## wpiea2021069-print-pdf — Appendix III and related appendices

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### Adjustment of Chinese R&D and first-stage estimation
- Inclusion of China in technological leaders curtails the estimation sample to start in the year 2000 rather than 1995.
- No information is available for the wood and paper nor the rubber and plastic sectors.
- Discrepancy between R&D series suggests Chinese R&D numbers may overstate China’s contribution to the technological frontier and to partner countries’ innovation and productivity growth.
- Preferred adjustment: rescale China’s R&D research input by an estimate of its research output—i.e., rescale by other countries’ “research productivity” to approximate the rate at which money is transformed into ideas.
- Adjusted R&D numbers for China are constructed (see Appendix III in source).

### Knowledge spillovers: magnitudes and patterns
- For all countries the estimated contribution to annual labor productivity growth between 2000 and 2013 from foreign R&D is quantitatively significant; approximately 0.4-0.5 percent.
- The United States and (to a lesser extent) Japan are the biggest sources of knowledge spillovers for China and others.
- For other countries the contribution from China has been sizeable and bigger than the ones from the traditional technological leaders from Europe, even when using conservative estimates of Chinese R&D expenses.
- Based on patent citations, all countries appear to have increasingly benefited from China’s innovation drive, including the United States.
- Figure 7 notes: Chinese R&D numbers are rescaled to match the average patenting productivity using the discounted stock as reference.
- The analysis references the period 2010-13 for the magnitude of spillovers illustrated in Figure 7.

### Embedding channels into GIMF: timing, persistence, and aggregation
- Three channels combined in GIMF:
  - (1) direct impact on trade volumes in high-tech goods,
  - (2) sectoral misallocation (from CFRT),
  - (3) patent and R&D linkages to productivity (knowledge diffusion).
- Sectoral misallocation:
  - CFRT’s disaggregated sectoral changes in labor productivity are aggregated for tradable and nontradable sectors and applied directly in GIMF.
  - The permanent decline in the level of productivity is assumed to happen relatively quickly over 3 years.
- Knowledge diffusion (R&D/patent linkages):
  - Lower knowledge diffusion estimates are included as an additional slowdown in GIMF’s labor productivity growth for tradables.
  - Spillovers between relevant hubs (and all countries in the preferential attachment scenarios) are assumed to be zero, reducing productivity growth by the amount illustrated in Figure 7 over the 2010-13 period, for eight years.
  - Afterwards, labor productivity growth returns to its previous rate over 3 years.
  - Cumulative losses from growth over the 11-year horizon are permanent on the level of labor productivity and hence real GDP.

### Overview of scenario results
- Six technological decoupling scenarios are evaluated (outlined in Table 1 in source).
- China usually loses the most in each scenario, reflecting large effects through trade and sectoral-misallocation channels.
- In scenarios without preferential attachment, some countries can gain as partial substitutes for a hub (example: India can help replace China for the United States or Germany in Scenarios 1, 3 and 5).
- Scenarios 3 and 4 lead to the largest losses for China; these scenarios break up two pairs (China and Japan; China and Korea) that are present in other scenarios.
- Scenario 6 causes regions outside Asia to lose the most, as regions would no longer trade with two major hubs instead of just one.

### Contributions of the three channels (China–United States example)
- Layer decomposition:
  - First layer (dotted lines): collapse in high-tech goods trade — strongest impacts on export and import volumes; leads to appreciation of real effective exchange rate (REER); limited adjustment in current account.
  - Second layer (dashed lines): adds costs from misallocation of labor and capital across sectors — significantly amplifies costs; reduces productive capacity and increases relative price of investment; discourages investment, lowers wealth and consumption; export demand falls.
  - Third layer (solid lines): temporary reductions in labor productivity growth in tradable goods due to lower knowledge diffusion — significant impact particularly for the United States; accumulates more slowly; behaves like misallocation but of greater magnitude; decreases tradables relative to non-tradables productivity and leads to a Balassa-Samuelson effect that depreciates the REER.
- Relative impacts:
  - Large impacts on both China and the United States, relatively larger on China given strong multichannel connections to the United States.
  - The United States loses almost as much through knowledge diffusion as China when only those two decouple.
  - The United States will lose more through knowledge diffusion than China when more countries decouple from the United States because of preferential attachments with China.
- Non-hub countries (example: Japan):
  - If only China and the United States stop trading, Japan marginally gains from trade diversion.
  - With preferential attachment to China, Japan loses because it breaks strong links to the United States through trade and sectoral misallocation.

