metadata: authors: 0: author: Decerf,Benoit Marie A
1: author: Fonton,Kike Yra
count: Nigeria
docna: 0: docna: Reconceptualizing Global Multidimensional
            Poverty Measurement, with Illustration on Nigerian Data
docty: Policy Research Working Paper
abstracts: cdata!: Multidimensional poverty measures can in
            theory make well-being comparisons that are less biased than
            those solely based on monetary poverty. However,
            multidimensional poverty measures suffer in practice from
            limitations that have led to criticisms. This paper presents
            the case for multidimensional poverty measures, two
            criticisms against their current implementations, as well as
            recently proposed solutions to improve on these criticisms.
            The paper develops a method for implementing these solutions
            in practice. The resulting well-being indicator is used to
            compare well-being across Nigerian states in 2019. This
            empirical illustration suggests that these solutions may
            substantially affect well-being comparisons. The paper also
            quantifies the potential bias inherent to comparing
            well-being solely based on monetary poverty. The results
            find substantially different well-being comparisons between
            the proposed well-being indicator and monetary poverty even
            though monetary poverty was (i) high in Nigeria in 2019 and
            (ii) very heterogeneously distributed across Nigerian
            states; and (iii) is integrated as one component of the
            proposed well-being indicator.
display_title: Reconceptualizing Global
            Multidimensional Poverty Measurement, with Illustration on
            Nigerian Data
listing_relative_url: /research/2023/10/34173629/reconceptualizing-global-multidimensional-poverty-measurement-illustration-nigerian-data
topicv3: Poverty m1326687 695,Poverty Measurement and Analysis m1326941 707,Mortality m1504365 3661
publishtoextweb_dt: 2023-10-02T00:00:00Z
dois: 10.1596/1813-9450-10577
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 49
author_keys: 0: author_key: 1947055
1: author_key: 1796685
model_extractions: Policy Research Working Paper 10577 Reconceptualizing Global Multidimensional Poverty Measurement, with Illustration on Nigerian Data _Benoit Decerf Kike Fonton_ Development Research Group & Poverty and Equity Global Practice October 2023 A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.
Policy Research Working Paper 10577

# **Abstract**

Multidimensional poverty measures can in theory make well-being comparisons that are less biased than those solely based on monetary poverty. However, multidimensional poverty measures suffer in practice from limitations that have led to criticisms. This paper presents the case for multidimensional poverty measures, two criticisms against their current implementations, as well as recently proposed solutions to improve on these criticisms. The paper develops a method for implementing these solutions in practice. The resulting well-being indicator is used to compare well-being across Nigerian states in 2019. This empirical illustration suggests that these solutions may substantially affect well-being comparisons. The paper also quantifies the potential bias inherent to comparing well-being solely based on monetary poverty. The results find substantially different well-being comparisons between the proposed well-being indicator and monetary poverty even though monetary poverty was (i) high in Nigeria in 2019 and (ii) very heterogeneously distributed across Nigerian states; and (iii) is integrated as one component of the proposed well-being indicator.

This paper is a product of the Development Research Group, Development Economics and the Poverty and Equity Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http:// www.worldbank.org/prwp. The authors may be contacted at bdecerf@worldbank.org. A verified reproducibility package for this paper is available at http://reproducibility.worldbank.org, click **here** for direct access.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Reconceptualizing Global Multidimensional Poverty Measurement, with Illustration on Nigerian Data<sup>1</sup> Benoit Decerf<sup>2</sup> and Kike Fonton<sup>3</sup> Originally published in the <u>Policy Research Working Paper Series on</u> _October 2023._ This version is updated on _December 2023._ To obtain the originally published version, please email <u>prwp@worldbank.org.</u> 1 We are grateful to Deon Filmer, Lain Jonathan and Tara Vishwanath for helpful discussions and suggestions. We thank Berk Ozler and Aart Kraay who commented on an earlier version of this paper. We thank all the participants at the Conference “Honoring Martin Ravallion’s Legacy” organized jointly by the World Bank and Georgetown University and an internal seminar of the World Bank and in particular Gaurav Datt, Jed Friedman, Christoph Lakner, Michael Lokshin and Daniel Malher. We are also thankful to the code reviewers Samih Ferrah, Anisur Bali, Muhsine Senart, for their invaluable help in reviewing the analysis codes compiled within this framework. We thank Maria Reyes Retana from the WB reproducibility team for her efforts. All errors remain ours. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author 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. E-mail address: bdecerf@worldbank.org.

2 World Bank.

3 Université Gaston Berger de Saint-Louis & Ghent University.
# **Section 1: Motivation**

Well-being indicators are important tools in any development agenda. These indicators allow monitoring progress and provide the basis for evidence-based policy making. They are necessary to allocate budgets where well-being is lowest.

In theory, multidimensional poverty measures (MPMs) constitute an appealing type of well-being indicator. The reason is that they can simultaneously account for the multi-dimensional nature of wellbeing and for the unequal distribution of well-being. In the decades following World War II, average monetary aggregates like GDP per capita were the mainstream indicators used to monitor development. Two main criticisms have been raised against GDP per capita (Hicks and Streeten, 1979; Fleurbaey, 2009). First, GDP per capita does not account for the unequal distribution of consumption in the population. The main response from policy makers to this “distributional” concern has been the development and adoption of monetary poverty indicators (Ravallion, 2015). Second, monetary indicators provide a too narrow coverage of human well-being because they ignore key non-monetary dimensions of well- being. In principle, MPMs can account for both the “distributional” and “dimensional” concerns.

Among the different types of well-being indicators that account for both the “distributional concern” and the “dimensional concern”,<sup>4</sup> MPMs stand out because they are widely used in practice. MPMs have for instance been adopted as official indicators by dozens of countries (Unicef, 2021). MPMs have also been adopted to track progress at the global level. The two highest-profile global MPMs are the World Bank’s MPM and OPHI-UNDP’s global MPI. The popularity of MPMs is in large part attributable to the relative simplicity of the methodology that Alkire and Foster (2011) proposed for their implementation. In a nutshell, the Alkire-Foster methodology identifies an individual as (multidimensionally) poor when the weighted sum of her deprivations surpasses some identification threshold (see Section 2).

However, the MPMs used in practice face criticisms related to their implementations. First, their weights are often selected in an ad-hoc fashion (Ravallion, 2011). This article does not improve on this criticism. Improving on this is not straightforward given the stringent data constraints. Indeed, the absence of welldefined prices between non-monetary outcomes implies the practitioner has little information on the relevant preference. Second, the Alkire-Foster methodology “wastes” available information because it only considers _dichotomous_ deprivation statuses (Ravallion, 2011). However, not all variables considered by MPMs are dichotomous: income or BMI are cardinal variables and crime-related events define categorical variables. Ignoring well-being relevant information may lead to a worse identification of the multidimensionally poor. Yet, with little knowledge of the relevant preference, it is unclear how to aggregate this additional information in a way that is broadly consistent with a preference-based definition of the poor. Third, the main global MPMs either entirely ignore or poorly capture key dimensions of well-being. Although the list of dimensions that are deemed most relevant to well-being is controversial, we argue that an indicator capturing low well-being should at least account for inadequate consumption, bad health, and premature death.<sup>6</sup> No doubt, data constraints complicate the monitoring of an MPM that simultaneously accounts for the monetary dimension, health, and mortality.

> 4 See Fleurbaey (2009) for a review of alternative types of well-being indicators.

> 5 Ravallion (2012) argue against aggregations that make implausible trade-offs across dimensions.

> 6 The main definition of the World Bank’s MPM ignores mortality and health. In turn, the global MPI ignores the monetary dimension and provides a narrow coverage of mortality. The global MPI accounts for the indirect impact that mortality has on the deceased’s relatives, but it ignores its direct impact on the deceased’s longevity.

2
However, besides data constraints, another reason why global MPMs barely cover mortality is related to conceptualization. At the time of their design, it was unclear how to meaningfully integrate mortality into MPMs, which may perhaps explain why the impact of mortality on longevity was ignored.

Recent papers study the latter two criticisms and propose theoretical solutions aimed at improving on these issues while remaining simple enough to allow for straightforward application. First, Decerf (2023) shows that a preference-based definition of the (multidimensionally) poor distinguishes two types of poor individuals: those who have low well-being because they have an extremely low achievement in at least one dimension (“extremors”) and those who have low well-being because they cumulate moderately low achievements in several dimensions (“cumulators”). That paper proposes a refinement of the AlkireFoster methodology able to simultaneously identify both types of (multidimensionally) poor individuals. This refinement is based on trichotomous variables, which contain more information than dichotomous variables. However, Decerf does not provide an illustration of how this refinement could be implemented in practice. Second, Baland et al. (2021) and (2022) study how to integrate the direct impact of mortality on longevity into poverty measurement. The difficulty is that poverty, which reduces the quality of life, is measured in a given year whereas the impact of mortality on longevity, which thus reduces the quantity of life, can only be properly accounted for by taking a lifecycle perspective. These papers show that mortality should be integrated into poverty measures in a specific way and propose several solutions for doing so. These solutions have limited additional data requirements: age-specific mortality rates are sufficient. However, these authors do not provide an empirical application probing the impact that mortality can make on multidimensional poverty comparisons.

This paper demonstrates how to design a multidimensional poverty measure based on these recent theoretical solutions and studies empirically its associated well-being comparisons across the 36 Nigerian states in 2019. The paper thus proposes one way of implementing the refined Alkire-Foster methodology proposed in Decerf (2023) and provides some conceptual guidance for the necessary choices. The illustration on Nigerian data probes the answer to two empirical questions:

- Question 1: what is the magnitude of the impact that the solutions proposed by Decerf (2023) and Baland et al. (2022) have on well-being comparisons?

- Question 2: what is the magnitude of the bias generated when comparing well-being while ignoring non-monetary dimensions? More precisely, how different are well-being comparisons based on monetary poverty from those based on our multidimensional indicator?

