## _wp1537

## Source details

**Canonical URL:** [_wp1537](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1537.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1537.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1537.pdf.json)

---

### Background and theoretical motivation
- WTO objective: liberalize international trade on a reciprocal basis.
- Standard theory: unilateral trade liberalization is optimal for small countries under perfect competition.
- Terms-of-trade rationale (Johnson 1953–1954; Bagwell and Staiger 1999):
  - A large country can improve its terms of trade by imposing a tariff; retaliation can lead to mutual tariffs and lower trade and output.
  - Reciprocal trade liberalization resolves the prisoner’s dilemma driven by manipulating the terms of trade.
- Recent empirical support cited: Broda et al. 2008; Bagwell and Staiger 2011.

### Model, innovations, and calibration
- Model framework:
  - New Keynesian two-country model with a fixed number of imperfectly competitive firms and price rigidities (Calvo pricing).
  - Numerical analysis for symmetric countries; periods interpreted as quarters.
  - Tariffs modeled as ad valorem; tariff process: τ̂_t = φ τ̂_{t-1} + ψ_t with φ ∈ [0,1], ψ_t zero-mean white-noise; tariffs assumed permanent so φ set to 1 in baseline.
- Main innovations relative to Eaton and Kortum (2002), Caliendo and Parro (2015), and Ossa (2014):
  1. Transitional dynamics via staggered price setting (Calvo pricing, γ = 0.75 baseline).
     - Sticky prices make the real wage temporarily higher; given a Frisch elasticity, labor supply increases and welfare temporarily rises.
     - Staggered price setting slightly increases the value of a trade agreement but cannot alone account for large quantitative differences.
  2. Altered steady state via endogenous labor supply and within-country imperfect substitutability.
     - Within-country substitutability θ is a key determinant of results.
- Key parameterization (baseline and ranges preserved exactly):
  - n — 0.5 (countries equal size)
  - periods interpreted as quarters
  - β — 0.99
  - ε — 1
  - θ — 11 [6-100]
  - ρ — 2 [0.5-11]
  - γ — 0.75 [0-0.75]
  - Initial tariff rate: 0.04 [0.02-0.06]
  - Home bias parameter (α): 1.47 [1.37-1.68]; α* = 0.53 [0.42-0.63]
  - Frisch elasticity ν: 1 [0.1-2]
  - Calvo parameter γ = 0.75 implies average delay of four periods (one year) between price adjustments.
  - Tariff reduction considered: 1 percentage point cut (from 4% to 3%) — baseline implies a reduction of 25%.
  - Import-to-output (baseline implied): 25%; World Bank OECD average: 26% (2003–2012); worldwide: 28%.

### Main quantitative findings
- Unilateral tariff reduction (domestic cut from 4% to 3%):
  - Domestic output: increases 0.24% in the first period and 0.13% in the long term.
  - Exchange rate: depreciates by 0.75% in the short run.
  - Terms of trade: deteriorate for the home country; ToT falls, reducing domestic consumption and increasing foreign consumption.
  - Current account: domestic households run a small short-term current account surplus (increase in domestic bond holdings) to smooth consumption.
  - Welfare (DPV): negative for the home country (domestic households would pay part of consumption to avoid the unilateral liberalization); positive for the foreign country and positive worldwide.
- Reciprocal (multilateral) tariff reduction (both countries 4% → 3%):
  - Output: increases 0.21% in the first period and 0.13% in the long term (identical in both countries by symmetry).
  - Terms of trade and exchange rate: remain constant.
  - Short-run period one willingness-to-pay: households are willing to pay 0.02% of initial consumption for the tariff reduction in the first period.
  - DPV (baseline): equals 1.3% of initial consumption for domestic and foreign households (computed using 1,000 periods).
  - Complete elimination of initial 4% tariffs would cause even greater welfare gains.
- Comparison with other studies:
  - Eaton and Kortum (2002): multilateral elimination of 5% tariffs improves welfare by less than 0.5%.
  - Caliendo and Parro (2015): NAFTA increased welfare on average by 0.42%.
  - Ossa (2014): average welfare gain of trade agreement eliminating actual tariffs is 0.5%.
  - This New Keynesian framework yields substantially larger multilateral gains than those studies under realistic parameter combinations.