### Economic mechanisms and policy reaction (United States under Scenario 2 example)
- Trade shock effects:
  - Fall in imports leads to substitution to domestic production, minimizing the impact from lower exports; real GDP falls by a limited amount; consumption falls.
  - Curtailing imports of high-tech goods raises the price of investment, even with substitution toward domestic high-tech goods.
- Misallocation effects:
  - Reduces productive capacity, increases price of investment, discourages investment and consumption; export demand falls because domestic goods become more expensive abroad.
- Knowledge diffusion effects:
  - Greater magnitude than misallocation; impacts accumulate more slowly; drives REER depreciation via Balassa-Samuelson mechanism.
- Macroeconomic policy responses:
  - Monetary policy follows an interest rate reaction function based on deviation of inflation from target and offsets some short-term effects as inflation contracts with economic activity and REER appreciation.
  - Fiscal policy acts as automatic stabilizer (transfers increase as output gap moves into excess supply) but plays only a small role; underlying shocks are supply-side so potential output falls almost as fast as output and the output gap does not move much from baseline.
- Cross-region differences:
  - More open economies (especially those with smaller shares in the global economy) experience larger negative impacts because monetary policy is less effective due to trade leakages.
  - Magnitudes are smaller for non-hub countries in scenarios without preferential attachment.

### Concluding remarks and suggested future work
- Framework developed to assess:
  - (1) possible ways global trade in high-tech sectors could fragment;
  - (2) channels through which fragmentation affects the global economy (reduced global trade volumes, sectoral misallocation effects, lower international knowledge diffusion).
- Decoupling is typically very costly for main technology hubs and most countries, especially China, followed by major hubs like the United States or Germany.
- Non-hub countries sometimes gain in scenarios without preferential attachment by acting as partial substitutes for a hub (example: India).
- Overall, most countries lose and losses scale up with degree of fragmentation; multipolar worlds with non-hub countries trading with a single technology hub are especially harmful.
- Future work should address channels not accounted for here, including effects from changes in foreign investment policies, trade in services, and industrial policies aimed at mitigating productivity impacts from loss of access to foreign technologies.

### Data sources, model features, and calibration highlights
- CFRT data:
  - Original Eora database: balanced global MRIO table linking 26 sectors across 190 countries, annual time-series 1990-2015; trade-flow data correspond to latest (2015) Eora table.
  - Eora combined with 2015 applied tariff data from UNCTAD’s Trade Analysis Information System accessed through WITS produces a combined input-output database with 17 sectors and 165 countries.
- Services treatment in GIMF:
  - Services produced like consumption and investment goods from combination of tradable and nontradable goods plus productivity term.
  - Services can be consumed domestically or by foreigners; trade in services tracked bilaterally between all regions.
- GIMF version and regional coverage:
  - Annual, multi-region, micro-founded general equilibrium model.
  - An eight-region version is used, focused on Asia-Pacific regions: China, the United States, the euro area, India, Japan, Korea, the other Asia-Pacific countries, and a remaining countries bloc.

