Optimal tariffs with heterogeneous agents
This paper by Eduardo Davila, Andrés Rodríguez-Clare, Andreas Schaab, and Stacy Tan, develops a comprehensive theory of optimal tariffs in dynamic economies with heterogeneous agents, extending the classic static tariff formula to modern intertemporal trade models. The authors show that intertemporal export supply elasticities are sufficient statistics for determining optimal tariffs in dynamic settings.
Key theoretical results
Intertemporal tariff formula: The paper generalizes the classic tariff formula to dynamic heterogeneous agent economies. While the traditional formula states that optimal tariffs equal the inverse of foreign export supply elasticity, the new framework shows that optimal tariffs depend on intertemporal export supply elasticities across all time periods, weighted by relative tariff revenue considerations.
Micro-foundations of export elasticities: The authors demonstrate that the structure of intertemporal export supply elasticities differs fundamentally across economic environments:
- In representative agent economies with permanent-income consumers, the intertemporal effects exactly cancel out, making the optimal tariff formula collapse to the static case.
- In heterogeneous agent economies with incomplete markets, households have limited planning horizons due to borrowing constraints, creating meaningful intertemporal linkages that affect optimal tariff policy.
- In New Keynesian models, business cycle dynamics and nominal rigidities further shape the export elasticity structure.
Second-best tariff theory: When the economy cannot achieve first-best efficiency, optimal tariffs must balance multiple objectives. The paper shows that second-best tariffs trade off intertemporal terms of trade manipulation against production efficiency, risk-sharing, and redistribution concerns.
Quantitative applications
The authors apply their framework to a calibrated heterogeneous agent New Keynesian (HANK) model with trade, finding several important results:
Positive effects of tariffs: A permanent 10% tariff increase leads to long-run consumption gains of 0.5% but reduces labor supply and output by roughly 1%. Surprisingly, exports fall more than imports, worsening the trade balance in the long run.
Optimal policy: The Ramsey steady state implies an optimal long-run import tariff of 5.4%. When home productivity rises by 1%, the optimal response is to temporarily increase tariffs by 0.5%, generating short-term trade balance improvements.
Policy implications
Trade balance effects: The analysis reveals that the relationship between tariffs and trade balances is complex and depends critically on the timing and persistence of tariff changes. Constant tariff levels have no effect on long-run trade balances, but optimal time-varying tariffs can influence both trade dynamics and steady-state outcomes.
Heterogeneity matters: The paper demonstrates that household heterogeneity and incomplete markets fundamentally change optimal tariff policy compared to representative agent models. The traditional focus on static export elasticities can be misleading in realistic economic environments.
The intertemporal nature of trade means that optimal tariff policy must account for how current decisions affect future trade flows and welfare. This creates a role for sophisticated, time-varying tariff policies rather than simple constant rates.
A Dynamic Theory of Optimal Tariffs
Authors: Eduardo Davila, Andrés Rodríguez-Clare, Andreas Schaab, Stacy Tan
From: Yale University, University of California, Berkeley
Geopolitical considerations and optimal tariffs
This paper by John S. Becko, Gene M. Grossman, and Elhanan Helpman examines how geopolitical considerations influence optimal trade policy design when large countries seek to attract smaller allies through preferential trade agreements. The authors develop a theoretical framework that extends the classic Mill-Bickerdike optimal tariff analysis to incorporate geopolitical objectives. The model structure includes large countries (hegemons/great powers) and a continuum of small countries that produce a homogeneous good (numeraire) and unique differentiated products. Markets are perfectly competitive with constant elasticity of substitution (CES) preferences.
Geopolitical framework
- Small countries face heterogeneous “valence shocks” (costs/benefits) from aligning with large powers.
- Large countries derive utility from having allies and incur costs when countries align with rivals.
- Alignment decisions are endogenous, based on economic incentives (preferential trade access) and political costs.
- Two scenarios analyzed: unipolar (single hegemon) and bipolar (competing great powers).
Policy instruments
- Large countries can offer Free Trade Agreements (FTAs) to aligned countries.
- MFN (Most Favored Nation) tariffs applied to non-aligned countries or rival-aligned countries.
- Trade policy serves as both “carrots” (preferential access) and “sticks” (punitive tariffs).
The authors calibrate their model using UN General Assembly voting patterns as proxies for geopolitical alignment (1995-1998 for unipolar; 2021-2024 for bipolar); GDP shares to determine country sizes (US: 27.7% in 1997, 26.5% in 2023; China: 17.0% in 2023); military spending to infer preferences for allies and finally, “vote-buying estimates” from existing literature to calibrate alignment costs.
Key findings
- Geopolitical tariff premium
When geopolitical concerns are active, optimal tariffs exceed the classic Mill-Bickerdike level. The optimal tariff balances traditional terms-of-trade considerations with strategic incentives to encourage alignment. - Tariff determinants
– Optimal tariffs increase with the importance placed on geopolitical allies
– Tariffs increase with factors that raise the “hazard rate” of alignment cost distribution
– Country size effects are ambiguous due to competing economic and geopolitical forces - Strategic interactions in Bipolar World
– Rival tariffs can be either strategic complements or substitutes depending on various channels
– Multiple offsetting forces make the net effect theoretically ambiguous - Unipolar scenario (US as Hegemon)
– Optimal MFN tariff is 22.6% (compared to 9.7% without geopolitical considerations)
– Geopolitical component accounts for nearly three-fifths of the total tariff
– Hegemon attracts countries comprising 52.7% of world GDP as allies
– Average applied tariff: 4.1% (much lower than MFN rate due to FTAs) - Bipolar scenario (US-China Competition)
– US optimal tariff: 12.4% (geopolitical component: ~30%)
– China optimal tariff: 7.0% (geopolitical component: ~18%)
– Strategic interactions are quantitatively modest in the calibrated model - Impact of rising geopolitical tensions
– Stronger preferences for alignment lead to higher non-cooperative tariffs in both settings
– A second great power’s emergence can significantly reduce trade volumes and contribute to deglobalization
– When China’s GDP share rises at the expense of smaller countries, global trade openness declines steadily - Distribution of alignment costs matters
– The distribution of small countries’ alignment costs critically shapes geopolitical impacts on trade policy
– Periods with many countries near the “margin of alignment” (like late 1990s) see stronger geopolitical effects
Optimal Tariffs with Geopolitical Alignment
Authors: John S. Becko, Gene M. Grossman, Elhanan Helpman
From: Princeton University, Harvard University
