When someone wins the lottery, it can be bad news for his neighbor's finances. A new study from the Federal Reserve Bank of Philadelphia examines the relationship between lottery winners in a particular Canadian province and bankruptcies in the same province — it found that neighbors of lottery winners are unusually likely to go bankrupt, and the larger the lottery prize, the more likely bankruptcy becomes.

Specifically, every $1,000 in lottery winnings translates to a 2.4 percent higher probability of a nearby neighbor declaring bankruptcy.

The researchers have an explanation for why this happens, too. When people declare bankruptcy in Canada, they have to disclose all their major assets — things like houses, cars, boats, and motorcycles — to the courts. The researchers found that the larger the lottery prize, the more money bankrupt neighbors spent on big-ticket vanity purchases — and the more likely they were to run out of money.

The clever study is one of the first to provide statistically rigorous evidence for a claim that seems plausible but is hard to prove: that rising inequality causes people to spend beyond their means in an effort to "keep up with the Joneses." This is the idea that when someone's wealth suddenly increases, her neighbors — and probably her friends and relatives — feel pressure to spend more to avoid being upstaged. Ultimately, this kind of competition can leave everyone worse off.

And while big lottery winnings are rare, the study could have much broader implications. Critics of income inequality have long argued that large income disparities make people unhappy. The Philly Fed study provides further evidence for this point of view. While it focuses on lottery winners, the same basic problem is likely to arise anytime some people enjoy rapid income growth at the same time that others' incomes are not rising.