One of the diagnostic criteria for Narcissistic Personality Disorder (NPD) is “lack of empathy.” But what kind? Affective, cognitive, or both?
So I read a study. Granted, I only read one study. You should probably read more before you decide if their findings are valid.
According to K. Ritter and a bunch of other researchers, narcissists have average cognitive empathy. They can see things from your perspective. They can’t always be bothered though.
However, they have impaired affective empathy. When you are distressed, they aren’t also distressed. Which I think probably explains a lot.
The same study looked at empathy in those with Borderline Personality Disorder (BPD). They found what other studies have found about borderlines and empathy. Individuals with BPD have impaired cognitive empathy but average or above-average affective empathy. They feel distressed when you are distressed–maybe even very distressed–but they don’t know why.