Using the Shapley Decomposition to Disentangle the Impact of Circumstances and Efforts on Health Inequality.

Following previous work on inequality in health opportunity, this paper attempts to determine the contribution of circumstances, efforts and lifestyle, and demographic variables to the overall inequality in health in Luxembourg. Health is measured via the answers given to a question on self-assessed health and is considered as an ordinal variable. The educational level of each parent, the financial situation of the family during childhood, the area of birth of the individual, and of his/her parents, and the year of immigration are considered as circumstances. Effort and lifestyle variables are proxied by information on the educational level of the individual, whether he/she smoked and whether he/she had a physical activity on a regular basis. Sex and age are considered as demographic variables. To solve the issue of correlation between circumstances and effort and lifestyle the estimation is implemented in two stages. In the first stage, each effort and lifestyle variable is regressed in a separate equation against the vector of circumstances and demographic variables and, in a second stage, the individual health status is regressed against the vector of circumstances and demographic variables along with the estimated residuals of the effort equations described previously. The respective impacts of the three categories of explanatory variables (circumstances, effort and lifestyle and demographic variables) on health inequality are derived via a Shapley decomposition of the likelihood ratio of the health ordered logit regression. It appears that differences in circumstances and effort and lifestyle explain each around a quarter of this likelihood ratio.