One must always be careful about reading an author's autobiography into their writings. It's also often unhelpful to apply pop psychology to our understanding of fiction. That said, Sylvia Plath's troubled attitude toward her father is well-known from her poetry. In The Bell Jar, Esther appears to have a sense of emptiness about life and incompleteness about herself. In her relationships with men, she views them cynically. The male characters in Plath's novel are prototypes of the male chauvinism of the 1950s, when the story takes place. Esther dissects their hypocrisy while, unfortunately, revealing how inwardly troubled she is herself. At the root of her trouble is her dysfunctional home life with her mother, since Mrs. Greenwood has little understanding of the conflicts going on within Esther's mind.

It is possible that the presence of an understanding father might have helped Esther. But given the power dynamic of the time, it's just as likely that a typically stern and judgmental father would have made things even worse for her. So, in my view, it remains an open question as to how much of Esther's troubled life is due to the loss of her father.

There is a definite sense in which Esther's mental instability is, at least in part, due to the loss of her father and the absence of a strong, male figure in her life. In a sense, Dr. Nolan becomes a kind of substitute father who helps provide her with that stability that she has never had since her father's death. The loss of Esther's father helps her to feel even more estranged than she does already because of her German heritage, and it is clear from the following quote that Esther feels the loss of her father keenly:

I had a great yearning, lately, to pay my father back for all the years of neglect, and start tending his grave. I had always been my father's favorite, and it seemed fitting I should take on a mourning my mother had never bothered with.

This is taken from Chapter 13, and the quote comes just before she tries to commit suicide. This is highly significant, as it suggests that the strong male figure she lacks is a key factor in her mental illness and her decision to try and end her life. Note how the quote suggests a need to "pay my father back for all the years of neglect," as if Esther blames her father for what he did in dying when she was young and leaving her by herself. It is strongly suggested therefore that Esther's character was greatly impacted by her father's death.