## _wp04185

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### III. Model framework (Romer (1990) based)
- Premises:
  - Growth driven by technological change.
  - Technological change results from intentional actions responding to market incentives.
  - Blue prints (designs) are nonrival.
- Structure:
  - Sectors: research and development (R&D), intermediate goods, final output.
  - Final output produced with human capital (H), labor (L), producer durables (x), and knowledge stock (A) in a Cobb-Douglas form (equation (1) in source).
  - New designs generated per Ȧ = θ H_A A − δ A (equation (2) in source; model emphasizes θ = 1 case).
  - Durable goods accounting: K = η A x and substitution x = K / (η A) affects returns to scale.
- Implications emphasized:
  - Nonrival knowledge stock A creates increasing returns in R&D and final output sectors.
  - Policy implication: promoting R&D and investing in human capital can sustain perpetual growth under model assumptions.

### III. Data and measurement
- Sample and period:
  - Sample includes 20 OECD and 10 non-OECD countries; many tables and estimations cover 1981–97. Some estimations use 19 OECD countries (1981–97) depending on regression.
- Innovation:
  - Patent flows: U.S. Patent and Trademark Office utility patent applications by foreign inventors (classified into five categories).
  - Patent stock constructed using 20 percent depreciation rate; patent flows used are applications (not grants).
  - Initial patent stock formula and annual update: Ps_t = (1 − δ) Ps_{t−1} + P_t (20 percent depreciation implied δ = 0.20).
- R&D:
  - Gross R&D expenditure (GERD) from OECD Main Statistics and Technology Indicators.
  - R&D stock constructed using 20 percent depreciation rate.
  - Series deflated to 1995 implicit price deflator and converted to U.S. dollars using monthly average exchange rates.
- Other variables and sources:
  - GDP, gross fixed investment, secondary school enrollments (WDI, 2002).
  - Labor population, imports and exports of manufacturing goods (OECD, 2002).
  - Openness in current prices (PWT.6).
  - Expropriation risk index (World Bank, International Country Risk Guide) ranges from 1 to 10 (high values = low risk).
  - U.S. trade share from IMF Direction of Trade Database (IMFDOT).
- Units and transformations:
  - All variables in constant 1995 U.S. dollars except shares of GDP, patent counts, and expropriation index.
  - Many series interpolated when gaps exist (R&D series via averaging; secondary school enrollments via five-year moving averages).

### IV. Econometric approach
- Methods:
  - Fixed-effects regressions.
  - Arellano-Bond Linear GMM (STATA 8).
  - OLS used as benchmark (detailed OLS results in Appendix).
- Estimation details:
  - Time dummies included in all regressions.
  - GMM lags and instruments: first lag of patent flows commonly used to instrument knowledge stock; GMM diagnostics reported via Sargan and AR(2) tests.
  - First-order autocorrelation addressed by differencing or Prais-Winsten estimation.
- Samples and groupings:
  - Samples: Full, Non-OECD, OECD; OECD further split into G-7, Non-G-7, Large market, Small market, High income, Low income (sample definitions per Table 5 in source).
  - Some regressions normalize variables by labor (per-labor measures) and use log levels or log differences depending on estimator.

### V. Main empirical findings — innovation production (estimation of θ and determinants)
- Core result on innovation → per capita output:
  - A 1 percent increase in innovation raises per capita income by around 0.05 percent in both OECD and non-OECD countries.
- R&D effect on innovation:
  - A 1 percent increase in R&D stock increases innovation by about 0.2 percent only in large market OECD countries (includes the G-7).
  - Fixed-effects G-7 and large-market elasticities: a 1 percent increase in per capita R&D stock increases innovation by 0.40 percent (FE result).
  - Low-income OECD FE elasticity: a 1 percent increase in per capita R&D stock increases innovation by 0.50 percent.
  - Arellano-Bond GMM second-lag elasticities:
    - G-7: second lag of R&D stock = 0.162 (Table 7 entry).
    - Large Market: second lag of R&D stock = 0.231 (Table 7 entry).
    - Low-income OECD: second lag of R&D stock = 0.298 (Table 7 entry).
    - Low Income OECD — Large Market subgroup: second lag of R&D stock = 0.513 (z = (4.50)) (Table 8).
    - Low Income OECD — Small Market subgroup: second lag of R&D stock = -0.423 (z = (1.01)) (Table 8).
- Patent-flow persistence (knowledge stock instrument interpretation):
  - First lag of per labor patent positive and significant in all country groups with magnitudes around 0.3 (examples from Table 7):
    - Full 0.297 (4.26)
    - Non-G-7 0.304 (3.72)
    - G-7 0.309 (2.42)
    - Large Market 0.576 (6.99)
    - Low Income 0.317 (3.89)
  - Interpretation: a 1 percent increase in knowledge stock leads to about a 0.3 percent increase in innovation when instrumented via lagged patent flows.
- Role of technology spillovers and trade:
  - Manufacturing import share (imports of manufacturing goods as share of total trade in manufacturing goods) is positive and significant, especially in countries without significant domestic R&D effects — indicating use of foreign know-how.
  - Examples (GMM Table 7): Full 1.844 (2.89); Non-G-7 1.761 (2.17); Small Market 2.633 (2.29); High Income 4.226 (3.72).
- Other controls:
  - Secondary school enrollments significant mainly in G-7 in GMM (G-7 second lag of Secondary school = 0.184 (1.84)).
  - Expropriation risk significant in large-market OECD and some FE specifications.
  - U.S. share of GDP significant in G-7, large market OECD, and low-income OECD countries.
- Diagnostics:
  - GMM Sargan and AR(2) p-values vary by sample (examples):
    - Full sample: Sargan p-value 0.00; AR(2) p-value 0.38.
    - Non-G-7: Sargan p-value 0.09; AR(2) p-value 0.56.
    - G-7: Sargan p-value 0.01; AR(2) p-value 1.00.

