Abstract

This paper investigates the trade elasticity, a key parameter in international economics, and examines biases in its estimation arising from dynamic treatment effects and staggered adoption. Leveraging the 2018 US trade war tariffs as a natural experiment, I apply a local projections difference-in-differences approach, estimating a short-run elasticity of -1.4 and a long-run elasticity of -3.7, with adjustments stabilising within 15 months. Failing to account for staggered adoption or dynamics introduces a downward bias of approximately 50%. I also propose a novel correction to the estimation of dynamic multipliers to cumulative policy changes in the presence of staggered treatment timing. This correction eliminates a systematic bias that can otherwise distort estimates.

Non Technical Summary

How much does trade respond to tariffs? This is a central question for international economics and trade policy, especially at a time when protectionism is on the rise. Economists use the concept of trade elasticity to answer this question, which measures how strongly imports fall when tariff costs go up. This elasticity determines the expected impact of tariff changes on trade flows, and it also plays a key role in calculating the welfare gains from trade in economic models.

While the trade elasticity has been studied extensively, estimates vary widely. Older studies often found large values (around -5), suggesting that trade is highly responsive to tariffs. More recent research, especially using difference-in-differences methods, has reported much lower numbers (around -1.5 to -2.5). But these lower estimates may suffer from biases, which this paper sets out to address.

Two key issues can distort estimates of trade elasticity. First, trade adjusts over time. When new tariffs are introduced, firms often need time to react (renegotiating contracts, switching suppliers, or reorganising production). This means that short-run responses to tariffs may be smaller than the long-run effects. Second, tariff changes are often implemented in stages. Rather than all products being affected at once, tariffs are typically introduced in waves across different goods and countries. This staggered rollout creates a problem for standard methods. When combined with dynamic responses – that is, gradual adjustments in trade over time – this can lead to a serious underestimation of how strongly trade actually reacts to tariffs.

To study this problem, I focus on the 2018 US trade war, one of the largest and most abrupt shifts in US trade policy in recent history. During this period, the United States imposed new tariffs on many products and countries, often with little warning and using rarely used trade laws. The policy shocks were large, sudden, and varied by product and country, making them well suited for empirical analysis.

Using monthly US imports data by product and country, I apply a modern econometric approach that carefully accounts for both dynamics – how trade responses unfold gradually over time – and staggered adoption – the fact that tariffs were introduced at different times for different products and countries.

The results speak clearly. When using standard methods, the long-run trade elasticity appears to be around -1.9, in line with previous estimates. But once we correct for dynamic responses and the staggered rollout of tariff changes, the long-run elasticity increases in absolute value to -3.7. In other words, standard approaches underestimate the true response by about 50%.

The short-run elasticity is estimated at -1.4, confirming that trade takes time to adjust. However, the adjustment is relatively quick: the elasticity stabilises after about 15 months. This is notably faster than suggested by previous studies, which often find adjustment periods of five years or more. One possible explanation is that firms perceived the trade war tariffs as temporary, encouraging quicker substitution away from targeted suppliers.

These results have important implications for economic modelling. The magnitude of the trade elasticity feeds directly into calculations of the gains from trade – or how much better off a country is compared to the hypothetical situation of complete self-sufficiency (autarky). Using the lower, biased estimate of -1.9 would imply that the US gains 4.5% in welfare from trade compared to autarky. Using the corrected estimate of -3.7 cuts those gains nearly in half, to 2.4%.

To validate these results, I show that the corrected elasticity estimates accurately predict observed declines in aggregate US imports from China during the trade war, as well as the effects of retaliatory tariffs imposed by the European Union on US products. In both cases, the estimated trade response closely matches what we see in the data.

The data also reveals nearly complete pass-through of tariffs into US import prices. In other words, the entire cost of the new tariffs was borne by US importers, not foreign exporters. However, there is some variation across sectors, with a few showing incomplete pass-through.

The findings have two key takeaways: first, policymakers and analysts using standard trade elasticity estimates may be underestimating the true responsiveness of trade to tariffs. Second, because the empirical setting closely resembles recent US tariff increases, these results can inform how we evaluate current and future protectionist measures.