No removing spanking doesn't cause good parenting but you would have to assume on a country-wide level parenting didn't suddenly get worse just because spanking was outlawed. I have the full pdf of the article if you would like it. Empirical data is always hard to come by when social "sciences" are involved because it is really pseudoscience. You cant come up with hard numbers on things as complex as human development.
The problem I have with most of those paper is the majority of them that deal with the affects of spanking reference the same study from 1998-2005. However, each paper cherry picks statistics from that study that correlate with the point they are trying to make (spanking is bad). You see over and over they mention mothers spanking 3 year olds (one of them even carries that title) and fathers with high-frequency spankings. That is because those are the only two outlying data points from that study that show a correlation between spanking and aggressiveness. When you look at all the data its becomes much much more muddled. In fact almost across the board the use of CP show almost no correlation with aggressiveness per the study they used to write their papers. This is just another case of cherry picking data to make it reinforce the point they set out to make before they looked at the data.