Using Rippin’s Approach to Estimate Multi-Dimensional Poverty in Central America

Jose Espinoza-Delgado and Jacques Silber

Introduction

The removal of poverty remains one of the most important aims of economic policy in many countries of the world (Chakravarty, 2018; Chakravarty & Silber, 2008); it continues to be one of the greatest global challenges and is an essential ‘requirement for sustainable development’ (UN, 2017, p. 1). In consequence, given that there is no meaningful development without the elimination of that source of un-freedom (Sen, 2000), Goal 1 of the Sustainable Development Goals (SDGs) calls for ending ‘poverty in all its forms everywhere’ (UN, 2015, p. 15). In this context, specifying how poverty is characterised, what its determinants are and finding appropriate poverty measures, our main concern in this chapter, become crucial elements for the design and assessment of policies aimed at alleviating this social problem (Ray, 1998).

As argued by Stiglitz, Sen and Fitoussi (2009a), the well-being of a population is multi-dimensional. Poverty therefore may be considered as a manifestation of the insufficiency of accomplishments in different domains of well-being; it is a multi-dimensional phenomenon characterised by deprivations in multiple dimensions of the individuals’ well-being. As a result, nowadays, the multi-dimensional nature of poverty enjoys a widespread consensus (Chakravarty, 2006, 2018; Chakravarty & Lugo, 2016; Kakwani & Silber, 2008a; Stiglitz et al., 2009a, 2009b), grounded, mainly, on the capability approach proposed by Sen (1985, 1992, 1997, 2000, 2010), which is regarded as the most comprehensive approach to grasp the concept of poverty (Thorbecke, 2008). This consensus is reflected in Target 1.2 of the SDGs, which demands that by 2030 there will be a reduction ‘at least by half of the proportion of men, women and children of all ages living in poverty in all its dimensions according to national definitions’ (UN, 2015, p. 15).

In this regard, diverse multi-dimensional approaches to the measurement of poverty (see, for instance, Alkire & Foster, 2011; Alkire et ah, 2015; Atkinson, 2003; Betti & Lemmi, 2013; Bourguignon 6c Chakravarty, 2003; Brandolini & Aaberge, 2014; Chakravarty, 2018; Chakravarty, Deutsch & Silber, 2008; Datt, 2019; Deutsch & Silber, 2005, 2008; Duclos, Sahn &

Younger, 2008; Kakwani Sc Silber, 2008b; Klasen, 2000; Lemmi Sc Betti, 2006, Rippin, 2013, 2016, 2017; Tsui, 2002), as well as multi-dimensional poverty indices, have become increasingly popular in recent years. Currently, the most influential and dominating methodology in developing countries is the counting approach proposed by Alkire and Foster (2011) (AF hereafter); this is a family of multi-dimensional poverty measures that employ a ‘dual cut-off method’ for the identification of the poor (p. 478), and it has been applied in a considerable number of studies.1 The most famous application of the AF approach is the household-based multi-dimensional poverty index or ‘global МРГ (Alkire et ah, 2015, p. 177). Developed originally by the Oxford Poverty and Fluman Development Initiative (OPHI) in collaboration with the United Nations Development Program (UNDP) (Alkire Sc Santos, 2010, 2014), the global MPI has been included in the Human Development Report since 2010 (UNDP, 2010) and has become very popular (Duclos Sc Tiberti, 2016).

More recently, Duryea and Robles (2017), as part of the report ‘Social Pulse in Latin America and the Caribbean 2017’, published by the Inter- American Development Bank (IDB), and Santos and Villatoro (2018), proposed a new household-based multi-dimensional poverty index for Latin America and the Caribbean (LAC) and suggested adopting the AF method to estimate multi-dimensional poverty in LAC. Likewise, several governments, especially from LAC, for instance, Chile (Ministerio de Desarrollo Social, 2016), Colombia (DANE-DIMPE, 2014), Costa Rica (INEC,

2015), Ecuador (Castillo Sc Jacome, 2015), El Salvador (STPP Sc MINEC- DIGESTYC, 2015), Honduras (SCGG-INE, 2016), Mexico (CONEVAL, 2011) and Panama (MEF, 2017), have adopted this approach to produce their official multi-dimensional poverty index.

The AF methodology has the advantage of simplicity, flexibility and clarity, when compared to other approaches, which is indeed what makes it extremely appealing (Silber, 2011; Thorbecke, 2011); it also has a number of other attractive properties (see Alkire Sc Foster, 2011; Alkire et ah, 2015). Yet, this approach also has some methodological shortcomings that have often been ignored in the literature (Duclos Sc Tiberti, 2016). Let us focus here on two of them, perhaps the most critical weaknesses of this methodology.

