A lot of self-selection would be involved in a study like this. Is it possible the people who are happier working longer hours for themselves are more likely to be self-employed? Generally speaking, it takes a certain kind of person to become an entrepreneur. There are people who don't even want to work for themselves. I'm not too sure about the accuracy of this statement.
This is kind of self selection in play here. Since having a job is the default, if you aren't happier being self employed then you simply stop being self employed and go back to having a job.
It should read "self employed people are happier and more engaged *when their business is actually providing a living for them. Other study shows only 18% of self-employed entrepreneurs stay self-employed for over 5 years."*
Emphasis mine. This is like saying " people that don't get in car accidents are much less likely to die in a car crash."
If the U.S.A. had national health care, there would be an explosion in self employment. People stay in jobs and careers they hate to maintain insurance.