The Pareto, Zipf and other power laws

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.

show abstract

“…The distribution (3.5) is known as the double Pareto distribution (Reed, 2001) and obeys the double power law with exponents (α, β).…”

Section: Theorymentioning

confidence: 99%

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

Toda

Walsh

2015

Journal of Political Economy

View full text Add to dashboard Cite

show abstract

“…However, a few brief points can be made. A popular explanation of the power-law tail of the income distribution is that it arises from an underlying stochastic multiplicative process, often thought to model the geometric growth of capital invested in financial markets [31,30,36,37,25,26,8]. The importance of financial markets in determining capital flows and hence capitalist income is undeniable.…”

Section: Phm ‡Ml Lognormalmentioning

confidence: 99%

The social architecture of capitalism

Wright¹

2005

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

A dynamic model of the social relations between workers and capitalists is introduced. The model is deduced from the assumption that the law of value is an organising principle of modern economies. The model self-organises into a dynamic equilibrium with statistical properties that are in close qualitative and in many cases quantitative agreement with a broad range of known empirical distributions of developed capitalism, including the power-law distribution of firm size, the Laplace distribution of firm and GDP growth, the lognormal distribution of firm demises, the exponential distribution of the duration of recessions, the lognormal-Pareto distribution of income, and the gamma-like distribution of the rate-of-profit of firms. Normally these distributions are studied in isolation, but this model unifies and connects them within a single causal framework. In addition, the model generates business cycle phenomena, including fluctuating wage and profit shares in national income about values consistent with empirical studies. A testable consequence of the model is a conjecture that the rate-of-profit distribution is consistent with a parameter-mix of a ratio of normal variates with means and variances that depend on a firm size parameter that is distributed according to a power-law.

show abstract

“…Nevertheless other PLs, such as double PLs also appear and are said to be a better fit in some cases [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Double power laws, fractals and self-similarity

Pinto

Lopes

Machado

2014

Applied Mathematical Modelling

View full text Add to dashboard Cite

a b s t r a c tPower law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems.In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

show abstract

The Pareto, Zipf and other power laws

Cited by 479 publications

References 6 publications

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

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

The social architecture of capitalism

Double power laws, fractals and self-similarity

Contact Info

Product

Resources

About