Page Authority has got absolutely nothing to do with Rankings. It is just a metric made up by Moz.
It is not a factor that Google Search Engine remotely considers. Page Authority, no matter how high or low, will not rank a website any better than one with lower or higher.
If you want to increase these amounts, you need to have more quality backlinks from high PR sites.
I wouldn't go so far as to say Moz PA/DA and other third party metrics such as Majestic CF/TF are made up... That's total nonsense... Whilst I agree with your point that these metrics are not ranking factors, they do have its uses.... I am sure most people do realize that these metrics are third party attempts to understand Googles ranking algo... Besides using third party metrics what else do we have? .... and NO its not PageRank.... PR has not been updated for a number of years publically and as such is dead....
So you have a choice of using nothing or third party metrics which help as an indicator when assessing domains for backlinks or for purchasing as part of PBNs etc....
I would say Moz is not one of the best metrics as its easy to game with spam links... Hence I also recommend Majestic in particular TF (Trust Flow) as that is harder to manipulate.. One good way to make a quick assessment is to divided CF (Citation Flow) by TF and if you get close to one that is a great indication of quality and above five you should for sure investigate further...
Besides third party metrics other checks one should make includes - checking the types of sites which are providing backlinks, how well the actual site ranks for its main keywords and also the websites internal linking structure and other on-page SEO factors....
Ultimately one should always be cautious when using third party metrics - as they only provide an estimate... But for sure they most certainly have its uses...