## Industrialization and the Big Push: Theory and Evidence from South Korea — Working Paper No. WP/2024/259

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### Overview and research question
- Examines whether a one-time “big push” of temporary, targeted subsidies for technology adoption could shift an economy from a low-adoption to a high-adoption industrial steady state, using Korea’s Heavy and Chemical Industry (HCI) Drive (subsidies concentrated 1973–1979) as a case study.
- Two main contributions:
  - Causal, firm-level evidence on direct adoption effects, local spillovers, and local complementarity from novel historical microdata.
  - A calibrated multi-region, multi-sector quantitative model pinned down by empirical estimates to assess multiplicity and whether Korea’s policy produced a permanent industrial shift.

### Data and empirical setting
- Universe of technology contracts: 1,634 contracts signed by 587 unique Korean firms (1970–1982); 85% in heavy manufacturing; 95% transferring know-how.
- Balance-sheet panel: 6,230 unique firms, 29,786 firm-year observations (1970–1982); covers firms with >50 employees; monetary values in 2015 USD; sample covers 70% of national manufacturing gross output.
- Geographic aggregation: 86 regions; 4 of 10 manufacturing sectors classified as heavy manufacturing.
- Policy instrument: allocation of foreign credit (government guarantees lowered dollar-denominated borrowing costs) concentrated 1973–1979; other concurrent policies (industrial complexes, export promotion, tariff exemptions) exist but analysis focuses on the technology-adoption channel.

### Principal empirical findings — direct effects on adopters
- Identification: winners vs. losers design (firms whose foreign contracts were canceled by foreign partners provide plausibly exogenous non-adoption controls), matched within region-sector and by size variables; event-study and pooled diff‑in‑diff specifications; robustness to alternative staggered-DiD estimators and inference.
- Key magnitudes (winners vs. losers pooled diff‑in‑diff):
  - Technology adoption increased winners’ sales by 0.91*** (interpreted as 91%).
  - Technology adoption increased winners’ revenue TFP (TFPR) by 0.94*** (interpreted as 94%).
- Event-study selected coefficients (log-sales; TFPR):
  - 4 years post-adoption: Sale 1.19**; TFPR 1.30*** (i.e., 119% and 130% increases).
  - Pooled estimates robust across inference methods; TWFE full-sample estimates smaller (Adoption×Post = 0.17** for Sale and 0.10** for TFPR in full-sample TWFE columns).

### Principal empirical findings — local spillovers (never-adopters)
- Outcome: long-difference regressions Δy_it on Δ Share(−i)_n j, t−2 (share of local adopters excluding firm i), with IV to address endogeneity.
- IV construction: leverage business-group networks using pre-existing group-level adopters located outside a 100 km radius of focal region; IV = long-difference of these pre-existing outside-group adopter shares (ΔZ_≥100km,t0).
- Preferred IV estimates (Panel A and B, long-differences 1972–1979 / 1973–1980):
  - A 1 percentage point increase in local adopter shares → 2.7% higher sales (Panel A preferred IV coefficient 2.70*** (0.74)).
  - A 1 percentage point increase in local adopter shares → 1.6% higher revenue TFP (Panel B preferred IV coefficient 1.60*** (0.55)).
- First-stage and instrument strength:
  - First-stage coefficient ≈ 0.19; KP‑F statistics reported across specifications (e.g., 17.83, 21.54, 20.25), indicating strong instruments by rule-of-thumb and Montiel Olea and Pflueger (2013) thresholds.
- Robustness:
  - Results robust to controls for predicted business-group sales shares, market access, distance-to-port interactions, cumulative directed credit, industrial-complex dummies, tariff interactions, exclusion of large business groups, alternative radii (50–150 km), and multiple inference procedures.

### Principal empirical findings — local complementarity in adoption decisions
- Outcome: probability of making a new adoption contract 1[New Contract_it] regressed on Δ Share(−i)_n j, t−2; IV strategy analogous to spillovers but applied to adoption entry.
- Main IV estimates (Table 4, preferred specifications):
  - IV coefficient ≈ 0.85 (standard error 0.41), statistically significant; i.e., a 1 percentage point increase in local adopter shares raises the probability of making a new contract by 0.85 percentage points.
  - Interpretation: 0.85 p.p. is about 14% of the average annual adoption probability in 1979 (the 1979 average probability = 6%).
- Market-access heterogeneity:
  - High-market-access regions show larger complementarity: High MA × ΔShare = 1.07 (0.56), Low MA × ΔShare = 0.29 (0.17); difference significant at 10% level.
- Robustness: consistent across alternative IV specifications, placebo tests, distance thresholds, and sample restrictions.

### Simple theoretical model — mechanisms and analytical results
- Firms decide whether to adopt a modern technology after paying fixed adoption costs F_T (in final goods); adopters gain direct productivity multiplier η and productivity also rises with lagged regional adopter share via f(λ_T,t−1) = exp(δ λ_T,t−1).
- Analytical results:
  - Dynamic complementarity: higher λ_T,t−1 raises λ_Tt via spillovers and lower effective adoption costs.
  - Multiple steady states: with intermediate ranges of η and δ, model can display a low-adoption (“pre-industrialized”) and a high-adoption (“industrialized”) steady state; a temporary subsidy can shift the economy across basins of attraction (big push).
  - Multiplicity requires η and δ in medium ranges; if too small or too large, multiplicity disappears.

### Quantitative model, calibration, and targeted mappings
- Model features: multi-region, multi-sector (commodity, light manufacturing, heavy manufacturing, services), input-output linkages, internal/international trade costs, heterogeneous firms with Pareto productivity distribution, adopters subsidized via input subsidies s_n j t.
- Period mapping: each model period = 4 years; calibration years t = 1 (1972), t = 2 (1976), t = 3 (1980); fundamentals held constant at 1980 thereafter.
- External calibration mappings:
  - σ = 4.
  - η mapped from winners vs. losers pooled diff‑in‑diff: η = exp(0.9/(σ − 1)) = 1.35 (0.9 is pooled estimate).
  - δ mapped from IV spillover semi‑elasticity: δ = 2.7/(σ − 1) = 0.90 (2.7 is IV average).
  - θ = 1.06 × (σ − 1).
  - Distance elasticity ξ = 0.43 (mapping ξ = 1.29/(σ − 1)); τ_nmj = Dist_nm^ξ; highway reduces travel times by 66% on connected routes.
- Internal calibration results (Table 5):
  - Calibrated subsidy rate ̄s = 0.081 (8.1%).
  - Subsidies in 1976 and 1980 equal 1.35% and 1.40% of GDP, respectively, on average across subsidized regions.
  - Pareto upper bound κ = 1.519 (identifies share of regions with zero adoption).
  - Fixed adoption costs imply Σ_n F_T c_n j t is 35.1 times larger than Σ_n F^x_j w_n t (total fixed export costs).
- Model matches targeted and non-targeted moments (e.g., average adopter shares, exporter shares, regional patterns, relationships with market access and distance-to-port).

### Counterfactuals and welfare effects (big push vs no-subsidy)
- Counterfactual: set s_n j t = 0 (no temporary adoption subsidies).
- Convergence: both baseline and counterfactual converge to steady states ≈ 24 years (6 periods) after 1980.
- Aggregate steady-state differences (Baseline minus No-subsidy):
  - Δ heavy manufacturing GDP share = 1.95 percentage points (reported as an 8.6% decrease in the no-subsidy steady state relative to baseline).
  - Δ export intensity = 3.33 percentage points (reported as a 16.2% decrease in the no-subsidy steady state).
  - Δ employment share = 0.68 percentage point (reported as a 9.6% decrease).
  - Δ aggregate welfare (population-weighted) = 1.27 percent (consumption-equivalent; discount factor 0.85 = 0.96^4).
- Local heterogeneity (ranges across 86 regions):
  - Δ heavy manufacturing GDP shares: [−1.43, 52.93] (percent).
  - Δ export intensities: [−7.92, 3.45] (percentage points).
  - Δ employment shares: [0.68, 10] (percentage points).
  - Δ welfare: [−1.44, 37.52] (percent).
  - 66 out of 86 regions experience welfare gains; 20 regions experience welfare losses.
- Mechanisms for uneven regional gains:
  - Productivity gains in subsidized regions lower prices via internal trade linkages, benefiting some regions but increasing competition and reducing profits in others.

### Firm scale, market access, and scenario experiments (Table 8)
- Baseline: ΔHeavy mfg. GDP shares (p.p) = 1.95; ΔAggregate welfare (%) = 1.27; Big push occurs = Y.
- Alternative counterfactual scenarios (temporary reductions in firm scale during policy periods only):
  1. Lower foreign demand (held at 1972 level in 1976 & 1980): ΔHeavy mfg. GDP shares = 0.25 p.p.; ΔAggregate welfare = 0.43%; Big push occurs = Y.
     - Context: foreign demand rose by 48% between 1972 and 1980 in the data.
  2. Higher tariffs (tariff rates increase 40% between 1972 and 1980): ΔHeavy mfg. GDP shares = 1.91 p.p.; ΔAggregate welfare = 1.14%; Big push occurs = Y.
     - Context: actual tariffs fell 40% (from 38.4% to 23.4%) between 1972 and 1980.
  3. No highway (reversing 66% travel-time reduction): ΔHeavy mfg. GDP shares = 1.71 p.p.; ΔAggregate welfare = 0.90%; Big push occurs = Y.
  4. No internal trade (prohibit internal trade within heavy manufacturing): ΔHeavy mfg. GDP shares = 0.00 p.p.; ΔAggregate welfare = 0.00%; Big push occurs = N.
  5. Joint adverse scenario (Lower foreign demand + Higher tariffs + No highway): ΔHeavy mfg. GDP shares = 0.00 p.p.; ΔAggregate welfare = 0.00%; Big push occurs = N.
- Key interpretation: market access (internal and international) and complementary policies (trade openness, infrastructure) amplify firm scale and are crucial for big-push success; shutting down internal trade prevents the big push.

### Alternative policy experiments and optimal subsidy
- Randomized subsidy allocation across regions (35 subsidized regions, 1,000 simulations):
  - Distance to port and market access are positively correlated with steady-state increases in heavy manufacturing shares and welfare; targeting low market-access regions makes the big push unlikely.
- General (untargeted) subsidies to all firms at the baseline 8.1% rate:
  - Do not generate the big push; welfare gains = 0.29%.
  - Mechanism: general subsidies increase domestic competition and reduce adoption incentives; targeted adoption subsidies are necessary to address coordination failures.
- Welfare-maximizing subsidy (numerical search):
  - Optimal subsidy rate ≈ 12%; yields welfare gains = 2.0% (0.78 percentage points higher than baseline); generates an even higher heavy-manufacturing steady state than baseline.

