Is it reasonable to ask for a research assistant position (field of economics) over email to a professor who doesn't live in my country/city?
I'm assuming that you want to stay where you are if accepted and carry out the research remotely from the professor and any of his/her research groups.
Whether reasonable or not, it is possible to ask. But also expect skepticism. If you don't know the person already then it isn't very likely to be accepted, but again, it is possible. But your mail would need to present interesting reasons why the professor would want to accept you.
A professor who meets regularly in seminar with groups of students would have more trouble with such a plan than one who prefers to meet individually. Computer mediated communication is pretty common now and as the field doesn't require lab work, I see no absolute block. But if the research requires working with human subjects then you have to figure out how and where to do that, complicated also by the rules and regulations, perhaps, of two places, not just one. But a lot of small groups work collaboratively while the members stay in their separate countries, meeting only occasionally.
But, it is easy to send an email, a bit harder to make it interesting, and possibly harder still to be convincing. But not impossible.
It is also possible for people working remotely to meet now and again, whether through travel direct to the other place or at a conference or other professional meeting.
In addition to Buffy's answer, another important aspect to consider is whether you expect to be paid for this research assistantship. At least in the universities I have worked at, it's fundamentally impossible to hire a student who is, and wants to remain at, a different university. There are so many administrative procedures and details that would need to be sorted out (will they pay out the money or send it to your university, which then handles payment? will their university pay overheads to your university to cover your workspace and other utilities? how will taxation work? etc.). Further, my impression is that administrators may also not be happy about it in general, as it would feel like university money is being drained to support research elsewhere.
That said, an acquaintance in the US actually sat up a paid undergraduate research programme with India, where the undergrads were hired in and stayed in India for the duration of the programme (with remote supervision and one or two on-site visits of their mentor). But this was a significant administrative process, and he ended up funding it entirely through external sponsors. It is unlikely that this could be set up on an individual basis for just one student.