## _wp11217

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---

### I. Introduction and main contributions
- Constructs a new dataset of total capital stock for 71 countries and disaggregates it into private and public capital, with public capital stock adjusted for the efficiency of public investment using the Public Investment Management Index (PIMI).
- Investigates the effect of PIMI-adjusted public capital on growth within a production-function framework.
- Examines effects of four stages of the public investment process—Appraisal, Selection, Implementation, Evaluation—on capital accumulation and growth.
- Two headline findings:
  - Statistically significant but relatively small contribution of efficiency-adjusted public capital to total income; public capital share larger in middle-income than in low-income countries. Marginal product of public capital relatively large in low-income countries because of lower efficiency-adjusted capital stock.
  - Project selection and implementation are important contributors to public capital and growth when specific stages are incorporated.

### II. Data and methodology: construction of capital stocks
- Perpetual-inventory approach used; alternative efficiency-adjusted perpetual inventory formulation replaces gross public investment I_t by effective investment q_i I_t where 0 ≤ q_i ≤ 1.
- Data sources and sample:
  - 71 countries with data from Penn World Table (PWT) version 6.2 and IMF World Economic Outlook (WEO); PIMI constructed for 71 countries (40 low-income, 31 middle-income).
  - For years before 1960 an artificial investment series built assuming investment grew by 4 percent a year to reach its 1960 level.
- PIMI:
  - Composed of 17 indicators grouped into four stages: (i) Project Appraisal; (ii) Project Selection; (iii) Project Implementation; (iv) Project Evaluation.
  - PIMI score is a simple average of stage scores; stage scores are between 0 and 1 so total PIMI score is between 0 and 4.
  - PIMI sources largely cover 2007–2010.
- Inputs and assumptions (Appendix B):
  - Depreciation rate: for low-income countries constant at 2.5 percent per year; for middle-income countries increases monotonically at a constant rate from 2.5 percent in 1960 to 4.3 percent in 2010.
  - Initial public capital stock in 1960 derived from artificial pre-1960 investment series and assumption of zero stock in 1860.
  - Effective public investment series = normalized overall PIMI index q_t times gross public investment I_t.

### III. Stylized facts and key statistics (period aggregates, 1960–2009)
- GDP growth, 1960-2009:
  - Low-Income Countries: 3.5
  - Middle-Income Countries: 4.3
  - All countries: 3.9
- Public Investment (% of GDP), 1960-2009:
  - Low-Income Countries: 4.4
  - Middle-Income Countries: 6.2
  - All countries: 5.1
- Public capital stock growth, 1960-2009:
  - Low-Income Countries: 4.2
  - Middle-Income Countries: 4.0
  - All countries: 4.1
- PIMI by income group (values with standard deviations in parentheses):
  - Low Income (40): PIMI = 0.5 (0.26); Appraisal = 0.4 (0.13); Selection = 0.3 (0.11); Implementation = 0.3 (0.10); Evaluation = 0.2 (0.10).
  - Middle Income (31): PIMI = 0.57 (0.25); Appraisal = 0.4 (0.09); Selection = 0.3 (0.11); Implementation = 0.3 (0.07); Evaluation = 0.22 (0.07).
  - All countries (71): PIMI = 0.51 (0.26); Appraisal = 0.4 (0.11); Selection = 0.3 (0.11); Implementation = 0.3 (0.09); Evaluation = 0.21 (0.09).
- Unadjusted vs PIMI-adjusted public capital (selected findings from Table 3):
  - For 71 PIMI countries, gap between traditional (unadjusted) and PIMI-adjusted public capital stock was about 7 percentage points of GDP in the 1960s and increased to more than 40 percentage points of GDP in recent years.
  - Effective public capital declined from 57 percent of GDP in the 1960s to 36 percent of GDP in recent years, while unadjusted public capital suggested an increase of almost 20 percentage points of GDP.
  - During 1960-90: Middle-income countries effective public capital increased by 10 percentage points of GDP; Low-income countries effective public capital fell by almost double that amount.

### IV. Growth rates of public capital (headline and printed sequences)
- Headline rate: "2.8 percent per year for all countries taken together, a rate that is 1.3 percentage points slower than the rate of growth of unadjusted public capital."
- Reported five-year average growth-rate sequences (as printed):
  - Unadjusted Public Capital Stock / PIMI-adjusted Public Capital Stock (five-year averages, as printed):
    - Low-Income (LICs): 4.4 5.1 2.9 4.4 4.2 2.6 2.7 2.0 3.7 2.7
    - Middle-Income (MICs): 4.5 6.2 3.0 2.3 4.0 3.0 4.2 2.4 1.9 2.9
    - All countries: 4.4 5.6 2.9 3.5 4.1 2.8 3.3 2.1 2.9 2.8
- PIMI-adjusted public capital stock shows a downward trend in contrast to the non-adjusted series; gap between unadjusted and adjusted series is "significant."
- Time-varying PIMI extension: ICRG Investment Profile used to extend PIMI backwards (ICRG indices available from 1985 onwards; PIMI fixed at its 1985 value for 1960–1985 in baseline).

### V. Estimation approach and baseline regression results
- Production-function panel:
  - Y_t = aggregate output; inputs: skill-adjusted labor S_t, private capital K_t, public capital G_t; Cobb-Douglas assumed with parameters A, α, β, γ.
  - Country fixed effects η_i and shocks υ_it; five-year average growth rates used; endogeneity addressed with dynamic system GMM (Blundell and Bond, 1998).
- Sample for baseline regressions:
  - Reduced sample of 52 countries due to missing observations: MIC = 24, LIC = 28; Observations = 414.
- Static fixed-effects results (Table 5, column 4 — ALL):
  - Skilled Labor: 0.523*** (0.19)
  - Private Capital: 0.265*** (0.07)
  - PIMI-adjusted Public Capital: 0.197*** (0.07)
  - Implied marginal productivities reported: Private Capital 0.45; PIMI-adjusted Public Capital 0.88
- Dynamic system GMM results (Table 6, column 4 — ALL):
  - Skilled Labor: 0.336* (0.19)
  - Private Capital: 0.297*** (0.09)
  - PIMI-adjusted Public Capital: 0.154* (0.08)
  - Implied marginal productivities reported: Private Capital 0.51; PIMI-adjusted Public Capital 0.69
  - Hansen J-test p-values: [1.00]; AR(2) test p-values: [0.71]
- Key contrasts:
  - PIMI adjustment raises coefficient estimates for private capital relative to unadjusted-capital regressions.
  - In fixed-effects baseline for ALL, unconstrained factor shares: Skilled Labor 52.3 percent, Private Capital 26.5 percent, Public Capital 19.7 percent.
  - In dynamic system-GMM, coefficient on public capital falls from 0.23 (unadjusted) to 0.15 (PIMI-adjusted) for the entire sample; for LICs public-capital factor share falls from 0.25 to 0.14; MICs coefficients nearly unchanged.
  - Dynamic GMM shows roughly a twofold difference between adjusted public and private capital in all three samples (around 15 percent for public capital and 30 percent for private capital).

### VI. Marginal productivities and interpretation
- Marginal product calculation: MP_X = a (Y/X); MPG = β (GDP/GPIMI) (notations used in source).
- Fixed-effects model: MPG jumps from 0.42 to 0.88 after PIMI adjustment for the entire sample.
- Dynamic GMM model: MPG increases from 0.52 to 0.69 after PIMI adjustment.
- Interpretation emphasized in the paper:
  - Ignoring public investment inefficiencies leads to underestimation of marginal productivities of both private and public capital.
  - With PIMI adjustment the absolute gap between public and private capital productivities widens.
  - Regressions with PIMI-adjusted public capital show lower error variance and "more than 11 percent reduction in the mean-squared-errors of predicted output levels."

### VII. Stages of the public investment process and their contributions
- Method: construct alternative PIMI-adjusted public capital stocks omitting one stage at a time (weighted average over remaining three stages) and estimate dynamic GMM; alternative two-step estimation used to obtain stage weights.
- Reported two-step estimated weights:
  - Appraisal: 0.215
  - Selection: 0.311
  - Implementation: 0.334
  - Evaluation: 0.140
- High-level findings (Table 7 and Appendix D):
  - LICs: exclusion of Implementation and Selection stages leads to lower implied marginal productivities and insignificant factor-share estimates → Implementation and Selection relatively more important in LICs.
  - MICs: omission of Appraisal and Evaluation reduces marginal productivities and factor shares → Appraisal and Evaluation relatively more important in MICs.
  - ALL sample: Implementation stands out as the stage with higher relative productivity.
- Regression evidence from Appendix D (dependent variable: log-difference of real GDP in international dollars; standard errors in parentheses; significance markers preserved):
  - Skilled Labor:
    - ALL: 0.486*** (0.18)
    - MIC: 0.400** (0.19)
    - LIC: 0.588*** (0.19)
  - Private Capital:
    - ALL: 0.332*** (0.09)
    - MIC: 0.402*** (0.04)
    - LIC: 0.316*** (0.07)
  - Appraisal Share:
    - ALL: 0.033** (0.02)
    - MIC: 0.028** (0.01)
    - LIC: 0.036* (0.02)
  - Selection Share:
    - ALL: 0.038** (0.02)
    - MIC: 0.012 (0.01)
    - LIC: 0.053*** (0.02)
  - Implementation Share:
    - ALL: 0.034** (0.01)
    - MIC: 0.007 (0.01)
    - LIC: 0.042** (0.02)
  - Observations: 414 (ALL), 186 (MIC), 228 (LIC).

