metadata: authors: 0: author: Decerf,Benoit Marie A
count: World
docna: 0: docna: Normative Indicators Combining Poverty and
            Mortality : A Survey
docty: Policy Research Working Paper
abstracts: cdata!: This paper surveys the small branch of
            welfare economics that studies indicators combining poverty
            and mortality. The paper distinguishes two reasons for
            constructing such indicators. The first reason is to perform
            multidimensional well-being comparisons. For this purpose,
            mortality has (negative) intrinsic value. The key question
            relates to the trade-off that the indicator makes between
            poverty and mortality, that is, between the quality and
            quantity of life. A lifecycle utility approach suggests
            expressing this trade-off as the number of years spent in
            poverty that is deemed equivalent to one year lost to
            mortality. The second reason is to investigate the
            instrumental role that selective mortality—the fact that the
            poor tend to die earlier—has on the evolution of poverty
            measures. Then, the key question is how to define the
            counterfactual situation against which the instrumental
            impact of mortality is assessed.
display_title: Normative Indicators Combining
            Poverty and Mortality : A Survey
listing_relative_url: /research/2022/05/33819617/normative-indicators-combining-poverty-mortality-survey
topicv3: Multi-dimensional Poverty m1326485 1151,Poverty Measurement and Analysis m1326941 707
publishtoextweb_dt: 2022-05-16T00:00:00Z
dois: 10.1596/1813-9450-10042
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 1947055
model_extractions: Policy Research Working Paper 10042 Normative Indicators Combining Poverty and Mortality A Survey _Benoit Decerf_ Development Economics Development Research Group May 2022
Policy Research Working Paper 10042

# **Abstract**

This paper surveys the small branch of welfare economics that studies indicators combining poverty and mortality. The paper distinguishes two reasons for constructing such indicators. The first reason is to perform multidimensional well-being comparisons. For this purpose, mortality has (negative) intrinsic value. The key question relates to the trade-off that the indicator makes between poverty and mortality, that is, between the quality and quantity of life.

A lifecycle utility approach suggests expressing this tradeoff as the number of years spent in poverty that is deemed equivalent to one year lost to mortality. The second reason is to investigate the instrumental role that selective mortality—the fact that the poor tend to die earlier—has on the evolution of poverty measures. Then, the key question is how to define the counterfactual situation against which the instrumental impact of mortality is assessed.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may be contacted at bdecerf@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Normative Indicators Combining Poverty and Mortality: A Survey**

Benoit Decerf<sup>1</sup> World Bank Keywords: Poverty measurement, Mortality paradox, Poverty-adjusted life-expectancy, Multidimensional poverty JEL Codes: D63, I32

## 1 World Bank, Development Research Group. Email : <u>bdecerf@worlbank.org.</u>

Acknowledgments : This survey will appear as a chapter in the forthcoming Handbook of Research on Measuring Poverty and Deprivation (Silber 2022). I am grateful to Jacques Silber and to an anonymous referee for useful comments and suggestions. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author and should not be attributed in any manner to the World Bank, its affiliated organizations, or members of its Board of Executive Directors or the countries they represent.
# **1) INTRODUCTION**

A vast literature documents the positive association between poverty and mortality, and the potential causality channels underlying this correlation (Mackenbach et al. 1997; Wagstaff 2000; Fritzell et al. 2015). This survey does not review these positive relationships, but takes a purely normative perspective and its focus is on indicators combining poverty and mortality.

We distinguish two reasons for building normative indicators combining poverty and mortality. The first reason is to perform multidimensional well-being comparisons. A summary indicator combining poverty and mortality may prove useful when evaluating policies that imply a trade-off between these two phenomena. Such summary indicator can also be used to compare human development across societies (Stiglitz et al. 2009), at least when assuming that poverty and mortality are the two major sources of well-being losses (Deaton 2013). The second reason is to investigate the instrumental role that selective mortality, i.e., the fact that the poor face higher mortality rates, has on the evolution of poverty measures. Poverty measures only account for those who are alive. If mortality rates among the poor increase, then, ceteris paribus, the fraction of poor individuals decreases, which constitutes a “mortality paradox” (Kanbur and Mukherjee 2007). One may thus wonder what proportion of the measured poverty change is due to changes in mortality rather than changes in living standards.

