The Rate Of Change In The Size Distribution Of Wages As A Vector

This paper attempts to measure the rate of change in the size distribution of wages over time in a rigorous, analytic way, and to relate that change to the business cycle. The basic problem for which this paper provides a solution is to relate changes in a size distribution to levels of and changes in single‐dimensioned variables (unemployment, Gross National Product, and the consumers price index). Let F stand for the cumulative relative size distribution of wages, a function of wages. F takes on values zero through one. Let F̄ be a given value of F, e.g., F̄= 0.25. The proposed solution to the basic problem is to measure the rate of change in consecutive F's at F̄. The composite of such measurements at F̄ over time forms a vector, the length of which depends upon the number of time periods observed. The number of vectors thus derived depends upon the number of values of F̄ selected. The various vectors are then related to the general economic conditions and the respective values of F̄. The general economic conditions have a differential effect on the various vectors; e.g., those wage earners with relatively low wages are affected differently by a given turn of the business cycle than are those with high wages. The paper includes several supplementary investigations: (a) estimating each of the annual cumulative relative size distributions of wages for a specific analytic function, (b) relating analytically the size distribution construct to the Lorenz curve concept and the Gini coefficient, (c) predicting and simulating size distributions for various economic conditions, (d) formulating tax trade‐offs, and (e) suggesting further uses and extensions.