## wpiea2026163-source-pdf - Appendix B.4 provides a formal analysis of how decreasing returns to scale would manifest in measured ## Source details **Canonical URL:** [wpiea2026163-source-pdf - Appendix B.4 provides a formal analysis of how decreasing returns to scale would manifest in measured](https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026163-source-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2026/english/wpiea2026163-source-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2026/english/wpiea2026163-source-pdf.pdf.json) --- ### Empirical findings on direct and indirect exposure - Data and measures: - Firm-to-firm transaction data used to construct indirect exposure: suppliers that supply commodity exporters but do not themselves export commodities. - Main empirical patterns: - Suppliers with greater indirect exposure experience larger increases in: sales, employment, materials expenditure, capital investment, productivity. - Directly exposed commodity exporters do not exhibit productivity gains. - Observed positive spillovers to suppliers align with productivity gains in Chile’s non-mining sectors during the commodity boom (Figure A.1) and are consistent with demand-driven productivity improvements documented elsewhere (Ilzetzki, 2024). ### Theoretical framework and mechanisms - Model environment and frictions: - Small open economy with heterogeneous firms. - Two distortions: firm-specific export wedges and an oligopsonistic labor market. - Export wedges: - Capture differential access to foreign markets (subsidies, policies, historical relationships). - Disciplined by three microfoundations and a measured policy component from administrative data (Section 6.4.2). - Labor market: - Modeled as oligopsonistic where firms have wage-setting power. - Firm-specific labor wedges reproduce wage increases and labor poaching documented in the data. - Mechanism of asymmetric effects: - Uniform increase in commodity demand produces asymmetric firm responses via differential sensitivity. - Firms with larger export wedges expand disproportionately, drawing labor and materials away from more productive but less export-favored competitors. - Reallocation exacerbates misallocation: resources shift toward firms generating high revenues due to privileged market access rather than superior technology. - Aggregate sectoral productivity, measured as the output-weighted average of productivities, can decline even as output and employment rise. - Labor-market implication: - In an oligopsonistic labor market, expanding low-productivity firms must offer higher wages to attract workers from more productive employers, generating observed “poaching” patterns. ### Calibration, quantitative simulations, and aggregate implications - Calibration targets and setup: - Targets: key moments from Chilean administrative data, including export shares, sales dispersion, and export intensity variation across firms. - Simulate j = 1 (commodity sector) with 10,000 firms; shock design selects half of firms to receive a large shock increasing export demand D^F_i1 by 206% (90–10 percentile difference) and scales up aggregate to match observed 83% aggregate export value growth between 2005 and 2013. - Model reproduction of empirical patterns (non-targeted regressions, Data vs Model): - Exports — Data: 0.767*** ; Model: 0.953 - Average wage — Data: 0.293*** ; Model: 0.195 - Materials — Data: 0.575*** ; Model: 0.736 - TFPR — Data: −0.024 ; Model: 0.041 - Employees (Entire sample) — Data: 0.403* ; Model: 0.538 - Employees (TFPR ≥ p50) — Data: −0.163 ; Model: 0.383 - Employees (TFPR < p50) — Data: 0.620** ; Model: 0.633 - Aggregate productivity impact: - Reallocation toward low-TFPR firms lowers sectoral productivity by 3.94 percent in the simulation. - This decline is roughly half of the 8% TFP decline documented by CNEP (2017) for Chilean mining between 2005 and 2013. - Interpretation: - The misallocation channel (interaction of export distortions and labor market power) can quantitatively explain a substantial portion (~50%) of the aggregate productivity decline; remaining gap likely reflects factors outside the parsimonious framework (capacity constraints in mining capital investment, within-firm productivity slowdown due to declining ore grades, other sector-specific shocks and frictions). ### Chile case facts and macro patterns during the China-driven boom - Role of commodities: - Mining products consistently accounted for over 50 percent of total exports during the 2000s. - Market and price dynamics: - Chile contributed less than 25 percent of global exports in 2003. - China’s share of global copper consumption exceeds 50 percent. - Global copper prices nearly tripled between 2003 and 2011. - Copper production in Chile grew by only 20 percent during this period while export revenues more than tripled. - Input and resource changes during the boom: - Energy use rose 79 percent. - Employment increased 157 percent. - Capital stock grew 178 percent. - These input changes are described as roughly an eightfold increase relative to what would be expected under constant productivity. - Aggregate productivity observations: - CNEP (2017) documented mining sector TFP declined by approximately 8 percent between 2005 and 2013, averaging roughly 1 percent per year. - CNEP noted sector-specific factors: declining ore grades and long gestation lags associated with mining capital investments. - Mining-sector heterogeneity: - In 2015, most efficient operation required 43 labor hours per kiloton moved; least efficient required 115 hours—nearly three times as much. - Inputs and domestic linkages: - According to the 2010 Input-Output table, mining was the largest purchaser of intermediate inputs from domestic suppliers, including specialized equipment and machinery, transportation services, construction materials, and business services. ### Firm-level data, identification, and empirical strategy - Administrative linkages and datasets: - Firm defined as a tax ID (following Huneeus (2018)); plant-level information not available. - Primary tax forms: Form F22 (annual fixed assets, 6-digit industry, headquarters) and Form F29 (monthly aggregated to annual: domestic sales, exports, material expenditures, investments). - Firm-to-firm transaction data (Form F3323) 2004–2010 records buyer/seller tax IDs and transaction values; reporting firms account for roughly 80 percent of Chile’s total value added (Huneeus, 2018). - Employer-employee matched data (Form DJ1887) links employees to employers with monthly labor income. - International trade datasets: Customs (transaction-level with firm tax IDs), BACI (CEPII), WITS (tariff AVE percentages). - Sample construction and product focus: - Merged sample spans 2003 to 2013; firms must have positive sales and material costs and at least one employee; non-missing industry classification required. - Analysis focuses on 83 commodity products actively sold from Chile and demanded by China from third countries; the 83 products include copper products, other metals, agricultural commodities, and industrial minerals. - Median commodity exporter specializes: median exporter earns 93% of export value from a single 6-digit product. - Empirical strategy: - Identifying variation: differential changes in global commodity prices across granular products, mapped to firms via initial export specialization. - Long-difference specification: shock measured over 2003–2011; outcomes measured over 2005–2013 (two-year lag for adjustment). - Regression: y_g_f = β_0 + β_1 shock_f + X'_f γ + ε_f where y_g_f = 2(Y_f,2013 − Y_f,2005) / (Y_f,2013 + Y_f,2005), bounded between −2 and 2. - Controls: 2-digit industry fixed effects and initial commodity share; standard errors clustered at the 4-digit industry level. - Construction of shocks and IV: - Baseline (direct) regressor: ∆ lnP_CL_p = ln P_CL_p,2011 − ln P_CL_p,2003 (Chilean export prices to China). - IV: ∆ lnP_OT_p = ln P_OT_p,2011 − ln P_OT_p,2003 (Chinese import prices from countries excluding Chile) to isolate exogenous Chinese demand. - Firm-level shock: shock^k_f = Σ_{p∈C} ω_pf ∆ lnP^k_p with ω_pf = firm f’s 2003 export share of product p. - Law of One Price (LOP) tests and IV relevance (Table 1 highlights): - Column (1): coefficient on ∆ lnP_OT = 0.45 ∗∗∗ (0.12); F-stat 14.5; r2 0.10; Observations 832. - Column (2) [2011 tariff = 0]: coefficient = 0.70 ∗∗∗ (0.20); F-stat 11.6; r2 0.30; Observations 855. - Column (3) [2011 tariff ≠ 0]: coefficient = 0.13 (0.13); F-stat 1.1; r2 0.00; Observations 832. - Interpretation: estimated pass-through substantially less than 1, confirming imperfect LOP and instrument relevance; tariffs drive deviations. ### Firm-level outcomes and productivity measurement - IV estimates (commodity price shock; Table 3): - Exports: 0.767*** (0.214) - Employees: 0.403* (0.205) - Materials: 0.575*** (0.142) - Capital: −0.331 (0.237) - TFPR: −0.024 (0.148) - Sales/emp.: −0.026 (0.179) - Domestic Sales: 0.062 (0.238) - OLS estimates (commodity price shock; Table 3): - Exports: 0.240* (0.133) - Employees: 0.077 (0.062) - Materials: 0.147** (0.064) - Capital: −0.055* (0.032) - TFPR: 0.024 (0.020) - Sales/emp.: −0.046 (0.029) - Domestic