These two objectives define two distinct branches of literature with specific characteristics. Indicators of multidimensional well-being attribute a (negative) intrinsic value to mortality. The key question is the trade-off that the indicator makes between mortality and poverty. In contrast, for the branch concerned by the mortality paradox, indicators need not attribute intrinsic value to mortality. The key question is how to define the counterfactual situation against which the instrumental impact of selective mortality is assessed. Even if the latter branch relates to a more technical question, we review it alongside the first in the hope to dissipate the confusion that may exist between the two.

We conjecture that the recently developed indicators combining poverty and mortality may complement standard normative indicators that are routinely used to express the trade2
off between the quality and quantity of life. Indeed, poverty reduces the quality of life while mortality reduces the quantity of life. Maybe the main advantage of these new indicators is to strike a good balance between simplicity and decent theoretical foundations.

In the next section, we introduce the notation and a simple framework in which individuals, for each period of their lives, are either poor or non-poor. We present the arguments why poverty and mortality should be aggregated using years of life as a common metric. We also introduce the concept of a stationary society, which plays a central role for normative indicators accounting for mortality.

In the following section we show how the expression for a newborn’s expected lifecycle utility simplifies in this framework of two statuses. The indicator obtained aggregates poverty and mortality using a single normative parameter. Importantly, this parametric family may sometimes unambiguously rank a pair of societies for which the two dimensions are “in conflict”.

Then we show how to adapt the indicator obtained in order to evaluate policies or shocks affecting both poverty and mortality. An adaptation is necessary when endorsing the idea that all years of life lost should have the same value.

In another section we show how the same idea applies to indicators of multidimensional deprivation. An individual is considered lifespan deprived if she dies prematurely. The same framework reveals that lifespan deprivation is a peculiar dimension that requires a specific treatment.

Finally, we turn to the instrumental role that selective mortality has on poverty measures and review the literature on the mortality paradox.

# **2) FRAMEWORK AND STATIONARY SOCIETIES**

The indicators we present are fairly simple. However, exposing their connection to lifecycle utility requires introducing a non-negligible amount of notation. The reason is that such indicators aim at evaluating a society _in a given period_ while mortality has consequences over many subsequent periods.

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There is a discrete set of periods { _...,t_ −1 _, t, t_ + 1 _,..._ }, each period being a calendar year. In each period, some individuals are born, then all alive individuals consume and then some individuals die. In each period, the consumption status of an individual is to be either poor ( _P_ ) or non-poor ( _NP_ ). The life of an individual _i_ is defined as the list _li_ = ( _l_ i0 _,...,lid_ ) of the consumption statuses she enjoys between age 0 and the age _di_ ∈ {0 _, ... , a_<sup>∗</sup> -1} at which the person dies, where for each age _a_ we have _lia_ ∈ { _NP, P_ } and _a_<sup>∗</sup> is the maximal lifespan. The set of lives is thus _L_ = ∪ _d_ ∈{0 _,...,a*-1_ } { _NP, P_ }<sup>d+1</sup> , where ∪ is the union symbol.

There are _nt_ individuals born in period _t_ . The number of individuals who are born in period _t_ and survive at least to age _a_ is denoted by _nt_ ( _a_ ), where _nt(0)=nt_ . The profile of lives for the cohort born in _t_ is denoted by _Ct_ = ( 1 _,...,_ ). The cohort born in _t_ defines a distribution on the set of lives, which we denote by Γnntt _t_ : _L_ → [0 _,_ 1], with ∑ _l_ ∈ _L_ Γ _t_ ( _l_ ) = 1. ll ll Following Harsanyi (1953), the social welfare of the cohort born in _t_ can be written as its average lifecycle utility where _U_ is the lifecycle utility function and _u_ is the period utility function, i.e., _U(li)=_ ∑ _au(lia),_ for which we assume that _u(NP)_ ≥ _u(P)_ ≥ 0. Observe that mortality is intrinsically valued through its opportunity cost: death reduces the number of periods a person is poor or non-poor. Also, period utility is not discounted. This simplification is called for when evaluating well-being in period _t_ in order to avoid giving lower social weights to older individuals.

