If I'm not wrong, productivity is measured as economic output/ hours worked. It seems pretty obvious that when people decide to reduce the hours worked, they will start pruning the less economically rewarding tasks first. How's that old adage: "work expands to fit the time available".
So I would expect that by cutting the hours, the economic output decreases less than proportionally, and therefore productivity grows.
I was trying to point out that the productivity has been steadily increasing without an obvious benefit to the workers (such as pay increase), so basically workers have been producing more without getting a larger share of that increase. Therefore, keeping all the other things constant, reduced workdays might be a benefit for that increased productivity.
So I would expect that by cutting the hours, the economic output decreases less than proportionally, and therefore productivity grows.