Is research experience in a different field relevant for PhD application? I am a economics major undergraduate student who will apply for grad schools in the coming semester. I think I have quite a strong research experience in mathematical statistics (asymptotic statistics to be specific), but, unfortunately, not much in economics itself. So I am curious if economics departments in graduate schools will care about my research experience in statistics?

Maybe a broader question is if grad schools care about applicants' research experience in a different (maybe even unrelated) field at all? I guess in my case statistics and economics are still quite correlated, but what about other more distant combinations of target departments and previous research experience?
While field-specific research experience is always the best kind, I think there is a role for good research experience in any related field. Close-by disciplines that share similar research methods and approaches will carry much more weight than something much further removed. (For instance, as a chemical engineer, I wouldn't put much stock in somebody doing sociology or clinical medical research, but somebody who had a background in research in applied mathematics or mechanical engineering would be potentially of interest.)

So, if you're going to go into an area of economics where your mathematical statistics background will be of benefit, I think that will (or at least should) be viewed favorably by an admissions committee.

That said, you will want to make sure that your research supervisor understands that you're applying to economics programs, and tailors her letter of recommendation accordingly. Also, if you have a lot of experience in a different field, you will need to make clear to the admissions committee why it is you want to pursue the new field.