### Key national accounts ratios in GIMF (percent of a region’s GDP, unless otherwise stated)
- Share of Global GDP (%, US$): China 15.74, United States 24.23, Europe 16.06, India 3.20, Japan 5.85, Korea 2.03, Other Asia-Pacific 5.77, Remaining Countries 24.23
- Domestic Demand:
  - Household Consumption: China 47.56, United States 65.25, Europe 58.66, India 60.15, Japan 52.54, Korea 54.76, Other Asia-Pacific 61.15, Remaining Countries 58.5
  - Private Investment: China 27.51, United States 17.42, Europe 3.17, India 7.02, Japan 25.51, Korea 19.31, Other Asia-Pacific 18.5, Remaining Countries 23.5
  - Government Absorption: China 25.01, United States 17.42, Europe 20.31, India 11.02, Japan 20.51, Korea 15.01, Other Asia-Pacific 13.4, Remaining Countries 20.0
- Trade — Goods Exports: China 17.7, United States 9.1, Europe 17.5, India 13.5, Japan 14.5, Korea 34.7, Other Asia-Pacific 35.5, Remaining Countries 20.6
- Trade — Consumption imports: China 8.2, United States 4.1, Europe 8.2, India 6.3, Japan 5.4, Korea 7.4, Other Asia-Pacific 13.7, Remaining Countries 5.8
- Trade — Investment imports: China 4.6, United States 1.5, Europe 4.3, India 1.9, Japan 4.1, Korea 8.3, Other Asia-Pacific 6.0, Remaining Countries 2.9
- Trade — Intermediate imports: China 4.9, United States 3.5, Europe 5.0, India 5.3, Japan 5.0, Korea 19.0, Other Asia-Pacific 15.8, Remaining Countries 11.9
- Trade — Service Exports: China 1.8, United States 4.7, Europe 7.4, India 8.3, Japan 3.8, Korea 4.6, Other Asia-Pacific 9.2, Remaining Countries 4.7
- Trade — Goods Imports: China 15.4, United States 11.3, Europe 18.7, India 17.4, Japan 11.4, Korea 31.8, Other Asia-Pacific 36.4, Remaining Countries 18.9
- Trade — Consumption imports (breakdown): China 3.1, United States 5.7, Europe 8.1, India 3.8, Japan 5.6, Korea 8.1, Other Asia-Pacific 11.7, Remaining Countries 8.1
- Trade — Investment imports (breakdown): China 2.2, United States 2.3, Europe 3.3, India 2.4, Japan 1.8, Korea 5.3, Other Asia-Pacific 8.3, Remaining Countries 4.3
- Trade — Intermediate imports (breakdown): China 10.1, United States 3.3, Europe 7.3, India 11.2, Japan 4.0, Korea 18.4, Other Asia-Pacific 16.4, Remaining Countries 6.5
- Trade — Service Imports: China 4.0, United States 2.5, Europe 6.2, India 4.3, Japan 6.9, Korea 7.6, Other Asia-Pacific 8.2, Remaining Countries 6.4

### Elasticities and adjustment costs (highlights)
- Services versus other consumption: relatively inelastic demands within region and abroad; more elastic between foreign markets.
- Goods trade: relatively elastic between domestic and foreign goods, with higher elasticity among foreign markets.
- Real rigidities set to 1 across regions for most variables, consumption by saving households set to 2.
- Nominal adjustment costs set same across domestic sectors; higher in the euro area. Import adjustment costs vary across regions (large import markets like the United States have high adjustment costs; small open economies are price takers).

### Appendix Table II.2: Calibration of Goods Trade and Services Elasticities
- Elasticity between Consumption and Services: 0.9
- Elasticity between Domestic / Foreign Services: 0.9
- Elasticity for Foreign Services (cross-reference cell): 1.5
- Elasticity between Domestic / Imported Goods and Different Regions' Goods:
  - Consumption: -1.5 and 1.5
  - Investment: -1.5 and 1.5
  - Intermediates: -1.5 and 1.5

### Prices and region calibration (excerpt)
- Real wage: China 100, Euro Area 150, United States 100, India 100, Korea 100, Japan 100, Other regions 100
- Consumption price: China 100, Euro Area 150, United States 100, India 100, Korea 100, Japan 100, Other regions 100
- Services price: China 100, Euro Area 150, United States 100, India 100, Korea 100, Japan 100, Other regions 100
- Investment price: China 100, Euro Area 150, United States 100, India 100, Korea 100, Japan 100, Other regions 100
- Intermediate prices: China 100, Euro Area 150, United States 100, India 100, Korea 100, Japan 100, Other regions 100
- Price of imports of Goods (by region, as tabulated): China 25, Euro Area 50, United States 100, India 10, Korea 0? 02533 17, Japan 2533, Other regions 17
- Price of imports of Services (by region, as tabulated): China 25, Euro Area 50, United States 100, India 10, Korea 25, Japan 33, Other regions 17
- (Note: table entries concatenated in source; values transcribed exactly as they appear.)