### Sensitivity analysis — exact reported numbers
- Import-to-GDP (Table 3 values — value of a reciprocal agreement, % of initial consumption):
  - Import-to-GDP = 15% → 0.76%
  - Import-to-GDP = 20% → 1.0%
  - Import-to-GDP = 25% → 1.3%
  - Import-to-GDP = 30% → 1.6%
- Within-country substitutability θ and Frisch elasticity ν (Table 4 entries: value of a trade agreement, % of consumption):
  - ν = 0.1: θ = 6 → 0.43; θ = 11 → 0.25; θ = 20 → 0.15; θ = 100 → 0.050
  - ν = 0.5: θ = 6 → 1.5; θ = 11 → 0.88; θ = 20 → 0.52; θ = 100 → 0.18
  - ν = 1 (baseline): θ = 6 → 2.3; θ = 11 → 1.3; θ = 20 → 0.78; θ = 100 → 0.26
  - ν = 2: θ = 6 → 3.1; θ = 11 → 1.7; θ = 20 → 1.0; θ = 100 → 0.35
- Price rigidity effect:
  - Fully flexible prices scenario reduces DPV from 1.31% (baseline) to 1.28%.
- Robust findings across tested parameter ranges:
  - Value of unilateral liberalization remains negative for the home country and positive for the foreign country across parameter combinations tested.
  - Value of a reciprocal trade agreement (DPV) is relatively insensitive to cross-country substitutability ρ in the tested range 0.5–11 and to initial tariff in the 2%–6% range for the reported results; baseline DPV = 1.3% reproduced across those combinations displayed.

### Mechanisms driving results
- Within-country imperfect substitutability (lower θ) raises steady-state markups and reduces initial output; reducing tariffs and moving output/consumption toward efficient levels yields larger welfare gains.
- Endogenous labor supply: higher Frisch elasticity ν amplifies welfare gains because households increase labor supply when real wages rise, moving consumption/output closer to efficient levels.
- Price rigidities and transitional dynamics (Calvo pricing) amplify short-run welfare gains, increasing DPV relative to fully flexible-price models, though sizable DPV remains under flexible prices.

### Policy implications and recommendations
- Unilateral tariff reductions:
  - Tend to reduce home-country welfare (DPV negative) because of terms-of-trade deterioration despite higher output.
  - Benefit foreign country and world welfare; unilateral liberalization is not incentive-compatible for countries in this model.
- Reciprocal (multilateral/WTO-style) tariff reductions:
  - Increase welfare for both countries and the world (baseline DPV = 1.3% of consumption for a 4% → 3% reciprocal cut).
  - Provide an escape from the prisoner’s dilemma created by terms-of-trade manipulation.
  - Welfare gains are larger with lower within-country substitutability (lower θ), higher Frisch elasticity (higher ν), and higher openness (higher import-to-GDP).
- Authors’ policy recommendation: completion of the Doha Round should be a high priority given the large welfare gains from multilateral trade liberalization indicated by the model results.

*Italic: Content unit drawn from _wp1537 (IMF working paper excerpt).*

### 1948. One aim of the WTO is to liberalize international trade on a reciprocal basis. To achieve

### 1948. One aim of the WTO is to liberalize international trade on a reciprocal basis. To achieve

### Background and theoretical motivation
- WTO has completed eight rounds of trade negotiations that have substantially lowered tariffs and other trade barriers.
- Standard economic theory calls for unilateral trade liberalization: small countries, under perfectly competitive markets, have no incentive to impose tariffs.
- The terms of trade theory (Johnson 1953–1954; Bagwell and Staiger 1999) underpins the WTO rationale:
  - Optimal tariff argument: in a two-country model, a large country can improve its terms of trade by imposing a tariff; retaliation by the other country can lead to mutual tariffs.
  - Tariffs reduce international trade and output in both countries.
  - Reciprocal trade liberalization aims to resolve the prisoner’s dilemma driven by manipulating the terms of trade.
- Recent empirical literature (Broda et al. 2008; Bagwell and Staiger 2011) supports the relevance of the terms of trade theory.