Importantly, we probe the answer to question 2 with a well-being indicator that integrates monetary poverty as one of its dimensions.<sup>7</sup> Moreover, we do so in a conservative context where monetary poverty is high -- 40.5 percent of Nigerians are below the “extreme” International Poverty Line (IPL) of the World Bank in 2019 -- and very heterogeneously distributed across Nigerians states -- their poverty rates range from 10 percent to 90 percent (Lain et al., 2022). This context is conservative in the sense that these two features should reduce the impact that non-monetary dimensions can have on well-being comparisons. The paper’s empirical ambitions are limited to these questions. We do not claim that our

> 7 Other studies contrasting monetary from non-monetary poverty measures in the context of developing countries, like Salecker et al (2020) need not integrate monetary poverty inside their multidimensional indicator. Studies that do integrate it, like Battiston et al (2013) or Evans et al. (2023), base their multidimensional indicator on the classical Alkire-Foster methodology and do not integrate the direct impact of mortality.

3
proposed well-being indicator is better suited for Nigeria than Nigeria’s official poverty indicators.

For question 1, the results suggest that each of the two theoretical refinements has the potential to substantially affect well-being evaluations, especially the inclusion of mortality. As explained in Section 2.1, the refinement proposed in Decerf (2023) suggests considering two types of dimension-specific deprivations: extreme deprivation and moderate deprivations. This could improve the identification of the multidimensionally poor by better accounting for the depth of individuals’ dimension-specific deprivation. Our results suggest that ignoring this information on depth – by bundling together extreme and moderate forms of deprivation -- may decrease the fraction of individuals identified as multidimensionally poor by about one quarter. In turn, integrating the impact of mortality in the MPM substantially increases the well-being losses captured. When assuming the smallest plausible normative weight to mortality – i.e., assuming that being dead is not worse than being multidimensionally poor – and using 50 years as the age threshold defining premature mortality, we estimate that premature mortality is responsible for more than 30% of the well- being losses our well-being indicator captures in Nigeria in 2019. However, mortality need not dominate well-being comparisons across Nigerian states because mortality is less heterogeneously distributed across states than monetary poverty. Our results reveal that the value selected for the normative weight given to mortality importantly affects the impact that mortality has on well-being comparisons.

For question 2, the results suggest that accounting for non-monetary dimensions substantially affects wellbeing comparisons and could thus have important policy implications. First, we find that non-monetary dimensions -- including mortality -- induce well-being losses that are at least as large as those coming from monetary poverty in Nigeria in 2019. Second, focusing on quality of life -- and thus excluding mortality -- we also find an important bias when ignoring non-monetary dimensions. We classify multidimensionally poor individuals into two categories that are _not_ mutually exclusive: “monetary” poor individuals -- who are below Nigeria’s national poverty line, which is virtually equal to the IPL in 2019 -- and “otherdimensions” poor individuals -- whose non-monetary deprivations are sufficient to classify them as multidimensionally poor. As expected, other-dimensions poverty is positively correlated with monetary poverty. However, the correlation is far from perfect. As a result, more than one-third of otherdimensions poor individuals are not monetary poor. Ignoring non-monetary dimensions leads to “omit” these individuals when identifying low well-being, which introduces a bias in well-being comparisons. Importantly, we show that this bias tends to be larger for states that have relatively _small_ monetary poverty rates. This suggests that this bias likely increases at the global level given the progress made since 1990 against extreme monetary poverty (World Bank 2022a).

Third, we quantify in two ways the impact that non-monetary dimensions have on well-being comparisons across Nigerian states. We find that 14 percent of pairwise comparisons of states are reversed when switching from a classic monetary poverty measure to our preferred version of our multidimensional indicator. This shows that pairwise comparisons from these two indicators are positively correlated, but this correlation is far from perfect. Our second method assumes that a hypothetical social protection budget is allocated across states proportionally to the well-being recorded in the different states. This second method quantifies the fraction of the budget that must be re-allocated across states when 4
switching from one well-being indicator to another. We find that 11 percent of the budget must be reallocated across states when switching from a classic monetary poverty measure to our preferred version of our multidimensional indicator. When interpreting these figures, recall that our well- being indicator integrates monetary poverty as one of its dimensions and that Nigeria has a high monetary poverty rate that is very heterogeneously distributed across Nigerians states.

The remainder is organized as follows. Section 2 presents the case for using MPMs as well as the classic and refined conceptualizations for MPMs. Section 3 presents two designs for our multidimensional indicator (“baseline” and “preferred”). Section 4 presents results on the extent of low well-being in Nigeria and how it can be decomposed into the contribution of alternative dimensions. Section 5 quantifies the impact that non-monetary dimensions have on well-being comparisons. Section 6 concludes.

# **Section 2: Refined conceptualization of MPM**

In this section, we present the conceptual foundations underpinning our well-being indicator. In Section 2.1, we expose a conceptual limitation of the Alkire-Foster methodology and present one pragmatic refinement that improves on this limitation. In Section 2.2, we discuss why mortality is a peculiar dimension and how it can be aggregated to MPMs in a meaningful way.

## **Section 2.1: Preference-based aggregation of non-monetary dimensions**

Among the well-being indicators that account for both the distributional concern and the dimensional concern, multidimensional poverty measures (MPMs) are the most used in practice. This popularity is perhaps the result of their simplicity. At its core, an MPM simply partitions the population into two groups: individuals who are (multidimensionally) poor and those who are not (multidimensionally) poor. The poor are those individuals whose well-being is considered too low. MPMs thus perform inter-personal comparisons of well-being. Such comparisons are required for identifying the worst-offs.

### **Preference-based definition of the (multidimensionally) poor**

A preference-based definition of the (multidimensionally) poor starts from a preference-based definition of well-being. Consider a utility function U that represents the relevant preference over achievement vectors 1 ) , which captures individual achievements in the key dimensions affecting wellbeing. An individual with achievement vector is defined to be (multidimensionally) poor if her utility is mm xx = (xx , ... , xx smaller than some utility threshold , i.e., . Observe this definition is purely ordinal: it only xx relies on the ranking over achievement vectors represented by function U. This definition can thus accommodate different frameworks used to conceptualize multidimensional poverty, like functionings UU<sup>∗</sup> UU(xx) < UU<sup>∗</sup> and capabilities or minimal rights.

5
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One simple refinement of the AF methodology that improves on this limitation is to consider three deprivation statuses, which requires using two cutoffs in each dimension j: one extreme cutoff and one moderate cutoff . Then, an individual can have three mutually exclusive deprivation statuses in jj zz<sup>ee</sup> each dimension j: extremely deprived when , moderately deprived when and nonjj zz<sup>mm</sup> deprived otherwise. Extremors can be properly identified by using the union approach on individuals who ee ee mm jj jj jj jj jj xx < zz zz ≤xx < zz have at least one extreme deprivation. Cumulators can be properly identified by using the intersection approaches on individuals who have several moderate deprivations. As illustrated in the right panel of Figure 3, the shape of the identification contour associated to this refinement better approximates indifference curve than the identification contours of the union and intersection approaches. This paper provides the first illustration of how this refinement could be implemented in practice. UU<sup>∗</sup>

# **Section 2.2: Accounting for the direct impact of mortality**

The direct impact of mortality is to curtail the quantity of life (the lifespan or longevity) of the deceased. This impact is virtually always ignored by the MPMs used in practice, which only account for quality of life.

There are several conceptual reasons why the impact of mortality on longevity should be accounted for. First, MPMs that ignore this impact may perversely react to mortality: they may record the death of poor individuals as an improvement (Kanbur and Mukherjee, 2007). Second, longevity is arguably highly consequential for low well-being. Cross-country well-being comparisons are very substantially affected when longevity is accounted for (Becker et al. 2005; Jones and Klenow, 2016). Third, from a capability perspective, being alive may be considered the most basic functioning. Mortality thus deprives the deceased of the most basic functioning. At the very least, any individual who dies too young should be considered “lifespan deprived”. To the extent that being prematurely dead is considered no better than being poor, being prematurely dead should be considered a form of extreme deprivation.

## **The direct impact of mortality requires a specific aggregation**

Integrating the direct impact of mortality into an MPM is tricky. The key conceptual difficulty is that MPMs capture low _quality_ of life _in a given year_ while properly accounting for the impact of mortality on the _quantity_ of life requires taking a _lifecycle_ perspective.

The solution proposed by Baland et al (2022) is that the well-being indicator aggregates years of life prematurely lost (YLLs) with years of life spent in poverty (PY). From a poverty perspective, in a given year t, alive individuals are either poor or non-poor. However, some individuals who should be alive in year t are already dead because they prematurely died before year t. Thus, three types of individuals should be accounted for in year t: the non-poor individuals whose contribution is normalized to zero, the prematurely dead individuals whose contribution is normalized to one and the poor individuals whose contribution takes an intermediate value θ in (0,1), at least when assuming that being poor is not worse than being dead. An obvious drawback with this approach is that its mortality component is affected by the premature mortality taking place _before_ year t, which is undesirable when evaluating policies in year t. The proposal of Baland et al. (2022) is to collect all years of life lost due to the premature deaths occurring in year t and attribute to year t all these years of life lost.<sup>10</sup> 10 For instance, when the age threshold defining premature mortality is 50 years, a 20-year-old who dies loses 30 years of life, which can all be attributed in the year when the 20-year-old dies.

9
This solution can still be perversely affected by the death of poor individuals. The reason is that they attribute negative intrinsic value only to _premature_ deaths. The next indicator, proposed by Baland et al. (2023) avoids these perverse effects by attributing negative intrinsic values to _all_ deaths. By doing so, it arguably better reflects the view that being alive is the most fundamental functioning.

The basic idea beyond this indicator is to aggregate the poverty and mortality observed in year t while assuming that the society is stationary. This assumption is not meant to be realistic but rather to allow for an aggregation of mortality that makes sense from a lifecycle perspective. Indeed, in a stationary population, the population in any given year completely reflects the lifecycle impacts of mortality in that year. In fact, the same assumption underpins the construction of life-expectancy, the most popular mortality indicator.

