The Nobel Prize

William S. Vickrey (1914–96)


William Vickrey was born in Victoria, British Columbia, Canada in 1914. He studied mathematics at Yale University and graduated with a BS in 1935. Vickrey joined Columbia University as a graduate student and was awarded an MA in 1937 and a PhD in 1948. After completing his MA he had jobs with both the National Resources Planning Board and the US Treasury, and, as a conscientious objector during the Second World War,18 he spent some time working on the development of an inheritance tax for Puerto Rico. In 1946, Vickrey joined Columbia University as Lecturer in Economics. He became professor in 1958 and McVickar Professor of Political Economy in 1972, before retiring as McVickar Professor Emeritus in 1982 (Nobel Foundation, 2004). Vickrey died on 11 October 1996, just three days after the announcement of his Nobel Prize.

Vickrey was a highly active and practical economist. He consulted on a wide range of public services projects from the late 1930s onwards, working on such diverse topics as public utility pricing, the fare structure on New York’s subway system, Japan’s tax arrangements and development activities for the United Nations.

Vickrey’s offices and honours included election to the National Academy of Sciences and presidency of the American Economic Association, both in 1992. He was a fellow of the Econometric Society and a recipient of the F.E. Seidman Distinguished Award in Political Economy. In 1996, Vickrey was awarded the Nobel Memorial Prize in Economics jointly with James Mirrlees ‘for their fundamental contributions to the economic theory of incentives under asymmetric information’ (Nobel Foundation, 2004).

Vickrey’s Nobel citation makes specific reference to two areas of work: auction theory and optimal income taxation. In both areas, Vickrey understands economic behaviour as the product of incentives operating in the context of asymmetric information. We begin with auction theory. In an auction where ascending bids are openly announced, participants have an incentive not to reveal their private valuations of a sale item: surviving bidders would clearly prefer to just outbid their rivals in order to induce them to leave the auction. Vickrey suggested an alternative auction design – a second price sealed-bid auction – in which the winning participant pays a price equal to that offered by the second-highest bidder. In these circumstances ‘the optimal strategy for each bidder … will obviously be to make his bid equal to the full value of the article or contract to himself’ (Vickrey, 1961, reprinted in Vickrey 1994, p. 66). As underbidding increases the individual’s risk of missing a profitable outcome, the design of the auction encourages all participants to be truthful about their private valuations of the sale item (Laffont, 2003). Accordingly, the Vickrey auction, as it has become known, is both efficient – in the sense that resources are allocated to their most profitable uses – and incentive compatible (Drèze, 1997). Vickrey’s insights into auctions (the relevant papers are Vickrey, 1961; 1962) paved the way for other researchers to develop theorisations of the willingness of consumers to pay for the provision of public goods (Royal Swedish Academy of Sciences, 1997; Sandmo, 1999).

Vickrey (1945) also provided the original formulation of the optimum income tax problem that James Mirrlees would eventually solve some 26 years later. As noted in the entry for Mirrlees in this volume, the distorting effects of redistributive taxation are well known: for example, high marginal income tax rates may help governments promote equity but they are likely to reduce efficiency because of their adverse influence on the incentive to work. Vickrey conceptualised the problem as one of asymmetric information between principal and agent: in this instance, workers (agents) know their own productivity but the government (the principal) does not. How then can government design an optimum income tax policy when it is ignorant of the economic capabilities of those it wishes to tax and where policy will affect agents’ decisions about work? In other words, what is the optimum income tax balance between efficiency (promoted by reducing the distortion of incentives associated with income tax) and equity (promoted by the redistribution of the revenue raised by income tax)? Although Vickrey was not able to provide a solution to the problem he had posed, this work is widely regarded as path-breaking and far ahead of its time (Arrow, 1994; Atkinson, 1994; Drèze and Arnott, 1994; Laffont, 2003; Sandmo, 1999).