First, the identification method of the AF methodology assumes implicitly that up to the second cut-off (k), which is used to identify the multi- dimensionally poor (Alkire Sc Foster, 2011), the variables (attributes) are ‘perfect substitutes’, whereas the same variables are ‘perfect complements’ from this cut-off onwards (Rippin, 2017, p. 37), an assumption difficult to justify theoretically.2 Choosing between substitutability and complementarity between attributes when there are more than two of them is certainly not an easy task. This issue, however, is of great significance within a dynamic framework and cannot be ignored (Thorbecke, 2008), if only because of its important policy implications (Silber, 2011; Thorbecke, 2011 ).3

Second, as emphasised by Rippin (2013, 2017), any index based on the AF approach is completely insensitive to inequality among the multidimensional!}' poor, a serious shortcoming according to Sen (1976, 1979). It should, however, be stressed that Alkire and Foster (2011) had mentioned the possibility of extending their analysis since they wrote:

It is sometimes argued that the cross partials should be positive, reflecting a form of complementarity across dimensions; alternatively, they might be negative so as to yield a form of substitutability. Since Ma is neutral, it is a trivial matter to convert Ma into a measure that satisfies one or the other requirement: replace the individual poverty function Ма;,г) with [Марг)]? for some у > 0 and average across persons. The resulting poverty index regards all pairs of dimensions as substitutes when у < 1, and as complements when у > 1, with у = 1 being our basic neutral case.

(p. 485)

The more recent paper by Alkire and Foster (2019) emphasises this approach. Datt (2017, 2019) also underlined the need for a distribution-sensitive multi-dimensional poverty measure, but his approach did not really deal with ordinal or dichotomised variables. It is also important to stress that, as pointed by Alkire et al. (2015, ch. 2), as well as by Alkire and Foster (2019) and Seth and Santos (2019), satisfying association sensitive properties in their strict form is incompatible with a full dimensional breakdown property. Incorporating sensitivity to inequality in the poverty measure has thus a cost that should be acknowledged.

Another issue that has generally been ignored in the literature is that in the vast majority of studies empirical indices of multi-dimensional poverty have been computed at the level of the household (Bessell, 2015; Chiappori, 2016; Pogge & Wisor, 2016). In other words, these studies used the household as the unit of identification to determine who is multi-dimensionally poor and who is not, equating the poverty condition of the household with the poverty condition of all individuals belonging to the household (Espinoza-Delgado & Klasen, 2018). This assumption, however, disregards intra-household inequalities that are known to exist (see, for instance, Asfaw, Klasen & Lamanna, 2010; Bradshaw, Chant & Linneker, 2017a, 2017b; Chant, 2008; Klasen & Wink, 2002, 2003; Rodriguez, 2016), and it may also hide inequalities between different generations living in the household (Atkinson, Cantillon, Marlier, 6c Nolan, 2002), leading thus to biased estimates of poverty and inequality in society (Deaton, 1997; Rodriguez,

2016). Given that the ultimate objective of poverty analysis is the welfare of individuals, limiting the empirical analysis to the household level ‘is simply unacceptable’ (Chiappori, 2016, p. 840).

In this chapter, we adopt the general framework proposed by Silber and Yalonetzky (2014)4 and Rippin’s methodology (2013, 2017) and propose to use an inequality sensitive multi-dimensional poverty approach, with dichotomous variables, that overcomes the problems discussed previously.5 The approach suggested is based on a ‘fuzzy’ identification function that specifies explicitly the kind of relationship existing between the dichotomous variables considered in the analysis. As shown in Berenger (2016,

2017), the class of multi-dimensional poverty measures that are adopted can be decomposed into the three Ps of poverty, incidence, intensity and inequality (Jenkins & Lambert, 1997). We implement such an approach by looking at poverty data in five Central American countries, namely Guatemala, El Salvador, Honduras, Nicaragua and Costa Rica. Our approach allows us to estimate multi-dimensional poverty among adults in that region and explore the determinants of multi-dimensional poverty on the basis of logit regression models.

The rest of the chapter is organised as follows. The next section explains the framework proposed; the following section introduces the data and justifies the dimensions, indicators and deprivation cut-offs, as well as the weighting structure used; the subsequent section discusses the main results and the results of the logit regression models, and the last section provides some concluding remarks.