Of course, we do not observe in period _t_ the profile of lives for the cohort born in _t_ . Rather, we observe the period’s natality, mortality and consumption statuses. A society in period _t_ is the list of profiles of lives for all cohorts born during the _a_<sup>∗</sup> periods preceding _t_ , which we denote by _St_ = ( _Ct_ − _a*+1, ..., Ct_ ). The poverty observed in period _t_ is summarized by the period’s head-count ratio where _pt_ ( _a_ ) denotes the number of individuals born in _t_ who are alive and poor at age _a_ . The mortality observed in period _t_ is captured by a vector of age-specific mortality 4
( ) <u>( )</u> rates μ<sup>_t_</sup> _=(_ μ<sup>_t_</sup> _0,...,_ μ<sup>_t_</sup> _a*-1)_ where = and is summarized by the period’s lifenntt−aa ii −nntt−aa ii+1 expectancy at birth μμii<sup>tt</sup> nntt−aa(ii) A society is stationary if all its cohorts have the same size and the same distribution of lives. Formally, society St is stationary if for any period t’ ∈ {t –a*+1, ... , t} we have _•_ Γt’ = Γt (constant distribution of lives), _•_ nt’ = nt (constant size of cohorts).

Stationary societies play a central role in the construction of normative indices combining poverty and mortality (Baland et al., 2021a). These indices should perform sound comparisons of stationary societies because they correspond to an “equilibrium” situation. In a stationary society, the mortality and poverty observed in a given period are the same as those observed in the next period. After a permanent mortality shock, say, caused by some policy intervention, a transition phase starts during which the population pyramid mechanically adjusts. After this transition phase, the long-run consequences of the shock are reached and the society is again stationary. Indicators should get it right when comparing these long-run “equilibrium” consequences.

Also, in a stationary society, we can compute a cohort’s average lifecycle utility from the poverty and mortality observed in the period of its birth. Indeed, the poverty and mortality observed in that period perfectly reflect the poverty and mortality that its members will be confronted with throughout their lives (Baland et al., 2021b). This insight has general validity. For simplicity, we illustrate it using an example. Consider a stationary society for which two individuals are born in each cohort, one living only for one period in poverty and the other living for three periods out of poverty, i.e. _n_ = 2, _l_ 1 = ( _P_ ) and _l_ 2 = ( _NP, NP, NP_ ). In period _t_ , four individuals are alive: the poor born in _t_ , the non-poor born in _t_ , the non-poor born in _t_ −1 and the non-poor born in _t_ −2. This shows that, in a stationary society, it is possible to match each person-year in _Ct_ , i.e. in the profile of lives of the cohort of newborns _,_ to an individual who is alive and has the same consumption status in _t_ . Also, two individuals die at the end of period _t_ : the poor born in _t_ and the non-poor born in _t_ −2. Hence, poverty and mortality in _Ct_ are perfectly reflected by the poverty and mortality observed in _t_ .

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# **3) THE QUANTITY AND QUALITY OF LIFE**

Indicators combining mortality and poverty may be used as summary indices for human development. There is a longstanding quest for such an index (Stiglitz et al. 2009). The multi-dimensional nature of well-being has led to the development of composite indices such as the Human Development Index of the UNDP. Two major critiques have been raised against standard composite indices. First, they aggregate different dimensions in an ad-hoc fashion. Second, they rely on arbitrary or implausible weights (Ghislandi et al 2019). In order to escape these critics, some authors even suggested to narrow down the number of dimensions to just one, mortality (Hicks and Streeten 1979; Silber 1983).

Baland et al. (2021b) propose a summary index that aggregates poverty and mortality while making progress on these two critiques. Their proposal is based on social well-being understood as the expected lifecycle utility of a newborn drawn at random (Harsanyi 1953). They simplify the sophisticated formulations of Becker et al. (2005) and Jones and Klenow (2016) by making quality of life a binary variable: being poor or non-poor. When normalizing the period utility of not being alive to 0 and assuming that _u(NP)_ ≥ _u(P)_ ≥ 0, the only remaining normative parameter is θ , the fraction of period utility lost when poor . (4) )<sup>) −uu(NN)</sup> Baland et al. (2021b) show that, fθθ=<sup>uu(N</sup> or any θ∈ [0 _,_ 1], the average lifecycle utility of newborns uu(N = L ), where ). They call this index the poverty-adjusted life-expectancy (PALE). Importantly, PALE is a normalization of the average lifecycle utility of newbornsθθ tt tt WW (SS ) = WW(CC even when mortality is selective.