### Robustness, sensitivity, and statistical uncertainty
- Sensitivity re-calibration across 95% CI ranges for mapped parameters:
  - Big push occurs only for medium ranges of (σ − 1)δ and η.
  - For (σ − 1)δ below 1.70 (1.5 std. lower than baseline), big push fails (Δ heavy mfg. GDP share = 0).
  - For η, big push occurs for lower half of 95% CI; fails for η above 1.2 (0.5 std. higher than baseline).
  - Conclusion: the calibrated big push is not robustly identified at 95% confidence for all parameter uncertainty; multiplicity is a quantitative (not qualitative) possibility.
- Extensions:
  - Myopic migration (spatial mobility) amplifies the big push (Δ heavy mfg. GDP share rises from 1.95% to 2.72%).
  - Lower σ or θ increases amplification (re-calibrated results reported).
- Empirical robustness:
  - Direct-effect, spillover, and complementarity results robust to alternative samples, matching procedures, IV definitions, exclusion of large groups, placebo windows, spatial radii, and various inference methods (randomization inference, wild bootstrap, spatial HAC, Anderson‑Rubin tests).

### Policy implications and conclusions
- Empirical evidence supports three channels necessary for a big push: large private direct returns to adoption, positive local spillovers to non-adopters, and local complementarity (coordination failures) in firms’ adoption decisions.
- Temporary, targeted subsidies that reduce effective adoption costs can trigger a permanent shift to a more industrialized steady state when market access and complementary policies enable firm scale and amplification.
- Policy recommendations:
  - Target interventions to adoption decisions (address coordination failures) rather than broad production subsidies.
  - Ensure complementary market-access policies (trade openness, export promotion, transportation infrastructure) to amplify subsidies’ effects.
  - Careful regional targeting is crucial: subsidizing regions with low market access is unlikely to produce a national big push; targeting regions with higher market access (or policies that raise market access) improves chances of success.
- Broader implication: big-push industrial policy can work but requires specific parameter ranges (moderate direct gains and spillovers), targeting of coordination failures, and supporting market-access-enhancing policies.

*Source: Industrialization and the Big Push: Theory and Evidence from South Korea — Working Paper No. WP/2024/259*

### 1. Introduction

### 1. Introduction

### Overview and research question
- Examines the possibility of industrialization through a one-time “big push” for technology adoption, focusing on Korea’s large-scale policy that temporarily subsidized adoption of modern technology in heavy manufacturing sectors from 1973 to 1979.
- Two main contributions:
  - Causal, firm-level evidence on adoption effects, local spillovers, and local complementarity using novel historical microdata.
  - A calibrated quantitative model where key parameters determining multiplicity (multiple steady states) are pinned down by empirical estimates to assess whether Korea’s policy shifted the economy to a more industrialized steady state.

### Dataset and context
- Universe of technology adoption contracts between Korean and foreign firms from 1970 to 1982, manually digitized from contract documents filed with government authorities.
- Technology adoption defined as transfers of industrial know-how: transfers of blueprints or provision of training services to facilitate mass industrial production.
- Empirical pattern highlighted:
  - Heavy manufacturing sectors’ share of GDP increased from 6% to 13% during the policy period.
  - Fourfold increase in the number of new adoption contracts in heavy manufacturing during the policy period.
  - Appendix Figure B1 shows similar patterns for employment and exports.

### Policy instrument and background
- Policy: Heavy and Chemical Industry (HCI) Drive launched late 1972 to modernize and expand chemicals, electronics, machinery, steel, non-ferrous metal, and transportation equipment.
- Main subsidy instrument: allocation of foreign credit functioning as subsidies because foreign transactions were denominated in dollars and government guarantees enabled lower borrowing costs.
- Policy was temporary, concentrated between 1973 and 1979; foreign credit to heavy manufacturing surged only in that interval.
- Other concurrent policies (industrial complexes, export promotion, input tariff exemptions) existed, but the analysis focuses on the technology-adoption channel.

### Novel empirical pattern consistent with the big push
- Heavy manufacturing share of GDP rose from 6% to 13% during the subsidy period.
- Number of adoption contracts in heavy manufacturing rose fourfold during the policy period.
- The economy continued to specialize in heavy manufacturing even after the policy ended.

### Key empirical identification strategies
- Winners vs. losers research design to address selection: compare successful adopters (“winners”) with firms that initially signed contracts but failed or were delayed due to foreign firms canceling contracts (“losers”); losers matched to observationally similar winners and analyzed in a stacked-by-event design.
- IV strategy for local spillovers and complementarity: use spatial networks of business groups with multiple firms across regions, exploiting group-level adoption decisions as exogenous shifters for regional adopter shares.

### Principal empirical findings (firm-level)
- Direct effects on adopters (winners vs. losers):
  - Technology adoption increased winners’ sales by 91%.
  - Technology adoption increased winners’ revenue total factor productivity (TFP) by 94%.
- Local spillovers to non-adopters (IV estimates):
  - A 1 percentage point increase in adopter shares led to 2.7% higher sales for non-adopters.
  - A 1 percentage point increase in adopter shares led to 1.6% higher revenue TFP for non-adopters.
- Local complementarity in adoption (IV estimates):
  - A 1 percentage point increase in adopter shares led to a 0.85 percentage point higher probability of adopting new technologies.
  - This 0.85 percentage point effect is about 14% of the average annual adoption probability in 1979 (the policy end year).
  - Complementarity was stronger in regions with larger market access.

### Interpretation of empirical findings
- Despite large private returns to adoption (direct effects), local complementarity indicates firms were less likely to adopt unless other local firms had already adopted—evidence of coordination failures.
- Local spillovers suggest private returns alone may be insufficient to resolve coordination failures, motivating targeted subsidies.

### Simple theoretical model — setup and analytical results
- Firms choose whether to adopt more productive modern technologies after incurring fixed adoption costs (in units of final goods).
- Spillovers operate with a one-period lag: current productivity increases with adopter shares in the previous period, making adopter shares a time-varying state variable.
- Three main analytical results:
  - Dynamic complementarity: higher adopter shares in the previous period lead to higher shares in the current period. This arises from spillovers and fixed adoption costs—larger spillovers reduce effective adoption costs in the following period.
  - Potential for a big push (multiple steady states): dynamic complementarity can generate a “pre-industrialized” steady state with low adopter shares and an “industrialized” steady state with high adopter shares. Temporary subsidies (a one-time big push) can permanently shift the economy away from the pre-industrialized basin of attraction.
  - Multiplicity arises only when the two parameters governing direct gains and spillovers are in medium ranges; if either parameter is too strong or too weak, multiple steady states do not arise. Thus, the big push is a quantitative question requiring specific parameter ranges.

### Quantitative model, calibration, and targeted moments
- Extended model features: costly internal and international trade, input-output linkages across multi-sectors, and heterogeneous firms with discrete adoption choices.
- Calibration approach:
  - Map two key parameters that determine multiplicity to reduced-form empirical estimates derived from the model.
  - Calibrate remaining parameters via indirect inference to match targeted and non-targeted moments.
  - Model matches both targeted and non-targeted moments, including relationships between regional adoption levels and market access.
- Subsidy calibration:
  - Calibrated subsidy implies adopters are subsidized with 8.1% of their input expenditures.
  - On average, about 1.4% of GDP is spent on these subsidies during the policy periods.

### Counterfactuals and welfare effects
- Counterfactual without subsidies (no big push) versus baseline with subsidies:
  - Without the big push, Korea would have converged to a less-industrialized steady state.
  - Heavy manufacturing sector’s GDP share would be 8.6% lower in the no-subsidy steady state than in the baseline steady state.
  - Export intensity (exports-to-gross-output ratio) would be 16.2% lower in the no-subsidy steady state than in the baseline steady state.
  - Aggregate welfare was modestly raised by 1.27% under the big push (baseline).
  - Regional welfare gains were uneven, ranging from −1.44% to 37.52%.
- Mechanisms behind uneven regional gains:
  - Productivity gains in some regions lowered prices via internal trade linkages, boosting welfare elsewhere.
  - Increased domestic competition reduced profits in other regions.

### Market access, amplification, and hypothetical scenarios
- Larger internal and international market access increased firm scale and amplified the big push effects.
- Three hypothetical scenarios temporarily reducing firm scale during the policy periods (post-1980 levels unchanged) and their impacts:
  1. Foreign demand held constant at its initial level (instead of growing).
  2. Protectionist tariff scheme: import tariff rates increased by 40% (opposite to the 40% reduction observed in the data), increasing costs of imported intermediates.
  3. No transportation improvements: undo the 66% reduction in travel times due to highway construction in 1970, increasing internal trade costs.
- Findings from scenarios:
  - Subsidies still change steady states but have weaker effects than the baseline.
  - Lower foreign demand has the greatest negative impact on the big push’s success.
  - When all three adverse scenarios are combined, the big push does not occur even with subsidies.
- Implication: market access and complementary policies are crucial for big-push success.

### Alternative policy experiments and optimal subsidy
- Randomizing subsidy allocation across regions:
  - Allocating subsidies to regions with lower market access makes the big push unlikely.
  - Emphasizes the importance of market access in subsidy targeting.
- General subsidies to all firms (non-targeted):
  - General subsidies do not generate the big push.
  - Highlights need for targeted subsidies that address coordination failures rather than untargeted transfers.
- Numerical search for welfare-maximizing subsidy rate:
  - The optimal subsidy rate exceeds the baseline calibrated rate.
  - The welfare-maximizing subsidy yields a steady state with even higher heavy manufacturing GDP shares than the baseline.

### Relation to literature
- Contributes to literature on big push, coordination failures, and industrial policy by quantifying an actual big push episode using a structural model disciplined by causal evidence.
- Model relates closely to Buera et al. (2021) and extends to an open, multi-region economy where complementarity arises from local spillovers and market access amplifies effects.
- Bridges theory and data in the spirit of recent structural quantifications of industrial policy but focuses on coordination failures and the technology adoption channel in a historical Korean episode.

*Source: wpiea2024259-print-pdf - 1. Introduction*

### 2.2  Data

### 2.2 Data

### Dataset construction
- Coverage: manufacturing firms between 1970 and 1982, classified into 10 broad manufacturing sectors; among these 10 sectors, 4 sectors are categorized as heavy manufacturing.
- Geographic aggregation: data is aggregated to 86 regions.
- Further details on data construction are in Appendix A.

### Technology adoption data
- Source: manually collected and digitized firm-level data on technology adoption from official technology contract documents (National Archives of Korea) and surveys published by the Korea Industrial Technology Association.
- Document coverage period: 1962 to 1988; overlap with balance sheet information: 1970 to 1982.
- Contracts and firms: 1,634 contracts signed by 587 unique Korean firms between 1970 and 1982.
- Contract characteristics:
  - 85% were in heavy manufacturing sectors.
  - 95% involved the transfer of know-how (e.g., blueprints or training services provided by foreign firms).
  - Geographic origin of contracts (among the 1,634): 57% came from Japan and 21% from the US (Appendix Figure B5).
- Institutional process: once approved for technology adoption, firms reported to the Economic Planning Board; related documents preserved in the National Archives of Korea.

### Balance sheet, business group affiliation, and geographic information
- Source: Annual Reports of Korean Companies published by the Korea Productivity Center (digitized).
- Coverage: firms with more than 50 employees; variables include sales, assets, fixed assets, and exports from 1970 to 1982 (employment available starting from 1972).
- Monetary values: converted into 2015 US dollars.
- Sample size and representativeness:
  - 6,230 unique firms.
  - 47% classified as heavy manufacturing.
  - Representative at the national level, covering 70% of national manufacturing gross output.
  - Authors note: “To the best of our knowledge, this is the first paper to use firm panel data from 1970s Korea.”
- Merge: balance sheet data merged with technology adoption data based on firm names.
- Employment data limitations:
  - Some observations missing employment.
  - Employment available only from 1972 onward.
  - Observations are dropped only when employment is required in analysis; robustness checks conducted on missing data issue.
- Plant addresses and business group (chaebol) affiliation recorded in surveys and used to link adoption activities to production locations and to construct instruments for local spillovers and complementarity.
- Business groups:
  - 59 business groups.
  - Average of 5 firms per group.
  - 306 firms affiliated with business groups (about 5% of 6,230 firms).
  - Appendix Table A2 reports business groups’ distributions of firms across sectors.

