A Note on the Size Distribution of Consumption: More Double Pareto than Lognormal

Toda, Alexis Akira (2015): A Note on the Size Distribution of Consumption: More Double Pareto than Lognormal. Forthcoming in: Macroeconomic Dynamics

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Gibrat's law, multiplicative idiosyncratic risk, inequality, power law
• Subjects: D - Microeconomics > D3 - Distribution > D31 - Personal Income, Wealth, and Their Distributions; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Yann Algan, Olivier Allais, and Wouter J. Den Haan. Solving heterogeneous-agent models with parameterized cross-sectional distributions. Journal of Economic Dynamics and Control, 32(3):875-908, March 2008.

Theodore W. Anderson and Donald A. Darling. Asymptotic theory of certain 'goodness of fit' criteria based on stochastic processes. Annals of Mathematical Statistics, 23(2):193-212, 1952.

Pierluigi Balduzzi and Tong Yao. Testing heterogeneous-agent models: An alternative aggregation approach. Journal of Monetary Economics, 54(2):369-412, March 2007.

James Banks, Richard Blundell, and Arthur Lewbel. Quadratic Engel curves and consumer demand. Review of Economics and Statistics, 79(4):527-539, November 1997.

Erich Battistin, Richard Blundell, and Arthur Lewbel. Why is consumption more log normal than income? Gibrat's law revisited. Journal of Political Economy, 117(6):1140-1154, December 2009.

Jess Benhabib, Alberto Bisin, and Shenghao Zhu. The distribution of wealth in the Blanchard-Yaari model. Macroeconomic Dynamics, 20:466-481, March 2016.

George M. Constantinides and Darrell Duffie. Asset pricing with heterogeneous consumers. Journal of Political Economy, 104(2):219-240, April 1996.

Xavier Gabaix. Zipf's law for cities: An explanation. Quarterly Journal of Economics, 114(3):739-767, 1999.

Xavier Gabaix. Power laws in economics and finance. Annual Review of Economics, 1:255-293, 2009.

Cecilia Garcia-Penalosa and Stephen J. Turnovsky. Income inequality, mobility, and the accumulation of capital. Macroeconomic Dynamics, 19(6):1332-1357, September 2015.

Kristian Giesen, Arndt Zimmermann, and Jens Suedekum. The size distribution across all cities-double Pareto lognormal strikes. Journal of Urban Economics, 68(2):129-137, September 2010.

Gholamreza Hajargasht and William E. Griffiths. Pareto-lognormal distributions: Inequality, poverty, and estimation from grouped income data. Economic Modelling, 33:593-604, July 2013.

Charles I. Jones. Pareto and Piketty: The macroeconomics of top income and wealth inequality. Journal of Economic Perspectives, 29(1):29-46, Winter 2015.

Samuel Kotz, Tomasz J. Kozubowski, and Krzysztof Podgorski. The Laplace Distribution and Generalizations. Birkhauser, Boston, 2001.

Takuma Kunieda, Keisuke Okada, and Akihisa Shibata. Finance and inequality: How does globalization change their relationship? Macroeconomic Dynamics, 18(5):1091-1128, July 2014.

Benoit Mandelbrot. Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29(4):517-543, October 1961.

Frank J. Massey, Jr. The Kolmogorov-Smirnov test for goodness of fit. Journal of the American Statistical Association, 46(253):68-78, 1951.

James B. McDonald. Some generalized functions for the size distribution of income. Econometrica, 52(3):647-663, May 1984.

Michael Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2):226-252, 2004.

William J. Reed. The Pareto, Zipf and other power laws. Economics Letters, 74(1):15-19, December 2001.

William J. Reed. On the rank-size distribution for human settlements. Journal of Regional Science, 42(1):1-17, February 2002.

William J. Reed. The Pareto law of incomes--an explanation and an extension. Physica A, 319(1):469-486, March 2003.

William J. Reed and Murray Jorgensen. The double Pareto-lognormal distribution--a new parametric model for size distribution. Communications in Statistics--Theory and Methods, 33(8):1733-1753, 2004.

Michael Reiter. Solving heterogeneous-agent models by projection and perturbation. Journal of Economic Dynamics and Control, 33(3):649-665, March 2009.

Alexis Akira Toda. The double power law in income distribution: Explanations and evidence. Journal of Economic Behavior and Organization, 84(1):364-381, September 2012.

Alexis Akira Toda. Incomplete market dynamics and cross-sectional distributions. Journal of Economic Theory, 154:310-348, November 2014.

Alexis Akira Toda and Kieran Walsh. The double power law in consumption and implications for testing Euler equations. Journal of Political Economy, 123(5):1177-1200, October 2015.

Thomas Winberry. Lumpy investment, business cycles, and stimulus policy. 2015.