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---

### Data (Section 2.1)
- Dataset construction:
  - Main dataset: combined technology adoption, patent, and balance sheet datasets based on firm names and business IDs.
  - Coverage: manufacturing firms, sample period 1970–1993.
  - Construction details referenced in Appendix A.
- Technology adoption data:
  - Base dataset: firm-to-firm technology adoption dataset constructed by Choi and Shim (2022), expanded with additional information on foreign firms and adoption fees, and extended sample period.
  - Coverage: all technology transfers between Korean and foreign firms from 1970 to 1993.
  - Contracts: 8,346 contracts total; 75% matched with firm-level balance sheet data.
  - Content composition:
    - 95% related to know-how transfers (technical and training services, sharing information, or transfers of blueprints).
    - 42% involved both know-how transfers and licensing rights for patents or trademarks.
    - 4% were exclusively for licensing.
  - Transactions between subsidiaries and headquarters within multinational firms: 3% of all contracts and were excluded.
  - Data source: documents submitted under the Foreign Capital Inducement Act (1962–1993) preserved by the National Archives of Korea.
  - Limitations: captures official measures of technology adoption from foreign countries; excludes diffusion from FDI, transfers between Korean firms, and unofficial adoption through reverse engineering.
  - Notes:
    - Role of FDI limited in Korea due to government regulation on FDI (Kim, 1997, p. 42-43).
    - Estimated adoption fees between domestic firms were only 6.3% of total expenses (Lee, 2022).
    - Unofficial adoption activities modeled as exogenous knowledge diffusion.
  - Examples and cost magnitudes:
    - Average annual royalty rate: 3% with a 5-year contract length.
    - Fixed fees account for 10% of yearly sales on average.
    - Total adoption fees account for 7.4% of foreign firms’ sales on average.
    - Distribution of foreign countries in contracts: Japanese firms account for 50%; US firms account for 26% (Appendix Table A.1).
- Patent data:
  - Source: Korean Intellectual Property Office (KIPO) patent data, cleaned per Lee et al. (2020).
  - KIPO includes the universe of patents registered in Korea by domestic and foreign firms; application year used as year of innovation; business ID of assignee used for merges.
  - Limitation: KIPO lacks citation information until the 1990s.
  - Supplement: incorporate United States Patent and Trademark Office (USPTO) data for patent citations since 1975.
- Balance sheet data:
  - Firm-level variables: sales, fixed assets, employment, sectors.
  - Domestic sources:
    - 1970–1982: Annual Reports of Korean Companies (Choi and Shim, 2022); covers firms with more than 50 employees; represents approximately 70% of manufacturing gross output on average across years.
    - 1983–1993: KIS-VALUE; covers firms with assets of more than 3 billion Korean won (2.65 million dollars in 2015).
  - Foreign firm sources: Compustat North America and Global.
  - Of 22,587 unique foreign firms, 769 firms have ever sold technology to Korean firms.
- Aggregate and sectoral data:
  - Aggregate expenditures on adoption and R&D obtained from Statistics Korea; aggregate adoption expenditure measured as total payments to foreign countries for the use of intellectual property.
  - Real GDP per capita from the Maddison Project (Bolt and Van Zanden, 2020; Cha et al., 2020).
  - Input-output tables from the Bank of Korea.
  - Trade data from Comtrade.
- Summary statistics (Table 2 highlights; averages 1970–1993, nominal values converted to 2015 US million dollars):
  - Emp.: Ever-Adopted 1,184 / Never-Adopted 297 / Ever-Patented 1,747 / Never-Patented 338 / All 626
  - Asset: Ever-Adopted 185 / Never-Adopted 193 / Ever-Patented 152 / Never-Patented 474
  - Sales: Ever-Adopted 205 / Never-Adopted 313 / Ever-Patented 193 / Never-Patented 5102
  - Sales per Emp.: Ever-Adopted 0.18 / Never-Adopted 0.15 / Ever-Patented 0.20 / Never-Patented 0.15 / All 0.17
  - Patenting (yearly dummy): Ever-Adopted 0.07 / Never-Adopted 0.01 / Ever-Patented 0.18 / All 0.03
  - Adopting (yearly dummy): Ever-Adopted 0.18 / Ever-Patented 0.19 / Never-Patented 0.04 / All 0.06
  - # of Unique Firms: Ever-Adopted 1,180 / Never-Adopted 5,613 / Ever-Patented 471 / Never-Patented 6,322 / All 6,793
  - # of Obs.: Ever-Adopted 18,679 / Never-Adopted 34,549 / Ever-Patented 8,394 / Never-Patented 44,834 / All 53,228
  - Summary observations:
    - Ever-adopters and ever-patenting firms were larger by sales, employment, and assets.
    - These firms had higher labor productivity (sales per employee) and were more likely to adopt foreign technology or register a patent in a given year.
    - Appendix Table A.3 compares foreign firms: technology sellers were larger than other foreign firms.

### Knowledge Spillovers from Adoption (Section 3.2)
- Measurement approach:
  - Knowledge spillovers measured using patent citations.
  - Identification: compare two foreign firms (one that sold technology to a Korean firm and one that never sold). Increased citations from never-adopting Korean firms to the seller’s patents after transfer interpreted as knowledge spillover.
- Empirical design and matching:
  - Matching-based event study: matched pairs contain one foreign seller and one observationally similar foreign non-seller.
  - Exact matching dimensions: country and primary patent field (IPC 3-digit).
  - Distance matching variables: cumulative patent stock, new patents in a given year, and new citations received (excluding self-citations); use values 1 year before event and last 4 years of growth.
  - Sample restrictions and trimming:
    - Countries restricted to the US, Japan, UK, and France.
    - Require each IPC 3-digit to have more than 20 observations.
    - Trim the top 98% of outliers in terms of distance to improve matching quality.
  - Matches obtained: 213 matches with 412 unique firms.
- Estimation specifications:
  - Event-study dependent variable: 1[Citation_Kor_fmt>0], dummy if any never-adopting Korean firms cite patents from foreign firm f in year t.
  - Event dummies D_τ_mt = 1[t − τ = t(m)].
  - Fixed effects: firm-match δ_fm and match-year δ_mt.
  - Standard errors: two-way clustered at foreign firm and match level.
  - Average (difference-in-differences) specification: 1[Citation_Kor_fmt>0] = β_DD · 1[Seller_fmt] × Post_mt + δ_fm + δ_mt + ε_fmt.
- Balance and pretrends:
  - No statistically significant differences between seller and control groups in observables.
  - Raw average citations by never-adopting Korean firms follow similar trends before events; divergence only after events (no pretrends).
  - Design notes: stacked-by-event design addresses heterogeneous treatment effect concerns.
- Main results:
  - Event-study coefficients show no pretrends before events.
  - Eleven years after the event, the probability of citation by never-adopting Korean firms to the seller group’s patents increased by around 10%, compared with the control group.
  - Table 5 — Average Effects (estimates of β_DD from Equation (5)):
    - Time horizon −7≤τ≤5 (column (1)):
      - 1[Treated_ft]×1[Post_mt] = 0.02** (standard error (0.01))
      - Firm-match FE: ✓ ; Match-year FE: ✓ ; Adj. R^2: 0.41 ; # Cl. (Foreign firm): 412 ; # Cl. (Match): 213 ; N: 5,404
    - Time horizon −7≤τ≤11 (column (2)):
      - 1[Treated_ft]×1[Post_mt] = 0.03*** (standard error (0.01))
      - Firm-match FE: ✓ ; Match-year FE: ✓ ; Adj. R^2: 0.51 ; # Cl. (Foreign firm): 412 ; # Cl. (Match): 213 ; N: 7,960
    - Notes: Standard errors two-way clustered at foreign firm and match level. *p <0.1, **p <0.05, ***p <0.01.
  - Interpretation: coefficients grow and become more precise with longer horizons, implying knowledge spillovers occur with lags and indicate positive externality from adoption.
- Placebo and robustness:
  - Placebo: replicate regression using citations from all other countries except Korea — shows no clear differences, ruling out unobserved shocks to foreign firms as alternative explanation.
  - Robustness: results robust to alternative numbers of matches (2 and 5 matches) and long-run difference specifications including additional controls and unit-specific random trends (Appendix Table B.5).
  - Long-run difference example: △1[Citation_Kor_fmt>0] = β Seller_fmt + X'_fm γ + δ_m + ε_fmt; matches microfoundation mapping of spillovers.