A Framework for the Measurement of Multi-Dimensional Poverty

Notations and Definitions

Let N = {1,...,?j} c N denote the set of и individuals, and letD = [,...,d] a N represent the set of d ordinal variables measuring various aspects of individual well-being. Let X = [x] be the n x d attainments matrix, where x,,(e N++) represents the attainment of the /th individual for the /th variable. Given that we assume that all the variables are dichotomous, x~ will always be equal to either 0 or 1. In this matrix, each row vector xj = (xn,...,xjd) gives the achievements of the /th individual, while each column vector x = (хг,...,хи.) provides the distribution of the /th variable across the population. Also, let w = (tvv...,wd) be the vector of variable-specific weights with

w, > 0 V/ e [1 ,d] and ^ w, = 1. Finally, k denotes the real-valued scalar

cut-off, with 0 < k < 1. k is the minimal deprivation score an individual needs to have in order to be considered as multi-dimensionally poor (‘the poverty cut-off’) (Alkire &t Foster, 2011, p. 478).

The Individual Multi-Dimensional Poverty Function

The construction of the individual multi-dimensional poverty function entails two steps. The first step checks for each well-being dimension j whether the individual is deprived, that is, whether xtj is equal to 0 or 1. A weighted deprivations score (c(.) is then computed for each individual as the weighted sum of the deprivations suffered by each of them. This score is called the ‘(real-valued) counting function’ (Silber & Yalonetzky, 2014, p. 11), and we write it as:

The Identification Function

The focus of the second stage of the analysis is on the identification of the multi-dimensionally poor individuals. In the AF approach, the counting function cj is compared with the poverty cut-off k. If c> k, then the individual i is considered as multi-dimensionally poor. The choice of k is evidently arbitrary, and Alkire and Foster (2011) propose to use an ‘intermediate cutoff’ that lies somewhere between 0 and 1 (p. 478). Let //AF (x, -,w-,k) be the identification function suggested by Alkire and Foster (2011); then, in our case of dichotomous variables, we can write that:

Note that 'FAF includes as particular cases the two conventional methods of identification introduced by Atkinson (2003) in the context of multidimensional poverty analysis: the union and the intersection approaches. The former assumes that the variables are perfect complements, while the latter supposes that the variables are perfect substitutes (Rippin, 2013, 2017)6. This is why Alkire and Foster (2011) proposed an intermediate approach as ‘a natural alternative’ to the two extreme methods of identification (p. 478).

In this chapter, we prefer to adopt a ‘fuzzy’ identification function, suggested by Rippin (2013, 2017), that makes explicit the relationship between the variables (attributes) considered in the analysis. Let у be a parameter describing the relationship between the attributes. The function is then defined as:

where [с,]у satisfies the conditions of being non-decreasing in cj and of having a non-decreasing marginal if the variables are assumed to be substitutes (y > 1) and a non-increasing marginal if the variables are assumed to be complements < l).7

Therefore, instead of dichotomising the distribution of the weighted deprivations scores, as proposed by Alkire and Foster (2011), the fuzzy identification function distinguishes between the multi-dimensionally non-poor, on

Pippin’s Approach to Multi-Dimensional Poverty 37

the one hand, and ‘different degrees of poverty severity’, on the other hand (Rippin, 2017, p. 42). Hence, it is considered to be fuzzy because unless c{ = 1 or c— 0, each individual is ‘somewhat’ multi-dimensionally poor (Silber Sc Yalonetzky, 2014, p. 13), depending on (i) the number of variables in which he/she is simultaneously deprived, and (ii) the type of relationship that exists among these variables. If у is between 0 and 1, the curve describing c, has a concave shape, while if у is greater than 1, this curve has a convex shape. The choice between these two options depends on whether it is assumed that the variables are substitutes or complements. If the variables are perfect complements, there is no compensation and we obtain the union case; if they are perfect substitutes, there is full compensation and we get the intersection case.

The variables may be substitutes in the short term but complements in the long term (Thorbecke, 2008). In this chapter, we assume different degrees of substitutability (y = 1.25, 1.50, 1.75, 2.00) and complementarity (y = 0.25, 0.50, 0.75) among the variables; we test thus the robustness of our conclusions to these assumptions.

