# Slutsky, Eugen

# Slutsky, Eugen

EugenSlutsky, or Evgenii Evgenievich Slutskii (1880-1948), Russianeconomist, statistician, and mathematician, was born in Yaroslavlprovince, the son of a schoolteacher. He entered the University ofKiev as a student of mathematics in 1899 but was expelled three yearslater for revolutionary activities. From 1903 to 1905 he studiedengineering at the Institute of Technology in Munich. After therevolution of 1905 he returned to Russia, obtaining a degree in lawfrom the University of Kiev in 1911. For a while he taughtjurisprudence in a technical college, but he became interested inpolitical economy and in 1918 he received a degree in that subjectand became a professor at the Kiev Institute of Commerce. In 1926 heleft Kiev for Moscow to join the Kon’iunkturnyi Institut(i.e., the Institute for the Study of Business Cycles). From 1931 to1934 he was on the staff of the Central Institute of Meteorology.Moscow State University conferred an honorary degree in mathematicson him in 1934. From that time until his death he held an appointmentat the Mathematical Institute of the Academy of Sciences of theSoviet Union.

One of Slutsky’s first published works washis famous article on the theory of consumer behavior (1915). Slutskyhere developed some ideas of F. Y. Edgeworth’s and VilfredoPareto’s on the relationship between the utility function andprices, income, and consumption. His main achievement was to showthat, with money income fixed, any change in the price of a commoditycan be divided into two parts. The first part is the change inrelative prices, with real (not money) income fixed. This is calledthe substitution effect; the consumer maintains approximately a givenindifference level. The second part is the balance of the pricechange (a proportional shift in all prices), which can be translatedinto an equivalent change in money income, with prices constant,causing a variation in real income. This is called the income effect;the consumer shifts from one indifference level to another. The twoeffects turn out to be independent and additive(“Slutsky’s relation”).

The distinctiondrawn between the substitution effect and the income effect is oftenleft ambiguous. There is a choice as to whether to define the holdingof real income fixed as (a) holding the consumer’s utilityfixed, or (fe) holding a Lespeyre measure of the purchasing power ofhis money income fixed. Slutsky clearly uses (a) in his mathematicalanalysis and (b) in his verbal explanation. The difference is,however, of the second order of smalls and unimportant whenconsidering small changes in price. (For a further discussion of thispoint, see Mosak 1942.)

Although in R. D. G. Allen’sopinion (1950) the present theory of consumer behavior is as much adevelopment of Slutsky’s work as of Pareto’s,Slutsky’s paper attracted no attention until Allen discoveredit in the mid-1930s (1936).

In his later years Slutsky did verylittle work in pure economics but made a considerable contribution tomathematical statistics and the theory of probability. His firstpaper on this subject, “On the Criterion of Goodness of Fit ofthe Regression Lines and on the Best Method of Fitting Them to theData” (1913), was written eight years before the work of R. A.Fisher on the same subject. Slutsky was interested in the problem offormalizing the theory of probability. In the article “Uberstochastische Asymptoten und Grenzwerte” (1925) he examinedthe accurate definition of the concept of asymptotic convergence inprobability, and so made an important contribution to the theory ofprobability (see also 1928; 1938).

Slutsky was one of theoriginators of the theory of stochastic processes. In his work“The Summation of Random Causes as the Source of CyclicProcesses” (1927) he proved that the“periodical” oscillations in economic, meteorological,and other time series do not necessarily show the presence of anyunderlying periodic cause; such oscillations are typical of allserially correlated random sequences, including those which resultfrom taking a moving sum in a sequence of mutually independent,purely random quantities. By repeatedly smoothing such sequences, onecan obtain a new sequence, which will in any limited period of timebe closely approximated (with probability one) by a sine curve. Thiseffect of averaging random series was studied by Slutskyindependently of G. U. Yule.

