Wellbeing inequality in a developing country: from theory to practice

This challenges the consensus of a moderate level, and stability in, wellbeing inequality using income proxied measures.. We argue that empirical studies of wellbeing need to incorporate

Wellbeing inequality in a developing country:

From theory to practice

PHAN VAN PHUC

University of Wollongong, Australia Can Tho University – pvphuc@ctu.edu.vn

of inappropriate proxies for wellbeing, and (2) ignorance of the interdependency between dimensions of wellbeing This paper develops a fundamental framework and applies a principal component analysis method for a calculation of the wellbeing level and wellbeing inequality in Vietnam Our results show that not only the level, but also inequality, of wellbeing increased in the period 1993–1998 and 2002–2008 This challenges the consensus of a moderate level, and stability in, wellbeing inequality using income proxied measures We argue that empirical studies of wellbeing need to incorporate multiple dimensions in addition to dimensional interdependency characteristic and thus, implementation in the wellbeing analyses of wellbeing using principal component analysis can obtain the unique results of the level and inequality of wellbeing

Keywords: inequality; principal component analysis; Vietnam; household wellbeing

1 Introduction

The concept of inequality has been extended in relation to multiple dimensions of wellbeing The rhetoric question ‘equality of what?’, raised by Sen (1980), requests a comprehensive examination of the facets of, and proxies used for measures of, inequality The income-proxied approach derived from the utility comparison becomes unbearable in terms of drawing a complete picture of interpersonal wellbeing differences (Sen 1997) Although perception of wellbeing varies among different contexts as it depends on social norms and values, the domains of wellbeing go beyond income dimension This idea is traced back to Sen (1985a)’s capability approach that emphasizes not only what people have, but also the extent to which they are free to do and to be

A general perception of wellbeing is anything making a good life (Deaton 2013, p.24) despite no consensus on the concept of wellbeing has been reached; differences in wellbeing achievements needs an assessment of ‘wellness’ of people’s state of being (Sen 2003b, p.36) In developed countries, a plethora of studies focus on wellbeing achievements or outcomes with a range of indicators including, but not limited to, income and wealth, health and feeling, education and social engagement (Deaton 2013, p.24) For instance, OECD (2013) chooses eleven indicators which represents plausible dimensions of wellbeing which specifies the eight components suggested in Stiglitz et al (2009) In developing countries, however, it is insufficiently concerned with research in wellbeing and inequality in wellbeing (Cho 2015)

Although data availability for assessments of inequality in wellbeing has emerged, serious problems with empirical analyses remains First, one-indicator proxy leads to a distorted picture of wellbeing which comprises a variety of factors For instance, Vietnam shows confusing levels of inequality with income and expenditure indicators which are equally accepted as proxies for wellbeing (Zhuang et al 2014) In 2008, there was a significant gap between the Gini coefficient of income (0.44) and that of expenditure (0.36)

Additionally, the development of measures of inequality in multiple dimensions disentangles the ambiguities of single indicator-proxied method Rather, it further provides confusing and inconclusive results corresponding to varying choices of parameters used and the sequence of aggregation across dimensions in the estimations

of inequality (e.g inequality aversion), even with the same methods and datasets (e.g Nilsson 2010, Justino 2012)

Finally, the assumption of non-interdependencies between variables is also violated

as there is plausible evidence of interrelations between economic, education and health indicators Russian data, for example, reveals a complexity of interrelations across dimensions Decancq and Lugo (2012) found that this correlation structure changed remarkably in the examined period (1995–2005) Unfortunately, they could not scrutinise thus far because of the paucity of data which is common in the majority of countries Therefore, the extent to which the indicator weights in a computation of inequality have not been thoroughly examined A postulation of equal variable weight

is, however, inconsistent with the fact that variables may have unequal influences on wellbeing, and thus on the level of overall inequality

To fill these deficiencies, this paper develops the analytical framework based on Sen’s capability approach and applies the polychoric principal component analysis (PCA) to Vietnamese data In doing so, this research contributes to the literature on wellbeing inequality in two main ways First, it extends the analysis of wellbeing by including the various wellbeing components We consider the contribution of non-economic dimensions and the interactions of all indicators to an overall trend in multidimensional inequality Furthermore, we compare wellbeing inequality trends over time and across different geographical areas