### Directed credit and export promotion (government support)
- Motivation: unobserved government support is a significant source of endogeneity for empirical analysis.
- Directed foreign credit:
  - Data on total amounts of foreign credit allocated by the government from Choi and Levchenko (2024).
  - Annual information on total credit received by each firm is available; specific amounts allocated to each contract are not available.
  - Credit data used as a primary instrument for subsidizing technology adoption.
- Export promotion:
  - Korea’s Trade Promotion Agency (KOTRA), established in 1962, promoted firm exports via international trade fairs.
  - KOTRA’s Annual Reports on International Trade Fairs used to obtain information on each firm’s total contract values and attendance at trade fairs.
- Use: firm-level information on directed foreign credit and export promotion used as control variables and to assess validity of identifying assumptions.

### Sectoral and regional data
- Import tariffs: obtained from Luedde-Neurath (1986).
- Input-output tables: from the Bank of Korea.
- Regional population: from the Population and Housing Census.

### Descriptive statistics (Table 1 highlights)
- Reporting structure:
  - Columns 1-7: descriptive statistics of balance sheet variables and dummies for exporting, adopting foreign technologies, and receiving government support (credit and export promotion) at the firm-year level between 1970-1982.
  - Columns 8-11: fraction of firms that ever exported, adopted foreign technologies, received directed credit, and participated in international trade fairs among unique firms operating at any time between 1970-1982.
  - Panels:
    - Panel A: All firms.
    - Panel B: Ever-adopters.
    - Panel C: Never-adopters.
    - Panel D: Business group firms.
- Key sample counts:
  - Firm-year observations: 29,786.
  - Unique firms: 6,230.
- Panel A (All firms) means (firm-year level):
  - Sales: 30.89 (mln 2015 USD)
  - Employment: 0.55 (thousands)
  - Fixed asset: 13.93 (mln 2015 USD)
  - Export dummy mean: 0.30
  - Adoption dummy mean: 0.03
  - Subsidy dummy mean: 0.01
  - Export promotion dummy mean: 0.03
  - Firm-level ever-fraction means (columns 8-11): ever export 0.39, ever adoption 0.09, ever subsidy 0.03, ever export promo 0.08
  - N (firm-years): 29,786; N (firms): 6,230
- Panel B (Ever-adopters) means:
  - Sales: 103.17 (mln 2015 USD)
  - Employment: 1.31 (thousands)
  - Fixed asset: 52.86 (mln 2015 USD)
  - Export dummy mean: 0.44
  - Subsidy mean: 0.18
  - Export promotion mean: 0.04
  - Firm-level ever export: 0.80, firm-level ever adoption: 0.65
  - N (firm-years): 4,871; N (firms): 587
- Panel C (Never-adopters) means:
  - Sales: 16.76 (mln 2015 USD)
  - Employment: 0.37 (thousands)
  - Fixed asset: 6.29 (mln 2015 USD)
  - Export dummy mean: 0.27
  - Subsidy mean: 0.01
  - Export promotion mean: 0.03
  - Firm-level ever export: 0.36
  - N (firm-years): 24,915; N (firms): 5,643
- Panel D (Business group firms) means:
  - Sales: 142.06 (mln 2015 USD)
  - Employment: 1.95 (thousands)
  - Fixed asset: 68.34 (mln 2015 USD)
  - Export dummy mean: 0.51
  - Adoption dummy mean: 0.13
  - Subsidy mean: 0.07
  - Export promotion mean: 0.12
  - Firm-level ever export: 0.75, firm-level ever adoption: 0.46, firm-level ever subsidy: 0.26, firm-level ever export promo: 0.30
  - N (firm-years): 2,601; N (firms): 306
- Summary patterns:
  - Out of the 6,230 firms, 9.4% (587 firms) adopted technologies at least once (“ever-adopters”).
  - Ever-adopters were larger on average: “516% higher sales and 254% higher employment” relative to never-adopters, and more likely to receive government support (Panels B and C).
  - Business group firms (about 5% or 306 firms) were larger and more likely to adopt technologies and receive government support (Panel D).

### Link to empirical analysis
- The data and descriptive patterns motivate empirical analysis in Section 3 on three firm-level effects of technology adoption that support the big push hypothesis: direct effects on adopters, local spillovers to non-adopters, and local complementarity in firms’ adoption decisions.

*Source: 2.2 Data (from the PDF wpiea2024259-print-pdf).*

### 3.1  Direct Effects on Adopters

### 3.1  Direct Effects on Adopters

### Winners vs. losers research design and matching
- Purpose: Address unobservable differences between adopters and non-adopters by comparing adopters who successfully adopted technology (winners, treated) with non-adopters who signed contracts but were delayed or failed to adopt due to plausibly exogenous cancellations by the foreign party (losers, control).
- Definition of losers: firms whose contracts were approved by the government but were canceled by the foreign partner for reasons plausibly exogenous to the Korean firm (examples: foreign firm bankruptcy, changes in foreign management, sudden contractual modification requests). Cancellations initiated by Korean firms (e.g., sudden cash flow issues) are excluded.
- Two types of losers: delayed-adopters (eventually adopted after delay) and never-adopters (never adopted after cancellations). Cancellations therefore create exogenous variation in adoption timing or status.
- Matching procedure:
  - Each loser matched with up to three winners who contracted in the same year as the loser’s canceled contract.
  - Step 1: exact match on region-sector.
  - Step 2: within region-sector, select winners most similar by Mahalanobis distance using four firm-size variables: log assets, log fixed assets, and their one-year growth rates.
  - Matching with replacement; if >3 candidates, choose the three most similar; if <3, include all.
  - Result: 38 matches among 106 unique firms. Among these 38 matches, there are 25 not-yet-treated losers and 13 never-treated losers.
  - For later-period cancellations where the main dataset (up to 1982) lacks post-treatment observations, the dataset is supplemented with KIS-VALUE (note: KIS-VALUE covers firms with assets over 3 billion Korean Won (2.65 million USD in 2015), capturing only a subset of larger firms).

### Econometric specifications and inference
- Event-study specification (described in text as equation (3.1)): estimates event-time coefficients for outcomes y using match-firm and match-year fixed effects; event dummies D_{τ m t} for τ ∈ [−5, +7]; winner status dummy 1[Winner_it]; normalize β_{−1}=0.
- Pooled diff-in-diff specification (described as equation (3.2)): y_imt = β (1[Winner_it]×1[Post_mt]) + δ_im + δ_mt + ε_imt, with post-treatment dummy 1[Post_mt].
- Full-sample TWFE event-study comparison (equation (3.3)): standard TWFE with first-time adoption dummy 1[Adopt_it] and region-sector-year fixed effects δ_njt; standard errors clustered at region level.
- Standard errors and clustering:
  - Winners vs. losers specifications: standard errors two-way clustered at the match and firm levels.
  - TWFE specifications: standard errors clustered at the region level.
- Measures of firm performance:
  - Log sales.
  - Revenue TFP (TFPR): obtained as residuals from production functions estimated via the control function approach (Levinsohn and Petrin, 2003; Ackerberg et al., 2015). Value-added production function estimated using KIS-VALUE over 1980-1995 to obtain labor and capital elasticities, then TFPR for 1970-1982. Some observations lost for TFPR due to missing employment data.
- Staggered DiD issue: adopt stacked-by-event design (rolling control groups) and drop matches when delayed-losers adopt later, ensuring coefficients identified from within-match comparisons.
- Additional inference checks: randomization inference (Young, 2019) for leverage concerns; wild bootstrap p-values for small cluster counts; alternative clustering at match or firm levels. Alternative staggered DiD estimators (Sun and Abraham, 2021; Borusyak et al., forthcoming) and Rambachan and Roth (2023) bounding show results robust and within baseline 95% CIs.

### Identifying assumption and balance tests
- Key identifying assumption: losers are valid counterfactuals for winners — losers and winners were ex-ante similar in observables and unobservables, and cancellations were uncorrelated with domestic firms’ unobservables.
- Empirical support for assumption:
  - Raw data plots: average log sales of winners begin to increase only after adoption; losers follow pre-trends after events (Appendix Figure B3). No pretrends detected.
  - Distribution of cancellations across sectors mirrors total contracts (Appendix Figure B4).
  - Covariate balance (Appendix Table B1): winners and losers well-balanced on matching variables and other observables (receipt of government support—credit and export promotion—and affiliation with large business groups).
  - Patenting activities of foreign contracting partners (US PTO data) are balanced between winners’ and losers’ foreign firms.
  - Balance with all adopters in same region-sector-year also confirmed.
  - Balance test: regress pre-event observables on loser status (Appendix Table B2) — none predict cancellations.
  - Pretrend inspection: no statistically significant pretrends found (pretrend tests by Borusyak et al. show no statistically significant pretrends for all four dependent variables).
- SUTVA concerns and spillovers:
  - If positive local spillovers existed from winners to losers, estimates would be conservative lower bounds.
  - Match-year fixed effects absorb region-sector-level common shocks.
  - No observed negative trend changes for losers after events in raw sales plots, arguing against competition-induced negative effects.
  - Manufacturing sectors are highly tradable and spatial unit is granular, reducing likelihood of competition bias.

### Baseline results and magnitudes (winners vs. losers and comparisons)
- Event-study window reported: τ from −5 to +7 years (Figure and table present coefficients for years since adoption).
- No pretrends detected.
- Main magnitudes (winners vs. losers event-study, equation (3.1)):
  - Four years post-adoption: sales rise by 119% and TFPR rise by 130%, with effects remaining persistent.
  - Reported event-study coefficients (selected):
    - Year of event: Sale 0.12; TFPR 0.11.
    - 1 year after: Sale 0.85***; TFPR 1.08**.
    - 2 years after: Sale 0.74***; TFPR 0.35.
    - 3 years after: Sale 1.08***; TFPR 1.37***.
    - 4 years after: Sale 1.19**; TFPR 1.30***.
    - 5 years after: Sale 1.02**; TFPR 1.36***.
    - 6 years after: Sale 1.05**; TFPR 1.39***.
    - 7 years after: Sale 0.96***; TFPR 1.58***.
  - Pooled diff-in-diff (Panel B winners vs. losers): Adoption×Post = 0.91*** (Sale) and 0.94*** (TFPR).
- Full-sample TWFE comparison:
  - TWFE event-study shows increases in adopters’ sales post-adoption but with noticeable pretrend at t = −4 and magnitude about 75% smaller than winners vs. losers baseline.
  - TWFE pooled diff-in-diff (Panel B, full sample) reports Adoption×Post = 0.17** (Sale) and 0.10** (TFPR) in columns 7-8 reported for subsidy and export promo. (Note: full-sample columns and interpretation differ; see table for column alignment.)
- Table 2 cluster counts and fixed effects (as presented):
  - # Clusters: 38×106 (winners vs. losers columns), 35×98 (some TFPR column), 826, 382, 82 (full sample columns as printed).
  - N: entries printed include "N85253785285221319  11,994   21,31921,319" (table as presented).
  - Fixed effects: Match×Firm, Match×Year (winners vs. losers); Firm, Region×Sector×Year (full sample).
- Inference robustness:
  - Randomization inference and wild bootstrap p-values produce p-values nearly identical to baseline (Appendix Table B4).
  - Alternative estimators (Sun and Abraham; Borusyak et al.) produce estimates within 95% confidence intervals of baseline event-study (Appendix Figure B6).
  - Rambachan and Roth (2023) methodology shows robustness to mild violations of parallel trends (Appendix Figure B7).

