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Top Incomes over 100 years: What can be learned about the determinants of income distribution?

A B Atkinson, Nuffield College, Oxford and Paris School of Economics

Trevor Swan Distinguished Lecture February 2007

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1. Framework for Analysis

• Earnings, Wealth and Income

• Distribution and Economic Growth

• Impact of top 1%

2. Empirical Evidence for a Selection of OECD Countries

• Incomes

• Earnings

• Wealth

3. Seeking Explanations

• Linking Theory and Evidence

• Disappearance (and re-appearance?) of rentiers

• Earnings at the top: superstars and managerial pyramids

Conclusions: Role of Public Policy

3

Meade Framework

Efficiency, Equality and the Ownership of Property (1964)

Individual income of person i Yi = Wi + ri Ki

• Factor shares

• Distribution of earnings

• Distribution of wealth

• Distribution of rates of return and their correlation with wealth

• Correlation of earned and investment income

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Growth and DistributionIn Solow/Swan neoclassical growth model

Growth of individual capital per head ki

dki/dt = swwi + srriki – nki

Aggregate growth

dk/dt = sw ∑i wi + sr ∑iriki – nk

If r same for all, and sw = sr = s, then steady state implies sr < n (Stiglitz) and hence ki converge to multiple of wi

BUT• Unequal inheritance: primogeniture → Pareto upper tail• Non-linear savings function• Stochastic creation of new fortunes

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Impact of top 1%

If S* is share of top 1%, then the Gini coefficient can be

approximated by

S* + (1-S*) G,

where G is the Gini coefficient for the rest of the population.

Considering gross incomes, this means that, if the Gini

coefficient for the rest of the population is 40%, then a rise of 8

percentage points in the top share causes a rise of 4.8

percentage points in the overall Gini.

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Share of top 1% and overall Gini coefficient in US 1947-2002

30

35

40

45

50

1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002

Note: Different definitions of income and income unit

Gin

i co

eff

icie

nt

%

0

5

10

15

Sh

are

of

top

1%

in t

ota

l in

co

me

Share of top 1%RH axis

Gini coefficient LH axis

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1. Framework for Analysis

2. Empirical Evidence for a Selection of OECD Countries

• Incomes

• Earnings

• Wealth3. Seeking Explanations

Conclusions: The Role of Public Policy

A B Atkinson, and T Piketty, editors, Top Incomes over the Twentieth Century, Oxford University Press, volume 1 forthcoming 2007.

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Share of top 1% in gross INCOME in English-Speaking countries

4

6

8

10

12

14

16

18

20

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Per

cen

t o

f to

tal

inco

me

AUS CA

IRL NZ

US UK

UK

US

CA

AUS

NZ

Australian results from A B Atkinson and A Leigh “The Distribution of Top Incomes in Australia”, Economic Record, forthcoming 2007.

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Share of top 1% in gross INCOME in Continental Europe

5

10

15

20

25

30

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Per

cen

t o

f to

tal

inco

me

GER

FR

NL

SWI

NL

DEU

CH

FRA

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Share of top 1% =

Proportion of earned income

x Share of top 1% of earners

x Alignment coefficient for earnings

+

Proportion of investment income

x Share of top 1% with investment income

x Alignment coefficient for investment income

Alignment coefficient =

Share in earnings of top 1% of income recipients / Share of top 1% of earners ( ≤ 1)

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Share of top 1% in total EARNINGS

3

4

5

6

7

8

9

10

11

1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998

% s

ha

re t

ota

l e

arn

ing

s

Share of Top 1%

FRANCE

US

CA

UK

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Decomposition: WEALTH

Top 1% of wealth distribution in six countries from Ohlsson, Roine and Waldenstrom (2006)

UK data adjusted for break in 1960

10

15

20

25

30

35

40

45

50

55

60

1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Sh

are

of

top

1%

FRA UK

SWE

DK

US

NOR

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Pareto coefficient for wealth in UK

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

1923 1928 1933 1938 1943 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998

Calculated from share of top 1% within top 10%α = 1 / [1 + Log10 [S1/S10] ]

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0

10

20

30

40

50

60

70

1923 1933 1943 1953 1963 1973 1983 1993

0

1

2

3

4

5

6

7

Top 1% of earnersScale

Top 1% wealth-holders

Scale

UK

Putting them together for the UK

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Figure 12 Contributions to share of top 1%

0

2

4

6

8

10

12

14

1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997

% t

ota

l in

com

e

Overall Share

Contribution of employment income

Contribution of investment income

UK

Other income

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MAJOR themes:

• Decline in concentration of capital 1900-1979

• Rise in top earnings post 1979 in some countries

MINOR themes

• Decline in top earnings up to 1979

• Modest recovery of capital post 1979

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1. Framework for Analysis

2. Empirical Evidence for a Selection of OECD Countries

3. Seeking Explanations

• Linking Theory and Evidence

• Disappearance (and re-appearance?) of rentiers

• Earnings at the top: superstars and managerial pyramids

Conclusions: The Role of Public Policy

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Linking Theory and Evidence

• Models of Individual Incomes

Micro-data

Independent• Models of Distributions

Moments

Percentiles or percentile shares

Summary measures (Gini)

Pareto coefficient

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CAMBRIDGE Accumulation Model (Pasinetti / Meade / Stiglitz)

Pareto upper tail

α = (n+δ) / [sr(1-t) - βn],

where n is rate of population growth, δ the rate of decay of fortunes

sr(1-t) is the rate of accumulation out of wealth (r is the rate of return and t the tax rate), and

βn captures the periodic effect of the division of estates at death.

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UK top tax rate and 1/alpha

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

19181923192819331938194319481953195819631968197319781983198819931998

1/al

ph

a

0

10

20

30

40

50

60

70

80

90

100

10

0-t

op

ta

x r

ate

on

inv

es

tme

nt

inc

om

e

1/alpha

LHS scale

(1-t)

RHS scale

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Superstar Theory(Alfred Marshall 1890s and Sherwin Rosen 1980s)

+ Gives role to both technology and trade

- No direct link to distribution

? Explain earlier periods when top earnings fell?

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Log (Earnings/median)

Log [1/(1 – F)]

Effect of trade and technology in expanding share of rents captured by top performers = fall in α

Superstar model generates extreme value distribution with Pareto tail with exponent α

Slope = 1/α

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Managerial Hierarchy Model (Lydall and Simon)

β =

loge[span of managerial control]

divided by

loge[1+ increment with promotion ]

span

increment 25%

5

7.2

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Log (Earnings/median)

Log [1/(1 – F)]

Superstar model not enough on its own, since not explain earlier rise in α

Hierarchical Salary Model

Hierarchical model not enough on its own, since predicted Pareto exponent β too large

-

+

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Conclusions: The Role of Public Policy

• Not just globalisation

• Progressive taxation

• Privatisation and pay policy

• A Return of Incomes Policy?