A unified structural equation modeling approach for the decomposition of rank-dependent indicators of socioeconomic inequality of health

In this paper we present a unified framework for the regression-based decomposition of rank-dependent indicators of socioeconomic inequality of health, of which the Concentration Index is the best known example. Such indicators of socioeconomic inequality of health are bivariate in nature because they measure the degree of correlation between health and socioeconomic status. Erreygers and Kessels (2013) have proposed a set of two-dimensional decompositions that investigate both variables simultaneously. The most salient of these decompositions is the simultaneous super-decomposition based on the bivariate multiple regression model explaining health and socioeconomic status simultaneously. This decomposition captures not only the direct contributions of the explanatory variables in the regressions, but also their combined contributions. However, the two-dimensional decomposition analysis suffers from the drawback that socioeconomic status is not included as an explanatory variable in the regression of health, and health as an explanatory variable in the regression of socioeconomic status. This was primarily done to compare the two-dimensional simultaneous super-decomposition to the one-dimensional decompositions that are based on regressions of only one of the two variables under consideration. For these one-dimensional decompositions, including either of the variables as an explanatory variable in the single regressions distorts the explanation of the correlation between health and socioeconomic status. Therefore, for the two-dimensional super-decomposition, the bivariate multiple regression modeling framework was chosen which includes neither health nor socioeconomic status as an explanatory variable. Nevertheless, several empirical studies have shown that one of the most important determinants of health is socioeconomic status. Another limitation of the bivariate multiple regression model is that the same set of variables was used to explain both health and socioeconomic status, which may not be the most appropriate assumption given that the determinants of health and socioeconomic status need not be the same. To bridge the gap between empirical observations and modeling practice, we provide a flexible modeling approach for the decomposition of socioeconomic inequality of health that makes use of a structural or simultaneous equation model (SEM) that incorporates socioeconomic status as an explanatory variable in the regression of health and health as an explanatory variable in the regression of socioeconomic status. Reference note: ERREYGERS, Guido and Roselinde KESSELS (2013), Regression-based decompositions of rank-dependent indicators of socioeconomic inequality of health, In: Rosa Dias, P., O'Donnell, O. (Eds.), Health and Inequality (Research on Economic Inequality, Volume 21), Emerald Group Publishing Limited, Chapter 9: pp. 227-259. We use a structural or simultaneous equation model (SEM) to determine the factors that explain socioeconomic inequality of health, which is bivariate in nature. We consider a set of two equations in which health and socioeconomic status are assumed endogenous or jointly determined by the system of simultaneous equations. The remainder of the variables in the SEM are exogenous and constitute two different sets in the two equations, which is also needed to consistently estimate all parameters of the SEM. We use two-stage least squares (2SLS) to estimate the SEM which is the most common estimation procedure for this purpose. The SEM approach is much more flexible than the bivariate multiple regression model used in Erreygers and Kessels (2013) because of the simultaneous feedback mechanism between health and socioeconomic status and the two different sets of possible determinants of health and socioeconomic status. As a result, the SEM approach provides an improved solution to the regression-based decomposition of socioeconomic inequality of health. We base our results on data from the Ethiopia 2011 Demographic and Health Survey (DHS) involving children under the age of five. The health variable we have chosen is actually an ill-health variable: the degree of stunting or malnutrition, which provides information on the depth of malnutrition with children. The 2SLS estimates of the structural equation system confirm that health is largely influenced by socioeconomic status, while the opposite relationship is only marginally true. We reformulated the 2SLS estimates into parameter estimates of the reduced form of the SEM, which we then used in the two-dimensional simultaneous super-decomposition developed by Erreygers and Kessels (2013). In accordance with the decomposition analysis, the results can be divided into two phases. First, we show that the reduced-form parameter estimates are much more accurate than the ordinary least squares estimates from the bivariate multiple regression model used in Erreygers and Kessels (2013). Second, the use of the reduced-form parameter estimates results in a more precise super-decomposition of socioeconomic inequality of health. Because the two-dimensional super-decomposition allows the construction of one-dimensional decompositions, similar improvements are also observed for the one-dimensional decompositions. To conclude, the SEM approach provides a unified framework for obtaining reliable decomposition results for indicators of socioeconomic inequality of health that are bivariate in nature. It is a very flexible approach because it takes into account all possible relationships between variables.