### Appendix II: Summary of assumptions underpinning the use of GIMF
- Model agents and expectations: All agents have perfect foresight.
- Regional structure: All regions share the same economic structures, differing only through parameterization and calibration.
- Frequency and dynamics: Annual frequency; some first-year investment dynamics are less detailed.
- Baseline calibration: Based on parameter values consistent with 2018 for capital stock, government debt and deficit, net foreign assets and current account balance, and national accounts aggregates.
- Non-linearities: Present in the financial accelerator; otherwise approximately linear for small shocks.
- Real exchange rate: Adjusts immediately in the first year; follows forward-looking, risk-adjusted uncovered interest rate parity.
- Financial market channels: No substantial financial market channels beyond the financial accelerator; all net foreign asset positions denominated in U.S. dollars.
- Policy behavior: Monetary and fiscal policy passive, using standard policy rules for inflation targeting and debt-to-GDP targeting with automatic stabilizers.

### Appendix III: Knowledge Diffusion — methodological details and estimation results
- Adjustment assumption: Chinese patenting productivity is assumed equal to the average of the other countries; R&D spending is adjusted accordingly.
- Adjustment formula (as presented): R R&D_CHN,i,t_adjusted = PPATCHN,i,t * (SUM_l≠CHN PPPl,i,t / R R&D_CHN,i,t_l≠CHN)
- Patenting measure choices:
  - PP... variables can refer to the stock or the annual flow of patenting.
  - Using discounted cumulative sums (stock) for both R&D and patenting produces reasonably stable relationships and more conservative adjustments than relying on the productivity of the patenting flow.
  - Using the flow of patenting increases PP..._CHN,i,t by more than the sum of other countries’ patent flows (footnote 14).
- Rationale and limitations:
  - Adjustment is an approximation, a “guesstimate” of the benefits of Chinese innovation to other technological leaders.
  - International patent families may underestimate China’s innovation due to deterrence from patenting abroad.
  - Patent productivity of European countries measured in international patents may set a relatively high bar for China.

### Estimation results — Patenting regressions (Appendix Table III.1)
- Regression columns: (1) Followers, (2) Top 5, (3) Top 7 - raw, (4) Top 7 - stock adjusted, (5) Top 7 - flow adjusted.
- Foreign R&D coefficients:
  - Column (1): 0.299*** (t-statistic: 5.89)
  - Column (2): 0.516** (t-statistic: 2.60)
  - Column (3): 0.549** (t-statistic: 2.43)
  - Column (4): 0.497** (t-statistic: 2.12)
  - Column (5): 0.483** (t-statistic: 2.09)
- Domestic R&D coefficients:
  - Column (1): 0.468*** (t-statistic: 8.48)
  - Column (2): 0.337 (t-statistic: 1.66)
  - Column (3): 0.309 (t-statistic: 1.37)
  - Column (4): 0.332 (t-statistic: 1.32)
  - Column (5): 0.350 (t-statistic: 1.42)
- Regression diagnostics:
  - Country-Year FE: Yes (all columns)
  - N: 3117 (col 1), 950 (col 2), 784 (cols 3–5)
  - R2: 0.777 (col 1), 0.745 (col 2), 0.691 (col 3), 0.720 (col 4), 0.722 (col 5)
- Notes:
  - Coefficients and t-statistics from panel regression with country-year fixed effects.
  - All regressions exclude the coke and petroleum sector.
  - Top 7 regressions additionally exclude the wood and plastic sectors given missing data for China.
  - Followers in column (1) are all countries excluding the Top 7.
  - Variables are in natural logarithms. Standard errors clustered at the country-industry level.
  - Significance: * p<0.10, ** p<0.05, *** p<0.01.
- Interpretation highlights:
  - Coefficient on foreign R&D substantially smaller for followers (column 1) than among technological leaders (columns 2–5).
  - Among technological leaders, the coefficient on foreign R&D is larger and more precisely estimated than on domestic R&D.
  - According to coefficients, domestic innovation would increase by 50 percent if foreign R&D was doubled, but only by one third if domestic R&D were doubled (interpretation retained from source).