### Government support and interpretation of estimates
- Concern: estimates might reflect joint effects of technology adoption and government support (directed credit/subsidies or export promotion).
- Evidence:
  - TWFE specification: coefficients for receiving government support become positive and statistically significant at the 1% level after adoption (columns 7-8).
  - Winners vs. losers specification: no increases observed in dummies for receiving government support following adoption (columns 3-4; Appendix Figure B3).
  - Conclusion: main results for sales and TFPR likely reflect the pure effects of technology adoption rather than joint effects with observed government support. For unobserved government support to explain results, it would need to be uncorrelated with observed directed credit and export promotion—considered unlikely.
- Additional rules-out:
  - Not driven by demand shocks related to government military spending: none of matched firms had military contracts (due to Act on Special Measures for Defense Industry and available pre-registered firm list).
  - No negative trend changes for losers after cancellations in raw sales plots, arguing against adverse effects from cancellations such as stranded investment.

### Alternative outcomes, samples, and robustness checks
- Alternative outcomes with positive impacts from adoption:
  - Labor productivity (sales per employee).
  - Revenue TFP based on Olley and Pakes (1996).
  - Log fixed asset.
  - Dummy for exporting.
- Alternative samples and procedures:
  - Subsample without missing employment data.
  - Different matching procedures (varying number of winners per loser or including all firms that adopted in event year within losers’ region-sectors).
- Robustness: results remain robust across alternative outcomes, samples, and matching (Appendix Table B5).

*Source: IMF working paper chapter 3.1, "Direct Effects on Adopters", as provided in the supplied PDF content.*

### 3.2  Local Spillovers

### 3.2  Local Spillovers

### Empirical specification and variables
- Adopter share (excluding firm i) in region-sector n j in year t−h:
  - Share(−i)nj,t−h = T(−i)nj,t−h / N(−i)nj,t−h. (Equation (3.4))
  - N(−i)nj,t−h is the total number of firms in n j in t−h, excluding firm i.
  - T(−i)nj,t−h is the number of firms in n j that ever adopted foreign technology in t−h, excluding firm i.
- Long-difference regression (baseline h = 2):
  - Δyit = β ΔShare(−i)nj,t−2 + ζ yit0 + X′injt γ + δn + δj + Σg Dg δjg + Δεit. (Equation (3.5))
  - Dependent variables: changes in log sales or TFPR.
  - Controls: initial dependent variable yit0, vector Xinjt, region fixed effects δn, sector fixed effects δj, and sector×group fixed effects δjg for group-affiliated firms (Dg = 1).
  - Standard errors two-way clustered at region and business group levels; individual unaffiliated firms treated as their own group-level clusters.
- Overlapping long differences used for 1972-1979 and 1973-1980 to increase coverage; dummies for each set of differences included.

### Instrumental variable (IV) strategy
- Motivation:
  - OLS may be biased by region-sector unobservables, measurement error in adopter shares, and selection from restricting to never-adopters.
  - Direction of OLS bias is ambiguous (could be upward due to positive regional shocks or downward due to unobserved subsidies or measurement error).
- IV construction (pre-existing firms and leave-out logic):
  - Define Z≥100km,t0 i n j,t−h as sum over ̃g ≠ g(i) of D̃g n j t0 × T≥100km,t0 ̃g(−n) j,t−h divided by ̃Np(−i)nj,t−h.
  - T≥100km,t0 ̃g(−n) j,t−h: number of sector-j adopters in t−h that operated and were affiliated with group ̃g in initial year t0, excluding firms located in region n or within a 100 km radius of region n.
  - D̃g n j t0: dummy indicating whether group ̃g had at least one firm in region-sector n j in initial year t0.
  - ̃Np(−i)nj,t−h is the predicted number of firms in n j in t−h, excluding i, constructed using national-level growth g(−n)j and initial counts N(−i)nj,t0−h.
  - IV is the long-difference: IV≥100km,t0 i n j,t−h = ΔZ≥100km,t0 i n j,t−h. (Equation (3.6))
  - Superscripts t0 and ≥100km indicate using only pre-existing firms located outside a 100 km radius of focal regions.
- Intuition example: group-level adoption (e.g., Samsung across distant locations) shifts adopter shares in focal regions where the group initially owned firms; remote group-level shocks act as exogenous shifters for local adopter shares for unaffiliated firms.

### Identification assumptions and threats
- Core identifying assumption:
  - For firm i, variation in adopters outside i’s region that operated before the initial year and were initially affiliated with groups owning a firm in i’s region is orthogonal to i’s unobservables, conditional on covariates.
- Threats and mitigations:
  1. Group expansion affecting region-level variables (violating exclusion):
     - Mitigation: include business groups’ sales shares within region-sectors in regressions; construct an IV for group sales shares and include it in reduced form to isolate adopter-share effects from size expansion effects (details in Appendix B.2).
  2. Business group sorting:
     - Type 1 (groups sorted into region-sectors during 1972-1980): IV uses only pre-existing firms, so not a concern.
     - Type 2 (persistent pre-1972 shocks affected initial group locations): placebo tests show IV does not predict firm performance before 1972/1973 (Appendix Table B11).
  3. SUTVA violations via spatial interactions (input-output linkages, supplier/buyer relationships):
     - Mitigation: exclude business group firms within a 100 km radius in constructing the IV; additional robustness using alternative radii (50 km to 150 km) and Moran’s I which shows spatial autocorrelation becomes insignificant beyond 75 km (Appendix Table B12).
- Additional checks:
  - Exclude group firms with fixed assets exceeding 30%, 50%, 70% of regional totals, and exclusion of the two largest groups (Samsung, Hyundai): results remain robust (Appendix Table B9).
  - No correlations found between the IV and observable credit or export promotion (Appendix Table B10).
  - Alternative inference methods: bootstrapped standard errors, spatial HAC standard errors, weak-IV-robust Anderson-Rubin test, two-step confidence intervals — results robust (Appendix Table B14).

### Baseline IV and OLS results (Table 3 summary)
- Sample: firms that never adopted technology during the sample period; long-differences for 1972-1979 and 1973-1980.
- Panel A: Dependent variable ΔlnSaleit (1972-1979 or 1973-1980)
  - OLS (col 1): coefficient on ΔShare(−i)nj,t−2 = 0.37 (standard error 0.42).
  - IV (col 2): coefficient = 3.19*** (standard error 0.74).
  - Preferred IV specification including predicted business group sales shares and additional controls (cols 3–8):
    - Col 3: 2.70*** (0.74)
    - Col 4: 2.45*** (0.77)
    - Col 5: 2.62*** (0.74)
    - Col 6: 2.65*** (0.73)
    - Col 7: 3.00*** (0.78)
    - Col 8: 2.77*** (0.84)
  - KP-F (Kleibergen-Paap F-statistics) reported in columns range: 17.83, 21.54, 17.87, 21.48, 20.25, 22.00, 16.12 (first-stage strength noted).
  - # Clusters: 79 × 1,294.
  - N = 1,492 across columns.
- Panel B: Dependent variable ΔTFPRit (1972-1979 or 1973-1980)
  - OLS (col 1): coefficient = −0.34 (0.38).
  - IV (col 2): coefficient = 1.93*** (0.62).
  - Preferred IV specifications (cols 3–8):
    - Col 3: 1.60*** (0.55)
    - Col 4: 1.52*** (0.55)
    - Col 5: 1.55*** (0.57)
    - Col 6: 1.61*** (0.54)
    - Col 7: 1.68*** (0.54)
    - Col 8: 1.61*** (0.54)
  - KP-F values reported: 18.54, 22.86, 19.87, 22.22, 22.69, 27.35, 19.42.
  - # Clusters: 67 × 742.
  - N = 824 (reduced due to missing employment information).
- Interpretation of preferred estimates:
  - A 1 percentage point increase in adopter shares leads to:
    - 2.7% higher sales (Panel A, preferred specification).
    - 1.6% higher revenue TFP (Panel B, preferred specification).

### Additional controls and robustness
- Market access (ΔlnMAp(−i)njt) constructed following Donaldson and Hornbeck (2016):
  - ΔlnMAp(−i)njt = Δln( Σm,k Σi′∈F(−i)mkt0 Dist−χ nm × γjk × Salepi′t0 ), with χ = 1.5 and γjk = 1970 input-output coefficients. Predicted sales used to avoid endogeneity.
- Controls added across specifications (columns described):
  - Predicted business group sales shares (equation (B.2), Appendix B.2).
  - Predicted market access and log distance to port interacted with predicted exports.
  - Inverse hyperbolic sine of cumulative directed credit received (1972-1979 or 1973-1980).
  - Industrial complex dummies and tax-favor variables (years under tax exemptions interacted with log sectoral effective marginal corporate tax rates).
  - Trade-related variables: log distance to port × changes in log import and input tariffs, predicted sectoral exports, cumulative contract values from international trade fairs, firm-level tariff exemptions for exporters interacted with input tariffs.
  - Column 8 includes all additional controls jointly; coefficient remains stable.
- Other robustness checks:
  - Alternative outcomes: labor productivity, revenue TFP (Olley and Pakes, 1996), export dummies, log fixed assets — results hold (Appendix Table B15).
  - Entry/exit dummies show no significant effects (Appendix Table B13).
  - Omitting yit0 and using a 3-year lag: results robust.
  - Subsample of firms unaffiliated with any business groups and operating in a single region: results robust.
  - Excluding firms in industrial complexes and those with missing employment: results robust.
- First-stage and IV strength:
  - First-stage coefficient for the IV reported as 0.19.
  - KP-F statistics around 18, above rule-of-thumb 10 and the Montiel Olea and Pflueger (2013) threshold of 15.1.

### Summary of substantive findings
- IV estimates indicate sizable local spillovers from technology adoption by nearby (but not too close) business-group-affiliated adopters:
  - 1 percentage point increase in local adopter shares → 2.7% higher sales for never-adopting firms.
  - 1 percentage point increase in local adopter shares → 1.6% higher revenue TFP for never-adopting firms.
- IV estimates are larger than OLS estimates, consistent with downward OLS bias from measurement error and/or targeted subsidies to lower-growth firms.
- Results are robust to:
  - Inclusion of predicted business group sales shares and a wide set of regional, credit, trade, and industrial-complex controls.
  - Alternative IV constructions, spatial radii, exclusion of large groups, alternative inference methods, and various sample restrictions and outcome measures.

