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Born in Cluj, Rumania, Wald came to Vienna in 1927 to study mathematics with Karl Menger, the geometer and son of the economist Carl Menger. Menger introduced Wald to the active mathematical group in Vienna, and secured for him a position as mathematical tutor to the economist Karl Schlesinger. This led to Wald’s producing the first proofs of existence for models of general equilibrium; his analysis was based on Cassel’s restatement of the Walrasian model, as modified by Schlesinger’s treatment of free goods. These works were published in the proceedings of Menger’s mathematical colloquium, and a summary was published in the Zeitschrift für Nationalökonomie in 1936. These papers were remarkable for their time and, with von Neumann’s paper on equilibrium in a model of an expanding economy, are the first significant contributions to the mathematical analysis of general equilibrium models in economics. Wald is the link between the early work by Walras and the later work by Kenneth Arrow, Gerard Debreu and Lionel McKenzie on the existence of competitive equilibria.

A fine mathematician, Wald was nevertheless prevented from gaining a regular academic position because of Viennese anti-Semitism. Menger helped Wald secure a consultancy position with Oskar Morgenstern who directed the Institut für Konjunkturforschung, where Wald took an interest in the statistical problems that were associated with the analysis of business cycles. Wald’s book on seasonal adjustment of time series was a result of his work at Morgenstern’s Institut.

Wald was able to escape from Vienna when the Nazis arrived, and made his way to the United States where he initially secured a fellowship, in 1938, at the Cowles Commission which was then at Colorado Springs. When the Commission moved to Chicago, Wald obtained a position, on a Carnegie grant, as Harold Hotelling’s assistant at Columbia University. He moved to a faculty post at Columbia in 1941, and was promoted to Associate Professor in 1943 and Professor in 1944.

Wald’s contributions to statistics are immense. His most significant paper appeared in 1939 in the Annals of Mathematical Statistics as ‘Contributions to the Theory of Statistical Estimation and Testing Hypotheses’ (in Wald, 1955). This paper, written before modern decision theory was developed, contained notions of decision space, weight and risk functions, and minimax solution (based on von Neumann’s 1928 paper on game theory). Wald’s paper was not appreciated at the time, much as was the case with his papers on general equilibrium theory. He did not return to statistical decision theory until 1946, after von Neumann and Morgenstern had presented the theory of games.

During the Second World War, Wald worked with the Statistical Research Group and developed much of the theory of sequential analysis. Although he did not create the idea of taking observations sequentially, Wald did invent the sequential probability ratio test. This original material was published in 1947 after wartime restrictions were lifted.

In 1950, at the height of his powers, Wald and his wife died in a plane crash in India.

See Also

Selected Works

  • In 1952 The Annals of Mathematical Statistics devoted the first part of its volume 23 to a memorial to Wald. Articles on Wald by Jacob Wolfowitz, Karl Menger and Gerhard Tintner were followed by a complete bibliography of Wald’s writings. Wald’s professional correspondence, and papers from his Viennese days, cannot be located, though it is possible that Karl Menger’s archives, currently closed to examination, may contain some material on Wald.

  • 1934. Über die eindeutige positive Lösbarkeit der neuen Produktions gleichungen I. In Ergebnisse eines mathematischen Kolloquiums, 1933–34, ed. K. Menger. Trans. W. Baumol as ‘On the unique non-negative solvability of the new production equations, Part I’, in Precursors in Mathematical Economics, ed. W.J. Baumol and S.M. Goldfeld, London School of Economics Series of Reprints of Scarce Works on Political Economy No. 19, London: London School of Economics, 1968.

  • 1935. Über die Produktionsgleichungen der ökonomischen Wertlehre II. In Ergebnisse eines mathematischen Kolloquiums, ed. K. Menger, 1934–35. Trans. W. Baumol as ‘On the production equations of economic value theory, Part II’, in Precursors in Mathematical Economics, ed. W.J. Baumol and S.M. Goldfeld, London School of Economics Series of Reprints of Scarce Works on Political Economy No. 19, London: London School of Economics, 1968.

  • 1936. Über einige Gleichungssysteme der mathematischen Ökonomie. Zeitschrift für Nationalökonomie. Trans. O. Eckstein as ‘On some systems of equations in mathematical economics’, Econometrica 19 (1951), 368–403.

  • 1947. Sequential analysis. New York: Wiley.

  • 1950. Statistical decision functions. New York: Wiley.

  • 1955. Selected papers in statistics and probability. New York: McGraw-Hill.