Sales: −0.052 (0.071) - Interpretation: - Positive shock yields substantial scale expansion (exports, materials, employment) for commodity firms (IV estimates). - No evidence of long-term capital accumulation: IV capital coefficient −0.331 (insignificant); OLS −0.055* (marginally significant decline). - No measurable efficiency gains: TFPR IV −0.024 (insignificant), sales per employee IV −0.026 (insignificant). - Domestic sales effects negligible. - Implication: extensive growth without intensive productivity improvement; unchanged TFPR may mechanically imply a decline in quantity-based productivity (TFPQ) if output prices rise. - Productivity measurement and robustness: - Solow-residual TFPR: logtfpr_fjt = logy_fjt − α_j logl_fjt − β_j logm_fjt − (1−α_j − β_j) logk_fjt with α_j and β_j from wage-bill and material ratios assuming CRS. - Alternative capital via perpetual inventory with depreciation 10% correlated at 0.95 with baseline capital. - Control function (Ackerberg et al. 2015) and alternative production specifications (Cobb-Douglas, translog, Leontief/gross output value added) yield consistent null productivity effects. - Results hold when excluding core copper mining (Table A.3). ### Labor reallocation toward low-productivity firms (Section 5.2) - Identification and test against selection: - Correlation of commodity price shock with initial TFPR is −0.027 (s.e. 0.028), indicating exposure uncorrelated with initial productivity. - Wages and worker flows (Table 4): - New workers (log wage differences 2005–2013, hired after 2004): Commodity price shock 0.255*** (IV). - Existing workers (hired in 2004): Commodity price shock 0.394*** (IV). - Worker mobility (IV): - Same sector movers: Commodity price shock 0.089***. - Higher TFPR movers: Commodity price shock 0.157*. - Differential employment by initial TFPR (Table 4, Panel C): - TFPR ≥ p50: Commodity price shock −0.163 (IV, not significant). - TFPR < p50: Commodity price shock 0.620** (IV). - Interpretation: - Less productive firms expand employment sharply (0.620) while higher-TFPR firms do not, consistent with labor poaching and reallocation that exacerbates misallocation. - Wage increases for both new and existing workers and net poaching from higher-TFPR firms documented. ### Firm-level TFPR, aggregation, and implications (Section 6.2 and Appendix B) - Firm-level TFPR definition (Equation (11) and (12)): - tfpr_ij ≡ (p^H_ij y^H_ij + p^F_ij y^F_ij) / (l^{γ_L}_ij k^{γ_K}_ij m^{γ_M}_ij). - Measured tfpr_ij = [1/(1−τ^F_ij)] s^F_ij · (μ^L_ij)^{γ_L} (s^L_ij)^{γ_L/(1+η)} · (W_j/γ_L)^{γ_L} (R/γ_K)^{γ_K} (P_M/γ_M)^{γ_M}. - Two channels generating TFPR dispersion: - Export wedge τ^F_ij (policy-induced): subsidies (more negative τ^F_ij) lower measured TFPR and increase export shares; primary source of misallocation in calibrated model. - Labor market power (oligopsony): greater μ^L_ij raises measured TFPR, partially offsetting export-wedge distortion; effect attenuated by higher worker mobility η. - Sectoral productivity A_j (Equation (13)): - A_j ≡ TFPR_j / PPI_j = (∑_{i∈F_j} (a_ij TFPR_j / tfpr_ij)^{σ−1})^{1/(σ−1)}. - Greater dispersion in tfpr_ij (holding a_ij constant) reduces A_j — compositional misallocation lowers aggregate productivity. - Calibration parameter values (Table 6): - σ = 3; η = 2.76; θ = 0.42; ρ = 2; ψ = 0.5. - Input shares: γ_L = 0.11; γ_M = 0.59; γ_K = 0.30. - Internally calibrated: σ_a = 1.20; σ_F = 0.53; ̄D_F = 1.76. - Quantitative assessment: - Simulated sectoral productivity falls by 3.94% in response to the modeled boom, explaining roughly half of the observed 8% decline in mining TFP. ### The export wedge: measurement, microfoundations, and empirical test (Appendix C) - Definition and role: - τ^F_ij captures net statutory subsidy or tax on export revenue in reduced form and enters first-order conditions and TFPR decomposition, driving misallocation where firms with more favorable net export treatment expand disproportionately. - Microfoundations (three): - C.1.1 Policy-induced per-unit advantages (export rebates, preferential rates). - C.1.2 Heterogeneous intermediary access (share of foreign-bound output exported directly vs. via intermediaries; τ^F_ij = (1 − η_ij) δ). - C.1.3 Variable markup in export market (τ^F_ij maps to endogenous markup differences); empirical TFPR–size gradient favors productivity-orthogonal wedges. - Statutory component measurement (C.2): - Four programs measured: Reintegro Simplificado (3% cash payment), Drawback (refunds import duties measured via input tariff t_h), Fisheries ITQ (≈15% implicit tax), Aquaculture concessions (2% restriction). - Product-level net wedge τ_h = subsidy_h − restriction_h with subsidy_h = max { 0.03·1[Reintegro_h], t_h·1[Drawback_h] } · s^norm_h and restriction_h = (0.15·1[ITQ_h] + 0.02·1[Aqua_h]) · s^norm_h. - Firm-level τ^F_f = Σ_h w_{fh} τ_h using 2003 FOB shares w_{fh}; measure is a conservative lower bound. - Empirical test (C.3): - Regression: g_f = β shock_f + δ τ^F_f + γ (shock_f × τ^F_f) + α_{h(f)} + ε_f on 2003–2011 export growth. - Main result (Table A.5): Shock × net wedge coefficient = 4.18** (1.96), robust across specifications (columns show 4.27** (2.04) and 4.17** (1.95); Firms = 760). - Interpretation: firms with higher net statutory wedge expand exports significantly more in response to the commodity shock, supporting the model’s misallocation mechanism. ### Appendix B.4: Decreasing returns to scale (DRS) and measured TFP - Setup and measurement mismatch: - True DRS production: Y_i = A_i · L_i^{α} · K_i^{β} · M_i^{γ} with α + β + γ < 1. - Measured TFP imposes CRS using factor shares s_L + s_K + s_M = 1: log[TFP_i] = log Y_i − s_L log L_i − s_K log K_i − s_M log M_i. - Scaling inputs by λ >1: - True output scales as Y'_i = λ^{α+β+γ} Y_i, with α + β + γ < 1 implying Y'_i < λ Y_i. - Measured TFP after expansion: log[TFP'_i] = log[TFP_i] + [(α + β + γ) − 1] log λ. - Since (α + β + γ) − 1 < 0, for λ >1 measured TFP declines: log[TFP'_i] < log[TFP_i]. - Empirical implication: - Firm-level DRS would mechanically generate declines in measured TFP when firms scale up; the appendix notes empirical findings are robust to specifications that do not impose CRS ex ante, suggesting firm-level DRS is not the primary explanation for observed patterns. *Italic: Content derived from wpiea2026163-source-pdf - Appendix B.4 provides a formal analysis of how decreasing returns to scale would manifest in measured* ### Appendix B.4 provides a formal analysis of how decreasing returns to scale would manifest in measured ### wpiea2026163-source-pdf - Appendix B.4 provides a formal analysis of how decreasing returns to scale would manifest in measured ### Empirical findings on direct and indirect exposure - Using firm-to-firm transaction data, the paper constructs measures of indirect exposure: firms that supply commodity exporters but do not themselves export commodities. - Suppliers with greater indirect exposure experience larger increases in: - sales, - employment, - materials expenditure, - capital investment, - productivity. - Directly exposed commodity exporters do not exhibit these productivity gains. - Observed positive spillovers to suppliers align with productivity gains in Chile’s non-mining sectors during the commodity boom (Figure A.1) and are consistent with demand-driven productivity improvements documented elsewhere (Ilzetzki, 2024). ### Theoretical framework and mechanisms - Model environment: - small open economy with heterogeneous firms, - two distortions: firm-specific export wedges and an oligopsonistic labor market. - Export wedges: - capture differential access to foreign markets (subsidies, policies, historical relationships, etc.), - disciplined by three microfoundations and a measured policy component from administrative data (Section 6.4.2). - Labor market: - modeled as oligopsonistic where firms have wage-setting power, - firm-specific labor wedges reproduce wage increases and labor poaching documented in the data. - Mechanism of asymmetric effects: - uniform increase in commodity demand has asymmetric effects across firms via differential sensitivity, - firms with larger export wedges expand disproportionately, drawing labor and materials away from more productive but less export-favored competitors, - reallocation exacerbates misallocation: resources shift toward firms generating high revenues due to privileged market access rather than superior technology, - aggregate sectoral productivity, measured as the output-weighted average of productivities, can decline even as output and employment rise. - Labor market implications: - in an oligopsonistic labor market, expanding low-productivity firms must offer higher wages to attract workers from more productive employers, generating the observed “poaching” patterns. ### Calibration, quantitative simulations, and aggregate implications - Calibration targets: - key moments from Chilean administrative data, including export shares, sales dispersion, and export intensity variation across firms. - Calibration results: - without targeting firm-level regression coefficients, the calibrated model reproduces: - the muted productivity response, - disproportionate employment