### Equilibrium (Section 4.4)
- Value function and state variables:
  - Home firm i ∈ I_H: m_i = {m_F_i, m_D_i}.
  - Foreign firm f: m_f = {m_h_f, m_̃h_f}.
  - Note: m_h, m_̃h, and m_f imply each other.
- Home firm Bellman (key structure):
  - r_Ht V_it(m_i) − ̇V_it(m_i) (9) = max_{x_it(m_i), a_it(m_i)} [ Π_Ht(m_i) − (1−κ_Hrt) α_Hr x_it(m_i)^{γ_r} / γ_r w_Ht − (1−κ_Hat) α_Ha a_it(m_i)^{γ_a} / γ_a w_Ht + x_it(m_i) Σ_n ̃f(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] + a_it(m_i) Σ_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] − (1−κ_Hrt) F_it(m_i) + x_{−i}t(m_{−i}) Σ_n ̃f(n; m_{−i}) [V_it(m_F_i, m_D_i−n) − V_it(m_i)] + a_{−i}t(m_{−i}) Σ_n ̃g(n; m_{−i}) [V_it(m_F_i, m_D_i−n) − V_it(m_i)] + [x_ft(m_f) + ̃x_ft(m_f)] Σ_n f(n; min_{i∈I_H}{m_i^f}) [V_it(m_F_i−n, m_D_i) − V_it(m_i)] + a_ft(m_f) Σ_n g(n; min_{i∈I_H}{m_i^f}) [V_it(m_F_i−n, m_D_i) − V_it(m_i)] + 1[m_D_i ≥ 0] × F_ft(m_f) + φ [V_it(0,0) − V_it(m_i)] ].
- Transition probabilities:
  - ̃f(n; m_i) = 1[m_D_i > 0] f(n; m_F_i) + 1[m_D_i ≤ 0] [ n(1−δ) f(n; m_F_i) + δ f(n + m_D_i; m_F_i − m_D_i) ].
  - ̃g(n; m_i) = 1[m_D_i > 0] g(n; m_F_i) + 1[m_D_i ≤ 0] [ n(1−δ) g(n; m_F_i) + δ g(n + m_D_i; m_F_i − m_D_i) ].
  - First/second terms correspond to leader (1[m_D_i>0]) and follower (1[m_D_i≤0]) cases; within-country spillovers mix distributions.
- Optimal innovation and adoption rates:
  - Optimal Home innovation rate (Equation (10)):
    - x_it(m_i) = [ Σ_n ̃f(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] / ( (1−κ_Hrt) α_Hr w_Ht ) ]^{1/γ_r − 1}.
  - Optimal Home adoption rate (Equation (11)):
    - a_it(m_i) = [ ( Σ_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] − (1−κ_Hat) F_it(m_i) ) / ( (1−κ_Hat) α_Ha w_Ht ) ]^{1/γ_a − 1}.
  - Foreign firms’ optimal rates derived in Appendix C.2.
- Adoption fee (Nash bargaining; Equation (12)):
  - F_it(m_i) = [ (1−ξ) Σ_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] − ξ Σ_n ̃g(n; m_i) [V_ft(m_i^f − n, m_{(−i)}^f) − V_ft(m_f)] ] / (1 − (1−ξ) κ_Hat).
  - Parameter 0 ≤ ξ ≤ 1 is adopter bargaining power.
  - Adoption fee internalizes Home adopter’s future gains and Foreign seller’s losses; fees vary with productivity gaps due to backwardness and competition effects.
  - Subsidy interaction: subsidy increases buyer surplus and can be partially passed to seller; response depends on ξ.
    - When adopter bargaining power ξ approaches zero, elasticity reaches maximum and adoption fee increases with subsidy rate by 1 / (1 − κ_Hat).
    - Conversely, when ξ converges to zero, subsidy rate does not affect adoption fee.
  - Conclusion: adoption subsidies more effective when adopters possess greater bargaining power.
- Total surplus and contract conditions:
  - Total surplus must be positive for contract occurrence.
  - Factors increasing total surplus: lower Home wage than Foreign wage; higher trade costs; lower elasticity of substitution.
- Distribution of productivity gaps (law of motion):
  - T_it(n; m_i) := ̃f(n; m_i) x_it(m_i) + ̃g(n; m_i) a_it(m_i).
  - T_ft(n; m_f) := f(n; min_{i∈I_H}{m_i^f}) (x_ft(m_f) + ̃x_ft(m_f)) + g(n; min_{i∈I_H}{m_i^f}) a_ft(m_f).
  - Law of motion (Equation (13)) for μ_t(m_h) provided with inflows from innovation/adoption and exogenous spillover φ; balanced growth path satisfies ̇μ_t(m_h) = 0.
- Market clearing, government budget, and trade balance:
  - Asset markets: A_Ct = ∫_0^1 ∑_{i∈I_C} C V_ijt dj.
  - Goods market: ∑_{i∈I_C} p_ijt y_ijt + p^*_fjt y^*_fjt = P_Ct Y_Ct = P_Ct C_Ct, ∀ j ∈ [0,1].
  - Labor market: L_Ct = ∫_0^1 ∑_{i∈I_C} [ l_ijt + α_Ca a_ijt^{γ_a} + α_Cr x_ijt^{γ_r} ] dj.
  - Government budget (balanced each period):
    - T_Ct = (1 + θ) ∫_0^1 ∑_{i∈I_C} [ κ_cat a_ijt F_ijt + κ_Cat α_Ca a_ijt^{γ_a} w_Ct + κ_crt α_Cr x_ijt^{γ_r} w_ct ] dj − t_Ct / (1 + t_Ct) ∫_0^1 ∑_{i∈I_{−C}} p^*_ijt y^*_ijt dj.
    - θ > 0 is deadweight cost of taxation.
  - Trade balance:
    - ∫_0^1 [ ∑_{i∈I_{−C}} p^*_ijt y^*_{ijt} + ∑_{i∈I_C} a_ijt F_ijt ] dj = ∫_0^1 [ ∑_{i∈I_C} p^*_{ijt} y^*_{ijt} + ∑_{i∈I_{−C}} a_{ijt} F_{ijt} ] dj.
- Equilibrium definitions:
  - Definition 4.1 (Markov perfect equilibrium): full set of objects { r_Ct, w_Ct, p_ijt, p^*_ijt, x_ijt, a_ijt, F_ijt, T_Ct, C_Ct, Y_Ct, A_Ct, μ_mt } satisfying static and dynamic conditions and market clears.
  - Definition 4.2 (Balanced growth path): equilibrium where { w_Ct, V_ijt, F_ijt, T_Ct, C_Ct, Y_Ct, A_Ct } grow at constant rate g, and r_Ct and μ_t are constant.

### Calibration (Section 5.2)
- Calibration approach:
  - Calibrate 23 parameters in three steps:
    - 6 parameters taken directly from data.
    - 7 parameters externally calibrated.
    - 10 parameters jointly estimated by simulated method of moments (SMM).
  - Solution strategy: given parameter guess, solve for transitions with initial conditions until convergence to balanced growth path; compute model moments and update parameters to minimize distance to data moments; incorporate time-varying policies and assume agents’ perfect foresight.
  - Home = Korea; Foreign = Japan. Initial year set to 1973.
- Parameters taken directly from data: {L_H, L_F, κ_Hat, κ_Hrt, t_Ht, t_Ft}
  - L_H = 1 ; L_F = 2.
  - κ_Hat and κ_Hrt: subsidy rates from tax credit data (Figure 1).
  - Import tariffs t_Ht and t_Ft: import-weighted average tariffs across sectors.
    - Korea product-level import tariffs for 1973–1988 from Korea Customs Service (CCCN 4-digit aggregated by import values).
    - Japan 1973–1988 average import tariff from Yi (2003).
    - From 1988 onward, World Development Indicators used for both countries.
    - Between 1973 and 2023, Korea’s tariffs decreased from 27% to 5%, while Japan’s tariff decreased from 8% to 3%.
- External calibration: {ρ, ψ_H, ψ_F, γ_r, γ_a, σ, θ}
  - ρ = 0.03.
  - ψ_H = 0.25 ; ψ_F = 0.5.
  - γ_r = 2 ; γ_a = 2.
  - σ = 6.
  - θ = 1.
- SMM parameters Θ = {λ, α_r, α_a, α_F, η_a, τ, ξ, δ, d, φ} and targeted moments:
  - Adoption fee / yearly sales: Data moment 0.224 identifies ξ.
  - Productivity gain from adoption over the initial gap: identifies η_a.
  - Patent citation increase after adoption: target 0.02 within 5 years identifies δ (mapping x̄ × δ = 0.02).
  - Manufacturing shares of exports to value-added: Data 0.392 identifies τ.
  - R&D and adoption fee expenditures as share of manufacturing value-added (1985 and 1990):
    - Innovation R&D = 0.0297 ; adoption fees = 0.0148; identify α_r and α_a.
  - Long-run GDP per capita growth rate: Data 0.021 identifies λ.
  - Real GDP per capita ratio Korea/Japan: 1973 ratio 0.210 identifies d; 2020 ratio 0.981 informs φ.
  - Long-run productivity ratio target = 1 identifies α_F.
- Estimation results (Table 6):
  - Jointly calibrated / SMM results:
    - λ = 1.056
    - η_a = 1.596
    - α_a = 1.334
    - α_r = 1.569
    - τ = 1.568
    - ξ = 0.556
  - Jointly estimated through SMM:
    - δ = 0.252
    - d = -17.551
    - α_F = 6.168
    - φ = 0.037
  - Interpretation highlights:
    - λ = 1.056 ⇒ one step improvement increases productivity by 5.6%.
    - η_a = 1.596 indicates advantages of backwardness magnitude.
    - α_a < α_r ⇒ lower labor requirements for adoption than for innovation.
    - τ = 1.568 (iceberg trade cost).
    - ξ = 0.556 ⇒ adopters have slightly larger bargaining power.
    - δ = 0.252 ⇒ probability of receiving knowledge spillovers.
    - d = -17.551 ⇒ initial productivity gap implies Japanese firms were initially 2.6 times more productive than Korean firms.
    - α_F = 6.168 ⇒ Japan’s relative innovation and adoption costs.
    - φ = 0.037 ⇒ exogenous spillover probability.
- Fit to targeted moments (Table 7; Model vs Data):
  - Adoption fee / annual sale: Model 0.224, Data 0.224
  - β_a: Model -0.065, Data -0.065
  - β_s: ∆Patent citation after adoption: Model 0.019, Data 0.019
  - Long-run growth rate: Model 0.021, Data 0.021
  - Adoption / value-added in manufacturing: Model 0.015, Data 0.015
  - R&D / value-added in manufacturing: Model 0.030, Data 0.030
  - Export / value-added in manufacturing: Model 0.392, Data 0.392
  - GDP ratio in 1973: Model 0.210, Data 0.210
  - GDP ratio in 2020: Model 0.981, Data 0.980
  - Long-run productivity ratio: Model 1.000, Data 1.006
  - Conclusion: model closely matches micro and macro moments and replicates Korea’s catching up with Japan.
- Validation (untargeted moments):
  - Declining share of total adoption fees relative to sum of adoption fees and innovation R&D:
    - Model matches declining trend; model generates decline even without subsidies.
    - Mechanism: firms prioritize innovation over adoption as productivity gaps narrow.
  - Relationship between adoption fees and productivity gaps:
    - Adoption fees become higher as Korean firms narrow productivity gaps, consistent with empirical fact in Table 4; highlights competition effects.

