I don't have a huge amount of evidence for this (I suspect you do not for your claim either), but I would guess that yes, it does make people happier.
The stuff I own is not keeping up with the neighbours, it's stuff that is meaningful to my hobbies. I have a cupboard full of board games because that makes me happy. My friend has a cupboard full of kitchen equipment because that makes them happy. My other friend has a basement with a home gym, my other friend has a mountain of books, and another friend has lovely furniture.
Which all implies that we're not really trying to keep up with each other, because if we were, we'd now be competing in completely different races. And even when I meet people with a similar interest to me (e.g. board games), the wealth and variety of the medium means that we'll probably still have very different interests within the world of board gaming.
So it logically seems to me that, if anything, the era of social competition is waning because people are more willing to accept that they want different things to their neighbours.
The stuff I own is not keeping up with the neighbours, it's stuff that is meaningful to my hobbies. I have a cupboard full of board games because that makes me happy. My friend has a cupboard full of kitchen equipment because that makes them happy. My other friend has a basement with a home gym, my other friend has a mountain of books, and another friend has lovely furniture.
Which all implies that we're not really trying to keep up with each other, because if we were, we'd now be competing in completely different races. And even when I meet people with a similar interest to me (e.g. board games), the wealth and variety of the medium means that we'll probably still have very different interests within the world of board gaming.
So it logically seems to me that, if anything, the era of social competition is waning because people are more willing to accept that they want different things to their neighbours.