Terms-of-Trade Theory of Trade Agreements

Terms-of-Trade Theory of Trade Agreements is the canonical economic theory of the General Agreement on Tariffs and Trade (GATT) and the World Trade Organization (WTO) in international economics and business and economics theory, developed by American economists Kyle Bagwell and Robert W. Staiger in their landmark 1999 American Economic Review article "An Economic Theory of GATT" and their 2002 book The Economics of the World Trading System. Confronting the long-standing puzzle of why sovereign governments—even when driven by special-interest lobbying as in the Protection for Sale model or Stolper–Samuelson income redistribution—view their own tariff reductions as painful "concessions" yet sign binding reciprocal tariff-cutting treaties, Bagwell and Staiger formulated a general equilibrium framework in which each government's political-economic welfare function W(p, p^w) depends separately on its local relative price p (which governs all domestic distributional and political-economy objectives) and the world / terms-of-trade relative price p^w (which governs the international distribution of tariff revenue and income between countries). Bagwell and Staiger proved a general theorem: unilateral Nash equilibrium tariffs are internationally Pareto-inefficient because and only because of the international terms-of-trade externality (W_p^w ≠ 0)—whereby each importing nation shifts part of the economic burden of its tariff onto foreign exporters by depressing the world price p^w, trapping trading nations in a terms-of-trade Prisoner's Dilemma. Furthermore, they demonstrated that the two foundational institutional pillars of GATT and the WTO—Reciprocity and Most-Favored-Nation (MFN) Non-Discrimination—neutralize the terms-of-trade externality and guide politically motivated governments to the international Pareto frontier.

Traditional National-Income vs. Political-Economy Perspectives

Since Robert Torrens (1844), John Stuart Mill (1844), and Harry G. Johnson (1953–1954), neoclassical trade theorists recognized that a large country wielding market power in world markets can raise its aggregate national real income above the free-trade level by imposing an optimal tariff τ^opt = 1 / ε^* (where ε^* is the elasticity of foreign export supply), which depresses the world price p^w of its imports and improves its terms of trade. When both countries impose optimal tariffs simultaneously in a non-cooperative Nash equilibrium, their terms-of-trade manipulations largely cancel out while global trade volume collapses, leaving both nations worse off than under mutual free trade.

However, policy observers and political economists objected that real-world trade negotiators rarely speak of manipulating aggregate national terms of trade; instead, politicians are preoccupied with protecting domestic import-competing industries and rewarding organized lobbies as modeled in the Protection for Sale model (Grossman and Helpman, 1994). If governments care about domestic political-economy redistribution rather than national income maximization, why do they still need an international trade agreement like GATT/WTO, and why do GATT/WTO rules center on reciprocal tariff concessions and Most-Favored-Nation (MFN) treatment?

Bagwell and Staiger's Separation of Local Prices (p) and World Prices (p^w)

Bagwell and Staiger (1999) resolved this debate by embedding arbitrary domestic political-economy preferences inside a two-country general equilibrium trade model and separating the domestic price channel from the international terms-of-trade channel.

Consider a two-country, two-good general equilibrium world economy in which the Home country exports good y and imports good x from the Foreign country (denoted by asterisks *):

• Let p = p_x / p_y denote the Home local relative price of import good x inside the Home market, and let p^* = p_x^* / p_y^* denote the Foreign local relative price of good x inside the Foreign market.
• Let τ denote the Home ad valorem import tariff (with tariff factor T = 1 + τ), and let τ^* denote the Foreign ad valorem import tariff on good y (with tariff factor T^* = 1 + τ^*).
• Let p^w ≡ p^w(τ, τ^*) denote the untaxed world (terms-of-trade) relative price of x in terms of y. By international price arbitrage, local prices in each country are linked to the world price p^w by the tariff wedges:

In balanced trade equilibrium (where Home imports equal Foreign exports, M(p, p^w) = E^*(p^*, p^w)), barring the Metzler and Lerner paradoxes, a higher Home tariff τ raises the Home local price p (∂p/∂τ > 0) and depresses the world price p^w of Home's import good (∂p^w/∂τ < 0), representing a terms-of-trade improvement for Home and a terms-of-trade loss for Foreign. Symmetrically, a higher Foreign tariff τ^* lowers p^* and raises p^w (∂p^w/∂τ^* > 0), improving Foreign's terms of trade at Home's expense.

