## _wp14182

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---

### 2.1 The model: Food prices and loss aversion — model setup and preferences
- Small open economy producing two goods: a numeraire and food.
- Numeraire:
  - y0 = l0; wage rate fixed = 1; tradable at unitary world price.
- Food:
  - Technology y = f(l; L) with constant returns to scale; land L fixed.
  - Return to specific factor: ρ(p) = max_l [p f(l; L) − l].
  - Domestic output y(p) = ρ'(p).
- Government policy:
  - Domestic price p = p̃ − t (t > 0: export tax or import subsidy protecting consumers; t < 0: export subsidy or import tariff protecting producers).
  - Government revenue: GR(p) = (p̃ − p) [y(p) − d(p)]?0 (equation (2) in source).
- Preferences with loss aversion (equation (1)):
  - U = c0 + u(c) − I · h(U − c0 − u(c))
    - u'(·) > 0, u''(·) < 0.
    - h' > 0, h'' < 0.
    - I = 1 whenever utility < reference level U; I = 0 otherwise.
  - Individual demand: d(p) = [u'(c)]−1.
  - Income: c0 = E − p d(p).

### 2.1 Social groups, indirect utilities, and government objective
- Population split:
  - Fraction β owns land (producers); share (1 − β) are workers/consumers.
- Indirect utilities:
  - Workers:
    - V_l^p(p) = 1 + CS(p) + GR(p) − I_l · h(V_l(p) − 1 − CS(p) − GR(p)) (equation (3)).
    - CS(p) = u[d(p)] − p d(p).
    - I_l = 1 whenever V_l(p) > 1 + GR(p) + CS(p).
  - Land owners:
    - V_L^p(p) = ρ(p)/β + CS(p) + GR(p) − I_L · h(V_L(p) − ρ(p)/β − CS(p) − GR(p)) (equation (4)).
    - I_L = 1 whenever V_L(p) > ρ(p)/β + GR(p) + CS(p).
- Government objective:
  - Total welfare G(p) = W(p) + H(p) (equation (5)).
    - W(p) = (1 − β) + ρ(p) + CS(p) + GR(p).
    - H(p) = −(1 − β) I_l · h(…) − β I_L · h(…).

### 2.1 Unilateral trade policy under loss aversion — regions and optimal policy
- Three main regions depending on international price p̃ relative to reference prices p (workers) and p (producers):
  - Intermediate: p̃ ∈ (p; p) → H(·) = 0 → optimal p = p̃ (free trade).
  - Low p̃: p̃ < p
    - Region of compensating protection where government sets export subsidy or import tariff to fully compensate producers.
    - There exists p_c < p such that for p̃ ∈ (p_c; p) optimum is corner: domestic price p set to producers' reservation price p and t = p̃ − p < 0 (equation (6)).
    - If p̃ ≤ p_c optimum interior; subsidy/tariff does not fully compensate producers.
  - High p̃: p̃ > p
    - Symmetric region of compensating protection where government imposes export tax or import subsidy to fully offset consumers' welfare loss.
    - Threshold p_c > p such that for p̃ ∈ (p; p_c) corner solution: domestic price = workers' reservation price p and t = p̃ − p > 0 (equation (7)).
    - If p̃ ≥ p_c optimum interior; tax/subsidy does not fully compensate consumers.
- FOC intuition:
  - Without loss aversion: optimal p = p̃.
  - With loss aversion: FOC W' + H' = 0; in corner regions marginal standard welfare may be zero but positive marginal loss-aversion pushes policy to reservation prices.
  - Diminishing sensitivity h'' < 0 implies full compensation less attractive as p̃ diverges further from reference prices.
- Proposition 1 summary:
  - p̃ ∈ (p; p): free trade.
  - p̃ < p: export subsidy (exporter) / import tariff (importer); full producer compensation region p̃ ∈ (p_c; p).
  - p̃ > p: export tax / import subsidy; full consumer compensation region p̃ ∈ (p; p_c).
- Political-economy note:
  - Politically motivated governments may deviate (e.g., favor land owners) especially when p̃ ∈ (p; p).

### Key quantitative/qualitative implications (preserve exact phrasing)
- Trade intervention increases one-to-one with world price movements within full-compensation ranges.
- As divergence increases, diminishing sensitivity and marginal cost make full compensation less attractive → interior solutions.

---

### 2.3 The multiplier effect of trade policy — setup and mechanism
- World trading structure: unit mass of small natural exporters and unit mass of small natural importers.
- Each exporter e ∈ [0;1] sets t(e); each importer i ∈ [0;1] sets t(i).
- Global market equilibrium (equation (8)):
  - ∫_0^1 x^e(p̃ - t(e)) de = ∫_0^1 m^i(p̃ - t(i)) di.
  - World price p̃(t(e); t(i)); free trade p̃(0;0) ≡ p̃_ft.
- Differential intuition: for any non-zero measure set S ⊆ [0;2], dp̃ = dt_S 2(0;1) (text statement).
- Heterogeneity and compensating protection:
  - Active sets E (exporters) and I (importers) with U > 0 follow Proposition 1; complements E^C and I^C with U = 0 opt for free trade.
  - When p̃ ∈ (p; p) no active policy; outside that interval regions of compensating protection and multiplier appear.
- Multiplier mechanism:
  - Exogenous shock raising p̃ above p triggers exporters in E and importers in I to impose export taxes and import subsidies to keep domestic price p.
  - Simultaneous action reduces world supply and raises world demand → pushes p̃ up further → triggers additional policy rounds → convergence at intersection of t(p̃) and p̃(t).

### 2.3 Formal characterization — Proposition 2
- Proposition 2(i):
  - Along compensating protection regions dt / dp̃_ft = ρ ∂t / ∂p̃_ft where ρ = 1 / (1 - dp̃ / dt) > 1.
- Proposition 2(ii):
  - No multiplier when p̃ ∈ (p; p̃) (i.e., inside non-activation interval).
- Limit case:
  - If E, I = [0;1] and dp̃ = dt = 1 then ρ → 1/(1-1) → ∞ (infinite multiplier).

### 2.3 Example 1 (linear supply and demand)
- x^e(p̃ - t) = β + γ(p̃ - t); m(p̃) = μ − ν p̃; β, γ, μ, ν ∈ R_+.
- World equilibrium: p̃ = p̃_ft + θ t where θ ≡ γ/(γ+ν) and p̃_ft ≡ (μ − β)/(γ+ν).
- Along compensating protection with p̃_ft > p and t = p̃ − p = p̃_ft + θ t − p → solves to:
  - t = 1/(1 - θ) (p̃_ft - p) > 0.
- Multiplier: dt / dp̃_ft = ρ ≡ 1/(1 - θ) with θ ∈ (0;1) ⇒ ρ finite and > 1.

---

### 2.4 Large economies and the multiplier — setup and equilibrium
- World with N large exporters and M large importers; equilibrium:
  - Σ_{e=1}^N x_e(p̃ - t_e) = Σ_{i=1}^M m_i(p̃ - t_i) → p̃(t).
  - p̃ increasing in any element of t; p̃(0) = p̃_ft.
- Generic country ! objective (equation (10)):
  - G_!(t_!; p̃(t)) = W_!(t_!; p̃(t)) + H_!(t_!; p̃(t))
  - W_!(·) = (1 − β_!) + ϕ_!(·) + CS_!(·) + GR_!(·) (equation (11)).
- Interpretation:
  - If domestic price ∈ [p; p̃] → H_!(·) = 0 → maximize W_!.
  - If domestic price outside interval → indicators I_l or I_L activate → maximize G_! (loss aversion matters).

