## wp1851

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---

### Patents and Corporate Innovation Network: Stylized Facts
- Data source and scope:
  - Primary patent data: Worldwide Patent Statistical Database (PATSTAT) maintained by the European Patent Office (EPO).
  - PATSTAT covers bibliographic data of patents from 90 patent issuing authorities.
  - Patents dated by date of application. Multiple filings of the same invention are identified as a "patent family" in PATSTAT; the application time of the first application is used to date a patent family.
  - Analysis restricted to patents that firms own directly and have been granted as of 2015.
  - Patents linked to firms' balance sheet data using patent-firm match through the Orbis database by Bureau van Dijk.
  - Total matched sample: 1,560,694 patents matched to 14,132 publicly listed firms in OECD countries.
  - Focus on publicly listed firms because private firms are not required to report R&D expenditure.

- Three important patterns in the global network of corporate innovation:
  1. Increasing number of corporate innovations carried out abroad (extensive and intensive margins):
     - 8,001 firms in the sample had patents invented abroad in 2013, compared to 801 in 1978 (Figure 5).
     - These firms had 138,048 foreign patents in 2013, compared to 1,217 in 1978 (Figure 6).
  2. Network has become increasingly multilateral:
     - Number of bilateral knowledge linkages between OECD countries increased from 132 in 1978 to 684 in 2013 (Figure 7).
     - In the sample, firms in 18 OECD countries did not have innovation presence in any foreign countries in 1978; this number decreased to 5 OECD countries by 2013.
     - Countries on average sourced from 14.7 (out of 33) foreign OECD countries in 2013, compared to 2.5 in 1978 (Figure 8).
     - In 2013:
       - The United States and Japan sourced from all other OECD countries.
       - Germany, Sweden, Finland, Netherlands, the United Kingdom, France, and Switzerland sourced from over 25 foreign OECD countries.
       - 21 countries in total sourced from more than 10 foreign OECD countries (Figure 9).
     - Definition: a bilateral knowledge linkage exists between country i and country j if firms in country i have patents invented in country j, and vice versa.
  3. Dominant hubs where a dominant share of patents are invented:
     - In 2013, 548,796 (35 percent) of all patents in the sample are invented in Japan.
     - 456,385 (29 percent) in the United States.
     - 227,894 (14 percent) in Korea.
     - 109,828 (7 percent) in Germany (Figure 10).
     - Japan, the United States, and Germany are three of the top source countries for foreign invented patents; together they account for 49 percent of all foreign invented patents in 2013 (Figure 11).
     - Note: The United Kingdom was another top source country for foreign patents in 2013, accounting for 13 percent of all foreign invented patents.
     - Korea is one of the top four countries for all patents, but the majority of patents invented in Korea are by domestic firms.

### Model and Methodology
- Objective:
  - Estimate the effect of foreign R&D on firm productivity using a firm-level production function augmented with knowledge, following Griliches (1979) and Griffith et al. (2006).

- Production function specification (Cobb-Douglas with knowledge):
  - Y_ijct = L_it^α * K_it^α * A_it^α * DOM_jct^γ1i * FOR_jct^γ2i
    - Indexes: i = firm, j = industry, c = country, t = year.
    - Y_ijct: output.
    - Z_it: productivity shifter.
    - L_it: labor.
    - K_it: physical capital.
    - A_it: firm's own R&D stock.
    - DOM_jct and FOR_jct: domestic and foreign R&D stock in the firm's industry.
  - “Domestic” and “foreign” may refer to a single country or the aggregate of multiple countries as specified later.

- Elasticities and dependence on innovation geography:
  - Elasticities of output w.r.t. domestic and foreign R&D stocks are γ1i and γ2i respectively.
  - γ1i and γ2i depend linearly on firm's innovation location:
    - γ1i = θ1 + Σ θ1d * W_i^d  (domestic shares)
    - γ2i = φ2 + Σ φ2f * W_i^f  (foreign shares)
    - d_iW and f_iW are the share of firm i's domestic and foreign innovation activities respectively.
    - Interpretation:
      - Positive estimate of θ2 (as in specification) = evidence of domestic knowledge spillovers.
      - Positive estimate of φ2 = evidence of foreign knowledge spillovers associated with technology sourcing.

- Productivity shifter parametric form:
  - z_it = η_i + η_d * W_i^d + η_f * W_i^f + V_it' δ + ε_it
    - d_iW and f_iW capture direct effect of locating innovation activities abroad.
    - V_it is a vector of controls such as demand shifters.
    - ε_it is a stochastic error term.