The Function Defining the Multi-Dimensional Poverty Breadth

In line with the literature, the individual multi-dimensional poverty function must not only identify the poor but also capture the intensity of the multi-dimensional poverty experience (Silber Sc Yalonetzky, 2014). However, with dichotomous variables the multi-dimensional poverty depth cannot be estimated as no poverty gap between the individual achievement in a given variable and the deprivation threshold for this variable may be calculated (Berenger, 2017). To consider the poverty breadth, we make the individual multi-dimensional poverty function depend on the number of deprivations, and we define it as the product of the identification function introduced previously and a function that captures the breadth of multi-dimensional poverty (for more details, see Silber Sc Yalonetzky, 2014).

As multi-dimensional poverty breadth function, we adopted the one proposed by Alkire and Foster (2011):

The Social Multi-Dimensional Poverty Function

In the last stage of the analysis, we derive a social multi-dimensional poverty function as the average of the individual poverty functions. We therefore end up with an index defined (for more details, see Rippin, 2017) as:

Data Sources, Deprivation Dimensions, Indicators and Cut-Offs and Weighting Structure

Data

The data used in this chapter are the household surveys periodically performed in the countries of the Central American region, conducted by the corresponding National Institutes of Statistics. Table 3.1 shows for each country details of the nationally representative survey used. In our assessment, the unit of identification is the individual.

Dimensions, Indicators and Deprivation Cut-Offs

The choice of the dimensions and indicators for our individual-based multidimensional poverty index is grounded on the SDGs and targets (UN, 2015, 2017). Five deprivation dimensions were selected and specific indicators were chosen for each of them. The corresponding deprivation cut-offs are presented in Table 3.2.

Education

There are quite a few reasons why education should be included in a multidimensional poverty analysis (see Dreze & Sen, 2002; Robeyns, 2006).

Table 3.1 Surveys used, samples size and estimated population

Country

Survey

Year

Sample Size

Estimated

population

(Individuals aged 18-59)

(Individuals aged 18-59)

Guatemala

Encuesta Nacional de Condiciones de Vida (GUA-ENCOVI2014)

2014

26,664

7,848,739

El Salvador

Encuesta de Hogares de Propositos Multiples (ELS-EHPM2016)

2016

40,842

3,553,224

Honduras

Encuesta Permanente de Hogares de Propositos Multiples (HON-EPHPM2013)

2013

15,760

4,070,318

Nicaragua

Encuesta Nacional de Hogares sobre Medicion de Nivel de Vida (NIC-EMNV2014)

2014

15,730

3,309,715

Costa Rica

Encuesta Nacional de Hogares (CR-ENAHO2016)

2016

21,760

2,891,584

Central

America

Encuestas Nacionales

Around

2015

120,756

21,673,580

Source: Authors’ estimates based on CUA-ENCOVI2014, ELS-EHPM2016, HON- EPHPM2013, NIC-EMNV2014 and CR-ENAHO2016.

Dimensions

Indicators

Weights

(%)

Deprivation indicators: he/she is deprived if he/she ...

1. Education (Goal 4 of the SDGs)

1.1. Schooling achievement

20.0

has not completed lower secondary school (nine years of schooling approximately).

2. Employment (Goal 8 of the SDGs)

2.1. Employment status

20.0

Scenario 1 (does not consider domestic workers and unpaid care workers): is unemployed, employed without pay, or a discouraged worker (hidden unemployment).

20.0

Scenario 2 (considers Scenario 1 plus domestic workers and unpaid care workers who reported that they ‘did not have a job’ but were available to work): is unemployed, employed without pay, or a discouraged worker (hidden unemployment).

20.0

Scenario 3 (considers Scenario 2 plus domestic workers and unpaid care workers who reported that they ‘did not have a job’ but were not looking for and were not available to work because of unpaid care and/or domestic chores): is unemployed, employed without pay, or a discouraged worker (hidden unemployment), or is unemployed, but is not looking for a job and is not available to work because he/she has to take care of his/her children and/or a relative (s) and/or has to do domestic work.

3. Water and sanitation (Goal 6 of the SDGs)

3.1. Improved water source

12.6

does not have access to an improved water source or has access to it, but out of the house and yard/plot.

3.2. Improved sanitation

7.4

only has access to an unimproved sanitation facility (a toilet or latrine without

treatment or a toilet flushed without treatment to a river or a ravine) or to a shared toilet facility.

4. Energy and electricity (Goal 7 of the SDGs)

4.1. Type of cooking fuel

5.4

is living in a household which uses wood and/or coal and/or dung as main cooking fuel.

4.2. Access to electricity

14.6

does not have access to electricity.

