Although Turn of the Screw, the 1898 novella by Henry James, is a psychological thriller that seems to be extremely ambiguous about the existence of the ghosts, the 1961 movie, The Innocents, based on the novella and directed by Jack Clayton, basically led me to believe the ghosts were figments of Miss Giddens' imagination.
Miss Giddens, played by Deborah Kerr, grew up in a small house and was very sheltered, then was all of a sudden thrust into a new and exciting life as a governess for two children in a lavish mansion. This abrupt change is enough to make anyone anxious, especially when the seed of the mysterious death of the old governess, Miss Jessel (Clytie Jessop), is planted into her curious mind.
The movie's setting helped me to see how easily a newcomer on the premises could imagine spooky going-ons. The atmosphere of the huge, dark house, with the shadowy flicks of candlelight playing on its walls, is within itself a breeding ground for imagination.
In the movie, when she plays hide-and-go-seek with the children, Miles (Martin Stephens) and Flora (Pamela Franklin), she is frightened in the attic, where she first sees the picture of Mr. Quint. She sights him in the window soon after and describes the apparition to Mrs. Grose (Megs Jenkins), who identifies it as Mr. Quint (Peter Wyngarde), yet she neglects to tell her she has previously seen the picture. In The Turn of the Screw, she does not see a picture of Mr. Quint before witnessing the apparition, which tends to make the possibility of the ghosts being real in the book more plausible. After she thinks she has seen Mr. Quint, she becomes obsessed with the stories and forces Mrs. Grose to keep telling her more about Mr. Quint and Miss Jessel. The more she learns, the more entranced she becomes.
I can also see how easy it would be for her to think that the children are possessed because they are strange. I do not feel they were truly possessed, but I think they have witnessed more than children should see or hear from Mr. Quint and Miss Jessel, I even hypothesize some sort of abuse either or perhaps both sexual or emotional. The children are very cunning and have picked up on the fact that Miss Giddens is afraid of them and use this to their advantage.
I think Miss Giddens' fanaticism finally goes too far and begins to frighten them. For instance, when she accuses Flora of seeing Miss Jessel across the lake. She makes her face the death of her old governess and upset her. In the end I really felt that she scares Miles to death rather than exorcizing him. He looks truly bewildered and afraid before he drops dead. Miss Giddens has been intent upon saving the children but instead seems to destroy them instead with her obsession.