Tino Sandanaji demonstrates this here. I've excerpted his key chart which shows that regardless of Unionization rates share of GDP going to wages is similar. Indeed the biggest dispersion of labor's share comes around some of the highest union rates. One would actually expect this: the more that wages are subjected to politics the more they are going to vary based upon political outcomes. Market wages by contrast will tend to coalesce across countries that trade freely with each other in the same way that real capital and goods costs tend to. This is, of course, bad news for unions because it demonstrates that they really don't do anything. Except perhaps retard the rate of economic growth and since labor's share is fairly constant, that retards the wage share. I suppose you could argue that they get 'their' members higher wages. But as the rate of unionization rises this differential must inevitably fall. It turns out that the old time guild cartels which are all skilled trades unions are are the only kind of union that can really generate superior returns in the long run (industrial unions where the employer has a strong monopoly or oligopoly also thrive a la the UAW for time but the very fact of their excess returns ruins the competitiveness of the employers and draws in competition for the excess rents that such an arrangement generates). This is because they are small, exclusive and the government helps police the competition. Without the state's help even these unions would be useless at generating excess share of output.
Labor share of GDP in percent on the Y axis and percent of the workforce covered by Collective bargaining is on the X axis.
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