This indicator is called poverty-adjusted life- expectancy (PALE). Formally, PALE is defined by the following expression: P P = P where LE is life-expectancy at birth, H is the multidimensional poverty headcount ratio and θ in [0,1] is θθ ∗(1 −θθ∗HH) (2) where LE is life-expectancy at birth, H is the multidimensional poverty headcount ratio and θ in [0,1] is the same normative weight. PALE takes the perspective of someone who expects to be confronted throughout her life to the (multidimensional) poverty and mortality observed in year t. The larger θ, the smaller the weight attributed to mortality. At one extreme, when θ = 0, i.e., spending one year in multidimensional poverty is considered the same as spending one year out of multidimensional poverty, PALE corresponds to life-expectancy at birth. At the other extreme, when θ = 1, i.e., spending one year in multidimensional poverty is considered the same as losing one year due to death, PALE can be interpreted as the poverty-free life-expectancy, an index proposed by Riumallo-Herl et al. (2018). More generally, PALE normalizes the lifecycle utility expected under a stationary perspective when θ captures the fraction of period-utility lost when multidimensionally poor.<sup>11</sup> For most purposes, our empirical illustration uses the PALE indicator to aggregate the direct impact of mortality (quantity of life) with other dimensions of deprivations (quality of life). This aggregation combines the advantages of (i) taking a lifecycle perspective, (ii) attributing negative intrinsic value to all deaths, and (iii) avoiding perverse reactions to the death of a poor individual. This indicator is also parsimonious in terms of data requirement because the necessary mortality data can be taken from a different source than the data on the quality of life. An important limitation of this well- being indicator is that PALE is not affected by the distribution across individuals of years of life lost and of years of life spent in poverty. This limitation thus makes PALE a second-best indicator, which is relevant when dataconstraints prevent from estimating this distribution.

> 11 Formally, we have θ=(u(NP)-u(P))/(u(NP)-u(D)) where u(NP) , u(P) and u(D) respectively denote the period-utility of being non-poor, poor or dead.

10
# **Section 3: Designing a refined MPM with Nigerian data**

In this section, we propose one way of implementing the conceptual refinements discussed in Section 2 in the context of Nigeria in 2019. We discuss how the necessary choices can be made consistently with the theory exposed in Section 2. Importantly, our design is intended as a mere illustration. Beyond providing a proof of concept, our empirical ambitions are limited to proposing a plausible design to probe the answer to the two questions raised in the introduction.

## **Section 3.1: Quality of life and the deprivation mapping**

In this section, we propose one way of implementing the refined identification method described in section 2.1. In fact, we propose two designs: a **“baseline” design** and a **“preferred” design** . The “baseline” design provides conservative answers to our two questions because it accounts for fewer dimensions and adopts the smallest plausible weight for mortality. The text presents all results for the “baseline” design, which is easier to discuss. Yet, we view the “preferred” design as more plausible and thus we also present the main results for the “preferred” design.

The unit of analysis is the individual. The main difficulty is that the relevant information is often available only at the household level. This is typically the case for monetary outcomes, which are only observed at household level. In contrast, health outcomes are sometimes available at the individual level. This is fortunate because health outcomes are expected to be very unequal across household members, if only because of lifecycle effects.<sup>12</sup> Observing outcomes for different units of analysis for different dimensions is not necessarily a problem, but it requires making strong assumptions to translate the observed household-level outcomes into individual-level outcomes. For instance, equal sharing of monetary resources is often assumed for the monetary dimension.

To capture quality of life, we consider the monetary dimension (consumption in Nigeria) together with several non-monetary dimensions. Ideally, the design should capture the main well-being-related dimensions for which comparable data are available. One difficulty is that the relative importance of alternative dimensions may differ by context. However, some dimensions are important in virtually all contexts. This is arguably the case of both consumption and health. On top of these two dimensions, we also consider security and housing. Finally, for our preferred design, we additionally consider education. We believe that all these dimensions make sense in the Nigerian context. The key aspect for our purpose is to consider both monetary and non-monetary dimensions, which allows reducing misidentification errors when data constraints permit.<sup>13</sup> Each dimension is covered by a series of dimension-specific indicators. The main step for the implementation of the refined AF methodology presented in Section 2.1 is to define what we call the “ **deprivations mapping** ”. For each individual and each dimension, the deprivation mapping defines the circumstances under which the individual is extremely, moderately, or not deprived in the dimension. The deprivation mapping makes the link between the individual outcomes captured by the dimension-specific indicators and the individual’s deprivation status.

> 12 Studies looking at intra-household distribution of monetary resources also find substantial inequalities (Lise and Seitz, 2011; Lechene et al. 2021).

> 13 As shown in the supplementary material S3 attached to Decerf (2023), an identification method that does not combine monetary and non-monetary dimensions makes more identification errors than some identification method that combines them.

11
Before discussing some conceptual principles guiding the definition of the deprivation mapping (see Section 3.2), we present in the remainder of section 3.1 what this mapping looks like in our illustration.

Table 1 defines our deprivation mappings for the baseline and preferred designs. Consider first our baseline design. We begin with the monetary dimension. In Nigeria, the monetary aggregate is defined as the market value of consumption. In 2019, the national poverty line was $1.93 per person per day in 2011 PPPs (see page 19 of World Bank, 2022b). The national monetary line was thus almost equal to the World Bank’s extreme poverty line, which is $1.9 per person per day (2011 PPPs). The deprivation mapping for the baseline design assumes that an individual is extremely monetary deprived if her consumption is below the national poverty line, otherwise she is not monetary deprived. Given that an extreme deprivation automatically confers (multidimensional) poverty status, this assumption is equivalent to the one used by the WB’s MPM, which automatically classify as (multidimensionally) poor individuals who are below the extreme monetary line.

We succinctly describe the non-monetary deprivations used in the baseline design. In the health dimension, individuals are extremely deprived in three cases: they suffer from a heavy disability, they are an underweight woman between 15 and 49 years old (age-window and gender for which we have data) or they are a stunted child.<sup>1</sup> In turn, individuals who are not extremely health deprived are moderately health deprived in two cases: they suffer from a mild disability, or they suffer from severe over-weight (obesity). In the security dimension, an individual is extremely security deprived if her household has been victim of an insecurity event with “physical” consequences or if she lives in a district where at least a quarter of the households have been victim of an insecurity event with “physical” consequences. In turn, an individual who is not extremely security deprived is moderately security deprived if her household has been victim of an insecurity event with “material” consequences or if she lives in a district where at least a quarter of the households have been victim of an insecurity event with “material” consequences. In the housing dimension, we consider whether an individual lives in a household that has access to electricity, limited-standard drinking water, limited-standard sanitation and whose dwelling is made of appropriate materials. An individual is extremely housing deprived if her household is deprived in the four housing indicators and moderately housing deprived if her household is deprived in three housing indicators.

The deprivation mapping for the preferred design is the same as that of the baseline design, except that the former additionally considers a moderate monetary deprivation status and the education dimension. An individual is moderately monetary deprived if her consumption is above the national poverty line but below the WB’s societal poverty line in her state.<sup>14</sup> An individual is extremely education deprived if she is a child not enrolled in school. An individual is moderately education deprived if she lives in a household where no adult has completed primary education and no adult can read or write.

14 The WB societal poverty line is a (weakly) relative monetary line whose monetary threshold increases with median income but is never smaller than the extreme poverty line (Jolliffe and Prydz, 2021). Considering individuals whose income is between the extreme and societal poverty lines as moderately monetary deprived is consistent with the view that being absolutely income poor is worse than being only relatively income poor (Decerf, 2017; Decerf and Ferrando, 2022).

> 1 Data-constraints imply that we don’t have information on underweight men. Therefore, our indicator, which we construct for illustrative purposes, cannot be used to compare low well-being across men and women. For parallel reasons, it cannot be used to compare low well-being across children and adults.

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_Table 1: Deprivation mapping: from dimension-specific indicators to deprivation statuses_

|**Dimensions**<br>**Deprivation status**|**Indicators**|
|---|---|
|Extreme<br>**Monetary**|The household annual consumption per capita is below national poverty line<br>evaluated to 137430 Naira annual per capita (PA NGA).|
|_Moderate_<br>_(only Preferred)_|_The household annual consumption per capita is above national poverty line but_<br>_below state societal poverty line: 1 + 0.5 x where x is the median state consumption_<br>_in$ per day per capita._|
|**Health**<br>Extreme|The individual suffers from at least one disability causing him a lot of difficulties in<br>daily life or/and suffers from an extreme bad nutritional status, meaning a stunting<br>condition for children (HAZ<sup>1</sup>< -2) or being undernourished (BMI<sup>2</sup>< 18.5) for adults.|
|<br>Moderate|The individual suffers from at least one disability causing him only some difficulties<br>in daily life and/or suffers from a moderate nutritional status, meaning being obese<br>(30 < BMI) for adults.|
|**Housing**<br>Extreme|The individual belongs to a household deprived regarding all following household-<br>level indicators: i) Household lacks access to limited-standard drinking water<sup>3</sup>; ii)<br>Household lacks access to limited-standard sanitation<sup>4</sup>; iii) Household has no access<br>to electricity; iv) Household has inadequate housing<sup>5</sup>|
|<br>Moderate|The individual belongs to a household deprived regarding three of the following<br>household-level indicators: i) Household lacks access to limited-standard drinking<br>water; ii) Household lacks access to limited-standard sanitation; iii) Household has no<br>access to electricity; iv)Household has inadequate housing|
|**Security**<br>Extreme|The individual belongs to a household, subjected the last 12 months to an extreme<br>insecurity event<sup>6</sup>or belongs to a local government area (LGA) with at least one<br>quarter of neighborhood households subjected to crime/violence with extreme<br>consequences the last 12 months.|
|Moderate|The individual belongs to a household, subjected the last 12 months to a moderate<br>insecurity event<sup>7</sup>or belongs to a local government area (LGA) with at least one<br>quarter of neighborhood households subjected to crime/violence with moderate<br>consequences the last 12 months.|
|**_Education_**<br>_Extreme_|_The individual is a school-age child up to the age of grade 8, not enrolled in school_|
|**_(only Preferred)_**<br>_Moderate_|_The individual belongs to a household in which no adult (age of grade 9 or above)_<br>_has completed primary education, and no adult can read nor write_|

_Source:_ Authors _Note_ :<sup>1</sup> Height for Age Z score 2 Body Mass Index 3Limited-standard drinking water refers to drinking water that comes from an improved source, defined as those that are likely to be protected from outside contamination, and from fecal matter in particular. It includes for example, piped, borehole, protected dug well, rainwater, or delivered water (PSPR 2018, WHO) 4Limited-standard sanitation refers to improved sanitation facilities, defined as those that hygienically separate human waste from human contact, including flush/pour flush to piped sewer system, septic tank, or a composting latrine (PSPR 2018, WHO) 5Inadequate housing refers to houses characterized by at least one of the following three conditions: the floor is of natural materials, the roof or the walls are of rudimentary materials (UNDP) 6Extreme insecurity events include events where any member of the household has been murdered, injured, or disabled, subjected to sexual violence, captured, or abducted, or made a refugee 7Moderate insecurity events include events where any member has been physically attacked, forced to work, restricted from going to school or hospitals, robbed, or where household’s dwelling has been damaged, or household’s land has been occupied or taken by force.

