I am finishing up a graduate degree and am looking for my first full-time job. I recently had a second interview (Skype) with a place I'm interested in and the interviewer asked me what my desired salary was. My plan for this question has been to politely refuse to be the first person to offer a number and that's what I did, in an indirect way. The interviewer pushed to get a number from me, even saying something along the lines of "what is your dream salary for this job, even if it's high?" I still refused to offer a number, eventually directly ("I don't want to offer a number right now, if that is all right.") After the direct refusal the interviewer moved on to other questions.
I've looked through other questions on this site on this topic, and there is lots of advice on how to answer the "desired salary" question. However, I didn't find anywhere that answered specifically the question is it okay to refuse entirely to answer the "desired salary" question? Are there any downsides to absolutely refusing (politely) to be the first party to throw out a number?
I'm wondering because, in my situation, I don't really have any previous salaries I can point to as a baseline for expectations, and many of the positions I'm applying to are specialized or at specialized companies that don't have enough people working those positions/companies to give Glassdoor, etc., a handle on estimating salaries. I suspect these places will pay well, but I don't want to inadvertently offend them with too high a desired salary or give myself a pay cut with too low a desired salary and that's why I have taken my stance of not wanting to offer the first number.
Duplicate? I believe the specific question as I have worded it is not a duplicate, though I realize my search may not have been exhaustive and/or its answer may have been addressed in another question. Please point me there if so, otherwise I argue that my specific question is not a duplicate.