### Labor productivity regressions (Appendix Table III.2)
- Regression columns mirror Table III.1.
- Foreign R&D coefficients (labor productivity):
  - Column (1): 0.0643*** (t-statistic: 3.57)
  - Column (2): 0.146** (t-statistic: 2.47)
  - Column (3): 0.139* (t-statistic: 1.83)
  - Column (4): 0.140* (t-statistic: 1.80)
  - Column (5): 0.144* (t-statistic: 1.90)
- Domestic R&D coefficients (labor productivity):
  - Column (1): 0.136*** (t-statistic: 6.72)
  - Column (2): 0.0389 (t-statistic: 0.73)
  - Column (3): 0.0939 (t-statistic: 1.38)
  - Column (4): 0.0776 (t-statistic: 0.99)
  - Column (5): 0.0736 (t-statistic: 0.96)
- Regression diagnostics:
  - Country-Year FE: Yes (all columns)
  - N: 3251 (col 1), 910 (col 2), 720 (cols 3–5)
  - R2: 0.813 (col 1), 0.584 (col 2), 0.876 (cols 3–5)
- Notes: same exclusions and clustering as Table III.1.
- Interpretation: coefficients smaller in magnitude than for patenting, implying productivity is less sensitive to R&D spending than innovation, but effects remain quantitatively important.

### Illustrative decomposition (Appendix Figure III.2)
- Figure shows implied contribution from knowledge spillovers among technological leaders to annual labor productivity growth.
- Bars described:
  - Solid red bar (CHN-st.a.): results based on Chinese R&D rescaled to match other leaders’ research productivity in terms of patent stocks.
  - Red dash: additional effect if patenting flow is used in adjustment.
  - Red empty bar: effects based on the actual R&D numbers (CHN-u.a.), described as implausibly large.

### Appendix IV: Empirical gravity model for accessibility weights
- Accessibility weights 휑_c,l constructed from a gravity regression of patent citations to technological leaders.
- Patent citations modelled as exponential function of dummies and distances:
  - diff.country, diff.border, diff.lang., dist.int., tech.spec., tech.dev.
- Estimated model (A1):
  - 휑_cli = exp[a + f_ci + f_li + b1(diff.country) + b2(diff.border) + b3(diff.lang.) + b4(dist.int.) + b5(tech.spec.) + b6(tech.dev.) + ε_cli]
- Two country-sector fixed effects f_ci and f_li control for patenting rates and institutional/cultural factors.
- Predicted 휑_hat equals 1 for within-country-sector citations (all explanatory variables zero), establishing a natural upper bound.

### Estimated barriers to knowledge flows (Appendix Table IV.1)
- Dependent variable: Bilateral Citations
- Estimated coefficients and t-statistics:
  - diff.country: -0.461*** (t-statistic: -3.83)
  - diff.next.: -0.217 (t-statistic: -1.86)
  - diff.lang.: -0.875*** (t-statistic: -12.16)
  - dist.int.: -4.734 (t-statistic: -0.41)
  - tech.spec.: -2.282*** (t-statistic: -3.30)
  - tech.dev.: -0.253*** (t-statistic: -6.81)
- Regression diagnostics:
  - N: 3447
  - R-sq: 0.997
- Notes:
  - Coefficients and t-statistics of gravity regression of bilateral citations with Top 7 as cited countries.
  - Standard errors robust and clustered at the citing country-industry level.
  - Significance: *p < 0.10, **p < 0.05, ***p < 0.01.
- Summary: Coefficients largely in line with Eugster and others (2018); expected negative signs, high significance for most variables except distance and contiguity.

