## 1. Introduction — Overview and research questions

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---

### Research questions and conceptual contribution
- Core questions:
  - How much do countries benefit from access to the international market?
  - Are welfare effects of foreign market access larger in some sectors than others?
  - Do some countries benefit more from globalization because of comparative advantage?
  - How should trade and industrial policy respond to sectoral differences?
- Key conceptual definitions:
  - External firm market access (FMA): a single sector-level variable summarizing external demand for a given country-sector in a wide class of multi-sector small open economy models with sector-level gravity equations.
  - Welfare elasticity (δ_x,k): elasticity of welfare (real per capita income) with respect to sector-specific external firm market access; captures long-run benefits of export market access aggregating microeconomic mechanisms and initial-economy features.

### Advantages of welfare-elasticity approach
- General equilibrium elasticities can be estimated econometrically in a theory-consistent way.
- Provide sufficient-statistic formulas for first-order welfare impacts of foreign tariffs, domestic export taxes, and (under additional restrictions) domestic production subsidies as functions of welfare elasticities.
- Empirical δ_x,k estimates can discipline structural quantitative models.

---

### 2. Methodology and identification

### Empirical strategy — challenges and solutions
- Two primary challenges:
  1. High dimensionality (many traded sectors, few country growth observations):
     - Use k-means clustering on 7 sectoral characteristics to group 233 manufacturing industries into 4 clusters; agriculture and mining form two additional clusters (6 clusters total).
  2. Omitted variables and endogeneity in cross-country regressions:
     - Provide formal conditions for identification of δ_x,k by OLS conditional on initial observables and an orthogonality assumption for unobserved contemporaneous domestic shocks.
     - Leverage small-country-in-world-markets approximation and construct foreign shocks with leave-one-out gravity estimation to minimize direct domestic influence.
     - Use Post-Double-Selection (Belloni et al., 2014b, 2017) to select controls while maintaining consistency and uniformly valid inference.

### Estimating equation (log-linear approximation)
- Log-change in real income approximated by:
  - d ln y_{i,t} ≈ κ + Σ_k δ_{xk} · [λ_{xik,t} d ln FMA_{ik,t}] + ζ d ln a_{it} + η x_{i,t} + ε_{i,t}
  - Exogeneity requirement for causal OLS interpretation: E[ε | {λ_xk dln FMA_k}, dln a, x] = 0.

### Identification threats and mitigations
- Domestic policy effects on τ_{Hn,k}: mitigated by leave-one-out foreign-only estimation of FMA.
- Violation of small-country assumption (feedbacks): robustness by dropping large importer links (λ_in,k,t > 0.25) and dropping country-decade observations among top 100 world export shares (top-100 observations are 2.3% of 4,304; smallest of these top 100 world export shares is 7.7%).
- Spatial correlation of domestic shocks: mitigate by omitting neighbors when constructing FMA, controlling for neighbors’ TFP growth, and including unweighted dln FMA as controls.

---

### 3. Data, clustering, and construction of external shocks

### Data inputs and sample
- Required inputs:
  - (i) real income per capita: Penn World Tables 9.0 (real GDP at constant national prices / population); drop countries with population < 2 million; per capita income growth computed at 10-year intervals (max 5 10-year growth rates per country).
  - (ii) sectoral bilateral trade flows and trade barriers: UN COMTRADE at 4-digit SITC Rev 2, converted to 1997 NAICS; 784 SITC items matched to 268 NAICS sectors (233 manufacturing, 26 agricultural, 9 mining).
  - (iii) sectoral characteristics for clustering: 7 features measured using U.S. data and converted to 1997 NAICS.
- Final sample:
  - 127 countries, 268 sectors, 5 decades from 1965 to 2015, total of 548 10-year GDP growth rate observations.

### Clustering of manufacturing sectors (k-means)
- Features used (7): investment sales shares; intermediates using shares; intermediates sales shares; 4-firm concentration ratios; skilled worker shares; physical capital intensities; contract intensity.
- K-means with k-means++ initialization applied to M = 233 manufacturing sectors, standardized characteristics.
- Manufacturing grouped into 4 clusters; agriculture = cluster 5; mining = cluster 6; total clusters G = 6.

### Manufacturing cluster summary statistics (preserve numeric values exactly)
- Cluster labels: Cluster 1 = Raw Materials Processing (RAW); Cluster 2 = Complex Intermediates (INT); Cluster 3 = Capital Goods (CAP); Cluster 4 = Consumer Goods (CONS).
- Investment Share:
  - Cluster 1: 0.00
  - Cluster 2: 0.05
  - Cluster 3: 0.52
  - Cluster 4: 0.04
  - Mean: 0.13
  - Std. Dev.: 0.22
- Intermediates, Using:
  - Cluster 1: 0.78
  - Cluster 2: 0.58
  - Cluster 3: 0.65
  - Cluster 4: 0.66
  - Mean: 0.66
  - Std. Dev.: 0.16
- Intermediates, Sales:
  - Cluster 1: 0.84
  - Cluster 2: 0.70
  - Cluster 3: 0.27
  - Cluster 4: 0.28
  - Mean: 0.57
  - Std. Dev.: 0.31
- Concentration Ratio:
  - Cluster 1: 0.47
  - Cluster 2: 0.27
  - Cluster 3: 0.38
  - Cluster 4: 0.56
  - Mean: 0.40
  - Std. Dev.: 0.21
- Skill Intensity:
  - Cluster 1: 0.32
  - Cluster 2: 0.28
  - Cluster 3: 0.35
  - Cluster 4: 0.36
  - Mean: 0.32
  - Std. Dev.: 0.13
- Capital Intensity:
  - Cluster 1: 0.68
  - Cluster 2: 0.55
  - Cluster 3: 0.54
  - Cluster 4: 0.70
  - Mean: 0.61
  - Std. Dev.: 0.10
- Contract Intensity:
  - Cluster 1: 0.26
  - Cluster 2: 0.56
  - Cluster 3: 0.73
  - Cluster 4: 0.52
  - Mean: 0.51
  - Std. Dev.: 0.22
- Number of industries:
  - Cluster 1: 60
  - Cluster 2: 34
  - Cluster 3: 47
  - Cluster 4: 42
- Trade share:
  - Cluster 1: 0.33
  - Cluster 2: 0.26
  - Cluster 3: 0.23
  - Cluster 4: 0.11

### Estimation of FMA_{i k,t} (external firm market access) — gravity and leave-one-out
- Gravity estimation:
  - Sector-specific PPML estimation of λ_ink,t = κ_x_{i k,t} · κ_m_{n k,t} · Distance^{ζ_{k t}}_{i n} · exp(ξ_{k t} · Contig_{i n}) · ε_{i n k,t} separately for 268 sectors and each of 5 decades (1965–2015).
- Constructing FMA_{i k,t}:
  - FMA_{i k,t} = Σ_{n≠i} E_{n k,t}(i) · κ_m_{n k,t} · Distance_{i n}^{ζ_{k t}} · exp(ξ_{k t}·Contig_{i n}), where E_{n k,t}(i) excludes country i.
- Two methodological wrinkles:
  1. Leave-one-out: estimate gravity N times per sector-time, each time omitting country i, so FMA uses only foreign data.
  2. Renormalize fixed effects by restricting sum of logged importer effects to zero to avoid numéraire effects.

---

### 4. Main empirical results

### Baseline estimation procedure (5 steps)
1. Leave-one-out gravity with PPML to recover foreign component of FMA and CMA for 268 sectors by country and decade.
2. K-means clustering of manufacturing sectors into 4 clusters; agriculture and mining separate.
3. Construct cluster-level d ln FMA_{i g,t} and d ln CMA_{i g,t}.
4. LASSO of d ln y_{i,t} and d ln FMA_{i g,t} on d ln a_{i t} and x_{i,t} to select controls (Post-Double-Selection).
5. OLS regression of d ln y_{i,t} on d ln FMA_{i g,t} and selected controls to estimate δ_{x g}.

### Baseline cluster-specific coefficients (numerical estimates preserved)
- Cluster order: RAW, INT, CAP, CONS, AG, MIN.
- OLS estimates (left panel, Figure 1):
  - Coefficients: 0.20, 1.27, 2.08, −0.47, 0.08, 0.07
  - F(5,126)=5.05
  - p=0.00
- Post-Double-Selection (LASSO) estimates (right panel, Figure 1):
  - Coefficients: 0.17, 1.32, 2.97, −0.52, 0.11, 0.05
  - F(5,126)=3.81
  - p=0.00
- Inference and interpretation:
  - Strong heterogeneity across clusters; equality rejected at 1% significance.
  - Complex intermediates (INT) and capital goods (CAP) have positive and substantially larger estimated real income effects.
  - Other clusters (RAW, CONS, AG, MIN): estimated elasticities close to zero (mostly positive) and relatively precisely estimated.
- LASSO details:
  - Full set of potential controls: 1,106 variables.
  - Post-Double-Selection selected 6 control variables in baseline.
  - Tuning: K-fold cross validation minimizing CV(λ) (baseline choice).

### Robustness checks (highlights and numeric thresholds)
- Small-country assumption:
  - Dropping importer n from summation when λ_in,k,t > 0.25 yields broadly similar results.
  - Dropping country-decade instances among top 100 world export shares (2.3% of 4,304 observations; smallest of these top 100 world export shares is 7.7%) yields similar results.
- Spatial correlation:
  - Omit neighbors (contiguous plus 5 closest) when constructing d ln FMA; control for neighbors’ average TFP growth; control for unweighted d ln FMA — all show very little change relative to baseline.
- Sample splits:
  - Developed vs. developing: complex intermediates positive and precise in both groups; capital goods coefficient larger for developing group, slightly smaller for developed group; standard errors differ across subsamples.
  - Five-cluster manufacturing grouping isolates a skill-intensive cluster with δ_x ≈ 0; other clusters’ δ_x unaffected.

### Foreign supply (CMA) findings
- Foreign supply shocks (CMA) exhibit much larger magnitudes and much larger standard errors than foreign demand shocks (FMA).
- Statistical implication: limited power to estimate δ_m,k; main baseline focuses on FMA while controlling for CMA where possible.
- Main FMA findings robust when treating d ln CMA as protected controls.

---

### 5. Quantitative implications and policy applications

### Application 1 — Comparative advantage and “neutral globalization”
- Aggregate elasticity to uniform log-change in FMA:
  - d ln y_{i,t} / d ln FMA = Σ_k b δ_x,k · λ_{x i k,t}  (equation (6.1)).
- Calibration and outcomes (using double-LASSO δ_x and 2015 trade shares):
  - Elasticity range: from essentially zero (some Sub-Saharan Africa countries) to around 0.5 for some Central European and East Asian countries.
  - Specific examples with elasticity around 0.5: Hungary, Slovakia, Malaysia, Taiwan.
  - Elasticities positively correlated with log PPP-adjusted income per capita but heterogeneity driven by export specialization and openness.
  - Key insight: countries specializing in complex intermediates and capital goods benefit much more from declining trade costs than agricultural and commodity producers.

### Application 2 — Trade and industrial policy using sufficient statistics
- Representative-country calibration inputs:
  - Export revenue shares λ_x,k: simple average across sample countries in 2015.
  - Y/V (ratio gross output to value added): set to 2.
  - Sectoral expenditure shares e_k and domestic sourcing shares θ_d,k: from WIOD, simple averages.
  - Trade elasticities: σ_k = 6 ∀ k (implies long-run trade elasticity of 5).
- First-order welfare impacts (computed via (2.9) and (A.17)):
  - Export subsidies:
    - 10% export subsidy produces:
      - Welfare gain of about 1.3% for complex intermediates.
      - Welfare gain of nearly 2% for capital goods.
    - Export subsidies in RAW, CONS, AG, MIN: welfare losses (i.e., taxing exports welfare-improving).
  - Production subsidies (Cobb-Douglas assumptions, equation A.17):
    - Similar qualitative conclusions; magnitudes larger due to larger subsidy base.
- Interpretation:
  - Export subsidy is welfare-improving only if demand-driven GE gains exceed subsidy fiscal costs and negative terms-of-trade effects (condition in (A.16)).
  - Gains from export subsidies increase with σ_k; positive gains remain for σ > 2.

### Application 3 — Informing structural model choice (macro-to-micro)
- Fit a small open economy model with intermediate input linkages, endogenous capital accumulation, and sector-level scale effects to match δ_x,k estimates.
- Best-fit parsimony (common parameters across sectors):
  - Best-fit parameters by MAE minimization:
    - σ = 3.2
    - γ = 0.29
  - Model-data fit:
    - Correlation between model-implied and data δ_x,k: 0.94
    - Average model δ_x across clusters: 0.73
    - Average data δ_x across clusters: 0.68
    - Baseline MAE referenced: 0.32
- Mechanisms:
  - Input-output linkages and positive scale effects (γ>0) are crucial; higher-order propagation through production networks drives heterogeneity.
  - Non-tradable large service sector amplifies GDP impacts for shocks in upstream/tradeable capital and complex intermediate sectors.
- Counterfactual experiments:
  - No intermediates: average δ_x falls by ~60%; cross-cluster variation largely disappears; capital cluster coefficient falls substantially.
  - No capital accumulation: average δ_x about 30% below baseline.
  - Constant-returns (γ = 0) models cannot match sectoral heterogeneity; matching average δ_x by lowering σ produces large errors in cluster-level fit.

