Estimating the absolute wealth of households

Abstract Objective To estimate the absolute wealth of households using data from demographic and health surveys. Methods We developed a new metric, the absolute wealth estimate, based on the rank of each surveyed household according to its material assets and the assumed shape of the distribution of wealth among surveyed households. Using data from 156 demographic and health surveys in 66 countries, we calculated absolute wealth estimates for households. We validated the method by comparing the proportion of households defined as poor using our estimates with published World Bank poverty headcounts. We also compared the accuracy of absolute versus relative wealth estimates for the prediction of anthropometric measures. Findings The median absolute wealth estimates of 1 403 186 households were 2056 international dollars per capita (interquartile range: 723–6103). The proportion of poor households based on absolute wealth estimates were strongly correlated with World Bank estimates of populations living on less than 2.00 United States dollars per capita per day (R2 = 0.84). Absolute wealth estimates were better predictors of anthropometric measures than relative wealth indexes. Conclusion Absolute wealth estimates provide new opportunities for comparative research to assess the effects of economic resources on health and human capital, as well as the long-term health consequences of economic change and inequality.


Introduction
The estimation of the economic status of individuals and their households is central to much work in epidemiology and the social sciences. Wealth is a key determinant of health and social achievement and an indicator of well-being in its own right. For this reason, the development and testing of novel measures of economic status is of interest. There is lively debate over the relative merits of the competing methods used to assess and compare the relative or absolute wealth of individuals and households. [1][2][3] Social scientists have developed several approaches to assess the economic status of households, including consumption expenditures, income, assets and national gross domestic product (GDP) per capita. 1,2,[4][5][6] The widely used demographic and health surveys have provided detailed data on household assets in over 60 low-and middle-income countries. 3,7 Estimates of relative household wealth based on asset data permit researchers to examine the effect of economic status on a wide range of health behaviours and outcomes, such as fertility, growth, malnutrition, disease risk and mortality. 3,[7][8][9][10][11] The commonly-used relative wealth indices derived from demographic and health survey data allow households to be ranked according to their relative wealth within a particular country in a particular survey year. However, methods of estimating relative wealth cannot be used to assess the effect of absolute economic resources on health behaviours and outcomes across countries and years. In contrast, estimates of absolute household wealth could be used to make meaningful comparisons across countries and years. They could also be used to compare wealth effects aggregated at multiple social scales -e.g. at country, province, city or household level -and to contribute to current debates about the importance of absolute and relative wealth in determining health outcomes. 5,12 Although several methods to estimate absolute household wealth have already been developed or proposed, each has its limitations, including sensitivity to the sample of countries as well as to the country selected as baseline. 13,14 Most also rely on arbitrary wealth indicators, cut-offs to anchor comparisons and/or a common set of assets. Such approaches often exclude countries using different assets in surveys, ignore assets that may be important in a specific country setting and assume that an asset in one country provides the same measure of wealth as it does in another country. [13][14][15] In an attempt to address these limitations, we have developed a method for estimating the absolute household wealth per capita -called the absolute wealth estimate -in units that permit meaningful comparisons across countries and years. We used the method to evaluate the prevalence of poverty and indicators of nutritional status and compared these results to common benchmarks.

Methods
Our method relies on two main inputs from a country in a given year: the rank of each surveyed household according to its material assets and the assumed shape of the distribution of wealth among the surveyed households. Demographic and health surveys provide a ranking of surveyed households, in the form of the wealth factor score. 3 We used three parameters to define the shape of the wealth distribution in a given country in a given year: (i) the mean wealth per capita; (ii) the Gini coefficient, as a measure of variance; and (iii) the best combination of the Pareto and log-normal distributions that we could identify as a way to estimate skewness. [16][17][18][19][20] By using the relative ranking of households by wealth and the shape of the wealth distribution, we could estimate the absolute wealth of each household by identifying the specific rank of the household in the wealth distribution.
Objective To estimate the absolute wealth of households using data from demographic and health surveys. Methods We developed a new metric, the absolute wealth estimate, based on the rank of each surveyed household according to its material assets and the assumed shape of the distribution of wealth among surveyed households. Using data from 156 demographic and health surveys in 66 countries, we calculated absolute wealth estimates for households. We validated the method by comparing the proportion of households defined as poor using our estimates with published World Bank poverty headcounts. We also compared the accuracy of absolute versus relative wealth estimates for the prediction of anthropometric measures. Findings The median absolute wealth estimates of 1 403 186 households were 2056 international dollars per capita (interquartile range: 723-6103). The proportion of poor households based on absolute wealth estimates were strongly correlated with World Bank estimates of populations living on less than 2.00 United States dollars per capita per day (R 2 = 0.84). Absolute wealth estimates were better predictors of anthropometric measures than relative wealth indexes. Conclusion Absolute wealth estimates provide new opportunities for comparative research to assess the effects of economic resources on health and human capital, as well as the long-term health consequences of economic change and inequality.