### VIII. Robustness checks and alternative specifications
- Time-varying PIMI using ICRG Investment Profile increases coefficient on adjusted public capital slightly to 0.17.
- Re-weighted PIMI using estimated stage weights yields results "very similar" to baseline.
- Alternative production technologies:
  - Nested CES tested; key elasticity-of-substitution parameter insignificant, supporting Cobb-Douglas baseline.
  - Imposing constant returns to scale yields public capital share of 17 percent and increases coefficient on skill-adjusted labor by more than 40 percent relative to baseline Table 6 estimates.
- Labor specification: splitting quality-adjusted labor into raw labor and human capital finds raw labor coefficient insignificant while human capital identifies the specification—supporting use of skill-adjusted labor.
- Sample variation: restricting to post-1980 increases coefficients slightly without changing statistical significance.

### IX. Key conclusions and policy implications
- Accounting for public investment efficiency materially changes measured public capital stocks and estimated contribution of public capital to growth.
- The stock of effective public capital might be up to one-half of the stock suggested by traditional methods for computing public capital stock.
- Public capital plays a significant role in explaining output variations; productivity of public capital has been grossly underestimated by previous studies.
- Policy recommendations:
  - Improve project implementation (including competitive bidding and internal audit), especially in low-income countries where implementation and selection are most binding.
  - Strengthen project selection (including existence of medium-term frameworks and linkage to annual budgetary policies), especially in low-income countries.
  - Tailor recommendations to country circumstances: in middle-income countries focus relatively more on improving appraisal and evaluation.

### X. Appendices highlights
- Appendix A: List of countries with PIMI scores; median overall PIMI = 1.65; S.D. = 0.65. Example country overall scores reported (as printed): Afghanistan 2.10; Brazil 3.12; Colombia 3.07; South Africa 3.53; Tunisia 2.97; Nigeria 1.14; Lao PDR 0.90; Belize 0.27; Congo, Republic of 0.50; West Bank and Gaza 0.80; Yemen 0.80.
- Appendix B: Detailed inputs for constructing PIMI-adjusted public capital stock series (depreciation schedules, initial conditions, mapping of PIMI to effective investment).
- Appendix C: Analytic continuous-time comparison of adjusted vs unadjusted capital stocks; if starting adjusted capital equals unadjusted starting capital then adjustment reduces to time-invariant proportional scaling.
- Appendix D: Notional stage-specific capital stocks and regression evidence on stage shares’ effects on growth (see Section VII).
- Appendix E: CES production function specification and exact algebraic mappings to recover CES parameters from estimated coefficients.

*Source: _wp11217 - 1. GDP Growth, Public Investment and Public Capital Stock Growth, 1960–2009 (PDF).*

### 1. GDP Growth, Public Investment and Public Capital Stock Growth, 1960–2009 .................8

### 1. GDP Growth, Public Investment and Public Capital Stock Growth, 1960–2009

### Overview of chapters and main sections
- 1. GDP Growth, Public Investment and Public Capital Stock Growth, 1960–2009 .................8
- 2. Public Investment Management Index (PIMI) by Income Group .......................................11
- 3. Unadjusted and PIMI-adjusted Public Capital Stock by Income Group .............................13
- 4. Growth Rate of Public Capital Stock by Income Group ......................................................13
- 5. Static Fixed Effects Regressions with PIMI-adjusted Public Capital ..................................17
- 6. Dynamic System GMM Regressions with PIMI-adjusted Public Capital ...........................18
- 7. Regressions for Public Investment Stage .............................................................................21
- 8. Results of Robustness Tests .................................................................................................23

### Figures included
- Figure 1. Investment Ratio and Growth Rate of Public Capital ............................................................9
- Figure 2. PIMI Distribution and Decomposition by Sub-Index ..........................................................11
- Figure 3. Spearman Correlation Between PIMI and other Indicies ....................................................12
- Figure 4. Unadjusted and PIMI-adjusted Capital Stock by Income Group.........................................14
- Figure 5. Time-varying PIMI ..............................................................................................................22

### Appendixes
- Appendix A. List of countries with Corresponding PIMI ........................................................................29
- Appendix B. Details on the Construction of PIMI-adjusted Public Capital Stock Series ........................32
- Appendix C. Initial Conditions and PIMI Effect on Efficiency Adjusted Capital ...................................33
- Appendix D. Alternative Approach to Assessing the Effect of Different Stages of Public Investment on Aggregate Output ................................................................................................................34
- Appendix E. Recovering the Parameters of the CES Production Function ..............................................36