expansion among low-TFPR firms, - both close to their empirical counterparts. - Aggregate simulation of a commodity boom comparable to Chile’s experience: - reallocation toward low-TFPR firms lowers sectoral productivity by 3.94 percent, - this decline is roughly half of the 8% TFP decline documented by CNEP (2017). - Remaining gap explanation: - likely reflects factors outside the parsimonious framework, such as: - capacity constraints in mining capital investment, - within-firm productivity slowdown due to declining ore grades, - other sector-specific shocks and frictions. - Conclusion: - the misallocation channel, operating through the interaction of export distortions and labor market power, can quantitatively explain a substantial portion of the aggregate productivity decline. ### Chile case facts and macro patterns during the China-driven boom - Role of commodities: - mining products consistently accounted for over 50 percent of total exports during the 2000s. - Global market shares and identification: - Chile contributed less than 25 percent of global exports in 2003, - China’s share of global copper consumption exceeds 50 percent. - Copper market dynamics (early 2000s boom): - global copper prices nearly tripled between 2003 and 2011, - copper production in Chile grew by only 20 percent during this period while export revenues more than tripled. - Input changes during the boom: - energy use rose 79 percent, - employment increased 157 percent, - capital stock grew 178 percent, - described as roughly an eightfold increase relative to what would be expected under constant productivity. - Aggregate productivity observations: - Chile’s National Productivity Commission (CNEP, 2017) documented mining sector total factor productivity (TFP) declined by approximately 8 percent between 2005 and 2013, averaging roughly 1 percent per year, - CNEP noted two sector-specific factors: declining ore grades and long gestation lags associated with mining capital investments, - these adjustments leave scope for additional mechanisms, motivating the firm-level analysis. - Mining-sector heterogeneity example: - in 2015, the most efficient operation required just 43 labor hours per kiloton moved, while the least efficient needed 115 hours—nearly three times as much (CNEP, 2017). - Inputs and domestic linkages: - according to the 2010 Input-Output table, mining was the largest purchaser of intermediate inputs from domestic suppliers, including specialized equipment and machinery, transportation services, construction materials, and business services. ### Contribution to the literature - Adds to research on commodity price shocks in small open economies by focusing on within-sector firm-level reallocation rather than only aggregate or cross-country outcomes. - Contributes to disaggregated analyses of transmission via upstream and downstream linkages, documenting a novel possibility that demand expansion can depress productivity at the center (commodity exporters) while benefiting connected suppliers. - Relates to literature on misallocation and productivity: - contrasts with studies showing positive shocks can reduce misallocation by relaxing constraints on productive firms, - shows positive external shocks can instead exacerbate misallocation within the booming sector when pre-existing export distortions channel inputs toward low-TFPR firms. - Connects to firm-level demand shock literature: - contrasts with findings where exporters increase productivity after gaining market access; here commodity exporters channel revenue gains into inputs without efficiency improvements, while upstream suppliers do experience productivity gains. _Italic: Content derived from wpiea2026163-source-pdf - Appendix B.4 provides a formal analysis of how decreasing returns to scale would manifest in measured_ ### 2004. Each firm and individual receives a unique tax ID, which allows us to link observations ### wpiea2026163-source-pdf - 2004. Each firm and individual receives a unique tax ID, which allows us to link observations ### Firm-level and linked administrative data - Firm defined as a tax ID (following Huneeus (2018)). Plant-level information is not available; firms may have multiple tax IDs but ownership not observed. - Primary tax forms: - Form F22: annual information including fixed assets, main 6-digit industry classification, and headquarters location. - Form F29: monthly data (aggregated to annual) covering domestic sales, exports, domestic and imported material goods expenditures, and investments. - Firm-to-firm transaction data (Form F3323) available 2004–2010: - Records buyer and seller tax IDs, transaction years, and values for each supplier-customer relationship. - Firms with total intermediate goods expenditures exceeding approximately USD 390,000 must report full supplier/buyer lists after meeting threshold once. - Reporting firms account for roughly 80 percent of Chile’s total value added (Huneeus, 2018). - Employer-employee matched data (Form DJ1887): - Links every formal-sector employee to their employer via tax IDs. - Monthly information on total labor income (wages, salaries, bonuses, tips, other taxable compensation). - Aggregated to annual level to track worker mobility, productivity of origin/destination firms, job switchers, and labor reallocation. - International trade datasets combined: - Customs data: transaction-level with firm tax IDs, destination/origin countries, transaction values, and 6-digit HS codes. Note: only the specific exposure share used in Section 4 may be matched to firm data. - BACI (CEPII): cleaned UN Comtrade, product-country-month level, includes month, transaction value, and quantity. - WITS (World Bank): tariff information, including MFN applied rates for China in 2003 and China’s preferential tariff rates applied to Chile in 2011. All tariffs used as Ad Valorem Equivalent (AVE) percentages. ### Sample construction and product focus - Merged sample spans 2003 to 2013 and includes firms with positive sales and material costs and at least one employee; non-missing industry classification required. - Analysis focuses on 83 commodity products actively sold from Chile and demanded by China from third countries (excluding Chile). - The 83 products include: - Copper products (refined copper, copper ore, copper concentrates, copper alloys, copper wire) - Other metals (molybdenum, iron ore) - Agricultural commodities (fresh fruit, wine, fishmeal, wood products) - Industrial minerals (lithium, iodine, sodium nitrate) - Typical commodity exporter specialization: median commodity exporter earns 93% of export value from a single 6-digit product. ### Empirical strategy overview - Identifying variation: differential changes in global commodity prices across granular products, mapped to firms via initial export specialization. - Long-difference specification captures cumulative, long-run effects: - Shock measured over 2003–2011; outcomes measured over 2005–2013 to allow a two-year lag for firm adjustment. - Regression specification (Equation (1)): - y_g_f = β_0 + β_1 shock_f + X'_f γ + ε_f - Dependent variable y_g_f is the growth rate of firm f’s outcome Y_f over 2005–2013, defined as y_g_f = 2(Y_f,2013 − Y_f,2005) / (Y_f,2013 + Y_f,2005), bounded between -2 and 2. - Outcomes: exports, domestic sales, material expenses, number of employees, sales per employee, investment, productivity, and worker mobility measures. - Controls X_f include 2-digit industry fixed effects and initial commodity share; standard errors clustered at the 4-digit industry level. - Results robust to controlling for initial firm size (sales or employment). ### Construction of product-level price changes and instruments - Analysis restricted to commodity products and the 2003–2011 period. - Baseline (direct) regressor: Chilean export prices to China: - ∆ lnP_CL_p = ln P_CL_p,2011 − ln P_CL_p,2003 - P_CL_p,t is price of product p (6-digit HS) exported from Chile to China at time t. - Instrumental variable (IV): Chinese import prices from countries excluding Chile: - ∆ lnP_OT_p = ln P_OT_p,2011 − ln P_OT_p,2003 - P_OT_p,t is Chinese import price of product p from countries other than Chile at time t. - IV isolates exogenous component of Chinese demand by purging influence of Chilean supply decisions. ### Law of One Price (LOP) tests and IV relevance - LOP implication: ∆lnP_CL_p = ∆lnP_OT_p if perfect; instrument requires significant but imperfect correlation. - Table 1 results (dependent variable: change in log Chilean export prices to China, 2003–11; independent: change in log Chinese import prices from other countries): - Column (1): coefficient on ∆ lnP_OT = 0.45 ∗∗∗ (standard error (0.12)); F-stat 14.5; r2 0.10; Observations 832. - Column (2) [2011 tariff = 0]: coefficient = 0.70 ∗∗∗ (0.20); F-stat 11.6; r2 0.30; Observations 855. - Column (3) [2011 tariff ≠ 0]: coefficient = 0.13 (0.13); F-stat 1.1; r2 0.00; Observations 832. - Columns (4)–(6) add initial (2002) tariff as control: - Column (4): coefficient = 0.44 ∗∗∗ (0.12); F-stat 7.7; r2 0.10; Observations 855. - Column (5): coefficient = 0.69 ∗∗∗ (0.21); F-stat 5.7; r2 0.30; Observations 855. - Column (6): coefficient = 0.19 (0.13); F-stat 1.0; r2 