*Source: 3.2 Local Spillovers, wpiea2024259-print-pdf*

### 3.3  Local Complementarity in Adoption Decisions

### 3.3  Local Complementarity in Adoption Decisions

### Empirical approach
- Regression of dummies indicating whether firms made new adoption contracts in given years (1[New Contract_it]) on local adopter shares using the full sample (both never-adopters and ever-adopters).
- A positive coefficient on adopter shares indicates local complementarity: firms are more likely to adopt when other local firms have already adopted.
- Estimation methods: OLS and IV (instrumenting adopter shares to correct for endogeneity). IV uses business groups’ predicted sales shares (detailed in Appendix B.2).

### Key empirical findings
- Table 4 main estimates:
  - OLS: coefficient on ΔShare(−i)_nj,t−2 = −0.08 (standard error 0.11).
  - IV (column 2): coefficient = 0.79 (standard error 0.36), **p<0.05.
  - IV with business groups’ sales share control (column 3): coefficient = 0.85 (standard error 0.41), **p<0.05.
  - Additional IV specifications (columns 4–8) with controls yield coefficients: 0.82 (0.43), 0.85 (0.42), 0.90 (0.41), 0.84 (0.40), 0.87 (0.39); coefficients remain positive, statistically significant, and stable.
- Magnitude interpretation:
  - The 0.85 percentage point increase implies a 0.85 percentage point higher probability of making new contracts for a 1 percentage point increase in adopter shares.
  - This 0.85 percentage point increase represents approximately 14% of the average probability of making new contracts in 1979 and 1980, which was 6%.
- Instrument strength:
  - Main IV is strong: KP-F of 17.7 (Kleibergen-Paap F-statistic). Table reports KP-F values (e.g., 13.91; 17.71; 17.47; 17.81; 17.15; 19.05; 18.09; 21.11) and min. SW-F reported as {48} in the table.
- Market access interaction:
  - Interaction of adopter shares with a dummy for regions with initial market access above the 80th percentile:
    - Low MA × ΔShare(−i)_nj,t−2 = 0.29 (standard error 0.17), *p<0.1.
    - High MA × ΔShare(−i)_nj,t−2 = 1.07 (standard error 0.56), *p<0.1.
  - Difference between high and low market-access coefficients is significant at the 10% level.
  - Results hold across alternative percentile cutoffs (Appendix Table B8).
- Robustness:
  - Specifications mirror those for local spillovers and rely on the same variation; identical robustness exercises conducted (first stage results in Appendix Table B6; two-endogenous-variable specification in Table B7; alternative IV construction in Table B9; placebo in Table B11; alternative inferences in Table B14; robustness checks with alternative lags, samples, and omission of initial dependent variable in Table B16).

### Interpretation and implications
- Evidence supports local complementarity: firms are less likely to adopt unless other local firms have already done so, indicating coordination failures at the local level.
- Local spillovers indicate positive externalities; private returns alone may have been insufficient to overcome coordination failures.
- Market access amplifies complementarity: larger market access strengthens the effect of local adopter shares on new adoption.
- Policy implication (empirical): one-time coordinated interventions that raise local adopter shares (a “big push”) can help overcome local coordination failures and trigger sustained adoption even after subsidies end.

### Connection to model (preview of Section 4)
- The empirical complementarity and spillover findings motivate a dynamic model where:
  - Firm productivity z_it = η_T_it × f(λ_T,t−1) × φ_it, with f(λ_T,t−1) = exp(δ λ_T,t−1) (spillovers operate with a one-period lag).
  - Adoption yields direct productivity gain η > 1; spillovers governed by δ.
  - Adoption incurs fixed costs F_T in units of final goods.
  - Firms adopt if additional operating profits exceed P_t F_T, leading to a cutoff for φ_it given in equation (4.1) and, under a Pareto distribution for φ_it, the cutoff relates to adopter share via (4.2).
  - The equilibrium adopter share evolves according to (4.3) and (4.4), with steady states satisfying λ_T = λ_T(λ_T; L, η, δ).
- The model maps three empirical findings into structural mechanisms: private returns (η), spillovers (δ), and dynamic complementarity in adoption driven by adoption costs measured in final goods.

*Source: wpiea2024259-print-pdf - 3.3  Local Complementarity in Adoption Decisions*

### 5.1  Quantitative Model

### 5.1  Quantitative Model

### Model structure: geography, sectors, trade, and equilibrium
- World divided into Home (small open economy) and Foreign (퐻 and 퐹); Home composed of regions n, m ∈ {1, ... , 푁} ≡ 풩 and sectors j, k ∈ {1, ... , 퐽} ≡ 풥.
- Varieties are tradable across regions and countries subject to import tariffs 푡
푗푡 and iceberg costs:
  - internal trade iceberg costs: 휏
푛푚푗 ≥ 1
  - international trade iceberg costs: 휏
푥
푛푗 ≥ 1
- Competitive labor markets in each region; households immobile and supply labor inelastically (labor mobility is later introduced as a robustness check).
- In each region-sector a fixed mass of monopolistically competitive firms (푀
푛푗) and perfectly competitive final goods producers produce nontradable local aggregates (푄
푛푗푡) using a CES aggregator over available varieties.
- Price index:
  - 푃
푛푗푡 = [Σ
푚
∫
푖∈Ω
푚푗
(푝
푖푛푗푡
)^{1−휎} d푖 + (휏
푥
푛푗 (1+푡
푗푡) 푃
푓
푗푡 )^{1−휎}]^{1/(1−휎)}, where 푝
푖푛푗푡 is firm price and Ω
푚푗 is set of sector-j varieties in region m.
- Home firms face foreign demand schedule 푝^{−휎}_{푖푡} 퐷
푥
푗푡; exporters incur fixed export costs 퐹
푥
푗 (in units of labor).

### Production, productivity, and adoption technology
- Firm production (Cobb-Douglas):
  - 푦
푖푡 = 푧
푖푡 퐿^{훾
퐿
푗}
푖푡 ∏_k (푀
푘
푖푡)^{훾
푘
푗}, with 훾
퐿
푗 + Σ_k 훾
푘
푗 = 1.
- Productivity decomposition:
  - 푧
푖푡 = 휂^{푇
푖푡} f(휆
푇
푛푗,푡−1) 휙
푖푡
.
  - Spillovers f(·) increase with previous period regional-sector adopter shares 휆
푇
푛푗,푡−1.
  - Heterogeneous firm productivity term 휙
푖푡 follows a bounded Pareto distribution:
    - 휙
푖푡 ∼ 1 − (휙
푖푡 / 휙
min
푛푗푡)^{−휃} / (1 − 휅^{−휃}), parametrized by 휙
min
푛푗푡, 휅, 휃.
    - Upper bound is 휅 휙
min
푛푗푡; region-sector adoption can be zero if cutoff > 휅 휙
min
푛푗푡.
- Fixed adoption costs (Cobb-Douglas form):
  - 퐹
푇 × 퐿^{훾
퐿
푗}
푖푡 ∏_k (푀
푘
푖푡)^{훾
푘
푗}; total expenditures on adoption costs = 푐
푛푗푡 퐹
푇, where unit cost c_{njt} ∝ w_{n t}^{훾
퐿
푗} × ∏_k P_{k n j t}^{훾
푘
푗}.
- Adoption subsidies modeled as input subsidies 0 ≤ 푠
푛푗푡 ≤ 1; adopters’ unit costs become (1 − 푠
푛푗푡) c_{n j t} / z_{i t}.
- Government finances subsidies through a common labor tax 휏
푤
푡; government budget balanced each period.

### Preferences, income, and equilibrium conditions
- Representative households with Cobb-Douglas preferences: ln(∏_{j=1}^{J} C_{n j t}^{훼_{j}}).
- Budget constraint:
  - Σ_{j} P_{n j t} C_{n j t} = (1 − 휏
푤
푡 + ̄휋_{푡}) w_{n t}, where ̄휋_{푡} denotes dividend income per unit labor.
- Equilibrium: given initial conditions {휆
푇
푛푗,−1, L_{n1}} and fundamentals paths {휙
min
푛푗푡, P^f_{j t}, D^x_{j t}}, tariffs {t_{j t}}, and subsidies {s_{n j t}}, firms and households optimize, markets clear, trade balanced, government budget balanced, and adoption decisions evolve state variable {휆
푇
푛푗푡}.

### Key theoretical comparative implications (discussion)
- Market access and firm scale:
  - Higher trade costs or smaller foreign demand reduce firms’ market size, increase intermediate input and adoption costs, reduce firm scale, and lower gains from adoption — making a big push harder to achieve.
- Industrialization and openness:
  - In closed economy (P^f_{j t} → ∞, D^x_{j t} → 0), heavy manufacturing GDP shares remain constant across steady states under Cobb-Douglas structures.
  - In a small open economy, higher productivity in heavy manufacturing raises comparative advantage and exports, increasing heavy manufacturing GDP shares in the industrialized steady state.
- Relationship to recent big-push models:
  - Similarity to Buera et al. (2021): final goods used for adoption costs can generate multiplicity; additional spillovers in this model create potential for multiple steady states.
  - Contrast with Kline and Moretti (2014): multiple steady states in that model arise from migration and agglomeration; here labor immobility shuts down that channel.

### Counterfactual experiment
- Construct counterfactual economy without the big push by setting s_{n j t} = 0 (no temporary adoption subsidies).
- Compute heavy manufacturing GDP shares and welfare changes under counterfactual.

### Mapping model periods, sector classification, and adoption scope
- Each model period corresponds to 4 years of data.
- Sectors: commodity, light manufacturing, heavy manufacturing, service.
  - First three tradable internally and internationally; service nontradable.
- Adoption assumed available only within heavy manufacturing (majority of adoption occurred there).
- Calibration years: 1972, 1976, 1980 corresponding to t = 1, 2, 3; after t = 3 fundamentals held constant at 1980 levels.
- Initial adopter shares λ_{T n j, 68} and population L_{n, 72} taken from data.

### Calibration strategy and parameter sets
- Parameters and identification sets:
  - Externally calibrated set: 횯_E = {η, δ, M_{n j}, θ, σ, γ_{L j}, γ_{k j}, τ_{n m j}, τ^x_{n j}, α_j} and tariffs t_{j t}.
  - Internally calibrated set: 횯_M = {κ, F^x_j, F_T} and subsidies s_{n j t}, fundamentals 횿_{t}.
- Estimation via indirect inference: match model moments m(횯_M, ̄s, 횿_t) to data moments m′ subject to constraint C(횯_M, ̄s, 횿_t) − C = 0 (equation (5.1)).

### External calibration choices and mappings
- Elasticity of substitution: σ = 4.
- Direct productivity gain η set from winners vs. losers mapping:
  - η = exp(0.9/(σ − 1)) = 1.35, where 0.9 is pooled diff-in-diff estimate (Panel B of Table 2).
- Spillover semi-elasticity δ set from spillover regression:
  - δ = 2.7/(σ − 1) = 0.90, where 2.7 is average IV estimate (Panel A of Table 3).
- Pareto shape parameter θ set to 1.06 × (σ − 1).
- Distance trade cost elasticity ξ set to 0.43 (Monte et al. (2018) mapping ξ = 1.29/(σ − 1)).
- Internal iceberg costs τ_{n m j} = (Dist_{n m})^{ξ}; international iceberg costs τ^x_{n j} = (Dist_{port n})^{ξ}, with τ^x_{n j} = 1 for regions with ports.
- Dijkstra algorithm used to compute fastest routes; Gyeongbu Expressway modeled as 66% reduction in travel times between connected regions.
- Mass of firms M_{n j} set proportional to 1972 GDP share with Σ_{n,j} M_{n j} = 1 (normalization).
- Cobb-Douglas shares (α_j, γ_{k j}, γ_{L j}) taken from input-output tables.

### Internal calibration specifics
- Adoption subsidies provided in t = 2, 3 (1976 and 1980) to regions in set N_s: 35 regions out of 86.
- Subsidy allocation:
  - s_{n j t} = ̄s if t ∈ {2,3}, n ∈ N_s, j = {heavy mfg.}; 0 otherwise.
- Parameters calibrated by minimizing normalized distance between model and data moments, with constraints matching sectoral export intensities, import shares, regional gross output distributions, sectoral PPI growth, and aggregate real GDP growth.
- Moments used to identify parameters:
  - Average adopter shares in 1972 identify F_T.
  - Average adopter shares in 1976 and 1980 identify ̄s.
  - Share of regions with zero adoption identifies κ.
  - Fixed export costs F^x_j for light and heavy manufacturing set using average regional exporter shares; commodity sector F^x_j set equal to light manufacturing.

### Estimated parameters and model fit (internal calibration results)
- Internally calibrated estimates (Table 5 and text):
  - Estimated subsidy rate ̄s = 0.081 (8.1%).
  - In 1976 and 1980, adoption subsidies equal 1.35% and 1.40% of GDP, respectively.
  - Fixed adoption costs F_T imply total adoption costs (Σ_n F_T c_{n j t}) are 35.1 times larger than total fixed export costs (Σ_n F^x_j w_{n t}).
  - Fixed export costs (internal calibration table):
    - F^x_j (light mfg.) = 0.60 (identified from exporter share, light mfg.)
    - F^x_j (heavy mfg.) = 0.055 (identified from exporter share, heavy mfg.)
  - Pareto upper bound κ = 1.519 (identifies share of regions with adoption).
- Model moments closely match targeted data moments (Table 6):
  - Avg. {λ^x_{n j t}}_{n∈N, t∈{72,76,80}}, light mfg.: Model 0.29, Data 0.28.
  - Avg. {λ^x_{n j t}}_{n∈N, t∈{72,76,80}}, heavy mfg.: Model 0.19, Data 0.19.
  - Avg. {λ^T_{n j, 72}}_{n∈N}: Model 0.07, Data 0.07.
  - Avg. {λ^T_{n j, 76}}_{n∈N}: Model 0.10, Data 0.09.
  - Avg. {λ^T_{n j, 80}}_{n∈N}: Model 0.11, Data 0.15.
  - Avg. shares of regions with positive adoption: Model 0.54, Data 0.47.

### Non-targeted validation moments
- Model reproduces:
  - Positive relationship between adopter shares and market access (Market access equation (3.7)).
  - Negative relationship between adopter shares and log distance to port (proxy for export costs).
  - Regional distributions of heavy manufacturing employment, exports, and exporter shares qualitatively and quantitatively related to adopter shares (Appendix Table E1).
  - Trajectories of aggregate employment shares between 1972–1980 (Panel C of Figure 5).

### Assumptions on static adoption decisions and implications
- Static adoption decisions render state variable backward-looking, simplifying computation and preserving spatial heterogeneity.
- If adoption costs were sunk and decisions forward-looking, multiple steady states could still arise via dynamic complementarity; static equilibrium outcomes would remain the same, though welfare effects and magnitudes could differ.

---

### 5.2  Counterfactual (summary)
- Counterfactual: set s_{n j t} = 0 (no temporary adoption subsidies).
- Compute heavy manufacturing sector’s GDP shares and welfare changes under this no-big-push scenario.

### 5.3  Taking the model to the data (summary of calibration timing and mapping)
- Model periods correspond to 4-year data intervals.
- Calibration to 1972 (t = 1), 1976 (t = 2), 1980 (t = 3); fundamentals held at 1980 levels thereafter.
- Initial adopter shares λ_{T n j, 68} and population L_{n, 72} used as data inputs.

### 6.1  Quantitative results — Aggregate and local effects of the big push
- Convergence:
  - Both baseline (with subsidies) and counterfactual converge to steady states about 24 years (6 periods) after 1980.
- Aggregate steady state differences (Baseline vs. counterfactual; Table 7, row "Aggregate level"):
  - Δ GDP share (heavy manufacturing) = 1.95 percentage points (reported as 8.6% decrease in counterfactual; stated as 1.95 p.p, with percent change 8.6%).
  - Δ Export intensity = 3.33 percentage points (reported as 16.2% decrease in counterfactual).
  - Δ Employment share = 0.68 percentage point (reported as 9.6% decrease in counterfactual).
  - Δ Welfare (aggregate, population-weighted) = 1.27 percent (aggregate welfare increase from the big push).
- Local heterogeneity (Table 7, row "Local level" ranges):
  - Δ heavy manufacturing GDP shares across regions range: [−1.43, 52.93] (percent).
  - Δ export intensities across regions range: [−7.92, 3.45] (percentage points).
  - Δ employment shares across regions range: [0.68, 10] (percentage points).
  - Δ welfare across regions range: [−1.44, 37.52] (percent).
- Regional distribution of welfare effects:
  - 66 out of 86 regions experience welfare gains; 20 regions experience welfare losses.
- Local dynamics:
  - Only four regions experience higher heavy manufacturing GDP shares in the baseline relative to the counterfactual due to technology adoption–driven productivity improvements.
  - Productivity gains in these few regions reduce heavy manufacturing shares elsewhere via increased competition, producing divergence rather than uniform growth.

### Welfare computation details
- Consumption-equivalent welfare changes computed by equating discounted utilities baseline vs. counterfactual.
- Discount factor used: 0.85 (equal to 0.96^{4}).
- Aggregate welfare changes are population-weighted regional welfare changes.

*Source: wpiea2024259-print-pdf - 5.1  Quantitative Model (IMF working paper content unit).*

### Appendix Figure E2 for the distribution of the welfare effects). These distributional effects arise due

### 6.2 Firm Scale, Market Access, and the Big Push

### Effects under alternative scenarios (summary of Table 8)
- Baseline: ΔHeavy mfg. GDP shares (p.p) = 1.95; ΔAggregate welfare (%) = 1.27; Does the big push occur? = Y
- Lower foreign demand (foreign demand held at 1972 level in 1976 and 1980): ΔHeavy mfg. GDP shares (p.p) = 0.25; ΔAggregate welfare (%) = 0.43; Does the big push occur? = Y
  - Context: Between 1972 and 1980, estimated foreign demand rose by 48% relative to total domestic demand.
- Higher tariffs (hypothetical protectionist scenario where tariff rates increase by 40% between 1972 and 1980): ΔHeavy mfg. GDP shares (p.p) = 1.91; ΔAggregate welfare (%) = 1.14; Does the big push occur? = Y
  - Context: Actual average import tariff rates for heavy manufacturing dropped by 40%, from 38.4% to 23.4% between 1972 and 1980. In the hypothetical protectionist case, increased production and adoption costs outweigh reduced foreign competition, weakening the big push.
- No highway (reversing the 66% reduction in travel time from highway construction): ΔHeavy mfg. GDP shares (p.p) = 1.71; ΔAggregate welfare (%) = 0.90; Does the big push occur? = Y
- No internal trade (prohibiting internal trade within the heavy manufacturing sector): ΔHeavy mfg. GDP shares (p.p) = 0.00; ΔAggregate welfare (%) = 0.00; Does the big push occur? = N
- Joint adverse scenario (Lower foreign demand + Higher tariffs + No highway): ΔHeavy mfg. GDP shares (p.p) = 0.00; ΔAggregate welfare (%) = 0.00; Does the big push occur? = N

### Key mechanisms and interpretation
- Two opposing forces from localized productivity improvements:
  - Positive: consumers and producers in other regions benefit from lower prices via internal trade linkages.
  - Negative: increased domestic competition reduces firms’ profits outside the subsidized regions.
- Factors that increase firms’ scale amplify the big push; factors that reduce firms’ scale weaken it.
- Internal trade is critical: shutting down internal trade within heavy manufacturing prevents the big push.
- Combined adverse policies (low foreign demand, protectionist tariffs, no highway) can prevent the big push even if each adverse policy alone does not.

### 6.3 Alternative Policy Schemes

### Randomized selection of subsidized regions
- Procedure: Randomly select 35 subsidized regions out of 86, apply same subsidy rate, simulate 1,000 times.
- Finding: Among four variables—log distance to port, population, market access, and natural advantage—only distance to port and market access are significantly positively correlated with steady state differences in heavy manufacturing GDP shares and welfare changes across simulations.
- Emphasis: Market access plays an important role.

### General subsidy versus targeted adoption subsidies
- General subsidy at 8.1% rate to all heavy manufacturing firms in subsidized regions:
  - Outcome: Does not lead to the big push.
  - Welfare gains = 0.29%.
  - Mechanism: General subsidies reduce production costs for all firms, increase domestic competition, and lower adoption incentives for potential adopters.
  - Implication: Industrial policy should target coordination failures (adoption incentives), not provide untargeted general subsidies.

### Optimal subsidy rate (numerical search)
- Optimal subsidy rate found = 12%
  - Welfare gains = 2.0% (a 0.78 percentage point increase relative to the baseline rate).
  - Leads to a different steady state with even higher heavy manufacturing GDP shares than the baseline.
- Note: Calibrated subsidies in baseline are not necessarily optimal; analytical derivation of optimal subsidy in multi-steady-state economy is beyond scope.

### 6.4 Additional Robustness Checks

### Statistical uncertainty in parameters
- Main calibration uses point estimates of (σ−1)η and (σ−1)δ without statistical uncertainty.
- Sensitivity exercise: consider a wide range within their 95% confidence intervals and re-calibrate remaining parameters and fundamentals for each value.
- Result: One-time subsidies lead to the big push only for medium ranges of these parameter values (Appendix Table E3), not across all values.
  - For (σ−1)δ below 1.70 (1.5 standard deviations lower than baseline), subsidies do not result in the big push.
  - For (σ−1)η, the big push occurs only in the lower half of the 95% confidence interval and fails for values above 1.2 (0.5 standard deviation higher than baseline).
- Conclusion: Difficult to claim the big push arises with 95% statistical significance; aligns with theory where multiple steady states emerge only within medium ranges of η and δ.

### Spatial mobility
- Extension with myopic migration decisions (as in Peters (2022); Appendix E.2):
  - Migration amplifies the big push as labor relocates to regions with higher adoption, reducing production and adoption costs there (see Appendix Table E4, col. 1).

### Alternative parameter values for σ and θ
- Lower σ amplifies effects because estimates do not separately identify η or δ from σ; both η and δ increase with lower σ.
- Lower θ increases effects by reducing dispersion in productivity, concentrating more firms just below the adoption cutoff and making them more responsive to subsidy-induced shifts in the cutoff.

