What do PhD programs, specifically finance and Econ programs, look for in research experience?
This probably depends a lot on your definition of "top."

To get a sense for what successful applicants look like, check the websites, CVs, and/or LinkedIn profiles of current students in the programs you are interested in. (Look at their history from before they entered the program, of course.)

For example, I looked up the list of current econ PhD students at NYU Stern and started Googling. All the ones I checked (the first five names or so currently on that list) had some kind of formal research experience prior to joining the program.