Reconceptualizing Global Multidimensional Poverty Measurement, with Illustration on Nigerian Data

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.


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.They help identify which policy is best suited to alleviate the most pressing needs.
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 entirely ignore key non-monetary dimensions of wellbeing.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", 4 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 for more details).
However, the MPMs used in practice face credible criticisms related to their implementations.First, the way in which the Alkire-Foster methodology aggregates across dimensions seems unrelated to preferences (Ravallion, 2011).Non-paternalism requires that the MPM should make similar trade-offs across dimensions as those made by (multidimensionally) poor individuals. 5Currently, it is unclear how the necessary choices --weights, deprivation cutoffs, identification threshold -can be made in a way that is consistent with preferences.Second, 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 at the global level should at least account for inadequate consumption, bad health, and premature death. 6Clearly, data constraints complicate the monitoring of an MPM that simultaneously accounts for the monetary dimension, health, and mortality.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 direct impact of mortality was ignored.
Recent papers study these 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 Alkire-Foster methodology able to simultaneously identify both types of (multidimensionally) poor individuals but 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 the deceased into poverty measurement.The difficulty is that poverty, which affects the quality of life, is measured in a given year whereas the direct impact of mortality, which affects the quantity of life, can only be properly accounted for by taking a lifecycle perspective.These papers show that the direct impact of 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 conceptual guidance for the necessary choices.Interestingly, this implementation does not require selecting explicit values for weights across dimensions, except for mortality.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. 7Moreover, 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 and the paper does not claim that its proposed well-being indicator is better suited for the Nigerian context 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.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 allows improving 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 direct 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 wellbeing losses our well-being indicator captures in Nigeria in 2019.However, mortality need not dominate well-being comparisons across 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.This points to the need to better understand the plausible range of values for this normative parameter.
For question 2, the results suggest that accounting for non-monetary dimensions substantially affects wellbeing comparisons and could 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.8As a result, more than one-third of otherdimensions poor individuals are not monetary poor.This shows that ignoring non-monetary dimensions leads to incorrectly identifying these individuals as non-poor, 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 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.We interpret these figures as being substantial.Recall that our wellbeing 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.
On top of affecting well-being comparisons, information coming from non-monetary dimensions of wellbeing is directly policy relevant.This information helps identify the most pressing needs of individuals who have low well-being, thereby pointing to the policies best suited to meet these needs.We discuss how different classification of multidimensionally poor individuals can inform policy.
Finally, the paper falls short of providing a ready-to-use design for an improved global MPM.The design proposed in the empirical illustration leaves several questions open.In the conclusion, we shortly discuss these questions and how one could approach them in future research.We emphasize that this paper overlooks data constraints at the global level, which severely constrain the design of a global MPM.
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 key conceptual limitation of the Alkire-Foster methodology and present one pragmatic refinement that improves on this limitation.We also remind why aggregating across dimensions is required for several key policy purposes.In Section 2.2, we discuss why mortality is a peculiar dimension and how it can be aggregated to MPMs in a meaningful way.In both sections, we present refinements of MPMs whose aim is to better reflect a preference-based definition of well-being.

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, which is the first step for the design of evidence-based social protection policies and for evaluating progress against low well-being.