### 2.4 Equilibrium characterization and propositions
- Active sets E (count E) and I (count I) with loss aversion U > 0; complements passive.
- Candidate Nash equilibria:
  - Loss aversion irrelevant: best responses maximize W_!; symmetric candidate ^t with domestic prices ^p_E and ^p_I; if ^p_E and ^p_I ∈ [p; p̃] ^t is Nash.
  - Loss aversion relevant: if ^p_E or ^p_I outside [p; p̃] best responses maximize G_!; possible compensating protectionism equilibrium maintaining domestic prices at reservation levels.
- Proposition 3:
  - (i) For p̃_ft ∈ [p_ft; p^c_ft], equilibrium trade policy is full consumer compensation: t^c s.t. p̃(t^c) − t^c = p̃ for all active countries.
  - (ii) For p̃_ft ∈ [p^c_ft; p_ft], equilibrium trade policy is full producer compensation: t^p s.t. p̃(t^p) − t^p = p for all active countries.
- Proposition 4 (strategic complementarities and multiplier):
  - (i) Trade policies are strategic complements: dt_! / dt_{-!} ∈ (0,1) for all active !.
  - (ii) Multiplier: dt_! / dp̃_ft = (∂t_! / ∂p̃_ft) where κ = 1 / [1 - (E + I) (dp̃ / dt_!)] > 1.
  - Limit: if E = N and I = M (all countries large) multiplier → ∞ along compensating protection regions.

### 2.4 Example 2 (linear example, two active exporters, one passive importer)
- Export supply per exporter: x_e(p̃ - t_e) = a/2 + b/2 (p̃ - t_e), a, b ∈ R_+.
- Passive import demand: m(p̃) = c − d p̃, c, d ∈ R_+.
- World equilibrium yields p̃ = p̃_ft + v(t_1 + t_2) where v ≡ b / [2 (b + d)] and p̃_ft ≡ (c − a)/(b + d).
- Upper compensating protection region:
  - Strategy complementarity dt_e / dt_{-e} = v / (1 - v) > 0 as v ∈ (0, 1/2).
  - Symmetric equilibrium tax: t_eq = [1 / (1 - 2 v)] * (p̃_ft - p̃) > 0.
  - Multiplier: dt_eq / dp̃_ft = κ = 1 / (1 - 2 v) > 1.

---

### Empirical motivation: 2008-2011 food crisis context
- Period 2008-2011:
  - Food prices > 80 percent higher than average 1990-2006.
  - In cereals, dairy, oils, sugar increases exceeded 100 percent.
  - Price volatility significantly higher during 2008-2011 vs. 1990-2006 (see Table 1 in source).
- Trade policy focus: export restrictions and import promotion (data do not contain subsidies); empirical analysis limited to increases in export restrictions and reductions in import protection.

---

### Section 3.2.3 Data, variables, and empirical specification (sample and regressors)
- Sample: monthly data for 77 countries and 33 commodity products.
- Dependent variable TPU_{i;k;t}: binary indicator = 1 if country i implements at least one trade measure in product k at time t (export restriction increase or import tariff/quota reduction), 0 otherwise.
- Main regressors:
  - price_{k;t-1} = (price_{k;t-1} − ref_price_{k;t-1}) / ref_price_{k;t-1}, reference = 3 year moving average.
  - GTPU_{-i;k;t-1} = weighted share of trade covered by measures in product k at t-1 (weighted sum over j ≠ i of export and import exposures).
- Controls: Prod_share_{i;k} (2005), logTrade_{i;k;t-1}, logGDP percap_{i} (2000–2005), product-time and country fixed effects, year fixed effects. Standard errors clustered at product-time level.
- Estimation: Logit and linear probability (LP) models.
- Instrumental variables:
  - For prices: rainfall measures from GPCP (logRain_{kt}, Rainvar_{kt}).
  - For global trade policy utilization: Elections_{kt} and TM_{-kt} (industry-level measures excluding product k).

### Section 3.2.3 Baseline regression findings (Table 4 and discussion)
- Price deviations:
  - 1 per cent increase in price_{k;t-1} → increase in probability of implementing a trade policy in t by 0.01 (logit) and 0.07 percent (LP).
  - 20 percentage point increase in prices → increase of 0.2 (logit) and 1.4 (LP) percentage points in likelihood.
- Global trade policy utilization:
  - Logit: 1 per cent increase in share covered by measures → raises probability by 0.05 percent.
  - LP: equivalent coefficient 0.6 percent.
  - One standard deviation increase in global trade policy utilization → 0.75 to 9 percent increase in probability, depending on model.
- Production share:
  - Including Prod_share_{i;k} reduces sample size ~50% but price effect sign unchanged; higher production shares increase likelihood of trade policy use.
- Controls:
  - logTrade positive and significant.
  - logGDP percap negative and significant (less likely to use trade policy if higher per capita income); loses significance when production shares included.

### Subsample: staple products (Table 5)
- For staples:
  - Impact of international price deviations more than doubles vs full sample.
  - After controlling for global trade policy, 1 percent increase in price deviation → almost 6 percent increase in probability of trade policy utilization.
  - Coefficient on global trade policy utilization ≈ 0.56 (similar to full sample).

### Large traders: heterogeneity and interaction effects (Table 6)
- Large trader indicator = 1 if country i's share of exports (imports) over world exports (imports) of product k > 75th percentile.
- Patterns:
  - Being a large importer → negative impact on probability of imposing trade measure.
  - Being a large exporter → positive impact.
  - Interaction price × large trader:
    - Positive and significant for whole sample (large traders react more to price increases).
    - Not significant for staple subsample (all react similarly).
  - Interaction global trade policy × large trader:
    - Positive for both large importers and exporters — consistent with a multiplier effect (global policy utilization has magnified effect for large players).

### Endogeneity concerns and mitigation (Section 3.2.3)
- Strategy 1: lagged regressors (t-2, t-3) → magnitudes similar to baseline (Appendix Table 1); price changes at t-3 for whole sample not significant.
- Strategy 2: IV approach for staples:
  - Instruments for prices: logRain_{kt}, Rainvar_{kt}.
  - Instruments for global trade policy utilization: Elections_{kt}, TM_{-kt}.
  - First-stage (Appendix Table 3):
    - Rainfall measures predict international prices; Rainvar negatively affects production.
    - Elections_{kt} negatively correlated with global trade policy utilization; TM_{-kt} positively correlated.
    - F-statistics indicate instruments not weak (e.g., F-statistics reported: 62.7, 62.4, 56.61, 56.14, 67.79, 67.52 for price first-stage; 10.38, 10.32, 10.91, 10.83, 10.45, 10.2 for GTPU first-stage).
  - Second-stage IV (Table 7) — staple sample:
    - Price deviations:
      - 1 percent increase in deviation → 0.47 average increase in likelihood of imposing trade measure (IV estimate).
      - Large importers: coefficient 0.40.
      - Large exporters: coefficient 0.6.
    - Global trade policy utilization:
      - 1 percent increase → almost 6 percent increase in likelihood (IV).
      - Large exporters ≈ 0.6; large importers ≈ 0.5.

---

### 3.3 The impact of trade policy on food prices — empirical system and main findings
- Simultaneous equations 2SLS system (as in source):
  - price_k,t = β0 + β1 GTPU_k,t + β2 logRain_k,t + β3 Rainvar_k,t + β4 ΔEnergy_t + α_k + γ_t + ε_kt
  - GTPU_k,t = φ0 + φ1 price_k,t-1 + φ2 Elections_k,t + φ3 TM_-k,t + γ_t + α_k + u_kt
- Controls: logRain, Rainvar, ΔEnergy_t; instruments: Elections proximity and TM_-k,t.
- Reference prices used: 3-year MA, 5-year MA, historical averages 1980-2006 and 2000-2006.
- Main empirical findings:
  - Global trade policy utilization raises international prices for a product k.
  - Quantified impacts (2SLS, staple foods; Table 8):
    - 1 per cent increase in share of world trade covered by measures → international price change from reference increases between 0.4 and 2.1 percent depending on reference price.
    - One standard deviation increase in GTPU → prices in staple foods increased between 8 and 42 percent in 2008-2011.
  - Results comparable in magnitude to related literature (e.g., Anderson and Martin (2011) noted in source).
- Theoretical mechanism consistent: trade measures set in response to price deviations and to other countries' measures produce feedback → multiplier that amplifies price movements.

