## _wp0467 - References

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### Introduction: research context and contribution
- Early work (Aschauer (1989a,b)) reported large positive output effects of government capital; later surveys (Gramlich (1994); Sturm, de Haan, and Kuper (1998); Seitz (2001)) find positive effects but generally much smaller magnitudes.
- Empirical constraint: lack of internationally comparable public capital stock data; most studies focus on the United States.
- Recent empirical trend: use of vector autoregressive (VAR) models to avoid imposing causal links; VARs often use public investment flows (quarterly) instead of public capital stocks (annual), implying an assumption of independence from capital stock level despite evidence of diminishing returns.
- Contribution of this paper:
  - Provides internationally comparable annual capital stock estimates for 22 OECD countries for 1960–2001 using the perpetual inventory method with geometric depreciation.
  - Estimates three investment categories: (1) private nonresidential gross fixed capital formation, (2) private residential gross fixed capital formation, (3) government gross fixed capital formation.
  - Sensitivity analysis for United States and Canada shows benchmark estimates are robust.
  - Compares production-function results using three public capital measures: author’s own, national authorities’, and OECD (1997).
  - Reports positive, statistically significant elasticity of output with respect to public capital; simple panel model yields average elasticity of 0.2 in OECD countries.

### Data: sources, coverage, and comparability issues
- Primary data source: June 2002 version of the OECD Analytical Database.
- Countries covered (22): Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.
- Series extracted: ITV (total gross fixed capital formation), IPV (total private gross fixed capital formation), IBV (private nonresidential GFCF), IHV (private residential GFCF), IGV (government GFCF).
- Time coverage: for most countries, 1960–2001.
- Public investment definitions vary across countries:
  - General government;
  - Nonfinancial public sector (general government plus NFPEs);
  - ISIC-based activity definitions: narrow and broad (broad may include private education spending).
- Stylized pattern: public investment–GDP ratio generally declined 1960–2001; pronounced declines in Austria and Ireland; increases in Greece, Portugal, and Spain since 1980s accession to the European Community.
- Cross-source discrepancies: OECD Analytical Database generally aligns with national sources except for Belgium, Canada, Italy, Japan, and Spain; OECD (1997) differs substantially in many cases due to 1968 SNA versus 1993 SNA and differing coverage.

### Methodology: perpetual inventory method (PIM) and key assumptions
- Estimation method: perpetual inventory method with geometric depreciation (following OECD (2001a) and U.S. BEA (1999)).
- Capital accumulation identity used:
  - K_{t+1} = (1 − δ) K_t + I_t
  - Infinite-sum representation under geometric depreciation: K_{t+1} = ∑_{i=0}^{∞} (1 − δ)^{i+1} I_{t−i}; implemented in practice with finite sum and initial capital stock K_1.
- Inputs and choices:
  - Gross investment flows from OECD Analytical Database, initial capital stock at beginning of 1960, assumption on magnitude and time profile of depreciation (geometric).
- Initial capital stock treatment:
  - No official information except for the United States (BEA series from 1914).
  - Constructed artificial investment series for 1860–1959 assuming investment increased by 4 percent a year to reach observed 1960 level.
  - Rationale: total gross investment in the 22 OECD countries grew by 4 percent a year on average during 1960–2001.
  - Sensitivity analysis indicates initial capital stock assumption has limited impact: contribution to capital stock level at end of sample is less than 10 percent on average.

### Depreciation assumptions and implicit scrapping rates
- Depreciation assumptions:
  - Time-varying for public capital and private nonresidential capital.
  - Constant for private residential capital.
- Implicit scrapping rate defined as:
  - s_t = 100 ⋅ (D_t / K_t)
- Assumed depreciation rates:
  - For 1860–1960: government 2½ percent, private nonresidential 4¼ percent, residential 1½ percent.
  - For 1960–2001: government gradually increases from 2½ percent to 4 percent; private nonresidential gradually increases from 4¼ percent to 8½ percent; private residential constant at 1½ percent.
- Empirical U.S. patterns (1960–2000):
  - Private nonresidential implicit scrapping rate rises from about 4½ percent in 1960 to about 9½ percent in 2000.
  - Private residential scrapping rate roughly constant over 1960–2000.
  - Government and private nonresidential scrapping rates tended to rise over time.
- Explanations: increasing weight of short-lived assets and shortening of asset lives (ICT-related), more pronounced for private nonresidential capital.

### Perpetual inventory implementation details and productive capital stock
- Capital stock constructed assuming new investment placed in service at midyear and geometric depreciation.
- K_1860 set equal to zero in formalization.
- Estimated public net capital stock corresponds to the “productive capital stock” (OECD (2001b, p. 62–63)), appropriate for productivity analyses.
- Practical limitation: public investment treated as homogeneous asset due to lack of disaggregated public investment data.

### Capital stock estimates for 22 OECD countries, 1960–2001: levels, ratios, and per capita
- Cross-country presentation: author’s estimates compared with available national and OECD (1997) estimates in Figure 3 (not reproduced here).
- German reunification adjustment: at beginning of 1991 East German capital stock set equal to 8 percent of West German capital stock (ratio of East to West GDP in 1991); capital stock increased by 8 percent and then depreciated normally from 1991 on.
- Table 2 highlights (government capital stock / GDP ratios in percent):
  - Average (unweighted) government capital–GDP ratio: 1980 57.8, 1990 55.3, 2000 51.4.
  - Average Reliability (contribution of 1960–1999 investment to 2000 net stock): 92.1 (unweighted average); standard deviation of Reliability 3.0.
  - Country-specific examples (Ratio in 2000, Rank, Reliability):
    - Japan: 117.1 (Rank 1), Reliability 97.0.
    - Ireland: 35.2 (Rank 22), Reliability 92.9.
    - United States: 50.0 (Rank 10), Reliability 89.4.
  - Average decline over 1980–2000: average public capital–GDP ratio declined by 6 percentage points.
  - Contribution of investment since 1960 to 2000 net stock: average 92 percent; assumed 1860–1959 contribution average 8 percent; country range of initial-contribution: 14.3 percent (Denmark) to 3.0 percent (Japan).
- Table 3 highlights (government net capital stock per head at 2000 PPPs, U.S. dollars):
  - Average (unweighted) public capital stock per person: 1980 9,270.8; 1990 10,883.6; 2000 12,137.1.
  - Average growth 1980–2000: increased by 30.9 percent (1.4 percent per year).
  - Country-specific examples (Capital per head in 2000, Rank):
    - Japan: 31,692.8 (Rank 1).
    - United States: 16,397.4 (Rank 2).
    - Portugal: 6,582.0 (Rank 22).
  - Noted that growth of public capital per head was lower than growth of real GDP, consistent with declining public capital–GDP ratio on average.
  - Greece, Portugal, Spain experienced faster-than-average increases in public capital per head over 1980–2000 due to infrastructure enhancements after European Community accession.

### Robustness checks and sensitivity analysis (Section V)
- Key assumptions tested:
  1. Investment growth of 4 percent per year in 1860–1959 to reach observed 1960 level.
  2. Time-varying depreciation rates increasing for all asset types except residential.
  3. Geometric depreciation.
- Sensitivity checks for United States and Canada compared benchmark estimates with alternatives and official series:
  - Initial capital stock construction variants (U.S.):
    - Benchmark: BEA public investment series for 1914–60 chained with OECD 1960–2001; assume 4 percent growth in 1860–1914.
    - Alternative: assume 4 percent growth in 1860–1959.
    - Steady-state approach (Fuente and Doménech, 2002) where K_t ≈ I_t / (δ_t + g_t); average growth rate of U.S. government investment 1960–2001 was 2.7 percent.
    - Findings: for 1960–2000, levels and dynamics of public capital stock series under alternatives are “almost indistinguishable”; differences mostly around 1940–50 and are short-lived; formal tests cannot reject equality of means and variances of growth rates versus BEA.
  - Depreciation-profile alternatives:
    - Alternative 1: increase from 3 percent to 6 percent over 1960–2001.
    - Alternative 2: constant depreciation equal to average implicit scrapping rate (3½ percent for government assets).
    - Findings: constant 3½ percent overestimates 1990s growth; steeper 3–6 percent profile underestimates growth in 1970s and early 1980s; benchmark profile judged most sensible.
  - Depreciation-method alternatives (Canada):
    - Straight-line, hyperbolic, geometric.
    - Hyperbolic and geometric yield similar estimates; straight-line differs considerably.
    - Author’s geometric estimates generally lower than Statistics Canada’s geometric series but higher than its linear series; dynamics similar except in the 1960s.
    - Formal tests on growth rates of geometric series cannot reject equality.
- Conclusion: benchmark public capital estimates appear sensible and robust for United States and Canada; visual inspection and formal tests support plausibility.