- Empirical estimation:
  - Take natural logarithms to obtain a log-linear estimation equation (equation (4)).
  - Estimation method: pooled ordinary least squares (OLS).
  - Controls to mitigate bias:
    - Time fixed effects, industry fixed effects, country fixed effects, and country-level macro variables included in z vector.
    - To address potential correlation between d_iW/f_iW and firm- or industry-level shocks, use presample information to construct d_iW and f_iW so that a firm's location of innovation activity is not affected by shocks in the same period.
    - Acknowledge potential residual bias if firms locate innovation activity in anticipation of positive productivity shocks; authors argue such biases are likely small because measures are based on presample patents resulting from R&D decisions taken many years prior to the sample period.

### Data and Measurement
- Main regression dataset:
  - Panel of publicly listed firms in OECD countries in 20 manufacturing and services industries between 2003 and 2012.
  - Data source: Orbis database by Bureau van Dijk.
  - OECD countries chosen because they represent a dominant share of patenting and R&D worldwide.
  - Example statistic: In 2010, 96 percent of all Triadic patent families—patent families filed at EPO, the Japan Patent Office (JPO) and the United States Patent and Trademark Office (USPTO)—are invented in OECD countries.
- Notes:
  - Patent-firm match information used is as of 2015.
  - Patents of a firm’s subsidiaries are not included.
  - Appendix references: Table A1 for industry definition and Table A2 for variable sources and definitions.

### Data, sample construction, and measurement
- Baseline sample: 11,858 firms after deleting firms with missing values on employees, capital, operating revenue, or less than 3 years of reported R&D expenditure.
- Time frames:
  - Presample patent window used to construct location measures: 1997-2006 (alternative robustness check: 1986-1996).
  - Regression analysis period: 2009-2013.
- R&D stocks:
  - Constructed using the permanent inventory method from R&D expenditure data sourced from OECD, Eurostat, National Science Foundation (NSF), and Japanese Ministry of Internal Affairs and Communications (MIC).
  - R&D stocks from non-OECD countries are excluded because only 1 percent of patents are invented in non-OECD countries in the sample.
- Innovation-location measures:
  - f_i^W (denoted W in tables): proportion of a firm's total worldwide patents invented in foreign countries (source: country of residence of patent inventors).
  - d_i^W (denoted W_dom/W_for in some specifications): share of firm’s innovation in own country vs foreign OECD countries.
  - For patents with multiple inventors, source countries are assigned on a pro rata basis (share can exceed one if inventors of the same patent are from different countries).

### Summary statistics (selected)
- Firms (all countries) average patents:
  - Average firm in OECD: 2,705 patents (All).
  - Firms in technology frontier countries: on average 662 patents invented in technology frontier countries and 2,983 patents invented in non-frontier countries.
  - Firms in non-frontier countries: on average 236 patents invented in technology frontier countries and 964 patents invented in non-frontier countries.
- Table 1 sample-level moments (selected):
  - Observations: 22,043 (summary statistics table).
  - Mean Ln(RD)_i,t: 9.499; Std. Dev.: 2.546; Min: -0.176; Max: 17.402.
  - Mean W_frontier_i: 0.698; Std. Dev.: 0.862; Min: 0.000; Max: 3.000.

### Main empirical findings
- Production-function estimates (R&D-augmented):
  - Labor-capital ratio coefficients (Ln(L/K)):
    - Frontier-country firms: 0.429 (Table 8, column 1).
    - Non-frontier-country firms: 0.673 (Table 9, column 1).
  - Private return to firm-specific R&D (Ln(RD)_i,t):
    - Firms in technology frontier countries: 0.183 (Table 8, column 1) — interpreted as about 18 percent private return to R&D.
    - Firms in non-frontier countries: 0.036 (Table 9, column 1) — 3.6 percent.

- Interaction of innovation-location and aggregate R&D (spillovers):
  - Frontier-country sample (Table 8, column 4):
    - W_frontier_i * Ln(RD)_frontier_c,j,t = 0.082** (standard error [0.033]).
    - W_other_i * Ln(RD)_other_c,j,t = -0.001 (not significant).
  - Non-frontier-country sample (Table 9, column 4):
    - W_frontier_i * Ln(RD)_frontier_c,j,t = 0.067** (standard error [0.026]).
    - W_other_i * Ln(RD)_other_c,j,t = -0.004 (not significant).
  - Interpretation: Firms with stronger inventor presence in technology frontier countries benefit disproportionately more from frontier aggregate R&D; spillovers from non-frontier countries’ aggregate R&D are not significant.