0.0; Observations 832. - Notes: robust standard errors in parentheses. * p<0.10, ** p<0.05, *** p<0.01. - Interpretation: - Estimated pass-through substantially less than 1 (e.g., 0.45), confirming imperfect LOP and instrument relevance. - Tariffs drive deviations: strong pass-through (0.70) for zero-tariff products; weak/insignificant (0.13) for positive-tariff products. ### Firm-level commodity price shock assignment - Firm-level shock construction: - shock^k_f = Σ_{p∈C} ω_pf ∆ lnP^k_p - ∆ lnP^k_p is product p price change (k = CL baseline or k = OT IV); C is set of commodity products; ω_pf is firm f’s initial (2003) export share of product p relative to firm’s total exports. - Two measures to ensure exogeneity: - ω_pf reflects product specialization across all export destinations, not only exports to China. - Shock assigned to all firms that exported at least one product China imported in 2003, regardless of whether the firm exported to China. - Practical implications: - Because the median exporter is nearly single-product (median earns 93% from single product), firm-level shock is essentially the price shock of the firm’s dominant product. - A shock built from each firm’s dominant product alone is almost perfectly correlated with the baseline and yields similar effects on firm outcomes. ### Firm market power and exogeneity evidence - Identification assumption: individual Chilean firms cannot significantly influence ∆ lnP_OT_p (Chinese import prices from other countries). - Table 2 evidence summarized: - Panel A (firm level): median firm accounts for essentially zero percent of global exports in its product category; largest firms average only 5%. - Panel B (country level): Chile supplies just 8% of global exports on average. - Panel C (influence on Chinese imports from third countries): median firm accounts for effectively zero percent of China’s imports; largest firms average just 7%. - These patterns support the exogeneity of the instrument and the firm-level shock. *Italic: wpiea2026163-source-pdf - 2004. Each firm and individual receives a unique tax ID, which allows us to link observations* ### Appendix A.3 provides further evidence showing that copper exporters also have limited market share ### Appendix A.3 provides further evidence showing that copper exporters also have limited market share individually. ### Chilean firm and product export shares (Table 2) - Panel A: Individual Firm Level - median Chilean firm’s share of global exports8300000 - max Chilean firm’s share of global exports83 .05.090 .01 .15 - Panel B: Country Level - Chilean share of global exports83 .08.110 .04 .24 - Chilean share of Chinese imports83 .11.190 .03 .34 - Panel C: Firm Influence on Chinese Imports - median Chilean firm’s share of Chinese imports 830.02000 - max Chilean firm’s share of Chinese imports83 .07.140 .01 .22 - Notes: Statistics summarize 83 commodity products in 2003. Panel A: Chilean firm shares in global exports. Panel B: Chile’s aggregate shares in global exports and Chinese imports. Panel C: Chilean firm shares in China’s total imports. Here, “median” and “max” refer to the median and largest Chilean firm by export value within each product. All shares calculated as firm (or country) exports divided by relevant global or Chinese import total. ### Pre-trend and identification considerations - The boom’s onset in the early 2000s is sharp and externally driven by China’s accession. - Exposure is uncorrelated with firms’ initial productivity: the correlation of the shock with initial TFPR is−0.027. - A fully dynamic event study across the pre-boom period would require firm-level export data before 2003, which the customs sample does not cover. ### The effects on upstream firms (Section 4.6) - Commodity exporters in Chile are largely supplied by other domestic firms. - Commodity exporters account for approximately 30% of the total revenues of these upstream suppliers. - Indirect exposure measure for an upstream non-commodity sector firm i is defined as: - indirect shock_i = Σ_{f ∈ customers of i} ω_if · shock_f (Equation (5)) - where ω_if denotes the share of non-commodity sector firm i’s sales to commodity firm f in firm i’s total sales, and shock_f is the direct commodity price shock faced by the commodity firm f. - For shock_f, the main regressor is the weighted average of Chinese commodity product import prices from Chile, and the instrumental variable is the weighted average of Chinese import commodity product prices from countries other than Chile. ### Empirical findings: firm-level outcomes (Section 5.1 and Table 3) - Table 3 reports IV and OLS estimates across seven outcomes: Exports, Employees, Materials, Capital, TFPR, Sales/emp., Domestic Sales. - IV estimates (commodity price shock): - Exports: 0.767*** (0.214) - Employees: 0.403* (0.205) - Materials: 0.575*** (0.142) - Capital: -0.331 (0.237) - TFPR: -0.024 (0.148) - Sales/emp.: -0.026 (0.179) - Domestic Sales: 0.062 (0.238) - OLS estimates (commodity price shock): - Exports: 0.240* (0.133) - Employees: 0.077 (0.062) - Materials: 0.147** (0.064) - Capital: -0.055* (0.032) - TFPR: 0.024 (0.020) - Sales/emp.: -0.046 (0.029) - Domestic Sales: -0.052 (0.071) - Sample and diagnostics: - N. of obs.758829828683682829808 - N. of clusters129838378788383 - First-stage F-stat. (IV)42.414.814.613.713.319.314.5 - Regression details: - Dependent variables are the DHS growth rates of exports, employees, materials expenditure, capital stock, TFPR, sales per employee, and domestic sales. - All regressions control for 2-digit industry fixed effects; standard errors clustered at the 4-digit industry level. - Export measured in Customs data as export value; other outcomes measured using firm-level administrative data. - Regressions weighted by export values for exports, by total sales for employees, domestic sales and materials expenditures. - * p<0.10, ** p<0.05, *** p<0.01. ### Interpretation of firm-level results - Positive external shock leads to substantial scale expansion for commodity-exporting firms: significant increases in exports, materials expenditures, and employment (IV estimates). - IV estimates generally exceed OLS estimates, consistent with classical measurement error and potential attenuation of OLS by negative supply shocks. - No evidence of long-term capital accumulation in response to the boom: - IV capital coefficient: -0.331 (statistically insignificant). - OLS capital coefficient: -0.055* (marginally significant decline). - No measurable efficiency gains: - TFPR (column 5) IV estimate: -0.024 (statistically insignificant). - Sales per employee IV estimate: -0.026 (statistically insignificant). - Domestic sales effects are negligible and statistically insignificant (Domestic Sales IV: 0.062; OLS: -0.052). - Implication: extensive growth (scale) without intensive improvement (productivity or capital accumulation). Unchanged TFPR may mechanically imply a decline in quantity-based productivity (TFPQ) if output prices rise. ### Productivity measurement and robustness - Firm-level productivity constructed as a Solow residual: - logtfpr_fjt = logy_fjt − α_j logl_fjt − β_j logm_fjt − (1−α_j − β_j) logk_fjt - Sector-level elasticities α_j and β_j derived from average ratios of wage bills to gross output and material expenditures to gross output, assuming constant returns to scale. - Alternative capital construction and robustness: - Baseline capital uses fixed assets in the tax form F22. - Alternative capital via perpetual inventory method assuming depreciation rate of 10%; the two measures are highly correlated (correlation coefficient of 0.95). - Control function approach (Ackerberg et al. 2015) and alternative production function specifications (Cobb-Douglas, translog, Leontief gross output with value added as in De Loecker and Scott (2025)) yield consistent results (Appendix Table A.4). - Results hold when excluding core copper mining (Table A.3), suggesting geological explanations alone do not drive across-firm reallocation toward lower-TFPR firms. ### Mechanisms and cross-sector propagation - The commodity boom reallocates labor toward less productive firms within the commodity sector, with low-revenue-productivity firms expanding workforce partly by attracting workers from more productive counterparts (see Figure 1 and Table 4). - Positive shocks propagate through domestic supply chain linkages to significantly improve the productivity of upstream firms (Table 5), consistent with productivity gains observed in other sectors (Figure A.1). *Source: Appendix A.3 and Sections 4–5 of the provided IMF working paper content.