I just moved to a new state (California) for a temporary job and am planning to apply to graduate school (physics PhD programs) at state schools here. If I want, I can establish residency here; this would be somewhat expensive and a take a bit of time, so I have not been particularly motivated to do so. I had assumed that since my tuition would be covered anyways in a PhD program, there was no advantage to being in-state. However, my supervisor raised the possibility that it might be to my benefit when applying to California grad schools to be a California resident; is this true? Does residency have an effect on PhD program admissions at state schools?
I had assumed that since my tuition would be covered anyways in a PhD program, there was no advantage to being in-state.
There's no financial advantage to you. There might be one to the department.
I believe that one common arrangement is that the department's budget is charged for the normal amount of your tuition, whether in-state or out-of-state. Although it's just money moving between internal university accounts, it makes a difference to the department.
I went to grad school at a University of California campus, and there was a rule that if you had come from another state, you had to establish California residency within your first year, so that the department only had to pay the out-of-state rate for one year. So if you plan to attend a California university, you'll likely have to go through that bureaucratic hassle eventually anyway; might as well get started now.
Being in-state also means that the department gets to pay the lower rate from the beginning, so you'd be a bit cheaper to support than an out-of-state student. I don't know whether departments actually make this an explicit factor in admissions, and I would guess that they don't, but it could make a very slight difference at the margin.
I won't repeat the points raised in Nate Eldredge's excellent answer, but I will point out a couple of other considerations. First, in general, I very much doubt that there is much of an academic advantage; that is, I doubt that you would be more likely to be accepted based on your residency status. Departments would normally make offers based on the quality of your application, not on how much you would have to pay.
Second, although Nate Eldredge said, "there's no financial advantage to you", that might not always be accurate. Some institutions might offer only in-state financial assistance; out-of-state students might have to make up the difference themselves. I have no idea how frequent that might be the case, but in my personal case as an international student in Louisiana, USA, my graduate assistantship did not waive the international student tuition supplement; I had to pay that out of my own pocket (although the assistantship did provide sufficient funds to cover that, it reduced my net receipts by thousands of dollars). Yes, I realize that my personal situation concerned international fees while yours concerns domestic but out-of-state fees, but I nevertheless recommend that you verify the specific situation in any school that you want to apply to; do not assume that they would always fully cover out-of-state tuition charges.
When I was in graduate school in Texas, my graduate program was flagged during a review for having too many non-Texan students and too many international students. After the review, the program tried to recruit more Texan students (and was successful).
However, I suspect that this experience is an outlier.