It's even a signal nowadays. Companies with women in mid to upper management positions are signaling they're not corrupt, and they're all about efficiency and quality of work.
At least in the Gulf, if you want it done, put an Arab woman in charge.
I heard the complaints from right-wing groups when they said "it's a place for boys and girls to sit side by side and learn useless abstract mathematics that will server neither God nor the nation", and I thought ... FUCK YEAH!
My younger sister finished medical school only a few years ago, but because she speaks 4-languages and has a master's degree, she went on to manage an entire clinic, and soon after that the investors sent her to training in hospitality and gave her a hotel to manage, then a second. This is in Oman, btw. I know it's anecdotal evidence, but you couldn't imagine a 27 year old woman managing hotels and hospitals with a staff of several hundred. (I was worried they might be framing her for "something", but I went over her paperwork and it's all kosher; she answers to a board of directors and has clear rights, responsibilities, budget, and reporting procedures. She has been at it for 3 years now.)
Similarly, when dealing with companies in Gulf, I have seen a few repeating patterns in management. You have the national institutions headed by tribal/military chiefs, you have the domestically owned companies headed by foreign expertise, then you have this new breed of "agile" companies headed by women and young people that don't seem to respect the traditional order and hierarchy. Ten years ago, a Request for Proposal was a joke; a formality to waste people's time before the contract was given to the CEO's cousin.
This has been documented in the U.S. and is pretty core to advertising agencies today who have a goal of generating revenue from minority groups: you need to hire the minority groups into your companies because people tend not to buy where they cannot work (DBWYCW, or "Don't Buy Where You Can't Work" is a popular acronym in the early 20th century from the United States). Don't read this the wrong way as "they only use minority groups to generate revenue," this is a marketing goal to do business with minority groups (it's not a bad or "evil" thing).
Revenue increases when you do this. There's a correlation there, but I really doubt that the cause is a supposed increase in productivity simply by giving people an opportunity they otherwise wouldn't have had. I think the key indicator is to look at the media and see if these people have boycotted against companies who refuse to hire members of their group (women and African Americans were the two major groups during the Great Depression who practiced this).
It was also suggested that women for example are cheaper, although if you have a company doing programming (just a random example) and you're hiring women for secretary jobs (another example), your revenues are going to be discounted by the fact that you have less programmers. I'm not sure what type of jobs they're filling, but I'm a bit skeptic about this although it at least sounds intuitive.
The typical economic argument is a variation on the general principle that when other people are making irrational decisions (e.g. not hiring the best candidate because of their gender), you can do better / take advantage of them.
The article also said the researchers were speculating that women made better decisions because they were traditionally in charge of household spending and therefor understood the consumer better.