Relative wealth index
The relative wealth index treats household wealth as an underlying, unobserved variable that can be estimated from the presence of household assets and used to assign each surveyed household to one of five wealth quintiles based on rankings on a wealth factor score. 3 For validation of our method, we used relative wealth indices recorded in demographic and health surveys, belonging to four waves of surveys in 66 countries.

Mean wealth per capita
We used estimates based on GDP and real per capita consumption data from national accounts (available from the corresponding author). 21,22 Our method can use any established measure of country-level wealth per capita.

Gini coefficient
The distribution of wealth across individuals or households in a given country can be summarized using a Gini coefficient. We obtained the Gini coefficients for wealth from Davies et al. 22

Statistical distribution
We investigated two statistical distributions commonly used to model wealth in populations: the Pareto and the lognormal. In the modelling of wealth, each of these distributions is defined by the mean wealth per capita -as the central tendency -and the Gini coefficient -as a measure of dispersion. Each distribution has a characteristic shape (Fig. 1). The logarithm of the Pareto distribution is heavily right-skewed, with a sharp cutoff on the left side. The logarithm of the log-normal distribution is a symmetric normal distribution, with no skew. By combining estimates from both of these distributions, we could therefore examine wealth distributions with varying degrees of skew.

Absolute wealth estimates
Assuming a country-specific wealth distribution, we allocated countrylevel wealth per capita to each surveyed household based on the household's wealth factor score ranking. Specifically, the per capita wealth of household i was estimated as: where rank i is the proportional wealth factor score ranking of household i and Wealthpercap is the country-specific estimate of the wealth per capita in a given year. For the Pareto distribution, ICDF is the inverse cumulative distribution function with shape parameter α, calculated as (1+Gini)/(2 × Gini), and a threshold of [1-(1/α)] × Wealthpercap. Otherwise, ICDF is the inverse cumulative distribution function for a log-normal distribution based on a normal distribution with a mean of: and a value for σ calculated as: We called absolute wealth estimates based on Pareto and log-normal distributions Wealth Pareto and Wealthlognormal respectively. Absolute wealth estimates varied -especially among the poorer households -depending on which distribution we used. To examine a wider range of possible distributions with differing degrees of skew, we examined weighted geometric means of the Wealth Pareto and Wealth lognormal values by using the equation: where γ is the weighting given to a Pareto distribution, relative to the corresponding log-normal distributions, in our calculation of an absolute wealth estimate. The absolute wealth estimate was thus Wealth lognormal when γ was set to zero and Wealth Pareto when γ was set to 1.0. All of the wealth distributions that we considered were therefore defined by three parameters: (i) the mean wealth per capita in a country during the survey year; (ii) the Gini coefficient for wealth; and (iii) γ -i.e. the relative weighting given to the corresponding Pareto and log-normal distributions. All absolute wealth estimates are given in 2011-constant international dollars with purchasing power parity and are therefore comparable over time.

Research
Estimating absolute wealth Daniel J Hruschka et al.

