A Note on Income Effects and Health Care Cost Growth in Medicare

See Charts 1–14 and 10–16 in MedPAC (2011). Chart 1–14 reports an average benefit per enrollee for Parts A and B of Medicare of $9505, and average cost sharing associated with these program components of $1616. Chart 10–16 reports average monthly spending per Part D enrollee of $228, for a yearly total of $2736. Of Part D costs, $39 monthly or $468 annually, are borne by enrollee. Part D cost sharing plus cost sharing from Parts A and B totals $2084 annually. Premium costs were calculated based on the standard Medicare part B monthly premium of $96.40 (see CMS 2009) and the average monthly Part D premium of $30. (See p. 163 of MedPAC 2011.) Together, these add to yearly premiums of $1517. Premiums, benefits, and cost-sharing together amount to the $15, 374 cited in the text. Some of the cost sharing is paid by supplemental policies (sometimes subsidized by former employers) and by Medicaid, implying that the 13.5% cost-sharing number is if anything too high.

In McClellan and Skinner’s term, Medicare is largely a “pay-as-you-go” financing system. Tax payments by current beneficiaries “have never come close to financing their lifetime expenditures.” Much of the subsidy in Medicare is thus from current taxpayers to current beneficiaries.

Hall and Jones study a social planning problem, not market equilibrium. Their model is demand only – there is no change in technology, and no insurance or subsidies.

Individual-level cross-sectional studies such as the RAND Health Insurance Experiment tend to find elasticities substantially below 1.0 (Newhouse 1993), whereas studies of populations over time tend to find elasticities above 1.0 (Fogel 2009). One interpretation of these differences is that a longer time period allows technology to adjust to changing income. Additionally, some cross-sectional studies control for insurance generosity, which might be a route through which income affects demand for health care. Acemoglu et al. (2013) question the ability of these studies to derive a causal effect. They estimate income effects on demand to be around 0.7 using geographic variation in the incidence of an oil-price shock to identify income effects.

For a more recent discussion related to productivity measurement in service industries, see Bosworth and Triplett (2003).

The analysis here also applies to the case in which γ<1, but the discussion will proceed as if unit costs are increasing over time.

There is no technological change elsewhere in the economy. If there were, the interpretation of these parameters would be the “excess” technological change in health care compared to the other sector.

Income could be growing at a fixed rate. This would add a parameter but no additional insight.

The purpose of these substitutions is to work dq/dt into a manageable form. The normal or uncompensated demand elasticity will also be affected by shape of the marginal benefit of consumption schedule, v.

Recall that q is quantity and γ^t is cost per unit of quantity. Spending is quantity times cost per unit.

Equation (2) confirms this. When ε_q=0, dq/dt=0.

Equation (2) also confirms this in the absence of income effects.

Over long periods of time, and especially as health care as a share of income changes, it is unlikely that preference parameters like demand elasticity will remain constant.

In the dismal case in which rate of unit cost growth exceed rate of value-enhancing growth, rate of cost growth will be less than ln(γ). Indeed, if demand is sufficiently elastic, q will fall enough so that health care cost growth will be negative.

The values chosen were as follows: ε_x=–1, ε_q=–1, γ=1.01, λ=1.01893. No subsidies from taxpayers means in the model that σ=1. The value of rate of growth of benefits of health care (λ) was chosen to bring the rate of cost growth to the desired value of 1.5%.

See Polsky and Grande (2009) who calculate health care costs for taxpayers – their own and what they pay to support others – as a share of disposable income for representative working families.

Transfers need to be collected by distortionary taxes, so would impose an efficiency cost on these grounds.

The main problem in Medicare is the availability of supplemental insurance through private insurers to pay Medicare cost sharing. The “subsidy” for this product derives from the fact that the private insurer does not pay for (and therefore charge the beneficiary for) the extra costs imposed on Medicare from demand response to reduced cost sharing. This is a separate issue from the tax subsidy of Medicare premiums. Pauly (1986) called attention to subsidies to purchase of health insurance as a fundamental cause of market failure in health care.

This policy does not lead to efficient sorting of beneficiaries between Part C and traditional Medicare which would require the premium difference between the plans to differ for beneficiaries according to the expected difference in their health care costs. See Glazer and McGuire (2013) for an analysis of the role of premiums in sorting beneficiaries between traditional Medicare and Medicare Advantage.