### Production-function approach: tests and regression results
- Production function specification estimated (Cobb-Douglas in logs):
  - yt = a0 + a1 t + α kP,t + β lt + γ kG,t + εt
  - If nonstationary and not cointegrated, first-difference formulation used: Δyt = a1 + α ΔkP,t + β Δlt + γ ΔkG,t + υt
- Unit root and cointegration diagnostics:
  - Augmented Dickey-Fuller tests on 165 variables: vast majority nonstationary in levels; panel tests (Levin, Lin, and Chu (2002); Im, Pesaran, and Shin (2003)) suggest integration of order 1.
  - Engle-Granger tests on levels fail to reject null of no cointegration in reported individual-country cases; model estimated in first differences.
  - Inference uses Newey and West (1987) HAC covariance estimator.
- Individual-country regression results (United States and Canada; estimated mostly in first differences):
  - Private capital defined as private nonresidential + private residential.
  - Benchmark private depreciation: private nonresidential increases from 4¼ percent to 8½ percent; private residential constant at 1½ percent.
  - Individual-country estimated elasticities of output w.r.t. public capital range from 0.40 to 0.86 (all statistically significant and positive) — implying "supernormal" returns per Aschauer (1995).
  - Regression anomalies: labor coefficients larger than one; private capital coefficients negative in many individual regressions (often statistically insignificant), suggesting functional-form, exogeneity, or multicollinearity issues.
- Panel (22-country) regression results (first differences, fixed effects):
  - Estimated elasticities (significant at the 5 percent level):
    - Public capital elasticity = 0.22
    - Private capital elasticity = 0.19
    - Labor input elasticity = 0.61
  - Test for constant returns to scale fails to reject the null hypothesis.
  - Panel advantage: much larger degrees of freedom (panel has more than 800 degrees of freedom vs about 37 for individual regressions), yielding more precise estimates.
- Cross-source comparisons:
  - Regressions using author’s own estimates cover 22 countries and yield many statistically significant but sometimes large public-capital coefficients.
  - Regressions using national or OECD (1997) sources cover fewer countries and often produce statistically insignificant coefficients.

### Table summaries: selected numeric highlights
- Table 2 (Government capital stock / GDP ratios, percent; Reliability = contribution of 1960–1999 investment to 2000 net stock):
  - Average ratios (unweighted): 1980 57.8, 1990 55.3, 2000 51.4.
  - Average Reliability: 92.1; standard deviation of Reliability 3.0.
  - Japan in 2000: 117.1 (Rank 1), Reliability 97.0.
  - Ireland in 2000: 35.2 (Rank 22), Reliability 92.9.
- Table 3 (Government net capital stock per head at 2000 PPPs, U.S. dollars):
  - Average per head: 1980 9,270.8; 1990 10,883.6; 2000 12,137.1.
  - Japan in 2000: 31,692.8 (Rank 1).
  - United States in 2000: 16,397.4 (Rank 2).
  - Portugal in 2000: 6,582.0 (Rank 22).
- Table 4 (United States and Canada: elasticities under alternative assumptions):
  - U.S. benchmark (Differences): elasticity 0.793 (t-value (3.146)); cointegration test statistic -2.323.
  - U.S. BEA capital stock (Differences): elasticity 0.786 (t-value (2.668)); cointegration test statistic -1.812.
  - Canada (Own geometric 1960–2001, Differences): elasticity 0.607 (t-value (3.364)); cointegration test statistic -2.809.
- Table 5 (Elasticities for individual countries and panel):
  - Selected author’s own estimates (sample and elasticity, t-value):
    - Australia (1960–2001): 0.648* (t-value (3.354)).
    - Denmark (1960–2001): 1.265* (t-value (5.030)).
    - Sweden (1960–2001): 0.551* (t-value (2.716)).
    - United States (1960–2001): 0.793* (t-value (3.146)).
  - OECD panel (1960–2001): elasticity 0.221* (t-value (3.677)).
  - Note: * denotes statistical significance at the 5 percent level; most models estimated in first differences based on Engle-Granger tests.

### Conclusions and suggested applications
- Main outputs:
  - New, internationally comparable government net capital stock estimates for 22 OECD countries, 1960–2001, using consistent PIM and OECD investment inputs.
- Empirical conclusions:
  - Benchmark capital stock estimates are broadly plausible versus BEA and Statistics Canada reference series.
  - Public capital–GDP ratios declined in most OECD countries since late 1970s; notable cross-country disparities with some convergence over recent decades.
  - Production-function regressions generally indicate a positive, statistically significant elasticity of output with respect to public capital; panel evidence supports an average elasticity around 0.22.
- Suggested uses of the dataset:
  - Assess public capital productivity for countries lacking prior data.
  - Estimate dynamic panel regressions to identify average effects across OECD countries.
  - Use in VAR models to analyze macroeconomic effects of public capital.

*Source: _wp0467 - References (excerpt) — text and figures/tables list from the IMF Working Paper chapter provided in the content unit.*

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

### _wp0467 - References

### Introduction: research context and contribution
- Early influential work (Aschauer (1989a,b)) found large positive output effects of government capital in the United States and suggested government capital was more productive than private capital.
- Subsequent literature (surveyed in Gramlich (1994), Sturm, de Haan, and Kuper (1998), and Seitz (2001)) finds:
  - Evidence for positive output effects of government capital exists, but
  - The magnitude is generally much smaller than Aschauer reported.
- Empirical work is constrained by lack of internationally comparable public capital stock data:
  - Most studies focus on the United States.
  - Few cross-country studies exist (examples: Ford and Poret (1991); Evans and Karras (1994)), relying on OECD (1997) data that were not internationally comparable because estimation methods differed widely across countries.
- OECD suspended publication of capital stock series after 1997; the Canberra Group on Capital Stock Statistics produced a manual on measurement of capital (OECD, 2001a), but internationally comparable capital stock data remain limited.
- Recent empirical trend:
  - Use of vector autoregressive (VAR) models (e.g., Mittnik and Neumann, 2001; Voss, 2002) to avoid imposing causal links.
  - VAR approach typically requires large samples; researchers often use public investment flows (available quarterly) instead of public capital stock (available annually).
  - Using public investment assumes effects are independent of capital stock level, a questionable assumption given diminishing returns; evidence suggests fast decline in marginal productivity of public capital (Demetriades and Mamuneas, 2000, p. 702).

- Contribution of this paper:
  - Provides internationally comparable annual capital stock estimates for 22 OECD countries for 1960–2001 using the perpetual inventory method with geometric depreciation.
  - Estimates capital stocks for three investment categories: (1) private nonresidential gross fixed capital formation, (2) private residential gross fixed capital formation, (3) government gross fixed capital formation.
  - Conducts sensitivity analysis varying estimation assumptions for two reference countries (United States and Canada) where official public capital stock estimates exist; finds benchmark estimates are robust.
  - Compares production function estimation results using three alternative public capital stock measures: (1) author’s own estimates; (2) national authorities’ estimates; (3) OECD (1997) estimates.
  - Reports that elasticity of output with respect to public capital is positive and statistically significant; simple panel model yields average elasticity of 0.2 in OECD countries.

### Data: sources, coverage, and comparability issues
- Primary data source: June 2002 version of the OECD Analytical Database.
- Countries covered (22): Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.
- Series extracted (OECD codes indicated in source):
  - total gross fixed capital formation (ITV)
  - total private gross fixed capital formation (IPV)
  - private nonresidential gross fixed capital formation (IBV)
  - private residential gross fixed capital formation (IHV)
  - government gross fixed capital formation (IGV)
- Time coverage: for most countries, 1960–2001.
- Countries excluded due to insufficient series: the Czech Republic, Hungary, the Republic of Korea, Luxembourg, Mexico, Poland, the Slovak Republic, and Turkey.
- Public investment series institutional coverage varies across countries and sources:
  - Three definitions encountered:
    1. public investment of the general government;
    2. public investment of the nonfinancial public sector (general government plus nonfinancial public enterprises (NFPEs));
    3. activity-based definitions using ISIC categories: narrow (“Public administration and defense services, compulsory social security services”) and broad (“Public administration, educational services, and health care and social assistance”).
  - ISIC-based broad category can include private spending on education (important in some countries, e.g., Canada).
- Figure 1 (in source) documents public investment–GDP ratio 1960–2001; general pattern:
  - Public investment–GDP ratio generally declined over the sample period.
  - Pronounced declines in Austria and Ireland.
  - Notable increases in Greece, Portugal, and Spain since accession to the European Community in the 1980s.
- Cross-source comparisons:
  - OECD Analytical Database ratios generally coincide with national sources except for Belgium, Canada, Italy, Japan, and Spain.
  - OECD (1997) data differ substantially in many cases, reflecting use of 1968 System of National Accounts versus 1993 SNA in other sources and data revisions; different coverage of public investment is a major reason for discrepancies.

