The Curse of Nonuniqueness

This post originally appeared on The Finance Buff.

This post reviews some academic literature relevant to a discussion about health reform referenced previously. The focus is Uwe Reinhardt’s paper “Can Efficiency in Health Care Be Left to the Market?” (2001, Journal of Health Politics, Policy and Law), for which I will use the shorthand “EHC” for “Efficiency in Health Care.” I highly recommend EHC to anyone wishing to understand welfare economics, even those without an economics background. It is quite accessible, more so than my own words below, selected in large part for space efficiency. (Duke University Press honored my request to provide a few months of unrestricted access to EHC.)

EHC is a review of certain themes in the seminal paper in health economics by Kenneth Arrow, “Uncertainty and the Welfare Economics of Medical Care” (1963, American Economic Review). In particular EHC’s focus is Arrow’s analysis of the application of foundational concepts of welfare economics to health care. Arrow himself made his argument so efficiently that, to quote Reinhardt, “nothing less than the academic analogue of talmudic scholarship” is required to extract its full value.

A central concept of neo-classical welfare analysis is that of Pareto efficiency, a “first do no harm” welfare criterion. A Pareto efficient distribution of a good (like health care) is one for which any change would make at least one individual worse off. Only a change that would make everyone better off is Pareto efficiency improving. A limitation of the criterion is nonuniqueness: every distribution for which there is no change that makes everybody better off is Pareto optimal, including those judged inequitable by other criteria. A redistribution of just one penny’s worth of care from a prince to a pauper does not increase Pareto efficiency, no matter how well off the prince or in desperate need the pauper.

The nonuniqueness of the Pareto criterion is often side-stepped through appeals to the first and second fundamental theorems of welfare economics. The first is that a perfectly competitive market achieves Pareto efficiency. The second is that any Pareto efficient distribution of resources (e.g. health care) can be achieved as a competitive equilibrium arising from a particular distribution of wealth. Thus, if the conditions of these theorems are met, any Pareto efficient distribution of health care resources could be brought about by a set of suitable initial endowments of wealth (e.g. achieved through the tax code). In Arrow’s words,

“by successive approximations a most preferred social state can be achieved, with resource allocation being handled by the market and public policy confined to the redistribution of money income.”

However, it is (or should be) uncontroversial that the market for health care is not perfectly competitive. Thus, it does not satisfy the conditions of the first and second fundamental theorems. In fact, this is one of the main themes of Arrow’s paper.

EHC’s critique is deeper, however. It is unlikely that any one initial distribution of wealth would achieve the desired distribution of health care and the desired distributions of all other goods and services. The maximization of utility by the recipient of wealth transfer may include the “right” amount of health care but also “undesirable” amounts of other goods (e.g. too much gin, not enough education). The first and second fundamental theorems are of no help at all in “optimizing” distributions over multiple goods simultaneously.

The public policy solution to such an undesirable outcome is distribution not of wealth but of in-kind benefits. In health care this has become commonplace: think Medicare and Medicaid. Is this sufficient justification for a public health plan available to all non-elderly Americans? EHC poses the question thus, “How are we to judge the merits of social health care policies?” Having seen that the nonuniqueness of the Pareto criterion makes it a particularly blunt tool, EHC turns to another pillar of welfare economics: Kaldor-Hicks efficiency.

Under the Kaldor-Hicks criterion, optimality is achieved when no voluntary exchange of compensation would motivate a change in distribution. If a unit of health care is more highly valued by the prince than the pauper Kaldor-Hicks efficiency justifies a shift of health services from the latter to the former. This is a direct appeal to individual utilities and therefore is subject to the same critique as levied against policy via wealth distribution: an “undesirable” distribution of a particular good may result. This is essentially the argument made in EHC. Other objections to the Kaldor-Hicks efficiency criterion are raised elsewhere.

My own sense is that it is asking far too much of welfare economics to point to a unique solution that optimizes a universally accepted criterion. Indeed, one ought to be suspicious of any claims of unique optimality. It is plausible that any such result is preordained by the form of the optimand, even if not explicitly stated. Extra-utility welfare analysis (also called extra-welfarism) can very likely recommend “optimal” policies distinct from “optimal” ones suggested by utility-based (welfarist) approaches.

But no approach has a unique claim to legitimacy. An unassailable argument does not exist for any one solution, whether public or private, to any problem, not even health care. Is this curse of nonuniqueness the death knell of welfare economics? Certainly not. The value of welfare economics in particular and economics in general is the clarity of thought it enforces. A welfare analysis of almost any type will lead the analyst to consider particulars and consequences that are opaque to casual thought. While it is relevant that health care is not a perfectly competitive market one misses the point of economics entirely to suggest that this renders it inaccessible to welfare analysis. Such a thought would be a grave mistake, especially since it appears as if private provision of health care and health insurance is here to stay.

The responsibility of the economist is to understand the assumptions and limitations of his tools. This is the great virtue of Reinhardt’s contribution. By expanding and clarifying Arrow’s words, in EHC he makes those facets of neo-classical welfare analysis plain, not just to the economist, but likely to any clear thinker motivated to read it.

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