Arrow and the Foundations of the Theory of Economic Policy

The man and the scholar are indistinguishable, to a degree. For those of us who are fascinated not only by Arrow’s fundamental contributions, but also by his personality (his mind, spirit, humanity, conscience, and enthusiasm), this chapter hardly needs justification. Great scholars are not always admirable individuals. This is not true of Arrow. To the extent that I succeeded (as always, with the exemplary and devoted assistance of my ‘permanent partner in crime’, Ida) in capturing, however imperfectly, his qualities, I hope that this portrait will stimulate the younger scholar to emulate Arrow’s example. But Arrow is human and this is not a hagiography. The task of painting Arrow’s intellectual portrait was formidable, but my defective vision was not only tempered by good advice from friendly critics, but it is also modified by the images of Arrow that can be found throughout both volumes and particularly by those so vividly sketched in the chapters in Part V of this volume.

Lindbeck (1985), in his discussion of the Nobel Prize in Economics, gives social choice theory barely half a sentence, though Arrow himself is otherwise treated quite fairly. So there is a view that the theory of social choice may not be Arrow’s greatest contribution to economic and social science. Yet it seems quite clearly to be his most distinctive and original contribution. One can argue indefinitely and fruitlessly over whether Gerard Debreu, Lionel McKenzie, Leonid Hurwicz and others would eventually have filled in the gaps left if Arrow had remained a meteorologist and never worked in general equilibrium theory. They might have filled the gaps, even though they would have been huge. One can also argue whether other aspects of Arrow’s work, in risk, uncertainty, information, etc. can be seen as pushing economic science much more rapidly in the right direction, but a direction it was moving toward anyway. Other workers in these fields have benefited enormously from the vast strides made by Arrow’s work, but they would probably have done similar things, perhaps considerably more slowly, even in his absence.

Kenneth Arrow has made a remarkable variety of splendid discoveries and has provided illuminating treatments of an impressive array of topics. The one part of his work to date that most strikes a moral philosopher is his critique of utilitarianism. The critique brought to moral theory the full force of the ‘ordinalist revolution’ in economics. Classical utilitarians assessed policies by their contribution to the general happiness — to the sum of the degree of happiness of everyone involved. In this century, economics was reformulated in ways that left no room for talk of degrees of happiness. Talk of economic agents’ ‘utility’ was reinterpreted as talk of preference orderings. Arrow followed Pareto and Bergson in bringing this change to welfare economics, beginning with his famous Impossibility Theorem. Very little of utilitarianism, the theorem showed, could survive a searching ordinalistic critique.

In the first of his 1985 Tanner Lectures at Harvard, Kenneth Arrow suggested that the doctrine of extended sympathy might, so to speak, come to the rescue of economists and philosophers left bereft by the Impossibility Theorem (according to which no social-choice function exists that satisfies a set of reasonable axioms of consistency, transitivity, independence or irrelevant alternatives, and …). Specifically, he made reference to the pre-Rawls suggestions of William Vickrey (1945) and of John C. Harsanyi (1955) as providing related derivations of additive interpersonal utilities by reliance on certain elements of extended sympathy.

The last paragraph of Kenneth Arrow’s Nobel Lecture is characteristic of the man:

The philosophical and distributive implications of the paradox of social choice are still not clear. Certainly there is no simple way out. I hope that others will take this paradox as a challenge rather than as a discouraging barrier (Arrow 1973a; 1974).

One of the most controversial and widely misunderstood components of Kenneth Arrow’s pathbreaking work on social choice (1951; 1963) is the condition of independence of irrelevant alternatives (IIA). It is thus not out of place on the occasion of Arrow’s 65th birthday to re-examine that condition and some related issues.

In many decision situations that individuals face it seems reasonable from either a philosophical or a personal psychological standpoint to concentrate on maximizing subsequent freedom of choice rather than current expected utility. It may be argued against this view that a sufficiently rich decision framework will take account of the utility of such second-order effects as future freedom of decision, properly discounted, of course. But I am deeply sceptical of such all-encompassing utility functions. Most of the time if we maximize in any evident way at all it is in some local and fragmentary fashion. John Stuart Mill’s classic but weak defence of liberty of thought, feeling and public opinion in utilitarian terms is another reason for scepticism about an unrestricted application of the maxim to maximize expected utility. Above all, what empirical studies of individual decision-making we have do not support any grand thesis about maximizing behaviour. The studies too are about local and fragmentary decisions: buying certain goods, betting on horses, buying lottery tickets, choosing a medical treatment, etc.

According to Kenneth Arrow, ‘the problem of social choice is the aggregation of the multiplicity of individual preference scales about alternative social actions’ (Arrow 1967, p. 12). Numerous problems, different from each other in many important respects, fit into this general characterization. The voluminous literature on the preference aggregation problems has extensively utilized the uniform and abstract framework of the axiomatic social choice theory (basically due to Arrow’s (1951) seminal work) for analysing these essentially different problems.

Already from the beginning in the eighteenth and early nineteenth centuries, economists unhesitatingly saw themselves as political economists. They firmly believed it was part of their duty to draw policy conclusions. And they held that they were entitled to do this on rational grounds—i.e., as logical inferences from their knowledge about the facts.

In this chapter, I propose to revisit the concept and the analysis of the optimum social order, a subject with which numerous authors have dealt, and to which I devoted twelve papers between 1958 and 1981.1 I feel I owe the reader some explanation why this thirteenth paper was written.

It is easy to contribute a chapter to a volume honouring Kenneth Arrow: there is hardly an area of concern to modern economic theory where he has not had fundamental insights. This chapter picks up on two themes on which he made early and important contributions.

Kenneth Arrow had a major hand in establishing two of the fundamental results of general equilibrium theory: the existence of a competitive equilibrium (Arrow and Debreu 1954) and the decentrali-zability of a Pareto optimum (Arrow 1951). In this chapter, we are concerned with general equilibrium in a setting where some goods are indivisible. Hence, several hypotheses that are standard in equilibrium analysis are not satisfied. None the less, as we will see, the classic Arrow-Debreu techniques can be suitably modified to overcome this difficulty.

The treatment of needs in assessing economic equity is a subject that arouses strong feelings. Very different approaches have been adopted in the study of this subject. There are those who regard differences in needs as sufficient grounds for rejecting any analysis of income inequality. For them to try to compare one distribution of income, Y₁,…, Y _h with another, Y₁*,…, Y _h *, is without meaning, since the people concerned may have quite different needs. ‘Welfare’ depends not just on income but also on other dimensions. Precisely what other dimensions we should take into account is open to debate, but most people would agree on certain factors such as health, handicap, age or family size. Arrow gives the example of ‘the haemophiliac who needs about $4,000 worth per annum of coagulant therapy to arrive at a state of security from bleeding at all comparable to that of the normal person’, an example he contrasts with the ‘facetious’ one of a person who is ‘desperate without pre-phylloxera clarets and plovers’ eggs’ (1973, p. 254).

In making international comparisons among countries, or in assessing the progress of a country over time, it is customary in applied research to act as though the relevant information could be summarized by a ‘sufficient statistic’, namely the country’s income distribution. From this one obtains the mean (per capita) income and the curve of concentration, or ‘Lorenz curve’, making possible comparisons of different economies with the same per capita income.1

