IDEAS home Printed from https://ideas.repec.org/a/cup/macdyn/v21y2017i06p1508-1518_00.html
   My bibliography  Save this article

A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal

Author

Listed:
  • Toda, Alexis Akira

Abstract

The cross-sectional distribution of consumption is commonly approximated by the lognormal distribution. This note shows that consumption is better described by the double Pareto-lognormal distribution (dPlN), which has a lognormal body with two Pareto tails and arises as the stationary distribution in recently proposed dynamic general equilibrium models. dPlN outperforms other parametric distributions and is often not rejected by goodness-of-fit tests. The analytical tractability and parsimony of dPlN may be convenient for various economic applications.

Suggested Citation

  • Toda, Alexis Akira, 2017. "A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1508-1518, September.
    • Handle: RePEc:cup:macdyn:v:21:y:2017:i:06:p:1508-1518_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S1365100515000942/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    2. Balduzzi, Pierluigi & Yao, Tong, 2007. "Testing heterogeneous-agent models: an alternative aggregation approach," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 369-412, March.
    3. Algan, Yann & Allais, Olivier & Den Haan, Wouter J., 2008. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 875-908, March.
    4. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2016. "The Distribution Of Wealth In The Blanchard–Yaari Model," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 466-481, March.
    5. Kunieda, Takuma & Okada, Keisuke & Shibata, Akihisa, 2014. "Finance And Inequality: How Does Globalization Change Their Relationship?," Macroeconomic Dynamics, Cambridge University Press, vol. 18(5), pages 1091-1128, July.
    6. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    7. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    8. Erich Battistin & Richard Blundell & Arthur Lewbel, 2009. "Why Is Consumption More Log Normal than Income? Gibrat's Law Revisited," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1140-1154, December.
    9. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    10. repec:hal:spmain:info:hdl:2441/41rhqgovpp8hnq9i7ndtl26ltm is not listed on IDEAS
    11. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
    12. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    13. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
    14. Charles I. Jones, 2015. "Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 29-46, Winter.
    15. García-Peñalosa, Cecilia & Turnovsky, Stephen J., 2015. "Income Inequality, Mobility, And The Accumulation Of Capital," Macroeconomic Dynamics, Cambridge University Press, vol. 19(6), pages 1332-1357, September.
    16. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    17. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    18. Hajargasht, Gholamreza & Griffiths, William E., 2013. "Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data," Economic Modelling, Elsevier, vol. 33(C), pages 593-604.
    19. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    20. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    21. 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.
    22. William J. Reed, 2002. "On the Rank‐Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17, February.
    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. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2017. "Optimal Tax Progressivity: An Analytical Framework," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1693-1754.
    2. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    3. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & AL-Dhurafi, Nasr Ahmed, 2020. "The power-law distribution for the income of poor households," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    4. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    5. Schulz, Jan & Mayerhoffer, Daniel M., 2021. "A network approach to consumption," BERG Working Paper Series 173, Bamberg University, Bamberg Economic Research Group.
    6. Masato Okamoto, 2022. "Lorenz and Polarization Orderings of the Double-Pareto Lognormal Distribution and Other Size Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 548-574, November.
    7. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    8. Toda, Alexis Akira, 2016. "Zipf's Law: A Microfoundation," MPRA Paper 78985, University Library of Munich, Germany.
    9. Wang, Frank Xuyan, 2021. "Shape factor asymptotic analysis II," MPRA Paper 110827, University Library of Munich, Germany.
    10. Brendan K. Beare & Alexis Akira Toda, 2022. "Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes," Econometrica, Econometric Society, vol. 90(4), pages 1811-1833, July.
    11. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2023. "Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain," Papers 2301.09438, arXiv.org.
    12. Mundt, Philipp & Alfarano, Simone & Milaković, Mishael, 2020. "Exploiting ergodicity in forecasts of corporate profitability," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    13. Akhundjanov, Sherzod B. & Devadoss, Stephen & Luckstead, Jeff, 2017. "Size distribution of national CO2 emissions," Energy Economics, Elsevier, vol. 66(C), pages 182-193.
    14. Alexis Akira Toda & Yulong Wang, 2021. "Efficient minimum distance estimation of Pareto exponent from top income shares," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 228-243, March.
    15. William Griffiths & Duangkamon Chotikapanich & Gholamreza Hajargasht, 2022. "A note on inequality measures for mixtures of double Pareto–lognormal distributions," Australian Economic Papers, Wiley Blackwell, vol. 61(2), pages 280-290, June.
    16. Staley, Mark, 2018. "The Knowledge-Diffusion Bottleneck in Economic Growth and Development," MPRA Paper 87255, University Library of Munich, Germany.
    17. Behzod B. Ahundjanov & Sherzod B. Akhundjanov & Botir B. Okhunjanov, 2022. "Power law in COVID‐19 cases in China," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 699-719, April.

    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. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    2. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    3. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    4. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
    5. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    6. Alexis Akira Toda & Yulong Wang, 2021. "Efficient minimum distance estimation of Pareto exponent from top income shares," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 228-243, March.
    7. Behzod B. Ahundjanov & Sherzod B. Akhundjanov & Botir B. Okhunjanov, 2022. "Power law in COVID‐19 cases in China," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 699-719, April.
    8. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    9. Sherzod B. Akhundjanov & Alexis Akira Toda, 2020. "Is Gibrat’s “Economic Inequality” lognormal?," Empirical Economics, Springer, vol. 59(5), pages 2071-2091, November.
    10. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
    11. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    12. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    13. Arturo, Ramos, 2019. "Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century," MPRA Paper 93562, University Library of Munich, Germany.
    14. Arturo Ramos & Till Massing & Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno, 2023. "Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain," Papers 2301.09438, arXiv.org.
    15. Akhundjanov, Sherzod B. & Devadoss, Stephen & Luckstead, Jeff, 2017. "Size distribution of national CO2 emissions," Energy Economics, Elsevier, vol. 66(C), pages 182-193.
    16. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    17. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
    18. Ramos, Arturo, 2015. "Log-growth distributions of US city sizes and non-Lévy processes," MPRA Paper 66561, University Library of Munich, Germany.
    19. Brendan K. Beare & Alexis Akira Toda, 2022. "Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes," Econometrica, Econometric Society, vol. 90(4), pages 1811-1833, July.
    20. Shuhei Aoki & Makoto Nirei, 2014. "Zipf’s Law, Pareto’s Law, and the Evolution of Top Incomes in the U.S," UTokyo Price Project Working Paper Series 023, University of Tokyo, Graduate School of Economics.

    More about this item

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:cup:macdyn:v:21:y:2017:i:06:p:1508-1518_00. 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/mdy .

    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.