### Relevant quantitative trade literature
- Eaton and Kortum (2002):
  - Developed a multi-country Ricardian general equilibrium model that can be calibrated to quantify welfare gains.
  - Found a unilateral tariff removal by the United States reduces U.S. welfare due to deterioration of the terms of trade, while all other countries benefit.
  - Showed multilateral elimination of 5% tariffs improves welfare (in case of immobile labor) by less than 0.5%.
- Caliendo and Parro (2015):
  - Studied tariff reductions from NAFTA.
  - Found NAFTA increased welfare on average by 0.42%.
- Ossa (2014):
  - Analyzed WTO trade agreements including terms of trade, production relocation, and political economy effects.
  - Calibrated to seven countries/regions and found the average welfare gain of a WTO trade agreement that eliminates actual tariffs is 0.5%.

### Model, innovations, and calibration used in this paper
- Model framework:
  - New Keynesian two-country model with a fixed number of imperfectly competitive firms and price rigidities.
  - Numerical analysis for symmetric countries.
  - Parameters chosen to reflect existing tariff rates and import-to-GDP ratios in the OECD countries.
- Two main innovations relative to Eaton and Kortum (2002), Caliendo and Parro (2015), and Ossa (2014):
  1. Introduce transitional dynamics via staggered price setting.
     - Sticky prices make the real wage temporarily higher, which, given a Frisch elasticity, increases labor supply and temporarily brings the economy closer to the efficient level of consumption, increasing welfare.
     - Staggered price setting only slightly increases the value of a trade agreement and cannot account for the large quantitative differences alone.
  2. Alter the underlying steady state by introducing endogenous labor supply and a different market structure:
     - Presence of imperfect substitutability between goods within the same country (within-country substitutability) is a key determinant of the main results.
     - In the quantitative macroeconomics literature, within-country substitutability is virtually always set between 6 and [text truncated in source].

### Main results and quantitative findings
- Unilateral tariff reduction:
  - A unilateral tariff reduction reduces welfare in the model.
  - Under plausible parameter combinations of key parameter values, unilateral trade liberalization is welfare decreasing.
  - This establishes a prisoner’s dilemma for tariff setting at the relevant parameter values.
- Welfare gains of WTO trade agreements:
  - Measured as the percentage of consumption households would pay to remain as well off with the trade agreement as without it (method of Schmitt-Grohe and Uribe 2007).
  - For realistic parameter combinations of the Frisch elasticity of labor supply and the elasticity of substitution between two goods produced in the same country (within-country substitutability), the discounted present value of the welfare gain of a WTO trade agreement that cuts tariffs by one percentage point is as high as 0.5% to 2% of initial consumption.
  - Complete elimination of initial 4% tariffs would cause even greater welfare gains.
  - The welfare effects of multilateral trade liberalization are substantially larger in this New Keynesian model than in Eaton and Kortum (2002), Caliendo and Parro (2015), and Ossa (2014).
  - Implication: WTO agreements are of high value.

### Policy implications and recommendations
- Completion of the Doha Round should be a high priority, given the large welfare gains from multilateral trade liberalization indicated by the model results.
- The quantitative importance of within-country imperfect substitutability and endogenous labor supply suggests policy analysis of trade agreements should incorporate:
  - Price rigidities and transitional dynamics (staggered price setting).
  - Endogenous labor supply responses to real wage changes (Frisch elasticity considerations).
  - Market structures featuring imperfect within-country substitutability.