The PALE index penalizes years spent in poverty by a factor θ . When assuming that θ = 0, i.e. being poor is the same as being non-poor, Eq. (1) reduces in a stationary society 0( <u>)</u> to = L , i.e., to life-expectancy at birth. In contrast, when assuming that θ = 1, ) WW SStt tt i.e. being poor is the same as being dead,uu(N Eq. (1) reduces in a stationary society to 1( <u>)</u> = L ), i.e., to the Poverty-Free Life-Expectancy index proposed by ) WW SStt tt tt uu(N (1 −HHCC 6
Riumallo-Herl et al. (2018). Clearly, these two cases are based on “extreme” views on the value for parameter θ .

In general, the comparison of two societies with PALE depends on the arbitrary value selected for parameter θ . Baland et al. (2021b) show that the comparison with PALE is sometimes robust to all plausible values for θ , even for some pairs of societies for which _HC_ and _LE_ yield opposite comparisons. Hence, the PALE index ranks more pairs of societies than a dashboard made of HC and LE would, even when there is no consensus on the value that its weight θ should take. In their application on developing countries, they find that poverty and mortality follow opposite trends in 28% of cases, and PALE is able to solve 38% of these ambiguous cases.

Of course, societies are seldom stationary, and the poverty and mortality observed in _t_ may not be reliable guides for the expected lifecycle utility of a random newborn in _t_ . Yet, Baland et al. (2021b) argue that, whether or not a society is stationary, PALE provides a meaningful aggregation of the poverty and mortality observed in period _t_ . In their view, it is as meaningful as using life-expectancy at birth in order to aggregate the mortality observed in period t in a society that is not stationary.

# **4) POLICY EVALUATION AND HYBRID SHOCKS**

In this section, poverty and mortality are still considered as two different sources of wellbeing losses. However, whereas the last section compared different societies based on their observed poverties and mortalities, we now compare one society with a counterfactual situation. Such comparison with a counterfactual situation is necessary when evaluating costly policies that save lives – e.g. investments enhancing the safety of transport infrastructures, health policies or some environmental policies – or when evaluating the welfare impact of a shock affecting both poverty and mortality, like a pandemic.

A priori, the indicator _Wθ_ could readily be used to perform these comparisons. However, mortality is a particularly sensitive topic and we will discuss the implications of the idea that the lives of all individuals should count the same. _Wθ_ violates this idea when comparing the respective values of a year of life lost by the poor and the non-poor. Decerf 7
et al. (2021) and Ferreira et al. (2021) address this point when evaluating the welfare losses associated to the poverty and mortality impacts of the Covid-19 pandemic.

Traditionally, the method used when performing such counterfactual comparisons is the value of a statistical life (VSL) (Viscusi 1993). In a nutshell, the VSL method compares mortality losses with economic costs by attributing a price to a human life (or to a year of human life). Once both dimensions are expressed in monetary units, their respective sizes can be compared. Decerf et al. (2021) and Ferreira et al. (2021) argue that the VSL method cannot provide the basis for a fruitful public debate because many people reject the mere idea of attributing a price to a human life. Another major shortcoming of the VSL method is that the distribution of economic costs is not taken into account. As a result, trade-offs between mortality and economic costs are seldom publicly discussed, and the view that human lives should be saved “whatever the costs” dominates by default in the media.

To help overcome these limitations, Decerf et al. (2021) propose an alternative normative method that could complement the VSL approach. They assess the welfare impact of the direct mortality and economic consequences of the Covid-19 pandemic using a method based on _Wθ_ . Instead of comparing the two dimensions in monetary units, they use years of human life as a common metric. The impact of mortality is measured by the number of years of life lost and the economic impact is measured by the number of additional years spent in poverty. This method requires a unique normative parameter: the number of poverty-years that yields the same well-being loss as one lost year.

Formally, Decerf et al. (2021) assess the impact of the pandemic on the welfare of the population that is alive at the period _t_ during which this hybrid shock occurs. For each individual _i_ , the pandemic may have two impacts. First, the pandemic may change the consumption status of person _i_ from being non-poor to being poor for one or more years following the outbreak. The period utility loss for each additional “poverty-year” is denoted by ∆ _up_ = _u(NP)_ – _u(P)_ . Second, the pandemic may kill person _i_ in period _t_ , in which case _i_ loses a number of years of life corresponding to her expected residual longevity in _t_ . The period utility loss for each “lost-year” is ∆ _ud_ .