The remainder of the paper proceeds as follows The next section discusses the capability approach The methodology, data and variables are described in Section 3 Section 4 compares the wellbeing index construction based on the polychoric PCA to the income-proxied wellbeing Section 5 analyses inequality in wellbeing The conclusive part investigates further steps to identify major causes of inequality

2 The capability approach

Capability indicates the individual ability to obtain real achievements in relation to external and internal conditions that influence personal transforming from commodity possession to personal wellbeing (Sen 1985b) Despite economic dimension is an important contributor to wellbeing, it could not capture all determinants of quality of life that people are able to do or live in their favoured ways

Sen (1985b) introduces his own approach to make the individual wellbeing comparable through a relationship between the two core concepts: ‘capability’ and

‘functioning’ This correlation is addressed by a simple equation which is slightly modified by Kuklys and Robeyns (2006) as follows:

Qi(Xi) = [bi|bi=fi(c(xi))|T(i,s,e) for several fi ϵ Fi, and several xi ϵ Xi] (1) where:

bi denotes individual i’s ‘being’; fi is a functioning and belongs to Fi (vectors of individual’s functionings);

c(xi) is a function of conversion from a vector of possession of commodities (xi) to their characteristics, xi ϵ Xi (different sets of commodities); and

T is the transformation conditions comprising three components; these are individual circumstances – Ti (e.g sex, physical ability), social factors – Ts (e.g public policies) and environmental conditions – Te (such as environmental pollution, weather) How ‘well’ of personal ‘being’ firstly depends on commodity ownerships and individual functionings Given a bundle of commodities (xi), different choices in Fi lead

to varieties in the wellbeing level (bi) This expression is called the personal capabilities – Qi(Xi) Xi refers to all kinds of resources and is subject to the personal budget constraint

The capability approach is totally and directly operational with respect to freedom of choices Kuklys and Robeyns (2006) appreciate its extendable characteristic by adding plausible functionings such as ‘being educated’ and/or ‘being employed’ Dang (2014) supports a concentration on the achieved functionings which are more operational than

on a set of capabilities in the case of inadequate information on freedom conditions Despite difficulties of data collection relating to achieved capabilities or functionings,

in practice, the data and variable suitability and analytical methods associated with such data should be thoroughly examined (Sen 2003a, p.53) Sen however does not provide

a specific discussion beyond that point, but he recommends a solution to choosing dimensions, indicator weights, and calculation metric through a democratic public decision Wellbeing evaluations should consider with respect to social and historical contexts (Jackson 2005, Qizilbash 2011)

An important characteristic of the capability is its ‘incompleteness’ of a contribution

of functionings which lead to the wellbeing level (e.g Sugden 1993) Alkire (2002b)

advocates that this incompleteness is not a shortcoming, but it opens for adaptations to

the cultural and personal circumstances She also appreciates Sen’s capability that does

not dwell on a fixed subset of capabilities, but proxies for capabilities should be adjusted

in favour of research perspectives ‘The capability approach can often yield definite

answers’ of the levels of individual wellbeing in such a case (Sen 2003a, p.46)

Finally, inequality should be assessed as a ‘failure of [and differences in] certain basic

capabilities’ (e.g being nourished, being sheltered) respectively as income and

preference are not accurate measurements to comparing interpersonal wellbeing (Sen

1985a, 2006) There is nothing mathematically wrong with the measurements of

inequality derived from income, ‘but [to] interpret them as utility comparison…would

be a complete non sequitur1’(Sen 1997, p.392)

3 Methodology, data and variables

3.1 The polychoric principal component analysis

We choose the polychoric PCA developed in Kolenikov and Angeles (2004, 2009) to

analyse wellbeing and inequality because this modified PCA is superior to its nạve

version The standard PCA is originally constructed to handle non-discrete variables An

application of PCA to the non-continuous data may have problems First, if one breaks a

categorical variable into more than two dummies, PCA could create numerous spurious

correlations Second, a transformation from ordinal variables to dummies cannot retain

the ordinal feature of indicators More importantly, if categorical variables are treated

as continuous ones, a violation in the assumption of a normally distributed variable in

