There are quite a few studies debunking the effectiveness of Open-Plan Offices (sometimes named Open Space), such as this study by the Queensland University of Technology. However, I wonder whether it might be true that OPOs might have any positive impacts. Is there any proof for that or is there only evidence to the contrary?
It depends. Among other things, it depends on how it's managed and what the occupants' expectations of sound-field are. Most organizations implementing open plan outside the financial industry don't seem to realize what they're getting into:
Where open plan works
The above picture is a typical trading floor. In this environment, the whole point of open plan is communications2 -- when Sally needs to get a piece of information to Bob 50 feet away, the fastest way for her to do that is to stand up and yell. Add hundreds of other sources like ordinary conversations, phone calls, and the always-on squawk boxes linking other floors worldwide by voice, dial all of them up to 11 as everyone tries to be heard over everyone else, and you have a continual roar. When something major happens somewhere in the world, you can actually hear it ripple through a trading floor, starting with the group(s) who are most immediately affected, spreading across the rest of the floor over the next few moments. This situational awareness is crucial4.
If you want to have an organization that is that much of an agile machine, and if everyone on the whole floor signs on to work in a high-energy sprint or hackathon-like environment full-time, then it can work. It's hard to put numbers on it, but the revenue per headcount of the financial industry on average does tend to be higher than that of tech5.
I used to go to the trading floor when I needed to hide and code -- the chaos of an unleashed open-plan environment is a sea of white noise, perfect for concentration, with plenty of ambient energy to keep you from drifting.
Where open plan doesn't work
Most open-plan offices I've seen in Silly Valley are expected to be as silent as libraries, and if any actual sound starts to emanate from one part of the floor, someone always pops up like a prairie dog to squelch it. It's never going to work that way -- a silent open-plan floor is an oxymoron and a productivity killer. If Jimmy starts tapping his fingers three desks over, everyone gets distracted.1
Office size matters
That "white noise" effect won't work if the open plan office is too small. In the comments below, @DevSolar and I discuss small offices of 5-10 people, including the likely size of Joel Spolsky's office when he first advocated office doors for developers.
As of this writing, a google search for "open plan office white noise" turns up articles discussing the use of noise generators to increase the masking effect in small offices.
About the author
I used to build trading floors in NYC before the open-plan office idea started catching on big in the San Francisco Bay Area.
I'll do my best to find citations for these claims, but it's going to take time. Much of what I describe above is just "generally understood" in the trading industry3, and most research about trading instead focuses on the instruments rather than the environment. I welcome comments and edits, and I'll return here myself as I run across things in the future.
 It's easy to find papers that talk about the productivity losses from open-plan offices -- here's one of many that came up on the first page in Google, citing distracting sounds as being a main issue: http://www.sciencedirect.com/science/article/pii/S0272494413000340
 Here's an article that talks about open plan in general, how the noise can be distracting in general offices, but how the need for open plan on trading floors is still there, mentioning communications as a main benefit: https://jpreis.com/2017/12/05/2417/
 Trading's culture of open plan and expectations of a noisy environment date back to the days of open outcry pits: https://en.wikipedia.org/wiki/Open_outcry
 As more trading has moved from pits and open floors to small and remote offices, an entire industry has sprung up to stream floor sounds over the internet to individual traders to give them that sound field gestalt that they would otherwise be missing. While this article's headline is about synthesized sounds, it also discusses some incidents where actual floor sounds mattered: http://www.post-gazette.com/business/tech-news/2006/06/14/Software-simulates-sounds-of-the-trading-floor/stories/200606140141
 It's hard to isolate out the benefit of open plan itself, but by industry, even in a challenging interest rate environment, the financial sector still eked out a 35% higher revenue/headcount ratio versus IT in 2016: https://craft.co/reports/s-p-500-revenue-per-employee-perspective
Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.
The cost of fit-out for open-plan areas is much lower than traditional offices.
For example, this interior decorator suggests:
An open plan office design traditionally cost approx $400 per square meter. An average office fitout with a few offices traditionally costs approx $550 - $750 per square meter depending on the level of finish required.
(That's Australian dollars, but the units are largely irrelevant.)
If you squeeze more people per square metre into an open-plan area than a traditional office, that is even more savings per employee.
(I'm half-expecting responses that this is a false economy, but that is largely dependent on the commercial conditions the company finds itself in. There may well be some situations where it makes good economic sense to sacrifice longer term productivity in order to reduce up-front costs.)