## _wp10174

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### Key empirical finding
- Initial government debt is associated with lower subsequent growth of real per capita GDP: an average effect of 0.2 percentage points per year.
- The impact is somewhat smaller in advanced economies (around 0.15 percentage points per year).
- Panel core result: a 10 percentage point increase in the initial debt-to-GDP ratio is associated with a slowdown in annual real per capita GDP growth of around 0.2 percentage points per year.

### Nonlinearity and heterogeneity
- Evidence of nonlinearity/thresholds: higher levels of initial debt have a proportionately larger negative effect on subsequent growth.
- High-debt episodes (above 90 percent of GDP) show more pronounced negative effects in some specifications.
- Advanced vs. emerging economies:
  - Initial debt coefficients in advanced economies range from -0.014 to -0.021 (BE, OLS, SGMM reported ranges).
  - Initial debt coefficients in emerging economies range from -0.034 to -0.041 (BE, OLS, SGMM reported ranges).
  - Interpretation: a 10 percentage point increase in initial debt-to-GDP ratio associated with growth slowdown around 0.15–0.2 percent in advanced economies, compared to 0.3–0.4 percent in emerging economies.

### Growth channels (growth accounting)
- Adverse effect on growth largely reflects a slowdown in labor productivity growth (output per worker).
- Productivity slowdown mainly due to:
  - reduced investment, and
  - slower growth of capital stock per worker.
- Growth-accounting results (examples):
  - Growth of output per worker: government debt, initial = -0.019** (BE), -0.013** (Pooled OLS), -0.002 (FE), -0.022** (SGMM).
  - Growth of TFP: government debt, initial coefficients generally insignificant and around -0.008 to -0.011 in BE/SGMM (negative but not always significant).
  - Growth of capital stock per worker: government debt, initial = -0.029* (BE), -0.022** (Pooled OLS), -0.021** (FE), -0.053*** (SGMM).
- Investment channel magnitudes:
  - Domestic investment regressions: government debt, initial = -0.099** (BE), -0.051* (Pooled OLS), -0.062*** (FE), -0.038* (SGMM).
  - SGMM implication: a 10 percentage point increase in initial debt-to-GDP ratio associated with decline in domestic investment by about 0.4 percentage points of GDP (Column 4 example).

### Data, sample, and methods
- Main sample period: 1970–2007.
- Panel: 38 advanced and emerging economies with population over 5 million; eight non-overlapping five-year periods (last period 2005–07 spans three years).
- Data sources:
  - PWT version 6.3 for GDP, population, investment, government size.
  - IMF WEO for fiscal data including government debt.
  - WDI (2009) for other explanatory variables.
  - Barro and Lee (2000) for schooling.
- Dependent variables measured over five-year periods (examples): growth of real per capita GDP; growth of output per worker; TFP growth; growth of capital per worker; domestic investment percent of GDP; volatility (log of std dev of annual growth).
- Growth accounting: Cobb-Douglas Y = A K^α (H L)^{1−α}, per worker y = A k^α H^{1−α}; α choices including α = 0.35 and labor share ≈ 0.65.

### Estimation strategy and methodological considerations
- Core empirical approach: use initial level of government debt to mitigate reverse causality.
- Estimators employed: pooled OLS, robust regression, between estimator (BE), fixed effects (FE), system GMM (SGMM).
- Rationale and trade-offs:
  - BE and SGMM preferred given mixture of omitted-variables bias, measurement error, endogeneity, and dynamic panel bias.
  - FE can exacerbate measurement error bias and may bias toward zero for steady-state determinants when time-fixed effects included.
  - SGMM risks weak instruments if instrument count not restricted; reported SGMM uses collapsed instrument matrix with lag limits.
- SGMM diagnostics examples:
  - Hansen J-test p-value = 0.28 (example) — cannot reject instruments validity.
  - Arellano-Bond AR(2) test p-value = 0.64 (example) — cannot reject null of no second-order serial correlation.
  - Difference-in-Hansen test p-value = 0.34 (example).

