Says the research. In response to your point a few posts up about explaining correlations with IQ being the parents influence, IQ is also correlated to social mobility.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3248886/

"Childhood IQ and achieved education level were significantly and independently associated with upward mobility between the ages of 5 and 49-51 years. Only education was significantly associated (positively) with upward social mobility between 5 and 25 years, and only childhood IQ (again positively) with upward social mobility between 25 and 49-51 years. Childhood IQ was significantly negatively associated with downward social mobility. Adult height, childhood housing conditions, adverse events in childhood and sex were not significant determinants of upward or downward social mobility in this cohort."