How to search who exactly to cold-email for a research internship? I am interested in cold-emailing some professors to ask whether they would be willing to offer a research position to me. However, I am not sure who exactly to email. I have an idea of the sub-fields of economics that I am interested in, and I've tried reading some of the journals in those subfields. However, as an undergraduate, most research methodologies don't make much sense to me (isn't this a universal undergraduate experience?). To be clear, it's not that I don't understand the research at all. Sometimes the choice of a particular statistical model used in a paper makes perfect sense, but at other times, the statistics involved is way too advanced.
I also do not attend a research university, so I cannot email any professors at my own institution (I am pretty sure no professors in the economics department at my university are taking on mentees; I've tried asking!)
So, how should I approach this process? Where should I begin this search? Should I target professors in my home state or who are otherwise geographically close? Should I target those who are tenured, old, and established? Should I target younger professors? What about those at lesser-known universities? My observation was there that there usually are a couple of professors at smaller universities who do some really interesting work and are also somewhat well known in the field. Should I target exclusively these professors? Should I look at recent articles from a field journal and just start emailing authors of those articles that I can understand, to a certain degree, and whose topics I am interested in? And what exactly should I write my email to the professor, given that the research they published was most likely beyond my understanding?
P.S. If this is relevant, the discipline is economics.
You're right that it's hard for an undergraduate to know where to start, and you've done the right thing by asking professors at your own university first.
The next thing to try would be to ask those professors again, but instead of asking to work with them, ask for their suggestions of a couple of people at other universities who you could get in touch with. You can do this iteratively: each time you email someone to ask for an opportunity, say that you understand if they're too busy to take on a student and ask if they have a suggestion for someone else you can contact.
Those more senior to me may weigh in on this, but it's generally frowned upon to offer your work for free. If the professor isn't able to compensate you financially, would you be able to get course credit for your work? I'm not too familiar with the US system, but perhaps it is possible. I would avoid working for free if you can -- it sets a precedent and allows professors to favour those who have their own financial support (and thus puts less well off students at a disadvantage when looking for research opportunities).
Keep studying the literature if you can, and persevere with emailing professors. To maximise your chances of a response, keep the email polite and to the point. Good luck!