The study, called Politics Matter, points out that it's the political climate that makes the difference.
If globalization and technological change made unions obsolete, you would expect union membership to fall at the same rate across countries with the same level of globalization and technology change. Writes CEPR:
Instead, for 21 rich economies, including the United States, what we see over the last five decades is a wide range of trends in union membership and collective bargaining.Concludes CEPR:
Countries strongly identified during the postwar period with social democratic parties – Sweden, Denmark, Norway, and Finland – have generally seen small increases in union coverage and only small decreases in union membership since 1980.Read the whole thing here.
Over the same period, countries typically described as “liberal market economies” – the United States, the United Kingdom, Australia, New Zealand, Ireland, Canada, and Japan – have generally seen sharp drops in union coverage and membership.
Countries in the broad Christian democratic tradition, sometimes referred to as “coordinated market economies” or “continental market economies” – Germany, Austria, Italy, the Netherlands, Belgium, France, and Switzerland – typically have had outcomes somewhere in between the social democratic and liberal market economies, with small drops in union coverage and moderate declines in union membership.
These patterns are consistent with the view that national politics are a more important determinant of recent trends in unionization than globalization or technological change.