*Source: Excerpt from the provided IMF working paper content.*

### 20. In the trade models, which have been used in the literature on trade agreements, competition

### 20. In the trade models, which have been used in the literature on trade agreements, competition

### Main findings on within-country substitutability and labor supply
- Competition within the industry is assumed perfect in prior trade models, implying very high within-country substitutability.
- In the macro model developed here:
  - "the lower within-country substitutability is, the lower the initial level of output is; the lower the initial level of output is, the more an increase in output and consumption (of given size) increases welfare."
  - Gains from trade agreements depend significantly on the degree of within-country substitutability.
- Labor supply endogeneity matters:
  - Trade models that assume utility depends solely on consumption make labor supply exogenous.
  - "We show that the higher the Frisch elasticity of labor supply is, the larger the welfare gains of multilateral trade liberalization."
  - If the Frisch elasticity is high, households respond to a tariff reduction by further increasing labor supply, bringing consumption and output of an imperfectly competitive economy closer to their efficient levels and thereby increasing welfare.
- Interaction effect: "the combination of elastic labor supply and imperfect competition within the country/industry (i.e., low within-country substitutability) accounts for the huge quantitative difference between our results and those of Eaton and Kortum (2002), Caliendo and Parro (2015) and Ossa (2014)."
  - For realistic parameter combinations of the Frisch elasticity and within-country substitutability, welfare gains of WTO trade agreements are much larger than those found in the new trade models.
  - Results become consistent with prior literature when model parameters are set to approximate their assumptions: very low Frisch elasticity and very high within-country substitutability (exogenous labor supply and perfect competition).

### Model overview
- A New Keynesian two-country model incorporating distortionary import tariffs.
- Key distinctions from prior work (Fender and Yip (2000); Reitz and Slopek (2005)):
  - Allow cross-country substitutability to differ from within-country substitutability.
  - Introduce an exogenous home bias in consumption to match observed import-to-output ratios.
  - Use Calvo-pricing, log-linearize around non-zero tariffs, and consider tariff reductions.
  - Welfare benefit measured as a percentage of consumption the household is willing to pay for a tariff reduction (following Schmitt-Grohe and Uribe (2007)), rather than percent change in utility.
  - Focus on quantitative gains of multilateral trade liberalization (previous literature focused on unilateral liberalization).
- World economy: two countries (home and foreign). Firms and households indexed by z ∈ [0,1]. Fraction n (1-n) located in domestic (foreign) country. Both countries impose ad valorem tariffs on foreign/domestic goods.

### Households: preferences, consumption aggregation, and first-order conditions
- Representative domestic household utility:
  - U = sum_{s=t}^{∞} β^{s-t} [log(C_s) + χ (M_s/P_s)^{1-ε}/(1-ε) + ... ] with Frisch elasticity of labor supply ν and price index as function of tariff (notation preserved as in text). (Equation (1) textual form preserved.)
  - 10 < β < 1 is specified in text as 10β (context clarifies β = 0.99 later).
  - χ is a positive parameter; M nominal money balances; 0 < ε is inverse of consumption elasticity of money demand.
- Consumption index (Armington aggregation):
  - C_t = [κ κ (h_t C)^{ρ-1} + (1-κ) (f_t C)^{ρ-1}]^{1/(ρ-1)} with ρ > 0 cross-country substitutability and κ depending on n and α. (Equation (2) internal structure preserved.)
- Within-country aggregation:
  - h_t C and f_t C are CES aggregates across differentiated brands with within-country substitutability θ > 1. (Equations (3) and (4).)
- Demand functions allocate consumption between domestic and foreign baskets and across brands governed by relative prices, tariffs, ρ and θ.
- Prices:
  - Domestic currency prices of domestic and foreign goods: p_ht(z) and p_ft(z). Price indexes h_t P and f_t P defined in equations (5) and (6).
  - Overall domestic price index with tariffs: [ρ expression] (Equation (7)).
- Budget constraint (domestic):
  - TPCPzlwMDDM)()()(11 τπτδ + + - + + = + - - (Equation (8) textual form preserved).
- First order conditions:
  - Euler consumption: equations (9) and (10) as given.
  - Labor supply: equations (11) and (12) show labor supply increasing in real wage and decreasing in consumption; tariffs reduce labor supply via prices.
  - Money demand: equations (13) and (14) show money demand increasing in consumption and decreasing in interest rate.

### Government
- Government abstracts from government spending and refunds tariff and seignorage revenues to households lump-sum.
- Government budget constraint per-capita (domestic):
  - 1* )()()( − − + = tttt f tttt MMSzpzcTP τττ (Equation (15) textual form preserved).
  - First term on RHS denotes revenue from import tariffs depending on tariff rate, consumption of foreign goods by domestic households and their domestic-currency price.
- Foreign tariff revenue:
  - R* = )1)(()( *** t t h tt Szpzc τ (textual form preserved).
- Tariff process:
  - τ̂_t = φ τ̂_{t-1} + ψ_t with φ ∈ [0,1], ψ_t zero-mean white-noise. Percentage changes denoted with hats; tariffs assumed permanent so φ set to 1.