*Source: wpiea2021069-print-pdf - Appendix III and Eugster and others (2018) for more details on the first stage estimation.*

### Appendix III a nd Eu gster and others (2018) for more details on the first stage estimation.

### Appendix Table II.2: Calibration of Goods Trade

### Appendix Table II.2: Calibration of Goods Trade and Services Elasticities

### Calibration of Elasticities (Goods and Services)
- Elasticity between Consumption and Services: 0.9
- Elasticity between Domestic / Foreign Services: 0.9
- Elasticity for Foreign Services (cross-reference cell): 1.5

- Elasticity between Domestic / Imported Goods and Different Regions' Goods:
  - Consumption: -1.5 and 1.5 (table layout shows Consumption-1.5 1.5)
  - Investment: -1.5 and 1.5 (Investment-1.5 1.5)
  - Intermediates: -1.5 and 1.5 (Intermediates-1.5 1.5)

### Prices and Region Calibration (excerpt)
- Real wage:
  - China: 100
  - Euro Area: 150
  - United States: 100
  - India: 100
  - Korea: 100
  - Japan: 100
  - Other regions: 100
- Consumption price:
  - China: 100
  - Euro Area: 150
  - United States: 100
  - India: 100
  - Korea: 100
  - Japan: 100
  - Other regions: 100
- Services price:
  - China: 100
  - Euro Area: 150
  - United States: 100
  - India: 100
  - Korea: 100
  - Japan: 100
  - Other regions: 100
- Investment price:
  - China: 100
  - Euro Area: 150
  - United States: 100
  - India: 100
  - Korea: 100
  - Japan: 100
  - Other regions: 100
- Intermediate prices:
  - China: 100
  - Euro Area: 150
  - United States: 100
  - India: 100
  - Korea: 100
  - Japan: 100
  - Other regions: 100
- Price of imports of Goods (by region, as tabulated):
  - China: 25
  - Euro Area: 50
  - United States: 100
  - India: 10
  - Korea: 0? (table shows sequence "02533 17"—preserve as listed)
  - Japan: 2533
  - Other regions: 17
- Services (price of imports of Services, by region, as tabulated):
  - China: 25
  - Euro Area: 50
  - United States: 100
  - India: 10
  - Korea: 25
  - Japan: 33
  - Other regions: 17

(Note: table layout in source presents some entries concatenated; values above are transcribed exactly as they appear in the source content.)

---

### Appendix II: Summary of Assumptions Underpinning the Use of GIMF

- Model agents and expectations:
  - All agents in the model (including households, firms and the fiscal and monetary authorities) have perfect foresight.
- Regional structure:
  - All regions in GIMF have the same economic structures, differing only through their parameterization and calibration.
- Frequency and dynamics:
  - The model is at an annual frequency, so degree of detail for some of the economy’s dynamics are lost, particularly in the first year for investment.
- Baseline calibration:
  - The baseline calibration of GIMF is based on parameter values consistent with 2018 for the great ratios to GDP such the capital stock, government debt and deficit, net foreign assets and current account balance, and national accounts aggregates as well as trade flows and services data.
- Non-linearities:
  - The model has non-linearities in the financial accelerator, and potential for non-linearities in the conduct of monetary policy by either encountering the zero-interest-rate floor or using monetary accommodation (features not used here). Otherwise, the model is approximately linear for small enough shocks.
- Real exchange rate:
  - The real exchange rate is a “jumper,” adjusting immediately in the first year to shocks, since it follows the standard forward-looking, risk-adjusted uncovered interest rate parity condition which equates the forward sum of national-U.S. interest rate differentials with the one-year-forward difference in the nominal exchange rate.
  - There is no financial friction in the equation required to bring the net foreign asset position to its steady state, as the net foreign asset position and its dynamics solve endogenously as part of the OLG framework.
- Financial market channels:
  - There are no substantial financial market channels. GIMF only has a financial accelerator (albeit using the full general equilibrium form with non-linearities) and assumes complete domestic ownership of firms.
  - All net foreign asset positions are denominated in U.S. dollars, in all countries.
- Policy behavior:
  - Monetary and fiscal policy in this paper’s scenarios are passive, relying only their standard policy rules for inflation targeting and debt-to-GDP targeting (with automatic stabilizers) respectively.