The classical peak-load pricing model is extended here in two ways: first, we incorporate a crucial attribute of most peak—off-peak issues in reality—the fact that the associated congestion causes disutility, through delays, crowding, etc. Second, we investigate formally the equity of the peak-pricing solution,1 comparing it with uniformity of pricing in all periods — an issue that has disturbed observers outside our profession, but that economists have often ignored. We offer a number of surprising conclusions: 1There are several cases, at least one of them apparently common and significant, where, paradoxically, the optimal price in the more congested of two periods is lower than that in the less congested period.2Even in the classical model, where required expansion of capacity is the only social cost of high-pcak demand, the optimal-peak price may be lower than the uniform price that just permits total cost to be covered. This will be true when there are sufficient diseconomies of scale in capacity construction, or when the required capacity is so expensive relative to the maximum amount peak users are willing to pay that its cost cannot be covered without a contribution by off-peak users, or where the Ramsey adjustment in prices required by the absence of constant returns is sufficiently favourable to peak users.3Where conclusion 2 holds, adoption of peak-off-peak prices may be a Pareto improvement over uniform pricing, but it need not be so since the price to off-peak users may actually be raised in the process.4In the model with disutility of congestion there seems to be a wider range of cases where the adoption of optimal-peak prices is a Pareto improvement. Nevertheless, this is by no means a foregone conclusion.

An attempt to deal with individual welfare functions seems appropriate in this volume. As early as 1951, Arrow summarized some other scholars’ views on individual welfare functions (Arrow 1951, p. 5). In contrast with Arrow’s pathbreaking theoretical work, this chapter will deal with some attempts to empirically specify individual welfare functions. These attempts are close to Levy and Guttman (1975) (which mentions Guttman’s previous work (1971)), and to van Praag (1971), which was followed by an impressive quantity of further empirical work by himself and his pupils.

Arrow (1981, p. 140) quite rightly argues:

The view that only real magnitudes matter can be defended only if it is assumed that the labor market (and all other markets) always clear — that is, that all unemployment is essentially voluntary … The view that only real magnitudes matter, even over the short periods of the business cycle, can only be defended on this extreme view of smoothly working labor markets. If the contrary view is held, that actual unemployment is to a considerable extent involuntary, then monetary magnitudes retain some of their traditional importance for the analysis of and policy toward short-term economic fluctuations.

The life-cycle theory of savings was developed in the mid-1950s by Modigliani and Brumberg (1954) and until recently provided the conceptual foundations of almost all modern work on the consumption and saving pattern of the family. Although this theory has been extremely useful in macroeconomic modelling and empirical implementations based on time series, in recent years a large and growing number of writers have raised serious questions with regard to this hypothesis. In this chapter we shall contribute to this discussion of the scientific viability of the life-cycle hypothesis. Since the issue of bequests is critical to our view, we wish to address it first. The ‘life-cycle theory’ is a statement of how an economic unit, like a family, allocates its resources intertemporally between consumption and capital accumulation during the life-cycle. However, in our view what distinguishes this theory is the idea that each family is not viewed as part of an infinite chain of families, each with ties to the past and obligations to the future, but rather that it is viewed as a single (and selfish) decision maker, without inheritances from past generations and bequests to future generations. Within this conceptual frame-work, each family selects a consumption and accumulation plan based on the present value of the anticipated flow of its own lifetime incomes.

The more that is issued of a mixed currency, the more will be wanted. The supply does not satisfy the demand: it excites it. Like an unnatural stimulus taken into the human system, it creates an increasing desire for more; and the more it is gratified, the more insatiable are its cravings.

Among distinguished economic theorists, Kenneth Arrow stands out, not just for his superb combination of analytical skill and economic intuition, but also for his wide philosophical interest in the social and psychological background to economic activity. More than most economists, he displays an awareness of (and sensitivity to) the limitations of the economic approach to society and a willingness to build bridges to cognate disciplines. My original thought in embarking on this chapter was to attempt to reconstruct Arrow’s views on such broader issues from his writings, but this proved too difficult and elusive a task. Stimulating comments upon (and insights into) such questions are to be found scattered through his work, but they tend to remain undeveloped — scattered pearls of wisdom not easily roped together.

Kenneth Arrow’s impeccable credentials as an economic theorist are celebrated in the 1972 Nobel Prize in Economics. Research in general equilibrium and social choice was massively reshaped by his original contributions. It is also well recognized that Arrow is much more than a virtuoso mathematical economist. His contributions to welfare economics include both theoretical and applied aspects. His studies of market and non-market organization include applications as well as pure theory. His interests in studying economic organization in a ‘rational spirit’1 have helped to demonstrate the unity between market and non-market modes.2 What is less widely remarked is that Arrow’s contributions to the study of complex economic organization have been very influential in helping to shape the New Institutional Economics (NIE).