### VI. Production function estimates — innovation and per-labor GDP
- Model and variables:
  - Production function with knowledge stock A entering to generate increasing returns; regression uses variables normalized by labor: yt (per labor output), it (investment), xt (new products measured by patent stock), ht (secondary school enrollments), plus openness and expropriation risk.
  - Data: 20 OECD and 10 non-OECD countries, 1981–97.
- Fixed-effects results (selected exact coefficients from Table 9):
  - Full Sample:
    - Investment: 0.312 (24.46)
    - Second lag of patent stock: 0.104 (9.18)
    - Second lag of secondary school: 0.009 (0.41)
    - Openness: 0.025 (1.43)
    - Expropriation Risk: -0.025 (1.72)
    - R-squared: 0.99
    - Observations: 449
    - Number of countries: 30
  - OECD sample (illustrative):
    - Investment: 0.274 (16.79)
    - Second lag of patent stock: 0.076 (4.94)
    - Openness: 0.071 (2.90)
    - Expropriation Risk: 0.131 (4.66)
    - Observations: 300
    - Number of countries: 20
  - G-7 sample (illustrative):
    - Investment: 0.296 (7.39)
    - Second lag of patent stock: 0.023 (0.87)
    - Expropriation Risk: 0.174 (2.09)
    - Observations: 75
    - Number of countries: 5
- GMM results (selected exact coefficients from Table 10):
  - Full Sample:
    - Investment: 0.206 (11.82)
    - Second lag of patent stock: 0.040 (3.35)
    - Second lag of secondary school: -0.044 (2.06)
    - Openness: 0.056 (3.74)
    - Expropriation risk: -0.048 (3.74)
    - First lag of GDP: 0.447 (7.52)
    - Fourth lag of GDP: 0.188 (5.36)
    - Constant: 0.025 (4.69)
    - Sargan test (p-value): 0.00
    - AR(2) test (p-value): 0.57
    - Observations: 359
    - Number of countries: 30
  - OECD sample (illustrative):
    - Investment: 0.194 (9.44)
    - Second lag of patent stock: 0.058 (4.17)
    - Openness: 0.135 (6.14)
    - First lag of GDP: 0.542 (8.71)
    - Constant: 0.006 (2.75)
    - Sargan test (p-value): 0.12
    - AR(2) test (p-value): 0.84
    - Observations: 280
    - Number of countries: 20
  - Non-OECD sample (illustrative):
    - Investment: 0.173 (6.54)
    - Second lag of patent stock: 0.038 (1.84)
    - First lag of GDP: 0.582 (6.29)
    - Sargan test (p-value): 0.02
    - AR(2) test (p-value): 0.42
    - Observations: 119
    - Number of countries: 10
- Estimated impacts on per-labor GDP from innovation (summary statements preserved):
  - 0.14 percent increase in per labor GDP in the non-G-7 and the OECD countries with small markets.
  - about a 0.09 percent increase in the high income and low-income OECD countries.
  - Per-sample FE/GMM magnitudes vary: FE full second lag of patent stock = 0.104 (9.18); GMM full second lag of patent stock = 0.040 (3.35).
- Returns to investment:
  - Positive and significant across methods and samples (examples: FE full 0.312 (24.46); GMM full 0.206 (11.82)).
- Secondary school enrollment:
  - Often not statistically significant; when significant magnitudes are small (example FE low-income OECD 0.08 noted in text earlier).

### VII. Stylized facts, correlations, and robustness
- Cross-sectional and time-series patterns:
  - Levels and growth rates of GDP, investment, R&D and patent applications are positively correlated across countries and over time.
  - Examples from Tables 3 and 4 (exact values preserved in source):
    - Aggregate figures (1981–97): Japan Investment rank 1 = 1,244,578 (millions 1995 U.S. dollars); Japan GDP rank 1 = 4,442,000 (millions 1995 U.S. dollars); Japan Patents rank 1 = 19,286; Japan R&D Expenditure rank 1 = 86,412 (millions 1995 U.S. dollars).
    - Per capita figures (1981–97): Per capita GDP rank 1: Switzerland 42,824; Per capita Investment rank 1: Japan 10,153; Per capita Patents rank 1: Switzerland 176 (per 100 mn); Per capita R&D rank 1: Switzerland 870 (per 10 mn).
- Correlation evidence (Table 14):
  - Strong positive correlations among GDP, investment, patent stock, and R&D stock (e.g., GDP–Investment 0.97* in full sample; GDP–Patent stock 0.92* in full sample).
- Sample summary statistics (selected exact entries from Table 15):
  - Full sample GDP: N 523; Min 505; Max 83,442; Mean 38,018; Median 40,166; Std Dev 22,330.
  - Full sample Patents: N 523; Min 0.01; Max 429; Mean 69; Median 39; Std Dev 88.
  - Full sample R&D Expenditure: N 340; Min 65.80; Max 2,780; Mean 776; Median 700; Std Dev 485.
- Diagnostics:
  - Fixed-effects R-squared values reported as 0.99 across many per-labor regressions.
  - Some GMM and OLS specifications show low Sargan p-values indicating model rejection in some samples (text notes full and OECD samples often have Sargan test rejection).

### VIII. Interpretation and policy-relevant conclusions
- Support for endogenous growth mechanisms:
  - Evidence of a significant relationship between R&D stock and innovation.
  - Evidence of a significant relationship between innovation (patent stock) and per capita GDP.
- Market size matters:
  - Only large-market OECD countries (including the G-7) reliably convert R&D investment into increased innovation; other OECD countries appear to rely on technology spillovers (imports in manufacturing goods as share of manufacturing trade) to raise innovation.
- Limits to constant returns to innovation:
  - Empirical results do not support constant returns to innovation with respect to R&D stock — innovation appears to raise growth rates in the short term but not provide unambiguous perpetual growth in the observed data.
  - Authors highlight caveat: patent and R&D data are incomplete measures of innovation and research activity; conclusions about rejection of R&D-based growth models should be tempered.
- Policy implications emphasized by analysis:
  - Promoting R&D sectors and investing in human capital are important, particularly in large-market economies where R&D translates more readily into innovation.
  - For countries with weak domestic R&D effectiveness, policies that facilitate technology absorption (trade openness, reduced barriers to importing manufactured goods embodying foreign know-how) can raise innovation.
  - Institutional quality (expropriation risk) and trade liberalization emerge as important determinants of per capita income in multiple specifications.