### Robustness checks and complementary analyses
- Robust regression used to limit influence of outliers (iterated re-weighted least squares; Cook’s distance > 1 used to drop extremes).
- Sample splits and period restrictions:
  - 1990–2007 restriction yields debt coefficients ranging from -0.021 to -0.028 (except FE), indicating a 10 percentage point increase associated with decline in per capita GDP growth of around 0.2–0.3 percent per year.
  - Expanding sample to 46 countries (removing population >5 million restriction) yields similar results.
- Specification checks:
  - Parsimonious specifications excluding fiscal deficit: initial debt coefficients between -0.014 and -0.026 (BE, OLS, SGMM; FE loses significance).
  - Using average debt instead of initial debt yields similar coefficient ranges: -0.019 to -0.027 (BE, OLS, SGMM).
  - Adding controls (population, aged-dependency, investment, fiscal volatility, urbanization, checks and balances) does not materially change main results.
- Time-fixed effects:
  - Including time-fixed effects reduces size of initial debt coefficients; pooled OLS and SGMM remain significant at 1–5 percent.
  - With time-fixed effects: a 10 percentage point increase in initial debt-to-GDP ratio associated with slowdown in per capita GDP growth around 0.2 percent per year (Appendix 2 example).
  - FE coefficient becomes insignificant and reduces to -0.004 when time-fixed effects included (compare Column 6 with Column 3 example).

### Selected regression coefficients and diagnostics (examples)
- Baseline panel regressions (Table 1 examples; sample: 1970–2007, Advanced and Emerging economies; obs = 166):
  - Government debt, initial: -0.026*** (BE), -0.020*** (Pooled OLS), -0.019*** (FE), -0.029*** (SGMM).
  - Initial per capita real GDP: -2.616*** (BE), -2.257*** (Pooled OLS), -3.598*** (FE), -2.555*** (SGMM).
  - Banking crisis: -1.143 (BE), -0.819** (Pooled OLS), -0.782*** (FE), -1.196* (SGMM).
  - R2 examples across specifications: 0.78, 0.55, 0.4, 0.66, 0.60.
- Table 6 (Impact of a 10 Percent Increase in Debt-to-GDP Ratio by debt group — sample averages and implied growth impacts):
  - Initial Debt Ratios (sample averages): <30: 15.8; 30-60: 45.1; 60-90: 70.3; >90: 111.9.
  - Regression coefficient, average 1/: <30: 0.022; 30-60: -0.025; 60-90: -0.023; >90: -0.017.
  - Growth impact of 10 percent increase in Debt/GDP from sample average 2/: <30: 0.04; 30-60: -0.11; 60-90: -0.16; >90: -0.19.
  - Notes: (1) average of BE, OLS, SGMM estimates on interaction terms; (2) growth impact = regression coefficient × 10 percent of the sample average debt ratios.
- Table 7 (Growth accounts and panel regressions; obs = 159 examples):
  - Growth of output per worker: government debt, initial = -0.019** (BE), -0.013** (Pooled OLS), -0.002 (FE), -0.022** (SGMM).
  - Growth of capital stock per worker: government debt, initial = -0.029* (BE), -0.022** (Pooled OLS), -0.021** (FE), -0.053*** (SGMM).
  - TFP growth: government debt, initial coefficients around -0.008 to -0.011 (BE/SGMM) and generally insignificant.
- Table 8 (Panel regression on investment; obs = 166 for BE/OLS/FE; 159 for SGMM examples):
  - Government debt, initial = -0.099** (BE), -0.051* (Pooled OLS), -0.062*** (FE), -0.038* (SGMM).
  - Lagged investment coefficient example = 0.828*** (BE).
  - SGMM Arellano-Bond AR(2) p-values examples = 0.99; Hansen J p-values examples = 0.42.