PCA occurs analogously to the case that discrete variables are used as independent

variables in OLS since discrete variables do not have a density but high skewness and

kurtosis (Kolenikov and Angeles 2004, 2009) The polychoric PCA minimises violation

of a normal distribution assumption when applied to discrete data The polychoric PCA

can also assign various weights for different units and categories of indicators and

describe more precisely wellbeing inequality (Ward 2014)

1 non sequitur: ‘a statement that is not connected in a logical or clear way to anything said before it’

(Merriam-Webster dictionary n.d.)

Correlation coefficients in the polychoric PCA are described in the following steps First, two ordinal variables xi, xj indicate asset ownership, educational outcomes, or health status They are discretised in dk categories (k = 1…m), and dr categories (r = 1…n) respectively Thus, the thresholds of xi, xj are denoted as τi,τj corresponding to dk,

dr These axioms yield the following two equations:

Second, ρ is obtained by maximising l function with the thresholds τi,τj which are equal to the inverse cumulative distribution function of the observed proportion in unit (k r) of the table (Olsson 1979):

Based on this theoretical framework, Ward (2014) resolves the factor loading of variable

xi corresponding to the category dk:

where: λi is the first component of polychoric PCA assigned for xi

The factor loadings (or weights) of variable have dual functions Moser and Felton (2007) explore a proportional contribution of variable weights in wellbeing These weights show how an indicator is important as a wellbeing determinant For example,

an asset indicating the presence (absence) of other assets may be assigned a positive (negative) correlation coefficient An asset with a very small coefficient is less relevant

to wellbeing and therefore, can be omitted A construction of wellbeing index is as follows:

𝑤ℎ is the level of wellbeing of household h;

X indicates variables representing household wellbeing;

dk1…kn denotes n categories of variable xi; and

y(xi|dk) is the achievement due to obtaining indicator xi with dkj

The PCA-based measurement of wellbeing outperforms the existing methods in three main ways (McKenzie 2005) First, results of measurement are unambiguous This aspect is more important in terms of policy implications Second, while other measurements avoid resolving interrelationships across dimensions, the PCA-based method can consider plausible interdependency of variables The factor loadings are calculated based on various categories and units of a variable This characteristic further enables us to estimate inequality in wellbeing with varying quantities of asset ownerships, various levels of educational achievement, and a wide range in health status Third, a computation of different weights is more reasonable than an allocation

of unified weight forall variables With these PCA advantages, this study goes beyond income inequality and analyses the importance of different factors contributing to inequality

The second role of variable weights indicates wellbeing inequality The higher the weights, the greater the share of variable in the total variance of the first component of PCA and thus, it shows the gap in wellbeing distribution If a variable has a minor standard deviation, it is assigned a small weight in PCA in the inequality index According to McKenzie (2005) and Ward (2014), the measurement of inequality using PCA is as follows:

𝐼𝑡 = 𝜎𝑡

where:

σt is the sample standard deviation of household wellbeing (wh) at time t;

λ is the first eigenvalue from the correlation matrix in PCA and also the variance held

by the first component across the whole population

3.2 Data

This study uses data extracted from the Vietnam Household Living Standard Surveys (VHLSSs) which combine the retrospective information about households that have participated in the previous wave and about the first-time additional participants A longitudinal dataset that is composed of more than two waves substantially decreases the number of observations, and this might cause measurement errors Additionally, no households interviewed in the 1990s took part in the later survey in the 2000s Therefore, this paper does not generate panel data, but uses pooled 1993–1998 and 2002–2008 data

Since the size of the VHLSS 2002 is threefold the size of any other wave, a random sample of 31% of its total observations is created with a remaining proportion of observations between provinces and urban–rural This technique of data combination computes unique weights for ordinal and cardinal variables so that the wellbeing level and inequality can be comparable across households inter-temporally

