Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/zbw/bamber/166.html
   My bibliography  Save this paper

How wealthy are the rich?

Author

Listed:
  • Schulz, Jan
  • Milaković, Mishael
Abstract
Underreporting and undersampling biases in top tail wealth, although widely acknowledged, have not been statistically quantified so far, essentially because they are not readily observable. Here we exploit the functional form of power law-like regimes in top tail wealth to derive analytical expressions for these biases, and employ German microdata from a popular survey and rich list to illustrate that tiny differences in non-response rates lead to tail wealth estimates that differ by an order of magnitude, in our case ranging from one to nine trillion euros. Underreporting seriously compounds the problem, and we find that the estimation of totals in scale-free systems oftentimes tends to be spurious. Our findings also suggest that recent debates on the existence of scale- or type-dependence in returns to wealth are ill-posed because the available data cannot discriminate between scale- or typedependence on the one hand, and statistical biases on the other. Yet both economic theory and mathematical formalism indicate that sampling and reporting biases are more plausible explanations for the observed data than scale- or type-dependence.

Suggested Citation

  • Schulz, Jan & Milaković, Mishael, 2020. "How wealthy are the rich?," BERG Working Paper Series 166, Bamberg University, Bamberg Economic Research Group.
    • Handle: RePEc:zbw:bamber:166
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/229178/1/1744583684.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Moshe Levy & Haim Levy, 2003. "Investment Talent and the Pareto Wealth Distribution: Theoretical and Experimental Analysis," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 709-725, August.
    2. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    3. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
    4. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    5. Sinha, Sitabhra, 2006. "Evidence for power-law tail of the wealth distribution in India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 555-562.
    6. Erzo G. J. Luttmer, 2010. "Models of firm heterogeneity and growth," Working Papers 678, Federal Reserve Bank of Minneapolis.
    7. Per Krusell & Anthony Smith & Joachim Hubmer, 2015. "The historical evolution of the wealth distribution: A quantitative-theoretic investigation," 2015 Meeting Papers 1406, Society for Economic Dynamics.
    8. Annette Alstadsæter & Niels Johannesen & Gabriel Zucman, 2019. "Tax Evasion and Inequality," American Economic Review, American Economic Association, vol. 109(6), pages 2073-2103, June.
    9. Drăgulescu, Adrian & Yakovenko, Victor M., 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 213-221.
    10. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    11. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-172, March.
    12. King, Mervyn A. & Leape, Jonathan I., 1998. "Wealth and portfolio composition: Theory and evidence," Journal of Public Economics, Elsevier, vol. 69(2), pages 155-193, June.
    13. Hui Guo & Robert F. Whitelaw, 2006. "Uncovering the Risk–Return Relation in the Stock Market," Journal of Finance, American Finance Association, vol. 61(3), pages 1433-1463, June.
    14. Castaldi, Carolina & Milakovic, Mishael, 2007. "Turnover activity in wealth portfolios," Journal of Economic Behavior & Organization, Elsevier, vol. 63(3), pages 537-552, July.
    15. Brzezinski, Michal, 2014. "Do wealth distributions follow power laws? Evidence from ‘rich lists’," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 155-162.
    16. Piketty, Thomas & Zucman, Gabriel, 2014. "Wealth and Inheritance in the Long Run," CEPR Discussion Papers 10072, C.E.P.R. Discussion Papers.
    17. Laurent E. Calvet & Paolo Sodini, 2014. "Twin Picks: Disentangling the Determinants of Risk-Taking in Household Portfolios," Journal of Finance, American Finance Association, vol. 69(2), pages 867-906, April.
    18. Blank, Aharon & Solomon, Sorin, 2000. "Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 279-288.