### Disaggregated (bilateral) spillovers by source country
- Frontier-country firms (Table 10, column 4; disaggregated DE, JP, US):
  - W_DE_i * Ln(RD)_DE = 0.106*** ([0.035]).
  - W_JP_i * Ln(RD)_JP = 0.174*** ([0.033]).
  - W_US_i * Ln(RD)_US = -0.135*** ([0.046]) — negative coefficient on the U.S. interaction in this specification.
  - Cross-country main effects: W_DE_i = -1.040***; W_JP_i = -2.158***; W_US_i = 2.038***.
- Non-frontier-country firms (Table 11, column 4):
  - W_DE_i * Ln(RD)_DE = 0.032 (not significant).
  - W_JP_i * Ln(RD)_JP = 0.085** ([0.038]).
  - W_US_i * Ln(RD)_US = 0.108** ([0.042]).
  - Interpretation: For non-frontier firms the strongest spillover effects often come from the United States and Japan; Germany is less consistently a significant source for non-frontier firms.
- Country-pair specific results among frontier countries (Table 12):
  - For German firms (column 1): positive and significant spillovers from Japan at 1-percent level; U.S. spillovers not significant.
  - For Japanese firms (column 2): positive and significant spillovers from Germany at 1-percent level and from the United States at the 10-percent level.
  - For U.S. firms (column 3): positive and significant spillovers from Germany and Japan at the 1-percent level.
  - Domestic vs foreign in frontier sample (Table 13, column 1): W_for_i * Ln(RD)_for = 0.184** ([0.078]); W_dom_i * Ln(RD)_dom = 0.115* ([0.064]) — foreign interaction about one and two-thirds the size of domestic interaction reported in text (foreign larger).

### Robustness checks and alternative measures
- Profit-shifting / tax-haven exclusion (Tables 14 and 15):
  - Excluding Ireland, Luxembourg, and Switzerland (non-tax-haven non-frontier sample) does not materially change the interaction terms: interaction with frontier aggregate R&D remains almost identical; interaction with non-tax-haven non-frontier R&D remains not significant.
  - Conclusion: profit shifting to tax-haven countries is unlikely to explain the small spillovers from non-frontier countries.
- Absorptive capacity (alternative location measure using number of patents N in thousands; Table 16):
  - Interaction with N_frontier_i * Ln(RD)_frontier is positive and significant when used alone for frontier firms, but when included jointly with the baseline W_frontier measure the coefficient on N becomes smaller and less significant while W_frontier remains positive and similar in magnitude.
  - Conclusion: baseline patent-share location measure (W) captures technology sourcing effects beyond simple firm absorptive capacity.
- Presample location window (W2 using 1986-1996):
  - Results using earlier presample patents (W2) are similar: interaction terms with frontier aggregate R&D remain positive and significant.
  - This mitigates concerns that innovation-location measures are endogenous to contemporaneous firm performance.

### Interpretation and policy implications
- Key empirical conclusion:
  - Strong evidence of international knowledge spillovers consistent with technology sourcing among OECD countries: firms with greater inventor presence in technology frontier countries benefit disproportionately more from frontier aggregate R&D.
- Magnitude and localization:
  - Foreign spillovers from technology frontier countries are often larger than spillovers from other foreign (non-frontier) countries and, in many specifications, larger than domestic spillovers for frontier-country firms (Table 13).
  - The tacit nature of knowledge implies partial localization of knowledge externalities and heterogeneous bilateral channels (Japan, Germany, U.S. play different roles depending on destination).
- Policy implications emphasized by the authors:
  - Optimal innovation policy should account for benefits of global innovation networks.
  - From the perspective of technology frontier countries: global knowledge externality is potentially large.
  - From the perspective of non-frontier countries: outward innovative FDI should be encouraged and viewed as complementary to domestic innovation.

