Did falling Social Security benefits generate higher labor force participation?

I spotted this story yesterday, reporting on a new study by David Blau of Ohio State and Ryan Goodstein of the Federal Deposit Insurance Corporation that argues that the decline in Social Security benefits – driven by increases in the Full Retirement Age from 65 to 66 – was a big part of why we've seen a rebound in labor force participation by men in recent years. The study concludes:

Since the early 1980s, Social Security rule changes have favored increased LFP. The rise in the [Delayed Retirement Credit] and the [Full Retirement Age] are estimated to account for one quarter to one half of the increase in LFP of older men since the 1980s. This amounts to a 1.2 to 2.4 percentage point increase in the LFPR of men aged 55-69. Rising LFP of married women and changes in the educational composition of the older male population contributed to the increase as well.

I'll admit I haven't read the study carefully yet, so these are my initial thoughts, which may well be wrong: I'm not sure why an increase in the DRC, which raises benefits for those who delay claiming after the Full Retirement Age, would necessarily increase labor force participation since there is no long a retirement earnings test for individuals beyond the FRA who claim benefits while continuing to work. It might, to the degree that claiming benefits and leaving the workforce are treated as a joint decision, but if they are treated separately then it may not. I'm also not convinced most people have any idea how delayed retirement credits work, which obviously would mute any response.

An increase in the Full Retirement Age can raise labor force participation in two ways. Directly, a rise in the retirement age is effectively a reduction in benefits, and if benefits are reduced people will tend to work a little longer to make up the difference. (That's one reason why I favor solvency based on reduced benefits rather than higher taxes, which would tend to encourage people to work a little less.) But second, the FRA acts as a signal that many will treat as the "correct" time to retire. As the retirement age increases, people's claiming behavior appears to rise as well.

This paper by my former SSA colleagues Joyce Manchester and Jae Song covers some similar ground and is worth checking out.