Is "response time" calculated only on initial requests, or does EVERY communication affect it?

Say I've been emailing back and forth with an owner, and their final response to me is "see you next time," or something else that doesn't require a response. Will it affect my response time negatively if I don't respond to that email? I don't want it to seem like I have to have the last word. A client and I could go back and forth forever!