### Policy implications and recommendations
- Results underline the need to:
  - Stabilize public debts and place them on a downward trajectory in the medium and long term.
  - Pay particular attention to debt levels above identified thresholds (notably above 90 percent of GDP in some specifications) where negative growth effects are more likely to be significant.
- Emphasize the investment channel:
  - Reducing excessive public debt may support higher investment and faster capital per worker growth, which in turn can support labor productivity and real per capita GDP growth.
- Cautions:
  - Effects vary across estimation methods and samples; FE estimates can be sensitive to time-fixed effects and measurement error.
  - SGMM requires instrument parsimony to avoid weak-instrument bias.

*Source: IMF working paper content (1970–2007 panel analysis; data sources and methodological details as described in the supplied content).*

### 0.2 percentage points per year, with the impact being somewhat smaller in advanced economies.

### 0.2 percentage points per year, with the impact being somewhat smaller in advanced economies.

### Key empirical finding
- Initial government debt is associated with lower subsequent growth of real per capita GDP: an average effect of 0.2 percentage points per year.
- The impact is somewhat smaller in advanced economies.

### Nonlinearity and heterogeneity
- There is evidence of nonlinearity: higher levels of initial debt have a proportionately larger negative effect on subsequent growth.
- Differences between advanced and emerging economies are reported, with the adverse effect being smaller in advanced economies.

### Growth channels (growth accounting)
- The adverse effect on growth largely reflects a slowdown in labor productivity growth.
- The productivity slowdown is mainly due to:
  - reduced investment, and
  - slower growth of capital stock.

### Data, sample, and methods
- Main sample period referenced: 1970–2007.
- Econometric methodologies referenced include BE, FE, and SGMM.
- Robustness checks and nonlinear/specification analyses are part of the empirical strategy.

### Additional empirical notes
- The main results of the analysis were published in the IMF’s May 2010 Fiscal Monitor.
- JEL Classification Numbers: O40, O47, H62, H63
- Keywords: Government debt, growth, growth accounts, crowding out, thresholds, capital per worker, total factor productivity
- Author contact E‑Mail Addresses: mkumar@imf.org, jwoo@imf.org

*This Working Paper should not be reported as representing the views of the IMF. The views expressed herein are those of the authors and should not be attributed to the IMF, its Executive Board, or its management.*

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

### _wp10174 - References .............................................................................................................

### I. Introduction — research question and core result
- Research question: empirical evidence on the impact of high public debt on subsequent growth of real per capita GDP for a panel of advanced and emerging market economies in the period 1970–2007.
- Core finding (panel results across a range of econometric techniques):
  - On average, a 10 percentage point increase in the initial debt-to-GDP ratio is associated with a slowdown in annual real per capita GDP growth of around 0.2 percentage points per year, with the impact being somewhat smaller in advanced economies.
  - Some evidence of nonlinearity: higher levels of initial debt have a proportionately larger negative effect on subsequent growth.
  - Growth decomposition indicates the adverse effect largely reflects a slowdown in labor productivity growth, mainly due to reduced investment and slower growth of capital stock.

### II. Channels and related literature
- Channels through which high public debt may adversely affect medium- and long-run growth:
  - Higher long-term interest rates (e.g., Gale and Orzag, 2003; Baldacci and Kumar, 2010).
  - Higher future distortionary taxation (Barro, 1979; Dotsey, 1994).
  - Inflation (Sargent and Wallace 1981; Barro 1995; Cochrane 2010).
  - Greater uncertainty about prospects and policies.
  - Amplification via banking or currency crises in extreme debt-crisis episodes (Burnside et al., 2001; Hemming et al., 2003).
  - Constraint on countercyclical fiscal policy leading to higher volatility (Aghion and Kharroubi (2007); Woo (2009)).
- Comparison to previous empirical findings:
  - Reinhart and Rogoff (2010): median growth difference of 2.6 percentage points between low debt (<30 percent of GDP) and high debt (>90 percent of GDP) groups in advanced economies (correlation-based analysis not controlling for other determinants or reverse causality).
  - Debt-overhang literature (developing economies): nonlinear negative effects at high external debt levels (Imbs and Ranciere (2009); Pattillo, Poirson, and Ricci (2002, 2004)); mixed findings in Cordella, Ricci, and Arranz (2005).

