Leaving No One Behind: An Individual-Level Approach to Measuring Multidimensional Poverty in Botswana

The Leave No One Behind principle is at the core of the 2030 Agenda for sustainable development and acknowledges that poverty is multidimensional and should be examined at individual level. Notwithstanding this, most empirical studies use the household as the unit of analysis for multidimensional poverty measurement. However, estimation of poverty levels at household-level underestimates poverty levels of the society and does not capture intra-household inequalities. The objective of this study is two-fold: (1) developing a country-specific individual-level multidimensional poverty measure; and (2) providing estimates of multidimensional poverty for Botswana. This study contributes to the limited literature on individual-level multidimensional poverty measurement. Empirically, this study offers the first attempt to estimate a nationally relevant and context-specific multidimensional poverty index for Botswana using the individual as a unit of analysis. The results reveal that an estimated 46.2% of individuals are considered multidimensionally poor based on individual-level analysis. This figure is higher than the household-level estimate of 36.5%, which indicates that using the household as a unit of analysis leads to underestimating poverty levels in the society. The results show that on average, the multidimensionally poor are deprived in 47.4% of all indicators under consideration. This finding indicates that multidimensional poverty intensity is also a considerable concern in Botswana. These findings warrant policy interventions.


Introduction
The worldwide adoption of the United Nation's Sustainable Development Goals (SDGs) in 2015, also known as the 2030 Agenda for Sustainable Development, has reinforced interest in multidimensional poverty measures (UN, 2016). The SDGs are framed around ending absolute poverty (Alkire et al., 2015a), recognising that poverty has many dimensions (UN, 1 3 2015). Specifically, SDG 1, calls to 'end poverty in all its forms everywhere' (UN, 2015: 14). Furthermore, target 1.2 of SDG 1 states that: 'by 2030, reduce at least half the proportion of men, women and children of all ages living in poverty in all its dimensions according to national definitions' (UN, 2015: 15).
The leave no one behind (LNOB) principle has emerged as a central theme of the 2030 Agenda of Sustainable Development (Fukuda-Parr & Hegstad, 2018;UN, 2015) and relates closely to three important dimensions of the 2030 Agenda: poverty, inclusiveness, and inequality (UN, 2016). LNOB aims to address two related concerns: ending absolute poverty in all its forms and reducing inequalities among both individuals and groups (Klasen & Fleurbaey, 2018;Stuart & Samman, 2017;UN, 2015). The LNOB principle acknowledges that poverty is multidimensional (Klasen & Fleurbaey, 2018;UN, 2015) and it should be examined at individual level (Klasen & Fleurbaey, 2018). It also recognises the importance of data disaggregation (UN, 2015).
Notwithstanding this, most empirical studies on multidimensional poverty measurement have used the household as a unit of analysis (Espinoza-Delgado & Klasen, 2018;Franco-Correa, 2014;Klasen & Lahoti, 2020). Using the household as a unit of analysis means that if the household is multidimensionally poor, all members of the same household are considered poor (Ervin et al., 2018;Espinoza-Delgado & Klasen, 2018). However, even though most empirical studies used the household as a unit of analysis, it has not escaped criticism.
First, the 'household' means different things to different people in different countries, and defining it can be tricky and complex (Bolt & Bird, 2003). The most widely used definition of a household is by the UN, which defines a household as 'a group of people who live and eat together' (Bolt & Bird, 2003: 10). However, this definition may be problematic since individuals residing in the same household may have different living arrangements making it difficult to differentiate traditional households from other ones (Franco-Correa, 2014). 1 Second, household measures are unable to capture possible intrahousehold inequalities in resource allocation (Alkire & Fang, 2019;Vijaya et al., 2014), and to distinguish individual poverty within the household (Alkire & Fang, 2019). Children and women are more likely to receive an unequal share of the resources or opportunities (Klasen & Lahoti, 2020;Rodríguez, 2016). Individuals' needs and preferences vary across age (Osberg & Sharp, 2014) and gender (Vijaya et al., 2014).
Third, and in addition to the stated above, using the household as a unit of analysis leads to underestimating poverty levels in the society (Haddad & Kanbur, 1990). This is because intrahousehold inequalities conceal deprived individuals within non-poor households (Brown et al., 2017), and this may, in turn, lead to biased assessments of social policies and targeting (Rodríguez, 2016). Poverty is an individual characteristic (Deaton, 1997), and therefore, deprivations that affect one household member do not necessarily affect all other household members.
Considering these limitations, the analysis performed in this study adopts the individual as the unit of analysis. The individual-level analysis allows for data disaggregation by demographic characteristics as required by the LNOB principle. Furthermore, the individual centred approach eases policy-making exercises because it takes into account individual deprivations (Franco-Correa, 2014), which will help highlight priorities for particular groups in specific places to ensure no one is left behind. However, studies that assessed individual-based multidimensional poverty across the entire population using the individual as a unit of analysis are scarce (Espinoza-Delgado & Klasen, 2018;Franco-Correa, 2014;Klasen & Lahoti, 2020). The scarcity of such studies could be a result of the unavailability of individual-level data. Another reason could be associated with the conceptual and empirical challenges in constructing individual deprivations (Klasen & Lahoti, 2020;Vijaya et al., 2014).
To the best of our knowledge so far, only three studies have attempted to estimate individual-level multidimensional poverty for the whole population using the Alkire and Foster methodology. The first study was done by Franco-Correa (2014) for the case of Chile, Columbia, Ecuador, and Peru. Following this study, Klasen and Lahoti (2020) examined the case of India, and Espinoza-Delgado and  did the case of Nicaragua. However, these studies did not provide an in-depth analysis of poverty levels by different socio-demographic characteristics of the population. For example, Espinoza-Delgado and  considered analysis by gender and age only, while Franco-Correa (2014) examined multidimensional poverty across age groups.
The main objective of this study is to develop an individual-level and country-specific multidimensional poverty measure. Also, the study aims to provide a multidimensional poverty estimate for Botswana. The study employs the Alkire and Foster (2011a) methodology for aggregation and the absolute measure of inequality proposed by Alkire and Seth (2014a) to examine inequality among the multidimensionally poor. Botswana presents a salient case study. The country has made significant progress in reducing monetary poverty. However, Botswana has not had an equally impressive record in terms of other key social indicators such as unemployment, rising inequalities, among others, an indication that the country has not been successful in transforming national wealth into improvements in human development. The country has also committed to the SDGs and the LNOB principle. To the best of our knowledge, this study constitutes the first attempt in Botswana and the African region to estimate the individual-level multidimensional poverty index and inequality for the whole population.
This study contributes to the conceptual and methodological aspects of the study of multidimensional poverty. The study also provides an attempt to operationalising the LNOB principle. Also, it adds to the literature on multidimensional poverty in Botswana. Empirically, this study offers the first attempt to estimate nationally relevant and contextspecific individual-level multidimensional poverty for Botswana. The study is structured as follows: Sect. 2 presents theoretical framework. Section 3 presents data sources and methodology. Section 4 presents and discusses empirical results, and Sect. 5 presents robustness analysis. Last, Sect. 6 presents conclusions and policy implications.

