Human-AI interaction in text production increases complexity in authorship. In two empirical studies (n1 = 30 & n2 = 96), we investigate authorship and ownership in human-AI collaboration for personalized language generation models. We show an AI Ghostwriter Effect: Users do not consider themselves the owners and authors of AI-generated text but refrain from publicly declaring AI authorship. The degree of personalization did not impact the AI Ghostwriter Effect, and control over the model increased participants' sense of ownership. We also found that the discrepancy between the sense of ownership and the authorship declaration is stronger in interactions with a human ghostwriter and that people use similar rationalizations for authorship in AI ghostwriters and human ghostwriters. We discuss how our findings relate to psychological ownership and human-AI interaction to lay the foundations for adapting authorship frameworks and user interfaces in AI in text-generation tasks.