Validation
We validated our evaluation of absolute wealth in two ways. First, we examined how well the distribution of the estimates from a single country survey approximated a commonly used benchmark for poverty in the same country. The benchmark we used was the World Bank's so-called poverty headcount -i.e. the World Bank's estimate of the number of people in a country whose household consumption expenditure, in a given year, fell below 2.00 or 1.25 United States dollars (US$) per day. 23,24 Although wealth and consumption expenditure are distinct concepts, we would expect a rough correlation so that, for any given World Bank consumption expenditure used as a threshold for poverty -e.g. US$ 2.00 per capita per day -there should be a comparable threshold value for absolute wealth estimatese.g. 800 international dollars per capita -that yields a similar estimate of the number of people in poverty.
Provided that the headcount and demographic and health survey years were separated by no more than three years, we used the World Bank's poverty headcount for the year closest to the demographic and health survey year. If no World Bank headcount was available for the three years after a survey or three years before a survey, we excluded that survey from our analyses. We used World Bank headcounts based on consumption expenditures from householdlevel microdata that had been converted to 2005-constant international units. We were able to match 112 headcounts with eligible surveys. We identified the poverty threshold for absolute wealth estimates and the value of γ that produced poverty headcounts that were closest to the corresponding World Bank poverty headcounts. For this purpose, we used threshold consumption expenditures of both US$ 1.25 and US$ 2.00 per capita per day.
In our second method of validation, we compared how accurately different wealth estimates predicted key indicators of nutritional status. We compared the results obtained using our absolute wealth estimates with the corresponding relative wealth estimates. We used demographic and health survey wealth index quintiles as measures of relative wealth. As very few of the surveys we investigated had collected anthropo-metric data from men, the five key measures were body mass index (BMI) of non-pregnant women aged 20-49 years and the heights and weight-for-height Z-scores of boys and girls.
To assess the relationship between these anthropometric measures and the various wealth estimates, we used a mixed regression model with random effects for country. We classified absolute wealth into 14 categories: less than 200, 200-299, 300-449, 450-679, 680-999, 1000-1499, 1500-2199, 2200-3299, 3300-4899, 4900-7299, 7300-10 999, 11 000-16 499, 16 500-24 999 and at least 25 000 international dollars per capita. The only weight-for-height Zscores that we considered were those of children aged 0-59 months when surveyed and had mothers who were aged 20-49 years when the children were surveyed. The only heights we considered were those of children whose height increase would be expected to be linear with age-i.e. those of children aged 11-59 months.
In the model of BMI, we included a linear and quadratic term for age, a dummy variable for whether a woman was breastfeeding when surveyed, 25 and interactions between wealth and breastfeeding and wealth and age. 20 In modelling children's height, we included an interaction term between wealth and age. In our model of weight-for-height Z-scores, we included age in months as a categorical variable and used an age of 24 months for reference.
To compare the usefulness of our absolute wealth estimates in predicting these key measures of physical growth with that of the wealth quintiles from the demographic and health survey, we ran each model with the estimates alone, with the quintiles alone and with both the estimates and quintiles. The relative fit of each model was assessed using the Akaike information criterion 26 as well as the proportion of variance accounted for by the absolute wealth estimates and wealth quintiles. We investigated the sensitivity of our method to variation in the Gini estimates and the ranking of households by wealth. We also investigated the sensitivity of the relative wealth analyses to the use of five categories.

Descriptives
We analysed wealth data, for 1 989 324 women in 1 403 186 households, collected during 156 surveys in 66 countries. The median absolute wealth estimate was 2056 international dollars per capita (interquartile range: 723-6103). Fig. 2, Fig. 3 and Fig. 4 illustrate the variation seen in absolute wealth estimates across countries in the year 2000 and across time and districts in one country (Bangladesh). Within countries, a uniformly high correlation between the absolute wealth estimates and corresponding relative wealth quintiles was observed (r > 0.85).

Poverty headcounts
The value of γ that gave the best fit between the poverty headcounts based on the absolute wealth estimates and the World Bank poverty headcounts was 0.32. We therefore used Wealth 0.32 in subsequent analyses (Fig. 1) (Fig. 5).

Physical growth
All of the anthropometric measures that we investigated showed a statistically significant positive correlation with our absolute wealth estimates. The latter estimates also accounted for substantial proportions of the between-country variation seen in these measures -e.g. 42%, 10-12% and 16-17% of the variation seen in women's BMI, children's heights and children's weight-for-height Z-scores, respectively -and smaller proportions -9%, 4-5% and 1%, respectively -of the corresponding withincountry variation. Compared with the relative wealth indexes, the absolute wealth estimates appeared to be much better predictors for the anthropometric measures. The Akaike information criterion values were reduced by 295 and 265 for the heights of boys and girls, respectively, and values were reduced by 2200, 2465 and 34 308 for the weightfor-height Z-scores of boys and girls and the BMI of non-pregnant women, respectively. The absolute wealth estimates also accounted for far more of the variance seen in all five of these measures of growth than the corresponding wealth indexes ( Table 1). The absolute wealth estimates not only captured at least as much of the within-country relationship between wealth and growth as captured by the wealth indexes but also captured the between-country covariation between wealth and growth (available from corresponding author). The results were robust to assuming a single Gini coefficient, to ranking households instead of individuals by wealth and to using a 14-category relative wealth index instead of the five-category index (available from corresponding author).

