SE typically frowns on long conversations in the comments.
Can we afford to take that attitude with Economics?
The topics are complex, clarification is often required, and the discussion is usually relevant to all.
Do we have any opinions as a community on this?
Exactly, SE typically frowns on long-conversations in the comments. In practice they happen every now and then. Apart from the point made by @Ubiquitous, I believe we should also distinguish between "clarification" comments, and comments that provide some aspect to the question/conversation that is useful but not long or complete enough to become an answer.
"Clarification" comments I think should be accompanied by a suggestion to the OP to enhance the body of the question with new information, rather than giving it in a comment -and when this is done, comments should be deleted (I think this is part also of a moderator's job!). To this category also belong comments that alert the OP (or an answerer) for a potential mistake in the question or in an answer. If the situation is clarified and any mistake is fixed, then they too have no further life.
The "other" comments though, in my opinion become an integral part of the thread, and have a permanent place alongside the question and its answers.
I think that as long as the discussion relates to a specific question or answer then comments are the most logical place to put it. Once a discussion starts to go off on a tangent we should probably look at moving it over to chat or setting up a new question or answer.
Commments are designed to be ephemeral, and are to all intents and purposes third-class citizens on the Stack Exchange network. And that's by design. They are not indexed by the site search, they can't be downvoted, and can be removed at any time for any reason.
Do we have a really good reason to operate differently to almost every other site on the network? No, no we don't.
Comments are useful for seeking clarification on questions or on answers. They can be used to point out errors on answers - but in general, it's better to post a correct answer.
They are not there for discussion. To use them for discussion is an abuse of the system.
We are not a forum. Questions are there to be answered, not to be discussed. Answers are there to be voted on, or to spur the writing of other answers, not to be discussed. When a page starts filling up with comments, then it pushes the really important content off the bottom of the screen. When someone new arrives on a question page, from a search engine (source of 80-95% of a site's traffic), if they see a question and a long discussion in comments, they will (1) think we're a discussion forum, which we're not; and (2) they won't see the awesome answers unless they think to scroll down past all the noisy chat cluttter.
Discussion about the status of questions and other operations of the site belong here on meta.
Discussion about economics belongs on the Economics chat site(s).
There's a really nice feature in chat (the feature is locally called "one-boxing"), where if you post the link to a question or an answer (click on the "share" link under either to get the link to it) on a line to itself in chat, then a preview of that post will appear instead of the link; and the title will be a link to the post. That makes it really easy to discuss particular questions and answers in chat. An example snapshot from chat just now:
