Self-reporting alone does not correlate with cognition and it is not rational to think it does.
* There exists no self-reporting test that correlates with cognition anywhere. In clinical work on cognition, when self-reporting tests are used they are used in combination with other test to measure cognition, for example in WAIS.
Self reporting will be correlated with longterm memories of self and others, that is why all self-reporting based testing will be correlated ..