One major conclusion of their research is that the family income of children whose parents divorce and remain divorced for at least six years falls by 40 to 45 percent.
http://www.nber.org/digest/jul02/w8786.html
As per the Census Bureau (table F-10), in 2014, married couple families with one or more children under 18 years, earned an average income of $111,278. In other words, traditional two-parent families earned an income that was more than three times higher than for households headed by a single mother.
http://www.forbes.com/sites/aparnamathur/2015/11/18/the-cost...
Saying that the income of a single-parent family is lower does not remotely answer the question of "What is the magnitude of the effect of single-parent homes on the size of the middle class?"
I actually went and looked up the tables in the census: https://www.census.gov/data/tables/time-series/demo/families...
We have the same percentage of single parent families now as in 1995 (29%). That's over 20 years, the number has barely budged. So how does your answer relate to the question of the decline of the middle class since then?
Citation needed.
What, exactly, is the magnitude of the effect of single-parent homes on the size of the middle class? Without answering that, your "gut instinct" explanation, if that's what it is, is meaningless.