Capability Approach
There has been a growing consensus regarding the insufficiency and limitation of monetary poverty measures (Alkire & Santos, 2014;Sen, 1992;Tsui, 2002). Having an income above the poverty line does not guarantee that other needs like education or health have been met. For example, a person's health status cannot be reduced to money (Kim, 2016). Therefore, this study employs the theoretical premise of the capability approach developed 1 3 by Sen (1985Sen ( , 1992Sen ( , 1999. The capability approach considers the multidimensionality of poverty. It consists of two core concepts: functionings and capabilities. While functionings refer to the various things a person succeeds in 'doing or being' (e.g., being healthy or participating in the social life), capabilities represent the set of all functionings an individual can choose from (Hick, 2016;Suppa, 2018). The capability approach advocates for an evaluation at the capability space and emphasises the capabilities a person has, irrespective of whether they choose to exercise these or not (Hick, 2016). However, considering the constraints in terms of available data and the limitations for the direct measurement of capabilities, obtaining appropriate information on the capability set is challenging.
On the other hand, the information on the functionings set is widely available in the existing data (Hick, 2016). Therefore, deprivation indicators are located in the functioning space and account for the functioning's infeasibility (Suppa, 2018). Poverty, then, is understood as capability deprivation, implying both a shortfall in one or several of the functionings deemed relevant and their infeasibility for the individual in question (Sen, 1992). In operationalising the capability approach, we made several decisions, including the unit of analysis, the selection of function dimensions and indicators, the weighting scheme, the poverty cutoff, and the aggregation method. Motivated by normative theories and expert studies, we developed our list of functioning dimensions and indicators. We also reviewed the literature of some empirical studies employing the capability approach using nationally representative data (e.g. Alkire et al., 2015b;Klasen, 2000;Qizilbash & Clark, 2005;Wagle, 2008). In addition, the functioning dimensions are included for their intrinsic and instrumental significance (Klasen, 2000). Also, the study relied on Botswana's policy commitments and development priorities such as Vision 2036, NDP 11, Botswana Poverty Eradication Policy and Strategy (BPEPS) and the SDGs to ensure that the measure is contextually relevant. Finally, data availability is considered. Thus, the selection is reasoned, transparent, open to modification, and subjected to public debate (see Sen, 2004).

Measuring Poverty in Botswana
Botswana, a landlocked country with about 2 million inhabitants, has pursued poverty reduction since 1966. As a result, the country has witnessed rapid GDP growth for most of its post-independence period (Lekobane & Seleka, 2017). The country has transitioned from the poorest country at independence to the current "upper middle income" status in four decades. Botswana's economy has proliferated during 1966-2008, with a real GDP average growth rate of 8.7% per annum, making Botswana one of the fastest-growing economies (MFDP, 2010). Such impressive economic growth performance was primarily propelled by the mining sector, which has accounted for the largest shares of GDP, exports and government revenue. However, the real GDP growth rate has declined, estimated at 3 per cent in 2019 (SB, 2020).
In Botswana, poverty is and has been almost exclusively measured using the traditional monetary approach. Statistics Botswana computes monetary poverty measure based on consumption expenditure (SB, 2018). 2 According to official monetary measure, poverty levels have declined over time, from 59% in 1985/86 to 47%, 30.6%, 19.3% and 16.3% in 1993/94, 2002/03, 2009/10 and 2015/16, respectively. Similarly, the proportion of people living in extreme poverty (below one dollar a day) (currently $1.90) has also been declining over time, from 23.4%, 6. 4% and 5.8% in 20024% and 5.8% in /3, 20094% and 5.8% in /10 and 20154% and 5.8% in /16 (respectively) (SB, 2018. However, impressive as they are, these figures do not tell the entire story of the country's poverty situation. Despite the significant progress in monetary poverty, Botswana has not had an equally impressive record on other key indicators such as unemployment, especially amongst the youth, rising inequalities, increasing HIV/AIDS prevalence rates, and child malnutrition. This indicates that Botswana has not successfully transformed national wealth into improvements in wellbeing for its citizens. Inequality, measured by the Gini coefficient, has increased from 0.495 in 2009/10 to 0.522 in 2015/16 (SB, 2018). Unemployment rates, especially amongst the youth, continue to pose a severe challenge. The youth (aged 15-35 years) unemployment rate stood at 25.2% in 2015/16, much higher than the average national rate of 17.7% in the same period (SB, 2018). The unemployment rate rose steadily from 10.2 in 1981 to 17.7% in 2015, and it has been consistently higher for females (SB, 2016), partially explaining higher incidences of poverty among females than males.

