To what extent is this practice effective or ineffective? Is there any
correlation between puzzle-solving performance and job effectiveness?
If there is evidence of correlation, then for what types of roles? And
what types of puzzles?
And if (as I currently understand to be the case) there is little or
no evidence to support the effectiveness of puzzle-based job
interviews, then why do companies persist with this practice?
Interviewers will often tell you that they use these questions to "see how you think", or "see how you think out of the box", or "see how you think under pressure" or some variant of that.
I don't believe any evidence exists to support such a claim. And I know of no company that can say "we have found that better puzzlers make better employees" with a straight face (puzzle-producing companies excepted).
Puzzle questions are a fad whose time has come and gone. At one time, companies like Microsoft used to ask questions like "why is a manhole cover round?" or "how many ping pong balls would it take to fill a jetliner?". Since folks equated Microsoft with "smart" and everyone wants to seem smart, they often chose similar questioning methods.
I once had a Developer ask a QA candidate I was recruiting "How would you find a needle in a haystack?". When I questioned the Developer if he thought that was a useful QA question, he said it would "tell him how the candidate thinks". When I pressed further, he said it was asked of him once in an interview and he thought it was a "good question". I never asked him to help with interviews again.
Apparently, Google no longer believes such questions are useful, and has some idea of the real purpose of these sorts of questions: http://www.nytimes.com/2013/06/20/business/in-head-hunting-big-data-may-not-be-such-a-big-deal.html?pagewanted=all&_r=0
According to Laszlo Bock, senior vice president for people operations at Google: "They don’t predict anything. They serve primarily to make the interviewer feel smart."
I agree with Laszlo.
Hiring and interviewing are hard. Coming up with relevant questions to discern the fit of a potential employee is hard. Asking puzzle questions is just lazy, in my opinion, and wastes valuable interview time. Unfortunately, most folks aren't trained on how to conduct an effective interview, so they just go with what they have heard is "smart" or "a best practice" and don't put any more thought into it.
After you are hired and advance in your career such that you are the hiring manager - choose better interview questions! No more "What is the air-speed velocity of an unladen swallow?" please.