Trade data are typically aggregated across space. In this article, we investigate the sensitivity of gravity estimation to spatial aggregation. We build a model in which micro regions are aggregated into macro regions. We then apply the model to the large literature on border effects in domestic and international trade. Our theory shows that aggregation leads to border effect heterogeneity. Larger regions and countries are systematically associated with smaller border effects. We test our theory with aggregate and industry-level trade flows for U.S. states. Our results confirm the model's predictions, with strong heterogeneity patterns.

中文翻译：

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估计边界效应：空间聚合的影响

贸易数据通常跨空间聚合。在本文中，我们研究了重力估计对空间聚集的敏感性。我们构建了一个模型，其中将微观区域聚合为宏观区域。然后，我们将该模型应用于有关国内和国际贸易中边境效应的大量文献。我们的理论表明，聚合会导致边界效应异质性。较大的地区和国家系统地与较小的边界效应相关联。我们用美国各州的总体和行业层面的贸易流量来检验我们的理论。我们的结果证实了模型的预测，具有很强的异质性模式。