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| |name = Herman Wold
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| |field = [[Statistics]] <br /> [[Econometrics]]
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| |birth_date = {{birth date|1908|12|25}}
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| |birth_place = [[Skien]], [[Norway]]
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| |death_date = {{death date and age|1992|02|16|1908|12|25}}
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| |nationality = [[Sweden|Swedish]]
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| |workplaces = [[Uppsala University]]
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| |alma_mater = [[University of Stockholm]]
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| |doctoral_advisor = [[Harald Cramér]]
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| |doctoral_students = [[Sten Malmquist]] <br /> [[Peter Whittle]]<br />[[Karl Jöreskog]]
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| |known_for = [[Wold's theorem]] <br /> [[Moving average|MA(<math>\infty</math>)]] [[Wold's theorem|representation]] of [[stationary stochastic process]]es <br /> [[Wold decomposition]] (Operator theory) <br />[[Cramér–Wold theorem]] <br /> [[Time series analysis]] <br /> [[Utility theory]] <br /> [[Consumer demand]] <br /> [[Latent variable]] <br /> [[Structural equation model]]s <br /> [[Consistent estimator|Consistent]] [[least squares]] [[estimator|estimation]] of [[Recursion|recursive]] [[Directed acyclic graph|triangular systems]] <br /> [[Causality|Causal inference]] in [[observational study|observational studies]] <br /> [[Partial least squares regression]]
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| }}
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| '''Herman Ole Andreas Wold''' (December 25, 1908 – February 16, 1992) was a [[Norwegian people|Norwegian]]-born [[econometrics|econometrician]] and [[statistician]] who had a long career in [[Sweden]]. Wold was known for his work in [[mathematical economics]], in [[time series]] analysis, and in [[econometric]] statistics.
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| In [[mathematical statistics]], Wold contributed the [[Cramér–Wold theorem]] characterizing the [[normal distribution]] and developed the [[Wold decomposition]] in [[time series analysis]]. In [[microeconomics]], Wold advanced [[utility theory]] and the theory of [[consumer demand]]. In [[multivariate statistics]], Wold contributed the methods of [[partial least squares regression|partial least squares ('''PLS''')]] and [[graphical model]]s. Wold's work on [[causality|causal]] [[statistical inference|inference]] from [[observational studies]] was decades ahead of its time, according to [[Judea Pearl]].<ref>''Causality'', 2nd ed.</ref>
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| ==Scientific Achievements== | |
| Herman Wold had a long and productive career, spanning six decades.
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| ===Studying with Harald Cramér=== | |
| {{Main|Cramér–Wold theorem}}
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| In 1927 Wold enrolled at the [[University of Stockholm]] to study [[mathematics]]. It was an opportune time, for [[Harald Cramér]] had been appointed Professor of Actuarial Mathematics and Mathematical Statistics. Wold would later write, "To belong to Cramér's first group of students was good luck, an advantage that simply cannot be exaggerated."
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| After graduating in 1930 Wold worked for an insurance company; he also did work on mortality data with Cramér and later designed a tariff for the insurance companies. He started work on a PhD on stochastic processes with Cramér as supervisor. Away from the thesis Wold and Cramér did some joint work, their best known result being the [[Cramér–Wold theorem]] (1936).
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| ===Time series and the Wold decomposition===
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| {{Main|Wold decomposition}}
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| {{See also|Wold's theorem|Stationary process}}
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| Wold's thesis, ''A Study in the analysis of stationary time series,'' was an important contribution. The main result was the "[[Wold decomposition]]" by which a [[stationary process|stationary series]] is expressed as a sum of a deterministic component and a stochastic component which can itself be expressed as an infinite [[moving average]]. Beyond this, the work brought together for the first time the work on individual processes by English statisticians, principally [[Udny Yule]], and the theory of stationary stochastic processes created by Russian mathematicians, principally [[Aleksandr Yakovlevich Khinchin|A. Y. Khinchin]]. Wold's results on univariate time series were generalized to multivariate time series by his student [[Peter Whittle]].
