The inequality process and the distribution of income to blacks and whites*

Thanks to Prof. Gerhard Lenski, University of North Carolina, for the suggestion to consider coalitions in the Inequality Process. This paper attempts to answer questions raised in reading George Zipf (1941, 1949). The simulations described in this paper were written in GAUSS. A copy of the program can be obtained from the author. This paper was presented to the mathematical sociology session of the 1990 American Sociological Association meetings. The views expressed in this paper are the author's and do not necessarily reflect the views or policies of the Economic Research Service.

Abstract

The Inequality Process with Coalitions is a stochastic process modelling competition for wealth. The equilibrium distribution of wealth to individuals in coalitions is found by computer simulation. Identifying the minority in the model with blacks, the majority with whites, six statistical features of the size distribution of personal income to blacks and whites in the U.S. are reproduced:

1. the smaller median income of blacks than whites;

2. the difference in shapes of the black and white distributions;

3. the % black effect, the greater difference between the median incomes of blacks and whites in areas with a larger % black;

4. the association by area between a high ratio of median black to median white income with a small Gini concentration ratio of white income;

5. the association by area between a high ratio of median black to median white income with high white median income;

6. the reduction of associations #4 and #5 with controls for level of development or % black in an area;

and, a feature of the behavior of individual people:

1. the greater discriminatory aggressiveness of poor whites to blacks than richer whites.

There is no difference between minority and majority people in the Inequality Process with Coalitions other than coalition membership. This paper shows that a model of pervasive competition among people as individuals and coalitions is consistent with empirical size distributions of personal wealth. Competition is milder in industrial societies than preindustrial because a greater proportion of industrial wealth is in a form that cannot be profitably confiscated: human capital. To recreate preindustrial conditions, according to the Inequality Process, is to provide much larger incentives to majorities to victimize minorities. See the “hill of hate”, Figure 2.

Key words:

• Social stratification
• income
• wealth
• race
• competition
• stochastic process
• gamma distribution

Notes

Thanks to Prof. Gerhard Lenski, University of North Carolina, for the suggestion to consider coalitions in the Inequality Process. This paper attempts to answer questions raised in reading George Zipf (1941, 1949). The simulations described in this paper were written in GAUSS. A copy of the program can be obtained from the author. This paper was presented to the mathematical sociology session of the 1990 American Sociological Association meetings. The views expressed in this paper are the author's and do not necessarily reflect the views or policies of the Economic Research Service.