There are no studies that show spanking has any long term positive outcomes. There are plenty of studies that show negative correlation with long term negative outcomes. Just as is the case with this study, it is fair to call into question correlation and causation but if there were some food additive, fertilizer or herbicide that had even 1/10 of the correlative impact on children, the public would be freaking out and protesting around some multinational business but when it is parents damaging their own children we get relative silence.
Studies have shown that poor parents are more likely to spank their children. Studies have shown a correlation in spanking with smaller brain sizes, lower IQs, lack of self control. Studies have shown a high correlation between lack of self control and poverty. Again we don't have great data on cause v.s. effect but there are good indications that the early violence is causative in this chain.