Some universities require a writing sample.  A suitable writing sample should demonstrate your analytical skills and understanding of econometric methods. The sample should ideally be a research paper or your undergrad/Master's thesis that shows your ability to think through a research question. You can find the one I used here.

As an applicant for a Ph.D. program, you are not expected to have groundbreaking research ideas. A writing sample only serves to show your ability to use data to answer a question you find interesting.