**This table presents, for each baseline and preferred scenario, the combination of basic indicators that allow to define, for each poverty dimension – monetary, education, health, housing, security-, a state of non-deprivation, moderate deprivation, and extreme deprivation.**

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# **Section 3.2: Principles guiding the necessary choices for our well-being indicator**

In this section, we finalize the baseline and preferred designs of our multidimensional well-being indicator. Two pieces are missing: the exact aggregation of an individual’s deprivation statuses into her (multidimensional) poverty status and the selection of a value for the normative weight , which defines the trade-off between quantity of life and quality of life. We also comment on some conceptual principles θθ guiding the design and the differences with the classical AF methodology.

## **Aggregation of deprivations related to quality of life**

The aggregation of quality of life requires both a deprivation mapping (section 3.1) and a method to aggregate deprivation statuses into (multidimensional) poverty status. For the latter method, we follow the theory presented in section 2.1. That is, two types of individuals are (multidimensional) poor. First, any individual who suffers from at least one extreme deprivation is identified as poor (extremor). Second, any individual who is not an extremor but cumulates enough moderate deprivations is identified as poor (cumulator). In this illustration, we assume that **two** moderate deprivations are sufficient to be considered poor. This choice completes the aggregation of quality of life, which means that all the necessary choices have been made to compute the fraction of (multidimensionally) poor, which we denote by H.

Five important remarks are in order. First, the design of the deprivation mapping should be made while accounting for the way in which deprivations statuses are aggregated. For extreme deprivation status, the selection of dimension-specific indicators conferring extreme deprivation should be plausibly consistent across dimensions. Assume as a starting point that an individual whose consumption is below the extreme poverty line ($1.9 per day in 2011PPPs) is considered extremely monetary deprived and thus (multidimensionally) poor. The components of the mapping related to extreme deprivations in other dimensions must be broadly consistent with this starting point. Take the health dimension for example. Loosely speaking, it should be plausible that, ceteris paribus, suffering from a heavy disability leads to a similarly low well-being level as having consumption below the extreme poverty line. Graphically, the extreme deprivation cutoffs selected in different dimensions should “approximate” the same indifference curve (recall the right panel of Figure 3 in Section 2.1). Then, the components of the mapping related to moderate deprivations must be consistent with both this starting point and the (arbitrary) assumption UU<sup>∗</sup> that two moderate deprivations are sufficient to be considered poor. Indeed, it should be plausible that suffering only from one moderate deprivation in one dimension leads to a higher level of well-being than suffering from one extreme deprivation. Loosely speaking, it should be plausible that, ceteris paribus, suffering only from a mild disability leads to a higher well-being level as having consumption below the extreme poverty line. Graphically, the moderate deprivation cutoff selected in one dimension should not approximate the same indifference curve approximated by the extreme deprivation cutoff in another dimension (recall the right panel of Figure 3 in Section 2.1). Then, it should also be plausible that suffering from **two** moderate deprivations leads to a similarly low well-being level as having consumption below the UU<sup>∗</sup> extreme poverty line. For instance, it should be plausible that suffering from a mild disability and belonging to a household that has been victim of crime with only material consequences leads to a similarly low well- being level as having consumption below the extreme poverty line. These are the considerations that should guide the design of the deprivation mapping. Ideally, empirical methods, like surveys using vignettes or subjective well-being questions, should be used to assess whether these principles plausibly hold.

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Second, beyond the selection of the number of moderate deprivation leading to poverty (in our case: two), our identification of the (multidimensionally) poor does not require to select explicit values for weights (across dimension-specific indicators related to quality of life). Of course, our refined AF method does assume trade-offs across such indicators, like the classical AF method. However, not having to select explicit values for weights may sometimes help improve identification by increasing the information used. At least this will be the case if practitioners feel compelled to use equal weights. Practitioners are likely to feel compelled to use equal weights because deviating from the “equal weights” dominant practice requires a good justification. Practitioners may lack the legitimacy or the scientific underpinning necessary to select a particular value for these weights. Thus, when using equal weights is the only easily defensible solution, the practitioner loses options that could help better identify individuals with low well-being. For instance, the practitioner may discard well-being relevant information by bringing together ordered categories. For instance, she would not discriminate between heavy and mild forms of disabilities (or between crimes with “physical” or merely “material” consequences), but rather bundle them together as health deprivation. Alternatively, in any given dimension, the practitioner may only consider dimensionspecific indicators leading to a similar level of well-being, excluding potentially useful indicators.

Third, comparing results across two nested designs, like our baseline and preferred design, does not require any adjustment. In contrast, to meaningfully perform such comparisons, the classical AF methodology would have to change the values selected for its weights and identification threshold (see Eq. 1). Our preferred design differs from our baseline design because the former considers an additional dimension and an additional moderate consumption deprivation status. The theory exposed in section 2.1 explains in which sense the results can be meaningfully compared across our two designs. Fundamentally, the preferred design can be assumed to make a better job at identifying the (multidimensionally) poor than the baseline design because the latter omits well-being relevant information. This is at least true if the extension of the deprivation mapping defining our preferred design is consistent with the deprivation mapping defining our baseline design. Given that the former is a mere extension of the latter, consistency only requires that the same principles described in our first remark (see above) also guide the design of the extension.<sup>15</sup> If it is the case, then the preferred design can be interpreted as making fewer exclusion errors. For instance, children who are not registered into school may not be identified as (multidimensionally) poor by our baseline design, which is an exclusion error whose origin is that our baseline design omits such extreme education deprivation.

Fourth, from a conceptual perspective, having information at the individual level allows accounting for extreme forms of deprivations that are not equally shared within the household. Think for instance of heavy disabilities. Arguably, individuals afflicted by such disabilities have a level of well-being that is too low and should thus be considered as (multidimensionally) poor. However, other individuals living in their household need not be considered poor if they are not themselves sufficiently deprived in other dimensions. When using the household as unit of analysis, accounting for such heavy disability leads to many identification errors.<sup>16</sup> Hence, a framework combining three deprivation statuses with the individual as unit of analysis holds the potential to reduce identification errors.

> 15 For instance, the definition of moderate monetary deprivation should lead to approximately the same wellbeing level as having a mild disability.

> 16 When using the household as unit of analysis, considering all household members as poor whenever one member has a heavy disability would imply many inclusion errors. An alternative would be to consider a household

15
Fifth, data-constraints prevent from adequately covering several dimensions or properly accounting for joint distribution. The issue arises in our design for the nutrition indicators considered as part of the health dimension. We do not have data on bad nutrition outcomes except between 15 and 49 years old and below 5 years old. For the large fraction of the population outside of these two age windows, we conservatively assume that their nutrition status is normal. Moreover, because nutrition outcomes come from a separate survey, we had to input the nutrition outcomes from DHS to NLSS (see Appendix 3 for details on the imputation model). This imputation is not expected to have a large impact on results given the small fraction of the population for which we have bad nutrition status (see Table A1 in Appendix 1). However, one should bear in mind that our results suffer from this limitation.

## **Aggregating quality with quantity of life**

For the reasons exposed in Section 2.2, we account for the direct impact of mortality on quantity of life using PALE. There only remains to select a value for its normative weight , which defines the trade-off between quantity of life and quality of life. θθ There are several ways one could select a value for . For instance, the selection could be grounded in the views of the individuals themselves. Such views should be collected through dedicated surveys. θθ Alternatively, parametric values for could be deduced from assuming a particular Bernouilli (period) utility function, as illustrated in Appendix 2. θθ For our purposes, we simply assume two different values for the baseline and preferred designs. We conservatively assume for the baseline design. From a policy making perspective, this choice provides the smallest plausible weight to mortality. The reason is that implies that being dead θθ = 1 provides the same well-being level as being (multidimensionally) poor. Arguably, no policy maker would θθ = 1 explicitly ground its decisions on the assumption that poor individuals would be better-off dead. Providing the smallest plausible weight to mortality is conservative when probing question 1, namely how much is lost when ignoring non-monetary dimensions of well-being. We then assume for our preferred design. We argue that is an implausible weight for mortality, so smaller values must be considered. The “middle of the road” value implies that one θθ = 0.5 θθ = 1 year of life lost is equivalent to two ( years of life spent in poverty. θθ = 0.5 = 1/θθ)

# **Section 4: Incidence of low well-being in Nigeria in 2019**

In this section, we present the data sources, the context and the basic results describing the _incidence_ of low well-being in Nigeria in 2019. This incidence is measured by our indicators H and PALE. We focus on the respective contributions of alternative dimensions and the impact of some assumptions underlying as moderately deprived when one of its members has an extreme form of deprivation. This alternative is clearly less attractive because it could also lead to different types of identification errors. For instance, the heavily disabled individual would incorrectly be considered non-poor if her disability is the only form of deprivation afflicting her household. Or, all other members of her household would incorrectly be considered poor if the household has only one other moderate form of deprivation.

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our design. In Section 5, we present the results quantifying the extent to which _well-being comparisons_ are altered when accounting for non-monetary dimensions.

