Add Health participants were asked to rate their intelligence. They were also given a vocabulary test--a decent measure of IQ.
Here are the Pearson correlations between the two variables listed by race:
Correlation (sample size = 6,504)
American Indians .35
Overall, the correlations are low. People are not good at evaluating how smart they are. But the ability varies by race. Asians are the most accurate; blacks the least. Objectively smart groups (i.e., Asians, whites) assess their IQs with greater accuracy than low-IQ groups (Hispanics, blacks).