The definition of ∆ _ud_ is the key normative consideration. An observed outcome, i.e., one 8
lost-year in some period _t’_ following _t_ , is contrasted with a counterfactual outcome, i.e. the consumption status the person would have had in _t’_ if she did not die in _t_ . Using a model in order to predict whether the person would have been poor or non-poor yields the normatively unappealing consequence of valuing the cost of premature mortality differently for the poor and the non-poor. Avoiding this requires attributing the same value for ∆ _ud_ to all lost-years.

Denoting by _LY_ the total number of lost-years for the population alive in _t_ and by _PY_ the total number of additional poverty-years, the impact on social well-being of the pandemic can be expressed as a weighed sum of poverty-years and lost-years where the normative parameter _α_ captures how many poverty-years have the same impact on social well-being as one lost-year. This social parameter should ideally be some aggregation of the answers that individuals might give to the following hypothetical question: “how many years of your remaining life would you be willing to spend in poverty in order to increase your remaining lifespan by one year?” Eq. (5) can be used to compare the sizes of the two sources of well-being loss. Decerf et al. (2021) and Ferreira et al. (2021) estimate for each country how many additional povertyyears have been generated for each lost-year, which we denote by ~~.~~ Any social NNPP observer can then contrast the empirical value of _α_ ˆ with her preferred value for the normative αα�= LLPP parameter _α_ . She concludes that the mortality costs are higher than the poverty costs if and only if _α_ ˆ _< α_ . Eq. (5) can also be used in order to contrast well-being costs across countries or well-being costs for alternative policy scenarios.

Decerf et al. (2021) assume that ∆ _ud_ = _u(NP)_ , i.e. the individual would have been non-poor if the year had not been lost. Hence, they assume a high opportunity cost for mortality. Under this assumption, we have _α_ = 1 _/_ θ and the minimal value that _α_ can take is 1. This seems to be a defensible lower-bound, at least for those who believe that one lost-year is at least as bad as one poverty-year. Then, the mortality loss is larger than the poverty loss for any country for which _α_ ˆ _<_ 1.

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# **5) MULTIDIMENSIONAL POVERTY**

The same approach based on years of life has been applied to measuring deprivation in the quantity and quality of life. In this multidimensional poverty framework, individuals may be deprived in their quality of life when their consumption is too low and they can be deprived in their quantity of life when they die before reaching a minimal age threshold, denoted by _a_ ˆ. Under this interpretation, premature mortality induces a deprivation in a key resource: the lifespan. Mortality is intrinsically valued, but only below the age threshold.

Baland et al. (2021a) show that lifespan deprivation is a peculiar dimension that requires a specific treatment. Multidimensional poverty measures cannot simply incorporate this dimension without adapting their methodology. The reason is that lifespan deprivation and poverty are mutually exclusive. In a given period, either the individual is prematurely dead or the individual is poor, but she cannot be both dead and poor. This is unlike other dimensions of deprivation that can simultaneously affect the same individual. Their mutually exclusive nature requires to add a term capturing the lifespan deprivation component.

However, the term capturing lifespan deprivation must be carefully constructed. Baland et al. (2021a) show that composite multidimensional poverty measures, like the Human Poverty Index (Watkins, 2006), are not “consistent”. That is, these measures do not hold constant the trade-off between one poverty-year and one prematurely lost-year. As a result, these measures sometimes record the premature death of a poor individual as povertyincreasing and sometimes as poverty-reducing. They show that this problem finds its source in the reference population considered by these measures, which does not account for the prematurely dead.

In the terminology of Baland et al. (2021a), a “total deprivation” measure combines deprivation while alive with lifespan deprivation. They propose two consistent total deprivation measures (“inherited deprivation” (ID) and “generated deprivation” (GD)) and Baland et al. (2021b) propose a third one (“expected deprivation” (ED)). All three have similar expressions and all three are equivalent when comparing stationary societies. We only introduce ID and ED. Let _A_<sup>_t_</sup> denote the number of individuals alive in period 10
0a ~~TT TT~~ a-1 (@-(a+D)*n* (un 0a ~~TT OT~~
If ID, GD and ED compare any two stationary societies in the same way, they differ when comparing non-stationary societies. ID and GD can be decomposed by subgroups, whereas it is not the case of ED. ID measures premature mortality taking place before period _t_ whereas GD and ED measure premature mortality taking place in period _t_ . They react with different speeds to permanent mortality shocks: ED exhibits the least inertia and ID the most.