# **Section 4.1: Data sources and the Nigerian context**

We compare well-being across the 36 states of Nigeria in 2019. As we explain below, this is a conservative context to probe the answer to question 1.

## **Data sources**

We rely on two main data sources: the 2018-19 Nigeria Living Standards Survey (NLSS) and the 2018 Nigeria Demographic and Health Survey (DHS). The NLSS 2018-19 is a large-scale household survey, focusing on measuring living conditions of the population, collected by the National Bureau of Statistics of Nigeria (NBS) between September of 2018 and October of 2019. The NLSS questionnaire includes wideranging modules, covering demographic indicators, education, health, labor, expenditures on food and non-food goods, non-farm enterprises, household assets and durables, access to safety nets, housing conditions, economic shocks, exposure to crime and farm production indicators (NLSS Report 2020). The additional data source, the 2018 NDHS is a survey implemented by the National Population Commission (NPC), whose data collection took place from 14 August to 29 December 2018. It provides up-to-date estimates of basic demographic and health indicators, especially, nutrition data relying on records of anthropometry measurements of children under 5 and women between 15 and 49. We complement these databases with mortality information taken from Human Development Indices for the UNDP Nigeria Human Development Report 2016.

## **Monetary poverty is high and heterogeneously distributed across Nigerian states**

Nigeria provides a conservative context for our purpose. Answering question 1 requires contrasting wellbeing comparisons obtained from the monetary dimension alone with well-being comparisons obtained from a multidimensional indicator aggregating the monetary and the non-monetary dimensions. As we show below, Nigeria has a high monetary poverty rate and this rate is very heterogeneous across the 36 Nigerian states. Accounting for non-monetary dimensions is less likely to reverse well-being comparisons in a context where the monetary dimension already provides a stark contrast across states.

Monetary poverty was high in Nigeria in 2019. That year, some 40.5 percent of Nigerians had their monetary aggregate below the national poverty line. Monetary poverty was also distributed unequally across Nigeria in 2019. That year, five states had less than 10 percent monetary poverty while two states had more than 85 percent. The map shown in Figure 4 illustrates this heterogeneity across geographical units called “zones”, which are groups of several states. The map shows the heterogeneity in poverty rates across the six zones of Nigeria. Each of the three zones in the south have less monetary poverty than each of the three zones in the north. Monetary poverty in the South-West zone is about 10 percent while monetary poverty in the North-East zone is about 70 percent.

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<!-- Start of picture text --> 43.1-618Povertyfra des headcount(4%)<br>362-431<br>208-382<br>97-208<br><!-- End of picture text -->
<!-- Start of picture text --> Health<br>Housing<br>IB Extremely deprived<br>HB Moderately deprived<br>IB Not deprived<br>Monetary<br>Security<br>ae<br>0 2 A 6 8 1<br><!-- End of picture text -->
<!-- Start of picture text --> Monetary Health<br>100 100<br>=e » =<br>6 6<br>gs 0 g<br>=2<br>o<br>Qa 40 oaS 40<br>00<br>B<br>Rc= a ro a GB BR = a ro aR a<br>& gs € 2 € € § gs €@ 2 € €<br>&® 3 6 € gs 2 8 B@ &@ € 2 2<br>o 6 * 2 6 4S os es * 2 6 A<br>Housing Security<br>100 100<br>= 0 Xs0S<br>> S60<br>J oO<br>S 60 =<br>% oT<br>2240 220<br>a<br>0<br>20 =B8soo4regJSs B=8zg<br>0 $$ € 2 = € 5<br>B 5 3 3B = S =<br>= €6 #8@ Egs =BSo S=2s 2= a° &<br>8££S «738 =6 °€ <S =2Ss . E<br>2 @ + 2 & A BE Extremely deprivedil] Moderately deprived<br><!-- End of picture text -->
<!-- Start of picture text --> 24 © Monetary poor<br>Only monetary poor @ Other-dimensions poor<br><!-- End of picture text -->
<!-- Start of picture text --> y © Health<br>@ Housing<br>@ Security<br><!-- End of picture text --> <!-- Start of picture text --> © Health<br>SS @@ SecurityHousing<br><!-- End of picture text -->
non-monetary dimensions leads to a larger bias when evaluating the _incidence_ of low well-being in the south zones than in the north zones. For instance, the two zones with the largest fraction of omitted poor are in the south. This finding may be surprising given that (1) zones in the south have a smaller fraction of other-dimensions poor than zones in the north and (2) other-dimensions poverty has a similar correlation with monetary poverty in the north as in the south, as suggested by the coefficient of overlap. A key reason for this larger bias in south regions is that other-dimensions poverty is less heterogeneously distributed across space than monetary poverty. Another fact worth highlighting in Table 2 is that consistent poverty is the type of poverty most heterogeneously distributed across space. Consistently poor individuals are highly concentrated in north zones. Clearly, this follows from the fact that north zones both have higher monetary poverty rates and higher other-dimensions poverty rates. This potentially suggests that chronic monetary poverty might be largely concentrated in the north zones (Bolch et al. 2022).

_Table 2: Prevalence of different types of multidimensionally poor individuals, per zone, baseline scenario_

|||||**Zo**<br>|**nes**<br>|||**Coefficient of**|
|---|---|---|---|---|---|---|---|---|
||**National**|**South**<br>**West**|**South**<br>**South**|**South**<br>**East**|**North**<br>**Central**|**North**<br>**West**|**North**<br>**East**|**variation across**<br>**states**|
|Multidimensionally|||||||||
|<br>poor|51.9%|23.3%|36.1%|45.1%|54.2%|71.7%|80.5%|0.44|
|Monetary poor|40.5%|9.7%|20.8%|38.2%|43.1%|61.8%|69.9%|0.61|
|Other- dimensions<br>poor|27.9%|16.2%|20.9%|15.4%|30.0%|37.0%|45.6%|0.47|
|Omittedpoor|11.4%|13.5%|15.3%|6.9%|11.1%|10.0%|10.6%|0.52|
|Consistently poor|16.5%|2.6%|5.6%|8.4%|18.9%|27.0%|34.9%|0.79|
|Coefficient of overlap|2.1|1.8|1.4|2.0|2.2|1.7|1.4|0.30|
|Life expectancyat birth|49|52|50|50|49|49|45|0.06|

_Source:_ Authors’ estimates based on data from NLSS 2019 _Note_ : The table shows different poverty rates: multidimensional poverty, monetary poverty, and non-monetary poverty at the national level and within Nigeria's six zones. The table also shows the level of overlap between monetary poverty and other dimensions poverty, materialized by the overlap coefficient and the life expectancy at birth. The variability of each of the above measures is compared using the coefficient of variation across stated presented in the last column.

# **Impact of assumptions on the fraction of poor**

We further study the sources of (multidimensional) poverty by using another method. We slightly change the assumptions of our design to study the impact of these assumptions.

First, we look at the respective impact of the three non-monetary dimensions of our baseline design (health, housing and security). More precisely, we contrast the fraction of other-dimensions poor and omitted poor when removing one of these three dimensions from our design. Table 3 provides the results. The results reveal that the importance of one dimension not only depends on the fraction of deprived individuals but also on the correlation between that dimension and monetary poverty. Indeed, for our baseline design, housing has the largest incidence of deprivation and removing it has the largest impact on the fraction of other-dimensions poor. However, housing is much more correlated with monetary poverty than health. As a result, health has the largest impact on the fraction of omitted poor. Table 3 23
also shows the result of the same analysis for the preferred design. For our preferred design, security, the dimension least correlated with monetary poverty has the largest impact on the fraction of omitted poor.

_Table 3: Impact of each non-monetary dimensions on other-dimensions poverty rates_

|||**Nationalpoverty headcounts**<br>||
|---|---|---|---|
||**Other-dimensions poor**|**Omitted poor**|**Consistently poor**|
||**(%)**|**(%)**|**(%)**|
|||**Baseline Scenario**<br>||
|All dimensions kept|27.9|11.4|16.5|
|Health|18.1|6.5|11.6|
|Housing|14.9|6.9|8.0|
|Security|21.4|7.6|13.8|
|||**Preferred Scenario**||
|All dimensions kept|34.9|15.7|19.1|
|Education|30.5|14.0|16.5|
|Health|27.0|11.2|15.8|
|Housing|22.8|11.4|11.4|
|Security|27.7|10.9|16.8|

_Source:_ Authors’ estimates based on data from NLSS 2019 _Note_ : The table shows, other-dimensions poverty rates when all non-monetary dimensions are taken into account and when one of them is removed, for the baseline and the preferred scenario. The overall other-dimensions poverty rate is decomposed into omitted poverty and consistent poverty.

Second, we look at the impact of considering both extreme and moderate deprivation statuses for nonmonetary dimensions, as suggested by the theory presented in section 2.1. To do this, we compute counterfactual poverty rates by converting any extreme deprivation into a moderate deprivation. More precisely, we compute the fraction of other-dimensions poor when counterfactually assuming that individuals who are extremely deprived in a non-monetary dimension are in fact moderately deprived in that non-monetary dimension. For these counterfactual estimates, individuals can be other-dimensions poor only if they cumulate deprivations in at least two non-monetary dimensions. The results are presented in Table 4 and reveal that these fractions are decreased by slightly more than one-third in the baseline design and by about a quarter in the preferred design. The smaller decrease for the preferred design reflects the fact that the preferred design features four non-monetary dimensions, instead of just three for the baseline design.<sup>19</sup> Overall, this significant reduction suggests that the extreme deprivation status, which allows accounting for the depth of deprivation, plays an important role in our methodology to identify the (multidimensionally) poor.

> 19 The more numerous are the non-monetary dimensions, the more numerous are the opportunities for individuals to cumulate deprivations in at least two non-monetary dimensions. At one extreme, with only one non-monetary dimension, the fraction of other-dimensions poor individuals would fall to zero when removing the extreme deprivation status (at least in our baseline design for which no individual is moderately monetary deprived).