### Policy-relevant implications (preserve exact phrasing of findings)
- Trade policy actions during high and volatile prices (2008-11) were not only reactive but contributed materially to raising staple food international prices.
- The multiplier effect implies unilateral, non-cooperative trade measures (export restrictions and import policy changes) can magnify international price volatility, particularly for staple foods.
- Empirical 2SLS evidence (using elections proximity and industry-level measures as instruments) supports simultaneity: trade policy utilization both responds to and influences international prices.

---

### Key tables and stylized numerical facts (selected exact figures from source)
- Table 1 (1990-2011 price statistics excerpt):
  - 1990-2006: Food mean 108.62 s.d. 12.87.
  - World Food crisis 2007-mid-2008: Food mean 179.78 s.d. 31.82.
  - World Food crisis mid-2008-2011: Food mean 197.88 s.d. 29.18.
- Table 2 (selected product coverage):
  - Hscode 1001 Wheat and meslin: a = 42; b = 986; c = 73.85.
  - 1005 Maize (corn): a = 36; b = 437; c = 38.16.
  - 1006 Rice: a = 6; b = 154; c = 35.72.
  - 1701 Sugar: a = 32; b = 403; c = 51.08.
  - 1003 Barley: a = 33; b = 735; c = 53.17.
  - 1511 Palm oil: a = 9; b = 192; c = 55.23.
- Table 3 (summary stats 2008-2011):
  - Full sample: TPU_ikt mean 0.045 sd 0.208 obs 114912; Price changes (3yrs MA) mean 0.054 sd 0.211 obs 100968; Global trade policy mean 0.080 sd 0.153 obs 114114.
  - Staple sample: TPU mean 0.128 sd 0.334 obs 21798; Price changes mean 0.065 sd 0.227 obs 19404; Global trade policy mean 0.166 sd 0.203 obs 21630.
- Table 8 (2SLS impact of GTPU on international prices, staple food):
  - GTPU_k,t (weighted) coefficients (Price changes from):
    - 3yrs MA: 1.3093*** [0.184].
    - 5yrs MA: 0.4403*** [0.123].
    - Hist avg (1980-2006): 2.1540*** [0.299].
    - Hist avg (2000-2006): 1.2005*** [0.146].
- Appendix Table 2 (lagged regressions, selected coefficients):
  - Global trade policy -i,k,t-x (weighted): e.g., column (1) 0.6239*** [0.056]; column (2) 0.5643*** [0.064].
  - Price changes × Large exporter (example): 0.0271*** [0.010] in columns (1)/(3).
  - Observations e.g., (1) 41360, (2) 18954; R-squared e.g., (1) 0.198, (2) 0.231.
- Appendix Table 3 (first-stage F-statistics):
  - Price first-stage F-statistics: 62.7, 62.4, 56.61, 56.14, 67.79, 67.52.
  - GTPU first-stage F-statistics: 10.38, 10.32, 10.91, 10.83, 10.45, 10.2.

*Source: _wp14182 - IMF working paper sections 2.1, 2.3, 2.4, 3.2.3, 3.3 and appendices as provided.*

### 2.1  The model: Food prices and loss aversion

### 2.1  The model: Food prices and loss aversion

### Model setup
- Small open economy producing two goods: a numeraire and a commodity referred to as food.
- Numeraire:
  - Produced with labor alone using constant returns to scale technology y0 = l0.
  - Wage rate fixed and equal to one (labor supply assumed sufficiently large).
  - Numeraire can be imported/exported at a unitary world price.
- Food:
  - Produced using labor and a specific factor in fixed supply, land (L).
  - Technology: y = f(l; L) with constant returns to scale.
  - Given domestic price of food p, return to owners of the specific factor is ρ(p) = max_l [p f(l; L) − l].
  - Domestic output of food y(p) = ρ'(p).
- Agents:
  - Continuum of individuals of measure one with identical preferences.
  - Government can create a wedge between international and domestic price of food: p = p − t, where t is trade policy (t > 0: export tax or import subsidy to protect consumers; t < 0: export subsidy or import tariff to protect producers).
  - Government revenue: GR(p) = (p − p) [y(p) − d(p)]?0: (equation (2)).
  - When positive, revenue redistributed uniformly; lump-sum taxes finance negative budgets.

### Preferences and loss aversion
- Individual utility (separable form):
  - U = c0 + u(c) − I · h(U − c0 − u(c)), (equation (1))
    - c0: consumption of the numeraire.
    - c: food consumption.
    - u(·): standard properties u'(·) > 0, u''(·) < 0.
    - h(·): increasing in the difference between a reference level U and actual utility (h' > 0) and displays diminishing sensitivity to losses (h'' < 0).
    - I: indicator variable equal to one whenever utility falls strictly below the reference level and zero otherwise.
  - Interpretation: welfare loss when utility < reference level U; no additional welfare gain when utility > U.
  - Individual demand of food: d(p) = [u'(c)]−1.
  - Remaining income spent on numeraire: c0 = E − p d(p) (E is individual income).

### Social groups, indirect utilities, and reference prices
- Population split:
  - Fraction  owns land = land owners/producers.
  - Remaining share (1 − ) are workers/consumers supplying one unit of labor each.
- Indirect utilities:
  - Workers (V_l^p(p)):
    - V_l^p(p) = 1 + CS(p) + GR(p) − I_l · h(V_l(p) − 1 − CS(p) − GR(p)), (equation (3))
    - CS(p) = u[d(p)] − p d(p) is consumer surplus.
    - I_l = 1 whenever V_l(p) > 1 + GR(p) + CS(p), and zero otherwise.
  - Land owners (V_L^p(p)):
    - V_L^p(p) = ρ(p)/ + CS(p) + GR(p) − I_L · h(V_L(p) − ρ(p)/ − CS(p) − GR(p)), (equation (4))
    - I_L = 1 whenever V_L(p) > ρ(p)/ + GR(p) + CS(p), and zero otherwise.
- Reference prices and reservation utilities:
  - Workers: reservation utility corresponds to a unique reference price denoted by p. Consumer surplus + government revenue strictly decreasing in p; when p > p workers incur loss (I_l = 1), when p < p no additional utility (I_l = 0).
  - Producers: if land owners are a sufficiently small fraction , they perceive negligible share of tax revenue; an increase in p strictly increases their utility. Their reference utility corresponds to unique price p. When p < p producers perceive a decline (I_L = 1); when p > p no additional gain.

### Government objective and total welfare
- Total welfare: G(p) = W(p) + H(p), (equation (5)).
  - Standard social welfare net of loss aversion:
    - W(p) = (1 − ) + ρ(p) + CS(p) + GR(p).
  - Loss aversion for entire economy:
    - H(p) = −(1 − ) I_l · h(V_l(p) − 1 − CS(p) − GR(p)) −  I_L · h(V_L(p) − ρ(p)/ − CS(p) − GR(p)).
- Government sets trade policy to maximize G(p).

### Unilateral food trade policy under loss aversion — scenarios and optimal policy
- Three main regions depending on international price p:
  - Intermediate values: p ∈ (p; p): loss aversion term H(·) = 0 and optimal trade policy is free trade (p = p).
  - Low international price: p < p:
    - There exists a region of compensating protectionism where government sets an export subsidy or an import tariff to fully compensate producers for welfare loss.
    - There is a critical level p_c < p such that for p ∈ (p_c; p) the first-order condition (FOC) is not satisfied in the relevant region and the optimum is a corner solution: domestic price set equal to reservation price for land owners p. Optimal policy (export subsidy or import tariff) is t = p − p < 0. (equation (6))
    - If p ≤ p_c the maximum is an interior solution and the subsidy/tariff does not fully compensate producers.
  - High international price: p > p:
    - Symmetrically, there exists a region of compensating protectionism where government imposes an export tax or an import subsidy to fully offset consumers' welfare loss due to higher p.
    - There is a threshold p_c > p such that for p ∈ (p; p_c) the FOC is not satisfied in the relevant region and the government sets domestic price equal to reservation price for workers p (corner solution). Optimal policy (export tax or import subsidy) is t = p − p > 0. (equation (7))
    - If p ≥ p_c the maximum is interior and the export tax/import subsidy does not fully compensate consumers.