*Source: wp1851 - Section VI concludes.*

### Section VI concludes.

### Section VI concludes.

### Patents and Corporate Innovation Network: Stylized Facts
- Data source and scope:
  - Primary patent data: Worldwide Patent Statistical Database (PATSTAT) maintained by the European Patent Office (EPO).
  - PATSTAT covers bibliographic data of patents from 90 patent issuing authorities.
  - Patents dated by date of application. Multiple filings of the same invention are identified as a "patent family" in PATSTAT; the application time of the first application is used to date a patent family.
  - Analysis restricted to patents that firms own directly and have been granted as of 2015.
  - Patents linked to firms' balance sheet data using patent-firm match through the Orbis database by Bureau van Dijk.
  - Total matched sample: 1,560,694 patents matched to 14,132 publicly listed firms in OECD countries.
  - Focus on publicly listed firms because private firms are not required to report R&D expenditure.

- Three important patterns in the global network of corporate innovation:
  1. Increasing number of corporate innovations carried out abroad (extensive and intensive margins):
     - 8,001 firms in the sample had patents invented abroad in 2013, compared to 801 in 1978 (Figure 5).
     - These firms had 138,048 foreign patents in 2013, compared to 1,217 in 1978 (Figure 6).
  2. Network has become increasingly multilateral:
     - Number of bilateral knowledge linkages between OECD countries increased from 132 in 1978 to 684 in 2013 (Figure 7).
     - In the sample, firms in 18 OECD countries did not have innovation presence in any foreign countries in 1978; this number decreased to 5 OECD countries by 2013.
     - Countries on average sourced from 14.7 (out of 33) foreign OECD countries in 2013, compared to 2.5 in 1978 (Figure 8).
     - In 2013:
       - The United States and Japan sourced from all other OECD countries.
       - Germany, Sweden, Finland, Netherlands, the United Kingdom, France, and Switzerland sourced from over 25 foreign OECD countries.
       - 21 countries in total sourced from more than 10 foreign OECD countries (Figure 9).
     - Definition: a bilateral knowledge linkage exists between country i and country j if firms in country i have patents invented in country j, and vice versa.
  3. Dominant hubs where a dominant share of patents are invented:
     - In 2013, 548,796 (35 percent) of all patents in the sample are invented in Japan.
     - 456,385 (29 percent) in the United States.
     - 227,894 (14 percent) in Korea.
     - 109,828 (7 percent) in Germany (Figure 10).
     - Japan, the United States, and Germany are three of the top source countries for foreign invented patents; together they account for 49 percent of all foreign invented patents in 2013 (Figure 11).
     - Note: The United Kingdom was another top source country for foreign patents in 2013, accounting for 13 percent of all foreign invented patents.
     - Korea is one of the top four countries for all patents, but the majority of patents invented in Korea are by domestic firms.

### Model and Methodology
- Objective:
  - Estimate the effect of foreign R&D on firm productivity using a firm-level production function augmented with knowledge, following Griliches (1979) and Griffith et al. (2006).

- Production function specification (Cobb-Douglas with knowledge):
  - Y_ijct = L_it^α * K_it^α * A_it^α * DOM_jct^γ1i * FOR_jct^γ2i
    - Indexes: i = firm, j = industry, c = country, t = year.
    - Y_ijct: output.
    - Z_it: productivity shifter.
    - L_it: labor.
    - K_it: physical capital.
    - A_it: firm's own R&D stock.
    - DOM_jct and FOR_jct: domestic and foreign R&D stock in the firm's industry.
  - “Domestic” and “foreign” may refer to a single country or the aggregate of multiple countries as specified later.

- Elasticities and dependence on innovation geography:
  - Elasticities of output w.r.t. domestic and foreign R&D stocks are γ1i and γ2i respectively.
  - γ1i and γ2i depend linearly on firm's innovation location:
    - γ1i = θ1 + Σ θ1d * W_i^d  (domestic shares)
    - γ2i = φ2 + Σ φ2f * W_i^f  (foreign shares)
    - d_iW and f_iW are the share of firm i's domestic and foreign innovation activities respectively.
    - Interpretation:
      - Positive estimate of θ2 (as in specification) = evidence of domestic knowledge spillovers.
      - Positive estimate of φ2 = evidence of foreign knowledge spillovers associated with technology sourcing.

- Productivity shifter parametric form:
  - z_it = η_i + η_d * W_i^d + η_f * W_i^f + V_it' δ + ε_it
    - d_iW and f_iW capture direct effect of locating innovation activities abroad.
    - V_it is a vector of controls such as demand shifters.
    - ε_it is a stochastic error term.

