Triangle Inequalities in International Trade: The Neglected Dimension

The so-called triangle inequality (TI) in international trade should, theoretically, hold for any three countries to avoid cross-border arbitrage. When trade costs change, re-routing opportunities – as captured by the TI – might arise because a shipment through an intermediary becomes cheaper under adjusted trade costs. We show that the widely used “exact hat algebra” approach, which does not require a calibration of trade costs, is unable to measure potential gains from re-routing. In addition, we show that standard empirical estimates of iceberg trade costs often violate the TI and are therefore inconsistent with the theory. We propose an estimation routine that respects the TI and yields estimates that are consistent with the workhorse models. This measure of trade costs allows us to compute the impact of changes in trade barriers while complying with the TI. First, we compute the welfare gains using only “direct” changes in trade costs (the standard approach). Second, we update the trade cost matrix to allow for re-routing whenever the TI is violated. We show that welfare gains are often substantially different (and usually higher) when taking the TI into account.