Unions during the 20th century
Farber and al. used many sources of survey data to estimate a union household income premium in 1936, 1942, 1946, and then nearly every year from 1952 onward. They find that despite important changes to union density during this period, we find a relatively steady effect: union households have income roughly fifteen to twenty log points higher than do other households with similar demographics and human capital proxies. During the period from 1940 to 1970 unions lifted the workers at the bottom of the distribution.
Unions and Inequality Over the Twentieth Century: New Evidence from Survey Data
Authors: Henry Farber, Dan Herbst, Ilyana Kuziemko, Suresh Naidu
From: Princeton University, Columbia University
Is there a trade-off between equality and efficiency?
No, argue Storm and Capaldo because:
(a) higher wage growth does not depress real income growth in economies operating under a balance-of payments constraint because the Marshall-Lerner condition is not satisfied; (b) the impact of higher wage growth on prices is limited because unit labor costs make up only a fraction of total production costs; and (c) higher wage growth is likely to induce higher labor productivity growth—through processes of ‘technology-forcing’ or ‘cleansing’, and this in turn reduces unit labor costs.

Labor Institutions and Development Under Globalization
Authors: Servaas Storm, Jeronim Capaldo
From: Delft University of Technology, Tufts University
…but the evidence on unions increasing productivity is inconclusive
First, unions can improve productivity. Unions’ presence can enhance labor voice inside the workplace and the firm, fostering labor productivity by improving cooperation between workers and releasing the communication between workers and the top management. Second, unions can decrease productivity. Unions’ presence, by giving a better protection against dismissal, can also encourage shirking because the negative consequences for supplying less effort are reduced. Moreover, if unions increase wages for low-wage workers at the expense of wages of high-wage workers, acting as internal redistribution operators, this wage setting can discourage high value-added employees to stay in the firm, impeding firm productivity.
Labor Unions and Profitability : The more the merrier?
Author: Fabien-Antoine Dugardin
From: Université Paris Dauphine
A more nuanced view
Krusell and Rudanko find that the effect of unions on wages and employment is not that straight forward in a frictional labor market. Under an egalitarian wage policy, if a union can commit to future wages it can attain an efficient level of unemployment in the long run. In the short-run though unemployment is inefficiently high because the union uses its market power to raise current wages above the efficient level to extract rents from firms with preexisting matches. This distortion can be mitigated when a union drops the egalitarian wage policy assumption and instead it extracts rents from firms with high wages for senior workers while setting the wages of junior workers low enough to encourage hiring.

Unions in a Frictional Labor Market
Authors: Per Krusell, Leena Rudanko
From: University of Gothenburg, Federal Reserve Bank of Philadelphia