Income Mobility in the United States

A new comprehensive, and apparently highly credible, study came out that contrary to conventional belief (another words what we've been told by our politicians and the media) income mobility in the United State has remained the same for the last 40 years. While this was barely covered in media reports for some reason,and has been generally absent from the political talk show conversations,I noticed that the President in his State of the Union address did modulate his words and referred to economic mobility having "stalled" rather than "declined" which is what I'm sure he would have said before the release of this study. The conclusion of this study did not fit the narrative of the Left, and indeed some on the Right, who take the position that economic mobility in the US has gotten worse over the years,and was much better in the past. However, the study did mention that income mobility in the U.S. was behind most developed countries. The study I read didn't go into detail about this issue and I'd like to see if the comparisons are really apples to apples. I've done a little digging myself and here's an example of how statistics often don't tell the whole story and can be used to distort political points of view. As mentioned, we hear that income mobility is so much better in other countries, such as Denmark, than in the United States. Put aside the lack of diversity of this small country, and other factors, compared to the US, we are told that income mobility is much better there than here. However what does that mean? Consider the following information I came across from a reliable source: A Danish family can move from the 10th percentile to the 90th percentile with $45,000 of additional earnings, while an American family would need an additional $93,000 to move from the bottom to the top. As best as I can tell both countries have similar costs of living. If so, who is better off; a Dane who's income has gone up $45,000, thus moving her into the top from the bottom percentile; or an American whose income went up twice as much as the Dane's ($90,000), but went up from the bottom to only the second highest percentile? Those who deprecate US economic mobility would say the Dane is better off. I don't think that Dane would agree; she'd rather have the increased income the American got, I assume. However, as I've often said statistics can be misleading , so where did I go wrong here?