### Firms: technology, profits, and demand
- Production function for firm z: y_t(z) = z l_t(z) (Equation (16)).
- Profit functions:
  - Domestic firm profit: π_t(z) = p_h t(z) y_t(z) - w_t l_t(z) (Equation (17)).
  - Demand for goods (domestic firm) governed by complex expression involving consumption aggregates, price indexes, tariffs, ρ, θ and n (Equation (18) textual form preserved).
  - Domestic profits expressed in expanded form (Equation (19) textual form preserved).
  - Representative foreign firm profits given by (Equation (20) textual form preserved).
- Without price rigidities, optimal domestic price is a constant mark-up:
  - p_h t(z) = θ/(θ-1) w_t (Equation (21) textual form preserved).
  - Mark-up determined by within-country substitutability θ.

### Price setting (Calvo)
- Calvo pricing: each firm can reset price with probability 1-γ in any period.
- Representative firm maximizes discounted profits when resetting price, leading to first-order condition (22) (text preserved).
- Log-linearized optimal price change:
  - p̂_h t(z) = βγ p̂_h t-1(z) + (1-βγ) ŵ_t (Equation (23) textual form preserved).
  - Change in optimal price is weighted average of current and future marginal cost changes.

### Consolidated budget constraint
- Domestic consolidated budget constraint:
  - )()( 1 z y z p D D C P t h t t t t + - = - δ (Equation (24) textual form preserved).
  - P_t is domestic price index without tariffs, defined as in (25).
- Foreign consolidated budget constraint (using global asset-market-clearing):
  - )()(11 **** 1 z y z p C P S D n n S D n n t f t t t t t t t + - - - = - - - δ (Equation (26) textual form preserved).
  - *P_t is foreign price index without tariffs.

### Initial steady state and role of tariffs and imperfect competition
- Log-linearization around symmetric steady state with initial net foreign assets zero (D^0 = 0).
- From equation (24), y^0 = C^0.
- Initial level of employment and output:
  - z l_0^0 = z y_0^0 = ( ν / (1+ν) ) ( θ/(θ-1) ) ( P_0 / p_0(z) )(1/(1-τ_0) )  (Equation (27) textual representation preserved in original form).
  - Equation (27) shows output depends on tariffs and degree of imperfect competition (within-country substitutability θ).
  - Tariffs reduce steady-state labor supply via price effects; higher imperfect competition (lower θ) lowers output.

### Parameterization (baseline and ranges)
- Countries equal size: n set to 0.5.
- Periods interpreted as quarters.
- Discount factor β = 0.99.
- Consumption elasticity of money demand (inverse) ε = 1.
- Table 2 (parameters reproduced as in text):
  - Parameter — Baseline value [range of parameters] — Description
    - β — 0.99 — Discount factor
    - ε — 1 — Inverse of the consumption elasticity of money demand
    - θ — 11 [6-100] — Within-country substitutability
    - ρ — 2 [0.5-11] — Cross-country substitutability
    - γ — 0.75 [0-0.75] — Calvo parameter
    - n — (set to 0.5 earlier in text)

*Italic: Text reproduced from the provided content unit.*

### 0.5 Relative size of the domestic

### _wp1537 - 0.5 Relative size of the domestic

### Model parameter values and calibrated ranges
- Initial tariff rate: 0.04 [0.02-0.06]
- Persistence of a tariff tax shock: 
- Size of a tariff shock:  -0.25
- Home bias parameter (α): 1.47 [1.37-1.68]
- Home bias parameter (α*): 0.53 [0.42-0.63]
- Frisch elasticity of labor supply (ν): 1 [0.1-2]

### Price rigidity (Calvo) calibration
- Calvo parameter (γ) set to 0.75.
- Rationale: γ affects the strength and duration of the expenditure switching effect of a nominal exchange rate change. Gopinath and Rigobon (2008) find that the trade-weighted median price duration of internationally traded goods is roughly one year. Based on this, γ = 0.75 implies an average delay of four periods (one year) between price adjustments.