---

### 6. Theoretical framework — key formulas and policy sufficient statistics

### External firm market access (FMA) and foreign demand
- Aggregate foreign revenues (export revenues) summarized as:
  - Σ_{n≠H} p_Hn,k q_Hn,k = c_H,k^{1−σ_k} · Σ_{n≠H} τ_Hn,k^{1−σ_k} · E_n,k / P_n,k^{1−σ_k} ≡ c_H,k^{1−σ_k} · FMA_H,k  (equation (2.4))
- First-order welfare log-change approximation:
  - d ln y ≈ Σ_k λ_x,k · [ δ_x,k · d ln FMA_k ]  (equation (2.7))
  - δ_x,k captures GE response of real income to exogenous foreign demand changes by industry.

### Policy sufficient-statistic formulas (first-order)
- Foreign tariff t_f,k effect:
  - d ln y / d ln(1−t_f,k) = λ_x,k · σ_k · δ_x,k  (equation (2.8))
- Home export tax/subsidy t_x,k effect (government balances budget with lump-sum taxation; Y aggregate gross output, V aggregate final expenditure, e_k sectoral share of final expenditure, θ_d,k domestic sourcing share):
  - d ln y / d ln(1−t_x,k) = λ_x,k · [ δ_x,k σ_k − Y/V − Σ_{k'} δ_x,k' e_k' θ_d,k' ]  (equation (2.9))
  - Interpretation of terms:
    - δ_x,k σ_k: positive GE demand effect.
    - −λ_x,k Y/V: direct fiscal cost of subsidy funded by lump-sum taxation.
    - −λ_x,k Σ_{k'} δ_x,k' e_k' θ_d,k': negative terms-of-trade/fiscal distortion channel.
- Production subsidies: sufficient-statistic formula under Cobb-Douglas assumptions derived in (A.17); used in representative-country calibration.

---

### 7. Key numeric summaries and robustness thresholds (compact)

- Sample: 127 countries, 268 sectors, 5 decades (1965–2015), 548 10-year GDP growth observations.
- Manufacturing clustering: 233 manufacturing industries grouped into 4 clusters; agriculture = cluster 5; mining = cluster 6.
- Baseline Post-Double-Selection coefficients (clusters RAW, INT, CAP, CONS, AG, MIN):
  - 0.17, 1.32, 2.97, −0.52, 0.11, 0.05
  - F(5,126)=3.81; p=0.00
- OLS baseline coefficients (for comparison):
  - 0.20, 1.27, 2.08, −0.47, 0.08, 0.07
  - F(5,126)=5.05; p=0.00
- Representative-country policy calibration:
  - Y/V = 2
  - σ_k = 6 ∀ k (implies long-run trade elasticity = 5)
  - 10% export subsidy yields welfare gain of about 1.3% for complex intermediates and nearly 2% for capital goods.
- Structural model best-fit parameters:
  - σ = 3.2
  - γ = 0.29
  - Correlation model vs data δ_x,k = 0.94
  - Average model δ_x = 0.73; average data δ_x = 0.68
  - Baseline MAE referenced: 0.32
- Robustness thresholds:
  - Drop importer when λ_in,k,t > 0.25 to address large-importer bias.
  - Top-100 world export-share observations constitute 2.3% of 4,304 country-cluster-decade observations; smallest of these top-100 world export shares is 7.7%.

---

*Source: wpiea2024051-print-pdf — IMF Working Paper (content unit provided).*

### 1. Introduction

### 1. Introduction

### Overview and research questions
- Core questions: How much do countries benefit from access to the international market? Are welfare effects of foreign market access larger in some sectors than others? Do some countries benefit more from globalization because of comparative advantage? How should trade and industrial policy respond to sectoral differences?
- This paper departs from the standard calibration-based “micro-to-macro” tradition (e.g. Eaton and Kortum (2002)) and instead directly estimates general equilibrium impacts of foreign shocks at the sector level, balancing quantitative-model clarity with model-robust empirical methods.

### Key conceptual contribution
- Define a single sector-level variable, external firm market access, that summarizes all relevant information about external demand for a given country and sector in a large class of multi-sector small open economy models with sector-level gravity equations.
- Define a welfare elasticity: the elasticity of welfare (real per capita income) with respect to sector-specific external firm market access. This elasticity captures long-run benefits of export market access in a sector, aggregating microeconomic mechanisms and features of the initial economy.

### Advantages of expressing impacts as welfare elasticities
- These general equilibrium elasticities can be estimated econometrically in a theory-consistent way.
- They are directly connected to welfare effects of trade and industrial policies: sufficient statistics are derived for first-order welfare impacts of foreign tariffs, domestic export taxes, and (under additional restrictions) domestic production subsidies as functions of the welfare elasticities.
- Empirical estimates of welfare elasticities can be used to discriminate between different quantitative models, providing a way to discipline general equilibrium responses of structural models.

---

### Methodology and identification
- To estimate welfare elasticities econometrically, the paper addresses two primary challenges:
  1. High dimensionality: hundreds of traded sectors but a small sample of real GDP per capita observations.
     - Use a machine learning technique to group sectors into a small number of clusters based on characteristics (position in production network, factor intensities).
     - Specifically, apply the k-means clustering algorithm (MacQueen et al., 1967) with 7 sectoral characteristics to group 233 manufacturing industries into 4 clusters: i) processing of raw materials, ii) complex intermediate inputs, iii) capital goods, and iv) consumer goods. Agriculture and mining sectors are grouped into their own clusters, yielding 6 clusters total; elasticities are estimated for each of the 6 clusters.
  2. Omitted variables and endogeneity in cross-country regressions:
     - Provide formal conditions under which welfare elasticities are identified by an OLS regression that fully conditions on initial observables, exploiting invertibility properties of gravity models and an orthogonality assumption on unobserved contemporaneous domestic shocks.
     - Leverage the small-country-in-world-markets approximation and construct foreign shocks to minimize direct effects of domestic shocks on foreign variables.
     - Use the Post-Double-Selection method of Belloni et al. (2014b, 2017) to select a lower-dimensional set of “important” controls while maintaining consistency and uniformly valid inference.

- Focus of empirical estimation: foreign demand shocks. The paper notes that foreign supply shocks exhibit much less variation across countries and time in measured series and produce noisy estimated impacts; hence the empirical focus is on effects of foreign demand shocks while controlling for foreign supply shocks. (See Sections 3 and 4 and Appendix B.5 in the source for detail.)

---

### Main empirical results
- Substantial sectoral heterogeneity in the impact of external firm market access on real income.
- Baseline point estimates:
  - A 1% increase in external firm market access causes a long run increase in real income of about 1.3%×export share in complex intermediates.
  - A 1% increase in external firm market access causes a long run increase in real income of about 3%×export share in capital goods.
- All other sectors have estimated impacts that are close to zero, economically and statistically.
- Interpretation: despite identical initial partial-equilibrium increases in export sales by construction, increases in export market access for complex intermediates or capital goods are much more valuable in the long run than comparable increases in other tradable sectors.

---

### Applications and policy implications
- Application 1 — Comparative advantage and “neutral globalization”:
  - Compute distribution of welfare impacts for a uniform increase in export market access in all countries and sectors.
  - Countries specializing in agricultural commodities, mining, and simpler manufactured products experience little long-run welfare benefit from a neutral globalization.
  - Open middle-income economies specializing in complex intermediate and capital goods (examples in text: Hungary, South Korea, Taiwan and Malaysia) experience large increases in welfare.
  - Conclusion: “what you export matters.”

- Application 2 — Trade and industrial policy using sufficient statistics:
  - Calibrate an economy with a global average initial state using the World Input-Output Database (WIOD); calibrate a standard trade elasticity; apply sufficient-statistic formulas for first-order gains from export taxes/subsidies and production taxes/subsidies.
  - Findings:
    - The average country benefits from export subsidies to complex intermediates and capital goods relative to laissez-faire.
    - Export subsidies in other sectors are not welfare-improving; instead, taxes are.
    - Effects of sector-specific production subsidies are similar, with even larger gains (subject to a caveat described below).
  - Caveats:
    - Export subsidies are generally not first-best policies and are controversial; results show a welfare rationale in some sectors but do not resolve broader normative or political-economy concerns.
    - With production subsidies, the analysis restricts attention to economies with Cobb-Douglas utility and production functions.

- Application 3 — Implications for quantitative trade models (macro-to-micro approach):
  - Use estimated welfare elasticities to infer what model features and parameter values can match empirically observed general equilibrium responses.
  - Fit a small open economy model with intermediate input linkages, endogenous capital accumulation, and industry-level scale effects external to the firm, calibrated to global average initial state using WIOD.
  - Best-fit parsimony: two structural parameters — the trade and scale elasticities — can match the welfare elasticity estimates well.
    - Best-fit parameters: Armington elasticity of 3.2; scale elasticity of 0.29.
    - The scale elasticity 0.29 closely matches the 0.30 mean sectoral scale elasticity estimated by Lashkaripour and Lugovskyy (2023).
  - Main modeling insight: the combination of input-output linkages and scale effects is crucial to replicate heterogeneous income responses to sector-specific foreign shocks. Models omitting one or both features perform much worse at matching the data. Heterogeneity in estimated coefficients is generated by differing internal propagation of foreign demand shocks within the home economy rather than by differing trade or scale elasticities across sectors.

---

### Broader contribution and positioning in the literature
- Methodological novelty: directly estimate general equilibrium responses to foreign demand shocks and use them as sufficient statistics for policy analysis, instead of relying solely on calibrated structural models.
- Empirical contributions relative to existing literature:
  - Considers multiple dimensions of trade patterns simultaneously and lets the data determine which export characteristics matter.
  - Focuses on exogenous foreign demand shocks rather than endogenous specialization patterns.
  - Uses theory to link empirical welfare-elasticity estimates to policy-relevant objects.
- Relation to strands of prior work:
  - Connects to literature estimating overall openness effects on real income and to work on export patterns and real income.
  - Complements quantitative trade model literature by providing empirically estimated general equilibrium elasticities that can discipline model responses.
  - Differs from partial-equilibrium empirical studies of policy episodes by leveraging cross-country and time variation in foreign demand shocks and offering sufficient-statistic policy formulas.

---

### Structure of the paper
- Section 2: Model and relationship to quantitative trade literature.
- Section 3: Identification and estimation.
- Section 4: Data description.
- Section 5: Results.
- Section 6: Quantitative implications.
- Appendices: Derivations, data construction/manipulation, and additional empirical results.

*Source: wpiea2024051-print-pdf - 1. Introduction*

### 2. Theoretical Framework

### 2. Theoretical Framework

### Model environment and technology
- Small open economy Home (H) in a world with N other countries indexed by i and n, K sectors indexed by k, and J factors indexed by j.
- Home is “small” in the sense that Home variables do not affect foreign aggregates, but Home may be large in its domestic market and face downward sloping demand in international markets.
- Each sector produces a homogeneous good. Primary factors L_H,j are in fixed supply and mobile across sectors. Input and output markets are competitive.
- Firms perceive constant returns to scale in their own inputs, with possible external economies of scale within and across sectors.
- Unit cost function for sector k in Home:
  - c_H,k = c_H,k(w_H, P_H, L_H; T_H,k) (equation (2.1))
  - where w_H and P_H are vectors of primary factor prices and intermediate goods prices, L_H is the matrix of primary factor allocations to sectors, and T_H,k is an exogenous productivity shifter.
- Unit cost function assumed continuously differentiable in all arguments.
- Trade is subject to iceberg bilateral trade barriers τ_i n,k.

### Demand structure and foreign demand for exports
- Sector k composite good in country n is an Armington aggregate:
  - Q_n,k = [ z_n,k · q_nn,k^{(σ_k−1)/σ_k} + Σ_{i≠n} q_in,k^{(σ_k−1)/σ_k} ]^{σ_k/(σ_k−1)} (equation (2.2))
  - q_in,k is quantity of sector k exported from i to n; z_n,k is an exogenous demand shifter controlling home bias.
- Foreign demand for Home’s exports in sector k takes the form:
  - p_Hn,k · q_Hn,k = (c_H,k · τ_Hn,k)^{1−σ_k} · E_n,k / P_n,k^{1−σ_k} (equation (2.3))
  - where p_Hn,k = c_H,k · τ_Hn,k is the price in destination n, and E_n,k and P_n,k are expenditure and CES price index in country n.

### External Firm Market Access (FMA)
- Total foreign revenues (summing export revenues across foreign destinations) summarized by:
  - Σ_{n≠H} p_Hn,k q_Hn,k = c_H,k^{1−σ_k} · Σ_{n≠H} τ_Hn,k^{1−σ_k} · E_n,k / P_n,k^{1−σ_k} ≡ c_H,k^{1−σ_k} · FMA_H,k (equation (2.4))
- Key features of FMA_H,k:
  - FMA_H,k is an exogenous sector-k demand shifter from Home’s perspective because it depends only on foreign variables when Home is small.
  - An x% change in FMA_H,k implies an x% change in the quantity that foreigners demand when holding the price fixed.
  - Changes in foreign demand affect Home equilibrium only through FMA_H,k; FMA_H,k has no bilateral dimension and varies at exporter-sector level.
  - FMA_H,k can be estimated from trade data using conventional techniques (details provided in Section 4).

### External Consumer Market Access (CMA)
- Sum of Home imports across source countries:
  - Σ_{n≠H} p_nH,k · q_nH,k = E_H,k / P_H,k^{1−σ_k} · Σ_{n≠H} (c_n,k · τ_nH,k)^{1−σ_k} ≡ E_H,k / P_H,k^{1−σ_k} · CMA_H,k (equation (2.5))
- From Home’s perspective, CMA_H,k is an exogenous supply shifter:
  - An x% change in CMA_H,k causes an x% change in Home’s expenditure on foreign goods, holding total sectoral expenditure fixed.
  - CMA_H,k summarizes relevant information about foreign supply (import prices c_n,k · τ_nH,k).
- Practical note: limited statistical power due to lower variability of the foreign component of CMA_H,k in trade data precludes reliable estimation of foreign supply effects in the baseline analysis. CMA_H,k will serve as control elements during estimation; welfare elasticities for CMA_H,k are discussed in Appendix B.5.

### Competitive equilibrium characterization
- Competitive equilibrium: goods and factor prices and allocations such that firms and consumers optimize, markets clear, and trade balances.
- Equilibrium determined by cost functions c_H,k(·), utility U(·), substitution elasticities σ_k, and exogenous variables (productivity and demand shifters, FMA and CMA, and primary factor supplies).
- The approach requires a locally unique and smooth mapping from exogenous variables to equilibrium outcomes; general equilibrium existence/uniqueness results are not pursued here.

### First-order welfare approximation and decomposition
- Using homothetic preferences and trade balance, Home’s welfare (real income) is:
  - y = Π_{k∈K} μ_k · c_k^{1−σ_k} · [ z_k · E_k / P_k^{1−σ_k} + FMA_k ]^{μ_k/(1−σ_k)}  (equation (2.6))
  - Welfare corresponds to real income of primary factors: nominal income divided by aggregate consumption price index P. Nominal primary factor income in sector k equals value of sectoral gross output times value-added share μ_k.
- Two channels through which FMA_k affects welfare:
  - Direct: changes in foreign sales when FMA_k changes.
  - Indirect: effects on domestic prices and quantities via production and consumption adjustments.
- First-order log-change relationship for total effect of log foreign demand changes on log welfare:
  - d ln y ≈ Σ_k λ_x,k · [ δ_x,k · d ln FMA_k ]  (equation (2.7))
  - where λ_x,k is the initial share of total sales accounted for by exports in sector k.
- Interpretation of δ_x,k:
  - δ_x,k are elasticities capturing first-order general equilibrium response of real income to exogenous changes in foreign demand by industry.
  - δ_x,k depend on structural parameters and initial state (trade and scale elasticities, input-output position, final use shares).
  - δ_x,k capture welfare impacts from terms-of-trade changes and resource reallocation across sectors (first-order impacts in distorted economies).
  - Appendix A.3 and Appendix A.4 provide further discussion and analytical solutions in richer environments; Section 6 presents a quantitative environment with scale economies, intermediates, and endogenous capital leading to an analytical δ_x,k formula.

### Policy implications and sufficient-statistic formulas
- δ_x,k relate to welfare effects of trade and industrial policies because they inform consequences of changing the size of sector k. Policies differ from δ_x,k effects due to fiscal incidence and government revenue/expenditure implications.
- Foreign tariff tf_k (on value of Home exports): small change in (1−t_f,k) for all trading partners yields welfare effect:
  - d ln y / d ln(1−t_f,k) = λ_x,k · σ_k · δ_x,k  (equation (2.8))
  - The effect of foreign tariffs is identical to foreign demand shocks, with the foreign demand elasticity translating tariff changes into demand shocks.
- Home export tax/subsidy tx_k (firm revenue per unit to foreigners ˜p_k = (1−t_x,k) p_f,k, evaluated at initially zero-tax equilibrium): with government using lump-sum taxation to balance its budget, let Y be aggregate gross output, V aggregate final expenditure, e_k sector k’s share of final expenditure, and θ_d,k the share of Home’s expenditure on k sourced domestically. Welfare effect of a small export subsidy:
  - d ln y / d ln(1−t_x,k) = λ_x,k · [ δ_x,k σ_k − Y/V − Σ_{k'} δ_x,k' e_k' θ_d,k' ]  (equation (2.9))
  - First term: positive GE effect of the demand shock (identical to foreign tariff effect).
  - Second term: direct cost of taxes needed to fund the subsidy, −λ_x,k Y/V.
  - Third term: negative terms-of-trade effect of lump-sum taxation that shrinks domestic market and induces more foreign sales; stronger in sectors with larger θ_d,k.
  - An export subsidy is welfare-improving only if positive demand effects exceed subsidy cost and negative TOT effects.
- Implementation: formulas (2.8) and (2.9) can be applied with estimates of σ_k and δ_x,k plus trade, production, and consumption shares from data.
- Caveat: Home import tariffs or production subsidies directly affect consumer and producer prices in ways not captured by δ_x,k alone; assessing those requires knowledge of sectoral elasticities of substitution in consumption and production.
- Appendix A derives a sufficient-statistic formula for welfare effects of production subsidies under Cobb-Douglas production and upper-tier utility (equation A.17). Section 6 implements these formulas with estimated δ_x,k.

### Conceptual and methodological positioning
- Contrast with fully structural approaches:
  - Standard approach: specify functional forms for c_H,k and U(·), estimate structural parameters via partial-equilibrium relationships, then compute GE responses. Examples cited in literature.
  - Alternative: recover structural parameters by matching simulated GE responses to data moments.
  - Both fully structural approaches impose a complete model on the data.
- This paper’s approach: econometrically estimate GE responses δ_x,k (reduced-form elasticities) rather than treating them as deep structural parameters.
  - Advantages: robustness to model uncertainty within the wide class of trade models encompassed by the framework; estimates directly relevant to foreign demand–welfare relationship.
  - Costs: less efficiency than correctly specified structural estimation; less explicit microfoundations; first-order (local) rather than full nonlinear counterfactuals for large shocks.
  - Uses: estimates can serve as moments for structural models or for out-of-sample validation.
- Isomorphisms and extensions:
  - Competitive Armington environment chosen for clarity; crucial assumptions are gravity in trade flows, homothetic upper-tier preferences, and unique smooth equilibrium mapping.
  - Models with alternative microfoundations for gravity (Eaton and Kortum (2002), Krugman (1980), Melitz (2003) with Pareto productivity) are isomorphic in first-order approximation (equation (2.7)) and interpretation of δ_x,k.
  - Equation (2.7) is also valid for small shocks in the steady state of dynamic economies with reproducible factors; Section 6 provides an example.

*Source: wpiea2024051-print-pdf - 2. Theoretical Framework*

### 3.1  Identification

### 3.1  Identification

### Identification strategy and equilibrium mapping
- Data view: collection of small open economies indexed by i observed over steady states indexed by t; observables include real income y_{i,t} and equilibrium outcomes {x_{ik,t}}.
- Foreign demand and supply shifters (FMA_{ik,t} and CMA_{ik,t}) are treated as observable after consistent estimation from trade data (see Section 4).
- Log change in real income between two steady states is written as a function of:
  - trade-share-weighted log changes in FMA_k,
  - other exogenous changes {dln a_k},
  - initial fundamentals {Z_k} (equation (3.1)).
- Assumption: equilibrium mapping G({Z_k}) → ({x_k}) is locally smoothly invertible (up to normalization), so observables reveal relevant aspects of the initial state; this justifies use of “exact hat algebra”.
- Using smooth invertibility, the log change in real income can be rewritten in terms of {λ_xk dln FMA_k}, {dln a_k}, and {x_k} (equation (3.2)).
- Domestic shocks ({dln T_k}, {dln z_k}, {dln L}) are decomposed into conditional expectations on the initial state and residuals with E[ε_k | {x_k}] = 0, allowing observables {ã_k} to be defined and incorporated (equation (3.3)).
- Taylor expansion leads to the log-linear estimating equation (3.4):
  - dln y_{i,t} ≈ κ + Σ_k δ_{xk} · [λ_{xik,t} dln FMA_{ik,t}] + ζ dln a_{it} + η x_{i,t} + ε_{i,t}
  - κ reflects the initial point of approximation; ε_{i,t} combines first-order domestic shock effects and approximation error.
- Exogeneity requirement for causal interpretation of OLS estimates \hat{δ}_{xk}:
  - E[ε | {λ_xk dln FMA_k}, dln a, x] = 0 (equation (3.5)).
  - Given E[ε | x] = 0 by construction, (3.5) states that adding foreign demand shocks does not predict the component of unobserved domestic innovations orthogonal to the initial state.
- Two sources of identifying variation:
  - Comparing growth of countries with similar initial export baskets but different foreign shocks (geographic position differences).
  - Comparing initially dissimilar countries that experience similar foreign shocks.

### Threats to identification
- Error term in (3.4) includes domestic productivity growth {dln T_k}, factor supply growth {dln L}, and changes in domestic tastes {dln z_k} orthogonal to initial observables.
- Three principal ways assumption (3.5) could be violated:
  1. Domestic policies affecting dln FMA:
     - dln FMA in (2.4) includes iceberg trade costs τ_{Hn,k} which may be influenced by domestic policymakers (e.g. export taxes).
     - Mitigation: estimate foreign shocks with a leave-one-out strategy using only foreign data so estimated dln FMA reflect components determined by foreign variables and exogenous geography.
  2. Violation of the small country assumption / international general equilibrium feedbacks:
     - A positive domestic aggregate productivity shock in a large Home economy lowers the price of its goods internationally and induces trading partners to reallocate imports, potentially lowering measured foreign demand shocks for Home (negative structural correlation between regressors and error term, biasing coefficients toward zero).
     - Quantitative relevance limited to country-sector combinations with substantial international market share.
     - Robustness checks (Section 5): drop trade partners for whom Home is a large source of imports; drop countries with large world export shares in industry clusters.
  3. Spatial correlation of domestic shocks:
     - Domestic shocks correlated across neighbors can induce a positive statistical association between measured foreign demand shocks (which depend on neighboring countries’ shocks) and Home’s unobserved domestic shocks (e.g., a geographic cluster of high-growth economies with high import demand).
     - Mitigations and checks:
       - Drop neighboring countries from the calculation of dln FMA.
       - Control directly for neighboring countries’ TFP growth in estimation.
       - Include the unweighted foreign demand shocks dln FMA as additional controls; this removes the first source of identifying variation (similar economies, different foreign shocks) and relies on the second (dissimilar countries, same foreign shocks), which is robust to spatial-correlation concerns.
- Note: reliance on first-order approximation requires countries to be relatively similar and shocks relatively small; heterogeneity in δ_{xk} across developed and developing countries is explored in Appendix C.

### Estimation challenges and solutions
- Estimation of equation (3.4) by OLS is consistent under smooth invertibility and exogeneity (3.5), but practical issues arise due to scarcity of medium- or long-run country growth rates relative to the number of industries:
  - Two related issues: i) large number of parameters {δ_{xk}}, ii) large number of controls.
- Reducing parameter dimensionality:
  - Group industries into G clusters and estimate a single elasticity per cluster (equation (3.6)):
    - dln y_{i,t} ≈ κ + Σ_{g∈G} δ_{xg} · [λ_{xig,t} dln FMA_{ig,t}] + ζ dln a_{it} + η x_{i,t} + ε_{i,t}
    - where λ_{xig,t} dln FMA_{ig,t} ≡ Σ_{k∈g} λ_{xik,t} dln FMA_{ik,t} (equation (3.7)).
  - Cluster-level elasticities δ_{xg} are weighted averages of industry-level elasticities; clustering reduces intra-cluster heterogeneity and improves estimation efficiency.
  - Clusters are constructed using machine learning to group industries with similar characteristics relevant for δ_{xk} (position in production network, factor intensities, contract intensity, etc.); Section 4 describes clustering in detail.
- Handling many controls:
  - Use the Post-Double-Selection estimator (Belloni et al., 2014b, 2017).
    - Select important controls by regressing each dependent and independent variable on the full set of potential controls using an estimator that sets some coefficients to zero (e.g. LASSO); take the union of selected controls and run OLS including them.
    - Belloni et al. show consistency and asymptotic normality under an approximate sparsity condition (true control vector admits an approximately sparse representation).
  - Implementation details in Section 5 and Appendix B.4.

### Data, clustering and foreign shock estimation (summary of data needs)
- Empirical inputs required:
  - (i) real income per capita,
  - (ii) sectoral bilateral trade flows and trade barriers,
  - (iii) sectoral characteristics.
- Income per capita: Penn World Tables 9.0, computed as real GDP at constant national prices divided by population.
  - Countries with population less than 2 million are dropped.
  - Per capita income growth computed at 10-year intervals for a maximum of 5 10-year growth rates per country (some missing values).
- Bilateral trade flow data: UN COMTRADE at 4-digit SITC Rev 2 level, converted to 1997 NAICS classification; 784 4-digit SITC items matched to 268 NAICS sectors (233 manufacturing, 26 agricultural, 9 mining).
- Geographic variables from CEPII.
- Final sample: 127 countries, 268 sectors, 5 decades from 1965 to 2015, total of 548 10-year GDP growth rate observations.
- Sectoral characteristics (used for clustering): 7 features measured using U.S. data (converted to 1997 NAICS):
  - investment sales shares,
  - intermediates using shares,
  - intermediates sales shares,
  - 4-firm concentration ratios,
  - skilled worker shares,
  - physical capital intensities,
  - contract intensity of inputs.
- Measurement details:
  - Investment sales, intermediates sales, and intermediates using shares from the 1997 Benchmark Detailed Make and Use Tables.
  - Four-firm concentration ratios from the 2002 Economic Census.
  - Skilled worker shares from the 2000 American Community Survey.
  - Capital intensity measured as 1 minus the labor share of value added (payroll) from NBER-CES Manufacturing Industry Database.
  - Contract intensity from Nunn (2007) (fraction of inputs not sold on organized exchanges and not reference priced).
- Clustering method: k-means algorithm applied to M = 233 manufacturing sectors, each with N = 7 sectoral characteristics, to assign sectors into G clusters minimizing within-cluster sum of squared deviations.

*Source: wpiea2024051-print-pdf, https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024051-print-pdf.pdf*

### 1. Initialize cluster centroids푚

### 1. Initialize cluster centroids푚

### Clustering procedure and cluster labels
- Algorithm:
  - K-means clustering with k-means ++ initialization (Arthur and Vassilvitskii (2007)).
  - Standardization: each characteristic normalized to have zero mean and unit variance.
  - Iteration steps:
    1. Initialize cluster centroids 푚1, 푚2, ... , 푚퐺 ∈ R풩.
    2. Assign each sector 푘 to cluster c(푘) = argmin푔∈{1,...,퐺} ||푥(푘) − 푚푔||2.
    3. Update centroid ˆ푚푔 = (Σ푀푘=1 1(c(푘)=푔)·푥(푘)) / (Σ푀푘=1 1(c(푘)=푔)).
    4. Iterate steps 2–3 until convergence.
- Number of clusters:
  - Silhouette width (Rousseeuw, 1987) used to assess fit; silhouette analysis suggests 4 or 5 clusters are good.
  - Baseline: group 233 manufacturing industries into 4 clusters for parsimony; results shown to be insensitive to this choice.
- Special clusters:
  - Manufacturing: 4 clusters.
  - Agriculture grouped into cluster 5; mining grouped into cluster 6.
  - Total sectors clustered: 268 into 6 clusters.

### Table 1 — summary statistics of clusters in manufacturing (preserve numeric values exactly)
- Rows report cluster means by characteristic; last two columns report Mean and Std. Dev. across all manufacturing sectors.

- Investment Share:
  - Cluster 1: 0.00
  - Cluster 2: 0.05
  - Cluster 3: 0.52
  - Cluster 4: 0.04
  - Mean: 0.13
  - Std. Dev.: 0.22

- Intermediates, Using:
  - Cluster 1: 0.78
  - Cluster 2: 0.58
  - Cluster 3: 0.65
  - Cluster 4: 0.66
  - Mean: 0.66
  - Std. Dev.: 0.16

- Intermediates, Sales:
  - Cluster 1: 0.84
  - Cluster 2: 0.70
  - Cluster 3: 0.27
  - Cluster 4: 0.28
  - Mean: 0.57
  - Std. Dev.: 0.31

- Concentration Ratio:
  - Cluster 1: 0.47
  - Cluster 2: 0.27
  - Cluster 3: 0.38
  - Cluster 4: 0.56
  - Mean: 0.40
  - Std. Dev.: 0.21

- Skill Intensity:
  - Cluster 1: 0.32
  - Cluster 2: 0.28
  - Cluster 3: 0.35
  - Cluster 4: 0.36
  - Mean: 0.32
  - Std. Dev.: 0.13

- Capital Intensity:
  - Cluster 1: 0.68
  - Cluster 2: 0.55
  - Cluster 3: 0.54
  - Cluster 4: 0.70
  - Mean: 0.61
  - Std. Dev.: 0.10

- Contract Intensity:
  - Cluster 1: 0.26
  - Cluster 2: 0.56
  - Cluster 3: 0.73
  - Cluster 4: 0.52
  - Mean: 0.51
  - Std. Dev.: 0.22

- Number of industries:
  - Cluster 1: 60
  - Cluster 2: 34
  - Cluster 3: 47
  - Cluster 4: 42

- Trade share (fraction of world trade accounted for by sectors in that cluster):
  - Cluster 1: 0.33
  - Cluster 2: 0.26
  - Cluster 3: 0.23
  - Cluster 4: 0.11

- Labels and abbreviations:
  - Cluster 1: Raw Materials Processing (RAW)
  - Cluster 2: Complex Intermediates (INT)
  - Cluster 3: Capital Goods (CAP)
  - Cluster 4: Consumer Goods (CONS)

- Cluster interpretations (summary):
  - RAW: highest intermediate sales and using shares; lowest contract intensity; first-stage processing of raw materials.
  - INT: second-highest intermediate sales shares; considerably higher contract intensity than RAW.
  - CAP: distinguished by average investment sales share of 0.52 (others range 0.00 to 0.05).
  - CONS: low intermediate sales share and negligible average investment sales share.

### Representative sectors
- Appendix Table A3 (referenced) lists the 3 most representative sectors per cluster (closest to centroid).

---

### Estimation strategy for 퐹푀퐴푖푘,푡 (external market access)
- Gravity setup (sector-specific, decadal intervals):
  - Target: obtain 퐹푀퐴푖푘,푡 for country i, sector k, time t.
  - Use structural sector-specific gravity equations on sectoral bilateral trade flows.
  - For t=1965 example: use three-year averages (1964, 1965, 1966) to reduce measurement error.
- Empirical specification (non-linear form):
  - 휆푖푛푘,푡 = 휅x푖푘,푡 · 휅m푛푘,푡 · Distance휁푘푡푖푛 · exp(휉푘푡·Contig푖푛) · 휀푖푛푘,푡
    - 휆푖푛푘,푡 denotes share of n’s expenditure on sector k sourced from i (calculated as share of import expenditure).
    - 휅x exporter fixed effect; 휅m importer fixed effect.
    - 휁푘푡 distance coefficient and 휉푘푡 common border coefficient (sector-time specific).
  - Estimated with Poisson Pseudo-Maximum Likelihood (PPML) separately for 268 sectors and each of 5 decades spanning 1965-2015.
- Constructing external market access:
  - 퐹푀퐴푖푘,푡 = Σn≠i E n k,t (i) · 휅m n k,t · Distance휁푘푡 i n · exp(휉푘푡·Contig i n)
    - Where E n k,t (i) ≡ Σi′≠n,i E i′ n k,t (total importer n expenditure in k at time t leaving country i out).
- Two methodological "wrinkles":
  1. Leave-one-out strategy: estimate equation (4.2) N times per sector-time, each time omitting country i, to construct country i’s foreign shocks using regression that omitted its data.
  2. Normalization of fixed effects: restrict sum of logged importer effects to be zero (instead of choosing a numéraire country) to avoid numéraire-driven fluctuations.
- Rationale:
  - Procedure uses only foreign data to construct external market access and projects flows onto distance and contiguity, excluding domestic average export-tax-like factors and idiosyncratic bilateral factors.

---

### 5. Empirical Results

### 5.1 Summary of empirical procedure (steps)
- 1. Leave-one-out gravity equation estimation with PPML to recover foreign component of 퐹푀퐴푖푘,푡 and 퐶푀퐴푖푘,푡 by country and decade for 268 sectors.
- 2. K-means clustering algorithm to group manufacturing sectors into 4 clusters; agriculture and mining are separate clusters.
- 3. Construct cluster-level dln퐹푀퐴푖푔,푡 and dln퐶푀퐴푖푔,푡.
- 4. LASSO of dln푦푖,푡 and dln퐹푀퐴푖푔,푡 on dln a푖𝑡 and x𝑖,𝑡 to select controls.
- 5. OLS regression of dln푦푖,푡 on dln퐹푀퐴푖푔,푡 and selected controls to obtain estimates of 훿𝑥𝑔.

### 5.2 Baseline estimates — cluster-specific coefficients
- Estimation outputs (coefficients on foreign demand shocks by cluster):
  - Clusters order used: RAW, INT, CAP, CONS, AG, MIN.
- OLS estimates (left panel, Figure 1):
  - Coefficients: 0.20, 1.27, 2.08, −0.47, 0.08, 0.07
  - F(5,126)=5.05
  - p=0.00
- Post-Double-Selection (LASSO) estimates (right panel, Figure 1):
  - Coefficients: 0.17, 1.32, 2.97, −0.52, 0.11, 0.05
  - F(5,126)=3.81
  - p=0.00
- Inference and interpretation:
  - Large heterogeneity across cluster coefficients; F-tests reject equality at 1% significance.
  - Complex intermediates (INT) and capital goods (CAP) clusters: positive and notably larger estimated real income effects; CAP confidence interval fairly wide.
  - Other clusters: estimated elasticities close to zero (mostly positive) and relatively precisely estimated.
- LASSO controls:
  - Full set of potential controls: 1106 variables.
  - Post-Double-Selection via LASSO selected 6 control variables.
  - LASSO tuning: K-fold cross validation used; baseline uses minimizing value (not the "one standard deviation above" rule).

### 5.3 Robustness checks (highlights and numeric thresholds)
- Small country assumption:
  - Mitigation: leave-one-out extraction of fixed effects.
  - Two robustness actions:
    1. Drop importer n from summation in equation (4.3) when 휆푖푛푘,푡 > 0.25 (i.e., drop importer if more than 25% of its imports in sector k are from country i). Results broadly similar (Appendix Figure A6 panel (a)).
    2. Drop country-decade instances where country is among top 100 world export shares at country-decade-cluster level:
       - Top 100 observations represent 2.3% of 4304 available country-cluster-decade observations.
       - Smallest of these top 100 world export shares is 7.7%.
       - Results similar to baseline (Appendix Figure A6 panel (b)).
- Spatial correlation in shocks:
  - Three checks (Appendix Figure A7):
    1. Omit neighboring countries (contiguous plus 5 closest by distance) when calculating dln퐹푀퐴 terms.
    2. Control for average TFP growth of neighboring countries in post-LASSO OLS (TFP from Penn World Tables).
    3. Control for unweighted dln퐹푀퐴푖푔,푡 in post-LASSO OLS (absorbs correlation between domestic and foreign shocks).
  - All three checks show very little change relative to baseline.
- Sample splits and cluster number:
  - Splitting by developed vs. developing countries: similar qualitative results.
  - Time splits (first 3 vs. last 3 decadal growth rates): could not reject equality of coefficients.
  - Allowing 5 manufacturing clusters: fifth cluster isolates skill-intensive industries; new cluster’s 훿𝑥𝑘 close to zero; other clusters’ 훿𝑥𝑘 unaffected (Table A5 and Figure A11).

---

### 6. Quantitative Implications

### 6.1 Specialization patterns and uniform foreign demand shocks
- Elasticity formula (country i’s real income to uniform log-change in 퐹푀퐴):
  - dln y𝑖,𝑡 / dln 퐹푀퐴 = Σk b 훿𝑥𝑘 · 휆𝑥𝑖𝑘,𝑡  (equation (6.1))
  - Counterfactual interprets uniform reduction in trade costs to every foreign destination.
- Calibration and calculation:
  - Use double-LASSO estimates (right panel Figure 1) and 2015 trade shares.
  - Elasticity outcomes:
    - Range: from essentially zero (countries chiefly in Sub-Saharan Africa) to around 0.5 for some Central European and East Asian countries.
    - Specific examples with elasticity around 0.5: Hungary, Slovakia, Malaysia, Taiwan.
  - Elasticities positively correlated with log PPP-adjusted income per capita, but substantial heterogeneity remains due to export specialization and openness.
  - Key insight: countries specializing in complex intermediates and capital goods benefit much more from declining trade costs than agricultural and commodity producers.

### 6.2 Policy implications — export and production subsidies
- Calibration inputs for representative country exercise:
  - Export revenue shares 휆𝑥𝑘: simple average across sample countries in 2015.
  - Y/V (ratio gross output to value added): set to 2.
  - Sectoral expenditure shares e𝑘 and domestic sourcing shares 휃𝑑𝑘: from WIOD (Timmer et al., 2015), simple averages across countries.
  - Trade elasticities: set 휎𝑘 = 6 ∀ k (implies long-run trade elasticity of 5).
- First-order welfare impacts (Figure 3 summary, computed using formulas (2.9) and (A.17)):
  - Export subsidies:
    - 10% export subsidy produces:
      - Welfare gain of about 1.3% for complex intermediates.
      - Welfare gain of nearly 2% for capital goods.
    - Other clusters (RAW, CONS, AG, MIN): export subsidies lead to welfare losses (equivalently, gains from taxing exports).
  - Production subsidies (assuming Cobb-Douglas expenditure and production functions, equation A.17):
    - Qualitatively similar conclusions to export subsidies; magnitudes larger due to larger subsidy base.
- Interpretation:
  - Sectors with 훿𝑥𝑘 > (1/휎𝑘)[Y/V + Σk′ 훿𝑥𝑘′ e𝑘′ 휃𝑑𝑘′ ] are inefficiently small; reallocating towards them increases welfare (see equation 2.9).
  - Results imply substantial gains from reallocating export activity toward complex intermediate and capital goods sectors at the margin.
  - These findings support the potential positive role of export subsidies in development for those sectors, subject to caveats on non-linearities and optimal policy magnitudes.
- Sensitivity to 휎𝑘:
  - Gains from export subsidies are increasing in 휎𝑘.
  - In practice, gains remain positive for 휎 > 2 (which would imply a trade elasticity of 1); lower long-run trade elasticities below 1 are deemed implausible.

*Source: wpiea2024051-print-pdf — IMF Working Paper (content unit provided).*

### Appendix Figure A12 presents the results under cluster-specific휎

### wpiea2024051-print-pdf - Appendix Figure A12 presents the results under cluster-specific휎

### Structural model setup
- Framework: quantitative small open economy with input-output matrix, endogenous capital accumulation, and sector-level scale economies.
- Households: representative consumer maximizes discounted utility ∑∞_{t=0} ρ^{t} C_{t}^{1−ψ}/(1−ψ) subject to period budget constraints P^{C}_{t} C_{t}+P^{I}_{t} I_{t} ≤ w_{t} L + r_{t} K_{t} and K_{t+1}=I_{t}+(1−χ)K_{t}.
- Aggregates: C_{t} = (∑_{k} C_{k t}^{e_{k}})^{1/e_{k}} and I_{t} = (∑_{k} I_{k t}^{ν_{k}})^{1/ν_{k}}; sectoral Armington aggregation for domestic and foreign varieties; gravity holds within each sector.
- Production unit cost in sector k:
  - c_{k t} = T_{k} L_{k t}^{−γ_{k}} [ w_{t}^{β} r_{t}^{1−β} ]^{μ} ∏_{l} P_{l t}^{α_{l,k}}
  - Features: intermediate inputs from other sectors; scale effects governed by parameter 훾_{k} (unit cost decreases in sectoral employment).

### Calibration, fitting target, and key quantitative results
- Objective: choose common 휎 and 훾 (no cross-sector heterogeneity) to minimize Mean Absolute Error (MAE) between model-implied δ_{x k} and empirically estimated δ_{x k} across 6 clusters.
- Best-fit parameters from MAE minimization:
  - 휎 = 3.2
  - 훾 = 0.29
- Model-data fit:
  - Correlation between model-implied and data δ_{x k}: 0.94
  - Average model δ_{x} across clusters: 0.73
  - Average data δ_{x} across clusters: 0.68
  - Baseline MAE reported elsewhere: 0.32 (baseline MAE referenced as comparison)
- Sensitivity around 훾:
  - MAE is flat from about 훾 = 0.17 (associated 휎 ≈ 4.9) to 훾 = 0.30.
  - Model matches capital goods cluster δ_{x} almost exactly for all 훾 between 0.13 and 0.3.

### Mechanisms driving results (input-output linkages, propagation, and role of service sector)
- Decomposition of model δ_{x} into components:
  - Direct effects: partial equilibrium effect on the directly shocked sector.
  - First-order effects: changes in intermediate demand by shocked sector and attendant value-added changes domestically (includes unit-cost responses through wages and scale effects).
  - Higher-order effects: propagation through input-output network as affected sectors change their own demands and relative costs.
- Quantitative findings on mechanisms:
  - Both levels and variation across clusters are driven by higher-order effects.
  - For the two highest-impact clusters (capital and complex intermediates), higher-order effects account for the large majority of total δ_{x}.
  - Higher-order effects matter for only about half of the clusters despite common 휎 and 훾, implying the full matrix of sectoral interconnections drives heterogeneity.
- Alternative model experiments (each keeps exports and imports as fraction of sectoral gross output constant):
  - No intermediates (set e_{k,l}=0 ∀k,l, μ=1): average δ_{x} falls by about 60% relative to baseline; cross-cluster variation nearly disappears; capital cluster coefficient falls to 0.5 (one-sixth of baseline/data).
  - No capital (β=1): better than no-intermediates; capital cluster coefficient = 1.8 (closer to data) but average δ_{x} still about 30% below baseline and data.
  - Investment composition same as consumption (e_{k} = ν_{k}): small quantitative effect.
  - No non-tradeable (make services as tradable as other sectors): average δ_{x} falls by more than 50%; model fails to match observed variation.
- Interpretation: the proximate reason for high GDP impact of shocks in tradeable capital and complex intermediates is expansion of the large, non-tradeable service sector through higher-order effects; non-tradeability insulates service expansion from negative terms-of-trade effects.

### Scale economies, alternative calibrations, and limitations of constant-returns models
- Constant returns to scale experiments (훾 = 0):
  - Table 2 reports model δ_{x} under 휎 = 1.01, 3, 10 and sector-specific 휎_{k} minimizing MAE.
  - Average δ_{x} is decreasing in 휎.
  - Matching average data δ_{x} is possible by lowering 휎, but this yields δ_{x} far too high in 4 of 6 clusters (data δ_{x} near zero or negative), producing MAEs 2–3 times baseline MAE = 0.32.
  - Sector-specific 휎_{k} in range 4−7 minimizing MAE yields average δ_{x} about one-third of data value and low dispersion; resulting MAE over twice baseline MAE.
- Conclusion on scale effects:
  - Constant-returns versions cannot match sectoral differences in δ_{x}.
  - Positive common scale elasticity (훾>0) generates sectoral differences because endogenous productivity gains from sectoral expansion are amplified for strongly connected (upstream) sectors that are "too small" in laissez-faire equilibrium; amplification is stronger when upstream from non-traded sector.
  - The calibrated 훾 = 0.29 closely matches independent mean sectoral scale elasticity estimates (0.30 from Lashkaripour and Lugovskyy (2023)); alternative literature reports a lower average around 0.13 (Bartelme et al. (2019)).

### Main conclusions and policy implications
- A parsimonious model with common 휎 and 훾 calibrated to representative sectoral production and trade structure can reproduce estimated real income responses to foreign demand shocks via internal propagation mechanisms (no sectoral heterogeneity in free parameters required).
- Two model features are crucial for quantitative success:
  - Scale effects (positive 훾)
  - Input-output linkages (higher-order propagation through intermediate networks)
- Other important features: capital accumulation and non-tradeability of large service sector.
- Policy implication from empirical and theoretical results:
  - Positive foreign demand shocks in sectors producing complex intermediates and capital goods yield significantly larger long-run welfare increases than shocks in other sectors; countries benefit from reallocating economic activity toward these sectors.
  - Results validate the importance of external environment and the role of sectoral trade and industrial policy in development.

*Source: wpiea2024051-print-pdf - Appendix Figure A12 presents the results under cluster-specific휎*

### References

### References

### Key literature themes
- Foundations of modern international trade theory and quantitative trade models:
  - Works by Adão, Costinot, Donaldson, Arkolakis, Eaton, Kortum, Melitz, Krugman, Armington, and others.
- Empirical and methodological contributions:
  - Gravity models, log of gravity (Silva and Tenreyro, 2006), computational analysis, high-dimensional methods (Belloni et al.), cluster and classification methods (MacQueen; Arthur and Vassilvitskii; Rousseeuw).
- Industrial policy, protectionism, and learning-by-doing:
  - Classic and modern treatments (Bardhan, Haberler, Prebisch, Rodrik, Hausmann, Lashkaripour and Lugovskyy, Choi and Levchenko).
- Trade, productivity, and welfare measurement:
  - Papers on gains from trade, variety, and quality upgrading (Broda and Weinstein; Burstein and Cravino; Fieler et al.; Caliendo and Parro).
- Natural resources, conflict, and growth:
  - Resource curse and terms-of-trade literature (Humphreys et al.; Sachs and Warner; Sala-i-Martin and Subramanian).
- Input linkages, networks, and spatial/general equilibrium extensions:
  - Works on input-output linkages and general equilibrium in space (Timmer et al.; Conte et al.; Baqaee and Farhi; Demidova et al.; Kucheryavyy et al.).

### Representative citation formats preserved from source
- Journal articles with volume and issue formatting (examples preserved exactly as in source):
  - “American Economic Review, 2017,107(3), 633–89.”
  - “Journal of Political Economy, 2020,128(2), 393–433.”
  - “American Economic Review, December 2007,97(5), 1611–1638.”
  - “Journal of International Economics, 2020,127, 103379.”
- Working papers and mimeos explicitly noted:
  - “May 2023. Mimeo, Chicago Booth and MIT.”
  - “August 2019. mimeo, UCLA and Harvard.”
  - “March 2020. Mimeo.”
- Books and edited volumes retained (publisher and year as in source):
  - “Computational Analysis of Global Trading Arrangements, Ann Arbor: The University of Michigan Press, 1990.”
  - “Escaping the Resource Curse, Columbia University Press, 2007.”
  - “Handbook of Commercial Policy, North-Holland, 2016.”

### A. Theoretical Appendix

### A.1 Competitive equilibrium
- The competitive equilibrium is represented as the set of solutions to the simultaneous system (equations referenced exactly as in source):
  - (A.1) Industry factor demand equations:
    - w_j L_{j,k} = μ_{j,k} · Y_k, ∀ j ∈ J, k ∈ K
  - (A.2) Factor market clearing:
    - Σ_{k∈K} L_{j,k} = ̄L_j, ∀ j ∈ J
  - (A.3) Aggregate expenditure equals total factor income:
    - V = Σ_k Σ_j w_j · L_{j,k}
  - (A.4) Price index definition:
    - P_k^{1−σ_k} = z_k c_k^{1−σ_k} + CMA_k, ∀ k ∈ K
  - (A.5) Gross industry revenues equal total industry sales:
    - Y_k = c_k^{1−σ_k} z_k e_k · V + [ Σ_{k′∈K} ̃α_{k,k′} Y_{k′} P_k^{1−σ_k} + FMA_k ], ∀ k ∈ K
- Variable and parameter definitions preserved:
  - e_k is the fraction of consumer expenditure devoted to industry k.
  - μ_{j,k} is the fraction of industry k’s gross output devoted to purchasing factor input j.
  - ̃α_{k,k′} is the fraction of industry k′’s gross revenue (Y_{k′}) used to purchase intermediate inputs from sector k.
- Structural assumptions and implications:
  - By Shephard’s lemma these shares equal elasticities of expenditure or cost functions with respect to price.
  - Under homotheticity and (perceived) constant returns these elasticities do not depend on total expenditure (V) or industry gross output.
  - If there is a unique solution for factor allocations L given factor prices w (i.e., a unique solution to (A.1) for given w), the system reduces to a set of J equations equating factor demand and supply.
  - In a closed economy the J equilibrium conditions are homogeneous of degree 1 and require a normalization; in the open economy they are not homogeneous of degree 1 due to fixed foreign prices and no normalization is required.

### A.2 First order welfare effects of policies
- Government instruments introduced (exact notation preserved):
  - Sector-level export taxes t^x_k on the value of exports, measured at the destination. If foreign consumer pays tax-inclusive price p^f_k, firm revenue per unit shipped is ̃p_k = (1−t^x_k) p^f_k.
  - Sector-level taxes −s_k on production costs (positive s_k denote a subsidy). If factor payments per unit are c_k, government collects revenue equal to −s_k c_k from the firm; effective unit cost faced by the firm is c_k (1−s_k).
- Demand and revenue implications (isoelastic foreign demand; formulas preserved exactly):
  - Foreign demand: q^f_k ∝ (p^f_k)^{−σ_k}, so q^f_k ∝ (̃p_k/(1−t^x_k))^{−σ_k}.
  - Total firm revenue from foreign sales:
    - X^f_k = ̃p_k q^f_k = ̃p_k^{1−σ_k} (1−t_k)^{σ_k} · FMA_k
  - Government revenue from export taxes in sector k:
    - t^x_k/(1−t^x_k) X^f_k
  - Total revenue from foreign sales:
    - X^f_k/(1−t^x_k)
- Budget and transfer setup:
  - The government imposes the two sector-level instruments above plus lump-sum transfers to balance its budget (lump-sum transfers noted in the setup description).

_Italic source attribution line preserved as required._

### 2. The subsidy revenue is equal to

### 2. The subsidy revenue is equal to

### Subsidy revenue and competitive equilibrium with taxes
- Subsidy revenue expression:
  - The subsidy revenue is equal to
    Í
    푘
    −푠
    푘
    푝
    ̃
    푘
    푐
    푘
    (푞
    푑
    푘
    +푞
    푓
    푘
    ), where 푞
    푑
    푘
    is the domestic quantity shipped.
  - Perfect competition and isoelastic domestic demand imply
    ̃
    푝
    푘
    =푐
    푘
    (1−푠
    푘
    ), so government revenue can be expressed as
    Í
    푘
    −
    푠
    푘
    1−푠
    푘
    (푋
    푑
    푘
    +푋
    푓
    푘
    ), where 푋
    푑
    푘
    is total firm revenue from domestic sales.
  - Total firm revenue from both sales and subsidy payments:
    푌
    푘
    =
    1
    1−푠
    푘
    (푋
    푑
    푘
    +푋
    푓
    푘
    ).

- Competitive equilibrium with taxes: solution to system (A.6)-(A.11)
  - (A.6) 푤
    푗
    퐿
    푗,푘
    =휇
    푗,푘
    ·푌
    푘
    , ∀푗∈퐽, 푘∈퐾
  - (A.7) Õ
    푘∈퐾
    퐿
    푗,푘
    =
     ̄
    퐿
    푗
    , ∀푗∈퐽
  - (A.8) 푉=
    Õ
    푘
    Õ
    푗
    푤
    푗
    ·퐿
    푗,푘
  - (A.9) 푃
    1−휎
    푘
    푘
    =푧
    푘
    (
    푐
    푘
    (1−푠
    푘
    )
    )
    1−휎
    푘
    +퐶푀퐴
    푘
    , ∀푘∈퐾
  - (A.10) 푌
    푘
    (1−푠
    푘
    )=
    (
    푐
    푘
    (1−푠
    푘
    )
    )
    1−휎
    푘

    푧
    푘

    푒
    푘
    ·(푉+푇)+
    Í
    푘
    ′
    ∈퐾
     ̃
    훼
    푘,푘
    ′
    푌
    푘
    ′
    푃
    1−휎
    푘
    푘
    !
    +(1−푡
    푘
    )
    휎
    푘
    퐹푀퐴
    푘
    !
    ∀푘∈퐾
  - (A.11) 푇=
    Õ
    푘
    푡
    푥
    푘
    1−푡
    푥
    푘
    푋
    푓
    푘
    −
    Õ
    푘
    푠
    푘
    푌
    푘
  - Welfare:
    (A.12) 푈(퐸,P)=
    푉+푇
    P
    , where P is the tax-inclusive price index and 푉 is the transfer-exclusive expenditures.

### Elasticity of welfare with respect to export taxes
- Thought experiment: small changes to {퐹푀퐴
  푘
  } and a small increase in export tax 푡
  푥
  ₗ from zero taxes; negative taxes indicate subsidies; lump-sum taxation balances government budget.
- Conditions for identical solutions in the two experiments (equate effects of foreign demand shocks and export tax):
  - (A.13) 휆
    푥
    ₗ
    푑ln퐹푀퐴
    ₗ
    =휆
    푥
    ₗ
    
    휎
    ₗ
    −푒
    ₗ
    ·휃
    푑
    ₗ
    
    푑ln
    
    1−푡
    푥
    ₗ
    

  - (A.14) 휆
    푥
    ₖ
    푑ln퐹푀퐴
    ₖ
    =−휆
    푥
    ₗ
    ·푒
    ₖ
    ·휃
    푑
    ₖ
    ·푑ln
    
    1−푡
    푥
    ₗ
    

    , ∀푘≠푙
  - Here 휃
    푑
    ₖ is the share of Home’s expenditure in 푘 that is sourced domestically.
- Welfare elasticity result:
  - (A.15) 푑ln푈
    푑ln
    
    1−푡
    푥
    ₗ
    
    =휆
    푥
    ₗ

    훿
    푥
    ₗ
    휎
    ₗ
    −
    푌
    푉
    −
    Õ
    푘
    훿
    푥
    ₖ
    푒
    ₖ
    휃
    푑
    ₖ
    !
    .
- Condition for a small export subsidy to sector ₗ to be welfare-improving:
  - (A.16) 훿
    푥
    ₗ
    >
    1
    휎
    ₗ

    푌
    푉
    +
    Õ
    푘
    훿
    푥
    ₖ
    푒
    ₖ
    휃
    푑
    푘
    !

### Elasticity of welfare with respect to production subsidies
- Assumptions: production functions and upper tier of utility are Cobb-Douglas so 휇
  푗,푘 and 푒
  푘 are parameters.
- Cost decomposition:
  - 푐
    푘
    =퐶
    푘
    ·
    Ö
    푙
    푃
     ̃
    훼
    푘
    ′
    ,푘
    푘
    ′
    where 퐶
    푘
    is endogenous and does not contain 푐
    푘 or (1−푠
    푘
    ) directly.
  - Therefore (A.9) becomes:
    푃
    1−휎
    푘
    푘
    =푧
    푘
    (
    (1−푠
    푘
    )푐
    푘
    )
    1−휎
    푘
    +퐶푀퐴
    푘
- Log-linear approximation (small changes in (1−푠
  푘
  ′ )):
  - 푑ln푐
    푘
    =푔
    푘
    +
    Õ
    푘
    ′
    ˆ
    푎
    푘,푘
    ′
    푑ln
    (
    1−푠
    푘
    ′
    )
    ,
    where
    ˆ
    푎
    푘,푘
    ′
    =
    
    (퐼−퐴
    푇
    퐷{휃
    푑
    })
    −1
    퐴
    푇
    퐷{휃
    푑
    }
    
    푘,푘
    ′
    ,
    퐴=
    [
     ̃
    훼
    푘
    ′
    ,푘
    ]
    ,
    and 퐷{휃
    푑
    }=퐷푖푎푔{휃
    푑
    푘
    }.
- Additional relationships:
  - 푑ln휃
    푑
    푘
    =(1−휎
    푘
    )(1−휃
    푑
    푘
    )(푑ln
    (
    1−푠
    푘
    )
    +푑ln푐
    푘
    ), ∀푘
  - 푌
    푘
    (1−푠
    푘
    )=휃
    푑
    푘
    (푒
    푘
    푉+
    Õ
    푘
    ′
    ∈퐾
     ̃
    훼
    푘,푘
    ′
    푌
    푘
    ′
    )−휃
    푑
    푘
    푒
    푘
    Õ
    푘
    ′
    푠
    푘
    ′
    푌
    푘
    ′
    +푋
    푓
    푘
    , ∀푘.
- Equating coefficients and evaluating at 푠
  푘
  =0 gives conditions for shocks to 퐹푀퐴
  푘 that deliver same positive implications as small change in (1−푠
  푙
  ):
  - For sector ℓ:
    휆
    푥
    ℓ
    푑ln퐹푀퐴
    ℓ
    =

    −
    푌
    ℓ
    푌
    +

    푋
    푑
    ℓ
    푌
    (1−휃
    푑
    ℓ
    )+휆
    푥
    ℓ
    !
    (1−휎
    ℓ
    )(1+
    ˆ
    푎
    ℓℓ
    )+휃
    푑
    ℓ
    푒
    ℓ
    푌
    ℓ
    푌
    !
    푑ln
    (
    1−푠
    ℓ
    )
  - For k≠ℓ:
    휆
    푥
    푘
    푑ln퐹푀퐴
    푘
    =

    푋
    푑
    푘
    푌
    (1−휃
    푑
    푘
    )+휆
    푥
    푘
    !
    (1−휎
    푘
    )
    ˆ
    푎
    푘,ℓ
    +휃
    푑
    푘
    푒
    푘
    푌
    ℓ
    푌
    !
    푑ln
    (
    1−푠
    ℓ
    )
- Welfare equality up to subsidy revenue and direct effect on domestic consumer price index:
  - (A.17) −
    푑ln푈
    푑ln
    (
    1−푠
    ℓ
    )
    =훿
    푥
    ℓ

    푌
    ℓ
    푌
    +(휎
    ℓ
    −1)

    푋
    푑
    ℓ
    푌
    (1−휃
    푑
    ℓ
    )+휆
    푥
    ℓ
    !!
    −
    푌
    ℓ
    푉
    −
    Õ
    푘
    훿
    푥
    푘
    휃
    푑
    푘
    푒
    푘
    푌
    ℓ
    푌
    (A.17)
    +
    Õ
    푘
    훿
    푥
    푘
    (휎
    푘
    −1)
    ˆ
    푎
    푘,ℓ

    푋
    푑
    푘
    푌
    (1−휃
    푑
    푘
    )+휆
    푥
    푘
    !
    +푒
    ℓ
    휃
    푑
    ℓ
    .

### A.3 Determinants of 훿
푥
 in simple examples — Planner’s problem and examples
- Planner’s problem formulation (quantities, factor allocations, production functions, trade balance constraint):
  - Define 푞
    푐,푑
    푘
    (final Home consumption of domestic goods), 푞
    푐,푓
    푛,푘
    (final consumption of foreign goods from country n), intermediate uses superscript m, export to n is 푞
    푥
    푛,푘
  - Define D
    푛,푘
    ≡휏
    1−휎
    푘
    푛,푘
    퐸
    푛,푘
    /푃
    1−휎
    푘
    푛,푘
    . Note: iceberg trade cost implies exporter price formula mentioned in footnote.
  - Planner’s maximization problem (concise form provided in source).

- Transformation to FMAs and CMAs using first-order conditions:
  - Ratios of exports across markets:
    푞
    푥
    푛,푘
    푞
    푥
    푖,푘
    =
    퐷
    푛,푘
    퐷
    푖,푘
    , ∀푖,푛∈푁, 푘∈퐾.
  - Define aggregate variables 푞
    푥
    푘
    , 푞
    푐,푓
    푘
    , 푞
    푚,푓
    푘
    to restate planner problem in FMA/CMA notation.
  - Envelope theorem yields closed form:
    훿
    푥
    푘
    =휗·
    1
    휎
    푘
    , where 휗 is multiplier on trade balance constraint and equals 푌/푉.

- Example without domestic distortions (Armington economy, laissez-faire vs planner):
  - With single-factor and Cobb-Douglas upper tier (expenditure share e
    푘
    ), equilibrium simplifies to a single equation (shown in source).
  - Log-linearization yields expressions for 푑ln푤 and 푑lnP in terms of 푑lnFMA
    푘
    .
  - Aggregate result:
    푑ln푦≈훿
    푥
    ·
    Õ
    푘∈퐾
    휆
    푥
    푘
    푑ln퐹푀퐴
    푘
    ,
    with
    훿
    푥
    =
    휆
    푚
    1−
    Í
    푘
    ′
    ∈퐾
    
    휆
    푑
    푘
    ′
    +
    (
    1−휎
    푘
    ′
    )
    
    휆
    푑
    푘
    ′
    휃
    푓
    푘
    ′
    +휆
    푥
    푘
    ′
    ]]
    .
  - Special case 휆
    푚
    푘
    =1, ∀푘 yields:
    훿
    푥
    =
    1
    1+
    Í
    푘
    ′
    ∈퐾
    휆
    푥
    푘
    ′
    (
    휎
    푘
    ′
    −1
    )
    ,
    and welfare-improving condition:
    휎
    푘
    −1>
    Õ
    푘
    ′
    ∈퐾
    휆
    푥
    푘
    ′
    (
    휎
    푘
    ′
    −1
    )
    .