### III. Estimation strategy and methodological considerations
- Empirical approaches:
  - Growth regressions and growth accounting; emphasis on addressing reverse causality and simultaneity bias; investigation of nonlinearities and threshold effects.
- Primary identification choice:
  - Use of initial level of government debt (to mitigate reverse causality where low growth may lead to high debt).
- Estimators employed (to address different biases and ensure robustness):
  - Pooled OLS, robust regression, between estimator (BE), fixed effects (FE) panel regression, and system GMM (SGMM) dynamic panel regression (Arellano and Bover (1995); Blundell and Bond (1998)).
- Rationale for estimator mix:
  - BE and SGMM are preferred given trade-offs among omitted-variables bias, measurement error, endogeneity, and dynamic panel bias; Monte Carlo evidence (Hauk and Wacziarg (2009)) suggests BE performs well in presence of heterogeneity and measurement error.
- Robustness checks:
  - Parsimonious specifications, inclusion of additional controls, robust regression to limit influence of outliers, single cross-country regressions for longer horizons.

### IV. Data, sample, and stylized facts
- Data sources:
  - Penn World Table (PWT) version 6.3 (Heston et al. (2009)) for GDP, population, investment, government size.
  - IMF World Economic Outlook database for fiscal data including government debt.
  - World Bank World Development Indicators (2009) for other explanatory variables.
- Sample:
  - Panel of 38 advanced and emerging economies with population over 5 million, period 1970–2007.
  - Panel comprises eight non-overlapping five-year periods (1970–74, 1975–79, ..., 2000–04, 2005–07) except last period which spans three years.
- Stylized facts and descriptive statistics:
  - OLS scatter (Figure 1): fitted line Growth = 4.31 - 0.025*Initial debt; initial debt coefficient is significant at 1%.
  - Interpretation of OLS fitted line: coefficient -0.025 suggests a 10 percentage point increase in initial debt-to-GDP ratio is associated with a subsequent slowdown in per capita GDP growth of 0.25 percentage points per year (ignoring endogeneity and other controls).
  - Average subsequent five-year per capita GDP growth by initial debt group:
    - Advanced economies: difference in average growth rates between low initial debt (<30% of GDP) and high initial debt (>90% of GDP) episodes = 1.3 percentage points.
    - Emerging economies: corresponding difference = 2.7 percentage points.
    - G7 countries: growth differential between low and high initial debt periods = 1.5 percentage points.
    - Full sample: growth differential between low and high initial debt periods = 2.8 percentage points.
  - Appendix Table 1 (referenced) contains summary statistics on growth components and investment at different initial government debt levels.

### V. Econometric model specification and controls
- Baseline panel regression (period = five-year interval, τ=4):
  - (y_{i,t} – y_{i,t-τ}) = α y_{i,t-τ} + X_{i,t-τ} β + γ Z_{i,t-τ} + η_t + ν_i + ε_{i,t}
  - y is log real per capita GDP; Z is initial government debt (percent of GDP); X is vector of initial economic and financial controls measured at start of period (except some period averages).
- Core controls X in baseline:
  - Initial level of real GDP per capita (catch-up).
  - Human capital proxy: log of average years of secondary schooling in population over age 15 (Barro and Lee (2000)).
  - Initial government size: government consumption share of GDP.
  - Initial trade openness (exports + imports as percent of GDP).
  - Initial financial market depth: liquid liabilities as percent of GDP.
  - Initial inflation: log(1 + inflation rate) measured by CPI inflation.
  - Terms of trade growth rates (averaged over each time period).
  - Banking crisis incidence (based on Reinhart and Reinhart (2008)).
  - Fiscal deficit (measured over the period t-τ to t).
- Additional variables considered for robustness:
  - Population size, aged-dependency ratio, investment, fiscal spending volatility, urbanization, private saving, institutional constraints (checks and balances).

