Harold Hotelling
Harold Hotelling | |
---|---|
Hotelling's location model Working–Hotelling procedure | |
Awards | North Carolina Award 1972 |
Scientific career | |
Fields | Statistics Economics |
Institutions | Univ. of North Carolina 1946–1973 Columbia University 1931–1946 Stanford University 1927–31 |
Doctoral advisor | Oswald Veblen |
Doctoral students | Kenneth Arrow Seymour Geisser Ralph A. Bradley |
Harold Hotelling (/ˈhoʊtəlɪŋ/; September 29, 1895 – December 26, 1973) was an American mathematical statistician and an influential economic theorist, known for Hotelling's law, Hotelling's lemma, and Hotelling's rule in economics, as well as Hotelling's T-squared distribution in statistics.[1] He also developed and named the principal component analysis method widely used in finance, statistics and computer science.
He was associate professor of mathematics at Stanford University from 1927 until 1931, a member of the faculty of Columbia University from 1931 until 1946, and a professor of Mathematical Statistics at the University of North Carolina at Chapel Hill from 1946 until his death. A street in Chapel Hill bears his name. In 1972, he received the North Carolina Award for contributions to science.
Statistics
Hotelling is known to statisticians because of
At the beginning of his statistical career Hotelling came under the influence of
In the United States, Hotelling is known for his leadership of the statistics profession, in particular for his vision of a statistics department at a university, which convinced many universities to start statistics departments. Hotelling was known for his leadership of departments at Columbia University and the University of North Carolina.
Economics
Hotelling has a crucial place in the growth of mathematical economics; several areas of active research were influenced by his economics papers. While at the University of Washington, he was encouraged to switch from pure mathematics toward mathematical economics by the famous mathematician Eric Temple Bell. Later, at Columbia University (where during 1933-34 he taught Milton Friedman statistics) in the '40s, Hotelling in turn encouraged young Kenneth Arrow to switch from mathematics and statistics applied to actuarial studies towards more general applications of mathematics in general economic theory. Hotelling is the eponym of Hotelling's law, Hotelling's lemma, and Hotelling's rule in economics.
Hotelling was influenced by the writing of
Spatial economics
One of Hotelling's most important contributions to economics was his conception of "
Hotelling considers a situation in which there are two sellers at point A and B in a
Let q1 and q2 indicate the quantities sold by A and B. The sellers profit are:
By imposing profit maximization:
Hotelling obtains the economic equilibrium. Hotelling argues this equilibrium is stable even though the sellers may try to establish a price cartel.
Hotelling extrapolates from his findings about spatial economics and links it to not just physical distance, but also similarity in products. He describes how, for example, some factories might make shoes for the poor and others for the rich, but they end up alike. He also quips that, "Methodists and Presbyterian churches are too much alike; cider too homogenous."[3]
Market socialism and Georgism
As an extension of his research in spatial economics, Hotelling realized that it would be possible and socially optimal to finance investment in public goods through a
Non-convexities
Hotelling made pioneering studies of
Producers with increasing returns to scale: marginal cost pricing
In "
Consumers with non-convex preferences
When the consumer's preference set is non-convex, then (for some prices) the consumer's demand is not connected. A disconnected demand implies some discontinuous behavior by the consumer as discussed by Hotelling:
If indifference curves for purchases be thought of as possessing a wavy character, convex to the origin in some regions and concave in others, we are forced to the conclusion that it is only the portions convex to the origin that can be regarded as possessing any importance, since the others are essentially unobservable. They can be detected only by the discontinuities that may occur in demand with variation in price-ratios, leading to an abrupt jumping of a point of tangency across a chasm when the straight line is rotated. But, while such discontinuities may reveal the existence of chasms, they can never measure their depth. The concave portions of the indifference curves and their many-dimensional generalizations, if they exist, must forever remain in unmeasurable obscurity.[18][19]
Following Hotelling's pioneering research on non-convexities in economics, research in economics has recognized non-convexity in new areas of economics. In these areas, non-convexity is associated with market failures, where any equilibrium need not be efficient or where no equilibrium exists because supply and demand differ.[7][10][11][12][13][14] Non-convex sets arise also with environmental goods and other externalities,[12][13] and with market failures,[9] and public economics.[11][20] Non-convexities occur also with information economics,[21] and with stock markets[14] (and other incomplete markets).[22][23] Such applications continued to motivate economists to study non-convex sets.[7]
Works
- Hotelling, Harold (September 1925). "A general mathematical theory of depreciation". .
- Hotelling, Harold (September 1927). "Differential equations subject to error, and population estimates". .
