I wouldn't exactly take Robert Reich's word for it...It's not so clear at all.
There's plenty of other variables to consider here and he just graphed two of them. Corporate taxes were much higher. Also it looks like share of income going to the top 10% hasn't really changed much at all in the last 100 years. 40% +/- 10%. That needle hasn't moved very far.
If you care to read the article you'd find links to a more detailed study that demonstrates the exact portion of income inequality that is known to have been caused by de-unionization.
That's not how this works. There's no study here showing how they were able to discount all other variables and show a provable link between A and B.
This is data cherry-picked to support a conclusion and published by a lobby group (a pro-union one and publihed on labor day, no less. It's flashy!). You may agree with said conclusion, but this is research presenting a theory not a proof.
There is no causation being shown here. It's a possible theory, but that is all that it is.
There's plenty of other variables to consider here and he just graphed two of them. Corporate taxes were much higher. Also it looks like share of income going to the top 10% hasn't really changed much at all in the last 100 years. 40% +/- 10%. That needle hasn't moved very far.