That paper doesn't attempt to make a causal link. It's possible that being broke during the courtship process (when the ring is purchased) is what leads to a lasting marriage. I also can't find any discussion of the cost of the ring to the cost that could have been afforded. Is there a comparable outcome from someone who could easily afford a $10k ring but instead spends $1k vs someone who can only barely afford the $1k ring in the first place?