The Inequality Process vs. The Saved Wealth Model. Two Particle Systems of Income Distribution; Which Does Better Empirically?

The Inequality Process (IP) is a stochastic particle system in which particles are randomly paired for wealth exchange. A coin toss determines which particle loses wealth to the other in a randomly paired encounter. The loser gives up a fixed share of its wealth, a positive quantity. That share is its parameter, ω_ψ, in the ψth equivalence class of particles. The IP was derived from verbal social science theory that designates the empirical referent of (1-ω_ψ) as worker productivity, operationalized as worker education. Consequently, the stationary distribution of wealth of the IP in which particles can have different values of ω (like workers with different educations) is obliged to fit the distribution of labor income conditioned on education. The hypothesis is that when a) the stationary distribution of wealth in the ψth equivalence class of particles is fitted to the distribution of labor income of workers at the ψth level of education, and b) the fraction of particles in the ψth equivalence class equals the fraction of workers at the ψth level of education, then c) the model's stationary distributions fit the corresponding empirical distributions, and d) estimated (1-ω_ψ) increases with level of education. The Saved Wealth Model (SW) was proposed as a modification of the particle system model of the Kinetic Theory of Gases (KTG). The SW is isomorphic to the IP up to the stochastic driver of wealth exchange between particles. The present paper shows that 1) the stationary distributions of both particle systems pass test c): they fit the distribution of U.S. annual wage and salary income conditioned on education over four decades, 2) the parameter estimates of the fits differ by particle system, 3) both particle systems pass test d), but 4) the IP's overall fits are better than the SW's because 5) the IP's stationary distribution conditioned on larger (1-ω_ψ) has a heavier tail than the SW's fitting the distribution of wage income of the more educated better, and 6) since the level of education in the U.S. labor force rose, the IP's fit advantage increased over time.labor income distribution; goodness of fit; Inequality Process; particle system model; Saved Wealth Model

Not a Hollowing Out, a Stretching: Trends in U.S. Nonmetro Wage Income Distribution, 1961-2003

Much of the U.S. labor economics literature asserts that U.S. wage income inequality increased in the last half of the 20th century. These papers point to two trends: 1) the increasing dispersion in U.S. wage incomes, and 2) the rapid growth in the relative frequency of large wage incomes of fixed size in constant dollar terms. A subset of the labor economics literature interprets these trends as a hollowing out of the wage income distribution. A hollowing out would yield fewer middling wage incomes. Since nonmetro wage incomes have, historically, been smaller than metro wage incomes, a hollowing out might disproportionately displace nonmetro wage incomes into the left mode of the hollowed out distribution, that of small wage incomes. However, there was no hollowing out of the nonmetro wage income distribution between 1961 and 2003. While trends #1 and #2 exist in U.S. nonmetro wage income data, they are aspects of the stretching of the distribution of nonmetro wage incomes to the right over larger wage incomes as all its percentiles increased between 1961 and 2003. This stretching means that all nonmetro wage income percentiles increase simultaneously with greater proportional growth in the smaller percentiles. The literature focused on the greater absolute gains of the larger percentiles and took them as evidence of growing inequality. This paper shows for nonmetro wage incomes in the U.S. that those gains are but one aspect of the stretching of the distribution and that other aspects of this transformation might as easily be taken as evidence of growing equality.distribution dynamics; hollowed out distribution; inequality; nonmetropolitan; wage income; wage inequality

The particle system model of income and wealth more likely to imply an analogue of thermodynamics in social science

The Inequality Process (IP) and the Saved Wealth Model (SW) are particle system models of income distribution. The IP’s social science meta-theory requires its stationary distribution to fit the distribution of labor income conditioned on education. The Saved Wealth Model (SW) is an ad hoc modification of the particle system model of the Kinetic Theory of Gases (KTG). The KTG implies the laws of gas thermodynamics. The IP is a particle system similar to the SW and KTG, but less closely related to the KTG than the SW. This paper shows that the IP passes the key empirical test required of it by its social science meta-theory better than the SW. The IP’s advantage increases as the U.S. labor force becomes more educated. The IP is the more likely of the two particle systems to underlie an analogue of gas thermodynamics in social science as the KTG underlies gas thermodynamics.Inequality Process; Kinetic Theory of Gases; labor income distribution; particle system; Saved Wealth Model, social science analogue of thermodynamics