* ### 5.2 Labor Reallocation Toward Low-Productivity Firms ### 5.2 Labor Reallocation Toward Low-Productivity Firms ### Motivation and identification - Question: whether firms benefiting from the commodity price boom expand in ways that misallocate resources and depress aggregate productivity in the commodity sector. - Two potential channels for disproportionate expansion of less productive firms: - Selection bias: less productive firms systematically exposed to larger positive commodity price shocks. - Differential sensitivity: less productive firms are more responsive to shocks due to pre-existing distortions (e.g., preferential access to export markets or subsidized financing). - Identification: methodology in Section 4 constructs the main regressor and an instrumental variable to address selection concerns. - Direct test: correlation between the commodity price shock (defined in Equation(4)) and firms’ initial TFPR is −0.027 (s.e. 0.028), indicating shock exposure is uncorrelated with initial productivity and ruling out selection as the primary driver. ### Empirical evidence on wages and worker flows (Table 4, Panels A–B) - Panel A: Wage Growth (IV and OLS reported; IV coefficients highlighted) - New workers (log wage differences 2005–2013, hired after 2004): Commodity price shock 0.255*** (IV) - Existing workers (hired in 2004): Commodity price shock 0.394*** (IV) - Interpretation: commodity-exporting firms increase wages for both new and existing workers, with a particularly large effect on existing workers. - Sample sizes and diagnostics: N. of obs. 804 (new), 729 (existing); N. of clusters 838 (new), 379 (existing); First-stage F-stat. 14.9 (new), 13.4 (existing). - Panel B: Worker Mobility (shares of movers among total movers; IV coefficients) - Same sector movers: Commodity price shock 0.089*** (IV) - Higher TFPR movers (share coming from firms with higher TFPR in the same sector): Commodity price shock 0.157* (IV) - Interpretation: commodity-exporting firms attract workers from within the same sector and notably from higher-TFPR firms—evidence of "labor poaching". - Sample sizes and diagnostics: N. of obs. 751 (same sector), 644 (higher TFPR); N. of clusters 808 (same sector), 807 (higher TFPR); First-stage F-stat. 13.7 (same sector), 13.5 (higher TFPR). ### Differential employment responses by initial firm productivity (Table 4, Panel C) - Specification: DHS growth rate of employees; firms split by initial within-sector median TFPR; weighted by initial sales. - IV estimates: - TFPR ≥ p50 (higher productivity firms): Commodity price shock −0.163 (IV, not statistically significant) - TFPR < p50 (lower productivity firms): Commodity price shock 0.620** (IV) - Interpretation: - Less productive firms (TFPR < p50) exhibit a large and statistically significant increase in employees (0.620). - Higher productivity firms (TFPR ≥ p50) show no positive expansion and possibly contraction (−0.163). - This pattern implies resource reallocation toward less productive firms during the commodity boom, supporting the misallocation hypothesis. - Sample sizes and diagnostics: N. of obs. 458 (high TFPR), 368 (low TFPR); N. of clusters 676 (high), 754 (low), 54 (?), First-stage F-stat. 15.0 (high), 9.3 (low). ### Interpretation and robustness considerations - Differential sensitivity mechanism supported: less productive firms appear more responsive to commodity price shocks because pre-existing distortions allow them to expand at suboptimal productivity levels. - Potential alternative channel—markup interpretation: - Concern: TFPR might proxy for export-market markups rather than an export-related distortion. - The markup channel implies a positive TFPR–size gradient; in the data the correlation is zero to weakly negative, favoring the productivity-orthogonal wedge adopted by the authors (Appendix C.1.3). - Exclusion robustness: Table A.3 (referenced) presents results after excluding firms in the copper production sector, which remain similar to main results. ### Mechanism summary and implications for aggregate misallocation - Direct channel identified: expanding commodity-exporting firms pay higher wages and attract workers—often from more productive firms—creating a reallocation of labor toward lower-productivity firms. - Empirical evidence highlights two complementary features: - Wage increases for both new and existing workers in commodity-exporting firms (0.255 and 0.394 IV estimates). - Labor poaching from higher-TFPR firms (0.157 IV estimate for share of movers from higher TFPR firms). - Net effect: the commodity boom can exacerbate aggregate resource misallocation by incentivizing the growth of firms that may already be operating at suboptimal efficiency due to underlying distortions. *Source: 5.2 Labor Reallocation Toward Low-Productivity Firms (wpiea2026163-source-pdf).* ### 6.2 Firm-Level TFPR ### 6.2 Firm-Level TFPR ### Definition and measurement - Firm-level TFPR is defined as total revenue divided by a Cobb-Douglas aggregate of inputs: - tfpr_ij ≡ (p^H_ij y^H_ij + p^F_ij y^F_ij) / (l^{γ_L}_ij k^{γ_K}_ij m^{γ_M}_ij). (Equation (11) in source) - Measured TFPR combining first-order conditions and production technology (see Appendix Section B.3 for full derivation): - tfpr_ij = [1/(1−τ^F_ij)] s^F_ij · (μ^L_ij)^{γ_L} (s^L_ij)^{γ_L/(1+η)} · (W_j/γ_L)^{γ_L} (R/γ_K)^{γ_K} (P_M/γ_M)^{γ_M} - where F_ij = p^F_ij y^F_ij / (p^H_ij y^H_ij + p^F_ij y^F_ij) is the firm’s export share. (Equation (12) in source) ### Sources of TFPR dispersion (model implications) - Two principal, opposing channels generate TFPR dispersion: - Export wedge (policy-induced): - Export subsidies (more negative τ^F_ij) lower measured TFPR because subsidies allow lower export prices and higher output, reducing revenue per unit of input. - Effect is amplified when export shares s^F_ij are larger; export subsidies also tend to increase export shares. - Export subsidies are the primary source of misallocation in the calibrated model. - Labor market power (oligopsony): - Greater monopsony power (higher μ^L_ij) leads firms to restrict employment and to pay higher wages for larger firms (high s^L_ij), which raises prices and increases measured TFPR, partially offsetting the export-wedge distortion. - The term 1/(1+η) on the wage-bill-share captures attenuation of this channel when workers are more mobile (higher η); as η → ∞ the labor-market power channel vanishes. - Frictionless benchmark: - With τ^F_ij = 0 and competitive labor markets (η, θ → ∞), TFPR equalizes across firms. - Uniform positive export demand shocks exacerbate misallocation: - Firms with lower initial TFPR (those with larger export subsidies) expand disproportionately, because their larger subsidies make them more export-oriented initially, so the same demand shock yields larger expansion. ### Sectoral real TFP (aggregation) - Sectoral productivity A_j defined as: - A_j ≡ TFPR_j / PPI_j = [Σ_{i∈F_j} (a_ij TFPR_j / tfpr_ij)^{σ−1}]^{1/(σ−1)}. (Equation (13) in source) - Implication: - Sectoral productivity A_j depends on physical productivity a_ij and on allocation of resources across firms; greater TFPR dispersion (larger gaps between tfpr_ij and TFPR_j) reduces aggregate productivity. - A commodity boom reallocating inputs toward low-TFPR firms (those with export advantages) can lower A_j even if no firm’s a_ij declines. ### Calibration and key parameter values (Table 6) - Externally calibrated parameters (Panel A): - σ = 3 - η = 2.76 - θ = 0.42 - ρ = 2 - ψ = 0.5 - Production input shares (Panel B, from Chilean administrative data): - γ_L = 0.11 - γ_M = 0.59 - γ_K = 0.30 (imposed via constant returns to scale γ_K = 1 − γ_L − γ_M) - Internally calibrated distribution parameters (Panel C): - σ_a = 1.20 - σ_F = 0.53 - ̄D_F = 1.76 - Calibration targets and moments (Table 7, Panel A): - Var(sales)/mean(sales) — Data: 5.150, Model: 5.151 - Var(export share) — Data: 0.210, Model: 0.212 - Aggregate Export Share — Data: 0.710, Model: 0.710 ### Measuring the export wedge in the data (empirical microfoundation) - The export wedge τ^F is not directly observed in standard data; the authors measure a conservative lower-bound net export wedge for 2003 using four predetermined Chilean trade programs: - Subsidy-side programs: export rebates (Reintegro Simplificado and Drawback). - Restriction-side programs: fisheries individual transferable quotas and aquaculture concessions. - This net wedge is aggregated to firms by their 2003 export shares and captures explicit, legislated instruments (predetermined with respect to the boom). - Empirical finding: - Within sectors, firms facing a more favorable net wedge expand exports significantly more when the commodity shock arrives; the restriction (implicit-tax) margin carries the predicted negative sign. - The measured wedge corresponds to the policy microfoundation of τ^F; Appendix C formalizes two further microfoundations (heterogeneous intermediary access and variable export markups) that yield similar firm-level behavior. ### Quantitative assessment and model validation (Section 6.4) - Simulation design: - Focus on j = 1 (commodity sector) with representative firms in other sectors. - Simulate 10,000 firms in the commodity sector. - Shock implementation: - Randomly select half of the 10,000 firms to receive a large shock increasing their export demand D^F_i1 by 206% (corresponding to the 90–10 percentile difference in the firm-specific commodity price shock measure). - Scale up export demand for all firms proportionally to match the observed 83% aggregate export value growth between 2005 and 2013. - Compute simulated outcomes (exports, employment, wages, materials, TFPR) and run the same DHS growth rate regression as in the empirical analysis. - Model reproduction of untargeted empirical patterns (Table 7, Panel