### Quantitative Results and Policy Evaluation (Sections 6.1–6.2)
- Contribution of adoption and innovation to TFP growth over time:
  - Aggregate TFP decomposition:
    - In 1973: adoption accounted for 37% of TFP growth; innovation accounted for 8%.
    - By 2023: adoption dropped to 7%; innovation rose to 74%.
  - Interpretation: adoption dominates early-stage growth; innovation dominates later-stage growth.
- Policy scenarios (budget-to-GDP share held constant):
  - Actual Korean stage-dependent policy (1973 onward): started with adoption subsidy, then switched to innovation subsidy.
  - No subsidies (undistorted case).
  - All budget to adoption subsidy only.
  - All budget to innovation subsidy only.
- Model-calculated subsidy statistics:
  - Total subsidy expenditure averages 1.75% of GDP.
  - Adoption subsidy share:
    - 1973 adoption share = 1 (only adoption subsidy present).
    - Adoption share gradually converged to zero by 2011.
- Consumption results (relative to no-subsidy case):
  - Adoption-only: higher growth rate in early stage; relative consumption larger than no-subsidy after several years; growth effect limited long-run.
  - Innovation-only: not higher growth initially vs adoption-only; yields higher growth rate at later stages.
  - Actual policy: consumption similar to adoption-only in early stages and yields higher growth rates in later stages.
- Welfare (consumption-equivalent change Ψ over infinite horizon):
  - Actual policy increases consumption-equivalent welfare by 4.3%.
  - Adoption-only: 2.7%.
  - Innovation-only: 3.5%.
  - Conclusion: actual stage-dependent policy implemented in Korea was quantitatively better than time-invariant alternatives.
- Foreign policy counterfactual — Japan prohibits technology transfers to Korea:
  - Scenario: Japanese government prevents firms from exporting technology to Korea; Korean government reallocates budget entirely to innovation subsidies (budget-to-GDP constant).
  - Results:
    - Short run: Japan’s consumption higher relative to baseline; Korea’s consumption lower.
    - Long run: Japan’s consumption becomes lower due to reduced innovation incentives.
    - Welfare effects:
      - Korea’s welfare decreases by −6.74%.
      - Japan’s welfare increases by 4.57%.
    - Mechanism: preventing transfers weakens competition and reduces innovation incentives in Japan; Korean welfare loss substantial.
- Robustness:
  - Checks on discount rates, elasticity of substitution, and deadweight cost of taxation show qualitatively similar results: actual policy yields greater welfare improvements than time-invariant policies.

### Optimal Policy (Section 6.3)
- Setup:
  - Governments choose the adoption subsidy share to maximize welfare while holding government budget/GDP equal to baseline.
  - Policy allowed to change every 10 years over a 50-year horizon.
- Optimal subsidy path and welfare outcomes:
  - Optimal subsidy share decreases rapidly from 45% to 17% in 2013.
  - Optimal subsidy path declines later than actual policy observed in data.
  - Welfare impact:
    - Optimal subsidy increases consumption-equivalent welfare by 5.3%.
    - Optimal time-varying policy yields larger welfare gain than actual policy and time-invariant alternatives.
- Quadratic specification:
  - Alternative optimal policy with subsidy share as quadratic function of calendar years yields similar dynamics and welfare increases close to piecewise-constant policy.
- Interaction with trade policy:
  - Import tariffs affect Foreign firms’ incentives to sell technologies; tariffs lower adoption fees by weakening competition.
  - Extreme case: infinitely high tariff reduces Foreign profit losses from selling technology, lowering equilibrium adoption fees.
  - Implication: protective trade policy makes adoption more affordable, increasing adoption rates toward social optimum and reducing effectiveness of adoption subsidies (shifts optimal budget toward innovation subsidies); liberal trade policy raises effectiveness of adoption subsidies.
- Counterfactual tariff scenarios:
  - Two scenarios with import tariffs set initially at 28% and 5%, respectively, and constant over time:
    - Under higher tariffs (28%), optimal policy allocates smaller portion of budget to adoption subsidies relative to baseline.
    - Under lower tariffs (5%), optimal policy allocates larger portion of budget to adoption subsidies relative to baseline.
- Key takeaways for policy design:
  - Time-varying, state-dependent subsidy policies produce larger welfare gains than static policies.
  - Trade policy materially alters optimal composition between adoption and innovation subsidies:
    - Higher tariffs reduce marginal effectiveness of adoption subsidies and tilt policy toward innovation support.
    - Lower tariffs increase effectiveness of adoption subsidies, making them more central in optimal policy.
  - Alternative functional forms (quadratic) deliver similar policy dynamics and welfare outcomes to piecewise-constant adjustments.

*Italicized source: wpiea2024154-print-pdf*

### 2.1    Data

### 2.1    Data

### Dataset construction
- Main dataset constructed by combining technology adoption, patent, and balance sheet datasets based on firm names and business IDs.
- Coverage: manufacturing firms, sample period 1970–1993.
- Construction details referenced in Appendix A.

### Technology adoption data
- Base dataset: firm-to-firm technology adoption dataset constructed by Choi and Shim (2022), expanded with additional information on foreign firms and adoption fees, and extended sample period.
- Coverage: all technology transfers between Korean and foreign firms from 1970 to 1993.
- Contracts: 8,346 contracts total; 75% matched with firm-level balance sheet data.
- Content composition:
  - 95% related to know-how transfers (technical and training services, sharing information, or transfers of blueprints).
  - 42% involved both know-how transfers and licensing rights for patents or trademarks.
  - 4% were exclusively for licensing.
- Transactions occurred between independent entities; contracts between subsidiaries and headquarters within multinational firms accounted for 3% of all contracts and were excluded.
- Data source basis: documents submitted under the Foreign Capital Inducement Act (1962–1993) preserved by the National Archives of Korea (see Appendix Figure A.1 for an example).
- Limitations: dataset captures official measures of technology adoption from foreign countries; excludes diffusion from FDI, transfers between Korean firms, and unofficial adoption through reverse engineering.
- Notes on FDI and domestic transfers:
  - Role of FDI limited in Korea due to government regulation on FDI (Kim, 1997, p. 42-43).
  - Estimated adoption fees between domestic firms were only 6.3% of total expenses (Lee, 2022).
  - Unofficial adoption activities will be modeled as exogenous knowledge diffusion.
- Examples (Table 1) include buyer, seller, contract length (years), date, technology, contents (know-how transfer, licensing), and fees (fixed amounts or royalty rates).
- Cost magnitudes and summary measures:
  - Average annual royalty rate: 3% with a 5-year contract length.
  - Fixed fees account for 10% of yearly sales on average.
  - Total adoption fees account for 7.4% of foreign firms’ sales on average.
  - Distribution of foreign countries in contracts: Japanese firms account for 50%; US firms account for 26% (Appendix Table A.1).

### Patent data
- Source: Korean Intellectual Property Office (KIPO) patent data, cleaned per Lee et al. (2020).
- KIPO includes the universe of patents registered in Korea by domestic and foreign firms; application year used as year of innovation; business ID of assignee used for merges.
- Limitation: KIPO lacks citation information until the 1990s.
- Supplement: incorporate United States Patent and Trademark Office (USPTO) data for patent citations since 1975.

### Balance sheet data
- Firm-level variables: sales, fixed assets, employment, sectors.
- Domestic Korean firm sources:
  - 1970–1982: Annual Reports of Korean Companies (Choi and Shim, 2022); covers firms with more than 50 employees; represents approximately 70% of manufacturing gross output on average across years.
  - 1983–1993: KIS-VALUE; covers firms with assets of more than 3 billion Korean won (2.65 million dollars in 2015).
- Foreign firm balance sheet sources: Compustat North America and Global (publicly listed firms starting from 1950 and 1987, respectively).
- Of 22,587 unique foreign firms, 769 firms have ever sold technology to Korean firms.

### Aggregate and sectoral data
- Aggregate expenditures on adoption and R&D obtained from Statistics Korea.
  - Aggregate adoption expenditure measured as total payments to foreign countries for the use of intellectual property.
- Real GDP per capita from the Maddison Project (Bolt and Van Zanden, 2020; Cha et al., 2020).
- Input-output tables from the Bank of Korea.
- Trade data from Comtrade.

### Summary statistics (Table 2 highlights)
- Table reports average values for firm groups between 1970 and 1993; nominal values converted to 2015 US million dollars.
- Selected group averages (Ever-Adopted / Never-Adopted / Ever-Patented / Never-Patented / All):
  - Emp.: 1,184 / 297 / 1,747 / 338 / 626
  - Asset: 185 / 193 / 152 / 474
  - Sales: 205 / 313 / 193 / 5102
  - Sales per Emp.: 0.18 / 0.15 / 0.20 / 0.15 / 0.17
  - Patenting (yearly dummy): 0.07 / 0.01 / 0.18 / N/A / 0.03
  - Adopting (yearly dummy): 0.18 / N/A / 0.19 / 0.04 / 0.06
  - # of Unique Firms: 1,180 / 5,613 / 471 / 6,322 / 6,793
  - # of Obs.: 18,679 / 34,549 / 8,394 / 44,834 / 53,228
- Summary observations:
  - Ever-adopters and ever-patenting firms were larger by sales, employment, and assets.
  - These firms had higher labor productivity (sales per employee) and were more likely to adopt foreign technology or register a patent in a given year.
  - Appendix Table A.3 compares foreign firms: technology sellers were larger than other foreign firms.

*Source: wpiea2024154-print-pdf - 2.1    Data*

### 3.2    Knowledge Spillovers from Adoption

### 3.2    Knowledge Spillovers from Adoption

### Measurement approach
- Knowledge spillovers are measured using patent citations following the literature (e.g., Jaffe et al., 1993; Aghion et al., 2019).
- Identification logic: compare two foreign firms (one that sold technology to a Korean firm and one that never sold). If Korean firms that never adopted cite the seller’s patents more after the technology transfer relative to the non-seller, this is interpreted as a knowledge spillover.

### Empirical design and matching
- Design: matching-based event study. Each matched pair contains one foreign seller and one observationally similar foreign non-seller (control).
- Exact matching dimensions: country and primary patent field (IPC 3-digit). Each foreign firm is assigned the most frequently occurring 3-digit IPC class in its patent portfolio.
- Distance matching variables: cumulative patent stock, new patents invented in a given year, and new citations received (excluding self-citations) in a given year. Distance matching uses values 1 year before the event and their last 4 years of growth.
- Sample restrictions and trimming:
  - Countries restricted to the US, Japan, UK, and France.
  - Require each IPC 3-digit to have more than 20 observations.
  - Trim the top 98% of outliers in terms of the distance to improve matching quality.
- Matches obtained: 213 matches with 412 unique firms.

### Estimation specifications
- Event-study specification (Equation (4)) uses the dependent variable 1[Citation_Kor_fmt>0], a dummy equal to 1 if any never-adopting Korean firms cite patents from foreign firm f in year t.
- Event dummies D_τ_mt = 1[t − τ = t(m)], where t(m) is the event year of match m.
- Fixed effects: firm-match fixed effects δ_fm and match-year fixed effects δ_mt.
- Standard errors: two-way clustered at foreign firm and match level.
- Average (difference-in-differences) specification (Equation (5)):
  - 1[Citation_Kor_fmt>0] = β_DD · 1[Seller_fmt] × Post_mt + δ_fm + δ_mt + ε_fmt,
  - where Post_mt is a dummy that equals 1 if the event has happened to match m.

### Balance and pretrends
- Balance checks: no statistically significant differences between seller and control groups in observables; observables do not predict treatment status (Appendix Tables B.3 and B.4).
- Pretrend evidence: raw average citations by never-adopting Korean firms for the two groups follow similar trends before events and start to diverge only after events, revealing no pretrends (Appendix Figure B.1).
- Design note: stacked-by-event design (e.g., Cengiz et al., 2019); event-study coefficients identified by comparing firms that switched to the seller group and those that never sold to Korean firms. This addresses potential heterogeneous treatment effect concerns (e.g., Borusyak et al., forthcoming).

### Main results
- Event-study coefficients (Panel A of Figure 2) show no pretrends before events.
- Eleven years after the event, the probability of citation by never-adopting Korean firms to the seller group’s patents increased by around 10%, compared with the control group.
- Table 5 — Knowledge Spillovers from Technology Adoption: Average Effects (estimates of β_DD from Equation (5)):
  - Time horizon −7≤τ≤5 (column (1)):
    - 1[Treated_ft]×1[Post_mt] = 0.02** (standard error (0.01))
    - Firm-match FE: ✓
    - Match-year FE: ✓
    - Adj. R^2: 0.41
    - # Cl. (Foreign firm): 412
    - # Cl. (Match): 213
    - N: 5,404
  - Time horizon −7≤τ≤11 (column (2)):
    - 1[Treated_ft]×1[Post_mt] = 0.03*** (standard error (0.01))
    - Firm-match FE: ✓
    - Match-year FE: ✓
    - Adj. R^2: 0.51
    - # Cl. (Foreign firm): 412
    - # Cl. (Match): 213
    - N: 7,960
  - Notes: Standard errors two-way clustered at foreign firm and match level. *p <0.1, **p <0.05, ***p <0.01.

- Interpretation: estimated coefficients are larger and more precisely estimated with longer horizons, implying that knowledge spillovers occur with lags. Results are consistent with Korean firms building on technology adopted by other Korean firms and imply a positive externality associated with adoption.

### Placebo and robustness checks
- Placebo exercise: replicate the regression using citations received from firms in all other countries except Korea.
  - Panel B of Figure 2 shows no clear differences in citations received by non-Korean firms between seller and control groups, which rules out the alternative explanation that unobserved shocks to foreign firms drove both contracts and broader citation increases.
- Robustness: results are robust to alternative numbers of matches (e.g., 2 and 5 matches) and alternative long-run difference specifications that include additional controls and unit-specific random trends (Appendix Table B.5).
  - Long-run difference specification example: △1[Citation_Kor_fmt>0] = β Seller_fmt + X'_fm γ + δ_m + ε_fmt, comparing 1 year before and 11 years after events; specifications also include transformations of initial citations and log initial patent stock, and stacked two long-differences with firm-match fixed effects to control for unit-specific trends.

### Implication highlighted in this section
- Empirical evidence points to positive knowledge spillovers from foreign technology adoption: adoption by some Korean firms increases subsequent citation incidence to sellers’ patents by never-adopting Korean firms, with effects materializing over multi-year horizons and peaking around an increase of around 10% eleven years after adoption.

*Source: IMF Working Paper — Section 3.2, "Knowledge Spillovers from Adoption" (wpiea2024154-print-pdf).*

### 4.4    Equilibrium

### 4.4    Equilibrium

### Value function
- State variables:
  - Home firm i ∈ I_H: m_i = {m_F_i, m_D_i}.
  - Foreign firm f: m_f = {m_h_f, m_̃h_f}.
  - Note: m_h, m_̃h, and m_f convey the same information and imply each other.
- Home firm value function (Bellman):
  - r_Ht V_it(m_i) − ̇V_it(m_i) (9) = max_{x_it(m_i), a_it(m_i)} (  
    Π_Ht(m_i)  
    − (1−κ_Hrt) α_Hr x_it(m_i)^{γ_r} / γ_r w_Ht  
    − (1−κ_Hat) α_Ha a_it(m_i)^{γ_a} / γ_a w_Ht  
    + x_it(m_i) ∑_n ̃f(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)]  
    + a_it(m_i) ∑_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)]  
    − (1−κ_Hrt) F_it(m_i)  
    + x_{−i}t(m_{−i}) ∑_n ̃f(n; m_{−i}) [V_it(m_F_i, m_D_i−n) − V_it(m_i)]  
    + a_{−i}t(m_{−i}) ∑_n ̃g(n; m_{−i}) [V_it(m_F_i, m_D_i−n) − V_it(m_i)]  
    + [x_ft(m_f) + ̃x_ft(m_f)] ∑_n f(n; min_{i∈I_H}{m_i^f}) [V_it(m_F_i−n, m_D_i) − V_it(m_i)]  
    + a_ft(m_f) ∑_n g(n; min_{i∈I_H}{m_i^f}) [V_it(m_F_i−n, m_D_i) − V_it(m_i)]  
    + 1[m_D_i ≥ 0] × F_ft(m_f)  
    + φ [V_it(0,0) − V_it(m_i)] ).
- Transition probabilities:
  - ̃f(n; m_i) = 1[m_D_i > 0] f(n; m_F_i) + 1[m_D_i ≤ 0] [ n(1−δ) f(n; m_F_i) + δ f(n + m_D_i; m_F_i − m_D_i) ].
  - ̃g(n; m_i) = 1[m_D_i > 0] g(n; m_F_i) + 1[m_D_i ≤ 0] [ n(1−δ) g(n; m_F_i) + δ g(n + m_D_i; m_F_i − m_D_i) ].
  - First/second terms correspond to leader (1[m_D_i>0]) and follower (1[m_D_i≤0]) cases; second term mixes f(n; m_F_i) and f(n + m_D_i; m_F_i − m_D_i) due to within-country spillovers.
- Interpretation of Bellman terms:
  - Π_Ht(m_i): operating profits.
  - Innovation and adoption labor costs appear net of subsidy rates: (1−κ_Hrt) and (1−κ_Hat).
  - Gains from own innovation and adoption captured by expected future value increases.
  - (1−κ_Hrt) F_it(m_i): endogenous adoption fee net of subsidy.
  - Losses from Home competitor innovation/adoption captured via competitor rates x_{−it} and a_{−it} and reductions in m_D_i by n.
  - Losses from Foreign incumbents/entrants via shifts m_F_i → m_F_i − n.
  - 1[m_D_i ≥ 0] × F_ft(m_f): adoption fee receipt when m_D_i ≥ 0.
  - φ [V_it(0,0) − V_it(m_i)]: exogenous spillover.

### Optimal innovation and adoption rates
- Optimal Home innovation rate x_ijt = x_it(m_i):
  - x_it(m_i) = [ ∑_n ̃f(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] / ( (1−κ_Hrt) α_Hr w_Ht ) ]^{1/γ_r − 1}. (10)
- Optimal Home adoption rate a_ijt = a_it(m_i):
  - a_it(m_i) = [ ( ∑_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] − (1−κ_Hat) F_it(m_i) ) / ( (1−κ_Hat) α_Ha w_Ht ) ]^{1/γ_a − 1}. (11)
- The optimal innovation and adoption rates of Foreign firms are derived in Appendix C.2.