*Source: _wp11217 - 1. GDP Growth, Public Investment and Public Capital Stock Growth, 1960–2009 (PDF).*

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

### _wp11217 - References

### I. Introduction
- Many developing countries have a long legacy of failed public projects, breeding skepticism about ability to scale up public investment.
- Paper's three contributions:
  - Constructs a new dataset of total capital stock for a large number of developing countries and disaggregates it into private and public capital. Novel feature: public capital stock is adjusted for the efficiency of public investment using the Public Investment Management Index (PIMI).
  - Investigates the effect of adjusted public capital on growth, following literature on the public capital-growth nexus.
  - Examines effects of four specific stages of the public investment process—appraisal, selection, implementation and evaluation—on capital accumulation and growth.
- Two main findings:
  - There is a statistically significant but relatively small contribution of efficiency-adjusted public capital to total income. The public capital share is larger in middle-income than in low-income countries. While the share of public capital is small in low-income countries, the marginal product of public capital is relatively large because of the lower efficiency-adjusted capital stock.
  - Project selection and implementation are important contributors to public capital and growth when specific stages of the public investment process are incorporated.

### II. Literature review (selected points)
- Early production-function studies (e.g., Aschauer 1989, 1998; Munnell 1990a) found large impacts of public capital on growth; Munnell’s estimates: impact of public capital on growth of 0.31–0.39.
- Methodological critiques (Gramlich, 1994) raised concerns about reverse causation and non-stationarity, producing a new generation of studies with substantially lower effects (Romp and de Haan 2007).
- Bom and Ligthart (2010) meta-regression:
  - Average output elasticity of public capital estimated to be 0.15; conditional benchmark estimate 0.17.
  - Implied marginal productivity of public capital for the United States: range of 28.8–32.6 percent in 2001.
- Arslanalp et al., 2010:
  - Estimated production function for 48 developed and developing countries.
  - Short-term effect stronger for developed countries: 0.13.
  - Long-term effect stronger for developing countries: 0.26.
  - Benefits of new investment in developing countries tend to accrue over time; may require extending debt sustainability timeframes.
- Pritchett (2000) critique: cumulated depreciated public investment effort (CUDIE) ignores efficiency with which public investment is turned into productive capital—motivates the paper’s efficiency-adjusted approach.

### III. Data and methodology: construction of capital stocks
- Perpetual inventory equation used (notation from source):
  - (1) ܭ
௜௧
ܭൌ
௜௧ିଵ
ߜെ
௜௧
ܭכ
௜௧ିଵ
ܫ൅
௜௧ିଵ
- For constructing series:
  - Data for 71 countries on total investment and GDP taken from Penn World Table (PWT) version 6.2 starting in 1960 for most of the sample.
  - Before 1960, an artificial investment series was built assuming investment grew by 4 percent a year to reach its level observed in 1960.
  - Total investment disaggregated by applying public and private investment shares from IMF World Economic Outlook (WEO) database.
  - Resulting dataset claimed as the largest available for developing countries; sample includes countries with (i) PWT and WEO data and (ii) an index of quality of public investment processes.
- Alternative, efficiency-adjusted perpetual inventory formulation:
  - (2) Ԣܭ
௜௧
Ԣܭൌ
௜௧ିଵ
ߜെ
௜௧
Ԣܭכ
௜௧ିଵ
ݍ൅
௜
ܫכ
௜௧ିଵ
  - ݍ
௜
 is a time-invariant index capturing efficiency of public investment, varying between 0 and 1. Traditional equation is special case with ݍ
௜
 = 1.
- PIMI used as proxy for ݍ
௜
:
  - PIMI composed of 17 indicators grouped into four stages: (i) Project Appraisal; (ii) Project Selection; (iii) Project Implementation; and (iv) Project Evaluation.
  - PIMI sources largely cover 2007–2010; include 71 countries (40 low-income countries and 31 middle-income countries).
  - PIMI score is a simple average of the score for each stage; stage scores are between 0 and 1 so total PIMI score is between 0 and 4.