### Methodology: perpetual inventory method and key assumptions
- Estimation approach: perpetual inventory method (PIM) with geometric depreciation, following OECD (2001a) and U.S. Bureau of Economic Analysis (1999).
- Net capital stock estimated for three subcategories from OECD Analytical Database:
  1. private nonresidential gross fixed capital formation;
  2. private residential gross fixed capital formation;
  3. government gross fixed capital formation.
- Capital accumulation identity:
  - K_{t+1} = (1 − δ) K_t + I_t
  - Under geometric depreciation, net capital stock at beginning of period t+1 is weighted sum of past investment: K_{t+1} = ∑_{i=0}^{∞} (1 − δ)^{i+1} I_{t−i}
  - In practice, replaced by finite sum incorporating initial capital stock K_1.
- Required inputs and choices:
  - Time series on gross investment flows (from OECD Analytical Database).
  - Initial capital stock (capital stock at beginning of 1960).
  - Assumption on magnitude and time profile of depreciation; geometric depreciation chosen.
- Treatment of initial capital stock:
  - No official info except for the United States.
  - Paper constructs an artificial investment series for 1860–1959 assuming investment increased by 4 percent a year during this period, reaching observed level in 1960.
  - Rationale: total gross investment in the 22 OECD countries grew by 4 percent a year on average during 1960–2001.
  - United States exception: BEA provides investment series starting in 1914; OECD data (1960–2001) chained with BEA growth rates for 1914–60.
  - Sensitivity analysis (Section V) indicates:
    - The initial capital stock assumption does not strongly affect dynamics of resulting capital stock series.
    - The initial capital stock’s contribution to the level of the capital stock at the end of the sample is less than 10 percent for the average OECD country.
- Notes on rebasing and price base:
  - All series expressed in constant prices of 1995.
  - Countries with different base years rebased to 1995: Australia 1999/2000; Canada, 1997; Iceland, 1990; Norway, 1997; Switzerland, 1990; United States, 1996.

### Robustness, war-damage considerations, and literature context
- Sensitivity analysis:
  - Conducted for United States and Canada where official public capital stock estimates exist; results suggest benchmark estimates are robust to variations in main assumptions (details in Section V).
- War damage and justification of smooth historical investment assumption (1860–1960):
  - Concern: whether severe World War II damage would make smooth pre-1960 investment assumption invalid.
  - Arguments why war damage likely had limited effect on 1960 initial capital stock:
    - Countries with largest war damage experienced much faster postwar growth, often returning GDP to long-run trend by 1960.
    - Rapid postwar investment increases likely restored capital stocks.
    - Empirical references: Broadberry (1988); Maddison (1982); Eichengreen and Ritschl (1998); Ritschl (2003) suggesting limited persistent war damage by 1960 in many cases.
  - Maddison (1991) estimates of war-related capital loss for six OECD countries cited as examples of large uncertainty in historical capital loss estimates.
- Literature and methodological precursors:
  - Jacob, Sharma, and Grabowski (1997): comparable estimation by industrial activity (ISIC).
  - Berndt and Hansson (1991): public capital stock for Sweden.
  - Sturm and de Haan (1995): public capital stock for the Netherlands.
  - Boskin, Robinson, and Huber (1987); Holtz-Eakin (1993); Munnell (1990): capital stock for local and state governments in the United States.
  - Emphasis on institutional-sector focus (public sector) rather than industrial-activity breakdown.

### Key empirical findings (as reported)
- Elasticities of output with respect to public capital:
  - Positive and statistically significant in production function estimations.
  - Panel-data average elasticity in OECD countries: 0.2.
- Data-coverage and comparative tables/figures included in source (listed without reproducing files):
  - Tables include coverage of government gross fixed capital formation, government net capital stock in 22 OECD countries, government net capital stock per head, and elasticities for the United States, Canada, and 22 OECD countries under alternative capital stock measures.
  - Figures include real government gross fixed capital formation 1960–2001, implicit scrapping rates for the United States 1960–2000, real government net capital stock 1960–2001, and government net capital stocks for alternative estimation assumptions.
- General historical pattern:
  - Public investment–GDP ratio generally declined 1960–2001 in most countries, with increases in Greece, Portugal, and Spain since 1980s accession to the European Community; marked declines in Austria and Ireland.

*Source: _wp0467 - References (excerpt) — text and figures/tables list from the IMF Working Paper chapter provided in the content unit.*

### 9.5 percent a year and in Germany by 7.2 percent. Calculations based on Luetzel (1977, p. 66) show that the total net

### _wp0467 - 9.5 percent a year and in Germany by 7.2 percent. Calculations based on Luetzel (1977, p. 66) show that the total net

### Growth rates, wartime effects, and historical investment
- Germany: total net capital stock grew by 7.9 percent a year on average between 1950 and 1960 (Calculations based on Luetzel (1977, p. 66)).
- Germany: net investment grew by 9.7 percent a year on average between 1950 and 1960 (Calculations based on Mitchell (1975)).
- Wartime disruptions: the fall in capital stocks due to wartime disruptions was less pronounced than the fall in output (Maddison, 1982, p. 55), implying the gap between capital stock levels at the end of World War II and their long-run trend was lower than for output.
- Decision: based on these considerations the paper does not correct the capital stock estimates at the beginning of 1960 for war damage.

### Depreciation assumptions and implicit scrapping rates
- Depreciation assumptions:
  - Time-varying for the public capital stock and the private nonresidential capital stock.
  - Constant for the private residential capital stock.
- Implicit scrapping rate definition:
  - s_t = 100 ⋅ (D_t / K_t)  (quotient of depreciation in period t and the net capital stock at the beginning of period t).
- Empirical patterns (United States, 1960–2000):
  - Implicit scrapping rates differ across asset types: highest for private nonresidential capital, lowest for private residential capital.
  - Private residential scrapping rate: roughly constant over 1960–2000.
  - Private nonresidential and government scrapping rates: tended to rise over time.
  - Private nonresidential scrapping rate: from about 4½ percent in 1960 to about 9½ percent in 2000.
- Possible explanations for rising scrapping rates:
  - Increasing weight of assets with relatively short asset lives.
  - Shortening of asset lives, especially for ICT-related assets (more pronounced for private nonresidential capital, to a lesser extent for government capital).
- International observation: similar rising implicit scrapping rates for private nonresidential and government capital observed in Canadian and Australian data.

### Time profile of depreciation rates used in the study
- Assumed depreciation rates for 1860–1960:
  - Government assets: 2½ percent.
  - Private nonresidential assets: 4¼ percent.
  - Residential assets: 1½ percent.
- Assumed depreciation rates for 1960–2001:
  - Government assets: gradually increase from 2½ percent to 4 percent.
  - Private nonresidential assets: gradually increase from 4¼ percent to 8½ percent.
  - Private residential assets: constant 1½ percent.
- Formalization: equation (6) defines the time profile of δ_j,t with j_min δ as the depreciation rate in 1960 and j_max δ as the depreciation rate in 2001.
- Note on profile choice: U.S. BEA data show a sharper acceleration after 1995 reflecting ICT; because ICT importance is lower in most other industrial countries, the study chooses a flatter depreciation profile for 1995–2001 than implied by U.S. data.

### Perpetual inventory method and capital stock construction
- Real net capital stock at beginning of period t+1 for investment category j:
  - Equation (7) incorporates time-varying depreciation rates and assumes new investment is placed in service at midyear.
  - Capital stock at the beginning of the initial period, K_1860, is set equal to zero.
- Depreciation method adopted: geometric depreciation.
- Productive capital stock: the estimated public net capital stock is equivalent to the so-called productive capital stock (OECD (2001b, p. 62–63)); appropriate for productivity analyses because it reflects flows of services provided by capital more appropriately than net or gross capital stock. Distinction vanishes only for a homogeneous asset and geometric depreciation.
- Practical constraint: public investment treated as a homogenous asset due to lack of disaggregated data.

