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in Germany, France, Spain, and Greece Global Economic Symposium, - - PowerPoint PPT Presentation

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Stefan Bach, Andreas Thiemann, Aline Zucco The Top Tail of the Wealth Distribution in Germany, France, Spain, and Greece Global Economic Symposium, 2015 Kiel, October 13, 2015 1 October 13, 2015 Andreas Thiemann Outline Background and

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October 13, 2015 Andreas Thiemann

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The Top Tail of the Wealth Distribution in Germany, France, Spain, and Greece

Stefan Bach, Andreas Thiemann, Aline Zucco

Global Economic Symposium, 2015 Kiel, October 13, 2015

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Outline

Background and motivation Data

HFCS Forbes and national rich lists

Estimation and imputation of the top wealth distribution Results for the adjusted top wealth concentration

Discussion Paper:

Stefan Bach, Andreas Thiemann, Aline Zucco: The Top Tail of the Wealth Distribution in Germany, France, Spain, and Greece. DIW Berlin Discussion Papers 1502, 2015.

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Background and motivation

Rising inequality in income and wealth, in particular at the top Poor information on the top tail of household wealth

Household surveys

  • German Socio-Economic Panel (SOEP), 2002, 2007, 2012
  • Household Finance and Consumption Survey (HFCS) 2009-11
  • Underrepresentation of top income and wealth

– Sampling error (“non observation bias“) – Selectivity (“non response bias“, “middle class bias“)

Administrative data

  • Wealth and estate taxation: Selectivity due to tax rules
  • Family owned firms, foundations, family offices: Non-disclosure

Rich lists of the big fortunes: Forbes World’s billionaires, national rich lists National and financial accounts: macro aggregates

Estimation of top wealth concentration in Germany, France, Spain, and Greece

Integration of HFCS and rich lists Estimation of Pareto distribution for the top tail

  • following Vermeulen (2014)

Imputation of the missing rich

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Pareto distribution

Good approximation of the top tail of income and wealth

Pareto (1896), Kuznetzs (1955), Piketty & Saez (2003)

Based on two parameters (Representation in appendix)

Minimum wealth and „Pareto-alpha“

Net Household Wealth (HFCS Definition)

Total household assets (excluding pension wealth)

  • Total outstanding household’s liabilities

= Household net wealth

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Conclusion

Top wealth concentration in Germany, France, Spain, and Greece

Underrepresentation in household surveys Integration of the big fortunes from rich lists

  • broader base of national rich lists compared with Forbes

Imputation of the missing rich by Pareto distribution

Adjustment substantially increases top wealth concentration

Top percentile share increases

  • from 24 to 33 percent in Germany
  • from 18 to 21 percent in France
  • from 15 to 17 percent in Spain
  • (from 8 to 12 percent in Greece)

National rich lists instead of Forbes increase top wealth concentration

  • especially in France and Spain

Research perspectives

Data quality: Surveys and rich lists Tax files from wealth taxes, estate taxes, financial statements of firms and foundations Microsimulation analyses of wealth taxation Distribution analyses of household wealth and income

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Thank You for Your Attention!

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Back-up slides

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Pareto distribution

Idea and representation

Top wealth distribution follows a power-law function

  • for any wealth wi that exceeds a threshold wmin, specified by the Pareto coefficient α

Density function 𝑔 𝑥𝑗 =

𝛽𝑥𝑛𝑗𝑜

𝛽

𝑥𝑗

𝛽+1 𝑗𝑔 𝑥𝑗 ≥ 𝑥𝑛𝑗𝑜

0 𝑗𝑔 𝑥𝑗 < 𝑥𝑛𝑗𝑜 (1) Distribution function 𝑄 𝑋 ≤ 𝑥𝑗 = 𝐺 𝑥𝑗 = 𝑔 𝑢 𝑒𝑢 = 1 − (

𝑥𝑛𝑗𝑜 𝑥𝑗 )𝛽 𝑥 𝑥𝑛𝑗𝑜

; ∀ 𝑥𝑗 ≥ 𝑥𝑛𝑗𝑜 (2) Complementary cumulative distribution function (ccdf) 𝑄 𝑋 > 𝑥𝑗 = 1 − 𝑄 𝑋 ≤ 𝑥𝑗 = (

𝑥𝑛𝑗𝑜 𝑥𝑗 )𝛽; ∀ 𝑥𝑗≥ 𝑥𝑛𝑗𝑜

(3) Interpreted as ranking (“Zipf's law”, Zipf/zeta distribution)

𝑜 𝑥𝑗 𝑜

≅ (

𝑥𝑛𝑗𝑜 𝑥𝑗 )𝛽; ∀ 𝑥𝑗≥ 𝑥𝑛𝑗𝑜

(4) 𝑚𝑜

𝑜 𝑥𝑗 𝑜

= −𝛽 ln

𝑥𝑗 𝑥𝑛𝑗𝑜

(5)

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Pareto distribution: Density and distribution function, complementary cumulative distribution function (ccdf)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

f(x), F(x), 1 - F(x) Net wealth in million Euro

f(x) F(x) α = 1

α = 2

1 - F(x) (ccdf)

α = 2

α = 1

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