### IV. Stylized facts, key statistics, and PIMI results
- Table 1 (period aggregates, 1960–2009) — selected figures reproduced exactly:
  - GDP growth, 1960-2009:
    - Low-Income Countries: 3.5
    - Middle-Income Countries: 4.3
    - All countries: 3.9
  - Public Investment (% of GDP), 1960-2009:
    - Low-Income Countries: 4.4
    - Middle-Income Countries: 6.2
    - All countries: 5.1
  - Public capital stock growth, 1960-2009:
    - Low-Income Countries: 4.2
    - Middle-Income Countries: 4.0
    - All countries: 4.1
- Observations:
  - Middle-income countries’ average GDP growth was almost 1 percentage point above low-income countries during last 50 years; middle-income countries invested on average over 2 percentage points of GDP more than low-income countries.
  - Growth rate differences in public capital stock are smaller, possibly due to base effects (a small addition yields large growth rate when base is low).
- Table 2. PIMI by income group (values with standard deviations in parentheses):
  - Low Income (40): PIMI = 0.5 (0.26); Appraisal = 0.4 (0.13); Selection = 0.3 (0.11); Implementation = 0.3 (0.10); Evaluation = 0.2 (0.10).
  - Middle Income (31): PIMI = 0.57 (0.25); Appraisal = 0.4 (0.09); Selection = 0.3 (0.11); Implementation = 0.3 (0.07); Evaluation = 0.22 (0.07).
  - All countries (71): PIMI = 0.51 (0.26); Appraisal = 0.4 (0.11); Selection = 0.3 (0.11); Implementation = 0.3 (0.09); Evaluation = 0.21 (0.09).
- Interpretation:
  - On average, only about half of public investment effort translates into actual productive public capital in the PIMI sample.
  - Substantial cross-country heterogeneity in overall PIMI and in sub-indices; variation across the four stages suggests different bottlenecks in different countries.
  - The paper constructs alternative capital stock series for each country corresponding to three out of four investment stages (leaving one stage out) to identify which stages matter most for capital accumulation and output.
- Correlations with other institutional indices (Spearman):
  - PIMI correlations: CPIA ≈ 0.5; Budget Institutions Index ≈ 0.6; positive but lower correlations with Kaufmann-Kraay governance indicators (Government Effectiveness, Control of Corruption, Average of Governance Indicators).
  - Implication: PIMI captures information on specific dimensions of institutional quality not fully captured by other indices.
- Table 3 (comparison of unadjusted and PIMI-adjusted public capital stock, percent of GDP) — selected findings:
  - For the 71 countries with PIMI, gap between traditional (unadjusted) and PIMI-adjusted public capital stock was about 7 percentage points of GDP in the first decade (1960s).
  - The gap increased to more than 40 percent of GDP in recent years.
  - Effective public capital declined from 57 percent of GDP in the 1960s to 36 percent of GDP in recent years, while unadjusted public capital suggested an increase of almost 20 percentage points of GDP.
  - During 1960-90:
    - Middle-income countries: effective public capital increased by 10 percentage points of GDP.
    - Low-income countries: effective public capital fell by almost double that amount.
- Growth rates of PIMI-adjusted public capital:
  - During 1960–2009 PIMI-adjusted public capital grew by about (text truncated in source at the end of provided content).

### V. Key conclusions and points emphasized by the paper (as presented)
- Accounting for public investment efficiency materially changes measured public capital stocks and thus the estimated contribution of public capital to growth.
- Differences in PIMI scores across countries and across stages of the investment cycle highlight the importance of institutional quality in converting public investment spending into productive capital.
- Project selection and implementation emerge as particularly important stages affecting capital accumulation and growth when stage-level measures are used.

*Source: Excerpts from IMF Working Paper _wp11217 (content provided).*

### 2.8 percent per year for all countries taken together, a rate that is 1.3 percentage points

### _wp11217 - 2.8 percent per year for all countries taken together, a rate that is 1.3 percentage points

### Growth rates of public capital
- Headline: "2.8 percent per year for all countries taken together, a rate that is 1.3 percentage points slower than the rate of growth of unadjusted public capital."
- Reported growth-rate sequences (as printed):
  - Table 4 title: Growth Rate of Public Capital Stock by Income Group (In Percent)
  - Unadjusted Public Capital Stock / PIMI-adjusted Public Capital Stock rows (as printed):
    - Low-Income (LICs)64.973.484.071.057.940.038.430.1
    - Middle-Income (MICs)62.7119.3119.193.256.966.558.044.4
    - All countries64.090.398.380.257.449.846.436.1
  - Unadjusted Public Capital Stock / PIMI-adjusted Public Capital Stock (five-year average growth rates, as printed):
    - Low-Income (LICs)4.45.12.94.44.22.62.72.03.72.7
    - Middle-Income (MICs)4.56.23.02.34.03.04.22.41.92.9
    - All countries4.45.62.93.54.12.83.32.12.92.8
- Data sources cited: PWT version 6.2, IMF WEO, and Dabla-Norris et al. (2011).