Discussion
We have developed a method to calculate a novel metric -the absolute wealth estimate -using demographic and health survey data that are regularly collected in many countries. Absolute wealth estimates can be compared across countries and years and with existing measures of relative wealth. This enables researchers to investigate the relationships between absolute economic status and health, fertility, growth and other outcomes of interest. We found that we could derive poverty headcounts from absolute wealth estimates that were consistent with World Bank poverty headcounts. Moreover, the absolute wealth estimates also account for more variation in important measures of human growth and nutrition both within and between countries. Our method for calculating absolute wealth estimates has several limitations. First, although useful for aggregate analyses, the absolute wealth estimates are likely to have high uncertainty at the level of individual households. Second, given the skewed distribution of wealth and the small number of very wealthy households included in most demographic and health surveys, the absolute wealth estimates for the wealthiest households will be particularly uncertain. We attempted to minimize the impact of such uncertainty by dividing the surveyed households into 14 wealth categories but other researchers may decide to exclude data from households that exceed a relatively high wealth threshold. Third, although we assumed that households in demo-

Research
Estimating absolute wealth Daniel J Hruschka et al. graphic and health surveys had similar social organization, this may not have always been the case since the concept of a household is not clear-cut. [27][28][29] Fourth, the values for country-level wealth per capita that we used relied on estimates of gross domestic products derived from national accounts. National accounts may be inaccurate, especially in poorer countries. 30 In situations where a large portion of a country's GDP arises from economic activity that does not contribute to household resources, the wealth available to individual households may be overestimated. In addition, informal economic activity may contribute substantially to household wealth but not be included in estimates of GDP. Finally, the derivation of the relative wealth index assumes that there is a single dominant ladder of wealth. In places with more than one system of wealth -e.g. in areas where cattle ownership may be more important than participation in the cash economy -the wealth score may undervalue household wealth. 31,32 We hope that our method for calculating absolute wealth estimates will enable some of these challenges to be resolved and facilitate research on the links between wealth and health.
A strength of our method to calculate absolute wealth estimates is its dependence on just two main inputs: a relative ranking of households within a survey and the shape of the wealth distribution in the survey population, as defined by three parameters. Unlike other methods for producing comparable estimates of economic status, our method does not depend on the sample of countries or the baseline country selected. In addition, since the relative ranking of households occurs within each country -as a routine part of a demographic and health survey -before estimation of the absolute wealth of the households, our method does not require that all surveys record the same assets or that all assets are weighted the same in terms of their relative importance to wealth in each country. As it enables comparison of wealth estimates without sacrificing information about country-specific assets, it preserves the key strengths of the previous demographic and health survey wealth factor -i.e. the accuracy, efficiency and flexibility of using different asset indicators to measure wealth as a latent variable. Given our method's relative simplicity, it should be possible to extend its use beyond demographic and health surveys, to other nationally  representative surveys that also collect data on material assets. We validated the absolute wealth estimate using anthropometric measures because of the well-established relationship between absolute deprivation and human growth. It appears that, compared with relative wealth, absolute wealth is a much more substantial contributor to at least some of the key measures of human growth and nutritional status. The derivation of absolute wealth estimates may permit researchers to examine how other social and health outcomes -e.g. literacy, cardiovascular risk, infection with human immuno-deficiency virus -may be patterned, within countries, provinces and cities, by both absolute and relative wealth. 31 For example, it may be that literacy is apportioned within countries so that (i) even in the poorest countries, the wealthiest 20% of individuals have high levels of literacy, and (ii) even in the wealthiest countries, the poorest 20% of individuals have low levels of literacy. If this is the case, we would expect relative wealth within countries to be an important, independent predictor of literacy. Absolute wealth estimates provide new avenues for comparing the effects of absolute and within-country relative wealth and investigating their possible interaction.