Data Sources
The analysis of this study utilises the 2015/16 Botswana multi-topic household survey (2015/16 BMTHS hereafter) collected by Statistics Botswana (SB). This survey is a crosssectional and nationally representative survey, allowing disaggregation by demographic characteristics, economic variables, and administrative district. The 2015/16 BMTHS collected socio-economic information, among others, on demographic characteristics, household expenditure and consumption, labour force, health, education, self-assessed well-being and food insecurity, housing, utilities, durable goods and anthropometric measurements (see SB, 2018). The dataset contains information from 24,720 individuals from 7,060 households surveyed in 2015/16. After applying sample weights, this resulted in an estimated 589,909 households and an estimated national population of 2,073,675 individuals (SB, 2018). The survey employed a two-stage stratified probability sample design (see SB, 2018).
In this study, the individual is adopted as a unit of identification. In terms of analytical strategy, this study classified the population of Botswana into four age groups: below 18 years (children), 18 to 35 years (youth), 36 to 64 years (adults) and 65 years and above

The AF methodology
This study employs the axiomatic counting methodology developed by Alkire and Foster (2011a) (henceforth AF) to estimate individual-level multidimensional poverty. 3 The AF methodology was chosen over other methods for several technical and practical reasons (Alkire et al., 2015b). First, this method can identify all poverty measures: incidence, intensity, MPI (adjusted headcount ratio) and inequality (Alkire & Foster, 2011a). Second, being an axiomatic family of measures, this method satisfies several desirable properties, including the axioms of population subgroup decomposability and dimension breakdown (Chen et al., 2019), which is useful for policymakers when developing interventions and targeted policies (Alkire & Apablaza, 2016). Third, from a practical perspective, the AF method uses the intuitive counting approach to identify the poor and explicitly assess the simultaneous or joint distribution of deprivations experienced by the poor people in a set of indicators (Alkire & Foster, 2011a). Fourth, it allows for the examining of the composition of poverty in different subgroups (socio-demographic and location), indicators and dimensions required by the LNOB principle. Fifth, this method is chosen for its methodological robustness, intuitive characteristics, and growing popularity in the field (Alkire et al., 2015b). Fifth, the AF method is simple, flexible and clear (Silber, 2011;Thorbecke, 2011), making it an attractive option to inform policy. Before describing the identification and the aggregation steps of the AF methodology, the achievements of all n persons within a society in all d indicators, summarised by an n × d-dimensional matrix X = x ij , where x ij refer to an indicator's achievement matrix for each individual under consideration, where i (i = 1, ⋯ , n) represent individuals and j (j = 1, ⋯ , d) are indicators within the selected dimensions. Thus, row i of X represents the achievement vector of person i, summarising the person's achievements in all d indicators, and its jth column contains the achievements of all n persons in indicator j. The AF methodology uses a two-step 'dual cut-off' process to identify the poor (Alkire & Foster, 2011b).
The first cut-off process is linked to deprivation cut-offs for each indicator, x i and is denoted by z j represented by a vector z = z 1 , z 2 ⋯ , z d , where d represents the number of indicators. Any person i is deprived in any indicator j if her achievement falls below the deprivation cut-off z j for indicator j and deprivation is given the value 1 when x ij < z j and 0 otherwise. From the X matrix and z vector, a matrix of deprivation g 0 g 0 ij is obtained such that g 0 ij = 1 if x ij < z j and g 0 ij = 0 if x ij > z j for all j = 1, ⋯ , d and i = 1, ⋯ , n . Next, let w = (w 1 , w 2 ⋯ , w d ) be the vector of indicators' weights. The weight attached to indicator j is denoted by w j such that w j > 0 . These weights sum to 1, that is, ∑ d j=1 w j = 1 and w j ∈ [0, 1]. Then, the deprivation score c i is computed for each person i, such that If an individual is not deprived in any indicator c i = 0 and if an individual is deprived in all indicators c i = 1 . The vector of deprivations for all individuals is given by c = c 1 , c 2 ⋯ , c n . The second step involves choosing poverty cut-off point, k, using the deprivation profiles in all indicators to identify the multidimensionally poor. 4 The choice of k is such that 1 ≤ k ≤ d. 5 The poverty cut-off is implemented by using the method of identification k . A person i is identified as multidimensionally poor using a poverty cut-off k, such that c i ≥ k . Algebraically, k x i ;z = 1 if c i ≥ k, and k x i ;z = 0 otherwise. Following Alkire and Santos (2014), this study uses a cut-off of 33.33% ( k = 0.3333 ). From the deprivation matrix g 0 g 0 ij , a censored deprivation matrix g 0 (k) is constructed by multiplying each element in g 0 by the identification function k x i ;z ∶ g 0 ij (k) = k x i ;z ∶ g 0 ij × k x i ;z for all i and all j. A censored deprivation score vector for all individuals is then obtained from the original deprivation score vector: The AF methodology proposes a family of multidimensional poverty measures M that is based on the Foster, Greer, and Thorbecke (FGT) class of poverty measures (Foster et al., 1984) to solve the problem of aggregation. This study uses the first measure of this family; the adjusted headcount ratio denoted by M 0 and contains both multidimensional headcount ratio (multidimensional poverty incidence), H and the average deprivation scores, capturing the intensity of poverty, A (Alkire et al., 2015b). Algebraically, M 0 is computed as: This study uses M 0 to estimate individual-level multidimensional poverty in Botswana. The advantages of this measure are based on its two key properties: the 'population subgroup decomposability' which allows for examining subgroup contributions to all poverty, and the breakdown property by indicator which makes it possible to find out the contribution of each indicator to the overall poverty.