### Adoption fee (Nash bargaining)
- Adoption fee F_ijt = F_it(m_i) solves Nash bargaining between Home adopter and Foreign seller:
  - F_it(m_i) = argmax_{F_it(m_i)} [ ( ∑_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] − (1−κ_Hat) F_it(m_i) )^{ξ} × ( ∑_n ̃g(n; m_i) [V_ft(m_i^f − n, m_{(−i)}^f) − V_ft(m_f)] + F_it(m_i) )^{1−ξ} ].
  - First-order condition yields:
    - F_it(m_i) = [ (1−ξ) ∑_n ̃g(n; m_i) [V_it(m_F_i+n, m_D_i+n) − V_it(m_i)] − ξ ∑_n ̃g(n; m_i) [V_ft(m_i^f − n, m_{(−i)}^f) − V_ft(m_f)] ] / (1 − (1−ξ) κ_Hat). (12)
- Parameters and interpretation:
  - 0 ≤ ξ ≤ 1 is the bargaining power of adopters.
  - Adoption fee internalizes Home adopter’s future gains and Foreign seller’s losses.
  - Adoption fees are higher when Foreign firms lose more and Home firms gain more.
  - Within-country spillovers enter equilibrium prices since they are part of value functions.
  - Adoption fees vary with productivity gaps due to two forces:
    - Advantage of backwardness: larger lag ⇒ larger gains from adoption ⇒ higher fees.
    - Competition effect: narrower gaps ⇒ small improvements can capture large market shares ⇒ Foreign sellers demand larger compensation ⇒ higher fees.
  - Therefore, adoption fees can increase or decrease with gaps depending on which force dominates.
- Subsidy interaction with bargaining:
  - A subsidy increases buyer surplus and can be partially passed to seller via higher adoption fee.
  - Response of adoption fee to subsidy depends on ξ:
    - When adopter bargaining power ξ approaches zero, elasticity reaches maximum and adoption fee increases with subsidy rate by 1 / (1 − κ_Hat).
    - Conversely, when ξ converges to zero, subsidy rate does not affect adoption fee.
  - Conclusion: adoption subsidies are more effective when adopters possess greater bargaining power since this minimally impacts the adoption fee.

### Total surplus and conditions for contracts
- Total surplus (sum of Home and Foreign firms’ net value increases from an adoption contract) must be positive for contract occurrence.
- Factors increasing total surplus:
  - Lower Home wage than Foreign wage ⇒ Home firms produce more output with same technology ⇒ larger total surplus.
  - Higher trade costs ⇒ more market segmentation, lower Foreign profits in Home market ⇒ Foreign firms may prefer to sell technology and collect fees ⇒ contracts help circumvent trade costs ⇒ larger total surplus.
  - Lower elasticity of substitution ⇒ weaker competition ⇒ boosts Foreign firms’ motivation to sell technology.

### Distribution of productivity gaps (law of motion)
- Transition probabilities for improvements:
  - T_it(n; m_i) := ̃f(n; m_i) x_it(m_i) + ̃g(n; m_i) a_it(m_i).
  - T_ft(n; m_f) := f(n; min_{i∈I_H}{m_i^f}) (x_ft(m_f) + ̃x_ft(m_f)) + g(n; min_{i∈I_H}{m_i^f}) a_ft(m_f).
- Let μ_t = μ_t(m_h) denote sector shares with gaps positioned at m_h.
  - m_h represents states since m_h, m_̃h, and m_f imply each other.
- Law of motion for μ_t(m_h):
  - ̇μ_t(m_h) = ∑_{n=1}^{m_F^h + ̄m} T_ht(n; m_F^h − n, m_D^h − n) μ_t(m_F^h − n, m_D^h − n)  
    + ∑_{n=1}^{m_D^{̃h} + ̄m} T_{̃h}t(n; m_F^{̃h} − n, m_D^{̃h} + n) μ_t(m_F^{̃h}, m_D^{̃h} + n)  
    + ∑_{n=1}^{m_h^f + ̄m} T_ft(n; m_h^f − n, m_{̃h}^f − n) μ_t(m_F^h + n, m_D^h)  
    + φ 1[m_h = 0]  
    − [ x_ht(m_h) + a_ht(m_h) + x_{̃h}t(m_{̃h}) + a_{̃h}t(m_{̃h}) + x_ft(m_f) + ̃x_ft(m_f) + φ ] μ_t(m_h).
  - First three lines: inflows due to innovation/adoption by firm h, firm ̃h, and firm f respectively.
  - Fourth line: exogenous cross-country spillover sets all firms to same productivity level.
  - Last line: outflows due to firms’ innovation/adoption and spillovers.
- Balanced growth path: ̇μ_t(m_h) = 0 for all m_h.

### Market clearing, government budget, and trade balance
- Asset markets clear each period: A_Ct = ∫_0^1 ∑_{i∈I_C} C V_ijt dj (sum of values of all firms in country C).
- Goods market clearing: ∑_{i∈I_C} p_ijt y_ijt + p^*_fjt y^*_fjt = P_Ct Y_Ct = P_Ct C_Ct, ∀ j ∈ [0,1].
- Labor market clearing:
  - L_Ct = ∫_0^1 ∑_{i∈I_C} [ l_ijt + α_Ca a_ijt^{γ_a} + α_Cr x_ijt^{γ_r} ] dj.
  - Right-hand side: sum of labor demand for production, innovation, and adoption.
- Government budget (balanced each period):
  - T_Ct = (1 + θ) ∫_0^1 ∑_{i∈I_C} [ κ_cat a_ijt F_ijt + κ_Cat α_Ca a_ijt^{γ_a} w_Ct + κ_crt α_Cr x_ijt^{γ_r} w_ct ] dj  
    − t_Ct / (1 + t_Ct) ∫_0^1 ∑_{i∈I_{−C}} p^*_ijt y^*_ijt dj.
  - θ is reduced-form deadweight cost of taxation; θ > 0 implies inefficiency of technology policies due to deadweight cost.
  - Second term: revenues from import tariffs.
- Trade balance (every period):
  - ∫_0^1 [ ∑_{i∈I_{−C}} p^*_ijt y^*_{ijt} + ∑_{i∈I_C} a_ijt F_ijt ] dj = ∫_0^1 [ ∑_{i∈I_C} p^*_{ijt} y^*_{ijt} + ∑_{i∈I_{−C}} a_{ijt} F_{ijt} ] dj.
  - Condition includes trade in goods and technologies.

### Equilibrium definitions
- Definition 4.1 (Markov perfect equilibrium): consists of { r_Ct, w_Ct, p_ijt, p^*_ijt, x_ijt, a_ijt, F_ijt, T_Ct, C_Ct, Y_Ct, A_Ct, μ_mt }_{t∈[0,∞), j∈[0,1], c∈{H,F}, i∈{h, ̃h, f, ̃f}, m∈{−̄m,...,̄m}^2} such that:
  - (Static equilibrium) Representative household maximizes discounted utility subject to budget; firms maximize profits; goods, labor, and asset markets clear; trade and government budgets balance in each country and period.
  - (Dynamic equilibrium) x_ijt and a_ijt solve the firm’s dynamic problem (Equations (10) and (11)); F_ijt solves Nash bargaining (Equation (12)); and {μ_{m0}}, {μ_mt}_{t∈[0,∞)} are consistent with x_ijt and a_ijt (Equation (13)).
- Definition 4.2 (Balanced growth path): the equilibrium in Definition 4.1 in which { w_Ct, V_ijt, F_ijt, T_Ct, C_Ct, Y_Ct, A_Ct } grow at constant rate g, and r_Ct and μ_t are constant over time.

*Italicized source: wpiea2024154-print-pdf - 4.4    Equilibrium*

### 5.2    Calibration

### 5.2 Calibration

### Calibration approach
- Calibrate 23 parameters in three steps:
  - 6 parameters taken directly from the data.
  - 7 parameters externally calibrated.
  - 10 parameters jointly estimated by simulated method of moments (SMM).
- Solution strategy:
  - Given a parameter guess, solve for transitions with initial conditions until convergence to the balanced growth path.
  - Compute model moments along transitions and update parameters to minimize distance between model moments and data moments.
  - Incorporate time-varying policies (adoption and innovation subsidies and import tariffs) and assume agents’ perfect foresight.
  - Home and Foreign correspond to Korea and Japan, respectively. Initial year set to 1973.
- Computational algorithm referenced in Appendix D.2.

### Parameters that directly match the data
- Parameters taken directly from data: {L_H, L_F, κ_Hat, κ_Hrt, t_Ht, t_Ft}.
- Specific data choices:
  - L_H = 1 (Korea’s labor endowment normalization).
  - L_F = 2 (to match Japan’s relative population size).
  - κ_Hat and κ_Hrt: subsidy rates calculated from tax credit data (Figure 1).
  - Import tariffs t_Ht and t_Ft: import-weighted average tariff across sectors.
    - Korea product-level import tariffs for 1973–1988 from Korea Customs Service (CCCN 4-digit aggregated by import values).
    - Japan 1973–1988 average import tariff from Yi (2003).
    - From 1988 onward, World Development Indicators used for both countries.
    - Between 1973 and 2023, Korea’s tariffs decreased from 27% to 5%, while Japan’s tariff decreased from 8% to 3%. Korea’s tariffs were much higher in the 1970s and gradually converged toward Japan’s level.

### External calibration
- Parameters externally calibrated: {ρ, ψ_H, ψ_F, γ_r, γ_a, σ, θ}.
- Calibrated values and rationale:
  - ρ = 0.03 (discount rate).
  - ψ_H = 0.25 and ψ_F = 0.5 (symmetry: Home has two operating firms, Foreign has one).
  - γ_r = 2 (curvature for innovation R&D costs; matches elasticity of successful innovation wrt R&D).
  - γ_a = 2 (adoption labor cost curvature set equal to γ_r).
  - σ = 6 (elasticity of substitution; average value from Broda and Weinstein (2006) in the 1980s).
  - θ = 1 (deadweight cost of taxation; implies government needs to collect 2 units of tax to finance 1 unit of expenditure).

