The institute where I'm doing my PhD has a formal policy not to hire local PhD graduates as postdocs. Is this normal?
I live in Europe.
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As far as I know, there are no official rules prohibiting institutes, universities or even labs to hire former PhD students as post-doc. Sometimes, a supervisor might hire you for a short period of time as Research Associate to wrap up papers and finish work at the lab, but this typically does not exceed 6 months to a year and should be considered to be part of the PhD work.
That said, although there are always exceptions, in general it is a pretty bad idea to do a post-doc at the same lab or department as your PhD. Some people even consider it to show a lack of ambition, competence and motivation; and I've been told it is frowned upon by hiring committees.
Successfully completing a PhD is the endpoint of an apprenticeship relation with the PI and lab. A post-doc is an opportunity to break that relation and take the experience and knowledge from your PhD to perform more independent research, build a new network, diverge into other topics, and experience a different lab culture.
It depends very much on the field and on the circumstances. A student in an experimental field who has done enough work to finish a thesis might well be invited to stay on for a year or two to do more work on the same broad experiment. A student who has finished a thesis late in the job-hunting season might be offered a one-year position as a post-doc or an instructor to enhance her CV before moving on to a longer term position. There simply are no general rules.