The Inequality Methodology
Inequality is one of the key priorities of the SDG agenda (UN, 2015). However, inequality has been neglected in the study of multidimensional poverty as evidenced by few studies assessing inequality in the empirical literature (e.g. Espinoza-Delgado & Hanandita & Tampubolon, 2016). Therefore, in line with LNOB, this study examines inequality among the multidimensionally poor and adds to the limited literature. Using inequality measure provides value addition to the information provided by the adjusted headcount ratio ( M 0 ). The study employs a separate decomposable inequality measure ( I q ) (1) The choice of k can be made normatively, either based on previous studies or what the society would consider reasonable. It can also be chosen to reflect the country's policy goal (Mushongera et al., 2017). 5 k represents the share of weighted deprivations that a person must experience to be considered multidimensionally poor. That is, in order to be identified as multidimensionally poor, a person's deprivation score must be equal to or larger than the poverty cut-off (c i ≥ k). 6 The censoring step retains the deprivation scores of those who are identified as poor and replaces the deprivation scores of those who are not identified as poor (c i < k) by 0 (Alkire et al., 2015b).
proposed by Alkire and Seth (2014a). 7 The inequality measure is based on the adjusted headcount ratio which is a part of the AF method. This proposed measure is based on a positive-multiple variance to overcome the obstacles stemming mainly from the use of non-cardinal indicator variables in the construction of M 0 (Alkire & Seth, 2014a; Hanandita & Tampubolon, 2016).
To assess inequality among the multidimensionally poor, and following Alkire and Seth (2014a), we suppose that the deprivation scores are ordered in descending order, and the first q persons are identified as poor. The elements are taken from the censored deprivation score vector y = c 1 (k), c 2 (k) ⋯ , c q (k) . Vector y is chosen such that it contains only the deprivation scores of the poor (t = q) . The average of all elements in y then is the intensity of poverty which for q persons is (y) = A . We then denote the inequality measure that reflects inequality in multiple deprivations only among the multidimensionally poor by I q , which can be expressed as: where q denotes the number of the multidimensionally poor, c i (k) is the deprivation score among the poor, A is the intensity of poverty, and ̃ is the normalisation factor that must be chosen such that I q = [0, 1] (Alkire & Seth, 2014a), representing the properties of any standard inequality (Hanandita & Tampubolon, 2016). Following Alkire and Seth (2014a) . 8 Therefore, = 4 in Eq. 2. This measure ( I q ) helps to reveal pockets of high intensities that might otherwise be missed by poverty measures, thereby helping to ensure that no one is left behind (Alkire & Seth, 2014b). In the SDGs, this is captured by SDG 10, which aims to reduce inequality within and among countries (UN, 2015). Inequality is a problem of inclusion, and LNOB can be viewed as a tool for addressing inequality (Fukuda-Parr & Hegstad, 2018).

Proposed Dimensions, Deprivation Indicators and Cut-Offs
Following other studies dealing with multidimensional poverty measures (Alkire & Foster, 2011a, 2011bAlkire et al., 2015b;Kuklys, 2005), this study employs the capability approach (Sen, 1985(Sen, , 1999, in conjunction with the normative approach in selecting dimensions and indicators (Alkire, 2002). The study also relied on Botswana's policy commitments and development priorities such as Vision 2036, NDP 11, BPEPS and the SDGs, to ensure that the measure is contextually relevant. Finally, data availability is considered. As a result, the following seven dimensions are included in the multidimensional poverty measure: (1) Assets, (2) Housing and living condition, (3) Water and sanitation, (4) Food security, (5) Health, (6) Education, and (7) Security. The selected dimensions cover most of the indicators and dimensions of the global MPI (Alkire & Santos, 2014), and the dimensions proposed in MODA child poverty study for Botswana (de Neubourg et al., 2015).
It should be noted that there are some conceptual and empirical challenges in the construction of individual indicators from those indicators defined and identified at the household level (for example, housing and living conditions, water and sanitation and asset indicators) (Espinoza-Delgado & . Most of these are public in nature within households (Klasen & Lahoti, 2020). This study follows other studies that attempted the individual level multidimensional poverty measure in conceptualising these indicators (see Espinoza-Delgado & Klasen, 2018;Franco-Correa, 2014;Klasen & Lahoti, 2020). The indicators are assumed to be true public goods, equally accessible to all individuals within the household (Espinoza-Delgado & Klasen & Lahoti, 2020). The selected household-level indicators are included for their intrinsic and instrumental significance (Klasen, 2000). Table 2 discusses the proposed dimensions, deprivations indicators, as well as the deprivation cut-offs, identification level and groups for which the indicators are applicable. 9

Asset Dimension
This dimension measures deprivations related to possession of household assets, and it provides insights into the household economic activity and reflects both past and future income-generating opportunities (Deere et al., 2012;McKay, 2009). Household durable assets are integral to the functioning and attainment of well-being. In reference to the capability approach, assets are closely connected with ends (functionings) they facilitate (Alkire & Santos, 2014). For example, homeownership is essential because it indicates a crucial functioning of 'security or protection' (Blank, 2008). Four deprivation indicators are considered for this dimension: information, durable goods, transport and homeownership (tenure).

