By request, here are some of my thoughts on applying for, and possibly interviewing for, another tenure(track) position when you already have one.
My expertise on this particular topic comes from having left one university for another before coming up for tenure at the first place, and from various situations that have arisen related to my possibly moving from my current university (post-tenure).
As with most such issues involving life and career, there is no one "rule" to follow regarding whether you should apply to other schools when you are already on the tenure-track. Getting an offer at another (better or peer) institution is a well-known route to early tenure or at least a retention offer of some sort, and there are many reasons why you might want to try to do this.
If you want to apply for other jobs, you should do it. You should try to get the best job you can and not worry (too much) about what your colleagues will think.
If, however, you are very happy where you are and are wondering whether you should look around anyway, I suggest checking out a few things, such as: (1) What is your department/university's track record with retention offers? What has your department chair and/or the relevant dean done in the past?; and (2) Is it worth it to you, economically and/or emotionally, to go through the process of applying, interviewing, and negotiating?
This is a tricky topic because if you interview at another university and have no intention of accepting an offer if you get one, you are wasting a lot of people's time and another institution's money. I know that this is how the game is played, "everyone does it", etc. etc., but whenever I am on the receiving end (i.e., in the interviewing department) for someone who is just trying to get something from their existing institution, it's hard not to feel some hostility towards the person who just wasted our time and department's resources.
At the same time, I don't like it when hiring committee members spend time cynically wondering about the motives of a tenure-track or tenured candidate. I think we have to take everyone's application at face value, assume (perhaps delusionally) that they are sincere, and try to hire the "best" person for the position.
There's no good solution to this. It is how the game is played.
I've heard that women are more reluctant than men to go out and get other offers and negotiate a retention offer, owing to feelings of loyalty or insecurity or some other emotional factor(s). I'm sure there have been studies about this, and in my own case, I definitely found it difficult to apply for other jobs while I was working hard to succeed in my existing job, which I liked very much. Nevertheless, I applied for other jobs because it was the only way my husband and I were going to find academic jobs anywhere near each other. I therefore stayed in the job market for personal reasons, sincerely trying to get another faculty position that was better for my family and me.
I wasn't quite close enough to the promotion year for it to be realistic for University 2 to hire me with tenure, even if they would have considered that, but I got credit for my years at University 1, and came up for tenure not long after starting my new position at University 2. Some Assistant Professors may be hired with tenure at their University 2 if that university needs to do that to recruit them and is convinced they would easily get tenure anyway.
Each institution is different. I have several colleagues who were hired as Assistant Professors at a new university after they were already Associate Professors with tenure at the university they left. This may occur when University 1 is not even close to being a peer institution to University 2, but I think it is always worth asking if you could be hired with tenure.
Another option for "senior" Assistant Professors moving to another university is to be hired as an Associate Professor without tenure, but to be evaluated for tenure soon after arriving. You still have to go through the tenure process, perhaps within 1-2 years of arriving at your new institution.
Summary: If you think you might like to be somewhere else and appealing options arise, go for it. If the thought fills you with dread and exhaustion and you are content where you are, don't do it You're the only one who can determine whether it is worth it to you.
If you want to leave your current institution for a better department, location, planet etc. or if you want to leave for personal reasons, just as in the pre-tenure case: go for it. Apply for whatever looks appealing and don't worry about what other people think. You can tell some trusted colleagues in your current department and even get a reference letter to attest to your sanity and awesomeness as a colleague. Then, if you get an offer and it's better than your retention package (relative to your reasons for applying in the first place), you can make your decision.
Another possible scenario is similar to one discussed for the pre-tenure cases: i.e., one in which you feel you need to get an outside offer to get ahead at your current institution. But again, do this only if it is worth it to you overall when considering all the factors, economic and emotional.
For some people, it seems easy. I have known faculty who were continually on the job market, accumulating offers and getting retention offers in return. Maybe that's how they gauge whether they still had "it".
The decision whether to apply to other institutions for reasons of dissatisfaction with your current institution might seem straightforward, but in fact it is not, especially when your spouse/family are in the equation. Even if there are things that make you unhappy at your current institution, how do you know that another place would be better? For example, if you have unpleasant colleagues in your current department, how do you know you won't have different unpleasant colleagues in another place? If you don't like your department chair, is it worth it to move, knowing that the insidious department chair might be replaced by someone more sympathetic in a few years?
Even if another place seems like it's great (colleagues, location etc.), there may be unexpected things that could profoundly affect your academic existence. Things like: how are graduate students funded? Do you have to raise grad student salary + other expenses entirely from your grants or is there some institutional support (TA, fellowship)? At your current level of funding, what are the consequences for the size of your research group in these different economic scenarios?
Also: If you rely on certain facilities, what is the situation at the Other University? At one place (to which I did not apply but which discussed employment options with me anyway), I was told that the institution would provide a substantial match to a proposal that I could write to get equipment that I already have at my current institution. That wasn't too appealing, although in some cases it might be a way to trade-up to a zippy new set of toys, if one is confident about getting an equipment proposal funded.
I have done one "official" post-tenure interview for a senior faculty position, and it wasn't hard to explain why I might want to leave University 2 for University 3. I didn't trash University 2, but just said that I was exploring other options, was interested in some of the new opportunities available at University 3, and that I was not considering leaving University 2 because I was unhappy there; it just seemed like a good time in my career to see what other possibilities there might be. The outcome of this adventure was reasonably satisfying for most concerned.
This is a strange one. At least, it has been a strange one for me. I would describe my position in my field of Science as "reasonably successful". I am not a cosmic superstar, but I am also doing pretty well -- well enough to be on the radar screen of other universities. I have been invited to give several talks that turned out to be more than just a talk (i.e., stealth interviews), I've been surprised by what I thought was a routine chat with a department chair who asked me if I'd be willing to move, and I've had several other somewhat surprising opportunities arise without my seeking them out. There seem to be a few of these every year. My husband has had similar experiences, as all these institutions know they would have to hire the both of us.
So what to do about these quasi-recruitment opportunities? In fact, we have been quasi-fortunate that our current department chair was proactive at one point and went to the Dean/Provost before another institution got too far with an offer. That's kind of an ideal situation, especially if you are relatively happy where you are and ambivalent about going somewhere else, however awesome the other place is in some ways.
There are still a few institutions with which we are in a maybe-in-a-few-years-we-can-talk-more limbo zone, and I guess it's nice to know there might be options in case our department/university becomes an inhospitable place. I'd rather not spend my entire career on the job market, but since I'm not actively applying for jobs, I don't really have to think about it much.
When an established faculty member moves to another institution, the move also has consequences for graduate students and postdocs, and there are good ways and bad ways to deal with moving with or without research group members (but that's too big a topic for this post).
1 month ago