Affordability is a vague concept. Bundorf and Pauly [Bundorf, M.K., Pauly, M.V., 2006. Is health insurance affordable for the uninsured? Journal of Health Economics 25 (4), 650–673] address this problem by establishing clear working definitions of affordability, and they use these definitions to estimate the percent of the uninsured who can afford insurance. When they establish their definitions of affordability, they use a microeconomic model that omits essential characteristics of the health insurance market. This comment suggests alternative definitions that better incorporate the structure of the health insurance market, discusses both endogeneity and specification problems that might occur when implementing their econometric model to estimate the fraction of “uninsured afforders,” and then recommends ways to reduce omitted variable bias and endogeneity bias.
It is conventional wisdom that the 47 million uninsured Americans cannot afford health insurance. However, when pundits use the word “afford”, there is no clear definition of affordability; it is at best a subjective notion. Bundorf and Pauly (2006) (here in after referred to as BP) help correct this by establishing alternative definitions of affordability, and then by estimating the fraction of the uninsured who can afford coverage. They “find that, depending on the definition, health insurance was affordable to between one-quarter and three-quarters of the uninsured.” This range seems quite large and indeed violates conventional wisdom.
Their study provides us with a good start and a rational way to specify affordability. Yet, defining affordability is a complex and controversial issue, and hopefully, their work will not be the “last word,” but instead, will inspire further research in this area.
Health insurance is complex, and tractable analysis requires simplification. However, BP make simplifications that omit essential elements of the health insurance market. They use a simple micromodel with divisible goods and no market failures. Under their model, consumer decisions should be Pareto optimal. Yet, they advocate compulsory insurance. But this would induce welfare losses since their model has a Pareto optimal equilibrium. BP do not account for unobservable heterogeneous characteristics and insurance prices that affect both insurance choice and utility levels. Since affordability depends on exceeding a certain utility, we cannot determine with certainty if one can afford health insurance. At best, we can integrate out the “unobservables” and then estimate a probability that one can afford health insurance.
BP’s empirical model that estimates the incidence of uninsured afforders suffers from endogeneity bias, omitted variables and identification problems. In this discussion, I account for unobserved heterogeneity in consumer characteristics, health plan quality, and health plan prices that lead to endogenous regressors of an insurance choice model. I treat health insurance as a discrete choice where unobserved heterogeneity can induce market failure. Although BP acknowledge that their insurance choice equation might suffer from omitted variable bias, their specification and endogeneity problems could lead to the counter intuitive result that those with poor health status have lower propensity to purchase insurance.
Section 1 discusses the key characteristics that are missing in BP’s alternative definitions of affordabilty. In this section, I present a simple discrete choice model of health insurance choice that replaces their model of two divisible, normal and homogeneous goods. Section 2 uses the theoretical model established in Section 1 to reframe their definitions of affordability. Section 3 reviews their econometric methods that estimate the percent of the uninsured who can afford insurance. Finally, Section 4 discusses how the definitions and estimations of affordability can be used to set policy that can increase insurance participation and social welfare at the same time.
1. Respecifying the model for insurance affordability
BP define two basic notions of affordability, normative and behavioral. In their normative definition, there is a “special good” (health insurance in their study) denoted as xhxh with price phph and a numeraire composite good denoted G . For the normative definition there are “socially defined minimum quantities of the special good” denoted as View the MathML sourcex¯h and the composite good denoted as View the MathML sourceG¯. The special good is “normatively” affordable for income y if