Kenneth Arrow’s

The Limits of Organization

(1974, p. 23) contains the following statement about trust (my italics):

Consider what is thought of as a higher or more elusive value than pollution or roads: trust among people. Now trust has a very important pragmatic value, if nothing else. Trust is an important lubricant of a social system:

It is extremely efficient

;it saves a lot of trouble to have a fair degree of reliance on other people’s word. Unfortunately this is not a commodity which can be bought very easily.

If you have to buy it, you already have some doubts about what you’ve bought

. Trust and similar values, loyalty or truth-telling, are examples of what the economist would call ‘externalities’. They are goods, they are commodities; they have real, practical, economic value; they increase the efficiency of the system, enable you to produce more goods or more of whatever values you hold in high esteem.

But they are not commodities for which trade on the open market is technically possible or even meaningful.

I would like to think back to the three-year period bracketing the mid-point of this century from 1949 to 1951.1 was then a graduate student in mathematics at the University of Michigan. Not only did I learn about Arrow’s work at that time but it profoundly affected how I looked upon my newly adopted world of mathematics as applied to the behavioural sciences. Whenever I became confused about which side of a philosophical debate I should take, and there were plenty of such occasions, I would start thrashing about a bit at first but at some point in my frustrating deliberations I would say to myself, ‘Enough of this, it’s about time go get serious. Let me do some Arrow-type analysis’. By that I meant: keep an open mind; stop espousing positions; explore underlying basic principles of desirable behaviour; articulate those desidarata as axioms and investigate their consistency; and, if consistent, characterize the family of compatible solutions. This axiomatic type of thinking may be old hat to mathematicians but to me, 35 years ago, when applied to social phenomena and to the theory of choice behaviour, it was radically new and exciting.

Kenneth Arrow’s paper ‘Uncertainty and the Welfare Economics of Medical Care’ (1963) is the premier theoretical treatment of health economics. Although written a quarter century ago, it is unsurpassed in clarity of analysis, breadth of coverage, and incisive exposure of the core problems. Arrow’s keen perception is revealed in the title of the paper: uncertainty with respect to health status and with respect to the consequence of care is the key to understanding the economics of health from both positive and normative perspectives. As Arrow says, ‘recovery from disease is as unpredictable as its incidence’.

Kenneth J. Arrow has made contributions in so many different branches of economic analysis that it is worthwhile identifying which of his many contributions has had the greatest impact.1 The purpose of this chapter is to determine the relative impact of Arrow’s various contributions through a tabulation of his most frequently cited works using the Social Science Citation Index.2 A simple tabulation of frequently cited works reveals, through the choices made by economists with regard to citations, which works have had the greatest impact. The number of citations provides a crude measure of the degree of their impact.3

Arrow is imbued with the vision of a complex and interdependent world; where everything depends on everything else, where disparate phenomena and ideas interact, and where the indirect links are sometimes as important (or even more important) than the direct ones. One should suspect simplistic, monistic, exclusively endogenous economic explanations, partial analysis, or what not. Similarly one should suspect short statements for, as Marshall so wisely noted, every short statement in economics is wrong except this one. The same holds if one tries to explain the personality and motivations of a complex intellectual such as Arrow, subject to many human frailties and self-generated and external tensions and conflicts. The problem is magnified if one aims beyond explanation to prediction; many who work with him are often driven to exclaim that it is quite beyond them to predict what Arrow is going to do next. Talk about uncertainty!

That my work has helped to motivate such a considerable number of excellent studies, queries, and even criticisms is a source of considerable satisfaction. A full set of comments would occupy more space than would be appropriate to the occasion. I will confine myself to scattered thoughts stimulated by reading the chapters that deal with impersonal scholarly issues. The reader of the chapters that deal with me more personally should I think be spared the refraction imposed by any comments I might make. I follow the grouping of chapters in the book.