If you recall, Robert D. Putnam, in his last book, expressed surprise that Chetty and Hendren, et.al. (2014) did not find evidence of a decline in intergenerational mobility. Putnam predicted that researchers would find such evidence soon enough. After all, it seems the returns to education have been rising, geographic mobility has been falling, market concentration is up slightly, life expectancy is behaving in funny ways, and regional disparities seem to have grown. Chetty and Grusky, et.al. (2016) seemed to paint a more pessimistic picture than did his work from a few years ago, and now we have a new paper by Jonathan Davis and Bhashkar Mazumder:
We demonstrate that intergenerational mobility declined sharply for cohorts born between 1942 and 1953 compared to those born between 1957 and 1964. The former entered the labor market prior to the large rise in inequality that occurred around 1980 while the latter cohorts entered the labor market largely afterwards. We show that the rank-rank slope rose from 0.27 to 0.4 and the IGE rose from 0.35 to 0.51. The share of children whose income exceeds that of their parents fell by about 3 percentage points. These findings suggest that relative mobility fell by substantially more than absolute mobility.
So far this seems to be the current version of the final word. The authors also argue, by the way, that Chetty (2016) is somewhat too pessimistic, though correct in suggesting mobility has indeed fallen.
By the way, this seems to be the best link for a download.