After taking the time to read the article, I would like to point out that, even after pointing out possible shortcomings, this is their final analysis:
"Still, a number of individual studies have found associations between spanking and negative outcomes, even after controlling for preexisting child behavior. So Gershoff says that in spite of the lingering controversy, the safest approach parents can take is not to spank their kids. “Studies continue to find that spanking predicts negative behavior changes—there are no studies showing that kids improve,” she says. And although Ferguson is not convinced that spanking is categorically bad, he is “certainly not an advocate of spanking.” Furthermore, there is a worrying body of research suggesting that parents who spank will later use harsher forms of punishment. “If spanking is not working, and spanking is all the parents are doing, then they’re going to escalate,” Gershoff says.