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| The [[Wold decomposition]] and the related [[Wold's theorem]] inspired [[Arne Beurling|Beurling]]'s [[Hardy space#Factorization|factorization theorem]] in [[Harmonic analysis#Abstract harmonic analysis|harmonic analysis]] and related work on [[invariant subspace]]s of [[linear operator]]s.<!-- Helson's lectures on invariant subspaces --> | |
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| ===Theory of consumer demand===
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| {{See also|Convex preferences}}
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| In 1938 a government committee appointed Wold to do an econometric study of consumer demand in Sweden. The results were published in 1940. In parallel, he worked on the [[supply and demand|theory of demand]]. His book ''Demand Analysis'' (1952) brought together his work on the theory of demand, the theory of stochastic processes, the [[regression analysis|theory of regression]] and his work on Swedish data.<ref>
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| * {{cite article|<!-- last=Wold|first=Herman|authorlink=Herman Wold -->|year=1943a|title=A synthesis of pure demand analysis '''I''' (Dedicated to Professor Harald Cramér on the occasion of his 50th birthday September 25th 1943)|journal=Skandinavisk Aktuarietidskrift [Scandinavian Actuarial Journal]|volume=26|pages=85–118<!-- Examining Wold's article, K.W. -->|mr=9296}}
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| * {{cite article|<!-- last=Wold|first=Herman -->|<!-- authorlink=Herman Wold -->|year=1943b|title=A synthesis of pure demand analysis '''II'''|journal=Skandinavisk Aktuarietidskrift [Scandinavian Actuarial Journal]|volume=26|pages=220–263<!-- Diewert gives wrong pages, according to Math Rev and my inspection of the article and of Wold's book with Jureen -->|mr=11939|ref=harv}}
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| * {{cite article|<!-- last=Wold|first=Herman|authorlink=Herman Wold|-->|journal=Skandinavisk Aktuarietidskrift [Scandinavian Actuarial Journal]|year=1944|title=A synthesis of pure demand analysis '''III'''|volume=27|pages=69–120|mr=11940}})
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| * {{cite book|last1=Wold|first1=Herman|<!-- authorlink=Herman Wold -->|last2=Juréen|first2=Lars (in association with Wold)|title=Demand analysis: A study in econometrics|location=New York|publisher=John Wiley and Sons, Inc. Stockholm: Almqvist and Wiksell|series=Wiley publications in statistics|year=1953|pages=xvi+358|mr=64385|ref=harv}}</ref>
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| ===Systems of simultaneous equations and causal inference===
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| {{See also|Simultaneous equation models|Least squares|Maximum likelihood|Graphical models|Causality}}
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| In 1943-4, [[Trygve Haavelmo]] put forward his ideas on the [[Simultaneous equation methods (econometrics)|simultaneous equations]] model, arguing that [[simultaneous equation methods (econometrics)|systems of simultaneous equations]] should be central in econometric research. Wold noted some limitation of the maximum-likelihood approach favoured by Haavelmo and the [[Cowles Commission for Research in Economics|Cowles Commission]]; Wold cautioned that the literature contained some exaggerated claims for the superiority of maximum-likelihood estimation.
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| In the years 1945-65, Wold proposed and elaborated on his "recursive causal chain" model, which was more appropriate for many applications, according to Wold: For such "recursive causal chain" models, the [[least squares]] method was computationally efficient and enjoyed superior [[estimation theory|theoretical]] properties, which it lacked for general time-series models. Wold's writings on causality and recursive-chain models have been recognized as scientific inventions by recent work on [[causality]] and [[graphical models]] in statistics, especially by [[Judea Pearl]] and Nanny Wermuth.
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| ===Multivariate analysis and partial least squares===
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| {{Main|Partial least squares}}
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| {{See also|Multivariate analysis}}
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| At the end of his career, Wold turned away from econometric modelling and developed multivariate techniques for what he called "soft" modelling. Some of these methods were developed through interactions with his student [[Karl Jöreskog|K. G. Jöreskog]], although the latter's focus was primarily on maximum likelihood methods.
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| ==Appointments==
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| The story of Wold's academic appointments is briefly told. In 1942 he became professor of statistics at [[Uppsala University]] and he stayed there until 1970. He then moved to [[Gothenburg]], retiring from there in 1975.
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| In 1960 Wold became a member of the [[Royal Swedish Academy of Sciences]]. He was a member of the Prize Committee for the [[Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel]] from 1968 to 1980.
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| ==Early life==
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| Herman Wold was born in [[Skien]], Southern [[Norway]] the youngest in a family of six brothers and sisters. In 1912 the family moved to [[Sweden]] and became Swedish citizens. Herman's father had a small fur and hide business.
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| ==Selected writings by H. O. A. Wold==
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| * 1938. ''A Study in the Analysis of Stationary Time Series'', Almqvist & Wiksell
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| * 1949. ''Statistical Estimation of Economic Relationships'', in [[Econometrica]],
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| * 1952. ''Demand Analysis: A Study in Econometrics,'' with Lars Juréen.
