The Double Power Law in Consumption and Implications for Testing Euler Equations

Abstract

We provide evidence suggesting that the cross-sectional distributions of U.S. consumption and consumption growth obey the power law in both the upper and lower tails, with exponents approximately equal to 4. Consequently, high order moments are unlikely to exist, and the GMM estimation of Euler equations that employ cross-sectional moments may be inconsistent. Through bootstrap studies, we find that the power law appears to generate spurious non-rejection of heterogeneous-agent asset pricing models in explaining the equity premium. Dividing households into age groups, we propose an estimation approach which appears less susceptible to fat tail issues.

The Dynamics of Inequality

“…15 For instance, it is messy to define a reflecting barrier in the presence of jumps. 16 See, for example, Champernowne (1953), Simon (1955), Nirei (2009), Toda and Walsh (2015), Aoki and Nirei (2015), Kim (2015), Jones andKim (2014), andLuttmer (2015) for models with similar reduced forms. Some of these are derived from individual optimization, but others are not.…”

“…A large theoretical literature builds on random growth processes to theorize about the upper tails of income and wealth distributions. Early theories of the income distribution include Champernowne (1953) and Simon (1955), with more recent contributions by Nirei (2009), Toda and Walsh (2015), Kim (2015), Jones and Kim (2014), and Luttmer (2015). Similarly, random growth theories of the wealth distribution include Wold and Whittle (1957) and, more recently, Benhabib, Bisin, and Zhu (2011, Jones (2015), and Acemoglu and Robinson (2015).…”

Power Laws in Economics: An Introduction

“…Typically, the Pareto exponent is around 1.5 for wealth and between 1.5 and 3 for income (recall that a lower Pareto exponent means a higher degree of inequality in a distribution). Indeed, power laws and random growth processes are rapidly becoming a central tool to analyze inequalities of income and wealth (Piketty and Zucman 2014;Atkinson, Piketty, and Saez 2011;Benhabib, Bisin, and Zhu 2011;Lucas and Moll 2014;Gabaix, Lasry, Lions, and Moll 2015;Toda and Walsh 2015).…”

Fat tails and spurious estimation of consumption‐based asset pricing models

“…In a recent paper (Toda & Walsh, 2015), we document that the cross-sectional distributions of US household consumption and its growth rate exhibit fat tails. The power law exponent > 0 is approximately four both in the upper and lower tails.…”

“…As a remedy, Toda and Walsh (2015) propose an alternative estimation approach (age cohort GMM) that divides households into age groups in order to mitigate the fat-tail problem. This approach is motivated by the finding in 1 See Grossman and Shiller (1981), Hansen and Singleton (1983), Mehra and Prescott (1985), Grossman, Melino, and Shiller (1987), Kocherlakota (1997), and Savov (2011), among many others.…”