### Simulated Method of Moments (SMM)
- Parameters jointly estimated via SMM: Θ = {λ, α_r, α_a, α_F, η_a, τ, ξ, δ, d, φ}.
- Estimation minimizes the objective:
  - min_Θ sum_{i=1}^{10} [ (M^D_i − M_i(Θ)) / (0.5(M^D_i + M_i(Θ))) ]^2
- Targeted data moments and identification links:
  - Adoption fee / yearly sales:
    - Data moment: average ratio = 22.4% (0.224).
    - Identifies ξ (bargaining power of adopters); higher ξ ⇒ lower adoption fees.
  - Productivity gain from adoption over the initial gap:
    - Match coefficient of interaction between productivity gap and adoption dummy (Table 3, column 3).
    - Identifies η_a (magnitude of advantages of backwardness due to adoption).
  - Patent citation increase after adoption:
    - Target: average increase in probability of being cited = 0.02 within 5 years from first technology adoption (column 1 of Table 5).
    - Identifies δ (strength of knowledge spillovers); mapping uses microfoundation where increased citations = x̄ × δ, calibrate δ to match x̄ × δ = 0.02 (see Appendix C.4).
  - Manufacturing shares of exports to value-added:
    - Data moment (1970–1993): 0.392.
    - Identifies iceberg trade cost τ (higher shares ⇒ lower τ).
  - R&D and adoption fee expenditures as share of manufacturing value-added:
    - Targets for 1985 and 1990 using manufacturing R&D expenses from The Ministry of Science and Technology (1990).
    - Shares: innovation R&D = 2.97% (0.0297) and adoption fees = 1.48% (0.0148).
    - Identify α_r (innovation cost scale) and α_a (adoption cost scale).
  - Long-run GDP per capita growth rate:
    - Target: average since 2010 for Japan and Korea = 2.1% (0.021).
    - Identifies λ (unit step size of adoption and innovation).
  - Real GDP per capita ratio Korea/Japan in 1973 and 2020:
    - 1973 ratio = 0.21 (0.210) identifies d (average initial productivity gap).
    - 2020 ratio = 0.981 (0.981) informs φ (exogenous spillover); higher φ ⇒ faster convergence.
  - Productivity ratio in the long run:
    - Target long-run productivity ratio between Home leader (Korea) and incumbent (Japan) = 1.
    - Identifies α_F (foreign R&D cost parameter), higher α_F ⇒ higher Japanese costs ⇒ lower long-run productivity.

### Estimation results (summary)
- Reported estimates (Table 6):
  - Jointly calibrated / SMM results:
    - λ = 1.056
    - η_a = 1.596
    - α_a = 1.334
    - α_r = 1.569
    - τ = 1.568
    - ξ = 0.556
  - Jointly estimated through SMM:
    - δ = 0.252
    - d = -17.551
    - α_F = 6.168
    - φ = 0.037
- Interpretation and highlights:
  - η_a = 1.596 (magnitude of advantages of backwardness); within ranges from Olmstead-Rumsey (2022) and Akcigit et al. (2022).
  - λ = 1.056 ⇒ one step improvement increases productivity by 5.6%.
  - α_a < α_r ⇒ lower labor requirements for adoption than for innovation.
  - τ = 1.568 (iceberg trade cost parameter).
  - ξ = 0.556 ⇒ adopters have slightly larger bargaining power with sellers.
  - δ = 0.252 ⇒ probability of receiving knowledge spillovers.
  - d = -17.551 ⇒ initial productivity gap implies Japanese firms were initially 2.6 times more productive than Korean firms.
  - α_F = 6.168 ⇒ Japan’s relative innovation and adoption costs.
  - φ = 0.037 ⇒ exogenous spillover probability, in the lower range of literature estimates.

### Fit to targeted moments
- Table 7 targeted moments (Model vs Data):
  - Adoption fee / annual sale: Model 0.224, Data 0.224
  - β_a: productivity growth and initial gap (adoption): Model -0.065, Data -0.065
  - β_s: ∆Patent citation after adoption: Model 0.019, Data 0.019
  - Long-run growth rate: Model 0.021, Data 0.021
  - Adoption / value-added in manufacturing: Model 0.015, Data 0.015
  - R&D / value-added in manufacturing: Model 0.030, Data 0.030
  - Export / value-added in manufacturing: Model 0.392, Data 0.392
  - GDP ratio in 1973: Model 0.210, Data 0.210
  - GDP ratio in 2020: Model 0.981, Data 0.980
  - Long-run productivity ratio: Model 1.000, Data 1.006
- Conclusion: Model closely matches micro and macro moments and replicates Korea’s catching up with Japan during the sample period.

### Validation (untargeted moments)
- Two untargeted moments presented:
  - Declining share of total adoption fees relative to sum of adoption fees and innovation R&D expenditures:
    - Model matches declining trend in data (Panel A of Figure 5).
    - Trend not solely policy-driven; model generates decline even without subsidies (Appendix Figure D.2).
    - Mechanism: firms prioritize innovation over adoption as productivity gaps narrow.
  - Relationship between adoption fees and productivity gaps:
    - Log adoption fees plotted against log ratio of sales per employee between Home and Foreign firms (Panel B of Figure 5).
    - Adoption fees become higher as Korean firms narrow productivity gaps, consistent with empirical fact in Table 4.
    - Highlights importance of competition effects in determining adoption fees.

### 6. Quantitative Results (selected highlights up to policy evaluation)

### Contribution of adoption and innovation to TFP growth over time
- Aggregate TFP defined as Z_Ht = Y_Ht / L^p_Ht; first-order approximation decomposes dlog Z_Ht into contributions from innovation, adoption, and exogenous spillover (equation (14)).
- Figure 6: Share of aggregate TFP growth over time:
  - In 1973: adoption accounted for 37% of TFP growth; innovation accounted for 8%.
  - By 2023: adoption dropped to 7%; innovation rose to 74%.
- Interpretation: Adoption from abroad dominates early-stage growth; innovation becomes dominant as country develops.

### Policy evaluation — actual policy vs counterfactuals
- Policy scenarios compared (budget-to-GDP share held constant across scenarios):
  - Actual Korean stage-dependent policy (1973 onward): started with adoption subsidy, then switched to innovation subsidy (Panel A of Figure 1).
  - No subsidies (undistorted case).
  - All budget to adoption subsidy only.
  - All budget to innovation subsidy only.
- Model-calculated subsidy statistics:
  - Total subsidy expenditure averages 1.75% of GDP.
  - Adoption subsidy share (adoption subsidy expenditure / (adoption + innovation subsidy expenditures)):
    - 1973 adoption share = 1 (only adoption subsidy present).
    - Adoption share gradually converged to zero by 2011.
- Consumption results (Panel B of Figure 7, relative to no-subsidy case):
  - Subsidizing only adoption: higher growth rate in early stage; relative consumption larger than no-subsidy after several years; growth rate of relative consumption decreases over time (limited long-run effect).
  - Subsidizing only innovation: not higher growth initially vs adoption-only; yields higher growth rate at later stages.
  - Actual policy: consumption similar to adoption-only in early stages and yields higher growth rates in later stages.
- Welfare (consumption-equivalent change Ψ over infinite horizon):
  - Actual policy increases consumption-equivalent welfare by 4.3%.
  - Adoption-only: 2.7%.
  - Innovation-only: 3.5%.
  - Conclusion: Actual stage-dependent policy implemented in Korea was quantitatively better than the time-invariant alternatives.

### Foreign policy counterfactual — Japan prohibits technology transfers to Korea
- Scenario: Japanese government prevents firms from exporting technology to Korea; Korean government reallocates budget entirely to innovation subsidies (budget-to-GDP constant).
- Results (Figure 8):
  - Short run: Japan’s consumption higher relative to baseline; Korea’s consumption lower.
  - Long run: Japan’s consumption becomes lower as long-run growth rate decreases due to weaker competition and reduced innovation incentives.
  - Welfare effects:
    - Korea’s welfare decreases by 6.74% (−6.74%).
    - Japan’s welfare increases by 4.57% (4.57%).
- Mechanism: Preventing transfers weakens competition and reduces innovation incentives in Japan; Korean welfare loss substantial.

### Robustness
- Robustness checks on discount rates, elasticity of substitution, and deadweight cost of taxation (Appendix Figures D.3–D.5) show qualitatively similar results: actual policy yields greater welfare improvements than the time-invariant policies.

*Source: IMF working paper chapter on calibration and quantitative results (sections 5.2–6.2) from the provided PDF content.*

### 6.3    Optimal Policy

### 6.3    Optimal Policy

### Setup
- Governments choose the adoption subsidy share to maximize welfare while maintaining the government budget over GDP equal to the baseline case.
- To mimic practical constraints and reduce computational burden, the government is allowed to change the policy every 10 years for 50 years.

### Optimal subsidy path and welfare outcomes
- The optimal subsidy share decreases rapidly from 45% to 17% in 2013.
- The optimal subsidy path declines later than the actual policy change observed in the data.
- Welfare impact:
  - The optimal subsidy increases consumption-equivalent welfare by 5.3%.
  - The welfare gain from the optimal time-varying policy is larger than those from the actual policy and other counterfactual time-invariant policies.

### Quadratic specification
- Appendix Figure D.6 reports an optimal policy where the subsidy share is a quadratic function of calendar years.
- The optimal quadratic policy reduces the share of the adoption subsidy at a comparable pace to the piecewise-constant (every-10-years) policy.
- Welfare increases under the quadratic policy are close to those of the linear (piecewise-constant) policy.

### Interaction with trade policy
- Mechanism: Import tariffs affect Foreign firms’ incentives to sell technologies; in the model, import tariffs lower adoption fees by weakening competition between Home and Foreign firms.
- Extreme case: If the tariff is infinitely high, foreign firms do not incur any profit losses from selling technology, leading to reduced equilibrium adoption fees.
- Implications:
  - A protective trade policy (higher tariffs) can make adoption more affordable, increasing adoption rates toward the socially optimal level, which reduces the effectiveness of adoption subsidies and shifts optimal budget allocation toward innovation subsidies.
  - A liberal trade policy (lower tariffs) enhances the effectiveness of adoption subsidies, raising the value of adoption subsidies in the optimal mix.

### Counterfactual tariff scenarios and optimal policy
- Two counterfactual scenarios were computed with import tariffs initially set at 28% and 5%, respectively, and remaining constant over time.
- Findings (Figure 10):
  - Under higher tariffs (28%), the optimal policy allocates a smaller portion of its budget to adoption subsidies relative to the baseline.
  - Under lower tariffs (5%), the optimal policy allocates a larger portion of its budget to adoption subsidies relative to the baseline.

