Agile Product Managers do not write specs
As we all know from experience, it is not sufficient for just the software team to follow agile processes.
You need the support of the rest of the organisation too, especially your product managers. Otherwise your developers end up having to answer all the wrong questions, such as "show me your commitments to a schedule and milestones", "how much will it cost?", "have you eliminated all the risks?" and "when will you be done?".
Atlassian is one of the companies that does agile well. Atlassian consistently delivers new features with customer involvement using agile processes.
Product managers explain why they don't write requirements, how they build risk assessment into their decisions about whether to build a prototype or not, how testing is done without specs, and how they deal with agile remote teams.
Good food for thought ( oh, also some beer recommendations too)