- FOC and intuition (as given in text):
  - FOC when H(·) = 0 yields optimal p = p.
  - With loss aversion, the FOC becomes W' + H' = 0. In corner regions where marginal welfare from standard terms is zero but marginal loss-aversion term is positive, the policy maker sets domestic price at the reference price of the losing group.
  - Diminishing sensitivity (h'' < 0) implies that as the world price diverges further from reference prices, full compensation becomes less attractive and interior solutions emerge.

### Proposition 1 (characterization)
- For international price p ∈ (p; p):
  - Optimal food trade policy for a small open economy is free trade.
- For p < p:
  - Optimal policy is an export subsidy for a food exporter and an import tariff for a food importer.
  - A region of full producer compensation (t = p − p) exists for p ∈ (p_c; p).
- For p > p:
  - Optimal policy is an export tax or an import subsidy.
  - A region of full consumer compensation (t = p − p) exists for p ∈ (p; p_c).

### Additional implications and political economy note
- Trade intervention increases as world food price diverges from the relevant reference price: protection rises one-to-one with price movements within the full-compensation ranges.
- As divergence increases, the marginal cost of intervention and diminishing sensitivity make full compensation less attractive; optimal policy shifts to partial compensation (interior solutions).
- Political economy considerations:
  - When p ∈ (p; p) a politically motivated government may set export subsidy or import tariff (favoring land owners) rather than free trade.
  - There exists a first region of full producer compensation when p is low (below p), and a region of full consumer compensation when p is high (above p), where politically motivated governments may still choose policies consistent with loss-aversion-driven full compensation.

*Source: _wp14182 - 2.1  The model: Food prices and loss aversion*

### 2.3  The multiplier e§ect of trade policy

### 2.3  The multiplier e§ect of trade policy

### Setup and intuition
- A small economy under loss aversion may use trade policy (export taxes/subsidies or import subsidies/tari§s) to insulate the domestic price from large international food price changes.
- A single small economy's trade measure has no e§ect on world markets, but simultaneous similar responses by many trading economies can a§ect the international price and induce further policy responses (the multiplier e§ect).
- Trading world structure in the model:
  - Unit mass of small natural food exporters and unit mass of small natural food importers.
  - Generic exporter e∈[0;1] can set an export tax/subsidy t(e).
  - Generic importer i∈[0;1] can set an import subsidy/tari§ t(i).
  - Global market equilibrium: 1 ∫_0^1 x^e(p̃ - t(e)) de = 1 ∫_0^1 m^i(p̃ - t(i)) di. (Equation (8))
  - The world price of food is p̃(t(e); t(i)), with free trade level p̃(0;0) ≡ p̃_ft.
- For any non-zero measure set S⊆[0;2], it is dp̃ = dt_S 2(0;1), where t_S denotes the trade policy of set S. The intuition: simultaneous export taxes (subsidies) lower (increase) world supply; simultaneous import subsidies (tari§s) raise (decrease) world demand — producing upward (downward) pressure on p̃.

### Heterogeneity and regions of compensating protection
- Countries di§er in propensity to intervene. Developing countries may be more likely to fall below the reference utility U and implement compensating protectionism.
- To capture heterogeneity, model considers two groups of identical countries:
  - A measure E⊆[0;1] of identical exporters and a measure I⊆[0;1] of identical importers with consumers strictly loss averse (U>0); Proposition 1 applies to these sets.
  - The rest of the world E^C = [0;1]\E and I^C = [0;1]\I have U = 0 and opt for free trade.
- Along the interval (p; p̃) no government is incentivized to employ active trade policy; when p̃ moves outside that interval, regions of compensating protection emerge and a multiplier e§ect can appear.

### Mechanism of the multiplier e§ect
- When an exogenous shock raises the international price above the domestic target p (p̃_ft > p), exporters in E and importers in I impose export taxes and import subsidies respectively to keep domestic price at p.
- Simultaneous action across exporters and importers:
  - Reduces world supply (due to export taxes) and raises world demand (due to import subsidies) → pushes p̃ up further.
  - Higher p̃ then triggers additional rounds of higher export taxes and import subsidies.
- Subsequent trade measures are reactions to policies set by other countries, not only to the initial shock.
- The process converges at the intersection of the policymakers' optimal trade policy function t(p̃) and the international price function p̃(t) — the equilibrium (p̃_eq, t_eq).

### Equilibrium process (graphical description)
- Individual optimal policy at initial p̃_ft > p is t_1.
- If all exporters/importers set t_1, global excess demand raises p̃ to p̃_1.
- At p̃_1, t_1 is ine¢ciently low; policymakers increase to t_2, raising p̃ further to p̃_2, and so on.
- The multiplicative process stops at the intersection point Q where p̃(t) intersects t(p̃); the uncoordinated behavior causes equilibrium p̃ to exceed free trade level.

### Formal characterization — Proposition 2
- Proposition 2(i): Along the regions of compensating protectionism identified in Proposition 1, a multiplier e§ect characterizes trade policy. In particular,
  - dt / dp̃_ft = ρ ∂t / ∂p̃_ft
  - where ρ = 1 / (1 - dp̃ / dt) > 1.
- Proposition 2(ii): There is no multiplier e§ect when the international price belongs to the interval (p; p̃).
- Intuition: Joint imposition of higher export taxes and higher import subsidies (or lower export subsidies and lower import tari§s) contracts world supply and expands world demand, thus resulting in even higher international food prices.
- Limit case: If E, I = [0;1], along regions of compensating protectionism dp̃ = dt = 1 and the multiplier is infinite: ρ → 1/(1-1) → ∞. This limit case is noted in the proof of Proposition 2.

### Example 1 (linear supply and demand)
- Consider E = [0;1], I = ?. Linear export supply and import demand:
  - x^e(p̃ - t) = β + γ(p̃ - t) for e∈[0;1]
  - m(p̃) = μ - ν p̃
  - β, γ, μ, ν ∈ R_+
- World market equilibrium yields p̃ = p̃_ft + θ t, where θ ≡ γ/(γ+ν) and p̃_ft ≡ (μ - β)/(γ+ν).
- For p̃_ft > p and along compensating protection, each country proposes t = p̃ - p = p̃_ft + θ t - p, solving to
  - t = 1/(1 - θ) (p̃_ft - p) > 0.
- Then dt / dp̃_ft = ρ ∂t / ∂p̃_ft with ρ ≡ 1/(1 - θ), the multiplier. Since θ ≡ γ/(γ+ν) ∈ (0;1), ρ is finite and strictly higher than 1.

*Source: IMF working paper section 2.3 (2.3  The multiplier e§ect of trade policy).*

### 2.4  Large economies and the multiplier e§ect

### 2.4  Large economies and the multiplier e§ect

### Model setup and key definitions
- Consider a world economy made up of N large exporting countries and M large importing countries. Market equilibrium in the food sector implies:
  - Sum_{e=1}^N x_e(p̃ - t_e) = Sum_{i=1}^M m_i(p̃ - t_i), which implicitly defines the world price p̃(t), where t = {t_1, t_2, ..., t_{N+M}}.
  - p̃ is increasing in any element of vector t. If t = 0, then p̃(0) = p̃_ft.
- A generic country ! in N ∪ M has objective:
  - G_!(t_!; p̃(t)) = W_!(t_!; p̃(t)) + H_!(t_!; p̃(t)) (equation (10)).
  - W_!(·) is standard social welfare: W_!(t_!; p̃(t)) = (1 - β_!) + ϕ_!(t_!; p̃(t)) + CS_!(t_!; p̃(t)) + GR_!(t_!; p̃(t)) (equation (11)).
  - H_!(·) is the loss aversion term defined in the source text (preserving the exact functional form and indicators I_l, I_L as given).
- Interpretation of p and p̃:
  - When the domestic price of country ! lies inside interval [p; p̃], the loss aversion term is null and the government maximizes W_!.
  - When domestic price in ! is higher than p (or lower than p), corresponding indicators I_l = 1 (I_L = 1) activate and the government maximizes G_! (i.e., accounts for loss aversion).