Slutsky’s study of stochasticprocesses centered on serial, or lag, correlation, that is,correlation between two members of a time series separated by a fixedtime interval. In many important applications serial correlationdepends only on interval length, not on position along the timeseries. The concept of serial correlation has broad applications inmany branches of science and technology, including radio engineering.Slutsky’s theory was generalized by A. Khinchin (1934).

Slutsky wrote several articles on the estimation of parameters ofstochastic processes. His complete works on the theory of probabilityand mathematical statistics have been published (see Izbrannyetrudy).

In the last years of his life Slutsky studied the problemof computing tables for functions of several variables. This workresulted in the posthumous publication of Tablitsy dlia vychisleniianepol-noi T-funktsii i funktsii veroiatnosti x^{2} (Tablesfor the Computation of the Incomplete T-function and thex^{2} Probability Distribution; 1950).

A. A. Konüs

[*For the historical context of Slutsky’s work, see the biographies of*Edgewobth and Pareto; *for discussion of the subsequent development of Slutsky’side as, see*Time Series; Utility.]

## WORKS BY SLUTSKY

1913 Onthe Criterion of Goodness of Fit of the Regression Lines and on theBest Method of Fitting Them to the Data. Journal of the RoyalStatistical Society 77:78-84. → Published in Russian in 1960in Izbrannye trudy (Selected Works).

1915 Sulla teoria delbilancio del consumatore. *Giornale degli economists* 3d Series51:1-26. → Published in Russian in 1963 by the Akademiia NaukSSSR, in Economiko-matematicheskie metody, Volume 1.

1925 liberstochastische Asymptoten und Grenzwerte. Metron 5, no. 3:3-89.→ Published in Russian in 1960 in *Izbrannye trudy.*

(1927) 1937 The Summation of Random Causes as the Source of CyclicProcesses. Econometrica 5:105-146. → First published inRussian. Reprinted in 1960 in *Izbrannye trudy.*

1928 Sur lesfonctions éventuelles continuées, intégrables etdérivables dans le sens stochastique. Académic desSciences, Paris, *Comptes rendus* hebdomadaires des seances187:878-880. → Published in Russian in 1960 in *Izbrannyetrudy.*

1938 Sur les fonctions aléatoires presquepériodiques et sur la décomposition des fonctionsaléatoires station-naires en composantes. Pages 33-55 inColloque consacré à la théorie desprobabilités. Part 5: Les fonctions aléatoires, by S.Bernstein, E. Slutsky, and H. Steinhaus. Actualltes scientifiques etindustrielles, No. 738. Paris: Hermann. → Published in Russianin 1960 in *Izbrannye trudy.*

1950 Tablitsy dlia vychisleniianepolnoi T-funktsii i funktsii veroiatnosti x^{2}. Edited byA. N. Kolmorgorov. Moscow: Akademiia Nauk SSSR. → Publishedposthumously.

Izbrannye trudy: Teoriia veroiatnostei,matematicheskaia statistika. Moscow: Akademiia Nauk SSSR, 1960.→ Contains papers originally published between 1913 and 1938.

## SUPPLEMENTARY BIBLIOGRAPHY

Allen, R. D. G. 1936 ProfessorSlutsky’s Theory of Consumers’ Choice. Review ofEconomic Studies 3:120-129. → A summary of Slutsky’s1915 article on consumer behavior.

Allen, R. D. G. 1950 The Workof Eugen Slutsky. Econometrica 18:209-216. → Includes aBibliography on pages 214-216.

Khinchin, A. 1934Korrelationstheorie der stationaren stochastischen Prozesse.Mathematische Annalen 109: 604-615.

Mosak, Jacob 1942 On theInterpretation of the Fundamental Equation of Value Theory. Pages69-74 in Chicago, University of, Department of Economics, Studies inMathematical Economics and Econometrics in Memory of Henry Schultz.Edited by Oskar Lange, Francis Mclntyre, and Theodore O. Yntema.Univ. of Chicago Press.

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