*Source: _wp04185 (selected extracts: model, data, methods, empirical findings, and tables from the PDF chapter/section).*

### References..............................................................................................................

### References

### Endogenous growth framework and research question
- Focus: empirical investigation of R&D-based endogenous growth model postulations:
  1. R&D investment increases innovation and there are constant returns to innovation.
  2. Innovation leads to permanent increases in per capita GDP.
- The paper uses panel data techniques on a sample of 20 OECD and 10 non-OECD countries for the period 1981–97.
- Innovation is treated as the output of R&D activity; both inputs (R&D) and outputs (patents/innovation) are analyzed.

### Literature context and empirical motivation
- Endogenous growth theory (pioneered by Romer (1986)) links R&D, human capital, and knowledge stock to sustained output growth under constant returns to innovation.
- Prior empirical studies:
  - Jones (1995b): finds no positive relation between TFP growth and numbers of scientists and engineers in France, Germany, Japan, and United States.
  - Aghion and Howitt (1998): argue GDP share of R&D investment is a more appropriate measure than counts of scientists/engineers because of increasing technology complexity and product proliferation.
  - Scherer (1982), Griliches and Lichtenberg (1984), Aghion and Howitt (1998), Zachariadis (2003): provide evidence in U.S. that R&D investment and TFP growth are positively related.
  - Frantzen (2000); Griffith, Redding and Reenen (2002): confirm positive relationship between countries’ own R&D and productivity growth in international panels.
  - Coe, Helpman and Hoffmaister (1995); Griffith, Redding and Reenen (2002): find R&D spillovers from industrialized to developing countries raise TFP growth in the latter.
  - Savvides and Zachariadis (2003): show both domestic R&D and foreign direct investment increase domestic productivity and value added growth.
  - Porter and Stern (2000): utilize aggregate-level patent data; find innovation positively related to human capital in R&D sectors and national knowledge stock, with a significant but weak relationship between innovation and TFP growth.
- Zachariadis (2003): effect of R&D is higher for aggregate economy than manufacturing sector.

### Data, methods, and scope
- Sample: 20 OECD and 10 non-OECD countries, 1981–97.
- Empirical strategy: various panel data techniques, including fixed effects and Generalized Methods of Moments (GMM), with controls for technology spillovers, human capital, institutional quality, and trade liberalization.
- Innovation measure: aggregate-level patent data used alongside R&D variables to examine determinants and effects of innovation.

### Main empirical findings
- Innovation raises per capita output in both developed and developing countries:
  - A 1 percent increase in innovation raises per capita income by around 0.05 percent in both OECD and non-OECD countries.
- R&D increases innovation in some countries but not uniformly:
  - A 1 percent increase in R&D stock increases innovation by about 0.2 percent only in large market OECD countries (which includes the G-7).
  - Remaining OECD countries appear to increase innovation primarily via using know-how from other OECD countries (technology spillovers) rather than domestic R&D accumulation.
- Implications for endogenous growth models:
  - Results support the idea that innovation is endogenously created and promotes economic growth.
  - Findings do not support constant returns to innovation with respect to R&D: innovation appears to lead to only short term increases in the growth rate of output rather than perpetual growth.
- Caveat: patent and R&D data are not complete measures of innovation; lack of full measurement should temper interpretation regarding rejection of R&D-based growth models.

### Contributions relative to prior work
- Broader country coverage: examines effect of innovation on per capita GDP for both developed (OECD) and developing (non-OECD) countries rather than a small OECD-only sample.
- Methodological breadth: applies multiple econometric techniques to improve result accuracy and controls for a larger set of innovation and production determinants.

*Source: _wp04185 - References (excerpt). PDF chapter/section.*

### Section III explains the data and methodology; Section IV documents the statistical

### _wp04185 - Section III explains the data and methodology; Section IV documents the statistical

### II. The model (Romer (1990) framework)
- Empirical model builds on the R&D based growth model of Romer (1990).
- Three premises of Romer’s model:
  - (1) Growth is driven by technological change.
  - (2) Technological change arises as a result of intentional actions taken by people who respond to market incentives.
  - (3) Blue prints (designs) used to produce new products are nonrival (can be replicated with no additional cost).
- Model sectors: research and development (R&D) sector, intermediate goods sector, and final output sector.
- Final output production (Cobb-Douglas form) as presented (equation (1)):
  - Y = integral form with inputs H (human capital), L (labor), x (producer durables), and knowledge stock A; formula displayed in source as equation (1).
- Creation of new designs in R&D (equation (2)):
  - Ȧ = θ H_A A − δ A (presented in source as Ȧ = A_A H_A θ δ = ? — see equation (2) in text for exact form).
- Crucial postulate: production of new designs is linear in human capital employed in R&D and knowledge stock (i.e., θ = 1).
  - Implications when θ = 1:
    - Devoting more human capital to research leads to a higher rate of production of new designs.
    - Larger total stocks of designs and knowledge increase productivity of an engineer in the research sector.
- Durable goods accounting:
  - It takes η units of forgone consumption to create one unit of any durable.
  - Relation: K = η A x; substitution x = K / (η A) into production function yields final production function (equation (4), showing A enters affecting returns).
- Increasing returns to scale arise in both R&D and final output sectors because non-rival knowledge stock A is an input.
- Policy implication emphasized by author: countries can attain perpetual economic growth by promoting R&D sectors and investing in human capital.