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| * 1954. "Causality and Econometrics," ''[[Econometrica]]'', 22(2), p [http://www.jstor.org/pss/1907540 p. 162]-177.
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| * 1964.''Econometric model building : essays on the causal chain approach'' (edited by Herman O.A. Wold).
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| * 1969. "Econometrics as Pioneering in Nonexperimental Model Building," ''Econometrica'', 37(3), p [http://www.jstor.org/pss/1912787 p. 369]-381.
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| * 1980. '' The Fix-Point Approach to Interdependent Systems'' (edited by Herman Wold), North-Holland.
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| * 1982. ''Systems under Indirect Observation: Causality, Structure, Prediction'' (edited by [[Karl Jöreskog|K. G. Jöreskog]] and H. Wold), North-Holland.
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| There is an extensive bibliography published with the ''ET'' interview (below).
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| ==See also==
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| {{col-begin}}
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| {{col-1-of-3}}
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| * [[Causality]]
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| * [[Harald Cramér|Cramér, Harald]]
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| * [[Convex preferences]]
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| * [[Cramér–Wold theorem]]
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| * [[Supply and demand|Demand (economics)]]
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| * [[Directed acyclic graph]]
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| * [[Econometrics]]
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| * [[Graphical model]]
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| {{col-2-of-3}}
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| * [[Karl Gustav Jöreskog|Jöreskog, Karl Gustav]]
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| * [[Latent variable]]
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| * [[Least squares]]
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| * [[Moving average]]
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| * [[Multivariate analysis]]
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| * [[Multivariate statistics]]
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| * [[Observational study]]
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| * [[Partial least squares regression]]
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| {{col-3-of-3}}
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| * [[Stationary process]]
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| * [[Structural equation model]]
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| * [[Time series]]
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| * [[Uppsala University]]
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| * [[Utility theory]]
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| * [[Peter Whittle|Whittle, Peter]]
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| * [[Wold decomposition]]
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| * [[Wold's theorem]]
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| {{col-end}}
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| ==Notes==
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| <references/>
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| ==References==
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| ;Autobiography
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| *J. Gani, ed. (1982). ''The Making of Statisticians,'' New York: Springer-Verlag. This has a chapter in which Wold tells the story of his life.
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| * See the ET interview under External Links.
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| ;Discussion
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| *Svante Wold "Wold, Herman Ole Andreas";, pp. 213–4 in ''Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present,'' (ed. N. L. Johnson and S. Kotz) 1997. New York: Wiley. Originally published in ''Encyclopedia of Statistical Science. ''
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| ==External links==
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| *[http://korora.econ.yale.edu/et/interview/wold.pdf ET Interviews: Professor H. O. A. Wold] on the [http://korora.econ.yale.edu/et/ Econometric Theory] page.
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| *[http://cepa.newschool.edu/het/profiles/wold.htm New School: Herman Wold, 1908-1992]
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| *[http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=44712 Mathematics Genealogy Project: Herman Wold]
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| ''There is a photograph at''
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| *[http://www.york.ac.uk/depts/maths/histstat/people/wold.gif H. O. A. Wold] on the [http://www.york.ac.uk/depts/maths/histstat/people/welcome.htm Portraits of Statisticians] page.
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| ''See also'' (external links, again) | |
| * [http://planetmath.org/encyclopedia/CramerWoldTheorem.html Cramér–Wold theorem]
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| * [http://www.xycoon.com/wolds_decomposition.htm Wold decomposition]
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| {{Authority control|VIAF=109217327}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| |
| | NAME = Wold, Herman
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Swedish economist
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| | DATE OF BIRTH = December 25, 1908
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| | PLACE OF BIRTH = [[Skien]]
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| | DATE OF DEATH = February 16, 1992
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Wold, Herman}}
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| [[Category:Members of the Royal Swedish Academy of Sciences]]
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| [[Category:Swedish statisticians]]
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| [[Category:Time series econometricians]]
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| [[Category:Swedish economists]]
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| [[Category:Probability theorists]]
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| [[Category:Researchers in stochastics]]
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| [[Category:Swedish mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Uppsala University faculty]]
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| [[Category:University of Gothenburg faculty]]
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| [[Category:1908 births]]
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| [[Category:1992 deaths]]
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| [[Category:Presidents of the Econometric Society]]
| |
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