5. Quality of dwelling (Goal 11 of the SDGs)

5.1. Housing materials

4.9

is living in a house with dirt floor and/or precarious roof (waste, straw, palm and similar, other precarious material) and/or precarious wall materials (waste, cardboard, tin, cane, palm, straw, other precarious material).

5.2. People-per-bedroom

2.9

has to share a bedroom with two or more people.

5.3. Housing tenure

7.5

is living in an illegally occupied house or in a borrowed house.

5.4. Assets

4.7

does not have access to more than one durable good of a list that includes: Radio, TV, Refrigerator, Motorbike, Car.

In the context of the SDGs, the inclusion of education is justified by Goal 4 that calls for ensuring ‘inclusive and equitable quality education and promote lifelong learning opportunities for all’ (UN, 2015, p. 17). The ordinal educational indicator selected refers to the schooling level attained by the individuals.

Employment

The inclusion of employment as a dimension is based on its instrumental significance as well as on its intrinsic importance (Atkinson et al., 2002; Klasen, 2000; Sen, 2000; Stiglitz et ah, 2009a, 2009b). The SDGs call for promoting ‘full and productive employment and decent work for all’ (Goal 8) (UN, 2015, p. 19), which is crucial in Central American countries, where the share of informal employment in total employment is estimated to be higher than 70%, with the exception of Costa Rica (ILO,

2018, p. 18).

The ordinal indicator that we defined takes into account the employment status of the individual but also unpaid care work and domestic work. This is in line with Target 5.4 of the SDGs: ‘Recognize and value unpaid care and domestic work through the provision of public services, infrastructure and social protection policies and the promotion of shared responsibility within the household and the family as nationally appropriate’ (UN, 2015, p. 18). The indicator distinguishes two groups of individuals, among those who reported that they did not work the week preceding the survey: (1) individuals whose main activity was to do domestic work and/or unpaid care work (hereafter ‘unpaid care and domestic workers’), and (2) individuals who were not involved in those activities. We therefore consider three scenarios (see Table 3.2).

Water and Sanitation

Water and sanitation are also of considerable instrumental and intrinsic importance (Klasen, 2000; Mara & Evans, 2018; Sorenson, Morssink & Campos, 2011). This dimension includes two indicators, improved water source and improved sanitation, which can be assumed to be related to Goal 6 of the SDGs: ‘Ensure availability and sustainable management of water and sanitation for all’ (UN, 2015, p. 18).

Energy and Electricity

The dimension of energy and electricity emphasises Goal 7 of the SDGs, which demands ensuring ‘access to affordable, reliable, sustainable and modern energy for all’ (UN, 2015, p. 19). This dimension is measured via two indicators named ‘type of cooking fuel’ and ‘access to electricity’.

Pippin’s Approach to Multi-Dimensional Poverty 41 Quality of Dwelling

Finally, our index also includes a dimension that accounts for the quality of dwelling. This dimension is included in Goal 11 of the SDGs: ‘Make cities and human settlements inclusive, safe, resilient and sustainable’ (UN, 2015, p. 21). To measure the quality of dwelling, we use four indicators: housing materials, people-per-bedroom, housing tenure and assets.

Weighting Structure

Since all the dimensions selected are a priori equally important, we attach an equal weight to each of the five dimensions (20%), but for a given dimension, following Cerioli and Zani (1990), the weight of an indicator j is defined as:

where ff denotes the relative frequency of individuals deprived in the ;th indicator (in this dimension), considering Central America as a whole.

Results

Estimating Multi-Dimensional Poverty Among Adults

We first illustrate empirically how the fuzzy identification function described above performs, considering Central America as a whole and only the first deprivation cut-off for employment (the first scenario). Figure 3.1 draws this function, assuming different values of у from 0.05 to 10.0. The solid curves both at the top and at the bottom of the figure approximate the cases in which the attributes are supposed to be perfect complements (y = 0.05) and perfect substitutes (y = 10.00), respectively; the solid line in the middle (the 45° line) assumes, in turn, that the attributes are independent (y = 1.00).

Figure 3.1 makes clear that the marginal increase in an individual’s poverty severity is larger, the lower the substitutability between indicators (moving from у = 10.00 to у = 0.05), and that an individual’s poverty level is higher, the harder the compensation of deprivation in one attribute. The degree of poverty of individuals depends thus not only on their weighted deprivation scores but also on the way in which these deprivations are correlated (Rippin, 2013, 2017).

The overall estimates of multi-dimensional poverty among adults in Central America as a region, as well as for each of the countries under analysis, considering the three scenarios discussed in Table 3.2 and several values of у, are displayed graphically in Figure 3.2.8

Fuzzy identification function for several values of y. Source

Figure 3.1 Fuzzy identification function for several values of y. Source: Authors’ estimates based on GUA-ENCOVI2014, ELS-EHPM2016, HON- EPHPM2013, NIC-EMNV2014 and CR-ENAHO2016.

Estimates of multi-dimensional poverty in Central America

Figure 3.2 Estimates of multi-dimensional poverty in Central America (CA) as a whole and in Guatemala (GUA), El Salvador (ELS), Honduras (HON), Nicaragua (NIC) and Costa Rica (CR), considering three scenarios and several values of y. Source: Authors’ estimates based on GUA-ENCOVI2014, ELS-EHPM2016, HON-EPHPM2013, NIC- EMNV2014 and CR-ENAHO2016. Note: In the case of El Salvador, the estimates corresponding to the second and third scenarios are the same, as the deprivation rates in employment are identical. This is so because the survey does not provide the information needed to determine whether the individuals considered as ‘unpaid care and domestic workers’ were available to work or were not.

Figure 3.2 shows that multi-dimensional poverty is lower, the higher the degree of substitutability among the indicators. Note also that each of the resulting curves moves upwards as the threshold used to determine deprivation in employment becomes more demanding (from the first scenario to the third one). The figure also suggests that multi-dimensional poverty among adults is highest in Guatemala, followed by Nicaragua, except under the first scenario when у takes a value of 1.50, 1.75 and 2.00, and, by contrast, it is the lowest in Costa Rica. Honduras and El Salvador appear in the middle but below the regional averages (the CA curve). Interestingly, under the third scenario, the differences in multi-dimensional poverty between Guatemala and Nicaragua become more substantial than the ones observed under the other scenarios because Guatemala has a larger percentage of unemployed adults who do unpaid care work and/or domestic work than Nicaragua.

As discussed above, the family of measures used in this chapter are sensitive to inequality among the poor and can be decomposed into the three I’s of multi-dimensional poverty (Jenkins & Lambert, 1997). Therefore, to complement the previous results, Figure 3.3 presents graphically estimates of the inequality among the poor, the poverty dimension ignored by the mainstream approach, measured via the Generalised Entropy Inequality

Inequality among the multi-dimensionally poor in Guatemala

Figure 3.3 Inequality among the multi-dimensionally poor in Guatemala (GUA), El Salvador (ELS), Honduras (HON), Nicaragua (NIC) and Costa Rica (CR), as well as in Central America (CA) as a whole, considering three scenarios and several values of y. Source: Authors’ estimates based on GUA-ENCOVI2014, ELS-EHPM2016, HON-EPHPM2013, NIC- EMNV2014 and CR-ENAHO2016. Note: In the case of El Salvador, the inequality among the poor, corresponding to the second and the third scenario, is the same. This is so because the deprivation rates in employment are identical, given that the survey does not provide the information needed to determine whether the adults considered as ‘unpaid care and domestic workers’ were available for work or not (see Table 3.2).

Index.9 Overall, it appears thus that the omission of inequality may lead to wrong poverty alleviation policies and programmes.

Results of Logit Regressions

As a complement to our descriptive analysis and to shed some light on the determinants of the multi-dimensional poverty of adults in Central America, in line with Wiepking and Mass (2005), we estimated logit regression models, for the region as a whole, where the endogenous variable was equal to 1 if the individual was multi-dimensionally poor, or to 0 otherwise, taking into account the three scenarios discussed previously.

As explanatory variables, we use the sex of the individuals (dummy variable equal to 1 for females), their age and the square of their age, the marital status [married, bachelor, divorced, widow(er)], the size of the household in which the individuals live and its square, the area of residence (urban, rural) and the country (Costa Rica being the country of reference), and some interaction terms between the sex of the individual and his/her marital status, as well as between the sex and the country of residence. The results are given in Table 3.3, separately for each scenario.

It seems that the pure gender effect is statistically significant, and it suggests that females are better-off than males in terms of multi-dimensional poverty; however, the final impact (size and direction) of the gender on the probability of being multi-dimensionally poor depends, ceteris paribus, on the marital status of the individual and the country in which he/she lives.

Table 3.3 also indicates that in Central America, regardless of the scenario considered, there is, ceteris paribus, a U-shaped relationship between the age of the individual and the probability that he/she will be multi-dimensionally poor. The same non-linear relationship is observed for the size of the household. It also appears that, ceteris paribus, adults living in rural areas have a much larger probability of being multi-dimensionally poor, this being true for all scenarios. This result was emphasised previously in the literature (see, for instance, Battiston, Cruces, Lopez-Calva, Lugo & Santos, 2013; ECLAC, 2013; Espinoza-Delgado & Klasen, 2018; Santos & Villatoro, 2018). In other words, poverty in Central America still largely remains a rural phenomenon, an observation that has evidently important policy implications. Finally, note that the marital status of an individual and the corresponding interaction terms have a significant impact on the probability of being multi-dimensionally poor.

Concluding Remarks

The AF methodology, as the mainstream approach to the measurement of multi-dimensional poverty in the developing world, is insensitive to inequality among the poor. Additionally, the vast majority of empirical studies of multi-dimensional poverty equate the poverty status of the household with

Table 3.3 Odds ratios of being multi-dimensionally poor by sex, age, household size, area and country of residence and marital status, considering three scenarios

Poverty

Scenario 1

Scenario 2

Scenario 3

Explanatory variables

Odds Ratio

Robust

SE

Odds Ratio

Robust

SE

Odds Ratio

Robust

SE

Sex

Male (ref.)

1.0000

1.0000

1.0000

Female

0.7782***

0.0296

0.7653***

0.0294

0.9152**

0.0355

Age

-0.0039***

0.0006

-0.0042***

0.0005

-0.0049***

0.0005

Age sq.

0.0001***

0.0000

0.0001***

0.0000

0.0001***

0.0000

Household size

-0.0225***

0.0025

-0.0211***

0.0023

-0.0188***

0.0021

Household size sq.

0.0038***

0.0003

0.0036***

0.0002

0.0033***

0.0002

Area of residence

Urban (ref.)

1.0000

1.0000

1.0000

Rural

5.4221***

0.1124

5.3645***

0.1150

5.4571***

0.1220

Marital status

Single (ref.)

1.0000

1.0000

1.0000

Married

1.1157***

0.0341

1.1286***

0.0347

1.1400**'

0.0352

Unmarried

2.1083***

0.0701

2.1237***

0.0709

2.1377***

0.0717

Divorced

1.4631***

0.0758

1.4804***

0.0768

1.5146***

0.0788

Widow(er)

2.1677***

0.4273

2.1965***

0.4332

2.2030***

0.4350

Country

Costa Rica (ref.)

1.0000

1.0000

1.0000

Guatemala

4.9466***

0.2034

4.9361***

0.2033

4.9443***

0.2048

El Salvador

2.9120* **

0.0880

2.9070***

0.0878

2.8817***

0.0873

Honduras

2.5024***

0.0987

2.5410***

0.1006

2.5645***

0.1024

Nicaragua

3.6196***

0.1428

3.6201***

0.1431

3.6004***

0.1428

Interaction (Sex - Union status)

Female (married)

1.3037***

0.0515

1.4877'**

0.0602

1.8504***

0.0766

Female (Unmarried)

1.2327***

0.0556

1.4061***

0.0654

1.7658***

0.0851

Female (Divorced)

1.2848***

0.0786

1.3243***

0.0822

1.3685***

0.0853

Female (widow)

1.1447

0.2407

1.1988

0.2540

1.2932

0.2755

Interaction (Sex - Country)

Female (Guatemala)

1.1221**

0.0633

1.1996***

0.0690

1.1099*

0.0665

Female (El Salvador)

1.0628

0.0442

1.4498***

0.0619

1.0923**

0.0471

Female (Honduras)

1.0290

0.0552

1.0288

0.0558

0.9509

0.0532

Female (Nicaragua)

0.8656***

0.0461

0.9013*

0.0486

0.8132***

0.0450

Constant

1.5237***

0.1507

1.7072

0.1718

2.0039***

0.2050

Observations

120756

120756

120756

Wald chi2

16132.39

16264.02

15338.95

Degrees of freedom

(22)

(22)

(22)

Prob. > chi2

0.0000

0.0000

0.0000

Pseudo R2

0.1768

0.1831

0.1821

Notes: Survey weights used; for age and household size variables, the marginal effects are reported; outcome (Poverty): dummy equal to 1 if an individual is multi-dimensionally poor, for each of the three scenarios. Significance levels: *p < 0.1.; **p < 0.05; ***p < 0.01.

that of all individuals in the household, thus disregarding intra-household inequalities. In this chapter, we therefore proposed individual-based inequality sensitive multi-dimensional poverty. We applied our approach to an analysis of multi-dimensional poverty among adults (18 to 59 years old) in Guatemala, El Salvador, Honduras, Nicaragua and Costa Rica.