### Capital stock estimates for 22 OECD countries, 1960–2001
- Presentation:
  - Figure 3 displays evolution of public net capital stock / GDP (both at 1995 prices) for 22 OECD countries over 1960–2001, including author’s estimates and, where available, national and OECD (1997) estimates.
- Cross-country comparability and caveats:
  - Differences in levels reflect the artificial investment series assumed for 1860–1959 and diversity of national methods.
  - Advantage: author’s estimates use the same methodology and homogeneous investment data across countries.
- German reunification handling:
  - OECD series cover West Germany only for 1960–90, include East Germany from 1991 on.
  - Assumption: ratio of East German capital stock to West German capital stock at beginning of 1991 equaled ratio of East German and West German GDP in 1991 (8 percent).
  - In estimation, German capital stock at beginning of 1991 is increased by 8 percent for the three asset types; from 1991 on this additional capital stock depreciates at the same rate as other assets.
- Table 2 summary (1980, 1990, 2000):
  - Average public capital–GDP ratio for 22 OECD countries declined by 6 percentage points over 1980–2000.
  - Public capital share of GDP declined in 13 countries since the early 1980s; slightly increased in 4 countries; strongly risen in Greece, Japan, Portugal, Spain, and Switzerland.
  - Japan had by far the largest public capital–GDP ratio among the OECD countries considered in 2000; Ireland had the lowest.
  - Contribution of government investment from 1960–2000 to government net capital stock in 2000:
    - Average contribution of investment from 1960 onwards: 92 percent.
    - Average contribution of assumed investment data (1860–1959): 8 percent.
    - Country range: contribution of initial capital stock varies between 14.3 percent (Denmark) and 3.0 percent (Japan).
- Per capita public capital at 2000 PPPs for GDP (Table 3, years 1980, 1990, 2000):
  - Average public capital stock per person for 22 OECD countries increased by 30.9 percent over 1980–2000 (that is, by 1.4 percent per year).
  - Growth of public capital per head was lower than that of real GDP, consistent with declining public capital–GDP ratio on average.
  - Japan: public capital stock per head highest, exceeding the average by more than 160 percent in 2000.
  - Country ranking differences: United States ranks higher in per capita terms than in public capital–GDP ratio ranking; Greece, Portugal, Spain rank lower in per capita terms.
  - In 2000, real GDP per head: Greece 66.3 percent of OECD average, Portugal 72.4 percent, Spain 79.5 percent (OECD, 2002b, p. 339).
  - Greece, Portugal, Spain experienced faster-than-average increases in public capital per head over 1980–2000 reflecting infrastructure enhancements after joining the European Community.

### Robustness checks and sensitivity of estimates (Section V)
- Key assumptions tested:
  1. Investment in 1860–1959 assumed to have grown by 4 percent per year to reach observed 1960 level.
  2. Depreciation rate time-varying and assumed gradually to increase for all asset types except residential assets.
  3. Depreciation assumed to be geometric.
- Sensitivity analysis:
  - Alternative public capital stock series estimated for two reference countries, the United States and Canada, by modifying each assumption in turn.
  - Results compared with benchmark estimates and with official sources; depicted in Figure 4.
- Initial capital stock construction variants (U.S. example):
  - Benchmark: uses BEA public investment series for 1914–60 and assumes public investment grew by 4 percent in 1860–1914.
  - Alternative: assumes public investment grew by 4 percent in 1860–1959 (as for other countries).
  - Steady-state approach (Fuente and Doménech, 2002, p. 47):
    - Growth rate identity: g_t = (I_t / K_{t-1}) - δ_t  (equation (8) rearranged).
    - Steady-state approximation for K_t: K_t = I_t / (δ_t + g_t) (equation (9)).
    - For g_t unknown, approximate by average growth rate of investment over 1960–2001.
    - For U.S. government investment, the average growth rate of investment over 1960–2001 was 2.7 percent.

*Italic: IMF Working Paper content unit _wp0467 (extracted text).*

### 5.4 percent in the case of private nonresidential investment, and 2.5 percent in the case of private

### _wp0467 - 5.4 percent in the case of private nonresidential investment, and 2.5 percent in the case of private

### Sensitivity analysis of public capital stock estimates
- Alternative assumption on initial public investment (assume constant 4 percent growth over 1914–59 versus historical BEA growth rates):
  - For 1960–2000, levels and dynamics of public capital stock series are "almost indistinguishable."
  - Pronounced differences occur over 1940–50 because BEA investment accounts for the large WWII increase; effect is short-lived.
  - Level of author’s estimates is lower than BEA series, but dynamics are very similar (strong comovement of growth rates).
  - Formal tests for equality between means and variances of author’s estimates and BEA series fail to reject the null hypothesis of equality (tests applied to growth rates because series are I(1)).
- Alternative assumptions on time profile of the depreciation rate (benchmark versus alternatives):
  - Benchmark: time-varying depreciation rate increasing from 2½ percent to 4 percent (see Section III).
  - Alternative 1: depreciation rate gradually increases from 3 percent to 6 percent over 1960–2001 (based on implicit scrapping rates for total capital).
  - Alternative 2: depreciation rate constant and equal to average implicit scrapping rate observed for the United States (3½ percent for government assets).
  - Findings:
    - Constant depreciation rate (3½ percent) overestimates growth of public capital in the 1990s.
    - Steeper time-profile (3–6 percent) underestimates growth in the 1970s and early 1980s.
    - Conclusion: benchmark assumption based on empirically observed implicit scrapping rates is the most sensible among alternatives.
- Alternative depreciation methods (Canada; official Statistics Canada series):
  - Methods: straight-line, hyperbolic, geometric.
  - Hyperbolic and geometric yield quite similar capital stock estimates.
  - Straight-line differs considerably in both levels and dynamics.
  - Author’s estimate (geometric depreciation) generally lower than Statistics Canada geometric series, but higher than its linear-depreciation series.
  - Dynamics of author’s estimates similar to Statistics Canada geometric series except for the 1960s.
  - Formal test for equality between means and variances of growth rates of the two geometric-series cannot reject null hypothesis of equality.
  - Conclusion: benchmark estimates appear sensible for Canada as well.

### Data coverage and key descriptive findings
- Dataset produced covers 22 OECD countries for the period 1960–2001 (42 years per country).
- Attractive dataset features:
  - Same estimation approach used across all countries for international comparability.
  - Investment data compiled by the OECD and homogenous across countries.
  - Investment data compiled according to the 1993 System of National Accounts (OECD (1997) used older 1968 SNA).
- Stylized facts from the estimates:
  - Public capital–GDP ratios have tended to decline in most OECD countries since the late 1970s.
  - A considerable disparity exists in public capital endowment across OECD countries, although some convergence occurred in the past two decades.
- Sensitivity analysis summary:
  - Visual inspection and formal equality tests versus U.S. BEA and Statistics Canada reference series indicate benchmark public capital estimates are reasonable.

### Production function approach: methodology and econometric diagnostics
- Production function specification (Cobb-Douglas form in logs) estimated as:
  - yt = a0 + a1 t + α kP,t + β lt + γ kG,t + εt  (equation (10) in text)
  - When variables are nonstationary and not cointegrated, first-difference formulation used:
    - Δyt = a1 + α ΔkP,t + β Δlt + γ ΔkG,t + υt  (equation (11) in text)
- Unit root and cointegration diagnostics:
  - Individual-variable augmented Dickey-Fuller tests applied to 165 variables used in regressions.
  - Vast majority of variables nonstationary in levels; only 10 variables stationary in level.
  - Many variables appear I(2) per some test results, but unit-root tests have low power, especially in small samples.
  - Panel unit root tests (Levin, Lin, and Chu (2002) and Im, Pesaran, and Shin (2003)) suggest variables are integrated of order 1.
  - Engle-Granger two-step cointegration tests applied to equation (10):
    - Engle-Granger test statistic is lower in absolute value than the 5 percent critical value in all reported individual-country cases (i.e., cannot reject null of no cointegration).
    - Implication: production function in levels does not constitute a stable long-run relationship in these samples; estimation proceeds in first differences.
  - Inference uses Newey and West (1987) HAC covariance estimator because of nonspherical disturbances.

### Regression results — United States and Canada (individual-country estimates)
- Private capital stock construction and depreciation assumptions:
  - Private capital = private nonresidential + private residential capital.
  - Benchmark depreciation assumptions for private assets:
    - Private nonresidential: depreciation rate increases from 4¼ percent to 8½ percent (over relevant period).
    - Private residential: depreciation rate constant at 1½ percent.
  - Alternative depreciation profiles for all private assets:
    - Alternative A: increases from 3.0 percent to 6.0 percent over 1960–2001.
    - Alternative B: time-invariant at 6.0 percent for private nonresidential and 1½ percent for private residential (based on average implicit scrapping rates for the United States).
- Elasticities of output with respect to public capital (individual-country regressions, estimated in first differences because no cointegration):
  - Estimated elasticities range from 0.40 to 0.86 (all statistically significant and positive).
  - These high values imply "supernormal" returns to public capital (terminology from Aschauer (1995, p. 91)).
- Additional regression anomalies and interpretational issues:
  - Coefficients on labor input are larger than one.
  - Coefficients on private capital are negative in all regressions (and statistically insignificant in most cases).
  - These anomalies may reflect:
    - Misspecified functional form.
    - Violations of exogeneity assumptions.
    - Multicollinearity among regressors.
  - Multicollinearity is frequently cited in production-function estimation; panel methods can help mitigate this problem.

