With REST you have Pros and Cons
I like REST precisely because It's quickly (to develop,
test, maintenance,etc) and you don't have so many restrictions as you have in SOAP. However, sometimes is good to have a wsdl, a "formal contract".
Regarding to your question, the companies often provide a "service catalog" which explains the response codes, the expected scenarios and examples of the common responses. However, don't misunderstand the schema concept. You have schemes in REST, but those schemes are provided but the owner of the web service, and they can change them with/out notification.
A couple of years ago I used the FB api, and was a mess, because they change the responses (schemes) all the time ...
Regards,