### Model specification note (incomplete in source)
- Based on the estimates of Basu and Fernald (1997), we set within-country substitutability θ to

*Content unit: _wp1537 - 0.5 Relative size of the domestic*

### 11. This implies a 10% markup over the marginal cost in the steady state (recall equation (21)).

### _wp1537 - 11. This implies a 10% markup over the marginal cost in the steady state (recall equation (21)).

### Parameter choices and calibration
- Within-country substitutability:
  - Common macro practice places it between 5 and 20 (implying price markups between 20% and 5%).
  - Benchmark within-country substitutability chosen such that initial steady state is realistic; the paper notes within-country substitutability affects only initial steady state and welfare results, not the response of endogenous variables.
  - Sensitivity examined up to θ = 100 (near-perfect competition; implies a low price markup of roughly 1%).
- Cross-country substitutability:
  - Baseline choice: 2.
  - Sensitivity range analyzed: from 0.5 to 11.
  - Empirical context: macro estimates ~1; micro/trade studies report much larger values (e.g., Romalis: between 6 and 11; Feenstra et al. medians: micro elasticity between suppliers 3.2–4.1, macro elasticity roughly 1).
- Tariff rates:
  - Initial (baseline) nominal tariff rate set to 4%.
  - Sensitivity of initial tariff rate analyzed in the 2% to 6% range.
  - Tariff change persistence parameter set to 1 (φ = 1), implying permanent changes.
  - Tariff reduction considered: a 1 percentage point cut (from 4% to 3%) — in the baseline this implies a reduction of 25%.
- Labor supply (Frisch elasticity ν):
  - Baseline ν = 1.
  - Sensitivity analyzed over the range including 0.1, 0.5, 1, 2.
  - Literature: Chetty et al. (2013) suggest 0.5 (micro evidence for macro use); Keane and Rogerson (2012) suggest macro-level range 1 to 2.
- Home bias and import-to-GDP:
  - α set to 1.47 to match import-to-output ratio.
  - Prices normalized to 1 in steady state; with a 4% tariff baseline, implied initial import-to-output ratio is 25%.
  - World Bank averages cited: OECD import-to-GDP 26% (2003–2012), worldwide 28%.
  - Sensitivity of import-to-GDP analyzed in 15% to 30% range.

### Unilateral domestic tariff reduction — quantitative effects
- Policy experiment: domestic tariff cut from 4% to 3% in period 1 (unilateral).
- Output and employment:
  - Domestic output increases 0.24% in the first period and 0.13% in the long term.
- Terms of trade and consumption:
  - Domestic terms of trade (ToT) deteriorate (ToT falls); deterioration reduces domestic consumption and increases foreign consumption.
  - As a result, even though output rises, domestic consumption falls and the DPV of the welfare benefit of the unilateral tariff reduction is negative for the home country.
- Exchange rate and current account:
  - Exchange rate depreciates by 0.75% (short-run depreciation reported).
  - Domestic households run a small current account surplus in the short term (increase in domestic bond holdings) to smooth consumption.
  - Empirical note: limited evidence on current account effects; Ju et al. (2012) find trade liberalization on average improves the current account in certain episodes.
- Welfare valuation (one-period and DPV measures):
  - Value of unilateral trade liberalization is negative for the home country in all periods (domestic households would pay part of consumption to avoid trade liberalization).
  - The DPV of the welfare benefit of trade liberalization is:
    - Negative for the home country (due to ToT deterioration and fall in consumption).
    - Positive for the foreign country and positive worldwide.
  - Interpretation: consistent with the optimal tariff argument (a large country can improve its terms of trade by imposing a tariff even if world welfare falls).

### Welfare measurement and formulas (conceptual)
- Welfare benefit of tariff reduction measured as percentage of consumption households would pay to be indifferent between tariff-reduction and no-tariff-reduction cases.
- Discounted present value (DPV) used to capture overall welfare change over time.
- World value of trade liberalization computed as population-weighted average: λ_W = n λ + (1 − n) λ* (equation (35) in text).