### Key takeaways for policy design
- Time-varying, state-dependent subsidy policies can generate larger welfare gains than static policies; allowing policy adjustments every 10 years over a 50-year horizon produces meaningful welfare improvements.
- Trade policy materially alters the optimal composition between adoption subsidies and innovation subsidies:
  - Higher import tariffs reduce the marginal effectiveness of adoption subsidies and tilt optimal policy toward innovation support.
  - Lower import tariffs increase the effectiveness of adoption subsidies, making them more central in optimal policy.
- Alternative functional forms for time variation (quadratic) deliver similar policy dynamics and welfare outcomes to piecewise-constant adjustments.

*Source: wpiea2024154-print-pdf - 6.3 Optimal Policy*

### References

### wpiea2024154-print-pdf - References

### Data: Technology adoption and firm balance sheets
- Technology transfer universe: contracts between Korean and foreign firms during 1962–1993 are stored in national archives; sample period reported in Table A.1 is 1970–1993 with total number of observations 8,346.
- Contract classification (Korea Industrial Technology Association, 1995):
  - 53% of contracts involve only know-how transfer.
  - 42% involve both know-how and licensing.
  - 4% involve only licensing.
- Top source countries and sector shares (Table A.1, sample 1970–1993):
  - Country shares: Japan 49.88, United States 26.29, Germany (West) 5.56, France 4.07, United Kingdom 3.69, Italy 1.75, Switzerland 1.60, Netherlands 1.36, Canada 0.94, Sweden 0.70, Others 4.16.
  - Sector shares: Machinery 26.66, Electronics 24.89, Chemical manufacturing 16.09, Chemical fiber 4.97, Metal 4.93, Food 3.08, Shipbuilding 2.70, Non-metallic products 2.66, Pharmaceutical 2.45, Construction 1.81, Others 9.76.
- Korean firm balance-sheet data:
  - Period 1970–1982: Annual Reports of Korean Companies (Korea Productivity Center); merged with KIS-VALUE (from 1980).
  - Variables used: firm-level sales, fixed assets, total assets, number of employees, industry.
  - All nominal values converted to 2015 US dollar values.
  - Industry classification based on ISIC Rev 3.1 (Table A.2 provides mapping).
- Foreign firm balance-sheet data:
  - Source: Compustat; PPEGT used to measure foreign firms’ capital.
  - Samples with missing employment, fixed assets, or sales dropped.
  - Summary statistics (Table A.3, averages in Compustat between 1970 and 1993):
    - Emp.: Ever-Sold 18,913; Never-Sold 3,973; All 4,530.
    - Fixed Asset: Ever-Sold 2,634; Never-Sold 796; All 885.
    - Sales: Ever-Sold 4,088; Never-Sold 1,040; All 1,180.
    - Sales per Emp.: Ever-Sold 0.40; Never-Sold 0.44; All 0.44.
    - # of Unique Firms: Ever-Sold 769; Never-Sold 21,818; All 22,587.
    - # of Obs.: Ever-Sold 7,997; Never-Sold 184,208; All 192,205.
  - Notes: Ever-sold refers to firms that engaged in at least one adoption contract as technology seller; all nominal values converted to 2015 US million dollars.
- Merging procedure:
  - Match technology adoption dataset to firm balance sheets by firm names.
  - Merge with Korean patent office using Business ID and firm names (KIS-VALUE provides Business IDs).
  - For foreign firms, merge names in technology adoption data to USPTO; then match foreign firms to Compustat using match from Bena et al. (2017).

### Motivating facts and empirical estimation
- Production function estimation:
  - Method: control function approach (Olley and Pakes, 1996; Ackerberg et al., 2015).
  - Value-added measured as log(Value Added) with industry-year estimation; investment measured by CAPX, capital by PPEGT deflated by NIPA price index for non-residential private fixed investment.
  - Production function estimated within 2-digit ISIC Rev 3.1 with year fixed effects.
  - Revenue-based TFP defined as:
    - TFP_rr_ijt = log(Value Added_ijt) − α_k^j log k_ijt − α_L^j log l_ijt
  - For Korean firms lacking value-added, industry-year value-added share multiplied by firm-level revenue (IO tables used to compute industry-year value-added shares).
- DHS growth regressions (Table B.1): productivity gap and productivity growth after adoption and innovation
  - Dependent variables: DHS growth rates of sales per employee and TFP_rr.
  - Key coefficients (selected, see Table B.1 for full specification details):
    - logGap_it coefficients across columns (1) to (8): -0.186***, -0.203***, -0.401***, -0.407***, -0.230***, -0.268***, -0.456***, -0.462*** (standard errors in table).
    - logGap_it × 1[Adopt_it] coefficients: -0.064**, -0.064**, -0.046**, -0.065***, -0.050*, -0.063**, -0.044**, -0.058***.
    - 1[Adopt_it] coefficients: 0.128***, 0.133***, 0.168***, -0.089**, 0.122***, 0.116***, 0.148***, -0.100***.
  - Sample size and clustering: # Cl. (Korean firm) 2,217; N varies (e.g., 12,824 etc.). Adjusted R^2 values reported (e.g., 0.17, 0.19, 0.30, 0.30).
  - Notes: 1[Adopt_it] and 1[Innovate_it] indicate first-time technology transfer or first patent filing by a Korean firm; specifications include various fixed effects and controls as described in table notes.
- Adoption fee regressions (Table B.2): adoption fee and productivity gap using different adoption fee measures
  - Two dependent variables: logged royalty fee (Panel A) and total fee (Panel B).
  - Royalties estimated as royalty rate × contract length × (1/5) Σ_{s=1}^{5} sales_{t+s} (contracts’ average duration 5 years).
  - Panel A (log Royalty Fee), key logGap_it coefficients across columns:
    - 0.274***, 0.274***, 0.840***, 0.796***, 0.432***, 0.390***, 1.110***, 1.060***.
  - Panel B (log Total Fee), key logGap_it coefficients across columns:
    - 0.259***, 0.261***, 0.782***, 0.746***, 0.418***, 0.372***, 1.024***, 0.986***.
  - Fixed effects and clustering: two-way clustered at domestic and foreign firm levels; # Cl. (Korean firm) and # Cl. (Foreign firm) reported per column; N reported per column (e.g., N 1,332; 1,329; 1,256; 1,188).
  - Adj. R^2 values reported (e.g., 0.30, 0.52, 0.59, 0.61, 0.33, 0.53, 0.63, 0.64).
- Knowledge spillovers and citation evidence (Tables B.3–B.5, Figure B.1):
  - Covariate balance (Table B.3): N 213 for technology seller and matched control; reported means and t-stat p-values for citation-based covariates (e.g., 1[# cite_fmt >0] means 0.78 vs 0.82, p-value 0.33).
  - Balance test (Table B.4): p-val (F) reported across columns (e.g., 0.33, 0.18, 0.46, 0.57, 0.48, 0.18, 0.28, 0.24, 0.24, 0.82); N 426 across columns.
  - Raw average of patent citations (Figure B.1): plots average number of citations from Korean never-adopters to foreign firms that sold technology and to those that did not; vertical lines are 95% confidence intervals; N = 8,896.
  - Knowledge spillovers regressions (Table B.5):
    - Dependent variable: 1[Citation_Kor_fmt >0].
    - Coefficients for 1[Seller_fmt]×Post_mt across alternative matches and specifications:
      - # match = 2: 0.02*.
      - # match = 5: 0.04***.
      - # match = 5 with alternative FE: 0.03***.
      - Long-difference specification: 0.06***, 0.08***, 0.07**, 0.15*** across columns (1)–(7).
    - Adj. R^2 values reported (e.g., 0.40, 0.47, 0.36, 0.42, 0.40, 0.42, 0.16).
    - # Cl. (Foreign firm) and # Cl. (Match) and N reported for each specification.

### Model: structure, optimal policy, and citations
- Value functions (C.1):
  - Foreign incumbent value function V_ft(m_f) described with components:
    - profit Π_ft(m_f),
    - innovation R&D cost term −(1−κ_Frt) α_Fr x_ft(m_f)^{γ_r}/γ_r w_Ft,
    - adoption labor cost −(1−κ_Fat) α_Fa a_ft(m_f)^{γ_a}/γ_a w_Ft,
    - gains from own innovation and adoption: x_ft and a_ft terms multiplied by expected value changes,
    - losses from innovation/adoption by Home firms,
    - adoption fee (1−κ_Fat) F_Ft(m_f),
    - replacement by entrant − ̃x_ft(m_f) V_ft(m_f),
    - exogenous spillover φ(V_ft(0,0) − V_ft(m_f)).
  - Foreign entrant value function ̃V_ft(m_f) specified with innovation cost and potential gains from entering.
- Optimal policy functions (C.2):
  - Foreign incumbent optimal innovation rate:
    - x_ft(m_f) = [ Σ_n f(n;m_i^f) (V_ft(m_hf+n, m̃_hf+n) − V_ft(m_f)) / ((1−κ_Frt) α_Fr w_Ft) ]^{1/(γ_r−1)}
  - Foreign incumbent optimal adoption rate:
    - a_ft(m_f) = [ Σ_n g(n;m_i^f) (V_ft(m_hf+n, m̃_hf+n) − V_ft(m_f) − (1−κ_Fat) F_ft(m_f)) / ((1−κ_Fat) α_Fa w_Ft) ]^{1/(γ_a−1)}
  - Foreign entrant optimal innovation rate:
    - ̃x_ft(m_f) = [ Σ_n f(n;m_i^f) V_ft(m_hf+n, m̃_hf+n) / ((1−κ_Frt) ̃α_Fr w_Ft) ]^{1/(γ_r−1)}
- Adoption fee (C.3):
  - Adoption fee F_ft(m_f) determined as the maximizer of foreign seller and buyer surplus sharing:
    - First-order condition yields:
      - F_ft(m_f) = [ (1−ξ) (Σ_n g(n;m_i^f) V_ft(m_if+n,m_−i^f+n) − V_ft(m_f)) − ξ (Σ_n g(n;m_i^f) V_it(m_Fi−n,m_Di) − V_it(m_i)) ] / (1−ξ κ_Fat)
- Simple model of patent citation (C.4):
  - Model extension: firms must cite pertinent patents when innovating on technology (consistent with patent laws).
  - If sector j firm h_j adopted from sector j foreign firm f_j, subsequent innovations by h_j that build on that technology must cite f_j.
  - Knowledge spillovers to other domestic firm ̃h_j cause citations to f_j when ̃h_j innovates related technology.
  - If firm f_j exported technology to h_j but foreign firm f_k in sector k did not, the probability of receiving patent citations from non-adopter ̃h_j to f_j increases by ̄x·δ, where ̄x is average innovation rate and δ is probability of knowledge spillover; probability to f_k does not change. The quantity ̄x·δ is matched to average increase in citation probability.