    19. Tullio Jappelli & Luigi Pistaferri, 2014. "Fiscal Policy and MPC Heterogeneity," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(4), pages 107-136, October.
    20. Joachim R. Frick & Markus M. Grabka & Jan Marcus, 2007. "Editing and Multiple Imputation of Item-Non-Response in the 2002 Wealth Module of the German Socio-Economic Panel (SOEP)," Data Documentation 18, DIW Berlin, German Institute for Economic Research.
    21. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    22. Charles I. Jones & Jihee Kim, 2018. "A Schumpeterian Model of Top Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 1785-1826.
    23. Cowell, Frank, 2011. "Inequality among the wealthy," LSE Research Online Documents on Economics 43897, London School of Economics and Political Science, LSE Library.
    24. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    25. Erzo Luttmer, 2017. "Slow Convergence in Economies with Organization Capital," 2017 Meeting Papers 1117, Society for Economic Dynamics.
    26. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    27. Bach, Stefan & Thiemann, Andreas & Zucco, Aline, 2019. "Looking for the missing rich: tracing the top tail of the wealth distribution," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 26(6), pages 1234-1258.
    28. Philip Vermeulen, 2016. "Estimating the Top Tail of the Wealth Distribution," American Economic Review, American Economic Association, vol. 106(5), pages 646-650, May.
    29. repec:bla:jfinan:v:58:y:2003:i:3:p:975-1008 is not listed on IDEAS
    30. Erzo G. J. Luttmer, 2011. "On the Mechanics of Firm Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(3), pages 1042-1068.
    31. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    32. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    33. Nirei, Makoto & 楡井, 誠, 2009. "Pareto Distributions in Economic Growth Models," IIR Working Paper 09-05, Institute of Innovation Research, Hitotsubashi University.
    34. Arthur B. Kennickell & R. Louise Woodburn, 1999. "CONSISTENT WEIGHT DESIGN FOR THE 1989, 1992 AND 1995 SCFs, AND THE DISTRIBUTION OF WEALTH," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 45(2), pages 193-215, June.
    35. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    36. Philip Vermeulen, 2018. "How Fat is the Top Tail of the Wealth Distribution?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(2), pages 357-387, June.
    37. repec:cep:sticas:/150 is not listed on IDEAS
    38. Levy, Shiki, 1998. "Wealthy People and Fat Tails: An Explanation for the Lévy Distribution of Stock Returns," University of California at Los Angeles, Anderson Graduate School of Management qt5zf0f3tg, Anderson Graduate School of Management, UCLA.
    39. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    40. Davies, James B. & Shorrocks, Anthony F., 2000. "The distribution of wealth," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 11, pages 605-675, Elsevier.
    41. Karen E. Dynan & Jonathan Skinner & Stephen P. Zeldes, 2004. "Do the Rich Save More?," Journal of Political Economy, University of Chicago Press, vol. 112(2), pages 397-444, April.
    42. Coelho, Ricardo & Néda, Zoltán & Ramasco, José J. & Augusta Santos, Maria, 2005. "A family-network model for wealth distribution in societies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 515-528.
    43. Jess Benhabib & Alberto Bisin, 2018. "Skewed Wealth Distributions: Theory and Empirics," Journal of Economic Literature, American Economic Association, vol. 56(4), pages 1261-1291, December.
    44. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
    45. Jessica A. Wachter & Motohiro Yogo, 2010. "Why Do Household Portfolio Shares Rise in Wealth?," The Review of Financial Studies, Society for Financial Studies, vol. 23(11), pages 3929-3965, November.
    46. Vincenzo Quadrini, 1999. "The Importance Of Entrepreneurship For Wealth Concentration And Mobility," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 45(1), pages 1-19, March.
    47. Carsten Schröder & Charlotte Bartels & Konstantin Göbler & Markus M. Grabka & Johannes König, 2020. "MillionärInnen unter dem Mikroskop: Datenlücke bei sehr hohen Vermögen geschlossen – Konzentration höher als bisher ausgewiesen," DIW Wochenbericht, DIW Berlin, German Institute for Economic Research, vol. 87(29), pages 511-521.