### Equilibrium characterization for large countries
- Focus on identical exporters E (count E ∈ [1, N]) and identical importers I (count I ∈ [1, M]) whose consumers are strictly loss averse (U > 0), so a non-degenerate interval [p; p̃] exists. Complementary sets E^C and I^C have U = 0 and are passive.
- Strategic interaction described as a simultaneous game with E + I active players choosing trade policy to maximize their welfare.
- Two cases for candidate Nash equilibrium:
  - Loss aversion does not play a role: best responses come from maximization of W_! (equation (11)). Candidate Nash equilibrium ^t (vector with ^t_E repeated E times and ^t_I repeated I times) solves the system of E+I best response functions.
    - Denote ^p_E ≡ p̃ - ^t_I - ^t_E as domestic price in exporters and ^p_I ≡ p̃ - ^t_I - ^t_E as domestic price in importers, with ^p_I > ^p_E because ^t_E > 0 (export tax) and ^t_I < 0 (import tariff/subsidy). If both ^p_E and ^p_I lie in [p; p̃], ^t is a Nash equilibrium.
  - Loss aversion plays a role: if either ^p_E or ^p_I (or both) lie outside [p; p̃], best responses come from maximization of G_! (equation (10)). Equilibrium policy may be compensating protectionism: policy makers choose trade policy to maintain domestic price at reservation level.

### Proposition 3 (regions of compensating protectionism)
- (i) For any p̃_ft ∈ [p_ft; p^c_ft], the equilibrium trade policy of both exporting and importing countries is full consumer compensation: t^c ≡ {t^c, ..., t^c} such that p̃(t^c) - t^c = p̃ for all e ∈ E and i ∈ I.
- (ii) For any p̃_ft ∈ [p^c_ft; p_ft], the equilibrium trade policy of both exporting and importing countries is full producer compensation: t^p ≡ {t^p, ..., t^p} such that p̃(t^p) - t^p = p for all e ∈ E and i ∈ I.
- Along these two regions of compensating protectionism, loss aversion is so strong that all governments set trade policy to maintain domestic price at reservation levels:
  - Large exporters set a tax t^c > 0 to fully compensate consumers and a subsidy t^p < 0 to fully compensate producers (analogously for importers with signs reversed).

### Proposition 4 (strategic complementarities and multiplier effect)
- Along the regions of compensating protectionism identified in Proposition 3:
  - (i) Trade policies are strategic complements: dt_! / dt_{-!} ∈ (0,1) for all ! ∈ E ∪ I.
  - (ii) A multiplier effect characterizes trade policy: dt_! / dp̃_ft = (∂t_! / ∂p̃_ft) for all ! ∈ E ∪ I, where
    - κ = 1 / [1 - (E + I) (dp̃ / dt_!) ] > 1.
- Intuition:
  - If country -! increases its trade policy t_{-!}, it raises the world price p̃, prompting country ! to adjust t_! in the same direction to keep its domestic price constant — hence strategic complementarity.
  - Complementarity magnifies effects of an exogenous common shock to export supply or import demand of food; i.e., a change in the untaxed world price is amplified by trade policy responses.
- Limit cases and properties:
  - When E = N and I = M (all countries large), the multiplier is infinite along the compensating protection regions (details in proof).
  - Uniqueness of equilibrium in this policy game is ensured because slopes of best-response functions are strictly less than 1 despite complementarity.

### Example 2 — linear import demand and export supply (two identical policy-active exporters, one passive importer)
- Export supply per exporter: x_e(p̃ - t_e) = a/2 + b/2 * (p̃ - t_e), for e = 1,2, with a, b ∈ R_+.
- Passive importing region import demand: m(p̃) = c - d p̃, with c, d ∈ R_+.
- World equilibrium condition (E = N = 2, I^C = M = 1):
  - a/2 + b/2 (p̃ - t_1) + a/2 + b/2 (p̃ - t_2) = c - d p̃.
  - Leads to p̃ = p̃_ft + v(t_1 + t_2), where v ≡ b / [2 (b + d)] and p̃_ft ≡ (c - a) / (b + d).
- Intermediate domestic price case (no loss aversion):
  - First-order condition yields t_e = Θ(a/b + p̃) - v (source gives form t_e = ϑ(a/b + p̃) - v; preserve relation).
  - With symmetry t_e = t_{-e} = ^t, symmetric equilibrium:
    - ^t = v / (1 - 2 v) * (a/b + p̃_ft).
  - p_ft defined by condition that domestic price resulting from ^t equals p:
    - p_ft = (1 - 2 v) a/b + p * (1 - 2 v^2)^{-1} * (1 - v)^{-1} (expression as given in source).
  - If p̃_ft < p_ft, equilibrium tax is ^t; if p̃_ft > p_ft, loss aversion matters and maximization of (10) yields a higher export tax ṫ > ^t and p^c_ft can be solved analogously (explicit p^c_ft requires functional forms for h(·) and u(·)).
- Upper region of compensating protection (domestic price kept at p̃):
  - Policy satisfies t_e = p̃_ft - p̃ / (1 - v) + v/(1 - v) t_{-e}.
  - Since v ∈ (0, 1/2), export taxes are strategic complements: dt_e / dt_{-e} = v / (1 - v) > 0.
  - Symmetric equilibrium tax:
    - t_eq = [1 / (1 - 2 v)] * (p̃_ft - p̃) > 0.
  - Multiplier:
    - dt_eq / dp̃_ft = κ = 1 / (1 - 2 v) > 1 (as v < 1/2).
- Lower region of compensating protection analogous, yielding strategic complementarity and multiplier.

### Empirical motivation and link to the 2008-11 food crisis
- Objective: empirically test the existence of a multiplier effect in food trade policy during 2008-2011 by:
  - Testing whether trade policy measures are related to changes in international food prices.
  - Testing whether countries respond to trade policy implemented by other governments (producing a policy multiplier).
  - Addressing endogeneity of trade policy and prices.
  - Estimating a simultaneous system to evaluate impact of overall trade policy on international prices.
- Period focus: 2008-2011, characterized by high food and commodity prices:
  - Food prices were more than 80 percent higher than average prices during 1990-2006.
  - In certain sectors (cereals, dairy products, oils, sugar) the increase exceeded 100 percent.
  - Price volatility was significantly higher during 2008-2011 compared with 1990-2006 (see Table 1 in source).
- Trade policy instrument focus:
  - Export restrictions and import promotion (because during high international food prices countries tend to use these measures to insulate domestic markets).
  - Data limitation: available data do not contain information on subsidies (export or import); empirical analysis limited to increases in export restrictions (export prohibitions, taxes, quotas) and reductions in import protection (tariffs and quotas).
- Data sources and summary statistics:
  - Trade policy implementation data from WTO Trade Monitoring Reports (TMR) and Global Trade Alert (GTA).
    - WTO monitoring reports used: October 2009, November 2010, March 2011, November 2011.
    - GTA includes measures collected from media and analysts; evaluated by expert analysts before publication.
  - During 2008-2011:
    - Total of 281 relevant trade policy instruments recorded in food products (see column 3 of Table 2).
    - On average, 9 countries imposed an export restriction and/or reduced import protection in a certain product during the period.
    - Number of countries using trade policy varies across products: less than 5 countries in ground nut and coffee/cacao beans; more than 30 countries in staples such as wheat and meslin (42), maize (36), barley (33).
    - Table 2 shows number of periods (months) × number of countries implementing a trade policy measure during 2008-2011: total coverage equals 5219 product-periods.
    - Share of imports or exports covered by trade measures varies by product:
      - For wheat, meslin and cocoa, > two thirds of trade covered by trade measures during 2008-2011.
      - For palm oil, barley and sugar, trade measures covered 50 percent of trade.
      - For rice, maize and sunflower seed, ~ one third of trade covered by trade measures.
  - Instrumental variables used in empirical work:
    - Rainfall data from Global Precipitation Climatology Project (GPCP) to instrument international prices.
    - Election data from Elections Guide dataset to instrument trade policy utilization.
- Data limitation noted:
  - Few instances report the size of measures; available information permits qualitative analysis of likelihood of measure utilization but not quantitative estimation of magnitudes.

