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The Work of Eugen SlutskyAuthor(s): R. G. D. AllenSource: Econometrica, Vol. 18, No. 3 (Jul., 1950), pp. 209-216Published by: The Econometric SocietyStable URL: http://www.jstor.org/stable/1905793.

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E

O O

E

T R

VOLUME 18

JULY,

1950 NUMBER 3

THE WORK OF EUGEN SLUTSKY

BY R. G. D. ALLEN

EUGEN

LUTSKY, whose

death

has recently been reported,was an out-

standing mathematician

and

statistician.

His work

has had a great and

lasting influence on the development of econometrics in two important

fields,

the

theory

of consumer's

behaviour

and

the analysis

of

time

series.In each case his basic article remainedalmost unknown ormany

years,

was later

rediscovered,

and

had an

increasing

effect

in

shaping

the

work of others in the field.

During the 1920's and early 1930's, Slutsky published a number of

statistical articles on

stochastic

processes

and

time series

analysis,

some

in

French, Italian,

and German. His main article

[23],

now

a

classic

contribution, appeared

in

Russian,

with

only a brief summary

in

English,

in a publication of the Moscow Conjuncture Institute

in

1927. His

treatment of the time series problem was akin to that of Yule in the

famous articles of 1921 and 1926

in

the Journal

of

the

Royal

Statistical

Society1and together they had a very great influence on the later work

in

the field. Slutsky's contribution, however, remained little known for

some

years,

until

Henry Schultz,

whose

eagle eye

missed

very little

in

his

field,

was

responsible

for the

preparation of

a translation. An

English

version

of the

work,

with the

addition of

later material,

was

finally

preparedby Slutsky

and

published

n

this Journal

n

1937

[42].

The main object of this work of Slutsky'swas to demonstrate hat

an

oscillatory

series

could

be

generated

from a random series

by taking

a

moving

sum or

difference,

with or without

weights

and with

or with-

outrepetition

of

the

process.

The

oscillatory eriessogenerateddisplayed

1

On the Time Correlation Problem

with

Especial Reference to the Variate-

Difference Correlation Method,

Journal

of

the

Royal

Statistical

Society,

Vol.

84,

July, 1921, pp. 497-526; and

Why

Do

We

Sometimes Get Nonsense-Correlations

between Time-Series?

A

Study

in

Sampling

and

the Nature

of

Time-Series,

Journal of

the

Royal

Statistical

Society,

Vol.

89, January, 1926, pp.

1-64.

EDITOR'S OTE:The following information regarding Eugen Slutsky (Evgenil

Evgenievic Sluckil) is drawn from

memorial articles written by A. N. Kolmogorov

[Uspekhi

Matematicheskikh

Nauk,

Vol.

3,

No. 4

(26), 1948, pp.

143-151]

and

N.

Smirnov [Izvestiica

Academiia Nauk

S.S.S.R., Mathematical Series, Vol. 12,

1948,

pp.

417-4201.

Eugen

Slutsky

was born in

1880. He studied in the department of physics and

mathematics at the University of

Kiev.

In

1901

he was expelled from the university

and

conscripted

into

the

army,

together

with other

students,

because

of

participa-

209

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8/11/2019 1905793

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210

R. G.

D. ALLEN

approximate

regularity,

with

varying length

and

amplitude

of

oscilla-

tion,

and they

were

very

similar

to

many

economic time

series.

Under

certain

circumstances,

the

generated

series could

be made

to

approximate

very closely to a sine-curve. Slutsky's results have been of great value

in

research

into

the

problem

of whether a

moving-average

trend distorts

the true

oscillations

in a series

and into

the wider

question of the

struc-

ture

of economic

time series.

Because

of the mathematical

complexities

involved,

the present

approach

to time

series

analysis,

by Kendall,

Orcutt,

and

others,

is

still the same

as

Slutsky's,

a

combination

of

deduc-

tion

with

experimentation

on

actual

or

(more

usually)

constructed

series.

Slutsky's basic article in the theory of consumer's behaviour was

earlier;

it

appeared

under

the title Sulla

teoria del bilancio del

con-

sumatore

in Giornali

degli

Economisti,

1915

[6].

He

put

his

argument

in

a

highly

mathematical form,

without

much

elaboration

of

the

economic

significance

of

his

results,

and he was unfortunate

in that

he

published

in wartime. Consequently,

like another mathematical

article

on

the

same

topic

by Johnson,2

his

work received little notice at the time. It

was only

rediscovered

in

the

middle 1930's

by

those

then

developing

the

theory

and measurement of consumer's demand. Even Henry Schultz did not

discover

Slutsky's

article

until around

1934,

and he included an

account

of

it

in

his

Interrelations

of

Demand,

Price and

Income 3

in

1935.

Independently,

though

a

little

later,

Hicks

and

I

were led

back

to

Slut-

sky's

original

work

by

various references

to

it,

and

I

published

a

sum-

mary

of

it

in the Review

of

Economic

Studies

in

1936.4

It

can be

said,

without

doubt,

that

the

present

theory

of

consumer's

behaviour,

as developed by

Hicks

and

others,

is

essentially

as

much

a

tion in student revolts, but was returned to the university as a result of further

student

protests

in the

country.

In

1902,

however,

he was

again

expelled

and

de-

prived of

the

right to study

in any

Russian

institution

of higher

learning.

