Is it typically preferable in academia to pursue postdocs in institutions other than the one one has received a PhD from? I have heard on the grapevine that this is the case, but is there anything to back up this assertion?
The extent to which it is frowned upon differs greatly by discipline and country. At least having been in different departments/universities is usually beneficial for young scholars. Departments differ quite a bit, so having been in different departments/universities/countries broadens the range of experiences. This is usually taken into account by hiring committees, but again, the extent to which that is the case differs substantially.
Here is a perspective from pure math, which is probably applicable to some but not all other disciplines.
It’s not really about “pursuing” or about “frowning upon”. You “pursue” a postdoc to broaden your mathematical horizons and develop yourself as a researcher in an environment where you are exposed to new ideas. Doing a postdoc at your PhD institution will not achieve those goals, and hence as a secondary effect won’t help you get a tenure track job, since everyone you are competing with will have been working on developing themselves in that way. So, to an almost perfect approximation, no person driven by a rational objective will “pursue” such a thing.
Consequently, no one will need to “frown upon it” either, since there isn’t a problem of fresh PhDs asking to do a postdoc at the departments they graduated from and needing to be frowned at. By and large, almost everyone at that stage knows that what’s best for them is to do a postdoc elsewhere if they want to stay in academia, or to get a much-better-paying-than-a-postdoc, non-academic job right away if they don’t.
In other words, a useful way of thinking about it is that a “postdoc at your PhD department” is (at least in the context of pure math, as I said) a kind of category error. The concept “does not compute”, so to speak.
(Source: personal experience in academia.)
Edit: some people (who are not mathematicians and don’t share my understanding of math research culture) insist on claiming that doing a postdoc at your PhD department is “frowned upon” even according to my own analysis. It seems to me that this is an argument about semantics, and as such, I don’t find it that interesting or essential. But for what it’s worth, I’m willing to concede that one can view it as frowned upon according to a reasonable interpretation (though one that differs from my own) of those words.
Even if that’s the case, that does not affect my main argument, which is that for a mathematician to do a postdoc at their PhD department would be counterproductive from both a career and personal development point of view, and would largely defeat the purpose of doing a postdoc at all and miss the point of what postdocs are for. And this is true to such a large extent that almost no one will be interested in pursuing such a thing, and were they to try, their department would be very unlikely to offer them the opportunity to do it in the first place, except perhaps under very rare sets of circumstances. Call it frowning or whatever else you like, it simply is a thing that doesn’t make a lot of sense.
I think the issue is less about frowning upon post docs at the same institution you graduate from, but rather the missed opportunities.
Working with a different group of people increases the pool of folks you have that are willing to vouch for your abilities. It increases the pool of people you are likely to collaborate closely with.
Moving to a different institution gives you some new perspectives, including different approaches both to academic research and to all the peripheral goings on at a university.
Even just living in different cities might help you decide what things are important or at least relevant to decisions you make about where you want to take a job, both in terms of academic and local culture. Academic jobs tend to be more fixed than industry ones - there are fewer opportunities to move around later.
All these things can be beneficial to your future academic career.
I echo the comments by others that it is more about missed opportunities than explicitly frowned upon. Through a post-doc at another institution, you have the opportunity to build your network, to get the seal of approval on your CV that some other institution thought you are good, and -- perhaps most importantly for your next job -- an additional set of senior peers to write you letters of reference going forward.
If you continue at the same institution, you miss these possible benefits. Is it a tragedy? No. If there is a compelling reason to continue where you are -- exactly the right facilities, colleagues, etc -- all this pales in comparison to doing good, increasingly independent research as a Post Doc. If this is your best bet forward to do that, go ahead. If you're not sure, broaden your horizons.
The key points we look at in a postdoc is the future ability to develop an independent research program - independent of your thesis director. It is easier to demonstrate this if you change institution but if you continue to publish with your former advisor that is of no help. On the other hand, if you remain at the same place but develop independent collaborations, then that’s perfectly fine.
In some disciplines it is expected to do a postdoc elsewhere, at least in another laboratory but often at another institution or country. The benefits to this are:
You will have access to new equipment and gain technical expertise with new techniques
You will spend time with a new mentor and be introduced to their network
You will see how different labs operate differently
A postdoc is often regarded as training for becoming an independent researcher. As such the more different experiences you have, the better it will inform your decisions when the time comes to run your own lab.
A wider ranger of experiences is also beneficial to establish an independent research direction. It will be difficult to get grant funding if you are too close to your previous supervisor. Why would they fund you to do it, if they are still there and have more experience? If you have a different focus or move to a different country, you will not competing directly with them for funding.
In smaller countries, such as Australia and New Zealand, most PhD graduates are expected to go overseas for their postdoc and most faculty applicants are expected to have experience and contacts overseas. This is not expected as much in non-English speaking countries such as Japan or Korea where many graduates choose to stay in their home country (study or postdoc overseas is still encouraged and their are alumni societies to support this). This is less necessary in places such as the US or EU where there are many opportunities but you may still need to travel to another city depending on the job market in your field. Unfortunately, many people have to relocate during their academic career whether they want to or not.
I would say it's beneficial to postdoc somewhere else, rather than "frowned on" not to. There are many valid reasons not to relocate such as family commitments, culture shock, and illness. However, depending on the opportunities in your area, it can be disadvantageous not to. For example, if other graduates can successfully land a position at a prestigious institution overseas and you did not (whether by choice or not).
There are benefits if the institution is large enough to extend some breadth to your work without the burden of the politics of the department. Also, being at the same institution allows you to finish up anything that you might want. I believe that career goals and politics are more of a factor of the success of a postdoc than perception.
Personally, I did my doctoral work in circuits at a large institution; however, I did my postdoc in cryptography and RF circuits with the E&M technical interest group at the same institution. We were able to leverage the resources that I knew about on the circuit side without any issues because the department is huge.
Whether it is actually the case or not would depend upon the culture and the persons deployed there. One bad apple can rot a whole bunch. It should not be the case since the focus should always be what benefit a person's contribution would bring to the wider humanity (though often this is debatable at the time and new approaches are frequently met with opposition and ego...)
If the question is personal to you I would weigh up the options. Depending on the weight "frowners" could bear upon you it might be self-destructive to remain if you could leave and get fresh air a new place. I would definitely aim for an upward climb no matter what field you are in. Sometimes negativity from others can be a reflection that you are actually on the right track but you must protect yourself wisely too.
Use your common sense, your gut instinct and remember in the end your own judgement is what counts.