B — non-targeted regression coefficients; Data vs Model): - Exports — Data: 0.767*** ; Model: 0.953 - Average wage — Data: 0.293*** ; Model: 0.195 - Materials — Data: 0.575*** ; Model: 0.736 - TFPR — Data: −0.024 ; Model: 0.041 - Employees (Entire sample) — Data: 0.403* ; Model: 0.538 - Employees (TFPR ≥ p50) — Data: −0.163 ; Model: 0.383 - Employees (TFPR < p50) — Data: 0.620** ; Model: 0.633 - Key validation points: - Exports and variable inputs expand substantially in the model, consistent with data. - The simulated TFPR coefficient is small and similar to the statistically insignificant empirical estimate (model: 0.041; data: −0.024), consistent with opposing forces from τ^F dispersion and labor market power. - The model reproduces the asymmetric employment response: low-TFPR firms expand substantially (model: 0.633 vs empirical 0.620), while high-TFPR firms show muted expansion (model: 0.383 vs empirical −0.163, noting empirical estimate not statistically significant). - Mechanism operating in simulations: - Subsidized firms (τ^F_ij < 0) have higher export shares (approaching 100% for most heavily subsidized) and lower measured TFPR, so positive foreign demand shocks cause disproportionate expansion of these low-TFPR firms. - Expansion operates through oligopsonistic labor markets: booming firms raise wages to attract workers from competitors, reallocating labor toward low-TFPR firms and away from higher-TFPR firms. ### Aggregate productivity impact and welfare implications - Simulated aggregate effect: - Sectoral productivity in the commodity sector falls by 3.94% following the simulated commodity boom. - This accounts for roughly half of the 8% decline in Chilean mining TFP observed between 2005 and 2013. - Interpretation: - The misallocation mechanism (interaction of pre-existing export distortions with oligopsonistic labor markets) can explain a substantial share (~50%) of the observed aggregate productivity decline via compositional shifts in resource allocation. - Remaining gap (the other ~50%) likely reflects factors outside the model’s scope: within-firm declines in TFPQ due to long gestation lags and capacity constraints in mining capital investment, ore deterioration or lower stripping ratio (CNEP (2017)), or negative spillovers to non-exporting firms. - Welfare and policy-relevant takeaway: - Despite an 83% surge in export revenues and substantial employment expansion, pre-existing distortions (export wedges and labor market frictions) caused the commodity boom to reallocate resources toward firms with artificially enhanced export access rather than those with superior underlying productivity a_ij, reducing the sector’s ability to convert inputs into output. - In an undistorted economy (τ^F_ij = 0 for all firms and competitive labor markets), the same demand shock would not have reduced aggregate productivity. *Source: wpiea2026163-source-pdf - 6.2 Firm-Level TFPR* ### References ### wpiea2026163-source-pdf - References ### Bibliographic scope and thematic emphases - The references list extensive literature on: - Market size and innovation (e.g., Acemoglu and Linn (2004); Aghion et al. (2024)). - Identification and estimation of production functions and productivity (e.g., Ackerberg et al. (2015); Gandhi et al. (2020); De Loecker and Scott (2025)). - Misallocation, selection, and productivity dynamics (e.g., Adamopoulos et al. (2022); Hsieh and Klenow (2009); Restuccia and Rogerson (2017)). - Commodity booms, Dutch disease, and macroeconomic effects of commodity shocks (e.g., Corden (1984); Corden and Neary (1982); Drechsel and Tenreyro (2018); Shousha (2016)). - Trade, exporting, and firm performance (e.g., Atkin et al. (2017); Bloom et al. (2016); Boehm et al. (2023)). - Shift-share and quasi-experimental designs (e.g., Adao et al. (2018); Borusyak et al. (2022); de Chaisemartin and d’Haultfoeuille (2020)). - Sector- and country-specific studies related to Chile, copper, and resource-rich economies (e.g., CNEP (2017); De Solminihac et al. (2018); Oberfield (2013); Heresi (2023)). ### Key cited methodological contributions (selected) - Production function estimation and endogeneity controls: - Ackerberg, Daniel A, Kevin Caves, and Garth Frazer (2015): “Identification properties of recent production function estimators,” Econometrica, 83 (6), 2411–2451. - Gandhi, Amit, Salvador Navarro, and David A Rivers (2020): “On the identification of gross output production functions,” Journal of Political Economy, 128 (8), 2973–3016. - De Loecker, Jan and Paul T. Scott (2025): “Markup Estimation using Production and Demand Data: An Application to the US Brewing Industry,” Review of Economic Studies, accepted. - Shift-share design and inference: - Adao, Rodrigo, Michal Kolesár, and Eduardo Morales (2018): “Shift-Share Designs: Theory and Inference,” NBER working paper No.24944. - Borusyak, Kirill, Peter Hull, and Xavier Jaravel (2022): “Quasi-experimental shift-share research designs,” The Review of economic studies, 89 (1), 181–213. ### Domain-specific empirical contributions (selected) - Misallocation and productivity in China and India: Hsieh, Chang-Tai and Peter J Klenow (2009): “Misallocation and manufacturing TFP in China and India,” The Quarterly journal of economics, 124 (4), 1403–1448. - Commodity price cycles, capital flows, and sovereign defaults over long horizons: Reinhart, Carmen M, Vincent Reinhart, and Christoph Trebesch (2016): “Global cycles: Capital flows, commodities, and sovereign defaults, 1815–2015,” American Economic Review, 106 (5), 574–580. - Empirical work on commodity booms and localization effects: Allcott, Hunt and Daniel Keniston (2018); Drechsel, Thomas and Silvana Tenreyro (2018). --- ### Supplementary Material — Appendix overview and empirical findings H3: Appendix A. Empirical Appendix — Major components - A.1 TFP in Non-mining and Aggregate Sectors - TFP estimation equation: TFP is estimated as the residual of the equation log V A_{jt} = α_{j} log K_{jt} + (1−α_{j}) log L_{jt} + ε_{jt}, where α_{j} is calibrated at the sectoral level. - Variable definitions: V A_{jt} is real value added (sectoral chained price deflators); K_{jt} is capital stock at constant prices, adjusted for utilization rate; L_{jt} is total working hours, corrected for quality of human capital. - Figure referenced: “Figure A.1: Chile’s Non-Mining and Aggregate TFP” (visualizes Non-mining TFP and Aggregate TFP over 2000–2012). - A.2 The Firm-Level Commodity Shock — construction and properties - Shock definition: shock_f = Σ_p ω_{pf} ∆P_p, combining product-level price changes ∆P_p with each firm’s 2003 export shares ω_{pf}. - Key empirical regularities: - Product-level heterogeneity: log price changes vary across 6-digit HS products (Figure A.2; example products and HS codes listed in the notes). - Specialization: commodity exporters are highly specialized. - Median share of a firm’s exports in its single largest HS6 product: 0.93. - Effective number of HS6 products per firm (1/HHI_f): median 1.15; mean 2.09 (horizontal axis truncated at 15 in the figure). - Dominant-product decomposition: - shock_f = ω_{d(f)f} ∆P_{d(f)} + Σ_{p≠d(f)} ω_{pf} ∆P_p, where d(f) is firm f’s largest 2003 export product. - The dominant-product term accounts for most variation: a shock built from the dominant product alone has a correlation of 0.96 with the baseline shock and accounts for about 94% of its cross-firm variance (Figure A.4). - Sample size for the comparison: N= 1,400 (each point in Figure A.4 is a firm in the commodity sample with both shocks defined). - A.3 Market Shares: Copper Exporters - Table A.2 highlights copper product statistics (selected entries shown): - HS code 740311 — Copper (refined, cathodes): Global product share 0.39; Median firm share 0.01; Max firm share 0.20. - HS code 260300 — Copper (ores & conc.): Global product share 0.37; Median firm share 0.01; Max firm share 0.11. - HS code 740200 — Copper (unrefined anodes): Global product share 0.25; Median firm share 0.01; Max firm share 0.09. - HS code 740319 — Copper (refined, unwrought): Global product share 0.25; Median firm share 0.00; Max firm share 0.29. - HS code 740110 — Copper (copper mattes): Global product share 0.02; Median firm share 0.21; Max firm share 0.21. - Interpretation provided in text: - Even for products with high “global product share,” the median firm’s share in China’s imports is low (e.g., 0.01), and maximum firm shares for major products remain limited (e.g., 0.20). - Where firms have larger shares, those products often have small global product shares (e.g., HS 740110). - This pattern supports the plausibility of the instrument’s exogeneity by indicating limited firm market power in 2003. - A.4 Excluding Copper Sectors — IV estimates (selected regression output) - Table A.3 reports results from Equation (1), dependent variables = DHS growth rates: - Employees, Materials, Domestic Sales regressions (columns labeled (1)(2)(3) and repeated formatting indicates multiple specifications). - Reported coefficient fragments in the table extract: - Commodity price shock coefficients: 0.076 (0.062), 0.392* (0.204), 0.148** (0.064), 0.578*** (0.144), −0.051 (0.071), 0.163 (0.230). - Sample