A link to that study would have been helpful.

But anyway, let's break this down:

1) Direct observation - In my two decades of work after college I personally have witnessed the difference between people happy to come to work and those who are not. The happy folks may goof off sometimes but they still get their jobs done. The unhappy folks gripe just as often as the happy folks goof around, and then they don't really care or follow through on work that needs done. It's a no brainer if you ask me.

2) Logically, if unhappy workers are more productive then the most productive situations of all are when you have violently oppressed slaves doing whatever you tell them to. (Not)

3) These type of results depend heavily on what type of work environment is surveyed. If you're looking at the results of ditch digging then happy or sad probably doesn't make much difference and in fact getting a little more ditch from the sad might actually happen just because they plod on. But if you're looking at professionals (lawyers, doctors), mid-level management, careers involving heavy interpersonal interaction (nurses, sales, customer service) then the results from the happy will utterly trounce the results from the sad.

I worked for three different companies in my years before retirement. I had very sad times at each, and very happy times at each. Neither situation had anything to do with my productivity. Pride was the deciding factor in either, and I produced whether I was happy or pissed off, probably the reason I was never fired. I could have been several times, even offered to quit. I talked to the boss just like I would talk to anyone else and they KNEW if I was unhappy. They also knew I got things done. Happy or sad. Being unproductive will usually come back to bite you. I always wanted them to miss me when I was gone.

When you're unhappy with your work, then you are likely going to be a lot less productive. When people are fed up with their job, then they won't do it as well.