### Regression results — 22 OECD countries and panel estimates
- Cross-country regressions using three sources of public capital stock (author’s own, national sources, OECD (1997)):
  - Author’s own estimates allow estimation for 22 countries; national and OECD sources permit only 10 and 11 country regressions, respectively.
  - For regressions based on national and OECD sources, most coefficients are statistically insignificant.
  - For regressions based on author’s own estimates, most public-capital coefficients are statistically significant but often large.
  - Some countries still show negative coefficients on private capital, complicating Cobb-Douglas interpretation.
- Panel fixed-effects regression (22-country panel; estimation based on first differences with country-specific intercepts):
  - Estimated output elasticities (all significant at the 5 percent level):
    - Public capital elasticity = 0.22
    - Private capital elasticity = 0.19
    - Labor input elasticity = 0.61
  - Test for constant returns to scale fails to reject the null hypothesis.
  - Panel advantage: much larger degrees of freedom (panel has more than 800 degrees of freedom vs about 37 for individual regressions), leading to more precise parameter estimates.
- Interpretation:
  - Panel result indicates public capital is productive on average in OECD countries with plausible elasticity magnitudes.
  - Individual-country regressions often yield implausible parameter signs/magnitudes, possibly due to multicollinearity and small-sample limitations.

### Conclusions and research applications
- Main contributions:
  - New estimates of government net capital stock for 22 OECD countries for 1960–2001 with consistent methodology and homogenous OECD investment inputs.
- Main empirical conclusions:
  - Benchmark capital stock estimates are plausible when compared with BEA and Statistics Canada series.
  - Public capital–GDP ratios declined in most OECD countries since the late 1970s, with substantial cross-country disparity but some recent convergence.
  - Production-function regressions generally indicate a positive, statistically significant elasticity of output with respect to public capital; panel evidence supports a sensible average elasticity (0.22).
- Suggested uses of the capital stock data:
  - Assess public capital productivity for countries lacking prior data.
  - Estimate dynamic panel regressions to uncover average effects of public capital across OECD countries.
  - Employ in VAR models to analyze macroeconomic effects of public capital.

*Source: _wp0467 - 5.4 percent in the case of private nonresidential investment, and 2.5 percent in the case of private; PDF at https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0467.pdf*

### Section III, the author’s own capital stock estimates will be compared to data from these sources

### Section III, the author’s own capital stock estimates will be compared to data from these sources

### Government Net Capital Stock in 22 OECD Countries (Table 2): Ratios of government capital stock to GDP (percent) and Reliability
- Australia: 1980 53.8 (Rank 11), 1990 46.5 (Rank 17), 2000 40.0 (Rank 19), Reliability 91.5
- Austria: 1980 75.4 (Rank 6), 1990 69.3 (Rank 3), 2000 57.0 (Rank 3), Reliability 90.8
- Belgium: 1980 40.2 (Rank 20), 1990 45.5 (Rank 18), 2000 37.9 (Rank 21), Reliability 94.4
- Canada: 1980 41.6 (Rank 19), 1990 40.0 (Rank 21), 2000 38.4 (Rank 20), Reliability 91.5
- Denmark: 1980 76.4 (Rank 4), 1990 60.8 (Rank 6), 2000 45.9 (Rank 15), Reliability 85.7
- Finland: 1980 43.7 (Rank 17), 1990 47.1 (Rank 16), 2000 46.9 (Rank 14), Reliability 94.6
- France: 1980 55.0 (Rank 10), 1990 53.0 (Rank 8), 2000 54.0 (Rank 6), Reliability 91.3
- Germany: 1980 58.4 (Rank 9), 1990 52.0 (Rank 10), 2000 47.1 (Rank 13), Reliability 91.4
- Greece: 1980 44.4 (Rank 16), 1990 51.9 (Rank 11), 2000 51.0 (Rank 7), Reliability 92.3
- Iceland: 1980 48.4 (Rank 13), 1990 50.5 (Rank 12), 2000 50.7 (Rank 8), Reliability 94.8
- Ireland: 1980 75.9 (Rank 5), 1990 66.8 (Rank 5), 2000 35.2 (Rank 22), Reliability 92.9
- Italy: 1980 44.7 (Rank 15), 1990 49.0 (Rank 13), 2000 47.9 (Rank 12), Reliability 90.8
- Japan: 1980 97.7 (Rank 2), 1990 95.7 (Rank 2), 2000 117.1 (Rank 1), Reliability 97.0
- Netherlands: 1980 80.2 (Rank 3), 1990 68.9 (Rank 4), 2000 56.4 (Rank 4), Reliability 89.0
- New Zealand: 1980 110.3 (Rank 1), 1990 102.4 (Rank 1), 2000 76.6 (Rank 2), Reliability 89.1
- Norway: 1980 49.3 (Rank 12), 1990 52.5 (Rank 9), 2000 50.5 (Rank 9), Reliability 94.6
- Portugal: 1980 27.9 (Rank 22), 1990 32.0 (Rank 22), 2000 43.3 (Rank 16), Reliability 96.2
- Spain: 1980 35.8 (Rank 21), 1990 40.9 (Rank 19), 2000 48.0 (Rank 11), Reliability 95.7
- Sweden: 1980 42.1 (Rank 18), 1990 40.2 (Rank 20), 2000 42.0 (Rank 17), Reliability 92.4
- Switzerland: 1980 46.1 (Rank 14), 1990 48.4 (Rank 15), 2000 54.7 (Rank 5), Reliability 94.7
- United Kingdom: 1980 63.9 (Rank 7), 1990 48.5 (Rank 14), 2000 40.3 (Rank 18), Reliability 86.8
- United States: 1980 59.9 (Rank 8), 1990 54.1 (Rank 7), 2000 50.0 (Rank 10), Reliability 89.4

- Average (unweighted): 1980 57.8, 1990 55.3, 2000 51.4, Average Reliability 92.1
- Standard deviation: 1980 20.6, 1990 17.0, 2000 17.1, Reliability 3.0

- Notes from table:
  - The columns labeled “Ratio” give the ratio of the government capital stock and GDP (in percent).
  - The columns labeled “Rank” give the ranking of the countries according to the size of their capital to GDP ratio, the country with the highest ratio ranking first.
  - The column labeled “Reliability” gives the contribution of government investment in the period 1960–1999 to the net capital stock at the beginning of 2000 (in percent). The difference between 100 percent and this figure reflects the contribution of government investment in the period 1860–1959, for which official data are not available.
  - Unweighted average.

### Government Net Capital Stock per Head in 22 OECD Countries (Table 3): Levels at 2000 PPPs in U.S. dollars
- Australia: 1980 8547.5 (Rank 12), 1990 8731.5 (Rank 16), 2000 9416.5 (Rank 16)
- Austria: 1980 13111.1 (Rank 5), 1990 14925.4 (Rank 3), 2000 14719.5 (Rank 4)
- Belgium: 1980 6756.7 (Rank 18), 1990 9282.5 (Rank 12), 2000 9272.4 (Rank 17)
- Canada: 1980 7960.2 (Rank 13), 1990 8894.2 (Rank 15), 2000 10124.8 (Rank 14)
- Denmark: 1980 13483.8 (Rank 4), 1990 12951.4 (Rank 8), 2000 11830.0 (Rank 10)
- Finland: 1980 6582.8 (Rank 19), 1990 9218.5 (Rank 13), 2000 10928.6 (Rank 12)
- France: 1980 9479.3 (Rank 9), 1990 10961.4 (Rank 9), 2000 12843.1 (Rank 7)
- Germany: 1980 12041.0 (Rank 7), 1990 13032.6 (Rank 7), 2000 11841.0 (Rank 9)
- Greece: 1980 4720.7 (Rank 20), 1990 5626.2 (Rank 21), 2000 6674.2 (Rank 21)
- Iceland: 1980 8705.8 (Rank 11), 1990 10666.7 (Rank 10), 2000 12429.0 (Rank 8)
- Ireland: 1980 6984.5 (Rank 16), 1990 8522.6 (Rank 18), 2000 8365.8 (Rank 20)
- Italy: 1980 6908.0 (Rank 17), 1990 9416.1 (Rank 11), 2000 10557.4 (Rank 13)
- Japan: 1980 16684.0 (Rank 1), 1990 23115.8 (Rank 1), 2000 31692.8 (Rank 1)
- Netherlands: 1980 13740.2 (Rank 3), 1990 13871.0 (Rank 6), 2000 14157.8 (Rank 6)
- New Zealand: 1980 14919.0 (Rank 2), 1990 16651.9 (Rank 2), 2000 14532.8 (Rank 5)
- Norway: 1980 6986.1 (Rank 15), 1990 9089.7 (Rank 14), 2000 11540.0 (Rank 11)
- Portugal: 1980 2391.7 (Rank 22), 1990 3759.9 (Rank 22), 2000 6582.0 (Rank 22)
- Spain: 1980 3831.6 (Rank 21), 1990 5645.3 (Rank 20), 2000 8465.1 (Rank 19)
- Sweden: 1980 7122.8 (Rank 14), 1990 8205.3 (Rank 19), 2000 9848.9 (Rank 15)
- Switzerland: 1980 11498.3 (Rank 8), 1990 14067.2 (Rank 5), 2000 16169.4 (Rank 3)
- United Kingdom: 1980 8862.1 (Rank 10), 1990 8574.1 (Rank 17), 2000 8627.5 (Rank 18)
- United States: 1980 12640.2 (Rank 6), 1990 14230.5 (Rank 4), 2000 16397.4 (Rank 2)