### III. Description of data and methodology
- Data components:
  - Patent applications (NBER Patent Citations database): all utility patent applications in manufacturing sectors made in the U.S. Patent and Trademark Office by inventors residing in different countries.
    - Utility patents classified into five categories: chemical; computers and communication; drugs and medical; electrical and electronic; others.
    - "Others" include: agriculture-husbandry-food, amusement devices, apparel and textile, earth working and wells, furniture house fixtures, heating, pipes and joints, receptacles and the miscellaneous.
    - Patent counts for a country-year: sum of all utility patent applications made by inventors of that country.
    - Patent stock constructed using 20 percent depreciation rate.
    - Patent flows used are patent applications (not grants) to avoid long application-to-grant lags.
    - Rationale for U.S. patent office data: to isolate effects of different national regulations; all inventors face same regulations and quality control in U.S. PTO.
- Gross R&D expenditure (GERD):
  - Source: OECD Main Statistics and Technology Indicators database.
  - Defined as total expenditure on R&D performed on national territory during a given period; includes R&D performed within country and funded from abroad; excludes payments made abroad for R&D.
  - Components: R&D expenditure in business enterprises, government sector, higher education and non-profit firms.
  - Series deflated using the 1995 implicit price deflator and converted to U.S. dollars using monthly average exchange rates from the OECD database.
  - Gaps interpolated by averaging preceding and succeeding years.
  - R&D stock constructed using 20 percent depreciation rate.
- Other macroeconomic variables and data sources:
  - GDP, gross fixed investment, secondary school enrollments (WDI, 2002).
  - Labor population, imports and exports of manufacturing goods (OECD, 2002).
  - Openness in current prices (PWT.6).
  - Expropriation risk index (World Bank, International Country Risk Guide).
  - U.S. trade share (IMF Direction of Trade Database (IMFDOT)).
- Units and transformations:
  - All variables in constant 1995 U.S. dollars except variables that are share of GDP, patent counts, and expropriation risk index.
  - Expropriation risk index ranges from 1 to 10 (high values = low level of risk of expropriation).
  - Trade in manufacturing goods = imports + exports in constant 1995 U.S. dollars.
  - Each country’s GDP share of U.S. trade = (total exports and imports of United States to and from partner country) / country GDP.
  - Gross ratio of secondary school enrollment = total enrollment (regardless of age) / population of the age group that officially corresponds to secondary school level.
  - Secondary school enrollment series available every five years; gaps interpolated using moving averages of five-year observations (example interpolation method given).
- Patent stock initial formula and subsequent updates:
  - Initial patent stock: Ps = P_t / (r + δ) (formula displayed in source as )/(1 δ+= − rPPs tt — see source for exact notation).
  - Subsequent years: Ps_t = (1 − δ) Ps_{t−1} + P_t (presented in source as 1)1( − −+= ttt PsPPsδ).
- Sample construction notes:
  - Some samples include non-OECD countries where R&D data are not used.
  - Countries grouped by aggregate GDP and investment rankings into "large-market" (first nine) and "small-market" (last nine).
  - Countries ranked by per capita GDP and investment: first nine = higher income countries; last nine = lower income countries.
  - Lists of countries in each sample are provided in Table 5.

### IV. Statistical analysis of data and stylized facts
- Time coverage and general properties:
  - Data examined for 1981–97 period in many tables and figures.
  - Panel unit root and heteroskedasticity findings: data do not have unit root and heteroskedasticity (in most countries), though they exhibit first order autocorrelation.
  - First order autocorrelation addressed by differencing data or using Prais-Winsten estimation.
- Cross-country rankings and correlations (Tables 3 and 4 summaries):
  - Table 3 (aggregate, 1981–97): G-7 countries are highest in aggregate GDP, investment, R&D and patent applications; Greece, Portugal, Ireland, New Zealand and Iceland are lowest ranks for all four variables.
    - Example aggregate figures from Table 3 (exact values preserved):
      - Investment rank 1: Japan 1,244,578 (millions 1995 U.S. dollars)
      - GDP rank 1: Japan 4,442,000 (millions 1995 U.S. dollars)
      - Patents rank 1: Japan 19,286
      - R&D Expenditure rank 1: Japan 86,412 (millions 1995 U.S. dollars)
    - Out of nine countries with both higher GDP and investment, eight also have higher R&D expenditure and patent applications → suggests positive correlation among these variables.
  - Table 4 (per capita, 1981–97): Switzerland and Japan rank highest in per capita levels; Portugal, Greece, Spain, and Ireland rank lowest in per capita GDP, investment, R&D and patents.
    - Example per capita figures from Table 4 (exact values preserved):
      - Per capita GDP rank 1: Switzerland 42,824
      - Per capita Investment rank 1: Japan 10,153
      - Per capita Patents rank 1: Switzerland 176 (per 100 mn)
      - Per capita R&D rank 1: Switzerland 870 (per 10 mn)
    - Of top ten countries in per capita patent, eight also rank high in per capita R&D; seven rank high in per capita GDP → positive relationship among per capita GDP, investment, patents and R&D.
- Country-group comparisons (Figures 1–4):
  - Country groups analyzed: OECD, non-OECD, large and small-market OECD, and high-income and low-income OECD countries (group construction per Table 5).
  - Figure 1 (average per capita levels of R&D and patents, 1981–97):
    - High income and large market OECD countries have highest per capita R&D expenditure and patent applications; low income and small market OECD countries have lowest.
    - Conclusion: income level and market size positively correlated with per capita R&D and patents; per capita R&D and patents are positively correlated.
  - Figure 2 (average growth rates of per capita R&D and patents, 1982–97):
    - Income level and market size positively associated with growth rate of R&D expenditure; negatively associated with growth rate of patents.
    - Positive relationship observed between per capita R&D growth rates and per capita patent growth rates.
  - Figure 3 (average per capita GDP and patents, 1981–97):
    - High-income OECD countries have highest per capita GDP and patents; low-income OECD and non-OECD countries have lowest.
    - Within OECD, market size positively associated with both per capita GDP and patent applications.
  - Figure 4 (average growth rates of per capita GDP and patents, 1982–97):
    - Growth rates negatively related with income level and market size (high-income and large-market OECD have lowest growth rates).
    - Both levels and growth rates of per capita GDP and patents are positively related across country groups.
- Time-series behavior (Figures 5 and 6):
  - Time series plots indicate per capita GDP, investment, R&D, and patent applications move closely over time in majority of countries.
- Summary stylized facts:
  - Cross-sectional and time-series comparisons reveal levels and growth rates of GDP, investment, R&D and patent applications are positively correlated across countries and over time.
  - These empirical observations are consistent with R&D based growth model premises: positive association between R&D and innovation, and between innovation and per capita GDP.