*Italic: Source — _wp14182 - 2.4  Large economies and the multiplier e§ect (PDF chapter).*

### Section 3.2.3. The rest of the data are from standard sources. International nominal prices come from

### _wp14182 - Section 3.2.3. The rest of the data are from standard sources. International nominal prices come from

### Data, variables, and empirical specification
- Sample: monthly data for a set of 77 countries and 33 commodity products.
- Dependent variable: TPU_{i;k;t} — dichotomous indicator equal to 1 whenever country i implements at least one trade measure in product k at time t (export restriction increase or import tariff/quota reduction) and 0 otherwise.
- Main regressors:
  - 
price_{k;t-1} — percentage difference of the price of product k from its reference price (price_{k;t-1} - ref_price_{k;t-1}) / ref_price_{k;t-1}, with reference price calculated as the 3 year moving average.
  - GTPU_{-i;k;t-1} — global trade policy utilization: weighted share of trade covered by export restrictions and import protection reductions in product k at t-1, computed as the weighted sum over j ≠ i of (exp_{j;k;t-1}/WldTrade_{k;t-1} * exp_res_{j;k;t-1} + imp_{j;k;t-1}/WldTrade_{k;t-1} * imp_red_{j;k;t-1}).
- Controls: Prod_share_{i;k} (production share, calculated for 2005), logTrade_{i;k;t-1} (log of total trade of product k in country i at month t), logGDP percap_{i} (per capita GDP of country i, calculated between 2000 and 2005), product-time (month) and country fixed effects, year fixed effects. Standard errors clustered at product-time level.
- Estimation approaches: logit model and linear probability (LP) model.

### Baseline regression findings (Table 4 and discussion)
- Impact of international price deviations:
  - A one per cent increase from reference price in t-1 increases the probability of implementing a trade policy in t by 0.01 (logit) and 0.07 per cent (LP).
  - A 20 percent percentage point increase in prices from their reference values leads to an increase of 0.2 (logit) and 1.4 (LP) percentage points in the likelihood of using trade policy.
- Impact of global trade policy utilization:
  - In the logit model, a 1 per cent increase in the share of trade covered by trade measures on a product raises the probability of imposing a trade measure on that product by 0.05 per cent on average.
  - In the LP model, the equivalent coefficient is 0.6 per cent on average.
  - A one standard deviation increase in global trade policy utilization will lead to a 0.75 to 9 per cent increase, depending on the model, in the probability of implementing a trade policy in country i.
- Role of production shares:
  - Including Prod_share_{i;k} reduces sample size by around half (data availability) but does not change the sign of price effects; higher production shares increase the likelihood of trade policy utilization.
- Control variables:
  - 4 (logTrade) is positive and significant.
  - 5 (logGDP percap) is negative and significant (lower per capita income associated with higher probability of using trade policy); this variable loses significance once production shares are included.

### Subsample: staple products (Table 5)
- For staple foods (e.g., corn, wheat, sugar):
  - The impact of international price deviations more than doubles relative to the full sample: after controlling for global trade policy measures, a 1 percent increase in international price deviations leads to an almost 6 percent increase in the probability of trade policy utilization.
  - The coefficient on global trade policy utilization is very similar to the overall sample and equivalent to 0.56.

### Large traders: heterogeneity and interaction effects (Table 6)
- Definition: a large trader indicator equals 1 if country i's share of exports (imports) over world exports (imports) of product k is above the 75th percentile.
- Main patterns:
  - Being a large importer has a negative impact on the probability of imposing a trade measure; being a large exporter has a positive impact.
  - Interaction of international price changes with large importer/exporter status:
    - Positive and significant for the whole sample of products (large traders react more to price increases).
    - Not significant for the subsample of staple foods (all countries react similarly to staple price deviations).
  - Interaction of being a large trader with global trade policy utilization is positive for both large importers and large exporters, consistent with a multiplier effect: global trade policy utilization has a magnified effect for large players.

### Endogeneity concerns and mitigation strategies (Section 3.2.3)
- Concern: international prices and global trade policy utilization may be endogenous due to simultaneity bias.
- Strategy 1 — lagged regressors:
  - Estimations using international price changes and global trade policy utilization lagged to t-2 and t-3 produce magnitudes very similar to baseline results (Appendix Table 1), with the exception that price changes at t-3 for the whole sample are not significant.
  - Interaction results with lagged global trade measures remain similar (Appendix Table 2).
- Strategy 2 — instrumental variables (IV) approach (focused on staple foods):
  - Instruments for international prices:
    - logRain_{kt}: total level of rainfall in the top 3 producer countries of product k at time t.
    - Rainvar_{kt}: total variability of rainfalls in the top 3 producer countries of product k at time t (count of top producers with monthly rain above 75th percentile or below 25th percentile versus historical mean).
  - Instruments for global trade policy utilization:
    - Elections_{kt}: indicator for whether there will be elections in the next six months in the top 3 exporter or importer countries of product k.
    - TM_{-kt}: total number of measures applied in the two-digit industry to which product k belongs, excluding product k itself.
  - First-stage IV results (Appendix Table 3):
    - Rainfall measures are good predictors of international prices: high rainfall is negatively correlated with staple food production and associated with higher international prices; greater deviations across top producers (Rainvar) negatively affect total production.
    - Elections_{kt} is negatively correlated with global trade policy utilization; TM_{-kt} is positively correlated with global trade policy utilization.
    - F-statistics indicate instruments are not weak (see Appendix Table 3).
  - Second-stage IV results (Table 7):
    - International prices:
      - A one percent increase in the deviation from the reference price increases the likelihood of imposing a trade measure by 0.47 on average (IV estimate).
      - For large importers the coefficient is 0.40.
      - For large exporters the coefficient is 0.6.
      - IV price coefficients are larger than baseline estimates, consistent with attenuation bias from measurement error in baseline regressions.
    - Global trade policy utilization:
      - A 1 percent increase in the share of world trade covered by increases in export restrictions and reductions in import protection increases the likelihood of using trade policy by almost 6 percent on average (IV estimate).
      - Coefficients are very similar for large exporters (0.6) and slightly smaller for large importers (0.5).

*Source: _wp14182 - Section 3.2.3. The rest of the data are from standard sources. International nominal prices come from*

### 3.3  The impact of trade policy on food prices

### 3.3  The impact of trade policy on food prices

### Empirical strategy and identification
- The analysis addresses endogeneity of trade policy utilization using a two-stage least squares (2SLS) estimation of a system of simultaneous equations consistent with the theoretical model:
  - First equation (of interest): percentage change of world prices of product k at time t from its reference price as a function of global trade policy utilization (GTPU), controls, product and time fixed effects:
    - price_k,t = β0 + β1 GTPU_k,t + β2 logRain_k,t + β3 Rainvar_k,t + β4 ΔEnergy_t + α_k + γ_t + ε_kt
  - Second equation (instrumenting GTPU): global trade policy utilization for product k depends on lagged price deviation, proximity of elections in top importing and exporting countries, number of trade measures at the two-digit industry level (excluding product k), and fixed effects:
    - GTPU_k,t = φ0 + φ1 price_k,t-1 + φ2 Elections_k,t + φ3 TM_-k,t + γ_t + α_k + u_kt
- Time-varying controls included: total level and variability of rainfall in top producer countries (as previously defined) and monthly changes in energy prices.
- Instruments used in the second stage: proximity of elections in top importing and exporting countries; number of trade measures at the two-digit industry level (excluding product k).
- Estimation focused on a subsample of staple food products and used alternative reference prices: the 3 and 5 years moving average and the historical average for the period 1980-2006 and 2000-2006.

