Eugen Slutsky

Eugen Slutsky (a.k.a. Eugene Slutsky and Yevgeni Slutsky) intended to become a mathematician, but he was expelled from the University of Kiev for participating in student revolts and, after some wandering through engineering and Europe, he returned to Kiev and ended up getting a doctorate in law in the end and then heading to teach at the Kiev Institute of Commerce. This was in 1911 and Slutsky had a fine sample from several fields.

It was the work of the Lausanne School in economics that attracted him and yielded up his first economics paper in 1915 – published in Italy (at the time, the last citadel of of Walrasian economics). In his 1915 paper, he presented the “Slutsky decomposition” of demand functions into substitution and income effects. His work was ignored and only much later, when the same principle was resurrected independently by John Hicks and R.G.D. Allen in 1934, did he eventually get some recognition.

His other prominent contribution to economics came in 1927, when he showed that a series of shocks can be summed up to yield regular cyclical properties. This paper, which paralleled that of Frisch was the beginning of the shock-dependent business cycle that precedes the New Classical theory of today. The famous SLUTSKY-YULE THEOREM (i.e. that the moving average of a random series may generate oscillatory movement when no oscillations exist in the original data) was also laid out in that paper.

The rest of his work, much of it accomplished after his move to the Moscow in 1920, was in probability theory. The famous Slutsky’s Theorem which argued that if a statistic converges almost surely or in probability to some constant, then any continuous function of that statistic also converges in the same manner to some function of that constant – a theorem with applications all over statistics and econometrics – was laid out in his 1925 paper. Other limit theorems were provided in 1928 and 1929.

Major works of Eugene Slutsky

– On the Criterion of Goodness of Fit of the Regression Lines and on the Best Method of Fitting them to Data, 1914, Journal of Royal Statistical Society
– Sulla teoria del bilancio del consummatore, 1915, Giornale degli Economisti
– Über stochastische Asymptoten und Grenzwerte, 1925, Matematischen Annalen
– The Summation of Random Causes as the Source of Cyclical Processes, 1927 (in Econometrica, 1937)
– Sur un criterium de la convergence stochastique des ensembles de valeurs eventuelles, 1929, Comptes Rendu des seances de l’Academie des Sciences
– Quelques Propositions sur les Limities Stochastiques Eventuelles, 1929, Compte Rendu des seances de l’Academie des Sciences
– Tables for the Computation of the Incomplete Gamma Function and the Chi-Square Probability Distribution, 1950
– Selected Works of Eugen Slutsky, 1960

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