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 smaller than some utility threshold  * , i.e., () <  * .As graphically illustrated in Figure 1, individuals are poor when their achievements vector falls below indifference curve  * .As argued in Decerf (2023), the shape of this indifference curve should obey two restrictions that reflect upper-and lower-bounds for the substitutability across dimensions.First, indifference curve  * admits a positive asymptote in each of the core dimension of well-being.This restriction reflects the view that if an individual achievement is below an extreme threshold   > 0 in a core dimension of well-being, she must be poor regardless of her achievements in the other dimensions (Sen 1999, Nussbaum 2009, Alkire et al., 2015).Second, indifference curve  * has strictly positive marginal rates of substitution.This restriction reflects the views that individuals with utility level  * are always willing to slightly decrease their achievement in one dimension provided their achievements in other dimensions are sufficiently increased (Ravallion, 2011).An immediate consequence of such preference-based definition of the poor is that there are two types of poor individuals.First, an "extremor" is poor because at least one of her achievements is extremely low, i.e.,   ≤   for some core dimension j.Second, a "cumulator" is poor because she cumulates moderately low achievements in several dimensions, even though none of her achievements is extremely low.In Figure 1, an individual with achievement vector  is an extremor and an individual with achievement vector ′ is a cumulator.Note that it is a priori not possible to rank these two types of poor as a function of well-being.Indeed, some cumulators have lower utility than some extremors (and vice versa).
Aggregating across dimensions improves the identification of the worst-offs Ravallion (2011) argues that aggregating across dimensions is not necessary for several policy purposes.Of course, this does not mean that aggregating across dimensions is never policy relevant.For instance, prioritarian policy making, whose aim is to provide special attention to the worst-offs, requires identifying who has low well-being and thus requires such aggregation.
Aggregating across dimensions allows improving the identification of the worst-offs.Figure 2.a illustrates this point when considering two dimensions of well-being: consumption and health.Consumption is measured by the monetary value of the commodities consumed while health is measured by some indicator of health status.Here, the worst-offs are the individuals with the lowest well-being, say those below indifference curve  * .In practice, the monetary approach identifies the worst-offs by selecting a "poverty line", which is a cutoff in the consumption dimension illustrated in Figure 2 by the monetary value 1.Individuals are thus identified as poor by the monetary approach when 1 < 1.The "identification contour" associated to this purely monetary approach is drawn in red in Figure 2.a.This approach makes both exclusion errors and inclusion errors.For instance, an individual with achievement vector  is identified as monetary deprived even though she is not (multidimensionally) poor.In turn, another individual with achievement vector ′ is not identified as monetary deprived even though she is (multidimensionally) poor.

Figure 2: A Monetary poverty measure makes identification errors (a). A multidimensional identification based on the union approach makes fewer identification errors (b).
Note: Indifference curve  * is in blue and identification contours are in red.
The fact that the monetary approach makes identification errors is not a sufficient reason to discard it.As shown in Decerf (2023), any identification method is bound to make identification errors as soon as (1) individuals do not freely optimize their achievements in all dimensions and (2) the practitioner only has partial information on indifference curve  * .Arguably, these two conditions hold in most cases.In particular, condition (1) holds when there are no well-functioning markets for some dimension, which is typically the case for non-monetary dimensions of well-being such as health.
However, aggregating across dimensions allows reducing the amount of identification errors.This is illustrated in Figure 2.b.Consider the (extreme) health deprivation cutoff 2 = 2.The union approach based on cutoffs 1 and 2, whose identification contour is in red, identifies the (multidimensionally) poor strictly better than the monetary approach.Indeed, it strictly reduces the number of exclusion errors (′ is now correctly identified as poor) and it does not make more inclusion errors.Observe that the same argument can be used to show that MPMs who integrate monetary poverty as one of their dimensions (like the World Bank MPM) have the potential to better identify the multidimensionally poor than MPMs that only integrate non-monetary dimensions (see Supplementary Material S3 from Decerf, 2023).
In general, a good identification method should strive to have the shape of its identification contour as close as possible to the shape of indifference curve  * to minimize identification errors.A method that does not aggregate across dimensions identifies the poor worse than some method that aggregates across dimensions.This does not mean that a dashboard of dimension-specific indicators, each one summarizing the population's achievements in one dimension, does not provide useful information.It does.However, such dashboard cannot estimate the incidence of low well-being nor satisfactorily identity the individuals with low well-being.

A refinement of the Alkire-Foster identification method
The most popular method for the identification of the (multidimensionally) is proposed by Alkire and  Foster (2011) and best exposed in Alkire et al. (2015).In a nutshell, this method starts from binary deprivation statuses in m dimensions.An individual is deprived in dimension j when her achievement   is smaller than the deprivation cutoff   , i.e.,   = 1 when   <   , otherwise   = 0.The AF methodology identifies an individual as poor when the weighted sum of her deprivation statuses is too large, i.e., where   is the weight given to dimension j and k is the identification threshold.This clever method avoids an important practical issue faced by both the intersection approach and the union approach.These latter approaches tend to irrelevance when the number m of dimensions increases, unless the deprivation cutoffs are changed to increasingly implausible values.9 One key limitation of the AF methodology is to rely on binary deprivation statuses, which follows from the use of a unique cutoff in each dimension.This feature prevents from properly identifying both cumulators and extremors.We illustrate the issue in Figure 3, which considers two dimensions only.Under two dimensions, the AF methodology essentially boils down to either the union approach or the intersection approach, depending on the values given to the weights.The union approach is well-suited to identify extremors but does not perform well at identifying cumulators.As suggested in the left panel, the reason is that the union approach requires rather small cutoffs   to limit the inclusion errors that larger cutoffs would entail.In contrast, the intersection approach is well-suited to identify cumulators, but does not perform well at identifying extremors.As suggested in the middle panel, the reason is that the intersection approach requires rather large cutoffs   ′ to limit the exclusion errors that smaller cutoffs would entail.
Figure 3: The refined AF approach (c) can identify the poor better than the union approach (a) or the intersection approach (b).
Note: Indifference curve  * is in blue and identification contours are in red.