Housing and Living Condition Dimension
This dimension relates to material capabilities (Sen, 1984) and directly captures capabilities of 'bodily health' and 'affiliation' (Nussbaum, 2003). It captures deprivations relating to housing and living conditions (quality and overcrowding) and access to basic amenities, to capture the functioning of 'being well-sheltered'. The BPEPS emphasised shelter poverty (Republic of Botswana, 2018). Housing is also reflected in the SDG agenda (SDG 11.2) (UN, 2015). This dimension is also related to health. For example, individuals living in overcrowded households often suffer from poor health conditions (Wanyeki et al., 2006) and educational outcomes (Leventhal & Newman, 2010). Similarly, the use of dirty fuel may cause high air pollution levels and may be harmful to their health (Duflo et al., 2008;Kaplan, 2010). Housing quality is also associated with morbidity from infectious diseases, chronic illnesses, injuries, poor nutrition, and mental disorders (see Krieger & Higgins, 2002;Vaughan & Platts-Mills, 2000). In line with the capability approach, six deprivation indicators are considered for this dimension: overcrowding, cooking fuel, electricity, floor material, roof material and wall material.

Water and Sanitation Dimension
Like household and living condition, water and sanitation are also of considerable instrumental and intrinsic significance (Klasen, 2000). The water and sanitation dimension is reflected in SDG 6 that calls to ensure availability and sustainable management of water and sanitation for all (UN, 2015). This dimension is linked to higher morbidity and infant and child mortality (Trani & Cannings, 2013). The United Nations General Assembly and the Human Rights Council recognise both access to water and sanitation as human right issues (UN, 2010). Water and sanitation are publicly provided (public goods) and accessible equally within the household (Klasen & Lahoti, 2020). Two indicators are used to capture this dimension: water supply and toilet facility.

Food Security Dimension
Deprivation in food is a good proxy for lacking the capability to avoid hunger or undernourishment (Sen, 1992). The issue of hunger and food insecurity features prominently in the 2030 Agenda and is reflected in SDG 2 (target 2.1) (UN, 2015). According to FAO (1996), there are four major food security dimensions: food availability, food access, food stability and food utilisation (FAO, 1996). Food insecurity is measured based on two indicators: food access and food utilisation (nutrition). These two are chosen based on data availability. 10 This study adopts the Household Food Insecurity Access Scale (HFIAS) methodology in developing the household food insecurity access indicator (see Coates et al., 2007). Two main indicators are created to derive the food access indicator: The Household Food Insecurity Access Scale Score (HFIASS) and the Household Food Insecurity Access Prevalence (HFIAP). 11 The second indicator (nutrition) goes beyond the 'access' indicator and captures food utilisation. This indicator captures the functioning of 'being well-nourished'. It is derived using anthropometric measure; child undernourishment based on WHO methodology (Alkire & Santos, 2014;WHO, 2006). 12

Health Dimension
Health is considered a central capability (Nussbaum, 2003;Sen, 2000). It has intrinsic as well as instrumental value (Alkire & Santos, 2014;Klasen, 2000). Being unhealthy can limit an individual's ability to participate in social activities, negatively influences his/ her emotions, and may prevent him/her from participating in active employment (Rippin, 2016). For example, prolonged chronic illness can utterly impoverish people (Chambers, 1983) and can lead to loss of income (due to inability to work) (Beatty & Fothergill, 2005) and asset depletion (Kyegombi, 2003). The health dimension is reflected in SDG 3 (target 3.8) of the SDGs (UN, 2015). Vision 2036 and NDP 11 both reiterates the importance of health (MFED, 2017; Republic of Botswana, 2016). The health dimension captures deprivations related to access and quality of the nearest health facility and chronic illness. Due 10 The 2015/16 BMTHS do not have variables to capture food availability and food stability, hence their exclusion in deriving the food insecurity dimension. 11 The HFIASS is a continuous measure of the degree of food (access) insecurity, ranging from 0 to 27. The HFIAP categorises households into four levels of household food insecurity: food secure, and mildly, moderately and severely food insecure (Coates et al., 2007). The algorithm used to compute household food insecurity access prevalence categories is based on Coates et al. (2007). 12 The algorithm provided by WHO Child Growth Standards was used to estimate the z-scores of weightfor-age. BMI is computed as: BMI = weight/(height/100) 2 .
to data constraints, this dimension is captured using two indicators: the condition of the nearest health facility and chronic illness.