### PIMI adjustment and time‑pattern of public capital
- The PIMI-adjusted public capital stock shows a downward trend, unlike the non-adjusted public capital stock; middle-income countries experienced some growth in earlier periods.
- The gap between unadjusted and PIMI-adjusted series is described as "significant."
- Initial conditions for PIMI matter: applying a time-invariant PIMI starting in 1860 (counterfactual) implies proportionality between unadjusted and adjusted stocks and equivalence of growth rates; in the sample PIMI is applied from 1960, so growth rates differ.
- Time-varying PIMI extension: observed variation in the ICRG Investment Profile is used to extend PIMI backwards (ICRG indices available from 1985 onwards; PIMI fixed for 1960-1985 at its 1985 value).

### Estimation method (production-function panel approach)
- Production function specified with inputs:
  - Yt = real aggregate output
  - Kt = aggregate private capital stock
  - Gt = aggregate public capital stock
  - St = skill-adjusted aggregate labor supply; St constructed using average years of schooling and stepwise linear φ(h) (returns to education).
- Cobb-Douglas assumption with parameters A, α, β, γ (A > 0, α, β, γ ∈ (0, 1)).
- Country-specific fixed effects ηi and idiosyncratic shocks υit; five-year average growth rates used to remove fixed effects and mitigate business-cycle effects.
- Endogeneity addressed by dynamic system GMM (Blundell and Bond, 1998) allowing for AR(1) in υit; dynamic representation yields nonlinear common-factor restrictions (see equation (6)).

### Baseline results — Static fixed effects (Table 5) and Dynamic system GMM (Table 6)
- Sample: baseline regressions use a sample reduced to 52 countries because of missing observations; subsamples: MIC = 24 middle-income countries, LIC = 28 low-income countries.
- Static fixed-effects (with PIMI; Table 5, column 4 — ALL):
  - Skilled Labor: 0.523*** (standard error (0.19))
  - Private Capital: 0.265*** (0.07)
  - PIMI-adjusted Public Capital: 0.197*** (0.07)
  - Implied marginal productivities (reported): Private Capital 0.45; PIMI-adjusted Public Capital 0.88
  - Observations: 414; Countries: 52
- Dynamic system GMM (with PIMI; Table 6, column 4 — ALL):
  - Skilled Labor: 0.336* (0.19)
  - Private Capital: 0.297*** (0.09)
  - PIMI-adjusted Public Capital: 0.154* (0.08)
  - Implied marginal productivities (reported): Private Capital 0.51; PIMI-adjusted Public Capital 0.69
  - Hansen J-test p-values: [1.00]; AR(2) test p-values: [0.71] (reported in table cells)
  - Observations: 414; Countries: 52
- Key contrasts and magnitudes:
  - Using efficiency-adjusted (PIMI) capital raises coefficient estimates for private capital relative to unadjusted-capital regressions.
  - In fixed-effects baseline for ALL, unconstrained factor shares: Skilled Labor 52.3 percent, Private Capital 26.5 percent, Public Capital 19.7 percent.
  - In dynamic system-GMM, coefficient on public capital falls from 0.23 (unadjusted) to 0.15 (PIMI-adjusted) for the entire sample; for LICs the public-capital factor share falls from 0.25 to 0.14; MICs coefficients are nearly unchanged.
  - Dynamic GMM shows roughly a twofold difference between adjusted public and private capital in all three samples (around 15 percent for public capital and 30 percent for private capital).

### Marginal productivities and interpretation
- Marginal product calculations use MPX = a(Y/X) with MPG = β(GDP/GPIMI).
- Fixed-effects model: MPG jumps from 0.42 to 0.88 after PIMI adjustment for the entire sample.
- Dynamic GMM model: MPG increases from 0.52 to 0.69 after PIMI adjustment.
- Policy-relevant interpretation:
  - Ignoring public investment inefficiencies leads to underestimation of marginal productivities of both private and public capital.
  - With PIMI adjustment the absolute gap between public and private capital productivities widens.
  - Regressions with PIMI-adjusted public capital show lower error variance and "more than 11 percent reduction in the mean-squared-errors of predicted output levels."