Applying these indices to developing countries, Baland et al. (2021a) show that the mortality term accounts for a non-negligible fraction of total deprivation and that the two terms are far from being perfectly correlated. As a result, the evolution of total deprivation in a country regularly contradicts the evolution of poverty alone in that country. Therefore, ignoring the mortality component leads to severe bias in the measurement of total deprivation.

One limitation of these measures is that they do not account for the overlap that may happen between poverty and mortality. In other words, the premature death of a poor person counts the same as the premature death of a non-poor person, even if the former case “concentrates” different deprivations on the same individual. The same remark is also valid for PALE. The reason is that the social welfare function that underlies these indices is not prioritarian, but purely utilitarian. Baland et al. (2021a) discuss how to adapt these indices in order to account for such concentration. However, such adaptation requires more information, notably on mobility in and out of poverty over the lifespan.

# **6) LITERATURE ON THE MORTALITY PARADOX**

The literature on the mortality paradox starts from the observation that there are two ways to exit poverty: becoming non-poor or dying. The latter case may lead to a mortality paradox. Consider for instance a stationary society for which two individuals are born in each cohort, one living only for two periods in poverty and the other living for three periods out of poverty, i.e. _n_ = 2, _l_ 1 = ( _P, P_ ) and _l_ 2 = ( _NP, NP, NP_ ). Assume that the health conditions for the poor deteriorate such that they only live for one period, i.e. the new stationary society has _n_ = 2, _l1’_ = ( _P_ ) and _l_ 2 = ( _NP, NP, NP_ ). The head-count ratio after this evolution is 1 _/_ 4 against 2 _/_ 5 initially. The mortality paradox is that the higher mortality faced by the poor reduces the poverty measure. Observe that the instrumental 12
role that mortality has on the poverty measure follows from the fact that mortality is selective. If mortality rates are the same for the poor and the non-poor, the paradox disappears.

Since selective mortality has an instrumental role on the poverty measure, one may wonder how much of the measured poverty change is explained by the mortality change, rather than by consumption change. Answering this question requires constructing a counterfactual situation for which the instrumental role of selective mortality is neutralized. Two alternative approaches have been proposed: one that relies on standard poverty measures and another that constructs new poverty measures specifically designed for this task.

The simplest approach consists in constructing a counterfactual situation that nets-out the differential mortality change over the time interval and then recalculates poverty. Ravallion (2005) follows this route using the head-count ratio as poverty index. He observes that the head-count ratio would take the same value for the counterfactual situation for which mortality was not selective as the value it would take if there was no mortality at all during the time interval. Therefore, he obtains his counterfactual situation by adding to the population observed at the end of the time interval all individuals who died during this interval, without changing their poverty status. The instrumental role of selective mortality on poverty is obtained by contrasting the observed and the counterfactual head-count ratios at the end of the time interval. His empirical findings show that selective mortality plays a non-negligible role, but that this role does not dominate the evolution of poverty in his data.

A more demanding approach consists in designing new poverty measures that are robust to mortality changes and evaluate the evolution of poverty with these new measures. Kanbur and Mukherjee (2007), Lefebvre et al. (2013) and Lefebvre et al. (2017) follow this approach. Their measures neutralize the effect of selective mortality by assigning fictitious incomes to those who are prematurely dead. They investigate various methods for assigning these fictitious incomes and the ability of these methods to neutralize the effect of selective mortality. These methods differ by the identity of those for whom fictitious incomes are constructed and the procedure used for this construction. In particular, the effect of selective mortality may be neutralized if the fictitious incomes are 13
correctly inferred, i.e. correspond to the “true” incomes that prematurely dead individuals would have earned. Their empirical results show that the impacts of extending the income profiles of the dead vary significantly with different methodological choices and databases.

We conclude by observing that mortality is not the only demographic phenomenon that affects poverty measures. Natality also plays an instrumental role, and one can similarly ask what the impact of selective natality is (Ravallion, 2005). Population growth also raises philosophical questions. There is for instance a debate on whether poverty measures should decrease or increase when the absolute number of poor increases while the fraction of poor decreases (Chakravarty et al., 2006).

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