According to this JHE study by Johnston, Schurer and Shileds, the answer is ‘yes’.
Importantly, we estimate an intergenerational correlation coefficient in mental health of 0.190, which means that a one-standard-deviation decrease in maternal mental health (measured when the cohort member was a child) is associated with a 0.19 standard deviation decrease in the child’s mental health some 20 years later. The size of this correlation coefficient is similar to the estimated intergenerational transmission of income and birth-weight.
This study may give parents with mental illness more reason to discuss their problems with their children. Not only could it help the child to understand their parents actions, but could help the child to cope with their own mental illness if the disease is passed down to them.
- David W. Johnston, Stefanie Schurer, Michael A. Shields. Exploring The Intergenerational Persistence Of Mental Health: Evidence From Three Generations. Journal of Health Economics, 13 September 2013.