### Contribution of public investment process stages (Table 7)
- Four stages considered: Appraisal, Selection, Implementation, Evaluation.
- Approach: create alternative PIMI-adjusted public capital stocks omitting one stage at a time (weighted average over remaining three stages) and estimate dynamic GMM.
- Reported findings (high-level):
  - LICs: exclusion of Implementation and Selection stages leads to lower implied marginal productivities and insignificant factor-share estimates → Implementation and Selection relatively more important in LICs.
  - MICs: omission of Appraisal and Evaluation stages reduces marginal productivities and factor shares → Appraisal and Evaluation relatively more important in MICs.
  - ALL sample: Implementation stands out as the stage with higher relative productivity.
- Alternative weights obtained via two-step estimation (reported weights):
  - Appraisal: 0.215
  - Selection: 0.311
  - Implementation: 0.334
  - Evaluation: 0.140

### Robustness checks and alternative specifications
- Time‑varying PIMI: applying ICRG Investment Profile variation increases coefficient on adjusted public capital slightly to 0.17, indicating robustness of baseline.
- Alternative weights for PIMI (re-weighted PIMI using estimated weights shown above) produce results "very similar" to baseline in factor shares and fit.
- Alternative production technology:
  - Nested CES specification tested; key parameter for elasticity of substitution is insignificant, supporting Cobb-Douglas baseline.
  - Imposing constant returns to scale (CRTS) yields a public capital share of 17 percent and increases coefficient on skill-adjusted labor by more than 40 percent relative to baseline Table 6 estimates.
- Labor specification:
  - Splitting quality-adjusted labor into raw labor and human capital: raw labor coefficient is insignificant while human capital identifies the specification — supporting the use of skill-adjusted labor in baseline.
- Sample variation:
  - Restricting sample to period after 1980 increases coefficients slightly but does not change overall statistical significance.
  - Expanding to the entire set of 122 developing countries (using unadjusted public capital) was undertaken (results truncated in provided extract).
- Additional robustness summary items reported in Table 8 (parameter estimates, standard errors, z-statistics, p-values and confidence intervals) and a set of model-fit comparisons (e.g., Constant Returns to All Inputs, Constant Elasticity of Substitution) consistent with baseline conclusions (table cells preserved in source).

*Source: Authors’ calculations using data from PWT version 6.2, IMF WEO, and Dabla‑Norris et al. (2011).*

### 16.7 percent is significant and somewhat larger than our baseline estimate. Therefore, even

### _wp11217 - 16.7 percent is significant and somewhat larger than our baseline estimate. Therefore, even

### V. Concluding remarks — key findings
- Constructed a new dataset on private and public capital accounting for public investment inefficiencies (PIMI).
- Controlling for PIMI shows that the actual accumulation of productive public capital was significantly slower than suggested by government spending on investment.
- The stock of effective public capital might be up to one-half of the stock suggested by the traditional method for computing public capital stock.
- Public capital plays a significant role in explaining output variations; baseline and robustness specifications show a consistently significant impact of public capital on output.
- The productivity of public capital has been grossly underestimated by previous studies.
- Controlling for the efficiency of investment processes, the productivity of public capital is significantly higher than the marginal cost of funds under normal financing conditions; this is especially true for LICs.
- Project implementation is identified as the most important component of the overall investment process (driven by LICs), followed by project selection. In MICs, project appraisal and evaluation are relatively more productive stages.

### Policy implications and recommendations
- Improving project implementation (including competitive bidding and internal audit) can significantly benefit public investment and growth in low-income countries.
- Strengthening project selection (including existence of MT frameworks and linkage to annual budgetary policies) can yield significant benefits for public investment and growth in low-income countries.
- Recommendations for strengthening public investment processes should be tailored to country circumstances, since MICs show relatively more productive gains from improvements in project appraisal and evaluation.

*Italicized final source attribution line will be provided by the pipeline.*

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### Appendix A — PIMI country scores (overview)
- Sample: 52 low-income and middle-income countries (overall sample described across appendices).
- Selected numeric summaries from overall PIMI scores:
  - Median 1.65
  - S.D. 0.65
- Example country overall scores (as reported): 
  - Afghanistan 2.10
  - Brazil 3.12
  - Colombia 3.07
  - South Africa 3.53
  - Tunisia 2.97
  - Nigeria 1.14
  - Lao PDR 0.90
  - Belize 0.27
  - Congo, Republic of 0.50
  - West Bank and Gaza 0.80
  - Yemen 0.80
  - Zimbabwe is not listed in the provided excerpt.

### Appendix A — Sub-index structure and sample statistics
- PIMI composed of four sub-indexes: Appraisal, Selection, Implementation, Evaluation.
- Table 1.b (by sub-index) reports for the overall sample:
  - Median by sub-index: Appraisal 1.33, Selection 1.60, Implementation 2.00, Evaluation 1.33
  - S.D. by sub-index: Appraisal 1.09, Selection 0.78, Implementation 0.76, Evaluation 0.82
- Examples of country sub-index quadruples (Appraisal, Selection, Implementation, Evaluation) from Table 1.b:
  - Afghanistan 2.67, 2.80, 1.60, 1.33
  - Brazil 3.00, 2.80, 3.33, 3.33
  - Colombia 4.00, 2.80, 2.13, 3.33
  - South Africa 4.00, 4.00, 2.80, 3.33