- Empirical estimation:
  - Take natural logarithms to obtain a log-linear estimation equation (equation (4)).
  - Estimation method: pooled ordinary least squares (OLS).
  - Controls to mitigate bias:
    - Time fixed effects, industry fixed effects, country fixed effects, and country-level macro variables included in z vector.
    - To address potential correlation between d_iW/f_iW and firm- or industry-level shocks, use presample information to construct d_iW and f_iW so that a firm's location of innovation activity is not affected by shocks in the same period.
    - Acknowledge potential residual bias if firms locate innovation activity in anticipation of positive productivity shocks; authors argue such biases are likely small because measures are based on presample patents resulting from R&D decisions taken many years prior to the sample period.

### Data and Measurement
- Main regression dataset:
  - Panel of publicly listed firms in OECD countries in 20 manufacturing and services industries between 2003 and 2012.
  - Data source: Orbis database by Bureau van Dijk.
  - OECD countries chosen because they represent a dominant share of patenting and R&D worldwide.
  - Example statistic: In 2010, 96 percent of all Triadic patent families—patent families filed at EPO, the Japan Patent Office (JPO) and the United States Patent and Trademark Office (USPTO)—are invented in OECD countries.
- Notes:
  - Patent-firm match information used is as of 2015.
  - Patents of a firm’s subsidiaries are not included.
  - Appendix references: Table A1 for industry definition and Table A2 for variable sources and definitions.

*Source: wp1851 - Section VI concludes.*

### 2009. Domestic expenditure on R&D as a percentage of GDP is on average 2.4 percent among OECD countries,

### wp1851 - 2009. Domestic expenditure on R&D as a percentage of GDP is on average 2.4 percent among OECD countries,

### Data, sample construction, and measurement
- Baseline sample: 11,858 firms after deleting firms with missing values on employees, capital, operating revenue, or less than 3 years of reported R&D expenditure.  
- Time frames:
  - Presample patent window used to construct location measures: 1997-2006 (alternative robustness check: 1986-1996).  
  - Regression analysis period: 2009-2013.  
- R&D stocks:
  - Constructed using the permanent inventory method from R&D expenditure data sourced from OECD, Eurostat, National Science Foundation (NSF), and Japanese Ministry of Internal Affairs and Communications (MIC).  
  - R&D stocks from non-OECD countries are excluded because only 1 percent of patents are invented in non-OECD countries in the sample.  
- Innovation-location measures:
  - f_i^W (denoted W in tables): proportion of a firm's total worldwide patents invented in foreign countries (source: country of residence of patent inventors).  
  - d_i^W (denoted W_dom/W_for in some specifications): share of firm’s innovation in own country vs foreign OECD countries.  
  - For patents with multiple inventors, source countries are assigned on a pro rata basis (share can exceed one if inventors of the same patent are from different countries).  

### Summary statistics (selected)
- Firms (all countries) average patents:
  - Average firm in OECD: 2,705 patents (All).  
  - Firms in technology frontier countries: on average 662 patents invented in technology frontier countries and 2,983 patents invented in non-frontier countries.  
  - Firms in non-frontier countries: on average 236 patents invented in technology frontier countries and 964 patents invented in non-frontier countries.  
- Table 1 sample-level moments (selected):
  - Observations: 22,043 (summary statistics table).  
  - Mean Ln(RD)_i,t: 9.499; Std. Dev.: 2.546; Min: -0.176; Max: 17.402.  
  - Mean W_frontier_i: 0.698; Std. Dev.: 0.862; Min: 0.000; Max: 3.000.  

### Main empirical findings
- Production-function estimates (R&D-augmented):
  - Labor-capital ratio coefficients (Ln(L/K)):
    - Frontier-country firms: 0.429 (Table 8, column 1).  
    - Non-frontier-country firms: 0.673 (Table 9, column 1).  
  - Private return to firm-specific R&D (Ln(RD)_i,t):
    - Firms in technology frontier countries: 0.183 (Table 8, column 1) — interpreted as about 18 percent private return to R&D.  
    - Firms in non-frontier countries: 0.036 (Table 9, column 1) — 3.6 percent.  
- Interaction of innovation-location and aggregate R&D (spillovers):
  - Frontier-country sample (Table 8, column 4):
    - W_frontier_i * Ln(RD)_frontier_c,j,t = 0.082** (standard error [0.033]).  
    - W_other_i * Ln(RD)_other_c,j,t = -0.001 (not significant).  
  - Non-frontier-country sample (Table 9, column 4):
    - W_frontier_i * Ln(RD)_frontier_c,j,t = 0.067** (standard error [0.026]).  
    - W_other_i * Ln(RD)_other_c,j,t = -0.004 (not significant).  
  - Interpretation: Firms with stronger inventor presence in technology frontier countries benefit disproportionately more from frontier aggregate R&D; spillovers from non-frontier countries’ aggregate R&D are not significant.  