Representing Arbitrary Domestic Political-Economy Objectives via W(p, p^w)

Within each country, all domestic production decisions, factor returns (wages and sector-specific rents via the Stolper–Samuelson theorem), and consumer surplus depend only on the local relative price p and aggregate tariff revenue (which for a given local price p depends on the world price p^w). Therefore, every major political-economy model of trade policy—including national income maximization, Hillman (1982) political support functions, Mayer (1984) median-voter tariffs, and the Grossman–Helpman (1994) Protection for Sale model—can be written in reduced form as a pair of government objective functions:

Holding each country's local price p (and thus all domestic factor incomes and industry profits) fixed, a decrease in the world price p^w transfers international tariff revenue from Foreign to Home without disturbing domestic income distribution:

Unilateral Nash Tariffs vs. Politically Optimal Tariffs

When Home and Foreign set their tariffs (τ^N, τ^*N) unilaterally without a trade agreement in a Nash equilibrium, each government maximizes its welfare taking the other country's tariff as given, yielding the first-order conditions:

Because λ < 0 and W_p^w < 0, the international cost-shifting term λ W_p^w is positive. When Home raises its tariff τ, part of the cost of delivering a higher local price p to domestic producers is shifted onto Foreign exporters via a lower world price p^w. Consequently, at the unilateral Nash equilibrium, W_p = −λ W_p^w < 0: both governments push their local prices p and tariffs τ higher than they would if they bore the full economic cost of protection domestically.

Define the Politically Optimal Tariffs (τ^PO, τ^**PO*) as the tariff pair chosen when neither government values terms-of-trade manipulation (W_p^w ≡ 0 and W^*_p^w ≡ 0):

Proof of the Fundamental Theorem of Trade Agreements

Theorem (Bagwell and Staiger, 1999):
1. Inefficiency of Nash Tariffs: The unilateral Nash equilibrium tariff pair (τ^N, τ^*N) is internationally Pareto-inefficient; a mutual reduction in both tariffs (Δτ < 0, Δτ^* < 0) raises both W and W^*.
2. Efficiency of Politically Optimal Tariffs: The politically optimal tariff pair (τ^PO, τ^PO*) satisfying W_p = 0 and W^*_p* = 0 lies on the international Pareto Efficiency Frontier**.
3. Terms-of-Trade Externality as the Source of Inefficiency: If governments were not motivated by the terms-of-trade externality (so λ W_p^w = 0 and λ^* W^*_p^w = 0, as in a small-country world), the Nash equilibrium would coincide with the politically optimal tariffs and would already be internationally Pareto-efficient.

Pillar 1: The Principle of Reciprocity

In GATT/WTO negotiations (Article XXVIII and tariff rounds), reciprocity refers to the norm that when one country reduces its tariff, its trading partner matches with a tariff cut of equivalent trade value, holding the world price p^w(τ, τ^*) constant:

At the Nash equilibrium (τ^N, τ^N*), W_p < 0 and W^*_p* < 0: each government prefers a lower local price p, and was deterred from cutting τ unilaterally only because a unilateral cut would worsen its terms of trade (dp^w > 0). Under a reciprocal tariff reduction** that holds dp^w = 0, the terms-of-trade penalty vanishes, so Home welfare rises: dW |_dp^w=0 = W_p(∂p/∂τ)*dτ* > 0 for dτ < 0. Moreover, under GATT Article XXVIII renegotiation rules (allowing tariff increases provided partners withdraw reciprocal concessions keeping p^w constant), the unique renegotiation-proof point on the Pareto frontier is the Politically Optimal Tariff pair (τ^PO, τPO*)** where W_p = 0 and W^*_p* = 0.