### Appendix B — Construction of PIMI-adjusted public capital stock series (methodology inputs and assumptions)
- Basic capital accumulation follows discrete-time accumulation equations (B1) and (B2) in the source.
- Inputs necessary:
  - Depreciation rate:
    - For low-income countries: constant at 2.5 percent per year.
    - For middle-income countries: increases monotonically at a constant rate from 2.5 percent in 1960 to 4.3 percent in 2010.
  - Initial public capital stock in year 1960:
    - Obtained by creating an artificial investment series before 1960 assuming public investment increased by 4 percent per year to its observed level in 1960.
    - These investment flows before 1960 and the assumption of a zero stock of capital in 1860 give a series up to 1960.
  - Unadjusted public investment series:
    - Obtained by applying the investment share from the WEO database to the total investment series from Penn World Table.
  - Effective public investment series:
    - Obtained by applying the normalized overall PIMI index q_t to the gross public investment series I_t.

### Appendix C — Initial conditions and effect of PIMI on efficiency-adjusted capital (analytic results)
- Continuous-time formulation compares adjusted capital stock K* and unadjusted K, allowing for time-varying depreciation.
- Key analytic points:
  - Adjusted capital stock at any date is a country-specific linear transformation of the unadjusted stock; the shift part is time- and country-dependent (see equations C2–C5).
  - If the starting (initial) adjusted capital equals the unadjusted starting capital (K*(0) = K(0)), then the adjustment reduces to a time-invariant proportional scaling down (equation C7).
- Important historical assumptions used in derivation:
  - If PIMI in 1860 is the same as today, analytic simplifications apply.
  - The derivation credits Mick Keen for the continuous-time derivation.

### Appendix D — Alternative approach: stages of public investment and output
- Notional capital stocks constructed for each PIMI component (appraisal, selection, implementation, evaluation) via equation (D1).
- Analysis includes percent shares of effective capital due to each stage (stage-specific public capital stock divided by total public capital stock).
- Purpose: assess whether, at a given overall investment-process quality, some combinations of PIMI components produce higher or lower effects on output and growth; provides indication on optimal allocation of resources among stages.
- Empirical result summary:
  - Increasing the share of project appraisal by one unit (relative to the share of evaluation) increases output or growth by about 3 percent. Results driven by LICs, where project selection and implementation appear most efficient.
- Regression table D1 — coefficients (dependent variable: log-difference of real GDP in international dollars):
  - Columns: ALL (entire sample of 52 countries), MIC (subsample of 24 middle-income countries), LIC (subsample of 28 low-income countries).
  - Coefficients (with significance markers and standard errors in parentheses):
    - Skilled Labor:
      - ALL: 0.486*** (0.18)
      - MIC: 0.400** (0.19)
      - LIC: 0.588*** (0.19)
    - Private Capital:
      - ALL: 0.332*** (0.09)
      - MIC: 0.402*** (0.04)
      - LIC: 0.316*** (0.07)
    - Appraisal Share:
      - ALL: 0.033** (0.02)
      - MIC: 0.028** (0.01)
      - LIC: 0.036* (0.02)
    - Selection Share:
      - ALL: 0.038** (0.02)
      - MIC: 0.012 (0.01)
      - LIC: 0.053*** (0.02)
    - Implementation Share:
      - ALL: 0.034** (0.01)
      - MIC: 0.007 (0.01)
      - LIC: 0.042** (0.02)
  - Observations: 414 (ALL), 186 (MIC), 228 (LIC)
  - Note: Standard errors in parentheses; [*] p<0.15, * p<0.1, ** p<0.05, *** p<0.01.

### Appendix E — Recovering parameters of the CES production function (specification and parameter recovery)
- Production function specified as a CES with quality-adjusted labor and human capital, private capital K, and PIMI-adjusted public capital Q (equation C1).
- Log-linearization and first-order linearization around ρ = 0 produce estimable form (equations C2–C4).
- Parameters directly and indirectly identified:
  - α is directly identifiable from the regression results.
  - Other parameters recovered via the identities:
    - β̂ = ( (α 1−) ) σ κ̂ ω?  (see original equations for the exact algebraic forms)
    - The source provides the set of equations relating estimated coefficients to CES parameters and the algebraic solution:
      - ܽ = (α1−) σ κ̂ ߜ⋯ (equations in original text)
      - Explicit recovery formulas in the source: ρ = σ, μ = …, etc. (see equations at end of Appendix E for precise mapping).
- The appendix supplies the exact algebraic mappings to solve unknown CES parameters using estimated coefficients (see equations immediately following C4).

*Italicized final source attribution line will be provided by the pipeline.*

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