The inequality process as a wealth maximizing process

The One Parameter Inequality Process (OPIP) long predates the Saved Wealth Model (SWM) to which it is isomorphic up to a different choice of stochastic driver of wealth exchange. Both are stochastic interacting particle system intended to model wealth and income distribution. The OPIP and other versions of the Inequality Process explain many aspects of wealth and income distribution but have gone undiscussed in econophysics. The OPIP is a jump process with a discrete 0,1 uniform random variate driving the exchange of wealth between two particles, while the SWM, as an extension of the stochastic version of the ideal gas model, is driven by a continuous uniform random variate with support at [0.0, 1.0]. The OPIP's stationary distribution is a Lévy stable distribution attracted to the Pareto pdf near the (hot) upper bound of the OPIP's parameter, Omega, and attracted to the normal (Gaussian) pdf toward the (cool) lower bound of Omega. A gamma pdf model approximating the OPIP's stationary distribution is heuristically derived from the solution of the OPIP. The approximation works for Omega 0. The gamma pdf model has parameters in terms of Omega. The Inequality Process with Distributed Omega (IPDO) is a generalization of the OPIP. In the IPDO each particle can have a unique value of its parameter, i.e., particle i has Omegai, The meta-model of the Inequality Process implies that smaller Omega is associated with higher skill level among workers. This hypothesis is confirmed in a test of the IPDO. Particle wealth gain or loss in the OPIP and IPDO is more clearly asymmetric than in the SWM (Lambda =/ 0). Time-reversal asymmetry follows from asymmetry of gain and loss. While the IPDO scatters wealth, it also transfers wealth from particles with larger Omega to those with smaller Omega, particles that according to the IPDO's meta-model are more productive of wealth, nourishing wealth production. The smaller the harmonic mean of the Omegai's in the IPDO population of particles, the more wealth is concentrated in particles with smaller Omega, the less noise and the more Omega signal there is in particle wealth, and the deeper the time horizon of the process. The IPDO wealth concentration mechanism is simpler than Maxwell's Demon

Economic Reward and Second Language Learning: Evidence from the 1971 Census in Montreal

http://deepblue.lib.umich.edu/bitstream/2027.42/50916/1/141.pd

Explanations of the Labor Market Reward for Bilingualism in Puerto Rico

http://deepblue.lib.umich.edu/bitstream/2027.42/50894/1/117.pd

What Happened to the Percent Able to Speak English in Puerto Rico Between 1940 and 1950? The Aggregate Reliability of a Census Language Question

http://deepblue.lib.umich.edu/bitstream/2027.42/50895/1/119.pd

The Kuznets Curve and the Inequality Process

Four economists, Mauro Gallegati, Steven Keen, Thomas Lux, and Paul Ormerod, published a paper after the 2005 Econophysics Colloquium criticizing conservative particle systems as models of income and wealth distribution. Their critique made science news: coverage in a feature article in Nature. A particle system model of income distribution is a hypothesized universal statistical law of income distribution. Gallegati et al. (2006) claim that the Kuznets Curve shows that a universal statistical law of income distribution is unlikely and that a conservative particle system is inadequate to account for income distribution dynamics. The Kuznets Curve is the graph of income inequality (ordinate variable) against the movement of workers from rural subsistence agriculture into more modern sectors of the economy (abscissa). The Gini concentration ratio is the preferred measure of income inequality in economics. The Kuznets Curve has an initial uptick from the Gini concentration ratio of the earned income of a poorly educated agrarian labor force. Then the curve falls in near linear fashion toward the Gini concentration ratio of the earned incomes of a modern, educated labor force as the modern labor force grows. The Kuznets Curve is concave down and skewed to the right. This paper shows that the iconic Kuznets Curve can be derived from the Inequality Process (IP), a conservative particle system, presenting a counter-example to Gallegati et al.’s claim. The IP reproduces the Kuznets Curve as the Gini ratio of a mixture of two IP stationary distributions, one characteristic of the wage income distribution of poorly educated workers in rural areas, the other of workers with an education adequate for industrial work, as the mixing weight of the latter increases and that of the former decreases. The greater purchasing power of money in rural areas is taken into account.conservative particle system; gamma probability density function; Gini concentration ratio; income distribution; Inequality Process; Kuznets Curve; purchasing power

A Theory of the Diffusion of Bilingualism in Populations: An Application of the Log-Linear Analogue of First Differences

http://deepblue.lib.umich.edu/bitstream/2027.42/50903/1/127.pd