How has income volatility evolved?

I’ve had many people asking me whether Jacob Hacker’s results about "the great risk shift" hold up.  The CBO weighs in:

Since 1980, there has been little change in earnings variability for both men and women.  There is some evidence that, between 1960 and 1980, earnings variability increased for men but was offset by a decrease for women.  Those findings are consistent with most existing studies of the topic that use publicly available survey data, which tend to find higher levels of earnings variability for men in the 1980s and 1990s relative to the 1970s, but little change since around 1980.

Here is the paper.  I’ll read through it soon, and report back if my deeper impression runs in the other direction.  If you know of relevant defenses of Hacker, please do leave them in the comments.  I’d like to get to the bottom of this.