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A NOTE ON THE SIZE DISTRIBUTION OF CONSUMPTION: MORE DOUBLE PARETO THAN LOGNORMAL

Published online by Cambridge University Press:  14 September 2016

Alexis Akira Toda
Alexis Akira Toda*
Affiliation:
University of California, San Diego
*
Address correspondence to: Alexis Akira Toda, Department of Economics, University of California, San Diego. 9500 Gilman Drive, La Jolla, CA 92093-0508, USA; e-mail: atoda@ucsd.edu.
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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.

Keywords

Gibrat's LawMultiplicative Idiosyncratic RiskInequalityPower Law
Type
Notes
Information
Macroeconomic Dynamics , Volume 21 , Issue 6 , September 2017 , pp. 1508 - 1518
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

I thank Kieran Walsh for collaboration and discussions, and Thomas Winberry, the associate editor, and two anonymous referees for comments and feedback that significantly improved the paper.

References

REFERENCES

Algan, Yann, Allais, Olivier, and Den Haan, Wouter J. (2008) Solving heterogeneous-agent models with parameterized cross-sectional distributions. Journal of Economic Dynamics and Control 32 (3), 875–908.Google Scholar
Anderson, Theodore W. and Darling, Donald A. (1952) Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Annals of Mathematical Statistics 23 (2), 193–212.Google Scholar
Balduzzi, Pierluigi and Yao, Tong (2007) Testing heterogeneous-agent models: An alternative aggregation approach. Journal of Monetary Economics 54 (2): 369–412.Google Scholar
Banks, James, Blundell, Richard, and Lewbel, Arthur (1997) Quadratic Engel curves and consumer demand. Review of Economics and Statistics 79 (4), 527–539.Google Scholar
Battistin, Erich, Blundell, Richard, and Lewbel, Arthur (2009) Why is consumption more log normal than income? Gibrat's law revisited. Journal of Political Economy 117 (6), 1140–1154.CrossRefGoogle Scholar
Benhabib, Jess, Bisin, Alberto, and Zhu, Shenghao (2016) The distribution of wealth in the Blanchard-Yaari model. Macroeconomic Dynamics 20, 466–481.CrossRefGoogle Scholar
Constantinides, George M. and Duffie, Darrell (1996) Asset pricing with heterogeneous consumers. Journal of Political Economy 104 (2), 219–240.Google Scholar
Gabaix, Xavier (1999) Zipf's law for cities: An explanation. Quarterly Journal of Economics 114 (3), 739–767.Google Scholar
Gabaix, Xavier (2009) Power laws in economics and finance. Annual Review of Economics 1, 255–293.Google Scholar
García-Peñalosa, Cecilia and Turnovsky, Stephen J. (2015) Income inequality, mobility, and the accumulation of capital. Macroeconomic Dynamics 19 (6), 1332–1357.Google Scholar
Giesen, Kristian, Zimmermann, Arndt, and Suedekum, Jens (2010) The size distribution across all cities–-Double Pareto lognormal strikes. Journal of Urban Economics 68 (2), 129–137.Google Scholar
Hajargasht, Gholamreza and Griffiths, William E. (2013) Pareto-lognormal distributions: Inequality, poverty, and estimation from grouped income data. Economic Modelling 33, 593–604.Google Scholar
Jones, Charles I. (2015) Pareto and Piketty: The macroeconomics of top income and wealth inequality. Journal of Economic Perspectives 29 (1), 29–46.Google Scholar
Kotz, Samuel, Kozubowski, Tomasz J., and Podgórski, Krzysztof (2001) The Laplace Distribution and Generalizations. Boston: Birkhäuser.Google Scholar
Kunieda, Takuma, Okada, Keisuke, and Shibata, Akihisa (2014) Finance and inequality: How does globalization change their relationship? Macroeconomic Dynamics 18 (5), 1091–1128.Google Scholar
Mandelbrot, Benoît (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica 29 (4), 517–543.Google Scholar
Massey, Frank J. Jr., (1951) The Kolmogorov–Smirnov test for goodness of fit. Journal of the American Statistical Association 46 (253), 68–78.CrossRefGoogle Scholar
McDonald, James B. (1984) Some generalized functions for the size distribution of income. Econometrica 52 (3), 647–663.Google Scholar
Mitzenmacher, Michael (2003) A brief history of generative models for power law and lognormal distributions. Internet Mathematics 1 (2), 226–252.Google Scholar
Reed, William J. (2001) The Pareto, Zipf and other power laws. Economics Letters 74 (1), 15–19.Google Scholar
Reed, William J. (2002) On the rank–size distribution for human settlements. Journal of Regional Science 42 (1), 1–17.Google Scholar
Reed, William J. (2003) The Pareto law of incomes–-An explanation and an extension. Physica A 319 (1), 469–486.Google Scholar
Reed, William J. and Jorgensen, Murray (2004) The double Pareto-lognormal distribution–-A new parametric model for size distribution. Communications in Statistics–-Theory and Methods 33 (8), 1733–1753.Google Scholar
Reiter, Michael (2009) Solving heterogeneous-agent models by projection and perturbation. Journal of Economic Dynamics and Control 33 (3), 649–665.Google Scholar
Toda, Alexis Akira (2012) The double power law in income distribution: Explanations and evidence. Journal of Economic Behavior and Organization 84 (1), 364–381.Google Scholar
Toda, Alexis Akira (2014) Incomplete market dynamics and cross-sectional distributions. Journal of Economic Theory 154, 310–348.Google Scholar
Toda, Alexis Akira and Walsh, Kieran (2015) The double power law in consumption and implications for testing Euler equations. Journal of Political Economy 123 (5), 1177–1200.Google Scholar
Winberry, Thomas (2015) Lumpy Investment, Business Cycles, and Stimulus Policy. Job market paper, University of Chicago Booth School of Business.Google Scholar