### Reciprocal (multilateral) tariff reduction — quantitative effects (WTO-style exercise)
- Policy experiment: both countries reduce applied tariffs from 4% to 3% (reciprocal, satisfying Bagwell–Staiger reciprocity).
- Output:
  - Output increases by 0.21% in the first period and 0.13% in the long term (identical in both countries given symmetry).
- Terms of trade and exchange rate:
  - Terms of trade remain constant (symmetric supply and demand changes).
  - Exchange rate remains constant.
- Short-run welfare:
  - Domestic and foreign households are willing to pay 0.02% of their initial consumption for the tariff reduction in the first period (Figure 2(f) reference).
- DPV results (baseline):
  - Under baseline parameterization, DPV of a WTO reciprocal trade agreement equals 1.3% of initial consumption for domestic and foreign households (Table 2; baseline: cross-country substitutability 2, initial tariff 4%).
  - This implies WTO trade agreements are valuable under the model; completion of the Doha Round is noted as a high priority (policy implication in text).
- DPV calculation method:
  - DPV computed using 1,000 periods (note from Table 2 footnote).

### Sensitivity analysis — key quantitative findings
- Cross-country substitutability and initial tariff:
  - Varying cross-country substitutability from 0.5 to 11 and initial tariff from 2% to 6%:
    - The value of unilateral trade liberalization remains negative for the home country and positive for the foreign country for all parameter combinations tested.
    - The value of a reciprocal trade agreement (DPV) is virtually unaffected by cross-country substitutability and initial tariff in the tested ranges — Table 2 shows DPV = 1.3% across combinations displayed.
- Import-to-GDP (degree of openness) — Table 3:
  - Import-to-GDP = 15% → Value of an agreement = 0.76% of initial consumption.
  - Import-to-GDP = 20% → Value = 1.0% of initial consumption.
  - Import-to-GDP = 25% (baseline) → Value = 1.3% of initial consumption.
  - Import-to-GDP = 30% → Value = 1.6% of initial consumption.
- Within-country substitutability (θ) and Frisch elasticity (ν) — Table 4 (sensitivity grid):
  - Columns denote θ = 6, 11 (baseline), 20, 100.
  - Rows denote ν = 0.1, 0.5, 1 (baseline), 2.
  - Table 4 entries (value of a trade agreement, % of consumption) exactly as reported:
    - Row 1 (ν = 0.1): 0.43, 0.25, 0.15, 0.050
    - Row 2 (ν = 0.5): 1.5, 0.88, 0.52, 0.18
    - Row 3 (ν = 1, baseline): 2.3, 1.3, 0.78, 0.26
    - Row 4 (ν = 2): 3.1, 1.7, 1.0, 0.35
  - Key implications:
    - The welfare gain of a trade agreement falls substantially as within-country substitutability increases (i.e., as domestic goods become closer substitutes and domestic monopoly power falls). Example: with θ = 100 the value can be as low as 0.050–0.35 depending on ν.
    - The higher the Frisch elasticity ν, the larger the welfare gains from a trade agreement, because labor supply responds more to tariff cuts and moves consumption/output closer to efficient levels.
    - Under baseline θ = 11 and ν = 1, DPV = 1.3% (reproduced in Table 4, Row 3, column θ = 11).
- Price rigidity:
  - Setting price rigidity parameter to zero (fully flexible prices) reduces the DPV of a trade agreement from 1.31% (baseline) to 1.28% (alternative scenario reported).
- Interpretation versus other literature:
  - Other quantitative trade literature (Eaton and Kortum 2002; Caliendo and Parro 2015; Ossa 2011, 2014) typically finds much smaller welfare gains from multilateral tariff reductions (often under 0.5% or smaller).
  - This paper identifies several potential reasons for larger gains here:
    - Different welfare metric (consumption compensation) — though authors note DPV of change in utility nearly equals DPV in consumption terms in their model, so metric alone does not explain the divergence.
    - Degree of openness differences (higher import-to-GDP in baseline here than some other calibrations) — but cannot fully explain differences.
    - Transitional dynamics from staggered price setting (New Keynesian Calvo pricing) elevate short-run gains, increasing DPV relative to fully flexible-price models; yet fully flexible prices still deliver a sizable DPV.
    - Imperfect within-country substitutability (domestic market power) changes the steady state: when internal markups are substantial (lower θ), bringing consumption and output closer to efficiency generates larger welfare gains from trade liberalization.
  - Quantitative bottom line: welfare gains from a multilateral one-percentage-point tariff reduction can be sizable in this framework (baseline DPV = 1.3% of consumption), and gains rise with lower within-country substitutability and higher Frisch elasticity.

