This paper theoretically shows that changes in the distance elasticity of trade can be connected to welfare changes that depend on bilateral distance measures and expenditure shares of countries. Empirical results based on international and domestic trade data from the last two centuries show that the negative effects of distance on trade have increased over time when zero trade observations are ignored in inconsistent OLS estimations, confirming the distance puzzle in the literature. The corresponding welfare implications suggest that the world economy has experienced a cumulative welfare loss (about $81\mathrm{\%}$) due to this puzzle in the last two centuries. When the puzzle is solved by considering zero trade observations in PPML estimations, the tables turn such that there are significant welfare gains from trade (about $58\mathrm{\%}$) during the same period due to the decreasing negative effects of distance on trade over time. Welfare gains from further reductions in the negative effects of distance are investigated as well, suggesting significant potential gains from trade in the future.

本文从理论上表明，贸易距离弹性的变化可以与取决于双边距离措施和国家支出份额的福利变化相关。根据最近两个世纪的国际和国内贸易数据得出的经验结果表明，在不一致的OLS估计中忽略零贸易观察结果时，距离对贸易的负面影响随着时间的推移而增加，这证实了文献中的距离难题。相应的福利含义表明，世界经济经历了累积的福利损失（约$81\mathrm{％}$），因为过去两个世纪以来一直存在这个难题。当通过在PPML估算中考虑零贸易观察结果解决难题时，表格将转为从贸易中获得可观的福利收益（约$58\mathrm{％}$），因为距离对交易的负面影响随着时间的推移逐渐减少。进一步研究了距离的负面影响进一步减少所带来的福利收益，这表明未来贸易可带来巨大的潜在收益。