### Main empirical findings
- Evidence supports a multiplier effect of trade policy in the food sector: global trade policy utilization in a given product k has a positive and significant impact on international prices of that product.
- Quantified impacts:
  - A 1 per cent increase in the share of world trade covered by export and import measures raises international price changes from their reference point between 0.4 and 2.1 percent, depending on the reference price used.
  - A one standard deviation increase in global trade policy utilization led prices in staple food products to increase by a range of 8 and 42 per cent in 2008-2011.
- Results are comparable in magnitude to other studies on the impact of trade policy on world food prices of staple foods, most notably Anderson and Martin (2011), notwithstanding methodological differences discussed in the paper.

### Theoretical mechanism summarized
- Theoretical model (Section 2) predicts:
  - Exporting governments offer export subsidies (import tariffs) when food prices are low; they set export taxes (import subsidies) when prices are high.
  - There exists a multiplier effect: world food price changes feed into increasingly active trade policy, amplifying price movements through policy interactions across countries.
- The multiplier arises because trade measures are set in response to deviations of world prices from reference prices and in response to other countries' trade policy utilization—creating feedback that can destabilize global food markets.

### Policy-relevant implications and interpretation
- Trade policy actions during periods of high and volatile prices (2008-11) were not only reactive but contributed materially to raising staple food international prices.
- The presence of a multiplier effect implies that unilateral, non-cooperative trade measures (export restrictions and import policy changes) can magnify international price volatility, particularly for staple foods.
- Empirical strategy using the 2SLS system and instruments (elections proximity; industry-level trade measures excluding the product) provides evidence that trade policy utilization both responds to prices and influences them, consistent with the model's simultaneity.

*Source: IMF Working Paper chapter 3.3, "The impact of trade policy on food prices".*

### 2. Food market equilibrium is obtained when global export supply equalizes global import demand,

### 2. Food market equilibrium is obtained when global export supply equalizes global import demand,

### Equilibrium condition and comparative statics
- Food market equilibrium: x(pt! ) = m(pt! ).
- Totally deriving the equilibrium condition, dp = dt! is expressed as:
  - dp dt! = dm dt! dx dt! dx dp dm dp : (20)
- The fact that dm=dt!; dx=dp >0 and dx=dt!; dm=dp <0 ensures that (20) is strictly positive.
- Disaggregation of global export supply and global import demand:
  - x(pt! )  E
xE(pt! ) + (NE)
x(NE)(p);
  - m(pt! )  I
mI(pt! ) + (MI)
m(MI)(p).
- Derivatives w.r.t. p:
  - dx dp = E dxE dp + (NE) dx(NE) dp
  - dm dp = I dmI dp + (MI) dm(MI) dp
- Using these in (20), and given:
  - (i) dxE = dp = dx=dt! , dmI = dp = dm=dt! ;
  - (ii) dx(NE) = dp >0, dm(MI) = dp <0;
  - guarantees that (20) is lower than 1=(E+I).
- Special case: when E = N and I = M, from (20) dp = dt! = 1=(E+I), implying an infinite multiplier, !1.

### The multiplier effect and reaction functions
- From the reaction function of country ! (equation (19)):
  - Partial derivative: @t! @p ft = @p @p ft ;
  - Total derivative:
    - dt! dp ft = @p @p ft + dp dt! dt! dp ft + X j2(E[In!) dp dt j dt j dp ft .
- Under identical compensating protectionism across the E+I countries:
  - dt! = dp ft = dt j = dp ft and dp = dt! = dp = dt j .
- Hence:
  - dt! dp ft =  @t! @p ft 8!2E[I;
  - where  1 1(E+I) dp dt! ;
  - which is strictly greater than 1 given that dp = dt! 2(0;1=(E+I)).
- Interpretation:
  - The total derivative of t! with respect to pft exceeds the partial derivative — i.e., a multiplier effect amplifies individual country responses through general equilibrium feedbacks.
  - In the symmetric case E = N and I = M the multiplier diverges (infinite multiplier).

### Empirical evidence and stylized facts (figures and tables summary)
- International food prices 1990-2011 are presented (Figure 1). The food price index is the average of five commodity group prices: meat, dairy, cereals, oils and fats and sugar, weighted by export shares; nominal prices deflated using World Bank Manufacturing Unit Values. Source: FAO commodity price statistics.
- Figures include: international food prices and trade policy measures (Figure 2); trade policy diagrams for small and large economies (Figures 3–5).
- Table 1: International food prices before and after 2006 — Means and s.d. for periods:
  - 1990-2006: Food mean 108.62 s.d. 12.87; Meat mean 115.09 s.d. 14.36; Dairy mean 100.03 s.d. 18.19; Cereals mean 102.42 s.d. 14.79; Oils mean 98.91 s.d. 21.08; Sugar mean 139.51 s.d. 38.65.
  - World Food crisis 2007- mid-2008: Food mean 179.78 s.d. 31.82; Meat mean 138.55 s.d. 14.09; Dairy mean 229.52 s.d. 42.05; Cereals mean 194.90 s.d. 50.38; Oils mean 205.12 s.d. 54.67; Sugar mean 154.82 s.d. 18.82.
  - World Food crisis mid-2008-2011: Food mean 197.88 s.d. 29.18; Meat mean 166.20 s.d. 18.82; Dairy mean 194.57 s.d. 35.70; Cereals mean 206.62 s.d. 37.78; Oils mean 207.17 s.d. 43.77; Sugar mean 308.50 s.d. 63.50.
- Table 2: Trade policy measures by product — selected entries (Number of trade measures a; Number of trade measures x time b; % Trade covered by trade measures c):
  - Hscode 1001 Wheat and meslin: Number of trade measures a = 42; Number of trade measures x time b = 986; % Trade covered c = 73.85
  - 1005 Maize (corn): a = 36; b = 437; c = 38.16
  - 1006 Rice: a = 6; b = 154; c = 35.72
  - 1701 Cane or beet sugar and chemically pure sucrose: a = 32; b = 403; c = 51.08
  - 1003 Barley: a = 33; b = 735; c = 53.17
  - 1511 Palm oil and its fractions: a = 9; b = 192; c = 55.23
  - Note: a = number of countries imposing at least one export restriction or import promotion measures over 2008-2011; b = number of countries multiplied by number of periods (months) imposing at least one measure over 2008-2011; c = sum of countries imposing measures between 2008 and 2011 in an hs4 product, weighted by average share of exports or imports over 2000-2005.
- Table 3: Summary statistics (Prices and trade policy measures 2008-2011)
  - Full sample: Trade policy utilization (TPU) ikt mean 0.045 sd 0.208 obs 114912; Price changes from 3yrs moving average k,t-1 mean 0.054 sd 0.211 obs 100968; Global trade policy -i,kt-1 (weighted) mean 0.080 sd 0.153 obs 114114.
  - Staple food sample: TPU ikt mean 0.128 sd 0.334 obs 21798; Price changes from 3yrs moving average k,t-1 mean 0.065 sd 0.227 obs 19404; Global trade policy -i,kt-1 (weighted) mean 0.166 sd 0.203 obs 21630.
  - Instruments and controls reported, e.g., log Rainfall top3 producers k,t-1: Full sample mean 9.383 sd 2.228 obs 73080; Staple sample mean 9.864 sd 2.070 obs 21798.
- Tables 4–7: Determinants of trade policy utilization (various samples and specifications)
  - Consistent positive and statistically significant association between contemporaneous price changes (Price changes from 3yrs moving average k,t-1) and trade policy utilization across Logit, LPM, 2SLS specifications.
  - Global trade policy -i,k,t-1 (weighted) shows large, positive, and statistically significant coefficients across specifications (e.g., Table 4 coefficients up to 0.5933***; Table 7 2SLS coefficients around 0.5965*** to 0.7132*** depending on sample).
  - Production Share i,k (2005) and log Trade i,k,t-1 also enter positively and significantly in many specifications.
  - For staple food products (Table 5), the coefficient on Price changes from 3yrs moving average k,t-1 is larger (e.g., 0.0637*** in Logit; LPM coefficients up to 0.1953***).
  - Large traders analysis (Table 6) indicates interaction effects: price changes and global trade policy weighted both have larger impacts for large exporters and large importers; interaction terms (e.g., Global trade policy weighted x Large exporter) show sizeable positive coefficients (0.3219***, 0.3285***).
  - Instrumental variables results (Table 7) indicate larger estimated impacts of price changes on trade policy utilization when using instruments (e.g., 2SLS Price changes from 3yrs moving average k,t-1 coefficients: 0.4642*** to 0.6043*** across samples).
- Table 8: Impact of trade policy utilization on international prices (2SLS, staple food)
  - Global trade policy k,t (weighted) coefficients:
    - Dependent variable Price changes from 3yrs moving average: 1.3093*** [0.184]
    - Price changes from 5yrs moving average: 0.4403*** [0.123]
    - Price changes from historical average (1980-2006): 2.1540*** [0.299]
    - Price changes from historical average (2000-2006): 1.2005*** [0.146]
  - Log Rainfall top3 k,t: small positive coefficients (e.g., 0.0168** [0.008]).
  - Energy prices changes t included but coefficients not consistently significant in these specifications.
  - Observations range 420–468; R-squared up to 0.808 in some specifications.
  - F-statistic first stage and p-values reported (e.g., P-value F statistic 0.0765 in one specification).

