Pseudo-economists like Robert Reich often call for more unions and more power for unions so they can increase worker's wages. It;s true that unions raise workers wages in the same way that it is true that cartels can get a higher price for their product if they reduce the supply of it.
Unions are labor cartels. They increase the wages of their members above market value, leading to a decrease in the quantity of labor demanded, and ultimately a decrease in the number of available jobs and hence increased unemployment.
Unions also reduce investment since the extra wages workers are paid often cut into profits and have the same effect as a corporate tax rate. This reduces investment in research and development, capital, and expansion. Reduced investment ultimately means less capital and correspondingly lower wages (since capital increases productivity and thus, increases wages).
According to Thomas E. Woods Jr.:
"In a study published jointly in late 2002 by the National Legal and Policy Center and the John M. Olin Institute for Employment Practice and Policy, economists Richard Vedder and Lowell Gallaway of Ohio University calculated that labor unions have cost the American economy a whopping $50 trillion over the past 50 years alone....That is not a misprint. "The deadweight economic losses are not one-shot impacts on the economy," the study explains. "What our simulations reveal is the powerful effect of the compounding over more than half a century of what appears at first to be small annual effects." Not surprisingly, the study did find that unionized labor earned wages 15 percent higher than those of their nonunion counterparts, but it also found that wages in general suffered dramatically as a result of an economy that is 30 to 40 percent smaller than it would have been in the absence of labor unionism." (1)
This isn't some right-wing conspiracy, economists of all stripes accept this. Keynesian economist Laurence Summers states:
"Another cause of long-term unemployment is unionization. High union wages that exceed the competitive market rate are likely to cause job losses in the unionized sector of the economy. Also, those who lose high-wage union jobs are often reluctant to accept alternative low-wage employment. Between 1970 and 1985, for example, a state with a 20 percent unionization rate, approximately the average for the fifty states and the District of Columbia, experienced an unemployment rate that was 1.2 percentage points higher than that of a hypothetical state that had no unions. To put this in perspective, 1.2 percentage points is about 60 percent of the increase in normal unemployment between 1970 and 1985." (2)
Markets should set wages. If we want wages to increase, we should focus on increasing productivity, not increasing the number of labor unions. As you can see in the graph below, which is taken from the St. Louis Federal Reserve website, worker compensation (adjusted for inflation) has exponentially increased over time whereas union membership has exponentially decreased over time.
(3)This Heritage Foundation article goes into great depth as to the negative effects unions have on the economy as a whole (the graph below is taken from this article: