I worked for several different multi nationals, I was a consultant for municipal governments, and I also worked for a paper manufacturer that had a significant recycling presence.
When you ask if they are effective, I guess it depends on how you measure that?
Are they effective diverting waste from landfills - yes (although the recent China issues may have changed that a bit. China would pay too much for contaminated loads and programs morphed into sloppy inventory because of it. It wasn't always like that and loads used to be much cleaner)
Is it cheaper than just throwing it all away into the landfill? No. Two trucks instead of one, lots of processing costs, but there is avoided landfill fees. It is somewhat of a local determination in this regard - if disposal fees are really high, it is more effective. Where landfill capacity is significant and costs are low, more of a challenge.
The design of the program and the education of the users make a big impact, as well as if your program is near major ports (transportation costs). Too many people that throw too much trash in the recycle bin because they aren't willing to educate themselves. Many states have mandatory recycling programs and create rate incentives to minimize volume. Those types or programs reduce the landfill volume pretty effectively. Where it is voluntary subscription basis, participation rates are generally abysmal.
Current recycling prices are very low, to even where you have to pay to get rid of materials that used to have a value. Driven by the change in China, but I have seen it like that even when there isn't that crisis - it is definitely cyclical.