Duke 2008 | ASHE | Equity and Efficiency in Health and Healthcare

Scholars working across scientific disciplines share a fairly common intuition about what they intend or interpret when they express or encounter the term 'interaction effect' ('IE') in scientific discourse. Yet it is not always obvious how such intuitions map into specific parameters or quantities of first-order scientific or policy concern. For instance, while textbooks in epidemiology and other disciplines provide rigorous characterizations of concepts like additive and multiplicative IEs, such characterizations are not necessarily informative regarding scientific questions at hand. Alternatively, while it is straightforward to point to a single parameter that multiplies a particular summand in a linear index function as an 'interaction parameter,' it is not obvious that this parameter on its own characterizes any quantity of fundamental scientific or policy interest (e.g. Ai and Norton, Economics Letters, 2003).

This paper synthesizes and expands on characterizations of IEs that have been utilized conceptually in fields ranging from econometrics to genetics, clinical sciences, and pharmacology. A key distinction is ultimately whether one is interested in 'difference-in-differences' ('D-I-D') type results involving what amount typically to cross-partial derivatives or differences, or instead interested in 'level-curve' ('isoquant', 'isobol') analysis that would be familiar to economists trained in production theory, e.g. The paper elucidates how these are conceptually distinct kinds of analyses -- the former focuses essentially on properties of marginal products, the latter on marginal rates of substitution -- that address different types of policy questions; indeed, in any given circumstance the directions of the IEs so described may or may not consistent in the two settings.

While the D-I-D-type results have been well studied in the economics literature, the level curve results have been less so. The paper derives various properties of these level-curve results in a familiar parametric context, and then proposes two classes of metrics that can be used (in conjunction with estimated parameters) to ascribe magnitudes to the interaction effects being estimated. The first, which can be deployed in any situation, is termed a 'Gini-type' metric because of its algebraic similarity to Gini coefficient formulae; the second, based on cost minimization criteria, is applicable when the interacting variables have associated with them meaningful unit prices. Although the main focus of the paper is on measurement moreso than inference, some suggestions for obtaining bootstrap confidence intervals for the estimated IE magnitudes are offered.

Finally, the methods described in the paper are used to study IEs using MEPS data on health outcomes and healthcare expenditures.