### VI. Sources of bias and estimator trade-offs
- Identified biases in panel growth regressions:
  - Omitted-variables (heterogeneity) bias from correlation between country fixed effects (ν_i) and regressors — affects pooled OLS and BE.
  - Endogeneity (regressors correlated with error term) — affects pooled OLS, BE, FE.
  - Dynamic panel bias due to lagged dependent variable correlation with fixed effects — makes FE inconsistent in dynamic panels.
  - Classical measurement error in independent variables — biases pooled OLS, BE, FE; FE exacerbates measurement error bias relative to BE and OLS.
  - Weak instruments concern in GMM estimators (SGMM generally more robust than difference GMM but can still suffer weak instrument bias).
- Specific estimator properties:
  - BE: reduces measurement error via time averaging but does not address omitted-variables bias.
  - Pooled OLS and BE: suffer from both omitted-variables bias and measurement error but measurement error can reduce heterogeneity bias.
  - FE: addresses omitted-variables bias via within-transformation but tends to exacerbate measurement error bias and is inconsistent in dynamic panels due to correlation between transformed lagged dependent variable and transformed error.
  - SGMM: addresses omitted-variables bias, endogeneity, and measurement errors (if instruments are valid), but may face weak instruments problems.
- Practical conclusion:
  - BE and SGMM are preferred estimation techniques given the mixture of biases and Monte Carlo evidence favoring BE in presence of heterogeneity and measurement error.

### VII. Robustness and complementary analyses
- Robust regression implemented to mitigate influence of outliers (iterated re-weighted least squares; Cook’s distance > 1 used to drop extreme observations).
- Cross-country (single-equation) regressions over longer time spans conducted to check whether five-year panel intervals obscure longer-term relationships; results broadly similar to panel regressions.
- Growth accounting exercises complement regression analysis by decomposing effects into factor accumulation versus factor productivity components.

*Source: IMF working paper content (1970–2007 panel analysis; data sources and methodological details as described in the supplied content).*

### Appendix 1 for more about SGMM).

### Appendix 1 for more about SGMM)

### Basic results
- Main results for advanced and emerging economies (Table 1): coefficients of initial debt are negative and significant at the 1 percent level, ranging from -0.019 to -0.029 across estimation techniques.
- BE (Blundell-­Bond) regression (Column 1): a 10 percentage points of GDP increase in initial debt is associated with a slowdown in subsequent growth in real GDP per capita of around 0.26 percent per year.
- Pooled OLS and FE (Columns 2 and 3): similar to BE, with initial debt coefficients somewhat smaller (around -0.02).
- SGMM estimate (Column 4): initial debt coefficient -0.029, significant at the 1 percent level.
- Other explanatory variables (initial income per capita, average years of schooling, financial market development, inflation, banking crisis, fiscal deficit) generally have expected signs and are mostly significant at conventional levels across estimators.
- Convergence rate estimates:
  - OLS coefficient of initial real per capita GDP: -2.26
  - FE coefficient: -3.6
  - SGMM coefficient: -2.56 (between OLS and FE, indicating likely consistent SGMM estimate)

### Consistency and specification tests for SGMM
- Hansen J-test of over-identifying restrictions: cannot reject validity of instruments (p-value=0.28).
- Arellano-Bond test for second-order serial correlation in first-differenced errors: cannot reject null of no second-order serial correlation (p-value=0.64).
- Difference-in-Hansen tests: do not reject exogeneity of instrument subsets for level equations (p-value=0.34).
- Notes on instruments:
  - Dynamic panel GMM can generate too many instruments and risk weak-instrument bias.
  - Recommended practice: be parsimonious in choice of instruments; restrict number of lagged levels, collapse instrument matrix, or combine both.
  - Reported SGMM results obtained by combining the “collapsed” instrument matrix with lag limits.

