# _Decomposition analysis_

This is yet another fruitful approach to disentangling the impacts on health inequalities of policies and other influences. While somewhat technical, the idea is simple (Wagstaff 2000; Wagstaff, van Doorslaer, and Watanabe 2001). Consider the case of inequalities in child survival. The expected survival time of a child will depend on a number of underlying determinants of child health. At the child level, these will include the child's gender and his or her birth order. At the household level, they will include the mother's education, the household's income, its drinking water and sanitation facilities, and the location of the household's dwelling in relation to, for example, health services. Also important will be various influences at the community level, such as the accessibility, availability and quality of health services, as well as infrastructure in the community (electricity, roads, public transport, community facilities such as shops, etc.). With data from household and community surveys, one can model the links between child survival and its determinants to estimate the responsiveness or "elasticity" of survival to each of its determinants. Estimating these elasticities is one part of the exercise of decomposing or unpacking the causes of socioeconomic inequalities in survival. The other part involves seeing how unequally distributed the various determinants are across income groups. The larger the elasticity of a particular determinant is, and the more unequally it is distributed, the more important it is in explaining survival inequalities. So, for example, if survival turns out to be highly sensitive to the availability of primary health care facilities in the child's community, and poor children are very much less likely to have such facilities in their community, these inequalities in primary care availability will account for a large fraction of the inequality in child survival. The two elements to the story are multiplicative. A determinant might be absolutely fundamental to child survival, but if it is not especially unequally distributed across income groups, it won't be a major part of the explanation of survival inequalities. Or, a determinant might be highly unequally distributed, but if survival isn't especially sensitive to it, inequality in the determinant will not help us explain inequalities in child survival. In principle, at least, if the data are good enough, this approach allows us to partition the causes of health inequalities into, for example, those that can be influenced by the health system, and those that can't.

**Figure** 17 shows the results of a study that uses this methodology to unpack the causes of inequalities in stunting in Vietnam in 1993 and 1998. The inequality captures the inequality in height-for-age (cf. Table 1), and the negative concentration index indicates inequalities in each year with poor children having lower height-for-age scores. The child's height-for-age score is linked via regression analysis in each year to various child-level and household-level underlying determinants of health, along the lines of the child survival example above. Being unable to capture the separate effects of the numerous possible community-level influences, the authors treated these as unobservable "fixed effects," which were then later "recovered" from the statistical results. In each year, it is inequalities in these community influences that are the single most important source of inequalities in stunting. These presumably reflect the fact that poorer children live in areas that are poorly endowed with health facilities, have poor infrastructure, and so on. The important each of these community-level inequalities could not be ascertained with the data available. Another large

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