparable multi-topic household surveys have improved significantly in the last decade.The DHS is typically updated, on average every 5 years, while MICS increasingly has coverage for every 3 years.Yet, there is scope for a continuous call on reducing the gap between survey releases and improving data.reFerenceS

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2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.

Figure 1 .
Figure 1.Uncensored Headcount Ratios by Indicator and World Region Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b) NU: nutrition; CM: child mortality; YS: years of schooling; SA: school attendance; CF: cooking fuel; SN: sanitation; DW: drinking water; E: electricity; HO: housing; AS: assets.(c) Vertical lines represent 95 percent confidence intervals.Source: Own calculations based on country-specific microdata.

Figure 2 .
Figure 2. Number of Simultaneous Deprivations by World Region Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b) Vertical lines represent 95 percent confidence intervals.Source: Own calculations based on country-specific microdata.

Figure 3 .
Figure 3. Distribution of Additional Deprivations by Indicator Note: (a) Bars sum up to 100 percent of the deprived population in each indicator.(b) NU: nutrition; CM: child mortality; YS: years of schooling; SA: school attendance; CF: cooking fuel; SN: sanitation; DW: drinking water; E: electricity; HO: housing; AS: assets.(c) Vertical lines represent 95 percent confidence intervals.Source: Own calculations based on country-specific microdata.
Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b) lb and ub denote, respectively, lower bound and upper bounds of the 95 percent confidence intervals.© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.

Figure 4 .
Figure 4. Censored and Uncensored Headcount Ratios by World Region Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b) NU: nutrition; CM: child mortality; YS: years of schooling; SA: school attendance; CF: cooking fuel; SN: sanitation; DW: drinking water; E: electricity; HO: housing; AS: assets.(c) For reasons of readability, we omit confidence intervals.Source: Own calculations based on country-specific microdata.

Figure 6 .
Figure 6.Complementary Cumulative Distribution Functions of H and MPI by World Region Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b) Gray-shaded regions represent 95 percent confidence intervals.Source: Own calculations based on country-specific microdata.

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Figure 7 .
Figure 7. Absolute Country Poverty Orderings by H and MPI for Different k-Values Source: Own calculations based on country-specific microdata.

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Figure 10 .
Figure 10.Quintile-Quintile Plot: Global Distributions of MPI Source: Own calculations based on country-specific microdata.

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, TV, telephone, bike, motorbike, or refrigerator, and
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TABLE 2
Note: NU: nutrition; CM: child mortality; YS: years of schooling; SA: school attendance; CF: cooking fuel; SN: sanitation; DW: drinking water; E: electricity; HO: housing; AS: assets.Source: Own calculations based on country-specific microdata.© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.
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TABLE 4
mpi and intenSity (a) by world region Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b)lb and ub denote, respectively, lower bound and upper bounds of the 95 percent confidence intervals.Source: Own calculations based on country-specific microdata.14754991, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/roiw.12573 by Readcube (Labtiva Inc.), Wiley Online Library on [29/10/2022].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License © 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.
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TABLE 5
diSaggregation oF h, a, and mpi by Urban-rUral area and world regionS , 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/roiw.12573 by Readcube (Labtiva Inc.), Wiley Online Library on [29/10/2022].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Note: (a) lb and ub denote, respectively, lower bound and upper bounds of the 95 percent confidence intervals.(b) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.Source: Own calculations based on country-specific microdata.© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.Note: (a) lb and ub denote, respectively, lower bound and upper bounds of the 95 percent confidence intervals.(b) AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.Source: Own calculations based on country-specific microdata.14754991© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.

TABLE 7
pairwiSe compariSonS USing alternative poverty cUtoFFS East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b) R pwc denotes the proportion of country pairwise poverty orderings that are similar in all the alternative k-values.In this proportion, countries that have similar levels of poverty at the baseline specification are considered.R * pwc is similar to R pwc , but omits country poverty orderings at the baseline that show undistinguishable poverty levels.(c) The publicly available data for South Africa (NIDS 2014-2015) lack information about the primary sampling unit and the strata, so standard errors of the estimates for this country cannot be computed.Source: Own calculations based on country-specific microdata.© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.
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TABLE 8 pairwiSe
Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.(b)Rpwc denotes the proportion of country pairwise poverty orderings that are similar in all the alternative weight structures.In this proportion, countries that have similar levels of poverty at the baseline specification are considered.R * pwc is similar to R pwc , but omits country poverty orderings at the baseline that show undistinguishable poverty levels.(c)Wecan only perform pairwise comparisons among 104 of the 105 considered countries.The publically available data for South Africa(NIDS 2014(NIDS  -2015) )lack information about the primary sampling unit and the strata, so standard errors of the estimates for this country cannot be computed.Source: Own calculations based on country-specific microdata.
Note: (a) AS: Arab States; EAP: East Asia and the Pacific; ECA: © 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.

TABLE 9
AS: Arab States; EAP: East Asia and the Pacific; ECA: Europe and Central Asia; LAC: Latin America and the Caribbean; SA: South Asia; SSA: Sub-Saharan Africa.Source: Own calculations based on country-specific microdata.14754991, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/roiw.12573 by Readcube (Labtiva Inc.), Wiley Online Library on [29/10/2022].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Note: © 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of International Association for Research in Income and Wealth.