What is the correlation between self-rated and objective measures of intelligence? In the context of a broader question, someone asked:


  Can the detailed analyses from, say, the Wechsler test, be used to inform decisions significantly better that gut feelings can?


While this question might be closed, I thought a more defined question regarding the correlation between self-rated and objective measures of intelligence would be good to have. I feel as if I've read papers that suggest the correlation is modest (e.g., r = .2 or .3). Presumably, Dunning-Kruger and a bunch of self-serving biases operate. But I could not find any authoritative reference off hand. So my questions:


What is the correlation between self-rated intelligence and objective measures of intelligence (i.e., full scale IQ scores from well-validated measures)?
To what extent does the correlation depend on how the self-ratings are obtained?
The term you are looking for is self-assessed intelligence (SAI) (sometimes subjectively-assessed intelligence or self-estimated intelligence).  The leaders in this field are Tomas Chamorro-Premuzic and Adrian Furnham.  From their book "Personality and Intellectual Competence" (2014):


  Correlations between SAI and psychometric intelligence have been
  significant and positive, albeit generally modest (r&lt;.30).


So you are spot on. :-) SAI is a subset of self-tests of intelligence, that can range from simple estimates, to full-fledged self-administered IQ tests.  As such, correlations can vary a lot.  However, SAI is generally considered to be an estimate, rather than a test, and this does not appear to be affected much by methodology.  From Paulhus et al (1998):


  Correlations between single-item self-reports of intelligence and IQ
  scores are rather low (.20–.25) in college samples. The literature
  suggested that self-reports could be improved by three strategies: (1)
  aggregation, (2)item weighting, and (3) use of indirect, rather than
  direct, questions. ... Although results showed some success for both
  direct and indirect measures, the failure of their validities to
  exceed .30 impugns their utility as IQ proxies in competitive college
  samples.


On the other hand, the SAI literature reveals significant gender differences in SAI estimates - with males significantly overestimating and females significantly underestimating their intelligence - as well as significant cross-cultural differences in estimates, suggesting that the correlation is more heavily affected by social stereotypes.