### 7. Conclusion

### Empirical and quantitative findings
- Three empirical findings consistent with the big push narrative:
  - Direct effects on adopters.
  - Local spillovers.
  - Local complementarity in adoption.
- Calibrated model allows for multiple steady states and a big push.
- Counterfactual implication: Without the intervention, the economy could have converged to a less-industrialized steady state.
- Market access played a quantitatively significant role in enabling the big push.

### Policy implications
- Addressing coordination failures is crucial to facilitate diffusion of advanced technologies in developing economies.
- Policies should focus on:
  - Targeted interventions that raise firms’ scale and adoption incentives (e.g., adoption subsidies).
  - Ensuring sufficient market access (e.g., trade openness, infrastructure) for sustainable industrial growth.
- Complementarity between export-oriented trade policies and government-led industrial policies: protectionist policies (avoiding export promotion, raising tariffs) could have prevented industrialization in this episode.

*Source: Excerpt from the content unit "wpiea2024259-print-pdf" (Appendix Figure E2 reference and Sections 6.2–7).*

### References

### References and Online Appendix (wpiea2024259-print-pdf - References)

### A. Data and Descriptive Facts
- Firm-level data:
  - Contract records provide names of domestic firms, foreign firms, and calendar years of contracts.
  - Balance sheet data includes firms with more than 50 employees; mergers treated as exits; missing sales imputed using asset information.
  - Production locations converted to the 2010 administrative divisions of Korea; regions aggregated up to 86 regions based on electoral districts.
  - Firms categorized into 10 sectors; four marked as heavy manufacturing (ISIC Rev 3.1 codes preserved in Table A1).
- Regional and sectoral data:
  - Regional population data: Population and Housing Census, 2% random sample.
  - Import tariffs digitized from Luedde-Neurath (1986) for years 1968, 1974, 1976, 1978, 1980, and 1982; CCCN codes converted to ISIC; missing years imputed using geometric average.
  - Input-output tables from Bank of Korea aligned to ISIC codes.

### B. Empirics — Key Methods, Variables, and Identification
- Empirical design components:
  - Winners vs. losers research design and stacked event-study specifications (baseline and estimators by Sun and Abraham (2021) and Borusyak et al. (forthcoming)).
  - Pooled diff‑in‑diff specification (equation (3.2)) with coefficient on 1[Winner_it]×1[Post_mt].
  - IV strategies:
    - Adopter-share IV: IV_≥100km,t0 (equation (3.6)), constructed from pre-existing adopters located outside a 100 km radius of the focal region and taking long-differences (IV_≥100km,t0 = ΔZ_≥100km,t0).
    - Business-group sales-share IV: IV_sale,≥100km,t0 (equation (B.2)), analogous construction using business groups’ sales outside focal region and ≥100 km.
  - Controls include predicted business-group sales shares (Share_sale(−i)_nj,t−h defined in (B.1)), initial dependent variables, region, sector, and sector-group fixed effects.
- Inference and clustering:
  - Standard errors two-way clustered at match and firm levels or region and business-group levels as noted.
  - Alternative inference reported: randomization inference (Young, 2019), wild bootstrap (Cameron et al., 2008), wild bootstrap (MacKinnon et al., 2023), spatial HAC (Conley, 1999), Anderson‑Rubin tests (Andrews et al., 2019), and two-step AR‑CI (Andrews, 2018).
- Distributional and sample notes:
  - Adopter sample: N=1,634 contracts; cancellation episodes N=38 (Figure B4).
  - Heavy manufacturing policy window: government subsidized adoption in heavy manufacturing sectors from 1973 to 1979 (figures B1, B2).

### B.1 POSCO Case (Empirical Illustration)
- Timeline and key numbers:
  - POSCO signed first technology adoption contract with Nippon Steel Corporation (NSC) in 1968.
  - POSCO began production in 1973.
  - The fee paid by POSCO amounted to 20% of NSC’s annual exports in plant engineering.
  - By 1980, locally produced equipment accounted for 35% of total expenditures on expansion, compared to 12% during the first adoption in 1968.
- Channels illustrated:
  - Direct effects: adopter profitability and technology transfer via contracts and engineer training.
  - Local spillovers: labor mobility of trained engineers spreading knowledge to smaller local mills and capital goods producers (e.g., water treatment systems, dust collection devices, large magnetic cranes from Enos and Park, 1988, p. 210-211).
  - Fixed-cost reduction for later adoptions: cheaper domestically produced capital inputs reduced setup costs for POSCO’s 1980 computerization adoption.

### B.2 IV Construction and Controls (Technical)
- Business-group sales-share control:
  - Share_sale(−i)_nj,t−h = sum_{g̃≠g(i)} Salẽ_{g̃,nj,t−h}^{(−i)} / Sale_{(−i),nj,t−h} (equation (B.1)), where Salẽ excludes firm i.
- Business-group sales IV:
  - Z_sale,≥100km,t0_{i n j,t−h} = Σ_{g̃≠g(i)} D̃_{g̃,nj,t0} × Sale_{≥100km,t0}^{g̃(−n) j,t−h} / Salê_{(−i),nj,t−h}, where D̃ indicates presence of business group g̃ in region-sector nj in initial year t0, and Salê is predicted sales constructed using national-level growth and initial sales.
  - IV_sale,≥100km,t0_{i n j,t−h} = ΔZ_sale,≥100km,t0_{i n j,t−h} (equation (B.2)).
- Distinction of IVs:
  - IV_sale,≥100km exploits business groups’ sales expansion outside focal region.
  - IV_≥100km captures business groups’ technology adoption outside the focal region.
  - Both IVs computed from pre-existing firms located outside a 100 km radius.

### B.3 Empirical Findings and Robustness Snapshots (Selected Results and Tests)
- Direct adopter effects (winners vs. losers design):
  - Event study shows normalized log sales and TFPR increases for winners relative to losers (Figures B3, B6).
  - Pooled diff‑in‑diff coefficient on 1[Winner_it]×1[Post_mt] for Sale and TFPR reported with baseline p‑values [<0.01] (Table B4).
  - Robustness across inference methods: baseline, randomization inference, wild bootstrap, MacKinnon bootstrap produce consistent p‑values for Sale and TFPR (<0.01) (Table B4).
- Local spillovers and complementarity (IV results):
  - First-stage: IV_≥100km,t0 strongly predicts ΔShare(−i)_nj,t−2 with coefficient ~0.19 and standard error (0.04) (statistically significant) (Table B6).
  - IV estimates: ΔShare(−i)_nj,t−2 positively associated with ΔlnSale_it and ΔTFPR_it (Table B7; e.g., ΔShare coefficient 4.06 with standard error (1.16) in column 1).
  - KP‑F and SW‑F statistics reported to assess instrument strength (e.g., KP‑F values such as 5.77, 6.46, up to 21.79 across specifications in Table B7).
  - Robustness to alternative IV definitions, exclusion of large business groups, varying distance thresholds (50 km, 75 km, 125 km, 150 km) — results remain positive and statistically significant (Table B9).
  - Placebo tests over pre-policy windows show no significant effects (Table B11).
  - Spatial autocorrelation tests (Moran’s I) do not indicate significant spatial residual autocorrelation across thresholds 75 km, 100 km, 150 km, 200 km (Table B12).
  - Sensitivity to parallel‑trend violations assessed via Rambachan and Roth (2023); reported 90% confidence intervals for β4 across different M values (Figure B7).
- Robustness on heterogeneous effects:
  - Heterogeneous complementarity by initial market access cutoff percentiles (70th, 75th, 80th, 85th) — interaction terms Low MA × ΔShare and High MA × ΔShare estimated; High MA coefficients positive and often significant (Table B8).

### C. Simple Model — Structure, Mechanisms, and Propositions
- Adopter cutoff and equilibrium share:
  - Adoption cutoff equation (C.1) and mapping to adoption probability λ_Tt = (φ̄_Tt)^(−θ).
  - Aggregate quantity Q_t and wage-price relation: Q_t = A(λ_Tt) f(λ_T,t−1) L and w_t / P_t = 1/μ A(λ_Tt) f(λ_T,t−1) (equations (C.2), (C.3)).
  - Equilibrium condition: λ_Tt = [ (η^(σ−1) − 1) / (σ F_T) × A(λ_Tt)^(2−σ) f(λ_T,t−1) L ]^(θ/(σ−1)) (equation (C.4)), bounded by 1 as in (C.5).
- Key propositions (summarized):
  - Proposition 1:
    - (i) Uniqueness: given λ_T,t−1, a unique equilibrium share λ_Tt exists each period (with boundary at 1).
    - (ii) Comparative statics: equilibrium λ̂_Tt increases in productivity gain parameter η and in spillover parameter δ.
    - (iii) Dynamic complementarity: ∂λ_Tt/∂λ_T,t−1 > 0 for non‑boundary solutions (equation (C.8) and derivatives in (C.9)-(C.10)).
    - (iv) Multiple steady states: strict convexity of λ̂_Tt in λ_T,t−1 implies at most two intersections with 45-degree line; parameter ranges for δ and η yield 1, 2, or 3 steady states (detailed argument C.11–C.14).
    - (v) Welfare: per‑period welfare w_t + Π_t/L P_t = f(λ_T,t−1) A(λ_Tt); welfare strictly increases in λ_T.
  - Proposition 2 (Big push and market-size effects):
    - (i) Big push: temporary subsidies to input costs or to fixed adoption costs increase equilibrium λ_Tt; sufficiently large temporary subsidy ̄s_t can move economy from underdeveloped steady state S_Pre or S_U to industrialized steady state S_Ind (equations (C.15)-(C.16)).
    - (ii) Market size: ∂λ_Tt/∂L < 0, implying larger L shifts short‑run equilibrium curve downward so that ∂S_U/∂L < 0 and ∂s/∂L < 0.
- Microfoundations for adoption spillovers:
  - Two channels presented:
    - Local diffusion of knowledge via innovation cost reduction g(λ_T,t−1) that falls with prior adopter share; dynamic complementarities arise because higher past adoption lowers innovation costs and raises current innovation/adoption incentives (derivation around equation (C.17)).
    - Learning externalities via labor mobility and intergenerational skill transmission: parents working in adopter firms raise children’s skills by γ1>1; random matching and Nash bargaining imply adoption incentives depend on λ_T,t−1 through expected partner skill (mapping to f̃(λ_T,t−1)).

### D. Quantitative Model — Structure and Aggregation
- Multi‑region, multi‑sector general equilibrium with firm heterogeneity and adoption choices:
  - Final goods CES aggregator across varieties and firms; price index P_njt specified.
  - Firm production: y_it = z_it L_i t^γL_j ∏_k (M_k i t)^γk_j; unit input bundle costs c_njt given as a function of wages and input price indices.
  - Firm pricing: constant markup μ over marginal cost; prices p_inmj t = μ τ_nmj c_njt / z_it for domestic sales and p_x i n j t = μ τ^x_nj c_njt / z_it for export prices.
  - Firm profit after maximizing over adoption T_it ∈ {0,1} and export decision x_it is given by expression (D.1), separating domestic operating profits π_d(T_it; φ_it), foreign operating profits π_x(T_it; φ_it), and fixed costs w_nt F_x j and c_njt F_T.
- Cutoffs and shares:
  - Export cutoff φ̄_x n j t and adoption cutoff φ̄_T n j t defined where operating profits equal fixed export or adoption costs, respectively.
  - Adopter share λ_T n j t and exporter share λ_x n j t computed from region-sector productivity distribution G_njt and mass of potential entrants M_nj.
- Aggregation and market shares:
  - Region-sector average firm productivity inclusive of subsidies φ̄_avg n j t and φ̄_avg,x n j t derived as functions of φ̄_T n j t and λ_T n j,t−1 (expressions preserved in text).
  - Price index, regional expenditure shares (π_m n j t and π_f n j t), regional gross output R_d n j t, and exports R_x n j t expressed as functions of φ̄_avg and φ̄_avg,x.
- Market clearing and government budget:
  - Labor market clearing: w_nt L_nt equals labor used in production plus fixed adoption and export costs (equation (D.2)).
  - Goods market clearing: R_d n j t equals sectoral demand across buyers (equation (D.3)).
  - Government budget balances period by period with import tariff revenues and labor tax τ_wt financing subsidy‑related transfers (equation (D.4)).