It appears that multi-dimensional poverty among adults is highest in Guatemala and Nicaragua and lowest in Costa Rica. We also decomposed our multi-dimensional poverty measure into the three I’s of poverty and found that Guatemala and Nicaragua have the highest and Costa Rica the lowest incidence and intensity of multi-dimensional poverty in Central America.10 El Salvador and Honduras, however, have the greatest levels of inequality.

Finally, the logit regression models corroborate the main findings of our descriptive analysis. These regressions also show that in Central America, there are country- as well as individual-specific gender differences in multidimensional poverty. It also seems that the total impact of gender is statistically significant, but, ceteris paribus, it also depends on the marital status of the individuals and on the country in which they live.

Acknowledgements

Jose Espinoza-Delgado would like to thank participants at workshops in Bielefeld, Goettingen, Puebla and Zaragoza for helpful comments and discussions on the topic, especially to Achille Lemmi, Stephan Klasen, Mariano Rojas and Julio Lopez-Laborda. He also would like to thank Nicole Rippin for clarifications and useful discussions on the Correlation Sensitive Poverty Index.

This chapter was completed when Jose Espinoza-Delgado was a guest researcher at the German Development Institute (DIE-GDI) between September and December 2019; he is very thankful to the DIE-GDI for its warm hospitality.

Notes

  • 1 A summary of studies that have applied the AF method can be found in Alkire etal. (2015, p. 178-181).
  • 2 In a graph plotting on the horizontal axis the cumulative percentage of deprivations and on the vertical axis the probability of being considered as poor, the curve obtained would be identical to the horizontal axis up to the cut-off (since an individual is not poor as long as the share of his/her deprivations in the total number of possible deprivations is smaller than the cut-off) while the curve will become horizontal at height 1 as soon as the percentage of deprivations of the individual is equal to or higher than the cut-off. This special curve implies that the deprivations are perfect substitutes up to the cut-off and perfect complements beyond the cut-off.
  • 3 ‘For instance, for a poverty analysis in the dimensions of education and nutritional status of children, there are production complementarities because better-nourished children learn better. If this complementarity is strong enough, it may overcome the usual ethical judgment that favors the multiply-deprived, so that overall poverty would decline by more if we were to transfer education from poorly nourished to the better nourished, despite the fact that it increases the correlation of the two measures of well-being. Similarly, one might argue that human capital should be granted to those with a higher survival probability (because these assets would vanish following their death). Increasing the correlation of deprivations, and increasing the incidence of multiple deprivations, would then be good for poverty reduction’ (Duclos, Sahn 8c Younger, 2006, p. 950).
  • 4 Some of the ideas raised by Silber and Yalonetzky (2014) appear already in Yalonetzky (2012, 2014).
  • 5 Such an approach has been used recently by Berenger (2016,2017), but using the household as the unit of identification.
  • 6 Here, the concepts of ‘substitutability’ and ‘complementarity’ follow the Auspitz- Lieben-Edgeworth-Pareto (ALEP) definition and not the well-known approach proposed by Hicks and Allen (1934a, 1934b) (Silber, 2007, p. 59). The ALEP definition considers that two attributes are substitutes (complements) if their second cross-partial derivatives are larger (less) than zero and independent if they are equal to zero (Rippin, 2013, 2017). Intuitively, on the basis of the ALEP definition, if two attributes are substitutes, poverty will decrease less with a rise in attribute 1 for individuals with larger quantities of attribute 2. The contrary is evidently true when the two attributes are supposed to be complements (Silber, 2007). For instance, assuming that income and education are substitutes, the reduction in poverty due to a unit increase in income is less important for individuals who have an educational level close to the education deprivation cut-off than for individuals with very low education. Conversely, the drop in poverty would be more substantial for individuals with a larger level of education if income and education were considered to be complements (Bourguignon 8c Chakravarty, 2003).
  • 7 As observed by Rippin (2017, p. 61), “A function f (x) as a non-decreasing marginal if f (xg+ )-f > f [x}, +1) —/”(*/,) whenever xg - xh ” The conditions

that have to be satisfied by [uj^are detailed in Rippin (2013, 2017).

  • 8 Point estimates and their bootstrapped confidence intervals at 95% are available upon request from the authors.
  • 9 Point estimates and their bootstrapped confidence intervals at 95% are available upon request from the authors.
  • 10 These results are available upon request from the authors.

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