There are none.
No studies have been done, nor any studies could have been done under a communist regime that would be critical of the state, nor any studies can be done now because no data was recorded at the time to do the sort of study you're looking for.
What is known for sure from people working there was that they were (a) understaffed, (b) overcrowded with orphans, (c) babies don't thrive when deprived of human touch, and (d) adopted kids from those orphanages exhibited psychopathic behavior as reported by the adoptive parents.
To make an analogy, what you're asking here is for a state-funded study that shows that women are unhappy in Saudi Arabia and they desire equal rights to men.
Just put 2 and 2 together.