Pillar 2: Most-Favored-Nation (MFN) Non-Discrimination in a Multi-Country World

When Home trades with multiple foreign partners, GATT Article I (Most-Favored-Nation / MFN) requires Home to levy the same non-discriminatory tariff τ on imports from all WTO members. Without MFN, after Home negotiated a tariff cut τ₁ with Foreign 1, Home and Foreign 2 would have a joint opportunistic incentive to negotiate a discriminatory tariff cut τ₂ < τ₁ that diverts trade away from Foreign 1 and depresses Foreign 1's export price p₁^w—eroding the concession Foreign 1 paid for. MFN non-discrimination combined with multilateral reciprocity prevents bilateral concession erosion and preserves a single world price p^w.

Broda, Limão, and Weinstein (2008) and Domestic Commitment

1. Empirical Confirmation of Terms-of-Trade Tariffs (Broda, Limão, and Weinstein, 2008; Bagwell and Staiger, 2011): Using product-level data across 15 non-WTO countries, Broda, Limão, and Weinstein showed that prior to WTO constraints, unilateral tariffs are positively correlated with inverse foreign export supply elasticities (1 / ε_g^*), even after controlling for Protection for Sale lobbying variables, and that WTO accession compresses these terms-of-trade markups.
2. Domestic Commitment Theory (Maggi and Rodríguez-Clare, 1998): Shows that even a small country may sign a trade agreement to tie its hands against domestic lobbying and prevent dynamic capital overinvestment in protected sectors.
3. Firm Delocation Externality (Ossa, 2011): In Krugman's new trade model and the Melitz trade model, unilateral tariffs also create a firm-relocation externality alongside the classical terms-of-trade channel.

If politicians care about domestic lobbies rather than national terms of trade, why does the terms-of-trade externality still drive trade agreements?

Whenever a politician raises a domestic tariff τ to reward a domestic lobby with a higher local price p, part of the economic burden of that tariff falls on foreign exporters via a lower world price p^w rather than on domestic consumers. Because foreign exporters do not vote or contribute to domestic campaigns, the domestic politician ignores the foreign terms-of-trade harm and sets a higher tariff than if the entire cost of rewarding the lobby were borne domestically.

Why do trade negotiators view tariff cuts as "concessions" if tariff cuts are beneficial?

At the unilateral Nash equilibrium (τ^N, τ^N*), a unilateral** tariff cut (dτ < 0 with dτ^* = 0) lowers Home's welfare because the resulting deterioration in Home's terms of trade (dp^w > 0) outweighs the domestic price benefit (W_p dp > 0). Only when Foreign reciprocates with a simultaneous tariff cut (dτ^* < 0) that neutralizes the terms-of-trade loss (dp^w = 0) do both countries gain.

Does the terms-of-trade theory require that GATT/WTO lead to complete free trade?

No. Neutralizing the terms-of-trade externality leads countries to the Politically Optimal Tariffs (W_p = 0 and W^*_p* = 0). Politically optimal tariffs equal zero (complete free trade) if and only if both governments maximize unweighted aggregate national income. If a government places extra political weight on an organized import-competing industry, its politically optimal tariff remains positive—lower than its Nash tariff by the terms-of-trade markup 1 / ε^*.

1. Bagwell, K., & Staiger, R. W. (1999). "An Economic Theory of GATT." American Economic Review, 89(1), 215–248. https://doi.org/10.1257/aer.89.1.215
2. Bagwell, K., & Staiger, R. W. (2002). The Economics of the World Trading System. Cambridge, MA: MIT Press. https://doi.org/10.7551/mitpress/2628.001.0001
3. Broda, C., Limão, N., & Weinstein, D. E. (2008). "Optimal Tariffs and Market Power: The Evidence." American Economic Review, 98(5), 2032–2065. https://doi.org/10.1257/aer.98.5.2032
4. Bagwell, K., & Staiger, R. W. (2011). "What Do Trade Negotiators Negotiate About? Empirical Evidence from the World Trade Organization." American Economic Review, 101(4), 1238–1273. https://doi.org/10.1257/aer.101.4.1238
5. Maggi, G., & Rodríguez-Clare, A. (1998). "The Value of Trade Agreements in the Presence of Political Pressures." Journal of Political Economy, 106(3), 574–601. https://doi.org/10.1086/250022