- Average (unweighted): 1980 9270.8, 1990 10883.6, 2000 12137.1
- Standard deviation: 1980 3766.3, 1990 4263.1, 2000 5182.5

- Notes from table:
  - The columns labeled “Capital” give the level of the government net capital stock per head at 2000 purchasing power parities (PPP) for GDP in U.S. dollars.
  - Purchasing power parities for GDP in national currency per U.S. dollar are taken from the OECD (2002b).
  - Population figures are taken from the OECD Analytical Database, Version June 2002.
  - The columns labeled “Rank” give the ranking of the countries according to the level of public capital per head, the country with the highest level ranking first.
  - Unweighted average.

### Elasticities of Output with Respect to Public Capital: United States and Canada, alternative assumptions (Table 4)
- Panel (a) United States: Alternative assumptions on the initial capital stock (Sample 1960–2001)
  - Benchmark: Levels elasticity 0.817 (t-value (7.153)), Differences 0.793 1/ (t-value (3.146)); Cointegration test statistic -2.323
  - Steady-state approach: Levels 1.032 (t-value (6.284)), Differences 0.855 1/ (t-value (2.536)); Cointegration test statistic -2.970
  - 4% growth rate 3/: Levels 0.771 (t-value (7.163)), Differences 0.757 1/ (t-value (3.281)); Cointegration test statistic -2.216
  - BEA capital stock: Levels 1.107 (t-value (7.500)), Differences 0.786 1/ (t-value (2.668)); Cointegration test statistic -1.812

- Panel (b) United States: Alternative assumptions on depreciation rates (Sample 1960–2001)
  - 3%–6% for all assets: Levels 0.710 (t-value (6.630)), Differences 0.688 1/ (t-value (3.004)); Cointegration test statistic -2.236
  - Constant 3/: Levels 0.815 (t-value (6.805)), Differences 0.723 1/ (t-value (2.857)); Cointegration test statistic -2.890

- Panel (c) Canada: Alternative depreciation methods (Sample 1961–2001 or 1960–2001)
  - Straight-line: Levels 0.413 (t-value (9.038)), Differences 0.398 1/ (t-value (4.879)); Cointegration test statistic -2.178
  - Geometric: Levels 0.505 (t-value (10.001)), Differences 0.506 1/ (t-value (5.690)); Cointegration test statistic -2.576
  - Hyperbolic: Levels 0.467 (t-value (8.013)), Differences 0.450 1/ (t-value (4.749)); Cointegration test statistic -2.220
  - Own (geometric) 1960–2001: Levels 0.711 (t-value (7.836)), Differences 0.607 1/ (t-value (3.364)); Cointegration test statistic -2.809

- Notes from table:
  - 1/ t-values based on the Newey and West (1987) heteroscedasticity and autocorrelation consistent covariance estimator in parentheses. * denotes statistical significance at the 5 percent level.
  - Elasticities in the column labeled “Levels” are printed in bold if the variables are cointegrated; otherwise the elasticity for the corresponding model estimated in first differences reported in the column labeled “Differences” is printed in bold.
  - 2/ This paper uses the so-called augmented Engle-Granger test, performing an augmented Dickey-Fuller test on the residuals of the model in levels (equation (10)). The MacKinnon (1991) 5 percent critical value for rejection of the null hypothesis of no cointegration is -4.795 for the sample 1960–2001.
  - 3/ The growth rate of investment in the period 1914–59 is assumed to be 4 percent per annum. The benchmark estimates, instead, rely on historical growth rates of investment reported by the BEA.
  - 4/ The depreciation rate is assumed to be constant over time. Based on the average implicit scrapping rate over the period 1960–2000 the depreciation rate is assumed to be 3½ percent for government capital, 6 percent for private nonresidential capital and 1½ percent for private residential capital.

### Elasticities of Output with Respect to Public Capital for 22 OECD Countries from Different Sources (Table 5)
- Australia: Author’s own estimates (Sample 1960–2001) Elasticity 0.648* (t-value (3.354)); National source 1960–2001 Elasticity 0.041 (t-value (0.320)); OECD (1997) 1970–95 Elasticity -0.179 (t-value (-0.528))
- Austria: Author’s own estimates (1965–2001) Elasticity 0.631* (t-value (2.275))
- Belgium: Author’s own estimates (1960–2001) (no elasticity printed in author’s column), National source 1970–2000 Elasticity 0.248* (t-value (3.877)), OECD (1997) 1970–95 Elasticity 0.041 (t-value (0.320)) and OECD (1997) 1970–95 Elasticity -0.463* (t-value (2.876)) [table structure indicates multiple entries for different samples/sources]
- Canada: Author’s own estimates (1960–2001) (no elasticity printed in author’s column), National source 1961–2001 Elasticity 0.608* (t-value (3.365)), OECD (1997) 1970–95 Elasticity 0.506 (t-value (5.690)) and 0.642* (t-value (2.397)) [table shows multiple source/sample entries]
- Denmark: Author’s own estimates (1960–2001) Elasticity 1.265* (t-value (5.030)); National source 1971–92 Elasticity 0.265 (t-value (1.159))
- Finland: Author’s own estimates (1960–2001) Elasticity 0.738* (t-value (2.953)); National source 1970–96 Elasticity -0.271* (t-value (-2.032))
- France: Author’s own estimates (1965–2001) Elasticity 0.777* (t-value (2.575))
- Germany: Author’s own estimates (1960–2001) (no elasticity printed in author’s column), National source 1960–1990 Elasticity 0.877* (t-value (4.072)), OECD (1997) 1970–94 Elasticity 0.762* (t-value (2.958)) and OECD (1997) 1970–94 Elasticity -0.875 (t-value (-1.727))
- Greece: Author’s own estimates (1961–2001) Elasticity 0.602 (t-value (1.360)); National source 1970–89 Elasticity 0.784* (t-value (4.598))
- Iceland: Author’s own estimates (1967–2001) Elasticity 0.045 (t-value (0.099))
- Ireland: Author’s own estimates (1960–2001) Elasticity -0.068 (t-value (-0.224))
- Italy: Author’s own estimates (1960–2001) Elasticity 0.153 (t-value (0.580)); National source 1980–2000 Elasticity 0.498 (t-value (1.271)); OECD (1997) 1979–96 Elasticity 1.369 (t-value (1.749))
- Japan: Author’s own estimates (1960–2001) Elasticity 0.570 (t-value (1.830)); National source 1990–2000 Elasticity -0.115 (t-value (-0.420))
- Netherlands: Author’s own estimates (1969–2001) Elasticity 0.897 (t-value (2.797))
- New Zealand: Author’s own estimates (1962–2001) Elasticity 0.087 (t-value (0.270)); National source 1987–97 Elasticity -1.726* (t-value (-2.479))
- Norway: Author’s own estimates (1960–2001) Elasticity 0.243 (t-value (0.811)); National source 1970–2000 Elasticity 0.053 (t-value (0.465)); OECD (1997) 1978–1994 Elasticity 0.032 (t-value (0.376))
- Portugal: Author’s own estimates (1960–2001) Elasticity -0.568 (t-value (-1.580))
- Spain: Author’s own estimates (1961–2001) Elasticity 0.346 (t-value (1.649)); National source 1980–95 Elasticity 0.180* (t-value (2.571))
- Sweden: Author’s own estimates (1960–2001) Elasticity 0.551* (t-value (2.716)); National source 1979–1994 Elasticity -0.353 (t-value (-1.499))
- Switzerland: Author’s own estimates (1960–2001) Elasticity 0.524* (t-value (2.905))
- United Kingdom: Author’s own estimates (1960–2001) Elasticity 0.404* (t-value (2.761)); National source 1986–1996 Elasticity 0.164 (t-value (0.763))
- United States: Author’s own estimates (1960–2001) Elasticity 0.793* (t-value (3.146)); National source 1960–2000 Elasticity 0.786* (t-value (2.666))
- OECD (Panel) 1960–2001 Elasticity 0.221* (t-value (3.677))

- Notes from table:
  - 1/ t-values based on the Newey and West (1987) covariance estimator in parentheses. * denotes statistical significance at the 5 percent level.
  - The model is estimated in first differences in all cases except one (Belgium for data from national sources) based on the results of Engle-Granger tests for cointegration.

