## RISING WAGE INEQUALITY: Data 4

Effects of Unions on Wage Inequality Naive Estimates

As a starting point for considering the effect of changing unionism on the inequality of wages, it is useful to begin with simple “two-sector” framework. Recall that if the union density u and the union relative wage effect are both constant across skill groups, then the effect of unions on the variance of wages (relative to what would be observed if all workers were paid according to the existing nonunion wage structure) is

A comparison of the size of this differential over time provides an obvious measure of the changing effect of unionism on wage inequality. Table 3 illustrates the application of this formula to male and female wage inequality in 1973-4 and 1993: the underlying data are drawn from Table 2. Note that if the union density is constant across skill groups, and the union wage and variance effects are constant across skill groups, then it is legitimate to use the unadjusted union wage gap and union variance gap in equation (5′).11 In fact, under these assumptions the adjusted union wage gap should equal the adjusted gap (since the union rate is orthogonal to individual characteristics) and the “raw” union variance gap should equal the gap in the adjusted variances of wage outcomes between the union and nonunion sectors.

Examination of Table 3 shows that ignoring differences in union coverage rates and union effects across groups, the decline in unionism between 1973-4 and 1993 would have been expected to cause the variance of male wages to rise by 0.020 and the variance of female wages to fall by 0.003. Virtually all of the difference for men is attributable to the change in average union density (-.121 = 0.308 – 0.187) multiplied by the union variance gap (Av ~ -0.18). For women, the union variance gap is smaller than for men, and the decline in union density is negligible, so the net contribution of unionism to widening inequality is trivial. As shown in the bottom rows of Table 3, between 1973-4 and 1993 the variance of wages rose by 0.067 for men and 0.074 for women. Thus, a naive calculation suggests that falling unionism can explains about 30 percent of the rise in male wage inequality but none of the rise in female inequality.