From

1902

to 1905

he

studied

in

the

engineering

department

of the Institute

of Tech-

nology at

Munich, Germany.

In 1905

he received permission

to study

in Ru3sia

and

entered

the

department

of

law,

University

of

Kiev,

with the intention

of

ap-

plying

mathematical

methods to

economics.

He graduated

from the university

with a gold medal

in 1911.

He

became

a

member

of the

faculty

at Kiev

Institute

of Commerce

in 1913,

reaching

the

position

of

full professor

in 1920. Three years

earlier

he received

a

degree

in

political

economy

from the University

of

Moscow.

From

1926

on,

he was a

staff member

of the Central

Statistical Board in Moscow.

In 1934

he became

a staff

member

of the

Mathematical

Institute

of the

University

of Moscow, and

in

1938

became

a

member

of

the Mathematical

Institute

of the

Academy

of Sciences

of the U.S.S.R. Slutsky

died

March

10, 1948,

in

Moscow.

2

The Pure

Theory

of Utility

Curves,

Economic Journal,

Vol. 23,

December,

1913,

pp. 483-518.

3

Journal

of

Political

Economy,

Vol.

43,

August,

1935, pp.

433-481.

4 Professor

Slutsky's

Theory

of

Consumers'

Choice,

Review

of

Economic

Studies, Vol. 3,

February,

1936, pp.

120-129.


8/11/2019 1905793

4/9

THE

WORK

OF

EUGEN SLUTSKY

211

development of

Slutsky's

work

as

of

Pareto's.

Quantities

demanded

by

an

individual consumer as

functions

of

given prices

and

income are

given by the

conditions for

an

extreme

value

of

an ordinal utility

func-

tion. The stability conditions, for a maximum as opposed to a minimum,

then

serve

to

determine

the

properties

of

the demand functions,

i.e.,

the

variation of demand with

changing prices and

income. A good deal

of

confusion

of

thought has

arisen

because

of

the

fact

that the restraint

set

by the

condition

of

given

total

expenditure

is

linear and

homogene-

ous

in

the variables (prices

and

income).

A

proportionate increase

in

all

prices with income

fixed is

equivalent

to a

decrease

in

income

with all

prices

fixed, each

corresponding

to

a

decrease

in

real income, i.e., a

shift

to a lower level on the consumer's preference scale. Slutsky's achieve-

ment

was to show

that any change

in

prices and

income must be

ana-

lysed into two

parts. The first is

a change

in

relative

prices with

fixed

real (not money)

income.

This is the substitution

effect and the

con-

sumer

maintains

a

given

indifference

level. The second

part

is

the

balance

of

the

price change

(a proportionate

shift in all

prices), which can

be

translated

into

an

equivalent

change

in

income and

added

to

whatever

change there

may

be

in

money

income to

give the

variation in

real in-

come. This is the income effect and the consumer shifts from one indif-

ference level

to

another.

The two

effects

turn

out

to

be

independent

and

additive,

as indeed is

intuitively

clear.

There

are

two

equivalent

ways

of

attacking the problem. For

the

substitution

effect,

real

(not

money)

income

is

kept

fixed either

by

taking

the

utility

level constant

and

minimising

expenditure

for

each

set

of

market

prices

or

by adding a

compensating

change

in

money income to

given price

changes

in

order to

maintain the

original

indifference level.

In

the

analysis

of

the income

effect,

either

the

minimised

expenditure

can be

compared

with actual

money

income

or

the

actual

change

in

money

income can be

adjusted

for

the

compensating income

change.

The second was the

method

adopted by

Slutsky,

and it is

certainly

the

easier

to

develop

and

expound.

With Hicks's

notation,5

n

commodities are demanded

in

amounts

xr

at

prices

pr

(r

=

1,

2, * ** , n)

and with

income M.

A

given

direction

of

price

change

is denoted

by

the

differentials

dp,,

and the

compensating

income

change

to

maintain

the indifference

level is

n

dM

=

Ex,

dps.

8=1

The

change

in

demand

for the

rth

commodity

is

dxr

=

E

OXr

dp, + dX

dM,

,8=

&9p8

am

6

J.

R.

Hicks,

Value

and

Capital,

second

edition,

Oxford:

Clarendon Press, 1946.


8/11/2019 1905793

5/9

R.

G.

D.

ALLEN

i.e.,

.-,

p

,

X

.

X

dp

This is

the

variation

in

demand

for

a

compensated

price change,

and

the

expressions [(Oxr/dp,)

+

x,(Oxr/Op,)]

represent

the

substitution ef-

fect.

These

expressions

were first

defined

by

Slutsky

and

analysed

by

him

in

terms

of

the

utility

functions.

He termed them

residual varia-

tions

in

demand

for a

compensated

variation

in

price.

As

Slutsky

showed,

the

substitution

expressions (residual

variations)

are

limited

in

various

ways by

the

conditions

for

equilibrium

and

for

stability. What is now seen, after much development of the basic Slut-

sky

theory,

is that

the

limitations

boil down

to one

equation

and one

inequality:

n

n

(1)

pr

dxr

=

0;

E

dprdXr

prXr;

r-l

r-1

212


8/11/2019 1905793

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THE

WORK OF EUGEN

SLUTSKY

(t

(Pr>

(p

+

Ap(

+

r)r

+

A,

n

n

r-1 r-1

(2)

prArg>

o;

;Ap.A

1905793

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