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A Brief History of Generative Models for Power Law and Lognormal Distributions
 INTERNET MATHEMATICS
"... Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a a lognormal distribution. In trying ..."
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Cited by 250 (7 self)
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Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a a lognormal distribution. In trying
Zipf’s law for cities: An explanation
 Quart J Econ 1999
"... Zipf’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, ..."
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Cited by 63 (1 self)
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Zipf’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf’s law. I.
The Double ParetoLognormal Distribution  A New Parametric Model for Size Distributions
, 2003
"... A family of probability densities, which has proved useful in modelling the size distributions of various phenomena, including incomes and earnings, human settlement sizes, oilfield volumes and particle sizes, is introduced. ..."
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Cited by 35 (2 self)
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A family of probability densities, which has proved useful in modelling the size distributions of various phenomena, including incomes and earnings, human settlement sizes, oilfield volumes and particle sizes, is introduced.
The evolution of city size distributions
 in V. Henderson and J.F. Thisse, eds, ‘Handbook of Regional and Urban Economics
, 2004
"... We review the accumulated knowledge on city size distributions and determinants of urban growth. This topic is of interest because of a number of key stylized facts, including notably Zipf’s law for cities (which states that the number of cities of size greater than S is proportional to 1/S) and the ..."
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Cited by 29 (7 self)
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We review the accumulated knowledge on city size distributions and determinants of urban growth. This topic is of interest because of a number of key stylized facts, including notably Zipf’s law for cities (which states that the number of cities of size greater than S is proportional to 1/S) and the importance of urban primacy. We first review the empirical evidence on the upper tail of city size distribution. We offer a novel discussion of the important econometric issues in the characterization of the distribution. We then discuss the theories that have been advanced to explain the approximate constancy of the distribution across very different economic and social systems, emphasizing both barebone statistical theories and more developed economic theories. We discuss the more recent work on the determinants of urban growth and, in particular, growth regressions, economic explanations of city size distributions other than Gibrat’s law, consequences of major
The emergence of hierarchy in transportation networks
 Annals of Regional Science
, 2005
"... A transportation network is a complex system that exhibits the properties of selforganization and emergence. Previous research in dynamics related to transportation networks focuses on traffic assignment or traffic management. This research concentrates on the dynamics of the orientation of major ro ..."
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Cited by 25 (16 self)
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A transportation network is a complex system that exhibits the properties of selforganization and emergence. Previous research in dynamics related to transportation networks focuses on traffic assignment or traffic management. This research concentrates on the dynamics of the orientation of major roads in a network and abstractly models these dynamics to understand the basic properties of transportation networks. A model is developed to capture the dynamics that leads to a hierarchical arrangement of roads for a given network structure and land use distribution. Localized investment rules – revenue produced by traffic on a link is invested for that link’s own development – are employed. Under reasonable parameters, these investment rules, coupled with traveler behavior, and underlying network topology result in the emergence of a hierarchical pattern. Hypothetical networks subject to certain conditions are tested with this model to explore the network properties. Though hierarchies seem to be designed by planners and engineers, the results show that they are intrinsic properties of networks. Also, the results show that roads, specific routes with continuous attributes, are emergent properties of transportation networks.
Persistent Inequality
 REVIEW OF ECONOMIC STUDIES
, 2003
"... When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state. This is true irrespective of the degree of divisibility in investments. However, divisibility ( ..."
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Cited by 25 (6 self)
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When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state. This is true irrespective of the degree of divisibility in investments. However, divisibility (or fineness of occupational structure) has implications for both the multiplicity and Paretoefficiency of steady states. Indivisibilities generate a continuum of inefficient and efficient steady states with varying per capita income. On the other hand, perfect divisibility typically implies the existence of a unique steady state distribution which is Paretoefficient.
The Virtues and Vices of Equilibrium and the future of financial economics
, 2009
"... The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we p ..."
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Cited by 13 (1 self)
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The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, and should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out,i.e.,where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models.We sketch some alternative approaches and discuss why they should play an important role in
The Distribution of Wealth and Redistributive Policies, unpublished working paper NYU
, 2006
"... We study the dynamics of the distribution of wealth in an Overlapping Generation economy with bequest and various forms of redistributive taxation. We characterize the transitional dynamics of the wealth distribution and as well as the stationary distribution. We show that the stationary wealth dist ..."
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Cited by 9 (0 self)
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We study the dynamics of the distribution of wealth in an Overlapping Generation economy with bequest and various forms of redistributive taxation. We characterize the transitional dynamics of the wealth distribution and as well as the stationary distribution. We show that the stationary wealth distribution is a Pareto distribution. Wealth is less concentrated (the Gini coefficient is lower) for both higher capital income taxes and estate taxes, but the marginal effect of capital income taxes is much stronger than the effect of estate taxes. Finally, we characterize optimal redistributive taxes with respect to a utilitarian social welfare measure. Social welfare is maximized short of minimal wealth inequality and with zero estate taxes.
Emergent statistical wealth distributions in simple monetary exchange models: A critical review
 in Econophysics of Wealth Distribution
, 2005
"... Abstract: This paper reviews recent attempts at modelling inequality of wealth as an emergent phenomenon of interactingagent processes. We point out that recent models of wealth condensation which draw their inspiration from molecular dynamics have, in fact, reinvented a process introduced quite so ..."
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Cited by 9 (2 self)
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Abstract: This paper reviews recent attempts at modelling inequality of wealth as an emergent phenomenon of interactingagent processes. We point out that recent models of wealth condensation which draw their inspiration from molecular dynamics have, in fact, reinvented a process introduced quite some time ago by Angle (1986) in the sociological literature. We emphasize some problematic aspects of simple wealth exchange models and contrast them with a monetary model based on economic principles of market mediated exchange. The paper also reports new results on the influence of market power on the wealth distribution in statistical equilibrium. As it turns out, inequality increases but market power alone is not sufficient for changing the exponential tails of simple exchange models into Pareto tails. 1
On the Distribution of City Sizes
, 2003
"... The city size distribution of many countries is remarkably well approximated by a Pareto distribution. We study what constraints this regularity imposes on standard urban models. We find that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto distribution fo ..."
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Cited by 8 (0 self)
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The city size distribution of many countries is remarkably well approximated by a Pareto distribution. We study what constraints this regularity imposes on standard urban models. We find that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto distribution for the underlying source of randomness. In particular, one of the following combinations can induce a Pareto distribution of city sizes: (i) preferences for different goods follow reflected random walks, and the elasticity of substitution between goods is 1; or (ii) total factor productivities in the production of different goods follow reflected random walks, and increasing returns are equal across goods.