3.3 Variables

Twenty–one and twenty–five variables are used as proxies for wellbeing in the 1990s and 2000s respectively Regarding changes in wellbeing standards, this section predetermines whether variables used for the period 1993–1998 remain sensible in the following decade Indicators with all correlation coefficients lower than 0.1 are

considered as ‘no containing information’ (Moser and Felton 2007) and excluded from the model

Asset indicators

Despite no consensus on a standard principle, several guidelines for variable choices are mentioned Assets need to be chosen carefully as several assets might represent prosperity in the past but poverty at present (Rutstein and Johnson 2004) An increased number of assets can also raise household capabilities (Ward 2014) As wellbeing is multidimensional, these variables must be plausible to avoid biases in ranking individual wellbeing

The magnitude of coefficients on original variables generated by PCA depends on how the proportion of total information is captured by the corresponding indicators; greater coefficient means that the variable is more important contribution to wellbeing This is an advantage of the PCA-based measurement of inequality because the chosen indicators indicate related variables that describe wellbeing irrespective of whether they are present in the measurement

The extent to which the role of asset ownership has changed could be explained by socioeconomic conditions When the average income was below US$300 in the 1990s (World Bank 2013a), Vietnamese people could expect to possess a radio, or a clock as essential things of an acceptable living standard However, these assets become less important in the twenty–first century as households own more valuable items that generate identical utilities (such as colour TVs, or wrist watches) Therefore, a list of indicators should be revised over time to avoid any inappropriate proxy for wellbeing Furthermore, this analysis also considers the quantities of the assets owned by the households, as these differences could be of importance to measure inequality Ward (2014) clarifies that a consideration to asset quantity can raise the effectiveness of the polychoric PCA regarding the rankings of household wellbeing

Educational indicators

Education is a vital wellbeing determinant because knowledge and experience not only reflect the household achieved functionings in the educational dimension itself but also influence other aspects of wellbeing

This study selects two variables as a proxy for the educational dimension (but only one for the 1990s due to data unavailability) Instead of the household head, the person with the highest educational attainment in the household is collected The reason for this is that household wellbeing could be affected by the members with the highest level

of education not only within the educational dimension but also in the economic and health aspects In Vietnam, there is a significant gap between parents and their offspring’s schooling because household heads were likely to have finished schooling early, but they encourage their children’s studies even though they are classified in the poor stratum

Housing and health related variables

The housing variables used include housing characteristics and housing facilities These variables can provide information on both the quality of accommodation and other conditions related to the health dimension The earlier indicator refers the types

of material used to house building (e.g wood, cement) and housing facilities reflect the quality of basic services consumed by households (e.g drinking water) A consideration

of housing indicators is found in studies in inequality underpinned Sen’s capability approach (Kuklys and Robeyns 2006, p.46) despite different choices of housing variables regarding wellbeing McKenzie (2005) uses the number of rooms, house ownership, and the quality of walls and roofs, as proxies for the housing dimension; Kuklys and Robeyns (2006) choose the indicators which investigate whether a household has problems of (water) condensation, rotting wood (windows or floors), keeping the home warm and the house capacity Moser and Felton (2007), and Ward (2014) add lighting sources, and toilet types in this group and classify them as ‘housing capital’ In this paper, the housing characteristics variables are combined with asset indicators

Additionally, housing facilities are interpreted as proxies for the health dimension because these variables can significantly impact individual physical wellbeing For example, using safe drinking water may reduce the probability of several infections Unfortunately, this type of information is unavailable in the 1990s waves and therefore, the number of sick days over a month is used as a proxy for the family health status

Table 1

Variables used for a measurement of wellbeing level and inequality over the period 2002–2008

Housing and Asset ownership

Housing variables Assets

Types of house: indicating the

quality and characteristics of

material used to build a house

Electricity: ordinal, indicating

energy resources for the lighting

purpose Assuming that using

national provision of electricity is

the highest benefit to a household

wellbeing

Car Motorbike Home phone Video player Colour TV Black and white TV

Refrigerator Air conditioner Water heater Washing machine Gas cooker Electric cooker/stove Electric generator