### V. Empirical analysis — estimation approach overview
- Estimation methods used:
  - Fixed-effects regressions.
  - Arellano-Bond GMM estimators.
  - Ordinary Least Squares (OLS) used as benchmark.
- Methodological notes:
  - Fixed-effects: accounts for country fixed effects; consistent if no endogeneity and no lagged dependent variable included.
  - Arellano-Bond GMM: accounts for country fixed effects and yields consistent estimators when lagged dependent variable included; includes instrumented lagged dependent variable to address endogeneity to some extent.
  - GMM uses first differences which may cause loss of information; both FE and GMM results reported, with more focus on GMM.
  - First-order autocorrelation addressed by Prais-Winsten or first-differencing.
  - Time dummies included in all regressions to control for time trend and common shocks.
  - Empirical analysis undertaken for nine samples (sample definitions per earlier notes and Table 5).
- Innovation function estimation (derivation from model equation (2)):
  - The innovation production equation (equation (5) in source):
    - Ȧ = A^θ H_A (presented as Ȧ = θ A H_A = ? — see source for exact notation).
  - Log-linearized version (equation (5′)):
    - Log Ȧ = θ Log A + Log H (presented in source as .()()( ).Log ALog ALog Hθ=+ (see source for exact notation)).
  - Interpretation: a 1 percent increase in A increases innovation by 1 percent; a 1 percent increase in H increases innovation by θ percent. Romer’s model predicts θ = 1 for sustained continuous output growth.

*Italic: Source — _wp04185 - Section III explains the data and methodology; Section IV documents the statistical*

### section is allocated for the estimation of θand other determinants of innovation using

### _wp04185 - section is allocated for the estimation of θand other determinants of innovation using

### Estimation approach and data
- Empirical analysis uses international panel data from 19 OECD countries for the period 1981-1997.
- Methods:
  - Fixed-effects regressions.
  - Arellano-Bond Linear GMM (Arellano and Bond (1991); STATA 8 reference).
  - GMM validity requires no AR(2) in differenced errors and regressors not correlated with the error term; AR(2) and Sargan test results are reported for each GMM estimation.
- Key variables and measurement:
  - Flows of innovation (Ȧ) measured by patent applications (patent flows), normalized by labor.
  - Human capital in R&D sector (H) proxied by stock of R&D expenditure (R&D stock), normalized by labor.
  - Knowledge stock (A) not directly observed; addressed by:
    - Using R&D stock to proxy accumulated knowledge and human capital in R&D.
    - Using the first lag of patent flows in GMM as an instrument for knowledge stock.
    - Accounting for initial differences in knowledge stock via fixed effects and GMM.
  - Other controls: expropriation risk index, imports of manufacturing goods as share of total trade in manufacturing goods, share of U.S. trade in each country’s GDP, secondary school enrollments (as overall human capital).
- Samples analysed:
  - Full Sample, Non-OECD, OECD; OECD further grouped into low income, high income, small market, and large market OECD countries (Chow test indicates coefficients are not constant across groups).

### Fixed-effects regression results (summary of Table 6)
- R&D stock:
  - Positive and significant in G-7, other large market OECD countries, and low-income OECD countries.
  - Elasticities reported:
    - G-7 and large market countries: a 1 percent increase in per capita R&D stock increases innovation by 0.40 percent.
    - Low-income OECD countries: a 1 percent increase in per capita R&D stock increases innovation by 0.50 percent.
- Secondary school enrollments:
  - High t values in large market and low-income OECD countries, but not statistically significant in any sample.
- Expropriation risk:
  - Significant only in large market OECD countries, including G-7.
- U.S. share of GDP:
  - Significant in G-7, large market OECD, and low-income OECD countries only.
- Manufacturing import share (imports of manufacturing goods as share of total trade in manufacturing goods):
  - Positive and significant in countries that do not have a significant R&D coefficient — suggesting use of foreign know-how where domestic R&D is ineffective.
- Table 6 model diagnostics and sample sizes (selected):
  - R-squared reported as 0.99 across samples.
  - Observations: Full 285; Non-G-7 210; G-7 75; Large Market 135; Small Market 120; High-Income 135; Low-Income 120.
  - Number of ifs (countries) reported: Full 19; Non-G-7 14; G-7 5; Large Market 9; Small Market 8; High-Income 9; Low-Income 8.
- Notes:
  - All variables are in natural logs and normalized by labor. All regressions include time dummies.
  - Greece excluded due to missing imports in manufacturing sector.

### Arellano-Bond GMM results (summary of Table 7 and Table 8)
- R&D stock (second lag, GMM):
  - Significant only in large-market OECD (including G-7) and low-income OECD countries.
  - Elasticities reported:
    - Large market OECD including G-7: around 0.20 percent increase in innovation for a 1 percent increase in R&D stock (Table 7 entry: Second lag of R&D stock = 0.162 for G-7; 0.231 for Large Market).
    - Low-income OECD: around 0.30 percent increase (Table 7: Second lag of R&D stock = 0.298).
  - Table 8 (Low Income OECD subgroups):
    - Low Income OECD — Large Market: second lag of R&D stock = 0.513 (z = (4.50)).
    - Low Income OECD — Small Market: second lag of R&D stock = -0.423 (z = (1.01)).
- Patent-flow lag effects:
  - First lag of per labor patent is positive and significant in all country groups, with magnitude around 0.3 (Table 7: e.g., Full 0.297 (4.26); Non-G-7 0.304 (3.72); G-7 0.309 (2.42); Large Market 0.576 (6.99); Low Income 0.317 (3.89)).
  - Interpretation: previous-year knowledge flows have a strong positive effect on current innovation; if interpreted as instrumenting knowledge stock, a 1 percent increase in knowledge stock leads to a 0.3 percent increase in innovation.
- Manufacturing import/trade:
  - Significant and positive for countries without effective R&D sectors in GMM results (Table 7: Full 1.844 (2.89); Non-G-7 1.761 (2.17); Small Market 2.633 (2.29); High Income 4.226 (3.72)).
- Other controls:
  - Secondary school enrollments significant mainly in G-7 in GMM results (Table 7: G-7 second lag of Secondary school = 0.184 (1.84)).
  - Economic alliance with the United States (U.S. trade/GDP) and openness generally do not show consistent significance for patent applications in the U.S.; institutional quality matters only in OECD countries with large markets.
- GMM diagnostics (Table 7 excerpts):
  - Sargan test (p-values) and AR(2) test (p-values) reported per sample; examples:
    - Full sample: Sargan p-value 0.00; AR(2) p-value 0.38.
    - Non-G-7: Sargan p-value 0.09; AR(2) p-value 0.56.
    - G-7: Sargan p-value 0.01; AR(2) p-value 1.00.
  - Observations and number of countries (selected): Full 247 observations, 19 countries; Non-G-7 182 observations, 14 countries; G-7 70 observations, 5 countries; Large Market 126 observations, 9 countries; Low Income 117 observations, 9 countries; Small Market 112 observations, 8 countries.
- Table 8 (Low Income OECD subgroup GMM):
  - Low Income OECD — Large Market:
    - Second lag of R&D stock = 0.513 (4.50).
    - U.S. trade/GDP = 0.516 (3.90).
    - First lag of per labour patent = 0.299 (2.40).
    - Observations 70; Number of countries 5.
    - Sargan p-value 1.00; AR(2) p-value 0.19.
  - Low Income OECD — Small Market:
    - Second lag of R&D stock = -0.423 (1.01).
    - U.S. trade/GDP = 0.715 (1.09).
    - Observations 42; Number of countries 3.
    - Sargan p-value 1.00; AR(2) p-value 0.34.

### Synthesis of innovation regressions — main conclusions (as stated in text)
- R&D intensity changes across countries with different market sizes and income levels.
- Only large market OECD countries (including the G-7 and some low-income OECD countries) increase innovation by investing in R&D sectors.
- There are no constant returns to innovation in the observed data.
- Technology spillovers (measured via imports in manufactured goods as share of trade in manufacturing goods) have significant effects on innovation for countries without efficient R&D sectors.
- Results are consistent with R&D-based growth models where innovation is endogenously created, but do not support constant returns to innovation — possibly due to data limitations in capturing the full range of innovation activities.

### B. Estimation of production function (relationship between innovation and per capita GDP)
- Model and variables:
  - Production function (equation (6)): Y = function(L, H, K, A) with constant returns to scale in L, H and K; increasing returns via knowledge stock A.
  - Regression uses variables normalized by labor; K decomposed into new products and physical investment; log-linearized regression equation shown as (6’).
  - Variables in regression:
    - yt: per labor output.
    - it: investment (measured by gross fixed investment).
    - xt: new products (measured by stock of patent applications from the U.S. Patent Office).
    - ht: human capital measured by secondary school enrollments as share of the relevant population.
    - Risk of expropriation index and openness included as controls.
  - Data include 20 OECD countries and 10 non-OECD countries for 1981–97.
- Fixed-effects regression results (Table 9 summary in text):
  - Patent stock:
    - Positive and significant in all samples except the G-7.
    - Magnitudes:
      - Non-OECD countries: 0.11 (highest returns to patent stock).
      - Small market OECD countries: around 0.06 (lowest returns).
      - All other countries: around 0.07 percent increase in per capita GDP for 1 percent increase in patent stock.
  - Investment:
    - Positive and significant in all samples.
    - Magnitudes range from 0.24 in high income OECD countries to 0.37 in non-OECD countries.
  - Secondary school enrollments:
    - Expected sign and high t values in many samples, statistically significant only in low-income OECD countries with magnitude 0.08.
  - Openness and expropriation risk:
    - Positive and significant in most samples — trade liberalization and institutional quality important determinants of per capita income levels.
- GMM estimation results (Table 10 summary in text):
  - Similar to fixed effects: patent stock positive and significant in all samples except the G-7.
  - Differences from fixed effects:
    - Large market and high-income OECD countries show higher returns to patent applications (0.06 percent) compared to the rest of samples (0.04 percent).
  - Returns to investment are positive and significant in all samples.
    - Example: a 1 percent increase in investment increases output by around 0.10 percent in the high income, low income and small market OECD countries (textual statement).

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04185.pdf*

### 0.17 percent in the non-G-7, non-OECD and large market OECD countries; 0.20 percent in

### _wp04185 - 0.17 percent in the non-G-7, non-OECD and large market OECD countries; 0.20 percent in the OECD, and 0.25 percent in the G-7 countries. Returns to schooling are not significant in any of the samples, presumably as a result of the small variation in this variable over time.

### Regression methods and samples
- Estimation approaches reported:
  - Pooled OLS (referenced in text; detailed OLS results in Appendix I, Table 13).
  - Fixed effects regression (Table 9) for per labor GDP, 1981–97.
  - Generalized methods of moments (GMM) regression (Table 10) for per labor GDP, 1981–97.
- Sub-samples analyzed: Full sample, Non-OECD, OECD, Non-G-7, G-7, Large market, Small market, High income, Low income.
- Data and variable notes:
  - All variables in Table 9 are in natural logs and normalized by labor. All regressions include time dummies.
  - Table 10 variables are log differenced once. GDP, investment, and patent stock normalized by labor. All regressions include time dummies.
  - Sources include: R&D stock (OECD, 2002), patent applications (NBER Patent Citation Database), openness (PWT 6), employment (WEO, 2002), corruption index (World Bank, International Country Risk Guide), import/trade (OECD, 2002), U.S. trade (IMF Direction of Trade Database), WDI (2002).