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_Table 4: Impact of two deprivations statuses (extreme and moderate) on poverty rates, baseline scenario_

||**Others-**<br>**dimensions poor**<br>**(%)**|**National poverty headco**<br>**Omitted**<br>**poor**<br>**(%)**|**unts**<br>**Consistently**<br>**poor**<br>**(%)**|
|---|---|---|---|
|Extreme deprivation considered|27.9|11.4|16.5|
|All non-monetary deprivations are||||
|assumed moderate|16.2|6.7|9.5|

_Source:_ Authors’ estimates based on data from NLSS 2019 _Note_ : The table presents other-dimensions poverty rates in Nigeria i) under the baseline scenario, ie, when the two-thresholds cutoffs (extreme and moderate deprivation) are applied for each non-monetary dimension and ii) under a modification of the baseline deprivation mapping such that only a one-threshold cutoff is applied for each non-monetary deprivation (that is, only the moderate deprivation status is considered: any extreme non-monetary deprivation is converted into a moderate deprivation). The overall other-dimensions poverty is decomposed into omitted poor and consistently poor to account for individuals who are both monetary and other-dimensions poor.

# **Section 4.3: Incidence of low well-being (quantity and quality of life)**

We focus in this subsection on the values taken by PALE, our well-being indicator that aggregates quantity and quality of life. Our objective is to get a sense of the impact of accounting for the direct impact of mortality when measuring low well-being as well as the impact of the value selected for the normative weight given to mortality. We first contrast PALE, which accounts for both quantity and quality of life, with H, which only accounts for quality of life. Then, we probe the relative importance of mortality and other dimensions of deprivations in determining low well-being.

## **PALE and its normative weight**

We begin by illustrating how our well-being indicator aggregates the direct impact of mortality with quality of life. Figure 9 provides a scatter plot that shows for each Nigerian state the value of PALE on the vertical-axis as a function of the (multidimensional) head-count ratio H on the horizontal axis. Recalling that by definition P P is obtained by “scaling down” its value for life-expectancy at birth (LE). This scaling down is more θθ<sup>= P∗ (1 − θθ ∗ HH), the figure illustrates that the value for PALE for a given state</sup> pronounced when the head-count ratio H is larger and when the weight given to mortality is smaller, i.e., the value for is larger. Consider for instance our baseline design, which conservatively assumes the largest value for compatible with the idea that being (multidimensionally) poor is not worse than being dead ( ) and which is illustrated in Figure 9. The value for PALE of any given state is thus θθ P P 1 = P , meaning that LE is scaled down by (1-H). A state with a small head-count ratio has its value θθ θθ = 1 of PALE that is close to its value of LE. Intuitively, a newborn in such a state is expected to live most of his ∗ (1 − HH) life out of poverty, assuming poverty and mortality remain constant. Such newborn is “expected” to live 40 years free from poverty if her life-expectancy at birth is 50 years and the head-count ratio is 20 percent. The perspective looks grimmer for a newborn whose life-expectancy at birth is 45 years and whose state has a head-count ratio of 90 percent because she then is “expected” to live only 4.5 years free from poverty.

25
<!-- Start of picture text --> 60<br>£4. , 4** x a a<br>i -— 2 ae ik<br>- ry a ry ay a - ra<br>+ ry PYtee 2<br>40 + ¢, too,<br>o* @ PALE<br>eS +<br>+<br>20 + +¢<br>~~ *%+ #e<br>0<br>0 2 A 6 8 1<br>Multidimensional poverty headcount<br>Variances across states (9 of mean):<br>Life expectancy 6<br>PALE 54<br>Multidimendionnal poverty headcount 43.7<br><!-- End of picture text -->
preferred design, the ranking of states according to PALE is still similar to the ranking of states according to H, but much less so. When assuming the maximal weight for mortality, which implies that PALE is equal to LE, the ranking of states according to PALE is very different from the ranking of states according to H.

# **Mortality generates substantial well-being losses**

The previous section showed that, when giving the minimal weight to mortality, well-being comparisons across Nigerian states are driven to a larger extent by quality of life (H) than by quantity of life (LE). The reason is that the former is distributed across states in a much more heterogeneous way. Importantly, this does not mean that mortality is less relevant to low well-being in Nigeria. To see this, observe that monetary poverty would play no role in well-being comparisons if all states had a monetary poverty rate of 100 percent. Clearly, monetary poverty would generate very large well-being losses, but its perfectly equal distribution would make it irrelevant for well-being comparisons across states.

We probe the respective sizes of the well-being losses coming from the direct impact of mortality with those coming from poverty. The theory presented in Section 2.2 provides the conceptual foundation for contrasting the relative sizes of the well-being losses they generate using years of life as units. Bad quality of life generates poverty-years (PY) while premature mortality generates years of life lost (YLL). Under the stationarity assumption, the number of poverty-years is simply the number of years a newborn expects to spend in (multidimensional) poverty (=LE*H). However, computing the number of years of life lost requires assuming a reference age-threshold defining premature mortality.<sup>20</sup> In order to get a sense of the number of YLL generated by premature mortality in Nigeria, we assume a reference age-threshold equal to 50 years. This means that an individual who dies at 30 years old prematurely loses 20 years of life, while an individual who dies at 55 years old prematurely loses 0 years of life. We use this logic to compute the number of years of life that a newborn is expected to prematurely lose given the prevailing age-specific mortality rates in her Nigerian state. We provide in Appendix 4 the details about the conceptual relationship between PALE and this way of estimating the number of YLL.

Figure 10 contrasts in “years of life” units the well-being losses coming from (multidimensional) poverty with the well-being losses coming from premature mortality. The poverty-years are further decomposed into those that can be attributed to monetary poverty, other-dimensions poverty or both. The upper panel shows the absolute number of PY and YLLs for each zone. The lower panel divides these numbers by PY+YLL to highlight the fraction of losses coming from each source.

> 20 Such age threshold is not necessary to compute PALE because PALE only depends on years of life in and out of poverty.

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<!-- Start of picture text --> So<br>So<br>—<br>ar<br>o<br>bad 46 32 31 436 41<br>Sa C] Only monetary poor<br>oO || Consistently poor<br>| | Omitted poor<br>4 , | Premature mortality<br>So<br>N<br>Oo — c — — = ~~ —<br>® Ss & Ss g & 6<br>= 8 Ww s = = uw<br>s=| <= =a =S oOs s5 =S<br>3 3 a = 3 Zz<br>co; is* + - oO<br><!-- End of picture text -->
suggested by these percentages. Indeed, these percentages implicitly assume the smallest possible weight to mortality, ie, one YLL is not worse than one PY. When assuming the normative weight used in our preferred design, we get that the fraction of well-being losses coming from mortality range from 40 percent in the North-West zone to 62 percent in the South-East zone (this fraction is even 73 percent in Lagos). Also, the upper panel shows that mortality losses are distributed more homogeneously across zones than losses coming from other-dimensions poverty, which is turn are distributed more homogeneously than well-being losses coming from monetary poverty.

More generally, non-monetary well-being losses are at least as large as monetary well-being losses in most states. We can use Figure 10 and Figure A5 in Appendix 1 to contrast the fractions of PY+YLL that respectively come from monetary poverty with that coming from non-monetary dimensions. Some individuals are both monetary poor and other-dimensions poor and we take the natural convention to attribute the corresponding poverty years (shown in red in the histograms) to both monetary losses and non-monetary losses. For instance, this implies for Nigeria that 54 percent of PY+YLL is attributed to monetary poverty and 68 percent of PY+YLL is attributed to non-monetary losses (including premature mortality). These percentages can be interpreted as follows: monetary poverty, alone, captures slightly more than half the well-being losses in Nigeria (assuming ), but non-monetary losses are larger than monetary losses in Nigeria. In all zones, monetary poverty captures less than two-thirds the well-being θθ = 1 losses, and it captures less than one quarter of well-being losses in South-West. In most zones, nonmonetary losses are larger than monetary losses.

# **Section 5: Impact on well-being comparisons**

In this section, we use two different methods to assess the impact of non-monetary dimensions on wellbeing comparisons. First, we quantify the frequency with which they reverse the well-being ranking between two states. Second, we quantify the fraction of the budget for a hypothetical social policy that should be transferred across states when allocating this budget according to our well-being indicator rather than monetary poverty.

## **Section 5.1: Quantifying re-rankings**

In Table 5 we report the fraction of all pairwise state comparisons that are reversed for different pairs of indicators. For instance, the fraction of states whose comparison is reversed when ranking them by monetary poverty rather than by mean consumption is 5 percent. This shows that the ranking of states by these two indicators is highly correlated. By comparison, when comparing two uncorrelated indicators, we expect the percentage of these “re-rankings” to be 50 percent. In the table, we consider the following list of indicators: mean consumption, monetary poverty ( ), multidimensional poverty (H) and PALE. Table 5 reveals the following findings. First, the rankings of all these indicators are highly correlated in MM HH Table 5 reveals the following findings. First, the rankings of all these indicators are highly correlated in Nigeria. This is not very surprising as it is typically the case for any two meaningful indicators of well-being. Yet, one key reason why the rankings of Nigerian states are highly correlated is that Nigerian states have highly heterogeneous well-being level (according to all three indicators). Recall for instance that monetary poverty ranges between 10 percent and 90 percent in those states. Clearly, it is unlikely to find that two indicators of well-being disagree when comparing two states with respectively 20 and 80 percent monetary poverty. This is especially true if both indicators account for monetary poverty, like is the case 29
for both H and PALE. To give a sense of the correlation between rankings among less dissimilar states, we also compute the fraction of re-rankings between states that have less than 50 percent poverty and the fraction of re-rankings between states that have more than 50 percent poverty. For instance, the fraction of re-raking between monetary poverty and mean consumption are 10 percent and 8 percent, respectively in the former and latter subset of states.

