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

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  • 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.

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  • 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
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    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.
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    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.

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    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

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