---

### Appendix III: Knowledge Diffusion — Methodological Details and Estimation Results

### Methodological approach to adjusting China’s R&D
- Assumption:
  - Chinese patenting productivity is by assumption equal to the average of the other countries and, taking patenting (the numerator) as given, the R&D spending is adjusted (the denominator) accordingly.
- Adjustment formula (as presented):
  - R R&D_CHN,i,t_adjusted = PPATCHN,i,t * (SUM_l≠CHN PPPl,i,t / R R&D_CHN,i,t_l≠CHN)  (equation (3) transcribed from source)
  - In prose: China’s “adjusted” stock of R&D spending is the product of its patenting measure and the research productivity of the other six top innovating countries.
- Patenting measure choices:
  - 푃푃푃푃푃푃 variables can refer to the stock or the annual flow of patenting.
  - Using discounted cumulative sums (stock) for both R&D and patenting produces reasonably stable relationships and more conservative adjustments than relying on the productivity of the patenting flow.
  - Using the flow of patenting increases 푃푃푃푃푃푃_CHN,i,t by more than the sum of other countries’ patent flows (as noted in footnote 14).

### Rationale and limitations
- The adjustment is an approximation producing a “guesstimate” of the benefits of Chinese innovation to other technological leaders.
- Using international patent families may underestimate China’s innovation due to deterrence from patenting abroad (language, size of domestic market, economic integration).
- Patent productivity of European countries measured in international patents might set a relatively high bar for China.

### Estimation results — Patenting regressions (Appendix Table III.1)
- Regression columns: (1) Followers, (2) Top 5, (3) Top 7 - raw, (4) Top 7 - stock adjusted, (5) Top 7 - flow adjusted.
- Foreign R&D coefficients:
  - Column (1): 0.299*** (t-statistic: 5.89)
  - Column (2): 0.516** (t-statistic: 2.60)
  - Column (3): 0.549** (t-statistic: 2.43)
  - Column (4): 0.497** (t-statistic: 2.12)
  - Column (5): 0.483** (t-statistic: 2.09)
- Domestic R&D coefficients:
  - Column (1): 0.468*** (t-statistic: 8.48)
  - Column (2): 0.337 (t-statistic: 1.66)
  - Column (3): 0.309 (t-statistic: 1.37)
  - Column (4): 0.332 (t-statistic: 1.32)
  - Column (5): 0.350 (t-statistic: 1.42)
- Regression diagnostics:
  - Country-Year FE: Yes (for all columns)
  - N: 3117 (col 1), 950 (col 2), 784 (cols 3–5)
  - R2: 0.777 (col 1), 0.745 (col 2), 0.691 (col 3), 0.720 (col 4), 0.722 (col 5)
- Notes:
  - Coefficients and t-statistics from panel regression with country-year fixed effects.
  - All regressions exclude the coke and petroleum sector.
  - Top 7 regressions additionally exclude the wood and plastic sectors given missing data for China.
  - Followers in column (1) are all countries excluding the Top 7.
  - Variables are in natural logarithms. Standard errors clustered at the country-industry level.
  - Significance: * p<0.10, ** p<0.05, *** p<0.01.
- Interpretation highlights:
  - The coefficient on foreign R&D is substantially smaller for followers (column 1) than among technological leaders (columns 2–5).
  - Among technological leaders, the coefficient on foreign R&D is larger in magnitude and more precisely estimated than the one on domestic R&D.
  - According to coefficients, domestic innovation would increase by 50 percent if foreign R&D was doubled, but only by one third if domestic R&D were doubled (interpretation retained from source).

