RISING WAGE INEQUALITY: Methods 1

Let
w6520-3
represent the variances of log wage outcomes for individuals in skill group с in the nonunion and union sectors, respectively. The union-nonunion variance gap for skill group с will be denoted by
w6520-4

Note that the mean wage gain for workers in skill group с associated with the presence of unionism is the product of the union coverage rate and the union wage effect. The variance of log wage outcomes for workers in skill group с is
w6520-5

This equation shows that unions exert a “within-sector” effect associated with any lowering (or raising) of the dispersion of wage outcomes relative to those in the nonunion sector and a “between-sector” effect associated with the potential widening of mean wage outcomes between the union and nonunion sectors.

In the presence of unions the dispersion of wage outcomes in the overall labor market is
w6520-6

where expectations (denoted by E[ ]), variances (denoted by Var[ ]) and covariances (denoted by Cov[ ]) are taken over the skill categories. On the other hand, if all workers were paid according to the wage structure in the nonunion sector, the variance of wage outcomes would be
w6520-7
Thus, the effect of unions on the variance of wage outcomes, relative to the variance that would occur if all workers were paid according to the structure in the nonunion sector3 is:

w6520-8

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