_Table 5: Percentage of states pairwise comparisons reversed between pairs of well-being indicators_

|||**Baseline**|||**Preferred**||
|---|---|---|---|---|---|---|
|<br>|**All states**|**States with**<br>HM**<50**|**States with**<br>HM**>=50**|**All states**|**States with**<br>HM**<50**|**States with**<br>HM**>=50**|
|Average consumption -VS-HM<br> <br>|5%|<br>10%|<br>8%|5%|<br>10%|<br>8%|
|<br>HM-VS- PALE<br> <br>|7%|17%|12%|14%|29%|23%|
|<br> <br>HM-VS-H<br>|7%|16%|13%|9%|22%|13%|
|<br> <br>H-VS- PALE|3%|8%|4%|10%|17%|19%|
|<br> <br>_Source:_Authors’ estimates based on data from<br>_Note_: The table shows the percentage of pairs<br>consumption, monetary poverty rate (HM),mu<br>for each scenario, baseline and preferred. For<br>rate below 50%, on the one hand, and those w<br>the disparity between compared states.|NLSS 2019<br>of states whose c<br>ltidimensional po<br>each scenario, re<br>ith a monetary p|omparison is rever<br>verty rate (H) and p<br>strictions are applie<br>overty rate above 5|sed between two dif<br>overty-adjusted life-e<br>d in order to consid<br>0%, on the other. Th|ferent well-being<br>xpectancy (PALE). <br>er only states with<br>e aim of these res|indicators: average<br>Results are presented<br>a monetary poverty<br>trictions is to reduce|<br> <br>|

Second, when comparing monetary poverty and (baseline) PALE, the fraction of re-rankings is 7 percent. This fraction increases to 17 percent (12 percent) when restricting comparisons to the subset of states that have less (more) than 50 percent monetary poverty. Those frequencies of re-rankings are arguably substantial given that PALE accounts for monetary poverty. The table suggests that, in the baseline scenario, moving from monetary poverty to multidimensional poverty generates more re-rankings than moving from multidimensional poverty to PALE. This reflects the fact that (1) mortality is less heterogeneous across states than other-dimensions poverty and, to a lesser extent, (2) mortality is more correlated with monetary poverty than security deprivations.

Third, the preferred design implies more frequent re-rankings than the baseline design. When comparing monetary poverty and (preferred) PALE, the fraction of re-rankings on the whole set of states increases to 14 percent. This fraction further increases to 29 percent (23 percent) when restricting comparisons to the subset of states that have less (more) than 50 percent monetary poverty, which arguably are very substantial re-rankings (recall that PALE accounts for monetary poverty). The table suggests that the more frequent re-rankings when moving from the baseline to the preferred design are mostly due to the larger normative weight given to mortality. Indeed, re-rankings between these two designs do not increase as much when comparing monetary poverty and multidimensional poverty, whereas they increase very substantially when comparing multidimensional poverty and PALE. This highlights the need to better understand the plausible values for this normative weight.

30
Overall, we find that well-being rankings are highly correlated but accounting for non-monetary dimension may imply substantial re-rankings, especially when giving an intermediate weight to mortality.

# **Section 5.2: Quantifying budget transfers across states**

Quantifying re-rankings is a binary method to probe changes in well-being comparisons. Indeed, a ranking between two states is either reversed or not. The limitation of this method is that, when the ranking is not reversed, the changes in the relative well-being levels of the two states being compared is not accounted for. The method used in this subsection accounts for such changes.

The next method is based on a hypothetical social policy. Assume that the Nigerian government has a budget for social protection policies. Further assume that this budget is distributed across states proportionally to needs as captured by a well-being indicator. In the case of poverty, this budget could be distributed proportionally to the number of poor individuals in each state. When contrasting monetary poverty with multidimensional poverty, our method reports the fraction of the total budget that must be redistributed across states when using the latter instead of the former. Consider the following simplified example with two states, where state A has 0 monetary poor and 1 multidimensionally poor individual while state B has 1 monetary poor and 3 multidimensionally poor individuals. Under monetary poverty, state B receives 100 percent of the budget, while under multidimensional poverty state B receives 75 percent of the budget and state A 25 percent. The fraction of the total budget that must be transferred is thus 25 percent, from state B to state A. We use a straightforward adaptation of this method that accounts for the fact that poverty _decreases_ with well-being while PALE _increases_ with well-being, which we describe in detail in Appendix 5.

Table 6 shows the fraction of the total budget that must be transferred when comparing two of the following list of indicators: monetary poverty ( ), multidimensional poverty (H) and PALE. The fraction transferred corresponds to 6 percent of the budget when moving from monetary poverty to PALE MM HH (baseline design). Again, the table suggests for the baseline design that moving from monetary poverty to multidimensional poverty impacts these transfers more than moving from multidimensional poverty to PALE. Then, the fraction transferred increases to 11 percent of the budget when moving from monetary poverty to PALE (preferred design). The table suggests again that this increase is more driven by the change in normative weight given to mortality than by the different designs for multidimensional poverty.

_Table 6: Fraction of (hypothetical) budget reallocated across states between pairs of well-being indicators_

||**Baseline**|**Preferred**|
|---|---|---|
|<br>|**(%)**|**(%)**|
|HM-VS- PALE<br> <br>|5.6|11.3|
|<br>HM-VS-H<br>|4.7|6.0|
|<br> <br>H-VS- PALE<br>_Source:_Authors’ estimates b|2.2<br>ased on data from NLSS 2019|13.5|

_Note_ : The table considers a hypothetical policy that allocates a budget across Nigerian states proportionally to (minus) the state’s total wellbeing (see Appendix 5 for details). The table presents the fraction of the budget that must be re-allocated across states when changing from one well-being measure to another: monetary poverty rate ( ), multidimensional poverty rate ( ) and poverty-adjusted life-expectancy (PALE). MM HH HH 31
The results of this section thus suggest that accounting for non-monetary dimensions has non-negligible implications, even in a country with high monetary poverty and when using our well-being indicator that also accounts for monetary poverty.

# **Section 6: Concluding comments**

Multidimensional poverty measures have the potential to improve well-being comparisons, but the mainstream methodology for their construction suffers from some limitations. The paper proposes one way to apply recent solutions to improve on some theoretical limitations affecting global MPMs. The empirical results suggest that these solutions may significantly affect well-being comparisons, at least in the context of Nigeria in 2019. However, the methodology proposed in this paper could be further improved.

For instance, the exact design of the mapping from dimension-specific indicators to deprivation statuses and the aggregation of deprivations statuses into multidimensional poverty status would benefit from empirical work. Again, these aspects can be investigated through preferences elicitation techniques, following the conceptual guidelines discussed in section 3.2. We emphasize that, unlike what is sometimes assumed, such investigation should not simply aim at estimating marginal rates of substitution across dimension-specific indicators. Clearly, these marginal rates of substitution depend on an individual’s achievements. Rather, as discussed in section 2.1, the goal is to estimate the whole indifference curve . The aggregation of dimension-specific indicators into multidimensional poverty status should be such that UU<sup>∗</sup> the identification contour approximates reasonably well indifference curve (Decerf, 2023; Jones, 2022). UU<sup>∗</sup>

> 21 Observe that it is _not_ needed that individuals in high-income countries are also frequently affected by the deprivation related to a dimension-specific indicator for that indicator to be considered relevant. Indeed, such deprivation captures valuable information about the benefit of living in high-income countries.

32
Also, one should select the values for the key normative parameter related to mortality. Our results reveal the importance of establishing what is the plausible range of values for the normative weight given to mortality. Again, preference elicitation methods should provide a sense of this range.<sup>22</sup> θθ

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34
<!-- Start of picture text --> Education<br>Health<br>HB Extremely deprived<br>Housing HE Moderately deprived<br>HE Not deprived<br>Monetary<br>Security<br>0 2 A 6 8 1<br><!-- End of picture text -->
<!-- Start of picture text --> Monetary<br>SSS(Sey oes¢ Aner O78eprivation - 877 rate (24)<br>s, Delta Im, 551-878<br>Neos ie eden<br>53‘ og 148-289<br>: me 45-148<br>Housing<br>Sen ao<br>— Helle Ima, p 447-55451-645<br>oe a eater<br>“Bay eleaewa| 137 -20.6<br>sayesafeniaD me 03-137<br>Life expanctancy at birth<br>betes peony! LEB<br>= . Oross Rive 52-54<br>‘ inne’ 50-52<br>a TE 48-50<br>yeaa [bom 47-88<br>haf 43-47<br><!-- End of picture text -->

<!-- Start of picture text --> Health<br>dinyi: ; p24jeprivation35.8 rate (35)<br>209-228<br>35 187-209267-187<br>eee | | 86-167<br>Security<br>a"ar [tossn River 433-967epson<br>< Ea sB7-424<br>; U7 -187<br>50-447<br><!-- End of picture text -->
<!-- Start of picture text --> O Health<br>@ Housing<br>@ Security<br><!-- End of picture text --> <!-- Start of picture text --> 60 a<br>a aA yh yhry aFy & ry a<br>ry a ryry 7: a+a. & FY ry ry<br>dl o i ryry a* i. rA A<br>AQ) + a<br>+ «*<br>Fa * + < +<br>& + oe o¢+ @ PALE<br>+ ¢<br>20<br>0<br>aa |<br>a A 6 & q<br>Multidimensional poverty headcount<br>Variances across states (% of mean):<br>Life expectancy 6<br>PALE 18.7<br>Multidimendionnal poverty headcount 37<br><!-- End of picture text -->
_Table A2: Impact of two deprivations statuses (extreme & moderate) on poverty rates, preferred scenario_

|||**National poverty headco**<br>|**unts**<br>|
|---|---|---|---|
||**Others-**<br>**dimensions poor**<br>**(%)**|**Omitted**<br>**poor**<br>**(%)**|**Consistently**<br>**poor**<br>**(%)**|
|Extreme deprivation considered|34.9|15.7|19.1|
|All non-monetary deprivations are||||
|moderate|25.0|11.8|13.2|

_Source:_ Authors’ estimates based on data from NLSS 2019 _Note_ : The table presents other-dimensions poverty rates in Nigeria i) under the baseline scenario, ie, when the two-thresholds cutoffs (extreme and moderate deprivation) are applied for each non-monetary dimension and ii) under a modification of the baseline deprivation mapping such that only a one-threshold cutoff is applied for each non-monetary deprivation (that is, only the moderate deprivation status is considered: any extreme non-monetary deprivation is converted into a moderate deprivation). The overall other-dimensions poverty is decomposed into omitted poor and consistently poor to account for individuals who are both monetary and other-dimensions poor.

