At the moment, however, there is no comparable site for economics. Why? It's possible that that one will emerge in time, but I think that economics faces difficulties unlike any in math or programming. Specifically, it's hard to wall off a community from non-experts.
In math, this is easy enough. Everyone has some academic exposure to mathematics (if only in grade school), and virtually everyone who is not qualified to comment on advanced mathematics is self-aware enough to realize it. The vocabulary alone is nearly impossible for an outsider to crack: at the moment, one of the top questions on Math Overflow is "Morphism Between Polarized Abelian Varieties." (Not very inspiring raw material for a troll!)
In economics, however, most people have opinions about the "big issues" regardless of their academic background. How much deficit spending can we tolerate? Is another round of trade liberalization warranted? Should the Fed be loosening monetary policy further? Any site advertising itself as a forum for economists would quickly be overwhelmed by outsiders preaching their own decidedly non-academic opinions. Good luck having a technical discussion about how to specify a vector autoregression when the board is filled with posts about impending hyperinflation and the evils of the Federal Reserve.
The only way to avoid an overwhelming influx of non-economists would be to label the site so that only economists have any clue what it's about. A site titled "Sunspot Equilibrium" wouldn't attract any aspiring investors searching for advice on Google, or monetary cranks chatting about the need to buy gold. With sufficiently aggressive moderation, it could remain the exclusive domain of experts almost indefinitely.
There's always the risk, of course, that a horde of ideologues would run in to do battle with mainstream economists, but I'm afraid that comes with the territory. Math Overflow has it easy; only the wildest cranks believe that the Evil Mathematics Establishment is ruining numbers. Inevitably, however, a lot of people believe just that about economists, and it'll be tough to develop the online institutions that are improving communication in so many other fields.