### Key analytical conclusions
- The theoretical model establishes that the equilibrium response dp = dt! is positive and bounded strictly below 1=(E+I) under heterogeneity, while the symmetric case E = N and I = M yields dp = dt! = 1=(E+I) and an infinite multiplier.
- There is a multiplier (general equilibrium amplification) whereby the total policy response to prices exceeds the partial response; the multiplier () satisfies:
  -  1 1(E+I) dp dt! ; and is strictly greater than 1 given dp = dt! 2(0;1=(E+I)).
- Empirical evidence indicates:
  - Countries respond to price increases by increasing trade policy utilization (TPU); responses are stronger for staple foods and for large traders.
  - Global trade policy activity (weighted) has a significant and sizable influence on individual country trade policy choices.
  - Trade policy utilization raises international staple food price changes (2SLS estimates show large, positive coefficients), implying policy actions are themselves a source of international price increases.

_Italic: Source: Excerpt from the supplied IMF PDF content unit._

### Appendix Table 2:

### Appendix Table 2: Determinants of trade policy utilization (lagged explanatory variables, large traders)

### Main regression results (Two lags x=2 and Three lags x=3)
- Columns: (1) All food products (x=2); (2) Staple products (x=2); (3) All food products (x=3); (4) Staple products (x=3); (5) All food products (x=2) [alt specification]; (6) Staple products (x=2) [alt specification]; (7) All food products (x=3) [alt specification]; (8) Staple products (x=3) [alt specification].

- Price changes from 3yrs moving average k,t-x
  - (1) 0.0185 [0.017]
  - (2) 0.1101*** [0.030]
  - (3) 0.0191 [0.015]
  - (4) 0.1082*** [0.028]
  - (5) 0.0065 [0.017]
  - (6) 0.1036*** [0.031]
  - (7) 0.0092 [0.015]
  - (8) 0.1060*** [0.029]

- Global trade policy -i,k,t-x (weighted)
  - (1) 0.6239*** [0.056]
  - (2) 0.5643*** [0.064]
  - (3) 0.5426*** [0.052]
  - (4) 0.4768*** [0.061]
  - (5) 0.5504*** [0.058]
  - (6) 0.4623*** [0.066]
  - (7) 0.4701*** [0.054]
  - (8) 0.3777*** [0.063]

### Interaction effects with large traders
- Large importer (main effect)
  - (1) -0.0144*** [0.004]
  - (2) -0.0234*** [0.005]
  - (3) -0.0140*** [0.004]
  - (4) -0.0235*** [0.005]

- Price changes from 3yrs moving average k,t-x x Large importer
  - (1)/(3) 0.0375*** [0.012]
  - (2)/(4) 0.0399*** [0.014]
  - (3)/(7) 0.0374*** [0.012]
  - (4)/(8) 0.0438*** [0.013]

- Global trade policy -i,k,t-x (weighted) x Large importer
  - (1)/(3) 0.1350*** [0.029]
  - (2)/(4) 0.0914*** [0.028]
  - (3)/(7) 0.1338*** [0.029]
  - (4)/(8) 0.0904*** [0.028]

- Large exporter (main effect)
  - (1) 0.0009 [0.003]
  - (2) 0.0150*** [0.005]
  - (3) 0.0025 [0.003]
  - (4) 0.0182*** [0.005]

- Price changes from 3yrs moving average k,t-x x Large exporter
  - (1)/(3) 0.0271*** [0.010]
  - (2)/(4) 0.0407*** [0.013]
  - (3)/(7) 0.0208* [0.011]
  - (4)/(8) 0.0304** [0.014]

- Global trade policy -i,k,t-x (weighted) x Large exporter
  - (1)/(3) 0.3915*** [0.025]
  - (2)/(4) 0.4063*** [0.024]
  - (3)/(7) 0.3862*** [0.026]
  - (4)/(8) 0.3958*** [0.025]

### Sample size and fit
- Observations
  - (1) 41360
  - (2) 18954
  - (3) 41360
  - (4) 18954
  - (5) 41360
  - (6) 18954
  - (7) 41360
  - (8) 18954
- R-squared
  - (1) 0.198
  - (2) 0.231
  - (3) 0.208
  - (4) 0.248
  - (5) 0.192
  - (6) 0.225
  - (7) 0.202
  - (8) 0.241

### Estimation notes
- Standard errors clustered at product-time level. *** p<0.01, ** p<0.05, * p<0.1.
- Other control variables included in the regression are GDP per capita, log Trade, Production shares and product, time (month) and year FE.

*Source: Appendix Table 2 from the provided content.*

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### Appendix Table 3: Determinants of trade policy utilization (first stage results)

### First-stage: Price changes from 3yrs moving average k,t-1 (instruments)
- log Rainfall top3 k,t-1
  - (1) 0.0873*** [0.001]
  - (2) 0.0873*** [0.001]
  - (3) 0.0874*** [0.003]
  - (4) 0.0874*** [0.003]
  - (5) 0.0864*** [0.002]
  - (6) 0.0865*** [0.002]

- Rainfall var top3 k,t-1
  - (1) 0.0336*** [0.002]
  - (2) 0.0336*** [0.002]
  - (3) 0.0370*** [0.003]
  - (4) 0.0370*** [0.003]
  - (5) 0.0326*** [0.005]
  - (6) 0.0326*** [0.005]

- F-statistic (relevant first-stage strength)
  - (1) 62.7
  - (2) 62.4
  - (3) 56.61
  - (4) 56.14
  - (5) 67.79
  - (6) 67.52

### First-stage: Global trade policy -i,k,t-1 (weighted) (instruments)
- Number of measures (hs2) i,-k,t-1
  - (1) 0.0017*** [0.000]
  - (2) 0.0017*** [0.000]
  - (3) 0.0018*** [0.000]
  - (4) 0.0018*** [0.000]
  - (5) 0.0016*** [0.000]
  - (6) 0.0016*** [0.000]

- Elections top3 traders k,t-1
  - (1) -0.1083*** [0.026]
  - (2) -0.1080*** [0.026]
  - (3) -0.0919*** [0.023]
  - (4) -0.0919*** [0.023]
  - (5) -0.1186*** [0.027]
  - (6) -0.1179*** [0.027]

- F-statistic (relevant first-stage strength reported)
  - (1) 10.38
  - (2) 10.32
  - (3) 10.91
  - (4) 10.83
  - (5) 10.45
  - (6) 10.2

### Sample size and estimation notes
- Observations
  - (1) 16976
  - (2) 16976
  - (3) 4606
  - (4) 4606
  - (5) 5308
  - (6) 5308
- Note: Standard errors clustered at product-time level. *** p<0.01, ** p<0.05, * p<0.1.
- Other control variables included in the regression are GDP per capita, log Trade, Production shares and product, time (month) and year FE. Columns (2), (4) and (6) also include country fixed effects.

*Source: Appendix Table 3 from the provided content.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14182.pdf_