Use of econometric models to estimate expenditure shares

Policy makers and researchers are often interested in understanding the health and financial burden on society from diseases or risk factors. For example, research has focused on quantifying the contribution of obesity, smoking, and other preventable risk factors or diseases on mortality (Mokdad et al. 2004; Flegal et al. 2005). Other research has attempted to allocate disability-adjusted life years (DALYs) across medical conditions or quantify the relative contribution of a specific condition to overall medical expenditures (Murray and Lopez 1996; Finkelstein, Fiebelkorn, and Wang 2003, 2004; Finkelstein et al. 2005). All of these studies have one common feature; they are attempting allocate shares of a total “pie” to specific conditions. Econometric methods are increasingly being used to estimate these shares (Akobundu et al. 2006) and, because the underlying relationship between the condition of interest and burden (be it morbidity, mortality, or economic) is likely to be nonlinear, sophisticated modeling strategies are required. With respect to medical expenditures, an extensive literature has developed alternatives to ordinary least squares (OLS). These models assume the relationship between conditions and expenditures is not additive and accounts for the special properties of expenditure data (see Jones 2000, for a review; Manning, Basu, and Mullahy 2005; Cantoni and Ronchetti 2006). Models that are multiplicative in levels of expenditures are increasingly recommended and estimated. These models include OLS on log (positive) expenditures, nonlinear least squares (Mullahy 1998), and generalized linear models (GLM). This study is the first to identify the problem of double-counting, which is unique to commonly applied regression models of medical expenditures. When applied individually for a set of conditions, the separate condition-specific expenditure estimates, each expressed as a fraction of total expenditures, can add up to more than 100 percent and thus generally cannot be interpreted as shares. This adding up problem is not well understood and as a result, policy makers are often misinformed of the relative burden of select conditions. In this analysis, we show that the fractions can only be interpreted as shares if (1) the true underlying generating function is additively separable or (2) conditions are mutually exclusive (i.e., only one condition per person). The fractions can be interpreted as indicating how much lower medical expenditures would be in the absence of particular conditions, all else constant. However, the implication for estimating shares is that, when expenditures associated with the joint occurrence of conditions are greater than the sum of the condition-specific expenditures (e.g., if expenditure functions are multiplicative across conditions), expenditures calculated separately for each condition double-count the contributions to expenditures of the joint occurrences. We provide two potential solutions. The first constructs bounds for condition-specific expenditures. The second provides a point estimate by distributing predicted expenditures for jointly occurring conditions to constituent conditions. The normalization involved in this method avoids double counting. Although our focus is on medical expenditures, analogous issues arise with DALYs, mortality, absenteeism, or other measures of burden.