sizes and clustering: - N. of obs.: 814 814 813 813 793 793 (as reported). - N. of clusters: 82 82 82 82 82 82. - F-statistics for first stage (reported): 14.5 14.6 14.5. - Notes: All regressions control for 2-digit industry fixed effects; standard errors clustered at the 4-digit industry level; regressions weighted by total sales. - A.5 Alternative Measures of Productivity — control function/TFPR estimates - Methodology: - Implemented Ackerberg et al. (2015) control function approach with a two-step GMM estimator, using materials as a proxy for unobserved productivity shocks. - Four specifications vary by output concept (gross output versus value added / Leontief) and functional form (Cobb-Douglas versus translog). - Value-added specifications follow De Loecker and Scott (2025), modeling gross output as Leontief of value added and materials. - Main empirical finding: - Across all four specifications, no significant effect of commodity price shocks on firm-level productivity, consistent with baseline estimates in Table 3. - Table A.4 selected entries (Commodity Price Shock coefficients and standard errors): - Column (1) Gross Output Cobb-Douglas: −0.018 (0.021). - Column (2) Gross Output Translog: 0.011 (0.132). - Column (3) Leontief Cobb-Douglas: −0.013 (0.017); other entries listed as 0.186 (0.273). - Column (4) Leontief Translog: −0.027 (0.038); other entries listed as 0.045 (0.25) and −0.014 (0.586) and 0.089 (0.687) depending on cell. - N. of obs.: 574 (repeated across columns). - N. of clusters: 75 75 75 75 75 75 (as reported). - F-statistics for first stage: 9.8 9.8 12.2 12.2. - Notes: Dependent variables are firm-level TFPR (Ackerberg et al., 2015; De Loecker and Scott, 2025). All regressions control for 2-digit industry fixed effects; standard errors clustered at the 4-digit industry level. *Source: wpiea2026163-source-pdf - References (supplementary material including Appendix A).* ### Appendix B Theoretical Appendix ### Appendix B Theoretical Appendix ### B.1 Foreign Household Problem (Global Consumer) - Foreign household maximizes utility from consuming composite imported good C_x. - Preferences across differentiated varieties exported by firm i are CES with elasticity of substitution ξ >1. - Aggregate variety: C_x = (∑_i φ_i^{1/ξ} (c_xi)^{(ξ−1)/ξ})^{ξ/(ξ−1)}. - Associated price index: P_F = (∑_i φ_i (p_xi)^{1−ξ})^{1/(1−ξ)}. - Demand for firm i’s exported variety: - c_xi = φ_i (p_xi)^{−ξ} (P_F)^{−ξ} C_x. (Equation (15)) - Define D_Fi := φ_i C_x (P_F)^{−ξ} as an exogenous export demand shifter. ### B.2 Multi-Product Extension and Bartik Microfoundation - Multi-product firm structure: C_x is a nested aggregate grouped by product j, providing the microfoundation for the firm-specific Bartik instrument. - Outer nest (across products j ∈ J) uses Cobb-Douglas aggregation with expenditure shares α_j, ∏_{j∈J} α_j = 1: - C_x = ∏_{j∈J} (C_xj)^{α_j}. - Product-level demand from expenditure minimization: - C_xj = α_j E_F / P_Fj. (Equation (16)) - Inner nest (within product j): CES aggregate of firm i varieties y_xij with elasticity ξ >1: - C_xj = (∑_i (φ_i)^{1/ξ} (y_xij)^{(ξ−1)/ξ})^{ξ/(ξ−1)}. - Variety demand: - y_xij = φ_i (p_xij / P_Fj)^{−ξ} C_xj. - Substituting (16): y_xij = φ_i (p_xij)^{−ξ} α_j (P_Fj)^{ξ−1} E_F. (Equation (17)) - Derivation of the Bartik instrument: - Firm i’s export revenue from product j: R_xij = p_xij y_xij = φ_i (p_xij)^{1−ξ} α_j (P_Fj)^{ξ−1} E_F. - Log-differencing: - ∆ log R_xij = ∆ log φ_i + (1−ξ) ∆ log p_xij + ∆ log α_j + (ξ−1) ∆ log P_Fj + ∆ log E_F. - Let ω_ij,0 ≡ R_xij,0 / R_xi,0 be initial revenue share of product j in firm i’s export revenue. - Aggregate log change in firm i’s total export revenue: - ∆ log R_xi = ∑_{j∈J_i} ω_ij,0 ∆ log R_xij. - Substituting yields: - ∆ log R_xi = (ξ−1) ∑_{j∈J_i} ω_ij,0 ∆ log P_Fj + Ξ_i, (Equation (18)) - where Ξ_i := ∆ log φ_i + (1−ξ) ∑_{j∈J_i} ω_ij,0 ∆ log p_xij + ∑_{j∈J_i} ω_ij,0 ∆ log α_j + ∆ log E_F. - Define firm-specific Bartik shock: - Bartik Shock_i ≡ ∆ log P_Fi := ∑_{j∈J_i} ω_ij,0 ∆ log P_Fj. (Equation (19)) - ∆ log P_Fj is measured using Chinese import prices from countries other than Chile (IV specification) or Chilean export prices to China (OLS specification). - Theoretical coefficient on the Bartik shock in Equation (18) is (ξ−1). - Empirical IV estimate of 0.767 is consistent with ξ ≈ 1.77, indicating substitutability of firm varieties within same commodity product. ### B.3 Derivation of TFPR Expressions - Purpose: complete derivation of firm-level and sectoral TFPR expressions used in Section 6.2. B.3.1 Firm-Level Input Demands - Labor first-order condition (Equation (9) in main text): - γ_L p_Hij y_ij μ_{Lij} = [1 + 1/ε_{Lij}] w_ij. (Equation (20)) - Rearranged labor demand: - l_ij = p_Hij y_ij μ_{Lij} / w_ij = p_Hij y_ij μ_{Lij} (s_{Lij})^{1/(η+1)} W_j / γ_L = γ_L (1−τ^F_{ij} s^F_{ij}) r_ij μ_{Lij} (s_{Lij})^{1/(η+1)} W_j. (Equation (21)) - Uses l_ij = (w_ij / W_j)^η L_j and s_{Lij} = w_ij l_ij / (W_j L_j). - Uses r_ij = p_Fij y_Fij + p_Hij y_Hij and s_Fij = p_Fij y_Fij / r_ij, with p_Fij = p_Hij / (1−τ^F_{ij}) from Equation (8). - Capital and materials demands: - k_ij = γ_K (1−τ^F_{ij} s^F_{ij}) r_ij μ_R. (Equation (22)) - m_ij = γ_M (1−τ^F_{ij} s^F_{ij}) r_ij μ_{PM}. (Equation (23)) B.3.2 Firm-Level TFPR - TFPR definition (Equation (11)) with input demands substituted: - tfpr_ij = r_ij / (l_ij^{γ_L} k_ij^{γ_K} m_ij^{γ_M}). - Imposing constant returns to scale (γ_L + γ_K + γ_M = 1) yields: - tfpr_ij = μ (1−τ^F_{ij} s^F_{ij}) · ( (μ_{Lij} / s_{Lij})^{1/(1+η)} W_j / γ_L )^{γ_L} · (R^{γ_K})^{γ_K} · (P_M^{γ_M})^{γ_M}. (reduces to Equation (12) in main text) B.3.3 Sectoral Aggregates - CES labor aggregator: - L_j = (∑_{i∈F_j} l_{ij}^{(η+1)/η})^{η/(η+1)}. - Substituting l_ij yields expression in terms of firm market shares S_ij = r_ij / R_j and total sectoral revenue R_j. - Capital and materials aggregates (non-CES): - K_j = ∑_{i∈F_j} k_ij = ∑_{i∈F_j} γ_K S_ij (1−τ^F_{ij} s^F_{ij}) μ_R R_j. - M_j = ∑_{i∈F_j} m_ij = ∑_{i∈F_j} γ_M S_ij (1−τ^F_{ij} s^F_{ij}) μ_{PM} R_j. - Sectoral TFPR defined: - TFPR_j ≡ R_j / (L_j^{γ_L} K_j^{γ_K} M_j^{γ_M}). - Simplified sectoral TFPR: - TFPR_j = μ (W_j / γ_L)^{γ_L} (R^{γ_K})^{γ_K} (P_M^{γ_M})^{γ_M} · [ ∑_i ( S_ij (1−τ^F_{ij} s^F_{ij})^{μ_{Lij}} s_{Lij}^{1/(η+1)} )^{(η+1)/η} ]^{η γ_L/(η+1)} · [ ∑_i S_ij (1−τ^F_{ij} s^F_{ij}) ]^{γ_K+γ_M}. - (Expression as presented in the appendix text.) B.3.4 Sectoral Productivity - Sectoral productivity A_j defined as TFPR_j deflated by sectoral price index PPI_j: - A_j ≡ TFPR_j / PPI_j. - Sectoral price index: - PPI_j = (∑_{i∈F_j} \tilde p_{ij}^{1−σ})^{1/(1−σ)}, where \tilde p_{ij} = p_Hij y_Hij / y_ij + p_Fij y_Fij / y_ij = r_ij / y_ij. - Using production function y_ij = a_ij l_{ij}^{γ_L} k_{ij}^{γ_K} m_{ij}^{γ_M} and tfpr_ij = r_ij / (l^{γ_L} k^{γ_K} m^{γ_M}) gives: - \tilde p_{ij} = r_ij / y_ij = tfpr_ij / a_ij. - Substituting yields: - A_j = TFPR_j (∑_{i∈F_j} (tfpr_ij / a_ij)^{1−σ})^{−1/(1−σ)} = TFPR_j (∑_{i∈F_j} a_{ij}^{σ−1} tfpr_ij^{1−σ})^{−1/(1−σ)}. - Equivalently: A_j = (∑_{i∈F_j} (a_{ij} / TFPR_j · tfpr_ij)^{σ−1})^{1/(σ−1)}. (Equation (13) in main text) - Key implication: Greater dispersion in tfpr_ij across firms—holding the distribution of a_ij constant—reduces aggregate A_j, representing efficiency loss from misallocation. ### B.4 Firm-Level DRS and Measured TFP B.4.1 Setup - True firm-level production function with decreasing returns to scale (DRS): - Y_i = A_i · L_i^{α} · K_i^{β} · M_i^{γ}, where α + β + γ < 1. (Equation (24)) - Measured TFP assumes CRS and uses factor shares s_L, s_K, s_M summing to one (s_L + s_K + s_M = 1): - log[TFP_i] = log Y_i − s_L log L_i − s_K log K_i − s_M log M_i. (Equation (25)) B.4.2 Scaling Up Inputs - Scale all inputs by λ >1: - L'_i = λ L_i, K'_i = λ K_i, M'_i = λ M_i. (Equation (26)) - Under DRS, true output scales as: - Y'_i = A_i (λ L_i)^α (λ K_i)^β (λ M_i)^γ = λ^{α+β+γ} · Y_i. (Equation (27)) - Since α + β + γ < 1, Y'_i < λ · Y_i. B.4.3 Measured TFP After Expansion - Measured TFP after scaling: - log[TFP'_i] = log Y'_i − s_L log(λ L_i) − s_K log(λ K_i) − s_M log(λ M_i). (Equation (28)–(31)) - Simplifies to: - log[TFP'_i] = log[TFP_i] + [(α + β + γ) − 1] log λ. (Equation (31)) - Because (α + β + γ) − 1 < 0 under DRS, for λ >1: - log[TFP'_i] < log[TFP_i]. (Equation (32)) - Conclusion: Under firm-level DRS, expanding firms would exhibit declining measured TFP when measurement imposes CRS. B.4.4 Empirical Implication - If firm-level DRS exists, a firm scaling up inputs by factor λ >1 experiences a decline in measured TFP proportional to (α + β + γ − 1) log λ (with α + β + γ < 1 under DRS). - The appendix notes that empirical findings are robust across multiple specifications that do not impose CRS ex ante, suggesting firm-level DRS is not the primary explanation for observed patterns. *Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026163-source-pdf.pdf* ### Appendix C The Export Wedge ### Appendix C The Export Wedge ### The export wedge: definition and role - The export wedge τ^F_ij captures the gap between gross and net export revenue at the firm level in reduced form; it is modeled without committing to a single source. - The wedge enters firm first-order conditions and