### Appendix I — National data sources: availability, methods, and coverage (selected entries)
- General note: This appendix provides summary information on 13 OECD countries for which public capital stock estimates from national sources are available. Public capital stock estimates from national sources are not available for the following countries: Austria, France, Greece, Iceland, Ireland, the Netherlands, Portugal and Switzerland. For Sweden, public capital stock data are available at http://www.scb.se/ for local governments only.

- Australia
  - Source/Agency: Australian Bureau of Statistics
  - Publication: “Australian System of National Accounts.”
  - Data availability: period 1960–2000 at http://www.abs.gov.au/
  - Method: Stocks calculated according to the perpetual inventory method; depreciation assumed hyperbolic.
  - Coverage: General government.

- Belgium
  - Source/Agency: National Accounts Institute (NAI)
  - Publication/database: National Socio-Economic Database.
  - Data availability: period 1970–2000 at http://www.nbb.be/belgostat/
  - Coverage: Public administration and defense services, compulsory social security services.

- Canada
  - Source/Agency: Statistics Canada
  - Data availability: period 1961–2001 at http://www.statcan.ca/english/CANSIM/ (CANSIM Table 031-0002)
  - Method: Stocks calculated according to the perpetual inventory method; estimates provided for three alternative depreciation schemes (straight line, geometric, and hyperbolic).
  - Coverage: Public administration, educational services, and health care and social assistance.

- Denmark
  - Source/Agency: Danmarks Statistics
  - Database: Danmarks Statistikbank.
  - Data availability: period 1966–2001 at http://www.statistikbanken.dk
  - Coverage: General government.

- Finland
  - Source/Agency: Statistics Finland
  - Data availability: period 1975–2001 provided by ETLA (The Research Institute for the Finnish Economy).
  - Coverage: General government.

- Germany
  - Source/Agency: Statistisches Bundesamt
  - Data availability: For West Germany, net capital stocks 1960–95 according to ESA 1979 at http://www-zr.destatis.de/; for Germany as a whole, only gross capital stocks 1991–2000 published in “Hauptbericht, Fachserie 18: Volkswirtschaftliche Gesamtrechnungen, Reihe 1.3” (not available online).
  - Coverage: Public sector (including NFPEs).

- Italy
  - Source/Agency: Istituto Nazionale di Statistica (ISTAT)
  - Data availability: period 1980–2000 at http://www.istat.it/
  - Method: Stocks calculated according to the perpetual inventory method; depreciation assumed straight-line.
  - Coverage: Public administration and defense services, compulsory social security services.

- Japan
  - Source/Agency: Economic and Social Research Institute (ESRI)
  - Publication: “Annual Report on National Accounts”.
  - Data availability: 1955–2000 at http://www.esri.cao.go.jp/
  - Coverage: Data available for the general government and for the public sector (including NFPEs).

- New Zealand
  - Source/Agency: Statistics New Zealand
  - Publication: “Upgraded National Accounts 2000.”
  - Data availability: 1987–97 at http://www.stats.govt.nz/
  - Coverage: Public sector (General government including all government-owned producer enterprises).

- Norway
  - Source/Agency: Statistics Norway
  - Publication: “Annual National Accounts.”
  - Data availability: period 1970–2000 at http://www.ssb.no/nr_en/
  - Coverage: General government.

- Spain
  - Source/Agency: Ministry of Finance (BD.MORES database)
  - Method: Stocks calculated by perpetual inventory method; depreciation assumed geometric.
  - Data availability: period 1964–95 at http://www.igae.minhac.es/
  - Coverage: Data available for the general government and for the public sector (including NFPEs).

- United Kingdom
  - Source/Agency: Office for National Statistics (ONS)
  - Publication: “Blue Book.”
  - Data availability: period 1948–2000 at http://www.statistics.gov.uk/statbase/
  - Method: Stocks calculated according to the perpetual inventory method; depreciation assumed straight-line.
  - Coverage: Public sector.

- United States
  - Source/Agency: U.S. Department of Commerce, Bureau of Economic Analysis (BEA)
  - Data availability: 1925–2000 at http://www.bea.gov/bea/dn/faweb/
  - Method: Stocks calculated according to the perpetual inventory method; depreciation assumed geometric.
  - Coverage: Public sector (general government plus government enterprises).

*Source: Author’s own estimates and calculations.*

### REFERENCES

### _wp0467 - REFERENCES

### Infrastructure and Public Capital
- Aschauer, David Alan, 1989a, “Does Public Capital Crowd Out Private Capital?” Journal of Monetary Economics, Vol. 24 (September), pp. 171–88.
- Aschauer, David Alan, 1989b, “Is Public Expenditure Productive?” Journal of Monetary Economics, Vol. 23 (March), pp. 177–200.
- Aschauer, David Alan, 1995, “Infrastructure and Macroeconomic Performance: Direct and Indirect Effects,” in The OECD Jobs Study: Investment, Productivity and Employment (Paris: Organization for Economic Cooperation and Development).
- Berndt, Ernst R., and Bengt Hansson, 1991, “Measuring the Contribution of Public Infrastructure Capital in Sweden,” NBER Working Paper No. 3842 (Cambridge, Massachusetts: National Bureau of Economics Research).
- Boskin, Michael J., Marc S. Robinson, and Alan M. Huber, 1987, “New Estimates of State and Local Government Tangible Capital and New Investment,” NBER Working Paper No. 2131 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Canning, David, and Peter Pedroni, 1999, “Infrastructure and Long Run Economic Growth,” Center for Analytic Economics (CAE) Working Paper No. 99-09 (Ithaca, New York: Cornell University).
- Demetriades, P.O., and T.P. Mamuneas, 2000, “Intertemporal Output and Employment Effects of Public Infrastructure Capital: Evidence from 12 OECD Economies,” Economic Journal, Vol. 110 (July), pp. 687–712.
- Ford, Robert, and Pierre Poret, 1991, “Infrastructure and Private-Sector Productivity,” OECD Economic Studies, Vol. 17 (Autumn), pp. 63–89.
- Gramlich, E.M., 1994, “Infrastructure Investment: A Review Essay,” Journal of Economic Literature, Vol. 32 (September), pp. 1176–96.
- Munnell, Alicia H., 1990, “How Does Public Infrastructure Affect Regional Economic Performance,” in Is There a Shortfall in Public Capital Investment? ed. by Munnell, Federal Reserve Bank of Boston Conference Series No. 34 (Boston).
- Mittnik, Stefan, and Thorsten Neumann, 2001, “Dynamic Effects of Public Investment: Vector Autoregressive Evidence from Six Industrialized Countries,” Empirical Economics, Vol. 26 (May), pp. 429–46.
- Seitz, H., 2001, “Infrastructure Investment and Economic Activity: Theoretical Results and International Evidence,” in Investing Today for the World of Tomorrow, ed. by Deutsche Bundesbank (Berlin: Springer-Verlag).
- Voss, Graham M., 2002, “Public and Private Investment in the United States and Canada,” Economic Modelling, Vol. 19 (August), pp. 641–64.
- Holtz-Eakin, Douglas, 1993, “State-Specific Estimates of State and Local Government Capital,” Regional Science and Urban Economics, Vol. 23 (April), pp. 185–209.
- Ligthart, Jenny, 2002, "Public Capital and Output Growth in Portugal: An Empirical Analysis," European Review of Economics and Finance, Vol. 1 (September), pp. 3–30.

### Econometric Methods, Unit Roots, and Cointegration
- Campbell, JohnY., and Pierre Perron, 1991, “Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots?” in NBER Macroeconomics Annual 1991, ed. by Oliver J. Blanchard and Stanley Fischer (Cambridge, Massachusetts: MIT Press).
- Dickey, David A., and Wayne A. Fuller, 1979, “Distribution of Estimators for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, Vol. 74 (June), pp. 427–31.
- Dickey, David A., and Wayne A. Fuller, 1981, “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica, Vol. 49 (July), pp. 1057–72.
- Dolado, Juan J., Jesus Gonzalo, and Francesca Marmol, 2001, “Cointegration.” in A Companion to Theoretical Econometrics, ed. by Badi H. Baltagi, Blackwell Companions to Contemporary Economics (Oxford: Blackwell).
- Enders, Walter, 1995, Applied Economic Time Series (New York: John Wiley & Sons).
- Engle, Robert F., and C.W.J. Granger, 1987, “Co-Integration and Error Correction: Representation, Estimation, and Testing,” Econometrica, Vol. 55 (March), pp. 251–76.
- Im, Kyung So, M. Hashem Pesaran, and Yongcheol Shin, 2003, “Testing for Unit Roots in Heterogeneous Panels,” Journal of Econometrics, Vol. 115 (July), pp. 53–74.
- Levin, Andrew, Chien-Fu Lin, and Chia-Shang James Chu, 2002, “Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties,” Journal of Econometrics, Vol. 108 (May), pp. 1–24.
- MacKinnon, J.G., 1991, “Critical Values for Cointegration Tests,” in Long-Run Economic Relationships: Readings in Cointegration, ed. by Robert F. Engle and Clive William John Granger (Oxford: Oxford University Press).
- Newey, Whitney K., and Kenneth D. West, 1987, “A Simple, Positive Semi-Definite, Heteroscedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica, Vol. 55 (May), pp. 703–08.
- Phillips, Peter C.B., and Zhijie Xiao, 1998, “A Primer on Unit Root Testing,” Journal of Economic Surveys, Vol. 12 (December), pp. 423–69.
- Stock, James H., 1987, “Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors,” Econometrica, Vol. 55 (September), pp. 1035–56.
- Kennedy, Peter, 1998, A Guide to Econometrics (Oxford: Blackwell; 4th ed.).