### Quantification: balanced growth path and transition strategy
- Balanced growth path (D.1):
  - On the balanced growth path, wage and consumption in each country grow at the same rate g; distributions of productivity gap μ_t(m_h), innovation rate x_it(m_i), adoption rate a_it(m_i), and relative price P_Ft remain constant. Price index normalized with P_Ht = 1.
  - Normalized variables defined: ̃V_it = V_it / Y_Ht, ̃w_Ht = w_Ht / Y_Ht, ̃F_ijt = F_ijt / Y_Ht.
  - Aggregate output share: S_Ht = Y_Ht / (Y_Ht + P_Ft Y_Ft).
  - Profit normalization and normalized Bellman equation provided (Equation (16)) with full listing of terms for maximization over x_it and a_it. From household Euler equation, r_Ht − g_t = ρ in any t.
  - Solution approach:
    - Two-layer iteration: guess {̃w_H, ̃w_F, S_H}; guess value function for each m and iterate using Equation (16) until convergence; after convergence, check labor market clearing and trade balance, update the three variables until labor market clears and trade is balanced.
- Transitional dynamics (D.2):
  - The appendix indicates solution steps for transitional dynamics are provided (full steps continue beyond provided excerpt).

*Italic: Source — wpiea2024154-print-pdf - References*

### 1.  We discretize the continuous time model where each period is divided as∆t= 2

### 1.  We discretize the continuous time model where each period is divided as∆t= 2
−5
.

### Numerical solution algorithm and simulation
- Discretization: each period is divided as∆t= 2
−5
.
- Balanced growth path: assume convergence to the balanced growth path until period T.
- Initial guess: X0t = { ̃wHt, ̃wFt, S Ht }t=T t=0.
- Backward solution: given the guess X0t, solve the value function, innovation, and adoption rate backward from period T to period 0.
- Forward distribution: given innovation and adoption decisions, solve the distribution of productivity gap {μt(mh)}t=T t=0 forward from period 0 to period T. μHm0 is given as the initial condition.
- Implied variables: solve implied ̃X1t = { ̃wHt, ̃wFt, S Ht }t=T t=0 using {μt(mh)}t=T t=0.
- Distance metric: compute the distance ∥X0t − X1t∥ between the guess and implied value using the Euclidean norm.
- Fixed point iteration with damping:
  - Update rule: Xi+1t = (1−∆)Xit + ∆ ̃X i+1 t, where 0<∆<1 is a dampening parameter.
  - Convergence criterion: stop when ∥X0t − X1t∥ < ε.
- Simulation: once equilibrium X is found, simulate 1,000,000 firms using the distribution μHmt, and calculate YHt.

### TFP decomposition (appendix D.3)
- Aggregate definitions:
  - LpHt = R1 0 Πi∈IH lijt.
  - ZHt = YHt / LpHt = YHt / R1 0 Πi∈IH yijt + τy∗ijt zijt dj = ( Z1 0 Πi∈IH yijt + τy∗ijt YHt 1 zijt dj )−1.
- First-order approximation:
  - dlogZHt ≈ Z1 0 Πi∈IH ∂logZHt / ∂logzijt dlogzijt.
- Influence weight ωijt:
  - ∂logZHt / ∂logzijt = zijt ZHt ∂ZHt / ∂zijt = zijt ZHt ( Z1 0 Πi∈IH yijt + τy∗ijt YHt 1 zijt dj )−2 yijt + τy∗ijt YHt 1 z2ijt = yijt + τy∗ijt YHt 1 zijt [ R1 0 Πi∈IH yijt + τy∗ijt YHt 1 zijt dj ] = ωijt.
  - Numerator expressed as:
    - yijt + τy∗ijt YHt 1 zijt = pijt yijt PHt YHt pijt zijt wHt wHt + p∗ijt y∗ijt PFt YFt PFt YFt PHt YHt p∗ijt zijt τwHt wHt = PHt YHt + PFt YFt PHt YHt S Ht sijt Mijt wHt + (1−SHt) s∗ijt M∗ijt wHt!, where the first equality comes from the normalization of PHt = 1.
  - Because markups and market shares are functions of productivity gap, ωijt is a function of productivity gap mi:
    - ωijt = ωit(mi) = [ SHt s t(mi) M t(mi) + (1−SHt) s∗t(mi) M∗t(mi) ] [ Pmh μt(mh) / P i∈IH SHt s t(mi) M t(mi) + (1−SHt) s∗t(mi) M∗t(mi) ].
- Approximation for dlogZHt:
  - dlogZHt ≈ Z1 0 Πi∈IH ωijt dlogzijt = Σm h Z m hjt=m h [ ωht(mh) dlogzhjt + ω ̃ht(m ̃h) dlogz ̃hjt ] dj.
- Expression for Rm hjt=m dlogzijt (step change in log productivity by productivity gap):
  - R m hjt=m dlogzijt(m i) dj = μt(mh) × [ xit(mi) Σn ̃f(n;mi) n + ait(mi) Σn ̃g(n;mi) n + φ0 max{−mF i, −mD i, 0} ] logλ + o(∆t),
    - first term: step size increase from innovation,
    - second: from adoption,
    - third: from exogenous spillover.
  - o(∆t) is the second order term; lim ∆t→0 o(∆t)/t = 0 holds in continuous time.
- Final decomposition (TFP contributions from innovation, adoption, spillover):
  - dlogZHt ≈ Σm h μt(mh) Σi∈IH ωit(mi) × [ xit(mi) Σn ̃f(n;mi) n |{z} Innovation + ait(mi) Σn ̃g(n;mi) n |{z} Adoption + φ0 max{−mF i, −mD i, 0} |{z} Exogenous Spillover ] logλ.

### Additional figures (appendix D.4) — key figure descriptions and notes
- Figure D.1: Import Tariff
  - Displays import-weighted tariff rate of Korea and Japan.
  - For 1973–1988: Korea’s tariff from Korea Customs Service; Japan’s from average import tariff of G7 countries calculated by Yi (2003).
  - Post-1988: tariff rates from World Development Indicators.
- Figure D.2: Adoption Expenditure Share in the Model and the Data
  - Plots adoption fee expenditure / (adoption fee + innovation cost) in model and data.
  - Solid red line: baseline with actual subsidies.
  - Dotted green line: counterfactual with no subsidies.
  - Dashed blue line: data.
- Figure D.3: Welfare Increase from Undistorted Case over Discount Rate
  - Plots welfare increase compared to undistorted case in infinite horizon over discount rates ρ.
  - Baseline ρ = 0.03.
  - Welfare increase calculated in consumption-equivalent unit (equation (15)).
  - Blue triangle: subsidizes only adoption.
  - Green square: subsidizes only innovation.
  - Solid red line: actual policy in Figure 1.
  - In all counterfactuals, the share of government spending relative to GDP remained constant.
- Figure D.4: Counterfactual Analysis with Elasticity of Substitution
  - Panels A and B: σ = 3.
    - Panels A and C plot real consumption in three scenarios divided by consumption in no-subsidies case. Dotted blue: adoption only; dashed green: innovation only; solid red: actual policy.
    - Panels B and D plot welfare increase compared to no-subsidies case in infinite horizon (consumption-equivalent, equation (15)).
  - Panels C and D: σ = 9.
- Figure D.5: Counterfactual Analysis with Deadweight Cost of Taxation Parameter
  - Panels A and B: θ = 0.
  - Panels C and D: θ = 0.5.
  - Panels A and C plot consumption relative to no-subsidies case; Panels B and D plot welfare increase (consumption-equivalent unit, equation (15)).
  - In all counterfactuals, share of government spending relative to GDP remained constant.
- Figure D.6: Optimal Policy and Welfare Increase
  - Panel A plots adoption subsidy share for actual policy, optimal-linear, optimal-quadratic.
    - For linear policy: government allowed to change adoption subsidy share every 10 years, keeping government spending/GDP equal to actual policy.
    - For quadratic policy: subsidy share κHat = α + β t + γ t2 and government chooses {α, β, γ} to maximize welfare.
  - Panel B plots consumption-equivalent welfare increase from undistorted case over different policies.
  - Reported welfare increases (panel annotations):
    - Adoption subsidy / Innovation subsidy / Actual policy: 2.66%, 3.49%, 4.33%, 5.31%, 5.42% (as shown in figure annotations).
- Figure annotations and numeric callouts in the figures:
  - Simulation size: 1,000,000 firms (from numerical algorithm section).
  - Welfare baseline discount rate: ρ = 0.03.
  - Elasticity scenarios: σ = 3 and σ = 9.
  - Deadweight cost scenarios: θ = 0 and θ = 0.5.

*From Adoption to Innovation: State-Dependent Technology Policy in Developing Countries — Working Paper No. WP/2024/154*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024154-print-pdf.pdf_