39
<!-- Start of picture text --> oO<br>co<br>oO+ |<br>|<br>=<br>oO | | |<br>qi |<br>| | | Only monetary poor<br>J | Consistently poor<br>|| Omitted poor<br>| Premature mortality<br>Oo<br>Q2S&EXClGCeooOSSaPEeE#SoFBS ssa2 Z0Uj>uTtEsSs SalnD StSSSO HXOZRBesezsesesesEevgeveseocsagge2 Jsel essesCc cecesac Sessssssessi=7] 2 — 2s<br>HStreHaAgSNR SNugAantaEX ST eeaeHVgr— ~6 BE w Fol= StigPUGS RiesCPC ESUSESSe<br>N NOME § os gear" ot THSas<br>ey oa woN ON<br><!-- End of picture text -->

<!-- Start of picture text --> S<br>oOo<br>co<br>aS<br>oO<br>c-)<br>a<br>| Only monetary poor<br>P<& | Consistently poor<br>| Omitted poor<br>|| Premature mortality<br>oO<br>aRQBSSFfSOoSOseSSZSCUSSoA SC SSESSEStSLSGLSSPFESSlOCs@CoxrsaseaeazreresesaeregseernsscsseGo AS HOEKSELL SSeSSEX SXSasESUOSS=ATPBeSSSsssaxsFEGLES<br>SeSSr MWe SnDGsFAr "LL BS2Z~—tS¥* Zu SoB8ns<br>Q NN NDR+ CS=Z—? oOes oN= Po) awoz teun= oOel—dsm9 ae)<br>oO o Nwo ION<br><!-- End of picture text -->
<!-- Start of picture text --> South East VS North Central 7i 36<br>South West VS North Central 3| 69<br>South West VS South East 2 7<br>a a a<br>-50 0 50 100 150<br><!-- End of picture text -->

<!-- Start of picture text --> South East VS North Central a)|: g 30<br>LL) coetcient overlap<br>Bel other. dimensions poverty<br>Be<br>South West VS North Central ms‘a c<br>South West VS South East 4 101<br><!-- End of picture text -->
# **Appendix 2: Parametric values for the normative weight of mortality**

In this appendix, we provide one way to derive a parametric value for the normative weight given to mortality. As shown by Baland et al (2022), from a theoretical perspective, the normative parameter θ captures the fraction of utility lost when poor, i.e.,<sup>uu(NNPP) −uu(PP)</sup> (3) θθ= where u denotes the Bernouilli utility associated with being (multidimensionally) poor (P) and not uu(NNPP) where u denotes the Bernouilli utility associated with being (multidimensionally) poor (P) and not (multidimensionally) poor (NP). By assumption, the Bernouilli utility of being dead is . As discussed in Section 3.2, under the two deprivation mappings presented in section 3.1 and in particular uu(DD) = 0 the fact that being below the national poverty line is considered an extreme monetary deprivation, the Bernouilli utility associated with being (multidimensionally) poor (P) can plausibly be equated to the Bernouilli utility associated with being below the national poverty line. As the national poverty line corresponds to the extreme poverty line, we can thus interpret as the Bernouilli utility associated with being below the extreme poverty line, which is $2.15 a day (2017 PPPs). uu(PP) Clearly , the value of θ will depend on the assumptions made on the Bernouilli utility function selected. Indeed, computing a parametric value for θ requires selecting a particular Bernouilli utility function of “income” (=the monetary welfare aggregate), say a constant elasticity of substitution function:

> <sup>mm1−εε−mm01−εε</sup> (4) where denotes income, 0 denotes the subsistence income, for which uu(mm) = 0) = 0 , and is the coefficient 1 −εε of relative risk aversion that captures the curvature of utility function . A parametric value for θ also mm mm uu(mm εε requires defining representative incomes for the (monetary) poor and not (monetary) poor status because ) and c ) . Typically, could be mean or median income among the uu (monetary) poor and ooc oo c could be mean or median income among the not (monetary) poor. cc−ooc oo ooc oo uu(PP) = uu(mm uu(NNPP) = uu(mm mm cc−ooc oo Parametric values obtained for θ are sensitive to the values selected for these parameters, and in mm particular for the curvature parameter and the subsistence income 0 . As an illustration we provide the results for the parametric values of 1/θ obtained for India in 2019 as a function of different parameter values for the CES utility function presented in Eq (4). We assume that εε mm and c respectively capture mean consumption among the (monetary) poor and the not (monetary) poor. We estimate these ooc oo cc−ooc oo mm mm two mean consumption values from the estimates provided by the Poverty and Inequality Platform of the World Bank. We check for robustness for different values of curvature parameter and the subsistence consumption parameter 0 . As suggested by the results shown in Table A3, the theoretical predictions for εε 1/θ based on these assumptions depend on the values selected for these two parameters.<sup>23</sup> mm

> 23 We consider a plausible lower bound for the value for the subsistence consumption y0 to be $0.5 a day. It is biologically impossible to survive with zero consumption. In the micro-data reported in PovCalnet, values for reported consumption below $0.5 a day are very infrequent. The value $0.5 a day is also consistent with the methodology outlined Ravallion (2016) to estimate minimum consumption levels.

42
_Table A3. Parametric values in India in 2019 for 1/θ when the poverty lines is $2.15 (2017 PPPs) per day. (1/θ =Number of years spent in monetary poverty yielding the same well-being loss as one year of life lost)_

|**y0 ($ a day)**|**0.5**|**0.75**|**1.0**|**1.25**|
|---|---|---|---|---|
|**ɛ (CRRA)**|||||
|**2.5**|7.8|4.1|2.6|1.8|
|**2.0**|4.7|3.0|2.1|1.6|
|**1.5**|3.0|2.2|1.7|1.4|
|**1.0**|2.1|1.7|1.5|1.3|

Note: According to the PIP platform, in India in 2019, mean consumption is 5.13 $/day (2017 PPPs). For the $2.15 a day line, mean consumption among the poor is $1.75 a day and mean consumption among the non-poor is $5.51 a day. The utility function considered is CES.

# **Appendix 3: Imputation model for nutritious outcomes**

Given the lack of available information on individual health in the Household Living Conditions Survey (NLSS), the main source of data used in this study, a related survey, the Nigeria's Demographic Health Survey (DHS) 2018, was exploited to infer information on the nutritional status of individuals. The general approach used was to build a model from DHS data, from which the nutritional status of individuals interviewed in the NLSS were inferred, in order to reproduce the representative distribution of the nutritional status in DHS. We succinctly describe in this Appendix the construction of this model.

## ⮚ **_Nutritional statuses_**

The nutritional status of individuals was first defined considering the age and sex of the individuals. Three main categories were thus retained: children, defined as all individuals between 0 and 5 years of age inclusive, and adult men and women, i.e., those over 5 years of age.

The nutritional status of children was measured on the basis of the height for age z score - number of standard deviations of the actual height of a child from the median height of the children of his/her age as determined from the standard sample - from which three standard classes were identified:

- -2 < HAZ Normal (Well nourished)

- -3 < HAZ < -2 Moderately Stunted (Moderately Malnourished)

- `o` HAZ < -3 Severely Stunted (Severely Malnourished)

Stunting is a condition that results from chronic or recurrent undernutrition, usually associated with poverty, poor maternal health and nutrition, frequent illness and/or inappropriate feeding and care in early life. Stunting prevents children from reaching their physical and cognitive potential. (WHO) As for the nutritional status of adults, it has been defined on the basis of the body mass index (BMI), which is calculated according to height and body mass, and which makes it possible to estimate the corpulence of a person. Three categories have been formed from the indicator:

- BMI < 18.5 Undernourished

- BMI >= 18.5 & BMI < 30 Normal (Well nourished)

- BMI > 30 Obese

43
# ⮚ **_Modeling approach_**

The nutritional status has been modeled from DHS data using a multinomial logit regression for each type of individual (children and adults). In order to capture the heterogeneity that may be present between zones - standard of living, local agricultural cultures, accessibility of markets, etc. - a model for each of the six zones of Nigeria was compiled. The following variables were identified as factors influencing the nutritional status of individuals:

- The asset index, which is supposed to represent the household's standard of living and includes characteristics of the dwelling, the movable and immovable assets owned by the household

- Socio-demographic characteristics of the household’s head such as age, gender, education level, marital status

- Socio-demographic characteristics of the individual when applicable

- Location (urban/rural) and household size

# ⮚ **_Inference approach_**

Nutritional status has been attributed in NLSS data using, on the one hand inferred probabilities from the model built in DHS data and on the other hand, estimated thresholds such that NLSS data could reproduce DHS individuals’ nutritional status per zone.

Especially, thresholds have been chosen such that shares of adult women categories (undernourished, normal, obese) and shares of children (normal, moderately stunted, extremely stunted) are similar to shares in DHS data per zone. However, due to lack of information in DHS data on other demographic categories of population (children between 6 and 14, adult men between 15 and 49 and elders over 50), some assumptions have been made on shares of undernourished/obese among those people, in a conservative approach, on the basis of available third source information:

- Half as many obese men as obese women in the 15-49 age group, in each of the zones of Nigeria, a conservative assumption in light of Chukwuonye et al (2013).

- No undernourished men in the 15-49 age group (conservative approach)

- All individuals in the 6-14 and over-50 age groups are in a normal nutritional condition (conservative approach)

# ⮚ **_Choice of classification thresholds_**

The process of classifying individuals into one or the other of the categories, once a binary logit probability model has been estimated, generally consists of assigning an individual to a group if its probability of belonging is greater than a certain level, and further, examining the distribution table between observed values and the predicted values. The choice of the classification threshold is therefore decisive since the quality of the predictions obtained depends on it.

Several methods are generally accepted for the choice of the binary categorization threshold, some of them relying on the choice of a 50% threshold assuming equi-probability between the events, or the 44
0a ~~TT~~ ~~OO~~ a-1 (@-(a+1))* = (-u
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The transfer when switching from monetary poverty to multidimensional is computed in a similar fashion.

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