### National Accounts, Measurement, and Data Sources
- European Commission, International Monetary Fund, Organization for Economic Cooperation and Development, United Nations, and World Bank, 1993, System of National Accounts 1993 (Brussels: Commission of the European Communities).
- International Monetary Fund, 2001, Government Finance Statistics Manual 2001 (Washington).
- Organization for Economic Cooperation and Development, 1997, Flows and Stocks of Fixed Capital 1971–1996 (Paris).
- Organization for Economic Cooperation and Development, 1998, National Accounts Vol. 1, Main Aggregates, 1960–1996 (Paris).
- Organization for Economic Cooperation and Development, 2001a, Measuring Capital: A Manual on the Measurement of Capital Stocks, Consumption of Fixed Capital and Capital Services (Paris). Available via the Internet: http://www.oecd.org/dataoecd/61/57/1876369.pdf.
- Organization for Economic Cooperation and Development, 2001b, Measuring Productivity: Measurement of Aggregate and Industry-Level Productivity Growth, OECD Manual (Paris).
- Organization for Economic Cooperation and Development, 2002a, Purchasing Power Parities and Real Expenditures: 1999 Benchmark Year, 2002 Edition (Paris).
- Organization for Economic Cooperation and Development, 2002b, National Accounts of OECD Countries, Main Aggregates, Vol. I., 1989-2000 (Paris).
- Organization for Economic Cooperation and Development, 2002c, Measuring the Information Economy (Paris).
- U.S. Bureau of Economic Analysis, 1999, “Fixed Reproducible Tangible Wealth in the United States 1925–94” (Washington: U.S. Department of Commerce). Available via the Internet: http://www.bea.doc.gov/bea/articles/NATIONAL/NIPAREL/Meth/wlth2594.pdf.
- Jacob, Verughese, Subhash C. Sharma, and Richard Grabowski, 1997, “Capital Stock Estimates for Major Sectors and Disaggregated Manufacturing in Selected OECD Countries,” Applied Economics, Vol. 29 (May), pp. 563–79.
- Boskin, Michael J., Marc S. Robinson, and Alan M. Huber, 1987, “New Estimates of State and Local Government Tangible Capital and New Investment,” NBER Working Paper No. 2131 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Florio, Massimo, 2001, “On Cross-Country Comparability of Government Statistics: Public Expenditure Trends in OECD National Accounts,” International Review of Applied Economics, Vol. 15 (April), pp. 181–98.
- Fonte, Angel de la, and Rafael Doménech, 2002, “Human Capital in Growth Regressions: How Much Difference Does Data Quality Make? An Update and Further Results,” CEPR Discussion Paper No. 3587 (London: Center for Economic Policy Research).
- Luetzel, Heinrich, 1977, “Estimates of Capital Stock by Industries in the Federal Republic of Germany,” Review of Income and Wealth, Vol. 23, No. 1, pp. 63–78.
- O’Mahony, Mary, 1996, “Measures of Fixed Capital Stocks in the Post-War Period: A Five-Country Study,” in Quantitative Aspects of Post-War European Economic Growth, ed. by Nicholas Crafts and Bart van Ark (Cambridge: Cambridge University Press).
- Feinstein, C.H., 1972, National Income, Expenditure and Output of the United Kingdom, 1855–1965, Studies in the National Income and Expenditure of the United Kingdom, Vol. 6 (Cambridge: Cambridge University Press).
- Mitchell, Brian R., 1975, European Historical Statistics 1750–1970 (London: Macmillan).

### Historical and Country Studies
- Broadberry, Stephen, 1988, “The Impact of the World Wars on the Long Run Performance of the British Economy,” Oxford Review of Economic Policy, Vol. 4 (Spring), pp. 25–37.
- Eichengreen, Barry, and Albrecht Ritschl, 1998, “Winning the War, Losing the Peace? Britain’s Post-War Recovery in a West German Mirror,” CEPR Discussion Paper No.1809 (London: Center for Economic Policy Research).
- Giersch, Herbert, Karl-Heinz Paqué, and Holger Schmieding, 1992, The Fading Miracle: Four Decades of Market Economy in Germany (Cambridge: Cambridge University Press).
- Maddison, Angus, 1982, Phases of Capitalist Development (Oxford: Oxford University Press).
- Maddison, Angus, 1987, “Growth and Slowdown in Advanced Capitalist Economies: Techniques of Quantitative Assessment,” Journal of Economic Literature, Vol. 25 (June), pp. 649–98.
- Maddison, Angus, 1991, Dynamic Forces in Capitalist Development: A Long-Run Comparative View (Oxford: Oxford University Press).
- Maddison, Angus, 1995, “Standardised Estimates of Fixed Capital Stock: A Six Country Comparison,” in Explaining the Economic Performance of Nations: Essays in Time and Space (Economists of the Twentieth Century), ed. by Maddison (Aldershot: Edward Elgar).
- Ritschl, Albrecht, 2003, “Modern Germany” (unpublished; Humboldt University, Berlin). Available via the Internet: http://www.wiwi.hu-berlin.de/wg/ritschl/pdf_files/ModernGermanyIn5000Words.pdf.
- Ritschl, Albrecht, and M. Spoerer, 1997, “Das Bruttosozialprodukt in Deutschland nach den amtlichen Volkseinkommens—und Sozialproduktsstatistiken 1901–1995,” Jahrbuch für Wirtschaftsgeschichte, No.2, pp. 27–54.
- Fitz Gerald, John, and others, eds., 1999, “National Investment Priorities for the Period 2000–2006,” ESRI Policy Research Series, No. 33 (Dublin: Economic and Social Research Institute).
- Seitz, H., 2001, “Infrastructure Investment and Economic Activity: Theoretical Results and International Evidence,” in Investing Today for the World of Tomorrow, ed. by Deutsche Bundesbank (Berlin: Springer-Verlag).

### Productivity, Growth, and Sector Studies
- Demetriades, P.O., and T.P. Mamuneas, 2000, “Intertemporal Output and Employment Effects of Public Infrastructure Capital: Evidence from 12 OECD Economies,” Economic Journal, Vol. 110 (July), pp. 687–712.
- Evans, Paul, and Georgios Karras, 1994, “Is Government Capital Productive? Evidence from a Panel of Seven Countries,” Journal of Macroeconomics, Vol. 16 (Spring), pp. 271–79.
- Fuente, Angel de la, and Rafael Doménech, 2002, “Human Capital in Growth Regressions: How Much Difference Does Data Quality Make? An Update and Further Results,” CEPR Discussion Paper No. 3587 (London: Center for Economic Policy Research).
- Ford, Robert, and Pierre Poret, 1991, “Infrastructure and Private-Sector Productivity,” OECD Economic Studies, Vol. 17 (Autumn), pp. 63–89.
- Voss, Graham M., 2002, “Public and Private Investment in the United States and Canada,” Economic Modelling, Vol. 19 (August), pp. 641–64.
- Sturm, Jan-Egbert, and Jakob de Haan, 1995, “Is Public Expenditure Really Productive? New Evidence for the USA and the Netherlands,” Economic Modelling, Vol.12 (January), pp. 60–72.
- Sturm, Jan-Egbert, Gerald H. Kuper, and Jakob de Haan, 1998, “Modelling Government Investment and Economic Growth on a Macro Level: A Review,” in Market Behaviour and Macroeconomic Modelling ed. by Steven Brakman, Hans van Ees, and Simon K. Kuipers (London: Macmillan Press).
- Ligthart, Jenny, 2002, "Public Capital and Output Growth in Portugal: An Empirical Analysis," European Review of Economics and Finance, Vol. 1 (September), pp. 3–30.

*Source: _wp0467 - REFERENCES*

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