- Hotelling, Harold (September 1927). "Statistical methods for research workers by R. A. Fisher".
- Hotelling, Harold; .
- Hotelling, Harold (March 1929). "Stability in competition". JSTOR 2224214.
- Hotelling, Harold (April 1931). "The economics of exhaustible resources". S2CID 222432341.
- Hotelling, Harold (1931). "The generalization of student's ratio". .
- Hotelling, Harold (October 1932). "Edgeworth's taxation paradox and the nature of demand and supply functions". S2CID 199140593.
- Hotelling, Harold (September 1933). "Analysis of a complex of statistical variables into principal components". .
- Hotelling, Harold (October 1933). "Note on Edgeworth's taxation phenomenon and Professor Garver's additional condition on demand functions". JSTOR 1907332.
- Hotelling, Harold (January 1935). "Demand functions with limited budgets". JSTOR 1907346.
- Hotelling, Harold (February 1935). "The most predictable criterion". doi:10.1037/h0058165.
- Hotelling, Harold (December 1936). "Relation between two sets of variates". .
- Hotelling, Harold; Pabst, Margaret R. (March 1936). "Rank correlation and tests of significance involving no assumption of normality". JSTOR 2957508.
- Hotelling, Harold (July 1938). "The general welfare in relation to problems of taxation and of railway and utility rates". JSTOR 1907054.
- Hotelling, Harold (December 1940). "The teaching of statistics". .
- Hotelling, Harold (1951). "A generalized T-Test and measure of multivariate dispersion". Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. 2. University of California Press: 23–41. Bibcode:1951bsms.conf...23H.
- Hotelling, Harold (March 1951). "The impact of R. A. Fisher on statistics". .
- Hotelling, Harold (1988). "Golden oldies: classic articles from the world of statistics and probability: 'the teaching of statistics'". .
- Hotelling, Harold (1988). "Golden oldies: classic articles from the world of statistics and probability: 'the place of statistics in the university'". .
Papers
- "Harold Hotelling papers, 1910-1975". Columbia University Libraries Archival Collections. Retrieved 5 December 2013.
See also
References
- ^ Dodge, Y. (2008). The concise encyclopedia of statistics, Springer
- ^ Turgeon, Lynn. Bastard Keynesianism : the evolution of economic thinking and policymaking since World War II. Westport, Conn: Praeger, 1997
- ^ JSTOR 2224214.
- ^ Palda, Filip (2013). The Apprentice Economist: Seven Steps to Mastery. Toronto. Cooper-Wolfling Press.
- ^ JSTOR 1907054.
- ^ Gaffney, Mason, and Fred Harrison. The corruption of economics. London: Shepheard-Walwyn in association with Centre for Incentive Taxation, 2006
- ^ ISBN 9780333786765.
- MR 0634800.
- ^ ISBN 978-0-262-19443-3.
- ^ a b c Salanié (2000, p. 36)
- ^ ISBN 978-0-262-12127-9.
- ^ MR 0449575.
- ^ ISBN 978-0-521-31112-0.
- ^ MR 0443878.)
- S2CID 6458099.
- JSTOR 1907054.
- ISBN 978-0-19-506553-4.
- ^ Hotelling (1935, p. 74):
Hotelling, Harold (January 1935). "Demand functions with limited budgets". Econometrica. 3 (1): 66–78. JSTOR 1907346.
- MR 0648778.
- ISBN 978-0-521-34801-0.
nonconvex OR nonconvexities.
- JSTOR 1909602.
- Drèze, Jacques H.(1974). "Investment under private ownership: Optimality, equilibrium and stability". In Drèze, J. H. (ed.). Allocation under Uncertainty: Equilibrium and Optimality. New York: Wiley. pp. 129–165.)
- ^ Page 371: Magill, Michael; Quinzii, Martine (1996). "6 Production in a finance economy". The Theory of incomplete markets (31 Partnerships ed.). Cambridge, Massachusetts: MIT Press. pp. 329–425.
- Arrow, Kenneth J. (1987). "Hotelling, Harold". The New Palgrave: A Dictionary of Economics. 2: 670–71.
- I. Olkina and A. R. Sampsonb (2001). "Hotelling, Harold (1895–1973)," International Encyclopedia of the Social & Behavioral Sciences, pp. 6921–6925. Abstract.
External links
- Harold Hotelling at the Mathematics Genealogy Project
- New School: Harold Hotelling
- American Statistical Association: Harold Hotelling Archived 2016-03-03 at the Wayback Machine
- Harold Hotelling
The following have photographs: