## wpiea2021091-print-pdf

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---

### Introduction, objectives, and dataset
- Primary objective: demonstrate that reducing international trade costs increases matches in the international market and alleviates congestion in the domestic supplier market, producing consumer welfare gains.
- Data: Ugandan administrative tax data combining Value-Added Tax (VAT) receipts and Customs receipts to form a dynamic transaction-level firm-to-firm input-output matrix for the formal economy from "2010" to "2016".
- Novelty claims:
  - First paper to combine this breadth of administrative firm-level transaction-data in a developing country.
  - Compares domestic and international search externalities and provides structural evidence that they differ between markets.

### Key descriptive statistics and context
- Consolidated dataset totals:
  - 7,000 import buyers
  - 13,000 domestic buyers
  - 24,000 foreign suppliers
  - 86,000 domestic suppliers
  - Over 12 million transactions
  - Over 490,000 firm-to-firm connections
- From Table 1 (Import sample — All firms / Retailers):
  - Number of buyers: 6788 / 2631
  - Number of suppliers: 24133 / 10008
  - Number of buyers (>3 matches): 3373 / 1410
  - Number of suppliers (>3 matches): 3451 / 1009
  - Firm-to-firm connections: 71,000 / 23,000
  - Transactions: 1.3m / 0.42m
  - Mean Age: 8.7 / 8.2
  - Median Wage Bill (USH): 422m / 123m
  - Median Sales (USH): 8.6b / 6.5b
- From Table 1 (Domestic sample — All firms / Retailers):
  - Number of buyers: 6293 / 9843
  - Number of suppliers: 8688 / 926139
  - Number of buyers (>3 matches): 4294 / 1928
  - Number of suppliers (>3 matches): 1729 / 37008
  - Firm-to-firm connections: 420,000 / 116,000
  - Transactions: 11m / 2.4m
  - Mean Age: 8.5 / 7.4
  - Median Wage Bill (USH): 283m / 97m
  - Median Sales (USH): 5.6b / 5.6b
- On average, each Ugandan firm has 2.7 domestic suppliers.
- Ugandan economic composition (World Bank, 2019):
  - Services: 56.6%
  - Agriculture, forestry and fishing: 24.2%
  - Industry: 19.2%
- Openness: imports reached 25.9% as a share of GDP in 2016/17 (International Monetary Fund, 2019).
- Trade-cost shock context:
  - In 2011 reforms, cost to import a 20-foot container fell from USD5807 to USD4396 (-24.3%), described as a 25% fall in transport costs.

### Reduced-form empirical findings (search externalities)
- Spatial diffusion and same-building facts:
  - 21% of suppliers’ new matches with domestic or foreign suppliers are in the same building as an existing customer.
  - Expanding neighborhood to same or next-door buildings increases proportion to 25% (an increase of 4 percentage points).
- Foreign suppliers (Table 2; coefficients multiplied by 100 to read as percentage point marginal effects):
  - Baseline probability of a match (foreign suppliers): 0.0039
  - Column (1): X_same−building_if,t−1: 0.0847 ∗∗∗ (0.0262); X_other−city_if,t−1: -0.00106 (0.00173); Observations: 4197300
  - Column (2): X_same−building_if,t−1: 0.0848 ∗∗∗ (0.0263); X_nextdoor_if,t−1: 0.000685 (0.00437); X_other−city_if,t−1: -0.00108 (0.00174); Observations: 4197300
  - Interpretation: each additional importer using foreign supplier f within the same building increases the probability of buyer i matching with supplier f by 0.085 percentage points; same-building marginal effect far larger than next-door.
- Domestic suppliers (Table 3; coefficients multiplied by 100):
  - Baseline probability of a match (domestic suppliers): 0.0040
  - Column (1): X_same−building_if,t−1: 0.00398 (0.0271); X_other−city_if,t−1: -0.00347 ∗∗∗ (0.000116); Observations: 11275450
  - Column (2): X_same−building_if,t−1: 0.00325 (0.0277); X_nextdoor_if,t−1: -0.00146 (0.00430); X_other−city_if,t−1: -0.00329 ∗∗∗ (0.00124); Observations: 11275450
  - Interpretation: same-building coefficient not statistically different from zero for domestic suppliers; evidence of negative congestion from buyers in other cities (an additional buyer in a different city decreases matching probability by 0.003 percentage points).
- Mechanism evidence:
  - Results consistent with information diffusion among nearby firms for international sourcing and greater congestion and supply-constraints in domestic markets.
  - Appendix D robustness: neighborhood regressions at 10km, 1km, next-door, same building show foreign-supplier spatial effects robust; balance tests suggest agglomeration at block rather than building level, not driving same-building contrast.

### Structural model overview (two-market buyer–supplier search)
- Populations and setup:
  - measure B continuum of buyers; S_D continuum of domestic suppliers; S_I continuum of international suppliers; simple assumption S_D = S_I = S in base model.
  - Buyers choose fixed search intensity σ and allocation a ∈ [0,1] (domestic share a, international share 1−a).
  - Iceberg trade costs: τ_I on international goods; τ_D normalized to 1.
- Matching technology:
  - Aggregate matches:
    - X_D = S^{γ_S} B_D^{γ_B}
    - X_I = S^{β_S} B_I^{β_B}
  - Market tightness:
    - θ_D = S^{γ_S} B_D^{γ_B} / B_D
    - θ_I = S^{β_S} B_I^{β_B} / B_I
  - Interpretation: γ and β exponents capture returns to scale and congestion; γ_S + γ_B < 1 implies decreasing returns (congestion) in domestic matching; β_S + β_B > 1 implies increasing returns in international matching.
- Buyer optimization (simple model):
  - Buyers maximize expected profit: max_a { a σ θ_D Λ π(s_D) + (1−a) σ θ_I Λ π(s_I) − k(a) } with convex search cost k(a).
  - First-order condition equates marginal expected profit across domestic and international search net of marginal search cost.

### Structural estimation and calibrated parameters
- Transfer-equation estimates (Table 4; N = 34016):
  - Column (1) OLS-FE: coefficient on ln h_{j|i,t} = 0.882 (0.0360) ∗∗∗
  - Column (2) IV-FE: coefficient on ln h_{j|i,t} = 0.910 (0.0411) ∗∗∗
  - Column (3) OLS-FE (full fixed effects): coefficient on ln h_{j|i,t} = 0.882 (0.0360) ∗∗∗; coefficient on ln n_it in column (3): -0.275 (0.0369) ∗∗∗
  - Implied values: using column 3 and α = 4.35 implies η = 3.45.
- Externally calibrated parameters (Table 5):
  - α = 4.35; η = 3.45; Λ = 0.5; v = 2; δ = 0.4; τ = 1.45; κ = 1.45; ρ = 0.05.
- Internally calibrated (SMM) estimates (Table 5; key entries):
  - I Import premium = 1.14 (0.080)
  - F International fixed cost = 0.26 (0.027)
  - γ_B^D = 0.49 (0.025)
  - γ_S^D = 0.46 (0.045)
  - β_B^I = 0.56 (0.049)
  - β_S^I = 0.70 (0.052)
  - Interpretation: domestic market exhibits decreasing returns to search (γ_S + γ_B < 1); international market exhibits increasing returns to search (β_S + β_B > 1).

### Model fit and heterogeneity
- Targeted vs data moments (Table 6; select comparisons):
  - Ratio of imports to domestic among importers: Model 0.59 vs Data 0.59
  - Proportion of firms which import: Model 0.20 vs Data 0.21
  - Mass of international suppliers: Model 0.30 vs Data 0.21
  - Mass of domestic suppliers: Model 0.26 vs Data 0.34
  - Prob. of a new match for international suppliers: Model 0.23 vs Data 0.26
  - Prob. of a new match for domestic supplier: Model 0.14 vs Data 0.22
- Heterogeneity (Figure 6):
  - Only lowest marginal cost firms pay fixed cost and import; convex search costs produce multi-market search for lowest-cost firms; marginal-cost bin 2 shows peak domestic search before import cutoff.

### Counterfactual simulations — transport-cost reduction (25% fall)
- Experiment 1 — 25% reduction in transport costs under estimated (IRS) matching:
  - Percentage of Importers: 21.2 → 24.6; Change 16%; Data 14%
  - Av. Foreign Suppliers: 2.10 → 2.37; Change 13%; Data 16%
  - Av. Domestic Suppliers: 2.90 → 2.78; Change -4.2%; Data -1.6%
  - Domestic Search (aσ): 0.12 → 0.11; Change -3.1%
  - Import Search ((1−a)σ): 0.71 → 0.84; Change 19%
  - Consumer Welfare: 3.7%
  - Mechanisms: increased import search and matches; existing importers increase international search; domestic market loosens allowing some higher-marginal-cost firms to increase domestic search.
- Experiment 2 — 25% transport-cost reduction under constant returns to scale (CRS) matching:
  - Comparative outcomes:
    - Percentage of Importers: IRS 16% vs CRS 13%
    - Av. Foreign Suppliers: IRS 13% vs CRS 9%
    - Av. Domestic Suppliers: IRS -4.2% vs CRS -6.1%
    - Domestic Search (aσ): IRS -3.1% vs CRS -4.1%
    - Import Search ((1−a)σ): IRS 19% vs CRS 16%
    - Consumer Welfare: IRS 3.7% vs CRS 3.3%
  - Interpretation: shutting down search externalities (CRS) reduces gains in foreign matches and lowers consumer welfare by "12%" relative to IRS in a 25% trade-cost reduction scenario; international increasing returns amplify matching and welfare effects.

### Counterfactual simulations — 25% search-cost reductions (Experiment 3; Table 9)
- Two scenarios: 25% reduction in domestic search costs vs 25% reduction in international search costs.
- Outcomes (change following 25% decrease in domestic search costs / change following 25% decrease in import search costs):
  - Percentage of Importers: -0.30% / 14.4%
  - Av. Foreign Suppliers: -0.52% / 19.1%
  - Av. Domestic Suppliers: 10.5% / -3.50%
  - Domestic Search (aσ): 10.2% / -1.82%
  - Import Search ((1−a)σ): -0.90% / 30.6%
  - Consumer Welfare: 2.2% / 3.7%
- Dynamics by marginal cost:
  - Reducing domestic search costs raises domestic search across all marginal-cost bins and increases domestic suppliers by 10.5%, but increases domestic congestion and only modestly raises welfare (2.2%).
  - Reducing international search costs raises import search by 30.6%, increases foreign suppliers by 19.1%, and raises consumer welfare by 3.7%; effects concentrated among low marginal-cost firms.
- Policy interpretation: targeting international search channels yields larger increases in matches and welfare than targeting domestic search channels due to domestic congestion effects.

### Policy implications and recommendations
- Trade liberalization lowering international trade costs produces consumer welfare gains via:
  - Direct access to foreign suppliers and lower marginal costs.
  - Reallocation of search away from a congested domestic market toward an international market with increasing returns to search, increasing matching efficiency.
- Policies to reduce search costs should prioritize international search channels (e.g., training on platforms like Ali Baba, promoting peer-to-peer learning, targeted supplier-development and anchor-firm support), since reducing domestic search costs alone can exacerbate domestic congestion and yield smaller welfare gains.
- Government of Uganda (2019) type interventions (internet platform training, peer groups, anchor firm support) can complement trade-cost reductions and produce sizable welfare gains.

### Literature and contribution
- Advances firm-to-firm search literature by modeling separate domestic and international search with different matching technologies.
- Extends quantitative trade literature on firm supply chains by incorporating a search channel together with intermediate goods.
- Empirically contributes detailed geographic and matched-supplier evidence from Uganda, documenting both positive local information spillovers for international suppliers and negative congestion externalities in domestic markets.

*Italic: Source — wpiea2021091-print-pdf*

### References  ............................................................................................................

### References and Appendix

### Appendix structure and contents
- References section spans page "55".
- Appendix begins on page "60" and contains:
  - A Context Appendix (starts page "60")
    - A.1. Map of Trade Corridor (page "60")
    - A.2. Data Comparison (page "60")
  - B A Quantitative Model of Buyer-Supplier Search in Two Markets (starts page "62")
    - B.1. Buyers and Suppliers (page "62")
    - B.2. Consumers (page "62")
    - B.3. Pricing and Division of Profits (page "63")
    - B.4. Search and Matching (page "65")
    - B.5. Search Cost (page "66")
    - B.6. Optimal Search (page "67")
      - B.6.1. Equilibrium (page "69")
  - C Mathematical Appendix (starts page "71")
    - C.1. Comparative Statics in the Two-Period Model (page "71")
      - C.1.1. Reallocation (page "71")
      - C.1.2. Matching Efficiency (page "72")
    - C.2. Transfer Equation (page "73")
  - D Empirical Appendix (starts page "74")
    - D.1. Descriptive Statistics (page "74")
    - D.2. Robustness Tests (page "74")
      - D.2.1. Alternative Specifications (page "74")
      - D.2.2. Very Local Shocks Drive Results (page "77")
      - D.2.3. Spillover Exists But is Not Search Related (page "77")

### List of Tables (selected entries and page references)
- Table 1 Descriptive Statistics (page "14")
- Table 2 Foreign Suppliers (page "20")
- Table 3 Domestic Suppliers (page "21")
- Table 4 Estimating the Transfer Equation (page "40")
- Table 5 Model Parameters (page "41")
- Table 6 Model Fit (page "42")
- Table 7 Outcomes from 25% Transport Cost Reduction (page "46")
- Table 8 Outcomes from 25% Transport Cost Reduction Under Different Matching Functions (page "49")
- Table 9 Outcomes from 25% Search Cost Reduction (page "50")
- Tables 10–14 (pages "75"–"79") reporting additional supplier and balance-table details

### List of Figures (selected entries and page references)
- Figure 1 Locations of firms in Uganda (page "13")
- Figure 2 Transport Costs and Imports (page "16")
- Figure 3 Percentage of suppliers’ matches which have an existing buyer in location (page "17")
- Figure 4 Model Environment (page "23")
- Figure 5 Model fit: buyer and supplier out-degree (page "44")
- Figures 6–13 analyze search by marginal cost, mass of firms with S_I international suppliers and S_D domestic suppliers, and welfare comparisons under CRS vs. IRS (pages "45"–"52")
- Figure 14 Map of trade corridor, Osawa, WCO (page "60")
- Figure 15 Exports data comparison (page "61")
- Figure 16 GDP and total output (page "61")
- Figure 17 Transport Costs and Imports (page "74")

### Introduction — key objectives and dataset
- Primary objective: demonstrate that reducing international trade costs increases matches in the international market and alleviates congestion in the domestic supplier market, producing consumer welfare gains.
- Data: Ugandan administrative tax data combining Value-Added Tax (VAT) receipts and Customs receipts to form a dynamic transaction-level firm-to-firm input-output matrix for the formal economy from "2010" to "2016".
- Novelty claims:
  - First paper to combine this breadth of administrative firm-level transaction-data in a developing country.
  - Compares domestic and international search externalities and provides structural evidence that they differ between markets.

### Empirical findings (reduced-form evidence)
- Firms located in the same building sequentially adopt the same foreign suppliers; effect is substantially larger for same-building than next-door building.
- For domestic suppliers:
  - The positive same-building effect is not significantly different from zero.
  - A buyer adding a specific new domestic supplier reduces the probability of buyers in a different region matching with that supplier (consistent with a congestion externality).
- These patterns are consistent with:
  - Information diffusion among nearby firms for international sourcing.
  - Greater congestion and supply-constraints in domestic markets.

### Model overview and structural estimation
- Model: dynamic quantitative model of optimal search in two markets (domestic and international) extending Eaton, Jinkins, Tybout and Xu (2016) with:
  - Market-specific matching functions.
  - Firm heterogeneity.
  - Search cost structure and endogenous search intensity and market allocation.
- Key structural calibration/estimation results:
  - Decreasing returns to scale to searching in domestic markets.
  - Increasing returns to scale to searching in international markets.
  - These parameter signs are consistent with reduced-form evidence.

### Policy experiments and quantitative counterfactuals
- Simulation of a 25% reduction in transport costs (mimicking East African Community reforms in "2010-2011"):
  - Proportion of firms that import increases from "21%" to "25%".
  - Average number of foreign suppliers increases by "13%".
  - Average number of domestic suppliers decreases by "4.2%".
  - Simulation direction and magnitude align with observed data.
- Counterfactual 1: impose constant returns to scale (CRS) matching in both markets versus estimated increasing/decreasing returns (IRS):
  - Average number of foreign suppliers increases by "9%" under CRS versus "13%" under IRS.
  - Average number of domestic suppliers decreases by "-6.1%" under CRS versus "-4.2%" under IRS.
  - Consumer welfare gain is "12%" smaller when search externalities are shut down (CRS) compared to structurally estimated parameters (IRS).
- Counterfactual 2: government reduces search costs by "25%" (Government of Uganda, 2019 target):
  - Consumer welfare increases by "2-4%", depending on targeting.
  - Reducing international search costs yields larger increases in matches and welfare than reducing domestic search costs because domestic reductions are dampened by increased domestic congestion.

### Policy implications and recommendations
- Trade liberalization that lowers international trade costs can produce consumer welfare gains not only via direct access to foreign suppliers but also by reducing domestic congestion externalities.
- Policies aimed at reducing search costs should consider targeting international search channels where positive externalities and increasing returns to search exist.
- Targeted supplier development and peer-learning interventions (examples of sub-targets listed in Government of Uganda, 2019) can complement trade-cost reductions.

### Literature contributions
- Advances firm-to-firm search literature by modeling separate domestic and international search with different matching technologies.
- Extends quantitative trade literature on firm supply chains by incorporating a search channel together with intermediate goods.
- Empirically contributes by providing detailed geographic and matched-supplier evidence from Uganda and documenting both positive and negative search externalities.

*Italic: References, Appendices, Figures and Tables as listed in the source document.*

### 2. Data, Context and Descriptive Statistics

### 2. Data, Context and Descriptive Statistics

### Datasets
- Four linked URA administrative tax datasets covering 2010-2016, confidential and linked via unique tax identification numbers; represent the universe of formal-sector firms and the universe of importing firms in Uganda. Inference on the informal sector is outside scope.
- Dataset 1: domestic firm transactions (VAT transaction-level) — line-by-line account of goods transacted, value, date, and transacting firm tax ID; constitutes a dynamic input-output matrix for the formal economy.
- Dataset 2: transaction-level international trade data — includes import origin, value, product, and matched foreign exporter.
- Dataset 3: monthly balance-sheet data from VAT records (2010-2016) — firms report total sales and total inputs monthly; variables winsorized at the 5% level and collapsed to annual frequency.
- Dataset 4: firm registration dataset — contains ISIC 4-digit industrial sector classification, description of main operations, and firm addresses (geolocated using Google Maps API).
- Sample restriction: include buyer firms registered as retailers and suppliers which sell to retailers to observe buyer–supplier pairs that are less likely to be in long supply-chains.

### Consolidated sample and descriptive statistics
- Consolidated dataset totals:
  - 7,000 import buyers
  - 13,000 domestic buyers
  - 24,000 foreign suppliers
  - 86,000 domestic suppliers
  - Over 12 million transactions
  - Over 490,000 firm-to-firm connections
- Restricting to buyers which are retailers reduces the number of firms by roughly two thirds; on average, retailers are younger, have a lower wage bill and have lower sales.
- From Table 1 (data combined from Uganda administrative tax datasets from 2010-2016):
  - Import sample — All firms / Retailers:
    - Number of buyers: 6788 / 2631
    - Number of suppliers: 24133 / 10008
    - Number of buyers (>3 matches): 3373 / 1410
    - Number of suppliers (>3 matches): 3451 / 1009
    - Firm-to-firm connections: 71,000 / 23,000
    - Transactions: 1.3m / 0.42m
    - Mean Age: 8.7 / 8.2
    - Median Wage Bill (USH): 422m / 123m
    - Median Sales (USH): 8.6b / 6.5b
  - Domestic sample — All firms / Retailers:
    - Number of buyers: 6293 / 9843 [as shown in table layout]
    - Number of suppliers: 8688 / 926139 [note: preserve numeric tokens exactly as presented in the table]
    - Number of buyers (>3 matches): 4294 / 1928
    - Number of suppliers (>3 matches): 1729 / 37008
    - Firm-to-firm connections: 420,000 / 116,000
    - Transactions: 11m / 2.4m
    - Mean Age: 8.5 / 7.4
    - Median Wage Bill (USH): 283m / 97m
    - Median Sales (USH): 5.6b / 5.6b
- On average, each Ugandan firm has 2.7 domestic suppliers.
- Sectors with largest number of connections include construction services, telecommunication services, accounting services, manufacturing of plastic products, metals, and paper products.

### Ugandan economic context (as described)
- Economic composition (World Bank, 2019):
  - Services: 56.6%
  - Agriculture, forestry and fishing: 24.2%
  - Industry: 19.2%
- Openness: imports reached 25.9% as a share of GDP in 2016/17 (International Monetary Fund, 2019).
- Import composition: largest components are consumables and capital goods for investment (World Bank, 2019).
- Importer characteristics: importers are on average larger than firms who only source domestically, with median sales and wage bill 1.5 and 2.5 times higher, respectively.
- Retail sector: primarily made up of firms with lower sales and smaller wage bills than the average Ugandan firm; younger on average; import final products such as building materials, food and beverages, and general merchandise. Biggest importing countries: China, India, UAE, Kenya and Japan.
- Trade costs and corridors:
  - Uganda ranked 136 out of 190 countries on World Bank’s Trading Across Border Index in 2017 (World Bank, 2016).
  - Majority of goods entering Uganda transit through the port of Mombasa, Kenya.
  - In 2010, 68% of Ugandan imports arrived from the Kenyan border (customs dataset); 25% arrived through the airport; remainder through Tanzanian, Rwandan, Congolese borders or lake port in Jinja.
  - Typical overland transit: goods transported over 1000km by road through Kenya before crossing the border into Uganda.
- 2011 reforms and impacts:
  - Reforms included longer border opening hours, improved port infrastructure at Mombasa, EU-funded road rehabilitation, and removal of several weighbridges.
  - Resulted in a 25% fall in transport costs in 2011; cost to import a 20-foot container fell from USD5807 to USD4396 (-24.3%).
  - The fall in transport costs corresponded with a rapid increase in the number of new importers and with an increase in the proportion of firms which are importers and in the number of foreign suppliers per firm.

### Research novelty and comparability
- To the author’s knowledge, first paper to link VAT transaction-level data with firm employee and importer–exporter matched customs data for Uganda, allowing observation of a complete and dynamic picture of the formal economy.
- Appendix A.2 compares the tax data used in this study to other freely-available data sources on firms in Uganda to address consistency concerns.

---

### Empirical evidence of search externalities — motivating evidence
- Figure 3 descriptive fact: 21% of suppliers’ new matches with domestic or foreign suppliers are in the same building as an existing customer.
- Expanding neighborhood to same or next-door buildings increases proportion to 25% (an increase of 4 percentage points), indicating much tighter proximity within the same building versus next-door buildings.

### Empirical strategy and sample construction
- Construct dataset of every buyer–supplier–year triplet separately for domestic and international suppliers; raw generation yields 6.8 billion observations given over 13,000 domestic buyers and 86,000 domestic suppliers over 6 years.
- Trim sample to likely matches:
  - Drop suppliers which have never sold to the buyer’s ISIC 4-digit industry.
  - Drop any buyer or supplier which does not make at least three matches over the entire sample period.
  - Drop observations from the sample following the first observed match (sample considers only first-time matches between active firms in likely-trading sectors).
  - Consider only matches where the buyer is the retailer (consistent with buyer–supplier relationship, not longer supply-chains).

### Main econometric specification
- Linear probability model (equation 1):
  - Y_ift = μ1 X_same−building_if,t−1 + μ2 X_nextdoor_if,t−1 + γ X_other−city_if,t−1 + α_i + δ_t + u_ift
  - Y_ift: dummy = 1 if buyer i adds supplier f for the first time in period t.
  - X_same−building_if,t−1: count of number of firms who matched with supplier f in i’s same building in period t−1.
  - X_nextdoor_if,t−1: count of number of firms who matched with supplier f in i’s next-door building in period t−1.
  - X_other−city_i,t−1: count of number of firms who added supplier f in t−1 but are not in i’s city.
  - Buyer and time fixed effects (α_i and δ_t) included.
  - Interpretation:
    - μ1 > 0 consistent with a positive local information externality.
    - μ1 > μ2 > 0 strengthens evidence of local information diffusion (same building vs next-door).
    - γ < 0 consistent with a negative congestion externality (capacity constraints) from matches elsewhere in the country.

### Main results — foreign suppliers (Table 2)
- Baseline probabilities: foreign suppliers sample baseline probability of a match = 0.0039; domestic suppliers = 0.0040.
- Table 2 coefficients (coefficients multiplied by 100 to read as percentage point marginal effects; standard errors clustered at buyer level):
  - Column (1):
    - X_same−building_if,t−1: 0.0847 ∗∗∗ (0.0262)
    - X_nextdoor_if,t−1: (not included in col 1)
    - X_other−city_if,t−1: -0.00106 (0.00173)
    - Observations: 4197300
    - Year and Firm FE: YES
  - Column (2):
    - X_same−building_if,t−1: 0.0848 ∗∗∗ (0.0263)
    - X_nextdoor_if,t−1: 0.000685 (0.00437)
    - X_other−city_if,t−1: -0.00108 (0.00174)
    - Observations: 4197300
    - Year and Firm FE: YES
- Interpretation:
  - Each additional importer using foreign supplier f within the same building increases the probability of buyer i matching with supplier f by 0.085 percentage points.
  - The same-building marginal effect (0.085%) is much larger than next-door building (0.0007%), consistent with a strong local information spillover within buildings.
  - No statistically significant evidence of negative congestion from buyers in other cities for foreign suppliers in these specifications.

### Main results — domestic suppliers (Table 3)
- Table 3 coefficients (coefficients multiplied by 100 to read as percentage point marginal effects; standard errors clustered at buyer level):
  - Column (1):
    - X_same−building_if,t−1: 0.00398 (0.0271)
    - X_other−city_if,t−1: -0.00347 ∗∗∗ (0.000116)
    - Observations: 11275450
    - Year and Firm FE: YES
  - Column (2):
    - X_same−building_if,t−1: 0.00325 (0.0277)
    - X_nextdoor_if,t−1: -0.00146 (0.00430)
    - X_other−city_if,t−1: -0.00329 ∗∗∗ (0.00124)
    - Observations: 11275450
    - Year and Firm FE: YES
- Interpretation:
  - The same-building coefficient is smaller and not statistically different from zero for domestic suppliers; magnitude much smaller than in the import case.
  - Evidence of congestion: an additional buyer in a different city in the previous year decreases the probability of matching by 0.003% (statistically significant at the 1% level).
  - Overall: results consistent with a positive search externality in international markets (notably within-building information diffusion for foreign suppliers) and a negative congestion externality in domestic markets.

### Mechanisms and alternative explanations
- Two main alternative explanations considered:
  1. Very local shocks (industry clustering within buildings) driving results.
     - Appendix Table 12 compares the proportion of firms in the same ISIC 4-digit sector in the same building versus next-door building: small difference, not statistically significant; agglomeration appears to occur at block level, not building level.
     - The agglomeration decreases over space, and the impact of an additional buyer in the neighborhood does not dramatically decrease between columns 1 and 3 of Table 10 (appendix), suggesting local shocks are not the primary concern.
  2. Spillovers exist but are not search related.
     - Appendix Table 13 interacts independent variables with whether the foreign supplier exported from the East African Community (EAC); expectation is that search frictions are smaller for suppliers exporting from EAC (e.g., Kenya) compared to more distant locations.
- Additional mechanism: capacity constraints of suppliers imply that suppliers not supply-constrained can match with multiple buyers and would not generate a negative congestion effect — consistent with the absence of strong congestion externality for foreign suppliers (characterized as large firms with cheap access to credit and multiple customers).

*Source: wpiea2021091-print-pdf - 2. Data, Context and Descriptive Statistics*

### Appendix Table14 show that domestic suppliers which are exporters, and hence less

### wpiea2021091-print-pdf - Appendix Table14 show that domestic suppliers which are exporters, and hence less

### Model environment and purpose
- Illustrates how search externalities differ between domestic and international firm-to-firm markets and how these externalities affect welfare following a trade cost reduction.
- Graphical representation: Buyers, Domestic Suppliers, International Suppliers, Matching, Buyers → Consumers, Varieties, Search (Figure 4).

### Buyers, suppliers, and consumers (Section 4.1)
- Populations:
  - measure B continuum of buyers.
  - measure S_D continuum of domestic suppliers and measure S_I continuum of international suppliers.
  - Simple model assumption: S_D = S_I = S.
- Suppliers: each produces one differentiated product; international suppliers produce higher quality but pay higher transportation cost.
- Trade costs:
  - Buyers pay iceberg trade cost τ_I on international goods and τ_D on domestic goods, with normalization τ_D = 1.
- Buyer search:
  - Buyers begin with marginal cost c and no matches.
  - Buyers have fixed search intensity σ and choose proportion a ∈ [0,1] to exert domestically and 1−a internationally.
- Consumer demand:
  - CES utility over products sold by buyers:
    C = [ ∫_{b∈B(s_I)} ψ_I C_b^{η−1/η} + ∫_{b∈B(s_D)} C_b^{η−1/η} ]^{η/(η−1)}
  - Assumptions: all international products share demand shifter ψ_I and all domestic products share ψ_D normalized to 1.
  - η > 1 is the elasticity of substitution (does not vary between imports and domestic products).

### Pricing and division of profits (Section 4.2)
- Bertrand competition in retail market yields CES constant mark-up rule:
  - (p_b − c_b) / p_b = 1 / η.
- Instantaneous profit flow for a buyer and matched supplier (L ∈ {D,I}):
  - π(s_L) = E η P^{1−η} [ (η/(η−1)) τ_L c_L ]^{1−η}
  - If domestic good: τ_D = ψ_D = 1.
  - Higher τ_I or smaller ψ_I → profits from international matches are smaller.
- Profit split: Nash bargaining with Λ ∈ [0,1] as seller’s bargaining coefficient and 1−Λ for buyer; avoids double marginalization inefficiencies.

### Search and matching (Section 4.3)
- Aggregate matching functions homogeneous of degree one in search:
  - Aggregate buyers’ search in each market: B_D = a σ B and B_I = (1−a) σ B.
  - Aggregate matches per unit time:
    - X_D = S^{γ_S} B_D^{γ_B}
    - X_I = S^{β_S} B_I^{β_B}
- Interpretation of exponents:
  - Positive externality to search indicated by high γ_S, γ_B, β_S, β_B.
  - Increasing returns to scale in domestic matching if γ_S + γ_B > 1; decreasing returns if γ_S + γ_B < 1.
  - Low γ_S indicates congestion on domestic supplier-side; low γ_B indicates congestion among domestic buyers.
- Match flow per unit of buyer search (market tightness):
  - θ_D = S^{γ_S} B_D^{γ_B} / B_D
  - θ_I = S^{β_S} B_I^{β_B} / B_I
  - Higher θ implies higher hazard-rate of finding a match.

### Optimal search (Section 4.4)
- Buyers maximize expected profits by choosing a to maximize:
  - max_a { a σ θ_D Λ π(s_D) + (1−a) σ θ_I Λ π(s_I) − k(a) }
- Search cost k(a): convex with ∂^2 k / ∂a^2 > 0 and minimized at a = 1/2.
- First-order condition (policy function):
  - σ θ_D Λ π(s_D) − σ θ_I Λ π(s_I) − ∂k/∂a = 0
- Interpretation: buyers equate expected profit flows (profit × match probability) across domestic and international search margins net of marginal search cost.

### Comparative statics: trade cost reduction (Section 4.5)
- Focus: effect of a reduction in τ_I (transport costs) on search allocation and welfare.

- Change in domestic search share ∂a/∂τ_I (Equation 10):
  - ∂a/∂τ_I = −σ θ_I Λ ∂π(s_I)/∂τ_I / [ σ^2 (1−β_B) θ_I B_I Λ π(s_I) + σ^2 (1−γ_B) θ_D B_D Λ π(s_D) + ∂^2 k / ∂a^2 ]
  - Interpretation:
    - Direct effect: fall in τ_I increases returns to importing, so a falls (firms shift away from domestic search).
    - Mitigating forces:
      - International congestion: as firms increase import search, θ_I increases via ∂θ_I/∂a, reducing marginal returns to further import search.
      - Domestic loosening: firms leaving domestic market increase ease of matching domestically via ∂θ_D/∂a, which reduces reallocation to imports.
- Role of matching exponents:
  - If β_B < 1, each additional buyer in international market reduces probability of other firms matching only slightly → international market can absorb many buyers before tightness rises.
  - If β_B > 1, each additional buyer in international market increases chance of existing buyers matching (positive externality).
  - If domestic externality γ is small (negative externality), leaving domestic market substantially reduces domestic market tightness, making domestic matching easier and dampening reallocation to imports.

### Consumer welfare and matching efficiency (Section 4.5.2)
- Consumer welfare W(a) decomposed into matching probability A and consumption C:
  - W(a) = [ a σ θ_D + ψ_I (1−a) σ θ_I ] × [ ∫_{b∈B} C_b^{η−1/η} ]^{η/(η−1)} = A × C
- Welfare channels from fall in τ_I:
  - Marginal-cost channel: ∂C/∂τ_I < 0 (lower trade costs raise consumption).
  - Matching channel: ∂A/∂τ_I captures how matching probabilities change with trade costs.
- Necessary and sufficient condition for matching-driven welfare gain (Equation 12):
  - ∂A/∂τ_I < 0 ⇐⇒ a^{γ_B−1} < (1−a)^{β_B−1} ψ_I S^{β_S−γ_S} B^{β_B−γ_B} / β_B^{γ_B}
  - Practical implication: for sufficiently large a and ψ_I ≥ 1, if γ_B < β_B and γ_S < β_S (returns to search higher in international market), a fall in trade costs increases welfare because search reallocates from a decreasing-returns domestic market to an increasing-returns international market, increasing matches for the same search intensity and raising consumer welfare via greater variety.

### Summary of mechanisms
- Fall in international trade costs:
  - Directly raises attractiveness of international matches (reduces τ_I → increases π(s_I)).
  - Induces reallocation of buyer search from domestic to international (a falls), moderated by congestion and changes in domestic tightness.
  - Net welfare effect depends on:
    - Relative sizes of matching exponents (γ_S, γ_B versus β_S, β_B).
    - Demand shifter for imports ψ_I and initial search allocation a.
    - Convexity of search costs k(a).

*Source: Excerpt from the PDF chapter "4. A Simple Model of Firm-to-Firm Search in Two Markets" (wpiea2021091-print-pdf).*

### 5. A Quantitative Model of Buyer-Supplier Search in Two

### 5. A Quantitative Model of Buyer-Supplier Search in Two Markets

### Model extensions and purpose
- Three motivations for building the full dynamic structural model:
  - The structurally estimated parameters substantiate reduced-form findings using a different yet complementary methodology.
  - The structural model elucidates mechanisms in how firms in Uganda respond to international trade cost reduction.
  - The model provides a quantitative estimate of the role of search externalities in welfare relative to a counterfactual that shuts down this channel.
- Three main extensions to the simple model:
  - The model is dynamic to allow firms to make multiple matches over time.
  - The model includes both buyer and seller search to capture both sides of the market.
  - The model incorporates buyer heterogeneity so only a subset of the most productive firms import.

### Buyers, suppliers, and consumers
- Buyer heterogeneity:
  - There are Γ buyer types indexed i ∈ {1,2,...,Γ} with marginal cost c_i drawn from a known distribution.
  - Buyers match with s = {s_I, s_D} suppliers.
- Consumer preferences and variety:
  - Consumers have nested CES utility over buyers (b) and products (x):
    - Aggregate: C = [∫_{b∈B} C_b^{η−1/η}]^{η/(η−1)} (equation 13).
    - Within-buyer product bundle:
      - C_b = [ ∑_{x∈J(s_I)_b} (ψ_I C_{x b})^{α−1/α} + ∑_{x∈J(s_D)_b} (C_{x b})^{α−1/α} ]^{α/(α−1)} (equation 14).
  - η and α are elasticities of substitution among products and buyers, respectively.
  - J(s_I)_b and J(s_D)_b denote sets of international and domestic products offered by buyer b.
  - ψ_I is an international demand shifter; for domestic suppliers τ_D = ψ_D = 1.

### Pricing and division of profits
- Buyers sell multiple goods and internalize cross-price effects across their product bundle, yielding first-order conditions:
  - q_{x b} + ∑_{x′∈J_b} ∂q_{x′ b}/∂p_{x b} (p_{x′ b} − c_{x′ b}) = 0 for all x ∈ J_b (equation 15).
- Instantaneous buyer profit flow given number of international and domestic suppliers s:
  - π_b(s) = E P^{1−η} [ ∑_{x∈J_b} η^{η−1} ]^{(1−α)} τ_L ˜c_b^{1−α} ]^{(1−η)/(1−α)} (equation 16) with L ∈ {D,I} and ˜c_b = c_b/ψ_L.
  - Condition α > η > 1 ensures profit is increasing in aggregate price index and decreasing in marginal cost, and implies diminishing returns to number of suppliers via exponent (1−η)/(1−α) < 1.
- Seller profit flows under Stole and Zwiebel (1996) bargaining:
  - Seller profit z_{j i}(s) = Λ ∂π^T_i(s)/∂s_L = Λ (α−1/η η−1)^{−η} E P^{1−η} [ ∑_{j∈J_b} τ_L ˜c_i^{1−α} ]^{(α−η)/(1−α)} τ_L ˜c_i^{1−α} (equation 17).
  - Observed firm-to-firm transaction revenue r_{j i}(s) expressed in structural form (equation 18):
    - r_{j i}(s) = (h_{j|i})^{(α−η)/(α−1)} E P^{1−η} η^{η−1} )^{−η} τ_L ˜c_{j i}^{1−η} [ B^{α−1} + λ ],
    - where h_{j|i} = τ_L ˜c_j^{1−α} / ∑_{l=1}^J s_l τ_L ˜c_i^{1−α} is within-buyer-i revenue share of type-j seller, and λ is the seller’s fraction of marginal cost.
  - Equation 18 is estimated to recover elasticity of substitution parameter η.
  - The constant fraction λ of variable costs attributable to the seller is assumed for estimation purposes.

### Search and matching
- Buyer search choices:
  - Buyer search intensity σ_B and proportion of search done domestically a (a ∈ [0,1]).
  - Type-i buyer visibility:
    - H^B_{i,D}(s) = a_i(s) σ^B_i(s) M^B_i(s)
    - H^B_{i,I}(s) = (1−a_i(s)) σ^B_i(s) M^B_i(s) (equation 19).
  - Aggregate buyer visibility in market L ∈ {D,I}:
    - H^B_L = ∑_{i=1}^I ∑_{s_L=0}^{s_L^{max}} H^B_{i,L}(s) (equation 20).
- Seller visibility:
  - H^S_D(n) = σ^S_D(n) M^S_D(n)
  - H^S_I(n) = σ^S_I(n) M^S_I(n) (equation 21).
- Matching functions (increasing in buyer and seller visibility):
  - X_D(H^S_D, H^B_D) = (H^B_D)^{γ_B} (H^S_D)^{γ_S} (equation 22).
  - X_I(H^S_I, H^B_I) = (H^B_I)^{β_B} (H^S_I)^{β_S} (equation 23).
  - High values of γ_S, γ_B, β_S, β_B indicate stronger positive search externalities.
- Market tightness (match flow per unit of buyer visibility):
  - θ_D = X_D(H^S_D, H^B_D) / H^B_D
  - θ_I = X_I(H^S_I, H^B_I) / H^B_D (equation 24).
  - Higher θ implies higher hazard-rate of finding a match.

### Search cost
- Buyers face positive, convex search costs with a fixed cost of international search F_I (paid only if firm searches internationally):
  - k_B = ( (a σ_B)^v + ( (1−a) σ_B )^v )^{v} + F_I, with v > 1 (equation 25).
  - F_I is structurally estimated in Section 6 of the source.
- Sellers face convex search costs (same for domestic and international suppliers by assumption):
  - k^S_L = (σ_S)^v for L ∈ {D,I} and v > 1 (equation 26).

### Optimal search (buyers and sellers)
- Buyer dynamic optimization (value function for type-i buyer with sellers s):
  - V^B_i(s) = max_{a, σ_B} { π^B_i(s) − k_B(a_i, σ^B_i) + s_D δ V^B_i(s_D − 1) + a σ^B θ^B_D V^B_i(s_D + 1)
    + s_I δ V^B_i(s_I − 1) + (1−a) σ^B θ^B_I V^B_i(s_I + 1)
    over denominator ρ + s_D δ + s_I δ + a σ^B θ^B_D + (1−a) σ^B θ^B_I } (equation 27).
  - Events considered: drop/add domestic supplier, drop/add international supplier; δ is exogenous link death parameter, ρ is time preference.
- Optimality conditions (policy functions) for buyers:
  - ∂k_B(σ_B, a) / ∂σ_B ≤ a θ^B_D Δ_{s_D} V^B_i + (1−a) θ^B_I Δ_{s_I} V^B_i (equation 28).
  - ∂k_B(σ_B, a) / ∂a ≤ σ_B θ^B_D Δ_{s_D} V^B_i − σ_B θ^B_I Δ_{s_I} V^B_i (equation 29).
  - Δ_{s_L} V^B_i = V^B_i(s_L + 1) − V^B_i(s_L) for L ∈ {D,I}. Equations hold with equality when firm searches both markets (a < 1).
- Supplier value and optimization:
  - Supplier value when matching with type-i buyer who has s suppliers (for L ∈ {D,I}):
    - V^S_{D,i,s} = r_i(s) + (s_D − 1) δ V^S_{D,i,s_D−1} + a_i σ^B_i θ^B_D V^S_{D,i,s_D+1} over ρ + s_D δ + a_i σ^B_i(s) θ^B_D (equation 30, and analogous for international).
  - Expected seller value across buyer types:
    - V^S_L = ∑_{i} ∑_{s=0}^∞ V^S_{L,i,s+1} P^B_i(s) for L ∈ {D,I} (equation 31), where P^B_i(s) = H^B_i(s) / H^B is share of matches involving buyer type-i with s sellers.
  - Seller optimal search policy functions:
    - ∂k^S_D(σ^S_D, s_D) / ∂σ^S_D = θ^S_D V^S_D (equation 32).
    - ∂k^S_I(σ^S_I, s_I) / ∂σ^S_I = θ^S_I V^S_I (equation 33).

### Equilibrium and law of motion
- Equation of motion for mass of type-i buyers with s sellers (flows in minus flows out):
  - Ḿ^B_i(s) =
    [ a_i σ^B_i θ^B_D M^B_i(s_D − 1, s_I)  (i)
    + δ (s_D + 1) M^B_i(s_D + 1, s_I)     (ii)
    + (1−a_i) σ^B_i θ^B_I M^B_i(s_D, s_I − 1) (iii)
    + δ (s_I + 1) M^B_i(s_I + 1, s_D)     (iv)
    ]
    −
    [ a_i σ^B_i θ^B_D  (v)
    + δ s_D                            (vi)
    + (1−a_i) σ^B_i θ^B_I               (vii)
    + δ s_I                            (viii)
    ] M^B_i(s_D, s_I) (equation 34).
  - Interpretation: flows in are items (i)–(iv), flows out are items (v)–(viii).
- Boundary cases for zero suppliers on one margin:
  - Ḿ^B_i(0, s_I) =
    [ δ M^B_i(1, s_I) + (1−a_i) σ^B_i θ^B_I M^B_i(0, s_I − 1) + δ (s_I + 1) M^B_i(0, s_I) ]
    − [ a_i σ^B_i θ^B_D + (1−a_i) σ^B_i θ^B_I + δ s_I ] M^B_i(0, s_I) (equation 35).
  - Ḿ^B_i(s_D, 0) =
    [ δ M^B_i(s_D, 0) + a_i σ^B_i θ^B_D M^B_i(s_D − 1, 0) + δ (s_D + 1) M^B_i(s_D, 0) ]
    − [ (1−a_i) σ^B_i θ^B_I + a_i σ^B_i θ^B_D + δ s_D ] M^B_i(s_D, 0) (equation 36).
- A symmetric system holds for suppliers.
- Equilibrium concept:
  - Stationary equilibrium at steady state obtained by setting Ḿ^B_i(s) = 0 and Ḿ^S_j(n) = 0 and solving the system across all buyer types and suppliers (equations 34–36).
  - Each buyer type is treated as exogenously given.

*Source: 5. A Quantitative Model of Buyer-Supplier Search in Two Markets (excerpt).*

### 6. Estimation

### 6. Estimation

### Estimating the transfer equation
- Purpose: identify elasticities of substitution between buyers and across buyers by estimating the structural transfer equation (equation 37).
- Estimated log-linear specification:
  - ln r_ji(s) = (η−1)/(α−1) ln h_{j|i} + (1−η) ln c̃_ji + d_t + ε_jit
- Transfer-equation estimates (Table 4):
  - Column (1) OLS-FE: coefficient on ln h_{j|i,t} = 0.882 (0.0360) ∗∗∗
  - Column (2) IV-FE: coefficient on ln h_{j|i,t} = 0.910 (0.0411) ∗∗∗
  - Column (3) OLS-FE (full fixed effects): coefficient on ln h_{j|i,t} = 0.882 (0.0360) ∗∗∗
  - Coefficient on ln n_it in column (3): -0.275 (0.0369) ∗∗∗
  - N = 34016 (unit: buyer i × supplier j × year t). Standard errors clustered at buyer level.
- Identification:
  - Instrument for ln h_{j|i} constructed as a share-weighted average of the number of buyers of other sellers at buyer j.
  - Alternative specification assumes identical suppliers except for import/domestic fixed effects and includes just ln(number of suppliers).
- Key inference:
  - The estimated coefficient (α−η)/(α−1) < 1 implies α > η — the elasticity of substitution across varieties (α) exceeds the elasticity of substitution across buyers (η).
  - Using column 3 estimate and α = 4.35 implies η = 3.45.
  - Conclusion: decreasing returns to adding new suppliers (distinct from returns to scale in the matching function).

### Externally calibrated parameters (Table 5)
- Externally calibrated parameters and values:
  - α Elasticity of sub. products = 4.35 (Eaton et al. (2016))
  - η Elasticity of sub. buyers = 3.45 (Estimated in transfer equation)
  - Λ Bargaining coefficient = 0.5 (Eaton et al. (2016))
  - v Convexity of search cost = 2 (Eaton et al. (2016))
  - δ Death parameter = 0.4 (Calculated in data)
  - τ Iceberg trade cost = 1.45 (Atkeson and Burstein (2008))
  - κ Pareto shape parameter = 1.45 (Melitz and Redding (2015))
  - ρ Time preference = 0.05 (Eaton et al. (2016))

### Internally calibrated parameters (Simulated Method of Moments; Table 5)
- Parameters estimated via SMM: ζ = {F, ψ_I, γ_S, γ_B, β_S, β_B}.
- SMM objective: ζ̂ = argmin_ζ (1/N)[M_m(ζ) − M_d]′ W_N (1/N)[M_m(ζ) − M_d], with W_N = identity.
- Internally calibrated parameter estimates (value (standard error) — most important moment):
  - I Import premium = 1.14 (0.080) — Ratio of imports to domestic among importers
  - F International fixed cost = 0.26 (0.027) — Proportion of firms import
  - γ_B^D buyer matching CD share = 0.49 (0.025) — Prob. of a new match for domestic buyer
  - γ_S^D supplier matching CD share = 0.46 (0.045) — Prob. of a new match for domestic supplier
  - β_B^I buyer matching CD share = 0.56 (0.049) — Prob. of a new match for import buyer
  - β_S^I supplier matching CD share = 0.70 (0.052) — Prob. of a new match for import supplier
- Interpretation:
  - Imports exhibit a 1.14 times quality premium over domestic goods.
  - Fixed costs of searching for imports ≈ 0.26, approximately a quarter of the average firm’s annual import volume.
  - Matching parameters imply:
    - Domestic market: decreasing returns to search (γ_S + γ_B < 1).
    - International market: increasing returns to search (β_S + β_B > 1).
  - Implication: increased matching efficiency in international market contributes to higher consumer welfare after transport cost reductions.

### Model fit (Table 6; Figures 5)
- Targeted and matched moments (Model Value vs Data Value):
  - Ratio of imports to domestic among importers: 0.59 vs 0.59
  - Proportion of firms which import: 0.20 vs 0.21
  - Mass of international suppliers: 0.30 vs 0.21
  - Mass of domestic suppliers: 0.26 vs 0.34
  - Mass of international buyers: 0.06 vs 0.08
  - Mass of domestic buyer: 0.30 vs 0.20
  - Prob. of a new match for international suppliers: 0.23 vs 0.26
  - Prob. of a new match for domestic supplier: 0.14 vs 0.22
  - Prob. of a new match for international buyer: 0.30 vs 0.38
  - Prob. of a new match for domestic buyer: 0.27 vs 0.24
- Fit assessment:
  - Close fit on targeted moments and good fit on many untargeted moments, including buyer out-degree distributions (model vs data).
  - Model overestimates density of suppliers with a small number of buyers (bottom two charts of Figure 5); shape similar but mass concentrated more at low-degree suppliers in model.
  - Explanation: model assumes homogeneous buyer marginal costs, reducing flexibility on supplier side; consistent with Lim (2017) underprediction of most-connected firms’ connections.

### Heterogeneity (Figure 6)
- Firms grouped into marginal cost bins 1 (lowest) to 10 (highest); y-axis shows average search by market.
- Findings:
  - Due to large fixed cost of importing, only lowest marginal cost firms search internationally.
  - Lowest marginal cost firms also search domestically because convex search costs induce multi-market search.
  - Firms just below import fixed-cost threshold increase domestic search (peak domestic search in marginal cost bin 2) because lowest-cost firms incur higher convex search costs from searching both markets.
  - As marginal cost increases beyond the peak, average search declines due to diminishing marginal returns to adding suppliers binding more for higher marginal cost firms.

### Counterfactual Simulations
- Setup: simulate a reduction in transport costs matching observed East African trade cost fall (25% fall in cost to import a shipping container into Uganda between 2010 and 2011).

Experiment 1 — Transport cost reduction under structurally estimated parameters (IRS)
- Outcomes from a 25% transport cost reduction (Table 7: High τ → Low τ; percentage change; data comparison):
  - Percentage of Importers: 21.2 → 24.6; Change 16%; Data 14%
  - Av. Foreign Suppliers: 2.10 → 2.37; Change 13%; Data 16%
  - Av. Domestic Suppliers: 2.90 → 2.78; Change -4.2%; Data -1.6%
  - Domestic Search (aσ): 0.12 → 0.11; Change -3.1%
  - Import Search ((1−a)σ): 0.71 → 0.84; Change 19%
  - Consumer Welfare: 3.7%
- Mechanisms and heterogeneity:
  - Increase in importers and import search intensity; average foreign suppliers up 13%.
  - Firms in marginal cost bin 2 become importers; existing importers increase international search and reduce domestic search (e.g., domestic search for bin 2 falls from 0.27 to 0.18).
  - Domestic market tightness falls, enabling higher-marginal-cost non-importers to increase domestic search (e.g., bin 3 domestic search 0.18 → 0.21).
  - Model results broadly match observed tax-data changes in direction and magnitude; main disparity: overestimated reduction in domestic suppliers due to domestic growth not captured by the trade-cost shock parametrization.
- Welfare:
  - 25% transport cost reduction yields 3.7% increase in consumer welfare.
  - Channels: (i) lower marginal cost of importing (income effect); (ii) increased matching efficiency from moving to increasing-returns international market.

Experiment 2 — Transport cost reduction under constant returns to scale matching function (CRS)
- Purpose: quantify role of search externalities by setting both markets to constant returns to scale.
- Comparative outcomes (Table 8: Change IRS vs Change CRS vs Real Change):
  - Percentage of Importers: IRS 16% vs CRS 13% (Real 16%)
  - Av. Foreign Suppliers: IRS 13% vs CRS 9% (Real 16%)
  - Av. Domestic Suppliers: IRS -4.2% vs CRS -6.1% (Real -1.6%)
  - Domestic Search (aσ): IRS -3.1% vs CRS -4.1%
  - Import Search ((1−a)σ): IRS 19% vs CRS 16%
  - Consumer Welfare: IRS 3.7% vs CRS 3.3%
- Interpretation:
  - With CRS matching, average foreign-supplier increase is smaller (9% vs 13% under IRS) because import market becomes tighter and matching gains per unit of search are lower.
  - Domestic supplier decline is larger under CRS (-6.1% vs -4.2%) because reduced domestic search is not mitigated by reduced congestion.
  - Non-linearity: Figure 10 shows divergence in predicted average international suppliers as trade-cost reductions grow (e.g., 10% reduction: IRS +2.7% vs CRS +1.8%; 25% reduction: IRS +13% vs CRS +9%).
  - Welfare non-linearity: consumer welfare increases faster under IRS; at 25% reduction, welfare increase is 12% larger under IRS than CRS (Figure 11).
- Conclusion: search externalities and increasing returns in international matching materially amplify the effects of trade-cost reductions on matching, firm networks, and consumer welfare.

*Italic source: Content from "6. Estimation" (wpiea2021091-print-pdf).*

### 1. The x-axis shows the reduction in trade costs from 0 to 30%. The orange line (IRS) shows the change in

### Experiment 3: Search cost reduction

### Experiment design
- Simulate the Ugandan government’s stated target for 2019 to reduce search costs for suppliers by 25% (Government of Uganda,2019).
- Specific sub-targets described:
  - Establish an internet platform support programme (e.g. organize quarterly trainings on the use of Ali Baba).
  - Encourage firms peer-to-peer learning (e.g. organize quarterly peer groups with Uganda business groups).
  - Target key firms in supplier development programmes (e.g. establish anchor firm support unit and annual public-supplier meetings).
- Two counterfactual experiments run:
  - Lowering domestic search costs by 25%.
  - Lowering international (import) search costs by 25%.

### Outcomes and key statistics (Table 9: Outcomes from 25% search cost reduction)
- Table shows the change in the model generated outcome variables under a 25% decrease in domestic search costs and a 25% decrease in international search costs. Average refers to the average number of suppliers over all firms.

- Change following 25% decrease in domestic search costs / Change following 25% decrease in import search costs:
  - Percentage of Importers: -0.30% / 14.4%
  - Av. Foreign Suppliers: -0.52% / 19.1%
  - Av. Domestic Suppliers: 10.5% / -3.50%
  - Domestic Search (aσ): 10.2% / -1.82%
  - Import Search ((1−a)σ): -0.90% / 30.6%
  - Consumer Welfare: 2.2% / 3.7%

### Dynamics by firm marginal cost (Figures 12 and 13)
- Buyers broken into 10 marginal cost bins (1 = lowest marginal costs, 10 = highest marginal costs).
- Reducing domestic search costs by 25%:
  - Sharp increase in buyers’ domestic search observed across all levels of buyer marginal cost.
  - Average number of domestic suppliers increases by 10.5% (reported as 10% in text comparing to Cai and Szeidl(2017) but Table 9 reports 10.5%).
  - Small decline in international search: -0.90%.
  - Increase in domestic search leads to increased domestic market congestion, muting impact on matches.
- Reducing international search costs by 25%:
  - Large increase in import search: 30.6%.
  - Foreign suppliers increase by 19.1%.
  - Effects concentrated among low marginal cost firms; other firms often still do not pay the import fixed cost.
  - Firms reduce domestic search given convex search costs in both markets, which frees space in domestic market for higher marginal cost firms.

### Welfare and mechanism
- Reducing international search costs increases consumer welfare by 3.7%.
- Reducing domestic search costs increases consumer welfare by 2.2%.
- Mechanisms:
  - Lower international search costs yield welfare gains through lower marginal costs and by shifting activity from a decreasing returns to scale market to an increasing returns to scale market.
  - Lower domestic search costs primarily raise domestic search, causing domestic congestion and muting welfare gains.

### Policy implications and recommendations
- Results support the Ugandan government’s policy of lowering search costs; impact on welfare from a 25% search cost reduction is of similar magnitude to lowering international trade costs by 25%.
- The impact of reforms will be greater if the government focuses on lowering international search costs.
- Recommended focus areas:
  - Train firms on using platforms such as Ali Baba and Amazon to lower international search costs.
  - Encourage firm peer-to-peer learning and meetings with experienced importers (analogous to interventions documented by Cai and Szeidl(2017)), to increase the number of suppliers and facilitate international matching.
- Caution: Lowering domestic search costs alone may increase domestic congestion and produce only modest increases in matches and welfare.

### Concluding remarks (selected)
- Presence of search frictions between buyers and suppliers in a low-income country can significantly affect firm responses to trade liberalization.
- Relative size of search externalities determines sourcing reallocation and consumer welfare changes.
- Structural estimation and reduced-form evidence indicate stronger positive externalities in international markets compared to domestic markets in the Ugandan context.
- While estimates are specific to Uganda, mechanisms are general to settings with buyer–supplier search frictions; effects may be larger in low-income countries where search frictions are substantial (noted as speculative without comparable data).
- First-best is removing search frictions entirely; infeasible in practice, so governments should focus on reducing search costs, with priority on international search cost reduction.

*Source: wpiea2021091-print-pdf (Experiment 3: Search cost reduction; Table 9 and Figures 11–13).*

### References

### wpiea2021091-print-pdf - References

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- Arnosti, Nick, Ramesh Johari, and Yash Kanoria, “Managing congestion in matching markets,” Available at SSRN 2427960, 2018.
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- Bustos, Paula, “Trade liberalization, exports, and technology upgrading: Evidence on the impact of MERCOSUR on Argentinian firms,” American economic review, 2011, 101(1), 304–40.
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- Eaton, Jonathan, David Jinkins, James R Tybout, and Daniel Yi Xu, “Two-Sided Search in International Markets,” Mimeo, 2016.
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### Appendix A — Context Appendix (selected contents)
- A.1. Map of trade corridor
  - Figure 14: Map of trade corridor, Osawa, WCO.
- A.2. Data comparison — key points
  - Figure 15 compares Uganda Revenue Authority (URA) export data with World Trade Organization (WTO) trade data; observation: WTO data appears to understate actual export volumes, but the two series track closely and are strongly correlated.
  - Figure 16 compares total output from URA tax data with GDP data from the World Bank; observation: URA tax data is smaller than World Bank GDP (tax data observes formal sector firms only), but the correlation between the two series is very strong.
  - Spray and Wolf (2016) show the distribution of firms in each sector is consistent with those in the Uganda Business Census.

### Appendix B — A Quantitative Model of Buyer-Supplier Search in Two Markets (structural model summary)
- Agents and markets
  - There is a measure B continuum of buyers, measure S_D continuum of domestic suppliers and measure S_I continuum of international suppliers.
  - Buyers have types indexed i ∈ {1,2,...,Γ} with marginal cost c_i drawn from a known distribution.
  - Suppliers produce differentiated products (x) sold to buyers (b) once matched. Buyers choose search intensity σ_B,i(s) and proportion a ∈ [0,1] of search exerted domestically (domestic share a, international share 1−a).
  - Iceberg trade costs: τ_I on international goods, τ_D on domestic goods with normalization τ_D = 1.
- Preferences and demand
  - Consumers: nested CES utility over buyers and products (Equations (B.1) and (B.2)); elasticities η (among products) and α (among buyers). International products share demand shifter ψ_I (domestic ψ_D normalized to 1).
- Pricing and profits
  - Buyers internalize multi-product pricing; first-order condition given by Equation (B.3).
  - Instantaneous profit flow for buyer b with supplier set J_b given by Equation (B.4); profit increasing in aggregate price index P and decreasing in marginal cost, with assumption α > η > 1 ensuring diminishing returns to number of suppliers.
  - Stole and Zwiebel (1996) bargaining gives seller profit flow z_ji(s) as in Equation (B.5).
  - Observable firm-to-firm revenue transfer r_ji(s) relates to fixed effects and observables (Equation (B.6)); includes seller’s fraction of variable costs λ.
- Search and matching
  - Visibility H of buyers and sellers defined in Equations (B.7)–(B.9); visibility depends on search intensity and mass of agents.
  - Matching functions (domestic and international) X_D and X_I are increasing in buyer and seller visibility with exponents γ_B, γ_S and β_B, β_S respectively (Equations (B.10)–(B.11)).
  - Match flow per unit of buyer visibility (market tightness) θ_D and θ_I defined in Equation (B.12).
  - Interpretations: γ_S + γ_B > 1 indicates increasing returns to scale in domestic matching; γ_S + γ_B < 1 indicates decreasing returns to scale (congestion). High γ exponents indicate positive externalities to search; low γ exponents indicate congestion externalities.
- Search costs and optimization
  - Buyers face convex search costs with fixed cost of search F_S and additional fixed cost of international search F_I; cost function k_B in Equation (B.13) with v > 1.
  - Sellers face convex search costs k_S,L = (σ_S)^v for L ∈ {D,I} (Equation (B.14)).
  - Buyers maximize present value V_B,i(s) choosing σ_B and a (Equation (B.15)); first-order conditions for optimal search and allocation of search across markets given by Equations (B.16)–(B.17).
  - Suppliers solve parallel problems with value functions V_S,L,i,s defined in Equation (B.18); expected supplier value aggregates over buyer types (Equation (B.19)).
  - Optimal seller search conditions given by Equations (B.20)–(B.21).
- Dynamics and equilibrium
  - Equation of motion for the mass of buyers with s suppliers given by Equation (B.22); boundary conditions for s_L = 0 given by Equations (B.23)–(B.24).
  - Stationary steady-state equilibrium found by setting ̇M_B,i(s) = ̇M_S,j(n) = 0 and solving the system for all buyer types and suppliers (steady state treatment follows Eaton, Jinkins, Tybout and Xu (2016)).

### Appendix C — Mathematical Appendix (select comparative statics and transfer equation)
- Two-period buyer reallocation problem
  - Buyer objective: maximize aσθ_D π(s_D) + (1−a)σθ_I π(s_I) − k(a) (Equation (C.2)), yielding FOC in Equation (C.3).
  - Comparative static of a with respect to τ_I given by Equation (C.4) with explicit expressions (Equations (C.5) and (C.6)); these highlight dependence on σ, θ_D, θ_I, π derivatives, second derivative of k, and matching exponents γ_B, β_B.
- Matching efficiency and welfare
  - Consumer welfare decomposed into matching efficiency A and consumption C (Equation (C.7)).
  - Matching efficiency A expressed as A = a^{γ_B} S^{γ_S} B^{γ_B−1} + ψ_I (1−a)^{β_B} S^{β_S} B^{β_B−1} (Equation (C.8)).
  - Sign of ∂A/∂τ_I depends on a, ψ_I, and matching exponents γ_B, γ_S, β_B, β_S (Equations (C.9)–(C.10)); key insight: if γ_B < β_B and γ_S < β_S (returns to search higher in international market), an increase in trade costs lowers welfare as firms move from international to domestic matching.
- Transfer equation (simplified)
  - If cost per unit quality does not vary across products within buyers, transfer equation collapses to Equation (C.11).

### Appendix D — Empirical Appendix (descriptive statistics, robustness, and regression outputs)
- Descriptive notes
  - Figure 17: Transport Costs and Imports — black line shows transport cost in USD per 20-foot container from the World Bank’s Trading Across Border Index; light grey bars show the average number of foreign suppliers for importers; dark grey bars show the proportion of firms which import. Shorter time series because identity of foreign suppliers is unknown prior to 2010.
- Robustness tests — overview and selected results
  - D.2.1. Alternative specifications: Specification 1 rerun using the full dataset (not just retailers); alternative geographic units: neighborhood of 10km, 1km, next door, same building. Results reported robust to these additions.
  - Table 10: Foreign Suppliers — regression results (unit of observation buyeri, supplierf, yeart). Selected coefficient estimates (coefficients multiplied by 100 to read as percentage point marginal effects):
    - X_10km_if,t−1: 0.0864 ∗∗∗ (0.00693)
    - X_1km_if,t−1: 0.0819 ∗∗∗ (0.00658)
    - X_same_if,t−1: 0.0910 ∗∗∗ (0.00624) and 0.0907 ∗∗∗ (0.00651) across columns
    - X_nextdoor_if,t−1: 0.00128 (0.00994)
    - X_other−city_if,t−1: -0.00347 ∗ (0.00179) etc.
    - Observations: 4834635; Year and Firm FE: YES.
  - Table 11: Domestic Suppliers — selected entries:
    - X_10km_if,t−1: 0.00513 (0.00606)
    - X_1km_if,t−1: 0.00502 (0.00612)
    - X_same_if,t−1: 0.00509 (0.00613) and 0.00465 (0.00631)
    - X_nextdoor_if,t−1: 0.000616 (0.000322)
    - X_other−city_if,t−1: -0.00515 ∗∗∗ (0.000962) etc.
    - Observations: 27975967; Year and Firm FE: YES.
  - Table 12: Same and next-door balance table — proportions and differences:
    - Same building: 0.097 (0.296)
    - Next-door building: 0.088; Difference with same building: -0.009 (0.014)
    - Next-door < distance < 0.1km: 0.060; Difference with same building: -0.037 *** (0.012)
    - 0.1km < distance < 0.15km: 0.051; Difference: -0.046 *** (0.017)
    - 0.15km < distance < 0.2km: 0.044; Difference: -0.053 ** (0.021)
    - 0.2km < distance < 0.25km: 0.040; Difference: -0.057 ** (0.026)
  - D.2.2. Very local shocks drive results: comparison of proportion of firms in same ISIC 4-digit sector in same building vs next-door building shows small, not statistically significant difference at building level; differences grow at block-level distances suggesting agglomeration at block level rather than building level.
  - D.2.3. Spillover exists but is not search related — tests of interactions with East African Community (EAC):
    - Table 13: Imports Suppliers from East African Community — regression (unit buyeri, supplierf, yeart). Selected coefficients (coefficients multiplied by 100):
      - X_same_t−1: 0.0931 ∗∗∗ (0.00665)
      - X_same_t−1 × EAC_f: -0.0346 ∗∗ (0.0151)
      - X_other−city_t−1: -0.00223 (0.00176)
      - X_other−city_t−1 × EAC_f: -0.00486 (0.00552)
      - Observations: 4834635.
    - Interpretation in text: suppliers in the EAC have a smaller positive spillover, consistent with search-frictions narrative (local neighbors reduce search frictions). Prediction: international suppliers (large, credit access, multiple customers) less likely to be supply-constrained and therefore less likely to generate negative congestion effects; domestic Ugandan firms (small, limited credit) more likely to face congestion in matching.
- Additional empirical material (tables continue beyond provided excerpt).

*Italic: Content unit: wpiea2021091-print-pdf - References*

### 0.00236 hhhh

### wpiea2021091-print-pdf - 0.00236 hhhh

### Empirical specification (equation)
- Y_ift = μ_1 X_same_if,t−1 + μ_2 X_same_if,t−1 × Exporter_f + γ_1 X_other-city_if,t−1 + γ_2 X_other-city_if,t−1 × Exporter_f + α_i + α_t + u_ift (D.2)

### Key coefficient estimates and statistics
- 0.00236 hhhh
  - (0.00358) hhhh
- X_same_t−1 × exporter_f: 0.00358 hhhh
  - (0.00802) hhhh
- X_other−city_t−1: -0.00574 ∗∗∗ hhhh
  - (0.000680) hhhh
- X_other−city_t−1 × exporter_f: 0.00268 ∗∗ hhhh
  - (0.000609) hhhh
- Observations: 27975967 hhhh

### Notes on estimation and interpretation
- Unit of observation is buyer_i, supplier_f and year_t.
- Y_if_t indicates a first match took place between buyer and supplier.
- X_k_if_t is a count of buyers in region k which added supplier f in t−1.
- exporter_f indicates supplier f is an exporter.
- Coefficients are multiplied by 100 to read as percentage point marginal effects.
- Standard errors in parentheses clustered at the buyer level.
- Significance notation: ∗ p <0.1, ∗∗ p <0.05, ∗∗∗ p <0.01

### Substantive finding
- Results in Table 14 show that domestic suppliers which are exporters, and hence less supply constrained, have a smaller negative effect from making a match elsewhere in the country. This is consistent with the search narrative.

*https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021091-print-pdf.pdf*

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