Education Dimension
Education, like health, has intrinsic and instrumental value (Klasen, 2000). It captures human capital and is vital for enhancing capabilities (Sen, 2000), and to be educated is a valuable achievement (Espinoza-Delgado & . Education enhances one's wellbeing, such as the likelihood of employment, future income, self-confidence, and the ability to social interaction (Rippin, 2016). Nussbaum (2003) captured the education dimension in her list of capabilities (senses, imagination, and thoughts). The education dimension is also included in the global MPI (Alkire & Santos, 2014). Education plays a vital role in achieving Botswana's national development aspirations and priorities (MFED, 2017; Republic of Botswana, 2016). In the SDGs, education has a stand-alone goal reflected by SDG 4 (UN,  2015). The education dimension is captured using three deprivation indicators: child enrolment, school attainment and literacy. 13

Security Dimension
This dimension captures the capability of 'being able to move freely from place to place' (Nussbaum, 2005). That is, to live a safe life free from crime and violence. Feeling unsafe diminishes numerous valuable capabilities (Nussbaum, 2005). This dimension is directly linked to the capability of 'bodily integrity' (Nussbaum, 2000(Nussbaum, , 2003. In the SDGs, this dimension is reflected in SDG 16, target 16.1, which aims to significantly reduce all forms of violence and related deaths rates everywhere (UN, 2015). This dimension is measured using two indicators (safety and crime) identified at household-level, due to unavailability of information at individual-level.

Weighting of Dimensions
The choice of weights for dimensions and indicators is another crucial step in constructing a multidimensional measure (Alkire et al., 2015b). Different weighting approaches exist in the literature (Alkire & Santos, 2014;Decancq & Lugo, 2013). 14 The most widely used is the equal weighting scheme across dimensions (see Alkire & Foster, 2011a, 2011bAlkire & Santos, 2014;Alkire et al., 2015b;Ervin et al., 2018). Advantages of this weighting scheme are that its use eases the interpretation of the index for policy, it is more transparent, and it allows comparisons over time (Alkire & Santos, 2014). The LNOB principle is also premised on the human rights approach, and rights are deemed to be equally important. Therefore, based on a normative approach, this study adopts an equally weighting scheme across dimensions and equal nested weights within dimensions for each indicator (Alkire & Santos, 2014;Ervin et al., 2018). However, actual weights per indicator will differ across age groups as the total number of indicators differs across age groups (as a result of using the individual as a unit of analysis). Table S8 (supplementary tables) presents the weighting structure across the age groups. However, for robustness analysis, the weighting structure across indicators are varied across the dimensions and indicators to test our results to different weights.

Association Between Deprivation Indicators
Before computing the aggregate MPI, it is important to check for associations between indicators. The Spearman rank correlation matrix is employed. Overall, the results show that most deprivation indicators are weakly correlated (Supplementary Table S1

Results and Discussions
The High-Level Panel of Eminent Persons on the Post-2015 Development Agenda proposed that to leave no one behind there is need to ensure that, 'no person -regardless of ethnicity, gender, geography, disability, race or another status -is denied basic economic opportunities and human rights' (UN, 2013: 29). Individuals at the intersection of these factors are at the risk of being left behind. 15 Therefore, this study disaggregates the analysis by individual characteristics, household-level variables, economic variables and geographical variables. Individual characteristics include gender, age, citizenship, disability status and household level variables include gender, age, marital status, educational attainment and employment status of the household head household size. Household per capita consumption quintiles are used to capture the economic status of the household. For geographical variable, administrative districts are used. 16 These selected variables are commonly used in the literature as key determinants of poverty (e.g., Grootaert, 1997;Lekobane & Seleka, 2017;Qi & Wu, 2016).

Deprivation Levels by Indicator
Before aggregating the results into a single index, the unidimensional results for each deprivation indicators across the whole population is examined. Table 3 presents 'the uncensored headcount ratio' (see Alkire & Santos, 2014), that is the estimated proportion of individuals deprived in each of the twenty-four indicators used. Even though Botswana has done well to reduce monetary poverty, this study finds a rather gloomy picture with respect to non-monetary deprivation indicators. Generally, the results show that most Batswana are deprived in indicators relating to asset and housing and living conditions dimensions. Concerning asset, the majority of the population are deprived in transport (71.4%) followed by durable goods (56.2%). In terms of housing and living conditions, cooking fuel (47.5%) and overcrowding (40.2%) exhibited higher levels (respectively) compared to other housing and living conditions indicators. Most of the population is deprived in sanitation (64.7%). Concerning food security, access to food recorded higher rates (49.2%). Concerning education, adults exhibited Despite free access to basic education, a section of children aged 5-17 is not enrolled in school (10.7%). Regarding health, access to a health facility exhibited higher deprivation levels (33.8%) despite free health services. In terms of security, a significant proportion of the population indicated they feel unsafe (39.7%). Overall, these findings confirm the need to shift from monetary measure to multidimensional measure of poverty.
In line with LNOB principle and SDG 1 (target 1.2), the deprivation incidences across all the indicators in all selected dimensions by different population groups are discussed. Figure 1 depicts deprivation levels across age groups. In general, the results reveal substantial differences in deprivation levels across age groups, with older persons exhibiting higher deprivation rates than other age groups in most of the deprivation indicators. Overall, varying deprivation levels exist across sub-groups of the populations (see Supplementary Tables S2-S4 for detailed results). Table 4 presents the results of the estimates of multidimensional headcount ratio (H), the average deprivation share across the multidimensional poor (A), and the adjusted headcount ratio (M 0 ). The results reveal that 46.2% of the population in Botswana can be considered to be multidimensionally poor. The results show that the incidence of multidimensional  poverty in Botswana remains a substantial problem. Multidimensional poverty intensity is estimated at 47.4%, meaning, on average, individuals are simultaneously deprived in at least eleven (11) out of the twenty-four (24) indicators considered. The adjusted headcount ratio is estimated at 0.219.