𝑗𝑗 𝑗𝑗
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 each dimension j: extremely deprived when   <   , moderately deprived when   ≤   <   and non-   deprived otherwise.Extremors can be properly identified by using the union approach on individuals who 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.
Section 2.2: Accounting for the direct impact of mortality The direct impact of mortality is to curtail the quantity of life (the lifespan) 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 direct impact of mortality should be accounted for.First, MPMs that ignore this direct impact may perversely react to mortality: they may record the death of poor individuals as an improvement (Kanbur and Mukherjee, 2007).Second, mortality outcomes are arguably highly consequential for low well-being.Cross-country well-being comparisons are very substantially affected when the direct impact of mortality 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.
There is also a practical reason to account for mortality.Mortality has two complementary desirable features.First, the lifespan is an outcome whose units can be transparently compared across individuals.Second, mortality reflects several key non-monetary dimensions like health, security or nutrition.These two features are complementary because several non-monetary dimensions that affect mortality are difficult to observe or measure in a parsimonious and comparable way.

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 a 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.10Another proposal by Baland et al. (2023) 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, which is the most popular mortality indicator.
These solutions 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 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.This indicator is called poverty-adjusted lifeexpectancy (PALE).Formally, PALE is defined by the following expression: 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.11 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 the necessary lifecycle perspective, (ii) attributing negative intrinsic value to all deaths, and (iii) always avoiding perverse reactions to the death of a poor individual.This indicator is also very 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 wellbeing 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 data-constraints prevent from estimating this distribution.Observe that such data-constraints typically prevent estimating this distribution because such estimation requires both information on mobility in and out of poverty throughout the lifecycle as well as information on differentiated mortality rates for poor and non-poor individuals.

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. Our design highlights some distinctive features of the refined AF methodology and why they may help practitioner better identify individuals with low well-being.
Importantly, our design is intended as a mere illustration.We do not claim that this design should be adopted by Nigerian policy makers.Beyond providing a proof of concept, our empirical ambitions are limited to proposing a plausible design that can be used 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.12Observing 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. 13ch 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.Before discussing the 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.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. 14An 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.

Extreme
The household annual consumption per capita is below national poverty line evaluated to 137430 Naira annual per capita (PA NGA).Monetary

Moderate (only Preferred)
The household annual consumption per capita is above national poverty line but below state societal poverty line: 1 + 0.5 x where x is the median state consumption in $ per day per capita.

Extreme
The individual suffers from at least one disability causing him a lot of difficulties in daily life or/and suffers from an extreme bad nutritional status, meaning a stunting condition for children (HAZ 1 < -2) or being undernourished (BMI 2 < 18.5) for adults.

Moderate
The individual suffers from at least one disability causing him only some difficulties in daily life and/or suffers from a moderate nutritional status, meaning being obese (30 < BMI) for adults.

Extreme
The individual belongs to a household deprived regarding all following householdlevel indicators: i) Household lacks access to limited-standard drinking water 3 ; ii) Household lacks access to limited-standard sanitation 4 ; iii) Household has no access to electricity; iv) Household has inadequate housing 5

Moderate
The individual belongs to a household deprived regarding three of the following household-level indicators: i) Household lacks access to limited-standard drinking water; ii) Household lacks access to limited-standard sanitation; iii) Household has no access to electricity; iv) Household has inadequate housing

Extreme
The individual belongs to a household, subjected the last 12 months to an extreme insecurity event 6 or belongs to a local government area (LGA) with at least one quarter of neighborhood households subjected to crime/violence with extreme consequences the last 12 months.

Moderate
The individual belongs to a household, subjected the last 12 months to a moderate insecurity event7 or belongs to a local government area (LGA) with at least one quarter of neighborhood households subjected to crime/violence with moderate consequences the last 12 months.