### Labor productivity regressions (Appendix Table III.2)
- Regression columns mirror Table III.1: (1) Followers, (2) Top 5, (3) Top 7 - raw, (4) Top 7 - stock adjusted, (5) Top 7 - flow adjusted.
- Foreign R&D coefficients (labor productivity):
  - Column (1): 0.0643*** (t-statistic: 3.57)
  - Column (2): 0.146** (t-statistic: 2.47)
  - Column (3): 0.139* (t-statistic: 1.83)
  - Column (4): 0.140* (t-statistic: 1.80)
  - Column (5): 0.144* (t-statistic: 1.90)
- Domestic R&D coefficients (labor productivity):
  - Column (1): 0.136*** (t-statistic: 6.72)
  - Column (2): 0.0389 (t-statistic: 0.73)
  - Column (3): 0.0939 (t-statistic: 1.38)
  - Column (4): 0.0776 (t-statistic: 0.99)
  - Column (5): 0.0736 (t-statistic: 0.96)
- Regression diagnostics:
  - Country-Year FE: Yes (all columns)
  - N: 3251 (col 1), 910 (col 2), 720 (cols 3–5)
  - R2: 0.813 (col 1), 0.584 (col 2), 0.876 (cols 3–5)
- Notes (same exclusions and clustering as Table III.1).
- Interpretation:
  - Coefficients are smaller in magnitude than for patenting, implying productivity is less sensitive to R&D spending than innovation, but effects remain quantitatively important.

### Illustrative decomposition (Appendix Figure III.2)
- Figure shows implied contribution from knowledge spillovers among technological leaders to annual labor productivity growth.
- Bars described in source:
  - Solid red bar (CHN-st.a.): results based on Chinese R&D rescaled to match other leaders’ research productivity in terms of patent stocks.
  - Red dash: additional effect if patenting flow is used in adjustment.
  - Red empty bar: effects based on the actual R&D numbers (CHN-u.a.), described as implausibly large.

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### Appendix IV: The Empirical Gravity Model for Accessibility Weights

### Model specification
- Accessibility weights 휑휑_c,l constructed from a gravity regression of patent citations to technological leaders.
- Patent citations modelled as an exponential function of dummy variables:
  - diff.country (distinct countries), diff.border (common border), diff.lang. (common language), dist.int. (geographic distance), tech.spec. (technological specialization distance), tech.dev. (technological development distance).
- Estimated model (A1):
  - 휑휑_cli = exp[a + f_ci + f_li + b1(diff.country) + b2(diff.border) + b3(diff.lang.) + b4(dist.int.) + b5(tech.spec.) + b6(tech.dev.) + ε_cli]
- Two country-sector fixed effects f_ci and f_li control for patenting rates and institutional/cultural factors.
- Predicted 휑_hat equals 1 for within-country-sector citations (all explanatory variables zero), establishing a natural upper bound for accessibility.

### Estimated barriers to knowledge flows (Appendix Table IV.1)
- Dependent variable: Bilateral Citations
- Estimated coefficients and t-statistics:
  - diff.country: -0.461*** (t-statistic: -3.83)
  - diff.next.: -0.217 (t-statistic: -1.86)
  - diff.lang.: -0.875*** (t-statistic: -12.16)
  - dist.int.: -4.734 (t-statistic: -0.41)
  - tech.spec.: -2.282*** (t-statistic: -3.30)
  - tech.dev.: -0.253*** (t-statistic: -6.81)
- Regression diagnostics:
  - N: 3447
  - R-sq: 0.997
- Notes:
  - Coefficients and t-statistics of gravity regression of bilateral citations with Top 7 as cited countries.
  - Standard errors robust and clustered at the citing country-industry level.
  - Significance: *p < 0.10, **p < 0.05, ***p < 0.01.
  - Constant and fixed effects not reported.
- Summary:
  - Coefficients largely in line with Eugster and others (2018). Expected negative signs, with high statistical significance for most variables except distance and contiguity.

*Source: Authors’ calculations (Appendix Tables and Figures as provided in the source content).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021069-print-pdf.pdf_