    48. James K. Galbraith, 2019. "Sparse, Inconsistent and Unreliable: Tax Records and the World Inequality Report 2018," Development and Change, International Institute of Social Studies, vol. 50(2), pages 329-346, March.
    49. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    50. Levy, Moshe & Solomon, Sorin, 1997. "New evidence for the power-law distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 90-94.
    51. Paul Eckerstorfer & Johannes Halak & Jakob Kapeller & Bernhard Schütz & Florian Springholz & Rafael Wildauer, 2016. "Correcting for the Missing Rich: An Application to Wealth Survey Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(4), pages 605-627, December.
    52. Stefan Bach & Martin Beznoska & Viktor Steiner, 2011. "A Wealth Tax on the Rich to Bring down Public Debt?: Revenue and Distributional Effects of a Capital Levy," SOEPpapers on Multidisciplinary Panel Data Research 397, DIW Berlin, The German Socio-Economic Panel (SOEP).
    53. Erzo G.J. Luttmer, 2010. "Models of Growth and Firm Heterogeneity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 547-576, September.
    54. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    55. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    56. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    57. Lin Peng & Turan G. Bali, 2006. "Is there a risk-return trade-off? Evidence from high-frequency data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1169-1198.
    58. Levy, Moshe, 2003. "Are rich people smarter?," Journal of Economic Theory, Elsevier, vol. 110(1), pages 42-64, May.
    59. González, Mariano & Nave, Juan & Rubio, Gonzalo, 2012. "The Cross Section of Expected Returns with MIDAS Betas," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(1), pages 115-135, February.
    60. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    61. H. Schneeweiss & J. Komlos & A. Ahmad, 2010. "Symmetric and asymmetric rounding: a review and some new results," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 247-271, September.
    62. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    63. Amit Goyal & Pedro Santa‐Clara, 2003. "Idiosyncratic Risk Matters!," Journal of Finance, American Finance Association, vol. 58(3), pages 975-1007, June.
    64. Shuhei Aoki & Makoto Nirei, 2016. "Pareto Distribution of Income in Neoclassical Growth Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 25-42, April.
    65. Marc-Michael H. Bergfeld & Felix-Michael Weber, 2011. "Dynasties of innovation: highly performing German family firms and the owners' role for innovation," International Journal of Entrepreneurship and Innovation Management, Inderscience Enterprises Ltd, vol. 13(1), pages 80-94.
    66. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    67. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    68. Sule Alan & Kadir Atalay & Thomas F. Crossley, 2015. "Do the Rich Save More? Evidence from Canada," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(4), pages 739-758, December.
    69. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Savin, Ivan & Mundt, Philipp, 2022. "Drivers of productivity change in global value chains: Reallocation vs. innovation," Economics Letters, Elsevier, vol. 220(C).
    2. Sahm, Marco, 2022. "Optimal accuracy of unbiased Tullock contests with two heterogeneous players," BERG Working Paper Series 175, Bamberg University, Bamberg Economic Research Group.
    3. Daske, Thomas & March, Christoph, 2024. "Efficient incentives with social preferences," Theoretical Economics, Econometric Society, vol. 19(3), July.
    4. Mundt, Philipp & Cantner, Uwe & Inoue, Hiroyasu & Savin, Ivan & Vannuccini, Simone, 2021. "Market selection in global value chains," BERG Working Paper Series 170, Bamberg University, Bamberg Economic Research Group.
    5. Schulz, Jan & Mayerhoffer, Daniel M., 2021. "A network approach to consumption," BERG Working Paper Series 173, Bamberg University, Bamberg Economic Research Group.