### Key empirical findings (summary of text and tables)
- General findings reported in the narrative:
  - Returns to investment are positive and significant in all samples (pooled OLS results).
  - Returns to patent stock are significant only in the full, OECD and non-OECD samples (pooled OLS).
  - The risk of expropriation and openness variables are significant with the expected signs in most samples (pooled OLS).
  - Returns to schooling are not significant in any of the samples, likely due to small variation over time.
  - Patent stock may not be significant in the G-7 sample possibly because of the small size of this sample.
  - In some samples (full and OECD), the coefficient of secondary school enrollment is negative and significant in OLS, but those models suffer from serial correlation between regressors and residuals (low p values of the Sargan test).

- Selected Fixed Effects (Table 9) coefficients and statistics (per labor GDP, 1981–97):
  - Full Sample:
    - Investment: 0.312 (24.46)
    - Second lag of patent stock: 0.104 (9.18)
    - Second lag of secondary school: 0.009 (0.41)
    - Openness: 0.025 (1.43)
    - Expropriation Risk: -0.025 (1.72)
    - R-squared: 0.99
    - Observations: 449
    - Number of countries: 30
  - OECD sample (illustrative):
    - Investment: 0.274 (16.79)
    - Second lag of patent stock: 0.076 (4.94)
    - Openness: 0.071 (2.90)
    - Expropriation Risk: 0.131 (4.66)
    - Observations: 300
    - Number of countries: 20
  - G-7 sample (illustrative):
    - Investment: 0.296 (7.39)
    - Second lag of patent stock: 0.023 (0.87)
    - Expropriation Risk: 0.174 (2.09)
    - Observations: 75
    - Number of countries: 5
  - (Table 9 contains comparable coefficient estimates and z statistics for other sub-samples: Non-OECD, Non-G-7, Large market, Small market, High income, Low income.)

- Selected GMM (Table 10) coefficients and statistics (per labor GDP, 1981–97):
  - Full Sample:
    - Investment: 0.206 (11.82)
    - Second lag of patent stock: 0.040 (3.35)
    - Second lag of secondary school: -0.044 (2.06)
    - Openness: 0.056 (3.74)
    - Expropriation risk: -0.048 (3.74)
    - First lag of GDP: 0.447 (7.52)
    - Fourth lag of GDP: 0.188 (5.36)
    - Constant: 0.025 (4.69)
    - Sargan test (p-value): 0.00
    - AR(2) test (p-value): 0.57
    - Observations: 359
    - Number of countries: 30
  - OECD sample (illustrative):
    - Investment: 0.194 (9.44)
    - Second lag of patent stock: 0.058 (4.17)
    - Openness: 0.135 (6.14)
    - First lag of GDP: 0.542 (8.71)
    - Constant: 0.006 (2.75)
    - Sargan test (p-value): 0.12
    - AR(2) test (p-value): 0.84
    - Observations: 280
    - Number of countries: 20
  - Non-OECD sample (illustrative):
    - Investment: 0.173 (6.54)
    - Second lag of patent stock: 0.038 (1.84)
    - Second lag of secondary school: -0.055 (1.05)
    - Openness: -0.012 (0.51)
    - First lag of GDP: 0.582 (6.29)
    - Constant: 0.049 (4.00)
    - Sargan test (p-value): 0.02
    - AR(2) test (p-value): 0.42
    - Observations: 119
    - Number of countries: 10
  - (Table 10 contains comparable coefficient estimates, lag structures of GDP, Sargan and AR(2) p-values, and observations/counts for other sub-samples: Non-G-7, G-7, Large market, Small market, High income, Low income.)

### Robustness, tests, and diagnostics
- Fixed effects regressions report very high R-squared values (0.99) across samples in Table 9.
- GMM diagnostics in Table 10 include Sargan test (H0: regressors are not correlated with the residuals) and AR(2) test (H0: errors in first difference regression exhibit no second order serial correlation). Reported p-values vary by sub-sample (examples above).
- Notes indicate some OLS models (full and OECD) suffer from serial correlation between regressors and residuals as indicated by low p values of the Sargan test.

### Specific patterns and notable contrasts
- Investment:
  - Positive and statistically significant across estimation methods and sub-samples (examples: FE full sample 0.312 (24.46); GMM full sample 0.206 (11.82)).
- Patent stock:
  - Significant in several samples (FE full: 0.104 (9.18); GMM full: 0.040 (3.35)), but not significant in the G-7 FE estimate (0.023 (0.87)), possibly due to small sample size.
- Openness (trade liberalization):
  - Positive and significant in many samples (GMM full: 0.056 (3.74); GMM OECD: 0.135 (6.14); FE OECD: 0.071 (2.90)), but not significant in some samples (text: effect positive and significant in all samples except for the G-7, large market OECD, and non-OECD countries).
- Expropriation risk:
  - Generally associated with negative coefficients in the full sample (FE full: -0.025 (1.72); GMM full: -0.048 (3.74)), but positive and significant in some OECD-related sub-samples in FE (e.g., FE OECD: 0.131 (4.66)).
- Secondary school enrollment:
  - Not significant in most samples; sign and significance vary across methods and samples (examples: FE full 0.009 (0.41); GMM full -0.044 (2.06)).

*Source: _wp04185 (selected extracts from Tables 9 and 10, and accompanying text).*

### 0.14 percent increase in per labor GDP in the non-G-7 and the OECD countries with small

### _wp04185 - 0.14 percent increase in per labor GDP in the non-G-7 and the OECD countries with small markets; and about a 0.09 percent increase in the high income and low-income OECD countries.

### Key empirical findings on innovation and GDP
- Innovation (patent stock) has a strong positive relationship with per capita GDP in both OECD and non-OECD countries.
- Estimated impacts on per labor GDP:
  - 0.14 percent increase in per labor GDP in the non-G-7 and the OECD countries with small markets.
  - about a 0.09 percent increase in the high income and low-income OECD countries.
- Expropriation risk index:
  - Coefficient signs are as expected and significant in most samples.
  - Highest magnitudes reported: 0.20 in the G-7 and 0.11 in large market OECD countries (sample references as reported).
- Only OECD countries with larger markets (including the G-7, Australia, Netherlands, Spain, and Switzerland) are able to increase innovation by investing in R&D; other OECD countries appear to promote innovation through technology spillovers from other OECD countries.

