Parents just don't respond. Thinking parents are going to respond is just a waste of time in my opinion. If you are doing something where you have to have an exact count then put on the invitation that anyone not responding will not be counted and not expected. But even with that there are going to be kids that show up because the parents just got busy and forgot.
Why not just invite people you know and can actually talk to on the phone. Most schools have a student phone book. Let them know you are sending their child an invitation.
So far we have had friend birthday parties. I set the date and time and my friends and I talk all the time so I knew they were coming.
My friend has had several parties where she just sent the invitations and as the kids showed up she bought more food. Those were at places like Chuck E. Cheese or other places where you can actually feed everyone and when the food is gone everyone has had at least some food.