Estimates by Demographic Characteristics
The analysis is disaggregated by different demographic characteristics to identify those left behind. The results reveal that poverty levels are almost equal for males and females, with females slightly worse off than males. With respect to age, poverty levels vary significantly and increase with an increase in age. Older persons exhibit higher levels of multidimensional poverty compared to other age groups. This finding is consistent with other researchers who found that multidimensional poverty is higher for older persons than children (Espinoza-Delgado & Franco-Correa, 2014). It is essential to note the substantially wider gap in poverty levels between persons with disabilities and those with no disability, with persons with disability exhibiting highest poverty levels. This finding is consistent with the recent literature that found multidimensional poverty to be higher for persons with disabilities (Trani & Cannings, 2013;Trani et al., 2016). Individuals residing in households headed by men are slightly better off than those in households headed by women. Similar studies in developing countries confirm this finding (Fransman & Yu, 2019;Trani et al., 2016). Individuals residing in households headed by older persons and children experience higher incidences of poverty than those living in other households. However, the intensity of poverty declines with an increase in age of household head. Poverty levels exhibit a U-shaped relationship with household size. With respect to marital status, individuals from households headed by married couples experience lower poverty levels than those from households headed by unmarried persons. As expected, poverty levels decline with higher levels of educational achievements.

Estimates by Economic Variables
It is interesting to examine how multidimensional poverty levels vary across income groups (Table 5). Per capita consumption is used as a proxy for income. The results reveal a wide disparity in poverty levels. Individuals from the poorest households (bottom quintile) exhibited the highest multidimensional poverty levels. For example, the incidence of poverty for individuals from the poorest quintile are almost six times higher than that of individuals from the wealthiest quintile. This finding is consistent with other studies (Fransman & Yu, 2019;Mushongera et al., 2017;Roelen, 2017). With respect to the employment status of the household head, the results reveal mixed and surprising findings. Poverty levels are more pronounced among individuals from households headed by family helpers (domestic workers) or engaged in subsistence agriculture than those from households headed by unemployed persons. The majority have lower educational attainments, resulting in low wages. As expected, individuals from households whose heads are engaged in formal paid employment exhibited lower poverty levels.

Estimates by Geographic Variables
To identify where those who are multidimensionally poor live, the results are analysed by geographical location. Table 6 presents poverty levels by geographic variables. The results reveal that multidimensional poverty levels are more pronounced in rural areas than in urban villages and cities/towns. This finding has been confirmed in developing countries (Fransman & Yu, 2019) and elsewhere (Alkire & Santos, 2014;Trani et al., 2016) in the empirical literature. With respect to administrative districts, the results reveal varying levels of poverty. For example, individuals from Ngamiland West and Kweneng West experienced the highest incidence of poverty (88.1% and 78.8% respectively), while in contrast, those from Sowa Town recorded lower levels (4.6%).

Individual-level and Household-level comparison
To compare individual-level and household-level estimates, the same index is calculated using indicators identified at household-level. The same indicators explained in Sect. 3.4 and presented in Table 2 are considered. Equal weighting across the seven dimensions and equal nested weighting for indicators within each dimension used is employed. In household-based multidimensional poverty measurements, thresholds are not defined based on the achievements of each individual but collectively for the household. Based on indicators identified at household level, all members of the household are assumed to have the identical deprivation vector. However, when dealing with indicators identified at the individual level, we classify the thresholds of using individual-level data to assess household-level deprivation into two types, restrictive and expansive (Klasen & Lahoti, 2020). The deprivation threshold is defined as restrictive when the entire household members are categorised as deprived in an indicator if at least one individual is deprived of that particular indicator (Klasen & Lahoti, 2020). For example, a household deprived of nutrition if at least one household member is undernourished is such a restrictive one. The deprivation threshold is expansive when the entire household members are categorised as non-deprived in an indicator if at least one individual is non-deprived of that particular indicator. For example, the entire household is deemed non-deprived in educational achievement if at least one household adult member has 9 years of education. Except for educational achievement, all individual-level indicators are defined in a restrictive way. Tables S9 and S10 in the supplementary tables presents an illustration based on three households comprising twelve individuals. Table 7 presents the results. Based on poverty incidence (H), 36.5% of the population is considered multidimensionally poor when using the household as a unit of analysis compared to 46.2% when using individual as a unit of analysis. This result in 9.7 percentage points between the two measures. The results confirm that householdlevel measure underestimate poverty levels of the population. The results point towards a U-shaped relationship between age and multidimensional poverty, while the results based on individual measure reveal a positive linear relationship. The results support the use individual as a unit of analysis to identify those left behind in line with LNOB principle.

Inequalities among the multidimensionally poor
Inequality across society is a growing and highly prominent issue (Alkire & Seth, 2014a). In the SDGs, this is captured by SDG 10, which aims to reduce inequality within and among countries (UN, 2015). Inequality is a problem of inclusion, and LNOB is a tool for addressing inequality (Fukuda-Parr & Hegstad, 2018). This measure summarises empirical information that enables policymakers to assess whether the poorest of the poor share the benefits of poverty alleviation (Alkire & Seth, 2014b). This index lies between zero and one, with zero indicating complete equality (no inequality) and one showing absolute inequality (Hanandita & Tampubolon, 2016). Table 8 presents the results of inequality estimates among the multidimensionally poor across different subgroups of the population. Inequality among the multidimensionally poor is estimated at 0.044. The results reveal a positive relationship between inequality levels and the individual's age, with older persons exhibiting higher inequality levels. These results are consistent with those based on the multidimensional poverty index. This finding is an indication that multidimensional poverty index and the inequality among the poor are positively related (Alkire & Seth, 2014b;Espinoza-Delgado & Klasen, 2018).