### Disaggregated (bilateral) spillovers by source country
- Frontier-country firms (Table 10, column 4; disaggregated DE, JP, US):
  - W_DE_i * Ln(RD)_DE = 0.106*** ([0.035]).  
  - W_JP_i * Ln(RD)_JP = 0.174*** ([0.033]).  
  - W_US_i * Ln(RD)_US = -0.135*** ([0.046]) — negative coefficient on the U.S. interaction in this specification.  
  - Cross-country main effects: W_DE_i = -1.040***; W_JP_i = -2.158***; W_US_i = 2.038***.  
- Non-frontier-country firms (Table 11, column 4):
  - W_DE_i * Ln(RD)_DE = 0.032 (not significant).  
  - W_JP_i * Ln(RD)_JP = 0.085** ([0.038]).  
  - W_US_i * Ln(RD)_US = 0.108** ([0.042]).  
  - Interpretation: For non-frontier firms the strongest spillover effects often come from the United States and Japan; Germany is less consistently a significant source for non-frontier firms.  
- Country-pair specific results among frontier countries (Table 12):
  - For German firms (column 1): positive and significant spillovers from Japan at 1-percent level; U.S. spillovers not significant.  
  - For Japanese firms (column 2): positive and significant spillovers from Germany at 1-percent level and from the United States at the 10-percent level.  
  - For U.S. firms (column 3): positive and significant spillovers from Germany and Japan at the 1-percent level.  
  - Domestic vs foreign in frontier sample (Table 13, column 1): W_for_i * Ln(RD)_for = 0.184** ([0.078]); W_dom_i * Ln(RD)_dom = 0.115* ([0.064]) — foreign interaction about one and two-thirds the size of domestic interaction reported in text (foreign larger).  

### Robustness checks and alternative measures
- Profit-shifting / tax-haven exclusion (Tables 14 and 15):
  - Excluding Ireland, Luxembourg, and Switzerland (non-tax-haven non-frontier sample) does not materially change the interaction terms: interaction with frontier aggregate R&D remains almost identical; interaction with non-tax-haven non-frontier R&D remains not significant.  
  - Conclusion: profit shifting to tax-haven countries is unlikely to explain the small spillovers from non-frontier countries.  
- Absorptive capacity (alternative location measure using number of patents N in thousands; Table 16):
  - Interaction with N_frontier_i * Ln(RD)_frontier is positive and significant when used alone for frontier firms, but when included jointly with the baseline W_frontier measure the coefficient on N becomes smaller and less significant while W_frontier remains positive and similar in magnitude.  
  - Conclusion: baseline patent-share location measure (W) captures technology sourcing effects beyond simple firm absorptive capacity.  
- Presample location window (W2 using 1986-1996):
  - Results using earlier presample patents (W2) are similar: interaction terms with frontier aggregate R&D remain positive and significant.  
  - This mitigates concerns that innovation-location measures are endogenous to contemporaneous firm performance.  

### Interpretation and policy implications
- Key empirical conclusion:
  - Strong evidence of international knowledge spillovers consistent with technology sourcing among OECD countries: firms with greater inventor presence in technology frontier countries benefit disproportionately more from frontier aggregate R&D.  
- Magnitude and localization:
  - Foreign spillovers from technology frontier countries are often larger than spillovers from other foreign (non-frontier) countries and, in many specifications, larger than domestic spillovers for frontier-country firms (Table 13).  
  - The tacit nature of knowledge implies partial localization of knowledge externalities and heterogeneous bilateral channels (Japan, Germany, U.S. play different roles depending on destination).  
- Policy implications emphasized by the authors:
  - Optimal innovation policy should account for benefits of global innovation networks.  
  - From the perspective of technology frontier countries: global knowledge externality is potentially large.  
  - From the perspective of non-frontier countries: outward innovative FDI should be encouraged and viewed as complementary to domestic innovation.  

*Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1851.pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1851.pdf_