Abraham Wald, 1902-1950

Born in Kolozsvar/Cluj, Transylvania (now Romania, then part of Austria-Hungary) in 1902, to a poor orthodox Jewish family.  In 1927, Wald enrolled in the mathematics department of the University of Vienna, receiving his PhD in 1931. He was one of Karl Menger's students, and an active participant in Menger's Vienna Colloquium. 

As a foreigner and a Jew, Wald was barred from academic positions in Austria.  Wald returned to Cluj in 1932, but his post-war hometown was no more welcoming, and his grasp of Romanian being weak, his options were limited.   Learning of Wald's precarious situation, Menger scrambled to get Wald back to Vienna, and arranged a position for Wald as the private tutor of the Viennese banker and amateur economist Karl Schlesinger in December 1932.  Another colloquium participant, Oskar Morgenstern, then the young director of Austrian Institute for Business Cycle research, managed to release some funds to secure a more permanent position for Wald.

It was Schlesinger who  introduced Wald to the problems of the system of Walras and Cassel, which he wanted to bring to the attention of the mathematicians in the Vienna Colloquium.  Abraham Wald wrote three papers (1935, 1936a,b) on the Walras-Cassel system, employing the important "Duality Principle" and complementary slackness conditions which he (together with Schlesinger) developed for the Walras-Cassel G.E. system - which did away with the counting-equations- and-unknowns method, but allowed the return of Wieser's imputation theory back into economics and the employment of linear programming. Wald's third paper was particularly important and contributed several factors besides linear programming. Wald's paper was also the first proof of the existence of an equilibrium in a G.E. setting in economics. It also introduced several important concepts: the weak axiom of revealed preference (WARP) - later employed and developed by Paul Samuelson. He also addressed (briefly) the issue of whether it would hold in the aggregate (a question ignored and unanswered until the mid-1970s). He also defined a primitive form of the idea of "gross substitution" and provided a proof of the uniqueness of equilibrium. He also used these tools to tackle the existence of an equilibrium in a Cournot duopoly model.

It is conjectured that Wald used a fixed point theorem (possibly derivative from von Neumman),  for another improved proof of equilibrium, that was apparently presented to the Vienna Colloquium session sometime in December 1935.  The details are unclear, and Wald's third paper was never published (it has since been lost).  Wald's summary of his first two papers, organized in an accessible form for economists, was published in the Zeitschrift fur Nationalokonomie in early 1936, makes no mention of it.

Wald was a mathematician and thus, naturally, had a tenuous understanding of the "economic" significance of his work. It was only after Morgenstern's badgering that Wald wrote a summary of his two papers, accessible for economists,  to be published in the Zeitschrift für Nationalökonomie in early 1936.  It nonetheless would take over a decade for the impressive economic implications of Wald's work to be appreciated.  Its significance only began being felt at the famous 1949 conference on activity analysis organized by Koopmans at the Cowles Commission., and Wald's results expanded later by Arrow, Debreu and others at the Cowles Commission.

 Mindful of his duties at Morgenstern's Institute, Wald dedicated himself to statistics after 1936.  In relation to this, Wald's published a volume on seasonal fluctuations in business cycles in 1936 and a 1937 article on economic indexes. 

The Vienna Colloquium was dispersed in 1937. shortly before the Germans took over Austria.  Wald was trapped in Austria after the Anschluss,  and dismissed immediately from the Institute by the Nazis.  He managed to leave Austria in the Summer of 1938, accepting an invitation from the Cowles Commission in Colorado Springs (arranged by Tintner). After only a few months, at Hotelling's urging, Wald gravitated to Columbia University in New York.  Wald continued his work on statistical theory, making several seminal contributions, such as the development of "sequential analysis" (1947) and the famous "Wald Test" (1939) so often employed in modern econometrics.  Kenneth Arrow, who would later provide his own seminal proof of existence with Debreu in 1954, was a student at Columbia during Wald's tenure.

Wald was part of the Statistical Research Group (SRG) at Columbia, undertaking projects for the US military during WWII.  Wald's work on statistical decision theory reportedly influenced fellow SRG researcher Leonard J. Savage.

Abraham Wald died tragically in a plane crash over India on December 13, 1950.

Wald's colloquium papers were translated into English by William J. Baumol in 1968 (in Reprints of Scarce Works).  His ZfN paper was translated earlier by Otto Eckstein (1951, Econometrica) 

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