Extreme
The individual is a school-age child up to the age of grade 8, not enrolled in school

Moderate
The individual belongs to a household in which no adult (age of grade 9 or above) has completed primary education, and no adult can read nor write Source: Authors Note: 1 Height for Age Z score 2 Body Mass Index 3 Limited-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) 4 Limited-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) 5 Inadequate 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) 6 Extreme 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

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 the conceptual principles 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 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 assumption 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 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 wellbeing level as having consumption below the extreme poverty line.These are the considerations that should guide the design of the deprivation mapping.Observe that different empirical methods, like surveys using vignettes or subjective well-being questions, could be used to assess whether these principles plausibly hold.
Second, our identification of the (multidimensionally) poor does not require explicit values for weights (across dimension-specific indicators related to quality of life).This does not mean of course that we do not assume trade-offs across such indicators.Of course, our refined AF method also requires making this kind of assumptions, like the classical AF method.However, not having to select explicit values for weights may help reduce identification errors.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 as health deprivation.Alternatively, in any given dimension, the practitioner may only consider dimension-specific 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. 15If 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. 16Hence, a framework combining three deprivation statuses with the individual as unit of analysis holds the potential to reduce identification errors.
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.
There are several ways one could select a value for .First, the selection could be done by a policy maker who has the necessary legitimacy.Second, the selection could be grounded in the views of the individuals themselves.Such views should be collected through dedicated surveys.Third, parametric values for  could be deduced from assuming a particular Bernouilli (period) utility function, as illustrated in Appendix 2.
For our purposes, we assume two different values for the baseline and preferred designs.We conservatively assume  = 1 for the baseline design.From a policy making perspective, this choice provides the smallest plausible weight to mortality.The reason is that  = 1 implies that being dead provides the same well-being level as being (multidimensionally) poor.Arguably, no policy maker would 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  = 0.5 for our preferred design.We argue that  = 1 is an implausible weight for mortality, so smaller values must be considered.The "middle of the road" value  = 0.5 implies that one year of life lost is equivalent to two (= 1/) years of life spent in poverty.In the absence of convincing evidence, we believe that this value is more plausible than that assumed for the baseline design.

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.
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

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.

Section 4.2: Incidence of low quality of life
We focus in this subsection on the fraction of multidimensionally poor individuals H.Our objective is to get a sense of the source of their (multidimensional) poverty both in terms of type of deprivation (extreme or moderate) and in terms of type of dimensions.

Incidence and geographic distribution of deprivations
We begin with results associated to the deprivation mapping for the baseline design.These basic results provide insights that will shed light on the respective impacts that alternative dimensions have in later results.
Figure 5 provides a first glance at the prevalence of different type of deprivations at the national level.
The baseline design considers four dimensions.For each of these dimensions the histogram shows the fraction of individuals in each of the three deprivation statuses: extreme, moderate or not deprived.The figure immediately reveals that the monetary dimension is by far the most consequential dimension given our design.Not only the monetary dimension has the largest incidence of deprived individuals (40.5 percent), but by assumption all of them are extremely deprived.All the non-monetary dimensions have a smaller incidence of deprivation, and much smaller incidence of extreme deprivation.Among the nonmonetary dimensions, housing is the most consequential.Observe that security has a larger deprivation incidence than health but a much smaller extreme deprivation incidence than health.Figure A1 in Appendix 1 provides the corresponding histogram for our preferred design.To provide a sense of the respective importance of dimension-specific indicators, Table A1 in Appendix 1 provides the incidence in the population for each of these dimension-specific indicators.For instance, 10 percent of the population suffers from an extreme health deprivation.This percentage results from the fact that 2.9 percent suffers from a heavy disability, 2.3 percent is an underweight woman between 15 and 49 years old and 5.5 percent is a stunted child.Also, a sense of the correlation between deprivation status in the three non-monetary dimension is given in the Venn diagram A3 in Appendix 1.For instance, this diagram shows that 1.7 percent of the population is deprived in the three non-monetary dimensions.
Figure 6 provides an idea of the distribution across zones of these deprivations.As illustrated in Figure 4, the monetary deprivation is very heterogeneously distributed across zones, with south regions having low and north regions having high monetary deprivation.The same holds for the housing dimension.Importantly, the geographic distribution of housing deprivation is roughly the same as that of the monetary deprivation.In contrast, the incidence of health deprivation is approximately equally distributed across zones.Interestingly, the geographic distribution of extreme health deprivation is positively correlated with that of monetary deprivation while that of moderate health deprivation is negatively correlated with that of monetary deprivation.17Finally, the security deprivation is geographically distributed in a way that seems uncorrelated to the monetary deprivation.The correlation between the distribution across states of alternative deprivations is illustrated in Figure A2 provided in appendix 1.

Fraction and types of multidimensionally poor individuals
The theory in Section 2.1 defines two types of (multidimensionally) poor: extremors and cumulators.By assumption, all individuals who are monetary deprived are extremors.However, some extremors are not monetary deprived, like for instance individuals whose sole extreme deprivation is in a non-monetary dimension.To answer question 1, it is interesting to consider a second classification of (multidimensionally) poor individuals.We call monetary poor the (multidimensionally) poor individuals who have an extreme monetary deprivation.We call other-dimensions poor the (multidimensionally) poor individuals who do not have an extreme monetary deprivation.We further distinguish otherdimensions poor individuals into two categories.First, the consistently poor are both monetary poor and other-dimensions poor. 18Then, the omitted poor are other-dimensions poor but they are not monetary poor.As the latter taxonomy suggests, the national consumption poverty indicator, which only accounts for the monetary dimension, makes exclusion error on the individuals that we call omitted poor.Finally, we call only monetary poor the monetary poor who are not other-dimensions poor.
Both classifications of (multidimensionally) poor individuals are policy-relevant in different ways.First, distinguishing extremors from cumulators is relevant because the policies to fight these two kinds of poverties are different.For instance, no extremor can exit (multidimensionally) poverty when government policies only reduce moderate deprivations.Second, distinguishing monetary poor from other-dimensions poor is not only useful for our purpose to contrast our well-being indicators with monetary poverty.As shown by Bolch et al. (2022), cross section data on non-monetary dimensions of deprivation help distinguish between transient and chronic monetary poor individuals.Their results suggest that the consistently poor are more likely to be chronic monetary poor than the only monetary poor.Again, the best policies to tackle chronic and transient monetary poverty are different.
The Venn diagram in Figure 7 illustrates the prevalence of these four types of (multidimensionally) poor in Nigeria.The diagram reveals that the fraction of (multidimensionally) poor individuals in Nigeria in 2019 is 51.9 percent.The fraction of monetary poor is (again) 40.5 percent and the fraction of other-dimensions poor is 27.9 percent.The fraction of other-dimensions poor is by definition the sum of the fractions of consistently poor and omitted poor, respectively 16.5 percent and 11.4 percent.Two facts are worth emphasizing here.First, being monetary poor is positively correlated to being otherdimensions poor.An intuitive quantitative sense of this correlation is provided by the coefficient of overlap between monetary and other-dimensions poverty, which is defined as and whose value is 2.1 in the Nigerian population.Loosely speaking, a monetary poor individual is 2.1 times as likely to be other-dimensions poor than an individual who is not monetary poor.Second, ignoring non-monetary dimensions of quality of life leads to a significant bias in terms of properly capturing low well-being.Indeed, 11.4 percent of the Nigerian population is not monetary poor but still has a well-being level that our indicator deems too low.Conversely, ignoring the monetary dimension of quality of life leads to an even greater bias in terms of properly capturing low quality of life.Indeed, 24 percent of the Nigerian population is only monetary poor, that is, not other-dimensions poor but monetary poor.
The Venn diagrams in Figure 8 further study the 11.4 percent of omitted poor, who are other-dimensions poor but not monetary poor.This diagram sheds light on the non-monetary dimensions and types of deprivations that make these individuals (multidimensionally) poor.Among the 11.4 percent who are omitted poor, 8.2 percent are extremors and 3.2 percent are cumulators.The left panel focuses on the 8.2 percent of omitted poor individuals who are extremors, which implies that the sum of all percentages in that panel is equal to 8.2 percent.The three bubbles each capture extreme deprivation status for one of the three non-monetary dimensions considered in the baseline design.The diagram reveals that 0.7 percent of the population (0.7=0.5+0.1+0.1+0) are omitted poor who suffer from at least two extreme forms of non-monetary deprivations.The right panel focus on the 3.2 percent of omitted poor individuals who are cumulators, which implies that the sum of all percentages in the intersections of the right panel is equal to 3.2 percent (3.2=0.1+1.5+0.4+1.2).The three bubbles each captures moderate deprivation status in one of the three non-monetary dimensions considered in the baseline design.These diagrams reveal that health and housing the most consequential extreme form of deprivation for omitted extremors while security is the most consequential moderate form of deprivation for omitted cumulators.Table 2 provides a sense of the geographic distribution of different types of (multidimensional) poverty.Each of the three zones in the North have a larger fraction of (multidimensionally) poor individuals than each of the three zones in the South.This pattern is no surprise given that monetary poverty has the same geographical distribution and monetary poverty has a larger incidence than other-dimensions poverty in Nigeria.A more interesting insight of Table 2 is that other-dimensions poverty is less heterogeneously distributed across space than monetary poverty.Indeed, the fraction of other-dimensions poverty varies between 16.2 percent and 45.6 percent while the fraction of monetary poor individuals varies between 9.7 percent and 69.9 percent.This is confirmed by comparing the respective coefficient of variations for these two forms of poverty.One implication of this different heterogeneity across space is that ignoring 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).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 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.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. 19Overall, this significant reduction suggests that the extreme deprivation status, which allows accounting for the depth of deprivation, plays an important role in identifying the (multidimensionally) poor.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   =  * (1 −  * ), the figure illustrates that the value for PALE for a given state is obtained by "scaling down" its value for life-expectancy at birth (LE).This scaling down is more 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 ( = 1) and which is illustrated in Figure 9.The value for PALE of any given state is thus 1 =  * (1 − ), meaning that LE is scaled down by (1-H).A state with a small head-count ratio has its value of PALE that is close to its value of LE.Intuitively, a newborn in such a state is expected to live most of his 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. Figure 9 provides a couple of insights.First, life-expectancy at birth (LE) is negatively correlated with H, but this correlation is far from perfect.In fact, LE is much less correlated with monetary poverty than H is correlated with monetary poverty.This is not surprising given that H accounts for monetary poverty, which is its most consequential component in our data.It is still worth emphasizing that, as suggested by the Figure A2 in Appendix 1, LE is also less correlated with monetary poverty than housing.
Second, the direct impact of mortality on quantity of life, as captured by LE, is distributed much more homogeneously across states than quality of life, as captured by H. Indeed, almost all states have values for LE between 45 and 55 years, while their range of values for H spans between 20 percent and 90 percent.The value for the coefficient of variation for LE is 6% while that of H is 44%.This implies that the well-being ranking between Nigerian states is driven to a larger extent by H than by LE, at least when giving a low normative weight to mortality.As shown in Figure A6 in Appendix 1 for the baseline design, the differences in PALE values across several pairs of zones is driven to a larger extent by H than by LE.The Shapley decomposition reported in Figure A6 suggests that monetary poverty has an important impact on these differences, which reflects the fact that monetary poverty is in Nigeria an important component of H and is very heterogeneously distributed across space.
Third, and most importantly, the value selected for the normative weight given to mortality has a strong impact on well-being comparisons across Nigerian states.When assuming the minimal weight for mortality, as in our baseline design, the ranking of states according to PALE is relatively similar to the ranking of states according to H (see Section 5 for a quantification).Indeed, states with larger values for H tend to have smaller values of PALE.When assuming an intermediate weight for mortality, as in our 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.This highlights the need for better understanding what are plausible values for this normative weight.

Mortality generates very 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 perfect homogeneity 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. 20In 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 in order to highlight the fraction of losses coming from each source.Figure 10 shows that premature mortality is always a very substantial source of well-being losses.The fraction of total years of life prematurely lost or spent in poverty coming from mortality ranges from 25 percent in the North-West zone to 45 percent in the South-East zone (this fraction is even 66 percent in Lagos).The contribution of premature mortality to well-being losses could in fact be much larger than 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  = 1), but non-monetary losses are larger than monetary losses in Nigeria.In all zones, monetary poverty captures less than two-thirds the well-being 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 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 decent 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 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.Results are presented for each scenario, baseline and preferred.For each scenario, restrictions are applied in order to consider only states with a monetary poverty rate below 50%, on the one hand, and those with a monetary poverty rate above 50%, on the other.The aim of these restrictions is to reduce the disparity between compared states.
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 again highlights the need to better understand the plausible values for this normative weight.
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 (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.The results of this section thus suggest that accounting for non-monetary dimensions when measuring low well-being has policy implications that are far from negligible, 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 conceptual limitations.The paper proposes one way to apply recent solutions to improve on the 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 paper falls short of providing a ready-to-use design for an improved global MPM.We briefly discuss here the main open questions and how one could approach these questions.
First, careful work is needed for the selection of non-monetary dimensions perhaps more importantly, of the dimension-specific indicators capturing these dimensions.The ideal dimensionspecific indicators should offer a good balance between (i) capturing a major source of well-being losses, (ii) being meaningfully comparable across individuals and (iii) having manageable data requirements.A good dimension-specific indicator from the perspective of point (i) should affect a significant fraction of individuals and should substantially reduce their well-being. 21The latter aspect can be investigated through various preferences elicitation techniques, e.g., through vignette or subjective well-being surveys.Point (iii) implies to favor dimension-specific indicators that are already widely available or are easy to collect in surveys.Given the importance for MPMs of capturing the joint-distribution of achievements in the dimension-specific indicators, one would ideally wish to be able to collect them all in an LSMS-type survey.If not possible, then one would need a robust method for estimating the (missing) joint distribution between achievements collected from separate surveys.Creative solutions should be investigated, like phone surveys collecting key missing information on the joint distribution.More work is certainly needed in that direction.
Second, 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 the identification contour approximates reasonably well indifference curve  * (Decerf, 2023; Jones, 2022).
Third, 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.22

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:

⮚ 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: o 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 o Socio-demographic characteristics of the household's head such as age, gender, education level, marital status o Socio-demographic characteristics of the individual when applicable o Location (urban/rural) and household size

⮚ Inference approach
Nutritional status has been attributed in NLSS data using, on the 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: o 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).o No undernourished men in the 15-49 age group (conservative approach) o 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 choice of a more or less demanding threshold depending on the impact of first or second species errors.
In the framework of this analysis, the method applied is based on the a priori information available on the observed values in the DHS data and on additional assumptions presented in the preceding paragraph.
However, since this analysis was conducted in the context of a multinomial regression model (three categories), the classification of individuals required the choice of not one, but two thresholds.To do so, a sequential approach was adopted.In a first step, a binary classification on the basis of discriminating one category from the two others was performed using the estimated initial probabilities.In a second step, a second binary classification in the class regrouping two categories was performed, this time, based on the conditional probabilities.

Appendix 4: Contrasting well-being losses to quality and quantity of life
Although PALE accounts for both quality and quantity of life, it cannot readily be used to compare their relative importance for the low well-being afflicting a given society.Indeed, the value of PALE does not additively decompose into the low well-being coming from mortality and the low well-being coming from multidimensional poverty.The reason is that PALE does not count years of life lost.Rather, PALE simply makes a weighed sum of numbers of years lived in and out of poverty.This contrasts with the expected deprivation indicator (ED), which is a solution to capture premature mortality proposed by Baland et al  (2023).ED has this additive decomposability property as it makes a weighted sum of years spent in poverty with years prematurely lost.These respective numbers of years are expected for a newborn, assuming that the poverty and mortality rates prevailing in the period of her birth remain fixed.Formally, ED is defined as where θ is the same normative parameter,  *  captures the number of years the newborn is expected to spend in (multidimensional) poverty, â denotes the age threshold defining premature mortality and   is the lifespan gap expectancy, which measures the number of years that a newborn is expected to lose prematurely with respect to â. Formally, letting   denote the mortality rate observed for age a, the lifespan gap expectancy () measures the number of years that a newborn is expected to lose prematurely if confronted by the age-specific mortality rates of vector µ throughout her  first years of life: LGE is a measure of mortality that can be thought of as the complement to LE below the age threshold â, as illustrated in Figure A7.This figure also illustrates that the denominator of ED measures a normative lifespan, which is at least as large as LE.
Importantly, PALE and ED are logically related to one another.PALE is ordinally equivalent to ED when the age threshold defining premature mortality corresponds to be the maximal age. Figure A7 illustrates the

Figure 1 :
Figure 1: Two types of poor individuals under a preference-based definition of the poor Note: Indifference curve  * is in blue, an individual is an extremor if she consumes x and a cumulator if she consumes x'.

Figure 4 :
Figure 4: Prevalence of monetary poverty in Nigeria, per zone.Source: Authors' estimates based on data from NLSS 2019 Note: The figure presents, for each zone, the share of individuals below the national poverty line.

Figure 5 :
Figure 5: Prevalence of extreme and moderate deprivations per dimension for Nigeria, baseline scenario Source: Authors' estimates based on data from NLSS 2019 Note: The figure presents, for each dimension considered in the baseline scenario -monetary, health, housing, security-, the share of individuals according to their state of deprivation: non deprivation, moderate deprivation, extreme deprivation.

Figure 6 :
Figure 6: Prevalence of extreme and moderate deprivations per dimension per zone, baseline scenario Source: Authors' estimates based on data from NLSS 2019 Note: The figure presents, for each dimension considered in the baseline scenario -monetary, health, housing, security-, the prevalence in % of moderate deprivation, extreme deprivation within each of the six Nigeria's zones classified in ascending order of monetary deprivation.

Figure 7 :
Figure 7: Classification of multidimensionally poor individuals in Nigeria, baseline scenario Source: Authors' estimates based on data from NLSS 2019 Note: Using a Venn diagram, the figure shows the decomposition of multidimensional poverty, defined within the baseline scenario, into "Only monetary poverty" (transparent area), "Other dimensions-additional poor" for individuals multidimensionally poor without being monetary poor (dark green) and "Other dimensions -twice poor) for individuals cumulating monetary and other dimensions (light green).
Figure 8: Overlap of the non-monetary deprivations suffered by omitted poor, baseline scenario Source: Authors' estimates based on data from NLSS 2019 Note: The left panel shows the fraction of the Nigerian population that is simultaneously (i) not monetary poor and (ii) suffers from an extreme non-monetary deprivation.The right panel shows the fraction of the Nigerian population that is simultaneously (i) not monetary poor, (ii) does not suffer from an extreme non-monetary deprivation and (iii) suffers from a moderate non-monetary deprivation.

Figure 9 :
Figure 9: Construction of PALE from H and LE, per states, baseline scenario Source: Authors' estimates based on data from NLSS 2019 Note: The graph shows a scatter plot of life expectancy at birth (LE) and Poverty Adjusted Life expectancy (in years) as a function of multidimensional poverty rates for Nigeria's 37 states, in the baseline scenario.Additional information below the figure provides variability across states of life expectancy at birth, PALE and multidimensional poverty headcount.

Figure 10 :
Figure 10: Decomposition of well-being losses between years of life prematurely lost and years spent in multidimensional poverty (partitioned into three types), per zone, baseline scenario Source: Authors' estimates based on data from NLSS 2019 Note: The figure panel shows the decomposition of well-being losses between premature mortality as computed by the lifespan gap expectancy (LGE), only monetary poverty, only other (than monetary) dimensions poverty and both monetary and non-monetary dimensions poverty (See Appendix 4 for details).The first figure presents the decomposition in absolute values while the second one presents the decomposition in relative values expressed in %.

Figure A1 :
Figure A1: Prevalence of extreme & moderate deprivations per dimension for Nigeria, preferred scenario

Figure A2 :
Figure A2: Geographic distribution of deprivation (extreme + moderate) per state, baseline scenarioSource: Authors' estimates based on data from NLSS 2019 Note: The figure presents, for each dimension considered in the baseline scenario -monetary, health, housing, security-, the geographic distribution within the 37 Nigeria's states of the deprivation (extreme and moderate) rate in %.Life expectancy at birth within each state is also presented.

Figure A4 :
Figure A4: Construction of PALE from H and LE, per states, preferred scenario Source: Authors' estimates based on data from NLSS 2019 Note: The graph shows a scatter plot of life expectancy at birth (LE) and Poverty Adjusted Life expectancy (in years) as a function of multidimensional poverty rates for Nigeria's 37 states, in the baseline scenario.Additional information below the figure provides variability across states of life expectancy at birth, PALE and multidimensional poverty headcount.

o
-2 < HAZ Normal (Well nourished) o -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: o BMI < 18.5 Undernourished o BMI >= 18.5 & BMI < 30 Normal (Well nourished) o BMI > 30 Obese 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.

Table 2 :
Prevalence of different types of multidimensionally poor individuals, per zone, baseline scenario 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

Table 3 :
Impact of each non-monetary dimensions on other-dimensions poverty rates Source: Authors' estimates based on data from NLSS 2019 Note:

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

Table 5 :
Percentage of states pairwise comparisons reversed between pairs of well-being indicators Authors' estimates based on data from NLSS 2019Note: The table shows the percentage of pairs of states whose comparison is reversed between two different well-being indicators: average consumption, monetary poverty rate (), multidimensional poverty rate () and poverty-adjusted life-expectancy (PALE). Source:

Table 6 :
Fraction of (hypothetical) budget reallocated across states between pairs of well-being indicators Source: Authors' estimates based on data from NLSS 2019 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).

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) 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.