Robustness Analysis
Following Alkire et al. (2015b), this study assesses if the main conclusions are robust to the different choices of parameters: (1) different poverty cut-offs (k values) and (2) changes in weighting structure (w). First, the complementary cumulative distribution function (CCDF) is employed to investigate whether the results are robust to the choice of a multidimensional poverty line (k). Figure 3 depicts the CCDFs for children, youth, adults, and older persons for various values of k, and the results do not find strict first-order stochastic dominance between the CCDFs for different k values. In general, the results show that older persons' distribution dominates those of other age groups. That is, no matter what value of k we choose, the proportion of multidimensionally poor individuals (H) will always be larger for older persons than for children, youth, and adults. The main conclusions also remain robust when using alternative weighting schemes (Supplementary Tables S5-S7). This robustness analysis proves that even though normative decisions were employed when constructing the index, the public policy conclusions drawn from the index are robust to a choice of diverse parameters.

Conclusions and Policy Implications
The LNOB principle is at the core of the 2030 Agenda for sustainable development. The call to end poverty in all its forms and for everyone, as emphasised by SDG 1.2, acknowledges the multidimensional nature of poverty and that poverty should be examined at the individual level. Notwithstanding this, most empirical studies use the household as the unit of analysis for multidimensional poverty measurement. However, household-based measures lead to biases in multidimensional poverty assessment and are not sensitive to demographic characteristics such as gender and age. Also, household based MPIs considerably underestimate the poverty levels of society. When using household-level measure, the incidence of female-headship as a sign of gendered poverty would be deeply misleading (Klasen & Lahoti, 2020). Therefore, the main objective of this study is to develop an individual-level and country-specific multidimensional poverty measure. Also, the study aims to provide estimates of multidimensional poverty for Botswana. This study contributes to the limited literature on individual-level multidimensional poverty measurement. Empirically, this study deepened the understanding of poverty in Botswana by providing a detailed analysis and data disaggregation in line with the LNOB principle. The results reveal that an estimated 46.2% of individuals are considered multidimensionally poor based on individual-level analysis. This figure is higher than the household-level estimate of 36.5%, which indicates that using the household as a unit of analysis leads to underestimating poverty levels in Botswana. The results show that, on average, the multidimensionally poor are deprived in 47.4% of all indicators under consideration. This finding indicates that multidimensional poverty intensity is also a considerable concern in Botswana. The extent and nature of multidimensional poverty vary significantly across different subgroups of the population. In Botswana, those left behind are mostly older persons and persons with disabilities. Significant disparities are observed across geography, with some districts such as Ngamiland West and Kweneng West West recording the highest poverty levels. In sum, the analysis in this study highlights the heterogeneity of different groups of the population. It suggests that more in-depth analyses of poverty at specific individual groups levels are needed to reveal the poverty situation of the society to inform policy better and improve the effectiveness of evidence-based planning. This way, interventions can be customised, taking into account these heterogeneities and improve the targeting of policy interventions.
The findings of this study have policy implications that might help the government, policymakers and researchers. The findings of this study are also expected to inform the poverty eradication initiatives as stipulated in the BPEPS, Vision 2036 and track the progress of the 2030 Agenda for Sustainable Development, especially SDG 1. The AF methodology used to construct the individual-level multidimensional poverty measure helps to explore the joint deprivation of the poor, thus helping policymakers to implement nationally appropriate social protection systems and to be able to cover those left behind as emphasised by SDG 1.3 of the SDGs. The analysis across different subgroups provides vital information that policymakers need since it shows the specific areas of who the poor are, where they live and how poor they are. Since different indicators are related to services whose provision falls under the mandate of different ministries/departments, an integrated approach to service delivery is key to reducing multidimensional poverty in Botswana. Also, disaggregating data analysis by different subgroups of the population allows for monitoring the SDG commitment of halving the proportion of men, women, and children experiencing poverty in all its dimensions and the LNOB commitment.
The finding that PWDs have higher multidimensional poverty levels warrants policy intervention. For example, there is a need to develop platforms for PWDs to have their voice heard regarding their specific lived experiences and priorities. Also, PWDs should be included in the broader decision-making processes as stipulated by the Convention on the Rights of Persons with Disabilities (CRPD). Notwithstanding this, Botswana is among the only five African countries that have not yet ratified the CRPD. Therefore, Botswana needs to sign the CRDP, which is intended as a human rights instrument for persons with disabilities. Also, there is a need to have specific interventions and policies aimed at older persons to prevent them from experiencing multiple deprivations.
The study concludes that mining plays a vital role in socio-economic development, as evidenced by lower multidimensional poverty levels in mining towns. However, whether mining contributes to socio-economic development for all is not clear-cut. Concerning tourism, the study concludes that it is not clear-cut that tourism plays an essential role in the socio-economic development of ordinary citizens. For example, Ngamiland West recorded the highest poverty levels, despite being rich in natural resources and providing some of the best tourist attraction places in the country. Therefore, the government of Botswana should put in place more inclusive tourism policies that will benefit communities living in areas with rich natural resources to leave no one behind.