As answered by an Android developer.
If the inflated view doesn’t have a background set, or the popup
window itself doesn’t have a background set (or has a transparent
background) then you won’t get a shadow.
which was my case and seems to be yours, since you are not using setBackgroundDrawable.
This worked for me
popupWindow.setBackgroundDrawable(new ColorDrawable(Color.WHITE));
I’ve opened a new issue suggesting that they update the documentation (https://code.google.com/p/android/issues/detail?id=174919)