the TFPR decomposition, driving a misallocation mechanism whereby firms with more favorable net export treatment expand disproportionately under a commodity shock. - The appendix presents: (i) three microfoundations that generate the same firm-level conditions and aggregate mechanism; (ii) a statutory, product-level measurement of a concrete component of the wedge using administrative customs data (C.2); and (iii) an empirical test showing that firms with more favorable measured wedges expand exports more when the commodity shock arrives (C.3). ### C.1 Microfoundations of the export wedge - Overview: Three microfoundations for τ^F_ij are provided. The first two assume the wedge is orthogonal to underlying productivity; the third makes τ^F_ij endogenous to firm productivity via markup heterogeneity. - Choice for quantitative analysis: The productivity-orthogonal formulation is retained in Section 6.4 because it better matches the cross-sectional moments in the Chilean data (in particular, the empirical TFPR–size gradient is zero to weakly negative, which the markup microfoundation fits less well). Subcases: - C.1.1 Policy-induced per-unit advantages - Interpretation: τ^F_ij represents an ad valorem policy wedge on export revenues; negative τ^F_ij capture exporter advantages such as DL600 tariff exemptions, preferential mining concession royalty rates, subsidized export financing (ProChile, CORFO). - Measured instances: The four programs measured in C.2—the Reintegro and Drawback rebates and the ITQ and aquaculture restrictions—are explicit, quantifiable instances of this policy wedge. The unmeasured implicit advantages imply the measured wedge is a lower bound. - Fiscal closure: Government rebates net policy revenue lump-sum to households; transfer T = Σ_j Σ_{i∈F_j} τ^F_ij p^F_ij y^F_ij. Under GHH preferences, T does not affect labor supply and the aggregate equilibrium coincides with the baseline. - C.1.2 Heterogeneous intermediary access - Mechanism: τ^F_ij arises because firms differ in the share of their foreign-bound output that they can export directly versus sell to domestic intermediaries who export after extracting a markdown. - Firm-level direct access fraction: - η_ij ≡ (Σ_{p∈P^A_{ij}} p^F_ijp^F_ij y^F_ijp) / (Σ_{p∈P_{ij}} p^F_ijp^F_ij y^F_ijp) ∈ [0,1]. - Bargaining/markdown: - Nash bargaining with firm weight β and intermediary weight 1−β implies firm receives β p^F_ijp^F_ij on intermediated products; define δ ≡ 1−β, so firm receives (1−δ)p^F_ijp^F_ij on intermediated units. - Aggregate firm revenue and mapping: - Total retained revenue = [1 − (1 − η_ij) δ] R^F_ij. - Mapping to baseline: τ^F_ij = (1 − η_ij) δ ∈ [0, δ]; firms with η_ij → 1 have τ^F_ij → 0, those with η_ij → 0 have τ^F_ij → δ. - Empirical relevance and closure: - Intermediated foreign-bound output appears as domestic sales in tax records, creating cross-firm dispersion in observed export shares—used as the calibration target in Section 6.4. - Intermediary profits Π_I = Σ_j Σ_{i∈F_j} (1 − η_ij) δ R^F_ij = Σ_j Σ_{i∈F_j} τ^F_ij R^F_ij are absorbed into aggregate profits Π; under GHH preferences this does not affect labor supply. - C.1.3 Variable markup in the export market - Mechanism: τ^F_ij derives from endogenous markup heterogeneity under oligopolistic export competition (Atkeson and Burstein, 2008). Firms’ export markups μ^F_ij are increasing in their within-sector world export share s^F_{ij,W}. - Export demand elasticity: - ε^F_ij = σ − (σ − ζ) s^F_{ij,W}. - Export pricing and mapping: - Export price p^F_ij = μ^F_ij MC_ij; the baseline front markup μ/(1 − τ^F_ij s^F_ij) is replaced by ̄μ_ij ≡ [ (1 − s^F_ij) μ + s^F_ij μ^F_ij ]^{-1}. - The equivalence τ^F_ij s^F_ij = [1 − μ/μ^F_ij] s^F_ij implies τ^F_ij = 1 − μ/μ^F_ij in this mapping. - Quantitative and cross-sectional implications: - High-productivity firms (μ^F_ij > μ) map to positive effective wedges and tend to under-produce relative to a frictionless benchmark, ceding scale to lower-productivity firms—leading to a misallocation mechanism analogous to the other microfoundations. - However, because μ^F_ij is endogenous and increasing in firm size, this microfoundation predicts a positive TFPR–size gradient, while the Chilean data show a zero to weakly negative gradient; therefore this microfoundation fits the cross-sectional moments less well and is not pursued for quantitative calibration. ### C.2 Measurement of a statutory component of the wedge - Definition implemented: The wedge is measured as the net statutory subsidy or tax a firm faces on its exports, as a percent of FOB value: subsidy side minus restriction side. The measure is statutory-imputed (rate × eligibility) and therefore a conservative lower bound on the true dispersion. - Data sources: Institutional program index combined with two administrative customs files: - AduanasSalidas (2003): taxpayer ID, HS6 product, FOB value, operation-type code (distinguishes genuine exports from re-exports and temporary movements). - AduanasEntradas (2003): CIF value and duties actually paid. - Programs included (four programs, two subsidy-side, two restriction-side): - Subsidy side: - Reintegro Simplificado (Law 18,480, 1985): cash payment of 3% of FOB to exporters of non-traditional goods. - Drawback (Law 18,708, 1988): refunds import duties paid on inputs incorporated into the export, with an ad valorem equivalent equal to the product’s input tariff t_h (defined below). Reintegro and Drawback are statutory alternatives; the subsidy rate on a shipment is the larger of the two. - Restriction side: - Fisheries individual transferable quotas (ITQ, Law 19,713, 2001): cap the catch and act like a tax on marginal catch worth roughly 15% of landed value. - Aquaculture concessions (Decree 125 of 2003): administrative limits on number and size of maritime sites, treated as a 2% restriction. - Product-level wedge construction (for each HS6 product h): - subsidy_h = max { 0.03·1[Reintegro_h], t_h·1[Drawback_h] } · s^norm_h - restriction_h = (0.15·1[ITQ_h] + 0.02·1[Aqua_h]) · s^norm_h - net product wedge τ_h = subsidy_h − restriction_h - Notes on components: - t_h (input tariff) construction from customs data: - national HS6 tariff t^nat_j = Σ_{2003} duties_j / Σ_{2003} CIF_j, capped at the statutory 11%; - firm input tariff t^input_f = Σ_j w^imp_{fj} t^nat_j, where w^imp_{fj} is firm f’s CIF share in input j; - product tariff t_h = Σ_f w^exp_{fh} t^input_f, the FOB-weighted average of t^input_f across firms exporting h. - s^norm_h is the 2003 FOB share of h shipped under the normal-export operation code; it down-weights products with high re-export or temporary-movement shares (median s^norm_h = 1). - Firm-level wedge aggregation: - τ^F_f = Σ_h w_{fh} τ_h, where w_{fh} is firm f’s 2003 FOB share in commodity-shock product h. - τ^F_f is predetermined relative to the 2003–2011 shock and lies in the same shift-share space as the firm shock. - In the commodity-exporter sample τ^F splits into: net-subsidy firms (Reintegro/Drawback-eligible, τ^F > 0), zero-wedge firms (mining, primary copper, raw agriculture, τ^F ≈ 0), and net-restriction firms (fisheries and aquaculture, τ^F < 0). - Scope and caveats: - The measure captures explicit statutory instruments only; implicit support (state financing for the national copper producer, DL 600 tax stability, sectoral promotion) is not measured, reinforcing the lower-bound interpretation. - The copper-export levy (Cobre Reservado, Law 13,196) is excluded since it falls by statute on a single firm whose net position is confounded by unmeasured state support. ### C.3 Empirical test: the wedge predicts differential export expansion - Hypothesis (misallocation prediction): If τ^F_f captures a genuine export advantage, firms with a higher net wedge should expand exports more when the commodity shock hits; formally the interaction coefficient γ on shock_f × τ^F_f should be positive. - Estimation specification: - g_f = β shock_f + δ τ^F_f + γ (shock_f × τ^F_f) + α_{h(f)} + ε_f - g_f is 2003–2011 export growth (Davis–Haltiwanger–Schuh mid-point growth); α_{h(f)} are dominant 2-digit sector fixed effects; the wedge is centered; standard errors clustered at the dominant HS2 level. - Main result (Table A.5): - Coefficient on Shock × net wedge = 4.18** (column 1), 4.27** (column 2), 4.17** (column 3). - Corresponding standard errors reported in parentheses: (1.96), (2.04), (1.95). - Sample size: Firms = 760. - Robustness: Effect is robust to dropping the normal-channel multipliers s^norm_h and to winsorizing the outcome at the 1st and 99th percentiles. - Decomposition: The net effect is driven by the restriction (implicit-tax) side; the subsidy side has little cross-firm variation in this sample and is imprecisely estimated. - Interpretation: - Comparing firms within the same broad sector (dominant HS2), those with a more favorable net wedge expand exports significantly more when the commodity shock arrives, consistent with the model’s misallocation mechanism. *Appendix C from "Commodity Booms, Productivity, and Misallocation: Evidence from Chile’s Administrative Data", Working Paper No. WP/2026/163* --- _Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026163-source-pdf.pdf_