### Time-fixed effects and sensitivity of estimators
- Columns 2–4 regressions do not include time-fixed effects; Columns 5–7 include time-fixed effects to allow for global factors.
- Including time-fixed effects reduces the size of initial debt coefficients; pooled OLS and SGMM coefficients remain significant at 1–5 percent.
- Estimated effect with time-fixed effects: a 10 percentage point increase in initial debt-to-GDP ratio is associated with a slowdown in growth of per capita GDP around 0.2 percent per year (Appendix 2).
- FE estimator sensitivity:
  - FE coefficient of initial debt becomes insignificant and reduces to -0.004 when time-fixed effects are included (compare Column 6 with Column 3).
  - FE can bias toward zero slope estimates on steady-state determinants (Islam, 1995); within-country variation is further reduced when time-fixed effects are included.
  - Measurement error bias can be exacerbated under FE.
- Given these caveats, time-fixed effects are included in remaining regressions.

### Robustness of results
- Sample period restriction (1990–2007, Columns 1–4 of Table 2): results similar to full period; impact of initial debt significant except FE, ranging from -0.021 to -0.028, indicating a 10 percentage point increase in initial debt-to-GDP ratio is associated with decline in per capita GDP growth of around 0.2-0.3 percent per year.
- Sample composition (Columns 5–8 of Table 2): including 46 advanced and emerging economies regardless of population size yields results much the same as the 38 economies with population over 5 million.
- Parsimonious specification excluding fiscal deficit (Table 3, Columns 1–4): coefficients of initial debt negative and significant at 1–5 percent, ranging from -0.014 to -0.026, except FE where initial debt loses significance.
  - BE estimates of initial debt coefficient stable around 0.23 to 0.26 across samples, periods, and specifications.
  - Using average debt instead of initial debt yields similar debt coefficient range under BE, OLS, SGMM (-0.019 to -0.027), significant at 1–5 percent, except FE.
- Additional controls (Table 4): adding log of initial population, aged-dependency ratio, investment, fiscal volatility, urbanization, checks and balances does not materially change results.
  - Columns 1–4 adding log of initial population: coefficients of initial debt negative and significant at 1 percent under BE, OLS, SGMM; FE insignificant in Column 3.

*Source: Appendix 1, _wp10174 - Appendix 1 for more about SGMM).*

### 0.18 percent to 0.25 percent per year. In contrast, the coefficients of population size are

### _wp10174 - 0.18 percent to 0.25 percent per year. In contrast, the coefficients of population size are

### Baseline regressions and robustness checks
- Initial domestic investment (percent of GDP) added to baseline (Columns 5–8 of Table 4):
  - Under BE, OLS, and SGMM, coefficients of initial debt are significant at 5 percent level and slightly smaller than baseline.
  - Investment coefficients are positive and significant at 5–10 percent under BE and OLS.
  - Under SGMM, investment coefficient becomes insignificant but its magnitude is similar to BE.
  - Under FE, coefficients of initial debt and initial investment are insignificant; initial investment coefficient changes sign to negative.
- Inclusion of fiscal spending volatility (log of standard deviations of annual growth in real general government expenditures) (Columns 9–12 of Table 4):
  - Coefficients of fiscal volatility are insignificant and change sign across estimations.
  - Coefficients of initial debt remain significant and similar in size to baseline regressions.
- Single cross-country regression for longer time periods (Appendix Tables 2 and 3):
  - Results broadly similar to panel regressions; size of estimated initial debt coefficients similar to baseline panel regression.