Water pump Personal computer Printer Camera Vacuum cleaner

Educational achievements

Schooling years (in the official universal educational system, from the pre-school level to grade 12) of the most educated member of a household

Highest educational qualification achieved by the most educated individual of a household

Health related indicators

Drinking water: ordinal variable (ranging from 1 to 5) indicates the quality of water source for the drinking purpose

Toilet: ordinal variable (ranging from 1 to 5) reflects the type of toilet used

Garbage: ordinal variable (ranging from 1 to 4) expresses the kind of rubbish disposal

4 The household wellbeing level: non-monetary vis-à-vis monetary indicator

To validate the wellbeing index and the analysis of wellbeing inequality, this paper makes a comparison between two proxies of wellbeing: non-monetary (wellbeing) indicators estimated by the polychoric PCA and a monetary variable – the consumption expenditure The theory behind this comparison is Sen’s (1985a) capability approach Consumption expenditure is a common proxy for economic rather than multidimensional wellbeing Sen argues that money is a means but not an end (outcome

of wellbeing); thus, use of the monetary variable could be misleading because income

‘gives a very inadequate and biased view of inequalities’ (1997, pp.384-385) We advocate this argument that using expenditure data for analyses of Vietnamese people’s wellbeing is inappropriate In contrast, the non-monetary indicators consider the level

of wellbeing and the contribution of various dimensions, adding but not limited to income, to wellbeing

Table 2 describes a relationship between household expenditure and the wellbeing index derived by Eq.(7) The two methodologies used for this comparison are the within quintile ranking consistency and the Spearman-rank correlation technique The population in each wave of survey is classified in five quintiles based on the household expenditure, and the household wellbeing indicator respectively Then, an identification matching technique is used to record the percent matched within the same quintiles by these two methods The second column shows that the level of consistency is around 40% across these four waves This means that about 60% of the wellbeing level measured by the non-monetary approach may not be covered by the expenditure variable The third column reveals the ranking correlation between the household expenditure and the wellbeing index Compared with the within-quintile matching, the Spearman-rank correlation method illustrates closer and significant correlation coefficients between the two proxies2 This technique indicates that over two–thirds of households are consistently ranked by the wellbeing index and the household expenditure

Results of a mismatch between the lowest quintile defined by the wellbeing index and the highest one identified by the expenditure data, and vice versa, are reported in the last two columns The percent of mismatched households between two methods are negligible

2 All results estimated by the Spearman correlation coefficients are significant at the 1% level

Spearman coefficient on ranking consistency

Wellbeing lowest quintile/ Income highest quintile 3

Income lowest quintile / Wellbeing highest quintile

Source: VHLSS 2002–2008; authors’ estimation

Another way to check the robustness to the wellbeing index is to compare the trends

in wellbeing using the two proxies As Vietnam did not experience any notable crisis (e.g political conflict or economic shock) which negatively affect the economic, health, or educational dimensions, the overall wellbeing level is expected to increase in the period 2002–2008

With the pooled VHLSS 2002–2008 data, values of wellbeing are calculated The polychoric PCA produces the zero-mean aggregate wellbeing values for the whole sample; hence, the wellbeing level of each wave could not be interpreted in its absolute values However, it is evaluated relatively through its variations Table 3 shows rises in the mean of wellbeing for the whole country and two selected regions The national wellbeing level, placed in the first column, increased spanning 2002–2008 This trajectory is compatible with socioeconomic progress in Vietnamese society This tendency is consistent with changes in household real expenditure presented in the last column

Table 3 also illustrates wellbeing movements in two distinct regions Changes in wellbeing in both the two regions follow the trajectory of national wellbeing This evidence confirms that the wellbeing indicator generated by the polychoric PCA is

a good proxy used for an analysis of inequality This comparison shows an analogous improvement in wellbeing found in Ward (2014) These results further

3 This fraction is estimated by the matching technique that expresses how many percent of households categorised

as highest expenditure quintile but as belong to the poorest quintile in wealth measured by the asset indicator approach