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

1. Trevor Swan Distinguished Lecture February 2007 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

2. 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 • 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

4. Growth and Distribution In 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

5. 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.

7. 1. Framework for Analysis • 2. Empirical Evidence for a Selection of OECD Countries • Incomes • Earnings • Wealth • 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.

8. 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.

9. NL FRA DEU CH

10. 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)

12. Decomposition: WEALTH

14. Putting them together for the UK UK

15. UK Other income

16. 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

17. 1. Framework for Analysis • Empirical Evidence for a Selection of OECD Countries • 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

18. Linking Theory and Evidence • Models of Individual Incomes Micro-data Independent • Models of Distributions Moments Percentiles or percentile shares Summary measures (Gini) Pareto coefficient

19. 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. CAMBRIDGE Accumulation Model (Pasinetti / Meade / Stiglitz)

20. 1/alpha LHS scale (1-t) RHS scale

21. 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?

22. Log (Earnings/median) 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 Log [1/(1 – F)]

23. 7.2 Managerial Hierarchy Model (Lydall and Simon) β= loge[span of managerial control] divided by loge[1+ increment with promotion ] 25% increment span 5

24. Log (Earnings/median) 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 Log [1/(1 – F)]

25. Conclusions: The Role of Public Policy • Not just globalisation • Progressive taxation • Privatisation and pay policy • A Return of Incomes Policy?