- Example with external economies (scale economies):
  - Cost function: 푐
    푘
    =
    푤
    푇
    푘
    퐿
    훾
    푘
    푘
    .
  - Assume 훾
    푘
    (휎
    푘
    −1)<1 for uniqueness and interior equilibrium.
  - Aggregate labor market equation and solution yield:
    푑ln푤≈휅
    Õ
    푘∈퐾
    
    1
    1−훾
    푘
    (휎
    푘
    −1)
    
    휆
    푥
    푘
    푑ln퐹푀퐴
    푘
    ,
    with
    휅=
    1
    1−
    Í
    푘
    ′
    ∈퐾
    (1+훾
    푘
    ′
    )(1−휎
    푘
    ′
    )
    1−훾
    푘
    ′
    (휎
    푘
    ′
    −1)
    휆
    푥
    푘
    ′
    .
  - Resulting income elasticities:
    훿
    푥
    푘
    =
    1
    1−훾
    푘
    (휎
    푘
    −1)
    ·
    1
    1−
    Í
    푘
    ′
    ∈퐾
    (1+훾
    푘
    ′
    )(1−휎
    푘
    ′
    )
    1−훾
    푘
    ′
    (휎
    푘
    ′
    −1)
    휆
    푥
    푘
    ′
    , ∀푘∈퐾.
  - Intuition: sectors with larger external economies generate larger welfare effects for foreign demand shocks.

### A.4 Quantitative model details
- Equilibrium definition: sequence of goods prices {푃
  푘푡
  }∀푘,푡, factor prices {푤
  푡
  , 푟
  푡
  }∀푡, factor allocations {퐿
  푘푡
  , 풦
  푘푡
  }∀푘,푡, and goods market allocations such that consumers maximize utility, firms maximize profits, and markets clear.
- Market clearing for sector k at time t:
  - 푌
    푘푡
    =
    푧
    푘
    푐
    1−휎
    푘
    푘푡
    푃
    1−휎
    푘
    푘푡

    푃
    푘푡
    퐶
    푘푡
    +푃
    푘푡
    퐼
    푘푡
    +
    Õ
    푙∈퐾
    e
    훼
    푘,푙
    푌
    푙푡
    !
    +푐
    1−휎
    푘
    푘푡
    퐹푀퐴
    푘푡
  - First term: domestic sales; second: exports; domestic sales depend on final and intermediate expenditures and domestic absorption share 푧
    푘
    (푐
    푘푡
    /푃
    푘푡
    )
    1−휎
    푘
- Steady state (drop time subscript):
  - Price of installed capital and investment price index proportional:
    푟=P
    퐼
    (휌
    −1
    +휒−1).
  - Aggregate gross revenue Y ≡ Í
    푘
    푌
    푘.
  - Steady state capital stock:
    풦=휇(1−훽)
    푌
    P
    퐼
    (휌
    −1
    +휒−1).
  - Investment: 퐼=휒풦, hence:
    P
    퐼
    퐼=
    휇휒(1−훽)
    (휌
    −1
    +휒−1)
    푌.
  - Consumption expenditure:
    P
    퐶
    퐶=휇
    
    1−
    (1−훽)휒
    (휌
    −1
    +휒−1)
    
    푌.
  - Combined consumption and investment expenditure on sector k:
    푃
    푘
    퐶
    푘
    +푃
    푘
    퐼
    푘
    =푓
    푘
    휇푌,
    where
    푓
    푘
    ≡푒
    푘
    
    1−
    (1−훽)휒
    (휌
    −1
    +휒−1)
    
    +휈
    푘
    (1−훽)휒
    (휌
    −1
    +휒−1).
  - Steady state system (A.18)-(A.22):
    - (A.18) 푌
      푘
      =
      푧
      푘
      푐
      1−휎
      푘
      푘
      푃
      1−휎
      푘
      푘
      Õ
      푙
      (
      푓
      푘
      휇+
      e
      훼
      푘,푙
      )
      푌
      푙
      +푐
      1−휎
      푘
      푘
      퐹푀퐴
      푘
      , ∀푘
    - (A.19) 푃
      1−휎
      푘
      푘
      =푧
      푘
      푐
      1−휎
      푘
      푘
      +퐶푀퐴
      푘
      , ∀푘
    - (A.20) 푐
      푘
      =푇
      푘
      퐿
      −훾
      푘
      푘
      푤
      훽휇
      Ö
      푙
      푃
      e
      훼
      푙,푘
      +휇(1−훽)휈
      푙
      푙
      , ∀푘
    - (A.21) 푤퐿
      푘
      =휇훽푌
      푘
      , ∀푘
    - (A.22) Õ
      푘
      퐿
      푘
      =퐿.

- Mapping to regression coefficients:
  - Empirical regressor is export-share-weighted firm market access: 퐹푀퐴
    W
    푘
    ≡휆
    푥
    푘
    퐹푀퐴
    푘.
  - Model solution stated in terms of 퐹푀퐴
    W to match regression coefficients.

- Analytical solution (first-order): vectors of log changes in revenues and prices from shocks 푑lnFMA
  W:
  - (A.23) 푑lnY=
    [ I− ( 횷
      풅
      +
      ( I−σ )
      
      ( I−π
      풙
      )
      
      I−θ
      풅
      ]+π
      풙
      
      I−Aθ
      풅
      ] )^{-1}
    ( γ ( λ⊗1−I ) +휇훽λ⊗1 ) ]^{-1}
    ×푑푖푎푔( λ )^{-1}
    푑lnFMA
    W
  - (A.24) 푑lnP=θ
    풅
    
    I−Aθ
    풅
    ]^{-1}
    (
    γ
    (
    λ⊗1−I
    )
    +휇훽λ⊗1
    )
    푑lnY.

- Matrix definitions (as in source): 횷
  풅
  , π
  풙
  , A, θ
  풅
  , λ, σ, γ, and diag(λ).

- Real GDP definition and conversion:
  - Real GDP:
    푦=
    푤퐿+푟풦
    P
  - Log change in price index: 푑lnP=f·푑lnP, where f collects final shares.
  - Real GDP change:
    (A.25) 푑ln푦=λ·푑lnY−f·푑lnP.
  - Model elasticities wrt foreign market access shocks:
    (A.26) 푑ln푦
    푑lnFMA
    W
    =
    [ λ−f·θ
    풅
    
    I−Aθ
    풅
    ]^{-1}
    (
    γ
    (
    λ⊗1−I
    )
    +휇훽λ⊗1
    )
    ]
    푑lnY
    푑lnFMA
    W
    , with 푑lnY/푑lnFMA
    W given by (A.23).
  - Interpretation: term in parentheses translates gross revenue changes into real income changes.

- Calibration:
  - Set value added share in gross output: 휇=0.5.
  - Labor share in value added: 훽=2/3.
  - Model parameterization uses 6 tradeable sector clusters plus a 7th non-tradeable services sector.
  - Data sources: COMTRADE for export/import shares; WIOD for domestic sectoral expenditure shares; mapping described in source.

- Direct, first-, and higher-order decomposition:
  - Define impact matrix (A.27):
    훀≡횷
    풅
    +
    (
    I−σ
    )
    
    (
    I−π
    풙
    )
    
    I−θ
    풅
    ]+π
    풙
    ] 
    I−Aθ
    풅
    ]^{-1}
    (
    γ
    (
    λ⊗1−I
    )
    +휇훽λ⊗1
    )
    .
  - Model solution as Leontief inverse expansion:
    푑lnY
    푑lnFMA
    W
    =
    { I−훀 }^{-1}
    ×푑푖푎푔( λ )^{-1}
    =
    [ I (direct) + 훀 (first-order) + 훀^2 + 훀^3 + ... (higher-order) ] ×푑푖푎푔( λ )^{-1}.
  - Interpretation:
    - Direct effect: diagonal, applies only to shocked sector.
    - First-order: sectors’ changed intermediate purchases (횷
      풅
      ), change in unit costs via factor reallocation (γ (λ⊗1−I)) and economywide wages (휇훽λ⊗1); these cost changes feed back into foreign and domestic sales via substitution matrices.
    - Higher-order terms propagate indirect effects through the production network; Leontief inversion captures infinite-order propagation.

*Italic: Source — wpiea2024051-print-pdf (section 2 and Appendix A.3–A.4 content as provided).*

### 3. The silhouette width of the observation푘is measured as푠

### 3. The silhouette width of the observation k is measured as s_k = (b_k − a_k) / max(a_k, b_k)

### Silhouette analysis and cluster selection
- Silhouette definition and interpretation:
  - s_k = (b_k − a_k) / max(a_k, b_k).
  - The silhouette ranges from -1 to 1.
  - High value indicates the point is well assigned to its own cluster and dissimilar to neighboring clusters.
  - A value of 0 indicates that the point is on or very close to the cluster boundary between two neighboring clusters.
  - Negative values indicate points might have been assigned to the wrong cluster.
- Use of average silhouette width:
  - The average silhouette width provides one evaluation of clustering validity and can be used as an input into selecting an appropriate number of clusters.
  - All else equal, one should prefer values of G with larger values of the average silhouette.
  - A desirable characteristic is minimizing potential misclassification; that is, having few observations with zero or negative silhouette.
- Empirical silhouette results reported:
  - Figure A3 plots silhouette values for industries when there are 4 clusters (left panel) and 5 clusters (right panel).
  - The silhouette analysis suggests that either 4 or 5 are good values for the number of clusters.
  - While the average silhouette value is slighly higher for 5 clusters than 4, the silhouette analysis suggests that with 4 clusters fewer industries are potentially miscalssified.

### Reported average silhouette values and improvement using selected variables
- Baseline K-means clustering using all characteristics:
  - The average silhouette value under 4 clusters is about 0.35, which indicates that the cluster structure is somewhat weak.
- K-means clustering using a subset of characteristic variables:
  - Subset used: investment sales share, intermediates sales shares and contract intensity.
  - These variables were identified as especially important through inspection and methods developed in Witten and Tibshirani (2010).
  - The average silhouette value using only that subset is now about 0.65 (Figure A5), suggesting a strong cluster structure.
  - The 4 clusters based on these three characteristics closely replicate the baseline cluster structure reported in Table 1.

### Table A2 (summary statistics of clusters using subset of sector characteristics)
- The source reports the summary statistics in a compact tabular form (rows list characteristic and cluster values; last two columns report overall Mean and Std. Dev.). Preserve numeric entries exactly as printed:
  - cluster 1 2 3 4   Mean  Std. Dev.
  - Investment Share0.01  0.07  0.56  0.05   0.130.22
  - Intermediates, Using   0.70  0.63  0.65  0.63   0.660.16
  - Intermediates, Sales   0.83  0.78  0.28  0.25   0.570.31
  - Concentration Ratio   0.41  0.30  0.34  0.48   0.400.21
  - Skill Intensity0.30  0.31  0.35  0.33   0.320.13
  - Capital Intensity0.64  0.55  0.55  0.64   0.610.10
  - Contract Intensity0.29  0.65  0.72  0.57   0.510.22
  - Number of industries   87    45    42    59
  - Trade share0.38  0.16  0.20  0.19
- Notes (verbatim): "This table reports the summary statistics of the sectoral characteristics among the sectors selected into each cluster, when only a subset of sectoral characteristics is used in the clustering procedure. The last two columns report the mean and standard deviations of those characteristics among all manufacturing sectors. The row “Number of industries” reports the number of sectors in each cluster, and “Trade share” reports the fraction of world trade accounted for by sectors in that cluster."

### Representative sectors (Table A3)
- The source lists the 3 most representative sectors (closest to the cluster centroid) for each cluster; entries preserved verbatim:
  - Cluster  Label Representative Sectors
  - Naics   Description
  - Raw Materials Processing
    - 324199  All Other Petroleum and Coal Products Manufacturing
    - 131131   Sugar Manufacturing
    - 32419   Other Petroleum and Coal Products Manufacturing
  - Complex Intermediates
    - 33512   Lighting Fixture Manufacturing
    - 233531   Electrical Equipment Manufacturing
    - 339994  Broom, Brush, and Mop Manufacturing
  - Capital Goods
    - 333911  Pump and Pumping Equipment Manufacturing
    - 3333994  Industrial Process Furnace and Oven Manufacturing
    - 333992  Welding and Soldering Equipment Manufacturing
  - Consumer Goods
    - 312130  Wineries
    - 4335211  Electric Housewares and Household Fan Manufacturing
    - 33521   Small Electrical Appliance Manufacturing
- Notes (verbatim): "This table lists the 3 sectors closest to the cluster centroid for each cluster."