    6. Schmitt, Sefanie Y. & Bruckner, Dominik, 2022. "Unaware consumers and disclosure of deficiencies," BERG Working Paper Series 178, Bamberg University, Bamberg Economic Research Group.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jennie Bai & Turan G. Bali & Quan Wen, 2019. "Is There a Risk-Return Tradeoff in the Corporate Bond Market? Time-Series and Cross-Sectional Evidence," NBER Working Papers 25995, National Bureau of Economic Research, Inc.
    2. Shuhei Aoki & Makoto Nirei, 2014. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S," Working Papers e074, Tokyo Center for Economic Research.
    3. Bali, Turan G. & Cakici, Nusret & Chabi-Yo, Fousseni, 2015. "A new approach to measuring riskiness in the equity market: Implications for the risk premium," Journal of Banking & Finance, Elsevier, vol. 57(C), pages 101-117.
    4. Bai, Jennie & Bali, Turan G. & Wen, Quan, 2021. "Is there a risk-return tradeoff in the corporate bond market? Time-series and cross-sectional evidence," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1017-1037.
    5. Turan Bali & Kamil Yilmaz, 2009. "The Intertemporal Relation between Expected Return and Risk on Currency," Koç University-TUSIAD Economic Research Forum Working Papers 0909, Koc University-TUSIAD Economic Research Forum, revised Nov 2009.
    6. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
    7. Juan Carlos Escanciano & Juan Carlos Pardo-Fernández & Ingrid Van Keilegom, 2017. "Semiparametric Estimation of Risk–Return Relationships," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 40-52, January.
    8. Osman Kilic & Joseph M. Marks & Kiseok Nam, 2022. "Predictable asset price dynamics, risk-return tradeoff, and investor behavior," Review of Quantitative Finance and Accounting, Springer, vol. 59(2), pages 749-791, August.
    9. Symitsi, Efthymia & Symeonidis, Lazaros & Kourtis, Apostolos & Markellos, Raphael, 2018. "Covariance forecasting in equity markets," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 153-168.
    10. Keunbae Ahn, 2021. "Predictable Fluctuations in the Cross-Section and Time-Series of Asset Prices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2021, January-A.
    11. Thomas C. Chiang & Jiandong Li, 2012. "Stock Returns and Risk: Evidence from Quantile," JRFM, MDPI, vol. 5(1), pages 1-39, December.
    12. Wang, Wenzhao & Duxbury, Darren, 2021. "Institutional investor sentiment and the mean-variance relationship: Global evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 415-441.
    13. Bali, Turan G. & Engle, Robert F., 2010. "The intertemporal capital asset pricing model with dynamic conditional correlations," Journal of Monetary Economics, Elsevier, vol. 57(4), pages 377-390, May.
    14. Wang, Wenzhao, 2018. "Investor sentiment and the mean-variance relationship: European evidence," Research in International Business and Finance, Elsevier, vol. 46(C), pages 227-239.
    15. Kim, Eung-Bin & Byun, Suk-Joon, 2021. "Risk, ambiguity, and equity premium: International evidence," International Review of Economics & Finance, Elsevier, vol. 76(C), pages 321-335.
    16. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    17. Dan Cao & Wenlan Luo, 2017. "Persistent Heterogeneous Returns and Top End Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 301-326, October.
    18. Ľuboš Pástor & Meenakshi Sinha & Bhaskaran Swaminathan, 2008. "Estimating the Intertemporal Risk–Return Tradeoff Using the Implied Cost of Capital," Journal of Finance, American Finance Association, vol. 63(6), pages 2859-2897, December.
    19. Jia, Yun & Yang, Chunpeng, 2017. "Disagreement and the risk-return relation," Economic Modelling, Elsevier, vol. 64(C), pages 97-104.
    20. Chiang, Thomas C. & Li, Huimin & Zheng, Dazhi, 2015. "The intertemporal risk-return relationship: Evidence from international markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 39(C), pages 156-180.

    More about this item

    Keywords

    Wealth inequality; stochastic growth; differential non-response; Hill estimator; tail index bias;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:bamber:166. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/bebamde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.