How important is the writing sample for PhD application in Political Economy
Of course this can vary from one department to the next, but in the humanities, the writing sample is generally considered very important.

According to the Department of Politics at Virginia Tech,


  Your writing sample is the most important part of your application.


Political science types are likely to weigh the writing sample more heavily than economics types, at least according to this political economist. 

If you do not have a thesis, you should at least have a relevant term paper or similar paper from your coursework that you can use as a starting point. Your writing sample should demonstrate critical and analytical writing (not merely descriptive).