---

### Estimation of FMA_{ik,t} (foreign Firm Market Access) and gravity framework
- Definition and expression:
  - FMA_{ik,t} for exporter i are expressed as:
    - FMA_{ik,t} = Õ_{n≠i} E_{n,k} P_{n,k}^{1−σ_k} · τ_{i n,k}^{1−σ_k} .
  - Gravity equation (2.3) rewritten as (B.1):
    - E_{i n k,t} ≡ p_{i n k,t} · q_{i n k,t} = c_{i k,t}^{1−σ_k} · E_{n k,t} P_{n k,t}^{1−σ_k} · τ_{i n k,t}^{1−σ_k} .
  - E_{i n k,t} denotes country n’s total sector k expenditure on goods from country i.
- Estimation approach:
  - Estimate share version à la Eaton et al. (2012) by dividing both sides by total imports of country n and regressing bilateral trade flows on exporter and importer fixed effects and bilateral geographic distance measures.
  - Estimating equation corresponds to (4.2) in the main text.
- Addressing endogeneity from large-country shocks:
  - Use a leave-one-out approach: for each country ω, estimate country-ω-specific importer and exporter fixed effects and distance/contiguity coefficients by dropping country ω from the gravity sample on both exporter and importer side.
  - Notation: {κ_m_{n k,t}(ω), κ_x_{i k,t}(ω), ζ_{k t}(ω), ξ_{k t}(ω)} denote estimates when country ω is left out.
  - Authors note in practice this does not affect conclusions; results are very similar if all countries are included.
- Renormalization of fixed effects:
  - Fixed effects of log trade flows are identified only up to a sector-time-specific additive constant; renormalize by restricting the sum of the log importer fixed effects to be zero:
    - ln κ_m_{n k,t}(ω) = ln κ_m_{n k,t}(ω) − ∑_z ln κ_m_{z k,t}(ω) / N_{k t}(ω)
    - where N_{k t}(ω) is the total number of countries with positive imports for industry k and time t when ω is left out.
  - The estimated FMA_{i k,t} is computed as in (4.3), where κ_m_{n k,t} denote the renormalized importer fixed effects when country ω is omitted.
  - These importer fixed effects estimate the destination-n demand shifter E_{n k,t} P_{n k,t}^{1−σ_k} · ∑_{i≠n} E_{i n k,t}.
- Estimation of bilateral iceberg component τ_{i n k,t}^{1−σ_k}:
  - Estimated using bilateral geographic distance and common border dummy and corresponding coefficients.
  - The estimated bilateral component is proxied by Distance_{i n}^{ζ_{k t}} · exp( ξ_{k t} · Contig_{i n} ).

---

### Post-Double-Selection method for growth estimation
- Estimating equation (structural form):
  - d ln y_{i,t} ≈ κ + ∑_{g∈G} δ_x_g · ( λ^x_{i g,t} d ln FMA_{i g,t} ) + ζ d ln a_{i t} + η_x_{i,t} + ε_{i,t} .
  - d ln FMA_{i g,t} = ∑_{k∈G} λ^x_{i k,t} d ln FMA_{i k,t} are the log-differenced market access terms aggregated to cluster level.
  - Time fixed effects and log initial per capita income are “protected regressors” (always included).
- Control variables:
  - x_{i,t} collects industry-level initial equilibrium variables: initial import and export shares (λ^m_{i k,t} and λ^x_{i k,t}), weighted initial firm and consumer market access (λ^x_{i k,t} · ln FMA_{i k,t} and λ^m_{i k,t} · ln CMA_{i k,t}).
  - d ln a_{i t} collects observed contemporaneous foreign supply shocks, i.e., λ^m_{i g,t} d ln CMA_{i g,t}.
- Need for dimension reduction:
  - OLS infeasible given large number of controls relative to sample size.
  - Authors implement the post-double-selection method of Belloni et al. (2014b, 2017).

### Post-double-selection procedure (implementation details)
- Rewriting the equation for method exposition:
  - d ln y_{i,t} = d_{i,t} δ + x_{i,t} β_y + μ_{i,t} , where d_{i,t} denotes the vector of treatment variables λ^x_{i g,t} d ln FMA_{i g,t} and x_{i,t} is the vector of control variables (including d ln a_{i t}).
- Double-selection rationale:
  - Direct LASSO on the main equation may omit controls correlated with treatment leading to bias.
  - Introduce reduced-form for treatment: d_{i,t} = x_{i,t} β_d + v_{i,t} for each element of d_{i,t}.
  - Substitute reduced-form into main equation to show omitted-variable risk and justify selecting controls predictive of both outcome and treatment.
- LASSO selection step:
  - Formulate a joint reduced form z_{i,t} = x_{i,t} β + ε_{i,t}, where z_{i,t} stacks d ln y_{i,t} and all treatment variables d_{i,t}.
  - Feasible double-selection via LASSO defined by minimizing:
    - min_β E(z_{i,t} − x_{i,t} β)^2 + λ_n || L β ||_1
    - where L = diag(l_1, l_2, ..., l_p) is a diagonal matrix of penalty loadings and λ is the penalty level.
  - Select controls with nonzero estimated coefficients.
- Post-selection OLS:
  - Take the union of controls selected from predicting d ln y_{i,t} and each d_{i,t}, then estimate δ_x_g by OLS of d ln y_{i,t} on d_{i,t} and the union of selected controls.

### K-fold cross-validation for penalty selection
- Penalty level λ controls penalization; choose λ by K-fold cross validation following Belloni et al. (2014a) online appendix.
- Procedure (verbatim steps):
  1. Randomly split the data (y_{i,t}, x_{i,t}, d_{i,t}) into K subsets of equal size, S_1, S_2, ... , S_K.
  2. Set the potential tuning parameter set to be [λ_RT −100 : grid : λ_RT +100], where λ_RT = 2.2 sqrt{n Φ(1−γ/2 p)} is the rule of thumb tuning parameter suggested in Belloni et al. (2012, 2014b), γ=0.1/log(p), n is the number of observations, p the number of variables, and grid = 10.
  3. Given λ, for k = 1,2, ... , K:
     - (a) (Training on (y_{i,t}, x_{i,t}, d_{i,t}), i ∉ S_k) Leave the kth subset out, and implement the post-double-selection method with tuning parameter λ on the K−1 subsets. Denote the estimated coefficients as \hat{δ}^{−k}(λ) and \hat{β}^{−k}_y(λ).
     - (b) (Validating on (y_{i,t}, x_{i,t}, d_{i,t}), i ∈ S_k) Given \hat{δ}^{−k}(λ) and \hat{β}^{−k}_y(λ) compute the error in predicting the kth subset,
       - e^k(λ) = ∑_{i ∈ S_k} ( d ln y_{i,t} − d_{i,t} \hat{δ}^{−k}(λ) − x_{i,t} \hat{β}^{−k}_y(λ) )^2 .
  4. This gives the cross-validation error
     - CV(λ) = 1/K ∑_{1}^K e^k(λ).

*Source: wpiea2024051-print-pdf (chapter/section content as provided).*

### 5. For each value of the tuning parameter휆∈[휆

### 5. For each value of the tuning parameter휆∈[휆
푅푇
−100,휆
푅푇
+100], repeat steps 3-4 and choose the tuning parameter that minimizes the퐶푉(휆).

### B.5 Foreign Supply: The Role of퐶푀퐴
- Extension of equation (2.7) to include foreign supply shocks (equation (B.2)):
  - 푑ln푦≈ Õ푘 훿푥푘 · (휆푥푘 dln퐹푀퐴푘) + Õ푘 훿푚푘 · (휆푚푘 dln퐶푀퐴푘). (B.2)
- Definition and construction of external Consumer Market Access terms:
  - From (2.5): 퐶푀퐴푛푘,푡 = Õ푖≠푛 푐1−휎푘 푖푘,푡 · 휏1−휎푘 푖푛푘,푡, with 푛 as importer; the (log)푐1−휎푘 푖푘,푡 is recovered based on exporter fixed effects.
  - After estimating gravity specification (4.2), foreign supply shock constructed as (B.3):
    - 퐶푀퐴푛푘,푡 = Õ푖≠푛 휅푥푖푘,푡 · 퐷푖푠푡푎푛푐푒휁푘푡 푖푛 · exp(휉푘푡 · 퐶표푛푡푖푔푖푛). (B.3)
  - These sectoral price-index components are then aggregated into clusters like foreign demand shocks.
- Empirical findings on foreign supply shocks (Figure A9):
  - Foreign supply shocks have much larger magnitudes and much larger standard errors relative to foreign demand shocks.
  - The large standard errors make it challenging to draw sharp conclusions about the impact of foreign supply shocks on income.
  - The one significant coefficient (on the Consumption goods cluster) does not survive reasonable robustness checks.
- Explanation for differing variation between 퐹푀퐴 and 퐶푀퐴:
  - The variation in the 퐹푀퐴 terms is an order of magnitude larger than the variation in 퐶푀퐴 terms.
  - Economic rationale: 퐹푀퐴 is determined by changes in foreign prices/costs and changes in overall foreign expenditure; 퐶푀퐴 is driven purely by changes in foreign costs.
  - Statistical implication: a regressor with a smaller standard deviation can have a higher point estimate; however, large standard errors imply a relative lack of confidence in those estimates.
- Robustness: Figure A10 results
  - Main results for foreign demand shocks are robust when controlling for the vector of dln퐶푀퐴’s.
  - In the robustness check, foreign supply shocks are treated as “protected” controls (included irrespective of selection by double-LASSO).
  - All double-LASSO estimation admits foreign supply shocks as potential controls.

### B.6 Developed vs. Developing Countries
- Sample split and classification:
  - Countries split using the World Bank’s 2016 country classification by income.
  - Developing countries: “low income” and “lower middle income” categories.
  - Developed countries: remaining group.
  - According to this classification, 70 countries belong to the developed group, and 57 to the developing group (Appendix Table A4).
- Estimation approach:
  - Elasticities of real income with respect to foreign shocks are estimated separately for the developed and developing groups.
- Key findings (Figure A8):
  - For both developed and developing groups, coefficients on demand shocks in complex intermediates are positive and precisely estimated.
  - Magnitude of the complex intermediates coefficient is larger for the developed country group.
  - Capital goods coefficient differs across samples:
    - Developed country sample: capital goods coefficient is slightly smaller than the baseline coefficient.
    - Developing country sample: capital goods coefficient is much larger than the baseline coefficient.
  - Standard errors:
    - The standard error on the capital goods coefficient is actually smaller for the developed country sample than in the full sample.
    - The standard error is larger for the developing country sample.
  - Interpretation: heterogeneity across country subsamples likely contributes to the relatively large standard errors and sensitivity to classification errors observed for the capital coefficient in the full pooled sample.

### C. Additional Appendix Tables and Figures (selected highlights)
- Table A4: Country list and classification:
  - Developed subsample contains 70 countries; developing subsample contains 57 countries (see Appendix Table A4).
- Table A5: Clustering of manufacturing industries (5-cluster grouping) and summary statistics:
  - Reports cluster-specific statistics including “Inv. Share”, “Int. Using”, “Int. Sales”, “Conc. Ratio”, “Sk. Share”, “Cap. Int.”, “Con. Int.”, “Num of ind.”, and “Trade share”.
  - Labels for clusters: Raw Materials Processing (RAW), Complex Intermediates (INT), Capital Goods (CAP), Consumer Goods (CONS), Skill Intensive (SI).
- Table A6 and A7: Controls selected in the double-selection LASSO procedure:
  - Table A6: Baseline estimation — various admissible controls and selected controls; Time effects included; Number of Controls Selected 633; Estimates Figures: Figure 1, Figure A8.
  - Table A7: Robustness checks (Dropping Large Trading Partners; Dropping Neighboring Countries) — Time effects included; Number of Controls Selected 139; Estimates Figures: Figure A6.
- Figures (selected):
  - Figure A6: Cluster-specific coefficients and confidence intervals, robustness to small country assumption (panels for Dropping Large Trading Partners and Dropping Large Exporters).
  - Figure A7: Robustness to spatial correlation (Dropping Neighboring Countries; Controlling for Neighboring Countries’ TFP; Controlling for Unweighted dln퐹푀퐴).
  - Figure A8: Developed vs. Developing Countries (panel (a) Developed Countries; panel (b) Developing Countries).
  - Figure A9: Foreign Supply (퐶푀퐴) — (a) OLS Estimates; (b) LASSO Estimates. Large magnitudes and wide confidence bands reported.
  - Figure A10: Foreign Demand (퐹푀퐴) controlling for foreign supply — (a) OLS Estimates; (b) LASSO Estimates. Main findings robust when controlling for 퐶푀퐴.
  - Figure A11: Results when grouping manufacturing industries to 5 clusters (OLS and LASSO panels).
  - Figure A12: First order gains from export and production subsidies, heterogeneous 휎푘 — Gains computed using formulas (2.9) and (A.17); cluster-specific elasticities 휎푘 sourced from Caliendo and Parro (2015), concorded to our 6 clusters.

*Specialization, Market Access and Real Income — Working Paper No. WP/2024/051*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024051-print-pdf.pdf_