### Main policy conclusions highlighted
- Unilateral tariff reductions:
  - Tend to harm the home country’s welfare (DPV negative) because of terms-of-trade deterioration, although output rises.
  - Benefit the foreign country and the world.
  - Therefore, unilateral liberalization is not incentive-compatible for countries in this model.
- Reciprocal (multilateral/WTO-style) tariff reductions:
  - Increase welfare for both countries and the world (baseline DPV = 1.3% of consumption for each country under the 4% → 3% reciprocal cut).
  - Provide an escape from the prisoner’s-dilemma created by terms-of-trade manipulations; WTO agreements are valuable in this framework.
  - Welfare gains from reciprocal liberalization are increasing in the degree of openness (import-to-GDP) and the Frisch elasticity of labor supply, and decreasing in within-country substitutability.
- Policy implication drawn by authors: completion of multilateral trade liberalization (e.g., the Doha Round) should be a high priority given the positive DPV gains from reciprocal tariff reduction in the model.

*Italicized source attribution: content unit drawn from _wp1537 - 11. This implies a 10% markup over the marginal cost in the steady state (recall equation (21)).*

### 2.  Table  4  shows  that  for  the  realistic  parameter  combinations  of  the  Frisch  elasticity  of  labor

### 2.  Table  4  shows  that  for  the  realistic  parameter  combinations  of  the  Frisch  elasticity  of  labor

### Key findings on welfare gains
- For realistic parameter combinations of the Frisch elasticity of labor supply and within-country substitutability, the value of the welfare gain of a trade agreement that cuts tariffs by one percentage point is 0.5% to 2% of initial consumption.
- In cases where the Frisch elasticity is very low )1.0( and within-country substitutability ( 20 or 100) is high, reciprocal trade liberalization that eliminates 4% tariffs induces welfare gains of 0.2% to 0.6% of initial consumption.

### Comparison with prior studies
- Eaton and Kortum (2002): multilateral elimination of 5% tariffs yields welfare gains that never exceed 0.5%.
- Caliendo and Parro (2015): welfare effects of tariff reductions caused by NAFTA are on average 0.42%.
- Ossa (2014): average welfare gain of a trade agreement that eliminates factual tariffs is 0.5%.
- The paper notes its main results contrast sharply with Eaton and Kortum (2002), Caliendo and Parro (2015) and Ossa (2011 and 2014) when the Frisch elasticity and within-country substitutability lie within empirical ranges; results are consistent with earlier studies only when the Frisch elasticity is very low and within-country substitutability is high.

### Model features and parameterization
- Model combines Armington and New Keynesian elements: goods differentiated by country of origin (Armington) plus staggered price adjustment, endogenous labor supply, and imperfect substitutability between domestically produced goods (New Keynesian elements).
- Parameters are set to reflect existing tariff rates and import-to-GDP ratios in the OECD countries to derive the main results.
- The paper identifies the key determinants of differences with other studies as:
  - the degree of within-country substitutability, and
  - the magnitude of the labor supply response to a tariff reduction.

### Conclusions and policy implications
- For realistic parameter combinations, WTO trade agreements that reduce tariffs are estimated to deliver substantial welfare gains (0.5% to 2% of initial consumption per one percentage point tariff cut).
- The authors conclude that WTO trade agreements are of high value and that completion of the Doha Round should be a high priority.

*Source: _wp1537 - 2.  Table  4  shows  that  for  the  realistic  parameter  combinations  of  the  Frisch  elasticity  of  labor*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1537.pdf_