One of the most noted of Vickrey’s practical applications of economics concerns his pricing proposals for the New York subway (Vickrey, 1955) in which he investigated the possibilities of marginal cost pricing as a means to improve the subway’s efficiency. To Vickrey’s lasting regret, his recommendations were never implemented (Laffont, 2003). Vickrey included this study in an overview of what he called his ‘innovative failures in economics’ (see Vickrey, 1993a). Also included was something Vickrey regarded as his ‘proudest accomplishment’ (O’Flaherty, 1996): a proposal for the ‘cumulative averaging’ of taxation which has been called a ‘masterstroke of simplification and tax neutralization’ (Drèze, 1997, p. 181); the original reference here is Vickrey (1939). According to Atkinson (1994), Vickrey’s best-known work on tax is his doctoral thesis Agenda for Progressive Taxation (Vickrey, 1947), since revisited in his paper ‘Federal Tax Policy for the 1990’s’ (Vickrey, 1992). A collection of Vickrey’s papers that bears testament to the range, depth and practicality of his work is Vickrey (1994). This contains his highly stimulating Presidential Address to the American Economic Association – ‘Today’s Task for Economists’ (first published as Vickrey, 1993b). Two of the editors of his collected papers pay Vickrey the following remarkable tribute:

No other economist exemplifies to the same degree the ability of treating a relevant problem all the way from conceptual clarification, through the careful efficiency analysis, down to the development of a practically implementable solution. In that respect, William Vickrey stands in a class by himself. (Drèze and Arnott, 1994, pp. 5–6)

Main Published Works
(1939), ‘Averaging of Income for Income Tax Purposes’, Journal of Political Economy, 47, June, pp. 379–97.
(1945), ‘Measuring Marginal Utility by Reactions to Risk’, Econometrica, 13, October, pp. 319– 33.
(1947), Agenda for Progressive Taxation, New York: Ronald Press.
(1955), ‘A Proposal for Revising New York’s Subway Fare Structure’, Journal of the Operations Research Society of America, 3, February, pp. 38–69.
(1961), ‘Counterspeculation, Auctions and Competitive Sealed Tenders’, Journal of Finance, 16, March, pp. 8–37.
(1962), ‘Auctions and Bidding Games’, in Recent Advances in Game Theory, Princeton University Conference, Princeton, NJ: Princeton University Press, pp. 15–29.
(1992), ‘Federal Tax Policy for the 1990’s’, American Economic Association Papers and Proceedings, 82, May, pp. 257–62.
(1993a), ‘My Innovative Failures in Economics’, Atlantic Economic Journal, 21, March, pp. 1– 9.
(1993b), ‘Today’s Task for Economists’, American Economic Review, 83, March, pp. 1–10.
(1994), Public Economics (eds R. Arnott, K. Arrow, A.B. Atkinson and J.H. Drèze), Cambridge: Cambridge University Press.

Secondary Literature
Arrow, K. (1994), Introduction to ‘Part I, Social Choice and Allocation Mechanisms’, in W.S. Vickrey, Public Economics (eds R. Arnott, K. Arrow, A.B. Atkinson and J.H. Drèze), Cambridge: Cambridge University Press, pp. 13–14.
Atkinson, A. B. (1994), Introduction to ‘Part II, Taxation’, in W.S. Vickrey, Public Economics (eds R. Arnott, K. Arrow, A.B. Atkinson and J.H. Drèze), Cambridge: Cambridge University Press, pp. 101–14.
Drèze, J. (1997), ‘Research and Development in Public Economics: William Vickrey’s Inventive Quest of Efficiency’, Scandinavian Journal of Economics, 99 (2), pp. 179–98.
Drèze, J.H. and R. Arnott (1994), ‘William Vickrey’, in W.S. Vickrey, Public Economics (eds R. Arnott, K. Arrow, A.B. Atkinson and J.H. Drèze), Cambridge: Cambridge University Press, pp. 3–10.
Laffont, J.-J. (2003), ‘William Vickrey: A Pioneer in the Economics of Incentives’, in T. Persson (ed.) Nobel Lectures, Economics 1996–2000, Singapore: World Scientific Publishing.
O’Flaherty, B. (1996), ‘Obituary: Professor William Vickrey’, The Independent, 14 October.
Royal Swedish Academy of Sciences (1997), ‘The Nobel Memorial Prize in Economics 1996’, Scandinavian Journal of Economics, 99 (2), pp. 173–7.
Sandmo, A. (1999), ‘Asymmetric Information and Public Economics: The Mirrlees–Vickrey Nobel Prize’, Journal of Economic Perspectives, 13, Winter, pp. 165–80.
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