### Total factor productivity (TFP) and innovation (from Table 11)
- First lag of TFP:
  - Full sample: 0.789 (z: 19.66)
  - OECD: 0.876 (z: 22.13)
  - Non-OECD: 0.726 (z: 12.10)
- Second lag of patent stock (TFP regressions):
  - Full sample: 0.012 (z: 1.53)
  - OECD: 0.016 (z: 1.25)
  - Non-OECD: 0.035 (z: 2.58) — patent stock coefficient significant only for non-OECD countries, suggesting innovation increases per capita GDP partly through its effect on TFP in non-OECD.
- Other coefficients reported in Table 11:
  - Second lag of secondary school: Full 0.029 (1.54); OECD 0.021 (1.31); Non-OECD 0.025 (0.67).
  - Openness: Full 0.001 (0.11); OECD 0.019 (1.00); Non-OECD 0.005 (0.28).
  - Expropriation risk: Full -0.038 (3.40); OECD -0.060 (2.64); Non-OECD -0.006 (0.29).
- Diagnostic tests (Table 11):
  - Sargan test p-values and AR(2) test p-values reported; for example, full sample Sargan test p-value 0.00 and AR(2) p-value 0.53, indicating model rejection by Sargan in some samples (the text notes the full and OECD samples are not conclusive as the model for these samples have been rejected by the sargan test).
- Sample sizes (Table 11):
  - Full: Observations 419, Number of countries 30.
  - OECD: Observations 280, Number of countries 20.
  - Non-OECD: Observations 139, Number of countries 10.

### Per-labor patent flow and per-labor GDP OLS results (selected coefficients)
- Per-labor patent flows (Table 12, OLS, 1981–97) — selected coefficients and contexts:
  - Initial patent flows: Full 1.118 (27.33); Non-G-7 1.046 (26.32); G-7 0.640 (9.40); Large Market 0.572 (11.96); Small Market 1.193 (19.67); High Income 1.056 (14.72); Low Income 0.923 (9.85).
  - Second lag of R&D stock: Full -0.194 (3.30); Non-G-7 -0.153 (2.37); G-7 0.298 (4.48); Large Market 0.428 (5.48); Small Market -0.291 (3.99).
  - Expropriation risk index: Full -0.511 (1.05); Non-G-7 -0.951 (1.65); G-7 0.238 (0.82); Large Market 0.706 (3.10); Small Market -2.021 (2.36).
  - Manufacturing import/trade: Full 1.253 (2.11); Non-G-7 1.480 (2.11); G-7 0.748 (2.31).
  - Openness and U.S. trade/GDP coefficients vary by subsample (values reported in Table 12).
  - R-squared reported as 0.99 across subsamples; observations and number of countries reported per subsample (e.g., Full observations 285, number of countries 19).

- Per-labor GDP (Table 13, OLS, 1981–97) — selected coefficients:
  - Initial GDP: Full sample 0.705 (25.66); Non-OECD 0.408 (12.08); OECD 0.597 (12.91); Non-G-7 0.620 (9.29); G-7 0.695 (11.12); Large Market 0.479 (6.90); Small Market 0.752 (9.49).
  - Investment: Full 0.295 (23.16); Non-OECD 0.482 (23.34); OECD 0.254 (13.94); other subsample values reported in Table 13.
  - Second lag of patent stock (per-labor GDP regressions): Full 0.022 (3.47); Non-OECD 0.075 (6.29); OECD 0.020 (3.06); G-7 0.009 (0.93); other subsample values reported in Table 13.
  - Openness and expropriation risk coefficients vary by subsample; R-squared reported as 0.99 across subsamples; observations and number of countries reported per subsample (e.g., Full observations 449, number of countries 30).

### Additional data summaries and diagnostics
- Correlation patterns (Table 14) highlight strong positive correlations among GDP, investment, patent stock, and R&D stock in full and OECD samples (e.g., GDP–Investment 0.97* in full sample; GDP–Patent stock 0.92* in full sample).
- Summary statistics (Table 15) — selected levels (preserved exactly as presented):
  - Full sample:
    - GDP: N 523; Min 505; Max 83,442; Mean 38,018; Median 40,166; Std Dev 22,330.
    - Investment: N 509; Min 251; Max 24,888; Mean 8,085; Median 7,819; Std Dev 4,985.
    - Patents: N 523; Min 0.01; Max 429; Mean 69; Median 39; Std Dev 88.
    - R&D Expenditure: N 340; Min 65.80; Max 2,780; Mean 776; Median 700; Std Dev 485.
    - Expropriation risk: N 523; Min 3.25; Max 11.00; Mean 8.74; Median 9.00; Std Dev 1.65.
  - OECD and Non-OECD subsample summary statistics reported in Table 15.
- Growth-rate summary statistics (Table 16) and sample country codes (Table 17) are reported in the appendix.

### Interpretation and policy-relevant conclusions
- The empirical results support endogenous growth frameworks in two respects:
  - A significant relationship between R&D stock and innovation.
  - A significant relationship between innovation (patent stock) and per capita GDP.
- Market size matters:
  - Only large-market OECD countries (including the G-7 and specified OECD members) are able to convert R&D investment into increased innovation, supporting theories emphasizing market size for effective R&D sectors (Acemoglu and Linn (2003) as cited in text).
  - OECD countries without effective R&D sectors appear to rely on technology spillovers from other OECD countries.
- Limits to full endogeneity:
  - The analysis does not find evidence for constant returns to innovation in terms of R&D stock, implying diminishing returns and that R&D-based models alone may not fully explain sustainable long-run growth.
  - The authors caution that patent and R&D data are incomplete measures of innovation and research activities; results should not be interpreted as a rejection of R&D models.
  - Even with diminishing returns to innovation from R&D, R&D models can still explain long-term growth if there are constant returns to produced factors such as capital, innovation, and knowledge stock (Aghion and Howitt (1998) as cited in text).

*Italic — Source: _wp04185 - 0.14 percent increase in per labor GDP in the non-G-7 and the OECD countries with small markets; and about a 0.09 percent increase in the high income and low-income OECD countries (PDF content provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04185.pdf_