### E. Quantification and Calibration Notes
- The quantitative exercises require the data inputs listed in Section E.1 (calibration inputs referenced but detailed inputs not included in provided excerpt).

*Italic: Source — wpiea2024259-print-pdf (References and Online Appendix content provided).*

### 1. Initial adopter shares{휆

### 1. Initial adopter shares{휆

### Data inputs
- Initial adopter shares and related data:
  - 푇, Data 푛푗, 68; 푛∈풩, 푗∈풥
  - 푇 and initial population {퐿, Data 푛, 72}; 푛∈풩
- Region-sector gross output:
  - {푅, Data 푛푗푡}, 푛∈풩, 푗∈풥, 푡∈{72,76,80}
- Sectoral exports and import shares:
  - {EX, Data 푗푡, 휋 푓 , Data 푗푡}, 푗∈풥, 푡∈{72,76,80}
- Sectoral PPI changes between 푡 and 푡−1, for 푡∈{76,80}
- Aggregate real GDP growth between 푡 and 푡−1, for 푡∈{76,80}
- Import tariffs:
  - {푡 푗푡}, 푗∈풥, 푡∈{72,76,80}

### Estimation / Calibration algorithm
- Goal: calibrate values of 횯_E (given) and obtain estimates of 횯_M, ̄푠, and 횿_푡 by minimizing an objective function through iterative solving and fitting to data.
- Algorithm steps:
  1. Guess parameters.
  2. Guess fundamentals {푐 푓 푗, 퐷 푓 푗} for 푗∈풥, and {휙_min 푛푗} for 푛∈풩, 푗∈풥.
  3. Given parameters {횯_M, ̄푠}, solve the model and update fundamentals 횿_푡 for each period; fit region- and sector-level aggregate outcomes to data counterparts (solving constraints of the minimization problem):
     - (a) Update {퐷 푓 ′ 푗푡} by fitting model export intensities to data EX_Data 푗푡 Í 푛 푅_Data 푛푗푡.
     - (b) Update {푃_퐹 ′ 푗푡} by fitting model import shares to data 휋 푓 ,Data 푗푡.
     - (c) For each sector, update {휙_min’ 푛푗푡} relative to the reference region until shares of regional gross output exactly match data counterparts 퐺푂_Data 푛푗푡 Í 푚 퐺푂_Data 푚푗푡. Within each sector, normalize Pareto lower bound parameters of the reference region 푛_0 to 1 for each sector and period.
     - (d) Recover absolute levels of {휙_min’ 푛_0 푗푡} using sector PPI and real GDP growth. PPIs are constructed as weighted averages of regional price indices, weighted by initial regional gross output in 1970. Because PPIs only identify relative changes of sectoral productivity growth relative to the reference sector, identify relative sector’s Pareto lower bound using real GDP growth. The 1970 Pareto lower bounds of the reference regions are set to 1.
  4. After updating geographic fundamentals, given parameters and subsidies, evaluate the objective function.
  5. Iterate steps 1–4 until values {ˆ횯_M, ˆs_푡} that minimize the objective function are found.

### Key methodological notes
- The calibration fits multiple observable moments at region-sector and sector levels (exports, import shares, regional gross output shares, PPIs, real GDP growth).
- Normalizations: Pareto lower bound parameters of reference regions set to 1 in 1970; amenities normalized to 1 in the reference region for each period when applicable.

### E.2 Spatial Mobility (model extension)
- Households make myopic migration decisions at the beginning of each period to maximize static utility, following (Peters, 2022). After relocating, households supply labor and earn wages in new regions.
- Household location choice maximizes:
  - max_n U_mn t(ε_mn t), where 풰_n m t(ε_n m t) = V_m t C_m t^d n m ε_n m t.
  - V_m t is exogenous amenity in region m; d_n m is utility cost of moving from n to m; ε_n m t is preference shock drawn i.i.d. from a Fréchet distribution with shape parameter 휈: F(ε)=exp(ε^−휈).
- Migration elasticity parameter:
  - 휈 is the migration elasticity governing responsiveness of migration flows to real income changes in destination regions.
- Share of households moving from n to m in period t:
  - 휇_n m t = (V_m t ω_m t / d_n m)^휈 Í_m′ (V_m′ t ω_m′ t / d_n m′)^휈.
- Population evolves as a state variable:
  - 퐿_n t = Í_m 휇_n m, t−1 퐿_m, t−1.
- Population 퐿_n t becomes a state variable in addition to adopter shares 휆_T n j t.

### E.2 Calibration of spatial mobility
- Period length: each period corresponds to 4 years.
- Set 휈 = 0.5 based on migration elasticity of 0.5 at the annual frequency estimated by Choi (2024) and alignment with long-run value of 2 in (Peters, 2022).
- Migration costs parameterization: d_n m = (Dist_n m)^휁.
- Gravity estimation for migration flows:
  - η: estimate equation 휇_n m = exp(휈휁 Dist_n m + 훿_n + 훿_m) ε_n m t.
  - Address attenuation bias from zeros using PPML estimation.
  - Data: migration flow data for individuals aged 20 to 55 from 1990 to 1995 obtained from the 1995 Population and Housing Census (closest available to sample period).
  - Estimated 휈휁 = 1.39.
- Amenities V_n t are backed out by fitting population distributions for years 1972, 1976, and 1980; amenities identified up to normalization, set V_n t = 1 in the reference region for each period.

### E.3 Additional figures, tables, and quantitative results (selected outputs)
- Table E1: Additional Non-Targeted Moments — model vs data non-targeted moments for region heavy manufacturing employment, exports, and exporter shares:
  - 휆_T n j t coefficients and standard errors (columns shown):
    - 0.256 ∗∗∗ (0.066)
    - 0.294 ∗∗ (0.117)
    - 0.702 ∗∗∗ (0.154)
    - 0.282 ∗ (0.142)
    - 0.310 ∗∗∗ (0.092)
    - 0.549 ∗∗∗ (0.166)
  - Adjusted R^2 reported per column:
    - 0.91, 0.55, 0.77, 0.73, 0.78, 0.37
  - N = 258 in each reported column.
- Figure E1: Local Effects of the Big Push — Panels show baseline (with subsidy) vs counterfactual (no subsidy) steady state local heavy manufacturing GDP shares and productivity M_n j [∫ z_i t(휙)^(σ−1) dG_n j t(휙)]^(1/(σ−1)). Notes: dots below 45-degree line (red) indicate regions with higher steady-state GDP shares and productivity in baseline than counterfactual.
- Figure E2: Regional Welfare Distribution — 66 out of 86 regions experience welfare gains; 20 out of 86 experience welfare losses. Horizontal red dashed line denotes aggregate welfare changes.
- Figure E3: Alternative Scenarios for Market Access and Other Policies — aggregate effects of the Big Push under:
  - A. Lower foreign demand: scenario with 25% lower foreign demand.
  - B. Protectionist import tariff: tariffs increase by 40% between 1972 and 1980.
  - C. No transportation improvements: reverses the 66% reductions in travel time from highway construction.
  - D. No internal trade: prohibiting internal trade within heavy manufacturing sector.
  - E. Joint (A + B + C): combined effects of A, B, and C.
- Table E2: Alternative Subsidy Scheme — Randomized Subsidy Regions (1,000 simulations; 35 subsidized regions per simulation). Selected coefficient estimates (standard errors in parentheses):
  - Avg.lnDist.Port_n: −0.63 ∗∗∗ (0.12) and −0.29 ∗∗∗ (0.06) in reported columns.
  - Avg.lnMA_n,heavy,72: 0.30 ∗ (0.16) and 0.18 ∗∗ (0.07).
  - Avg.ln휙_min_n,heavy,72: −0.15 (0.39) and −0.17 (0.18).
  - Avg.ln퐿_n,72: −0.18 (0.16) and −0.06 (0.07).
  - N = 1,000 for each column.
  - Notes: Dependent variables are steady state differences in log heavy manufacturing GDP shares and welfare changes between baseline and counterfactual. Statistical significance: * p<0.1, ** p<0.05, *** p<0.01.
- Figures E4–E5: Alternative Subsidy Schemes and Optimal Subsidy Rate:
  - Figure E4 compares heavy manufacturing GDP shares under general subsidies (purple), baseline adoption subsidies (red), and no subsidies (blue).
  - Figure E5 presents heavy manufacturing GDP shares with optimal subsidy rate of 12% (purple), baseline adoption subsidies (red), and no subsidies (blue). Optimal subsidy rate reported: 12%.
- Table E3: Robustness — Statistical Uncertainty for spillover parameter 훿 and direct gain parameter 휂 (sensitivity analysis across confidence intervals):
  - Panel A. Spillover parameter 훿 (parameter value (σ−1)훿):
    - 3.4, 2.7, 2.35, 2.0, 1.70, 1.48, 1.24 (columns listed as "0.5 std higher", "Baseline", "0.5 std. lower", "1 std. lower", "1.5 std. lower", "Lower 90% CI", "Lower 95% CI")
    - ΔHeavy mfg. GDP share (%): 2.35, 1.95, 1.77, 1.66, 1.36, 0, 0 (corresponding entries)
    - "Does the big push occur?" entries: Y Y Y Y Y N N
  - Panel B. Direct gain parameter 휂 (parameter value 휂):
    - 1.2, 0.9, 0.75, 0.6, 0.45, 0.40, 0.30
    - ΔHeavy mfg. GDP share (%): 0, 1.95, 1.69, 1.47, 1.36, 1.25, 1.20
    - "Does the big push occur?" entries: N Y Y Y Y Y Y
  - Note: geographic fundamentals and remaining parameters re-calibrated for each parameter value.
- Table E4: Robustness — Spatial Mobility and Alternative Parameter Values:
  - Columns: Baseline, Spatial Mobility, Alternative parameter values (휎=3, 휎=5, 휃=1.02, 휃=1.10)
  - ΔHeavy mfg. GDP share (%): 1.95 (Baseline), 2.72 (Spatial Mobility), 2.95 (휎=3), 1.22 (휎=5), 1.99 (휃=1.02), 1.86 (휃=1.10)
  - "Does the big push occur?" entries: Y Y Y Y Y Y
  - Note: for each alternative set, geographic fundamentals and remaining parameters are re-calibrated. Appendix E.2 explains spatial mobility calibration in detail.

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024259-print-pdf.pdf_