### Nonlinearities and differences between advanced and emerging economies
- Interaction terms between initial debt and debt-range dummies (Table 5, Columns 1–4):
  - Dum_30 (below 30 percent of GDP): coefficients insignificant and change sign under FE and SGMM.
  - Dum_30–90 (30–90 percent of GDP): OLS coefficient significant at 5 percent with estimated coefficient -0.025; BE, FE, and SGMM show insignificance.
  - Dum_90 (over 90 percent of GDP): coefficients negative and significant under BE, OLS, and SGMM (except FE).
- Interaction terms between initial debt and advanced/emerging dummies (Table 5, Columns 5–8):
  - Coefficients of both interaction terms negative and significant at various levels, except FE.
  - Under BE, OLS, and SGMM:
    - Initial debt coefficients in advanced economies range from -0.014 to -0.021.
    - Initial debt coefficients in emerging economies range from -0.034 to -0.041.
    - Interpretation: a 10 percentage point increase in initial debt-to-GDP ratio is associated with growth slowdown around 0.15–0.2 percent in advanced economies, compared to 0.3–0.4 percent in emerging economies.
  - Possible explanation: limited borrowing capacity of emerging economies due to less-developed domestic financial markets or fragile access to international capital markets.
- Proportionate increase analysis (Table 6):
  - Debt groupings: <30%; 30-60%; 60-90%; >90%.
  - Finding: higher initial debt levels produce greater negative impact of a given increase on subsequent growth.
  - Example: a 10 percent increase in the debt ratio for countries with debt ratio above 90 percent associated with decline in growth of 0.19 percent; identical increase in the 30–60 percent group associated with decline in growth of around 0.11 percent.
  - Note: coefficients of low debt level (initial debt*Dum_30) not statistically different from zero; statistical significance of other interaction terms varies across estimations.

### Growth accounting: channels through which debt affects growth
- Framework: Cobb-Douglas Y = A K^α (HL)^(1-α), per-worker y = A k^α H^(1-α); growth decomposition (Equation (2)):
  - ẏ/y = Ȧ/A + α k̇/k + (1-α) Ḣ/H.
- Output per worker regressions (Table 7, Columns 1–4):
  - Coefficients of initial debt significant at 5–10 percent under BE, OLS, and SGMM, ranging from -0.013 to -0.022; insignificant under FE.
  - Preferred estimators (BE and SGMM) imply a 10 percentage point increase in initial debt-to-GDP ratio associated with slowdown in labor productivity growth (output per worker) of around 0.2 percent per year.
- TFP growth regressions (Table 7, Columns 5–8):
  - Significant conditional convergence in TFP (log of initial TFP negative and significant).
  - Coefficients of initial debt insignificant across all four regressions, with negative sign; BE and SGMM coefficients around -0.01.
- Capital per worker growth regressions (Table 7, Columns 9–12):
  - Initial debt coefficients significant across estimation techniques, ranging from -0.02 to -0.05.
  - With capital income share α = 0.35, BE and SGMM estimates imply a 10 percentage point increase in initial debt-to-GDP ratio induces slowdown in output per worker growth of around 0.1–0.2 percent per year via reduced capital per worker growth.
- Human capital growth:
  - No significant effects of debt on human capital growth (not reported).

### Investment, volatility, and additional mechanisms
- Domestic investment regressions (Table 8):
  - Baseline specification (Columns 1–3): coefficients of initial debt significant at 1–10 percent, ranging from -0.05 to -0.1 (dependent variable: average domestic investment percent of GDP over five-year periods).
  - Dynamic panel SGMM (Columns 4–5): lagged average investment included instead of initial income per capita.
    - Column 4: coefficient of initial debt significant at 10 percent; implies a 10 percentage point increase in initial debt-to-GDP ratio associated with decline in domestic investment by about 0.4 percentage points of GDP.
    - Column 5: interaction between initial debt and advanced/emerging dummies; both interaction terms significant at 10 percent and suggest adverse impact on domestic investment from debt in emerging economies is almost twice as large as in advanced economies.
- Macroeconomic volatility:
  - Simple scatter suggests mild positive correlation between macroeconomic volatility and initial government debt.
  - Regressions on volatility (log of standard deviation of annual real GDP growth) using baseline specification:
    - Coefficient of initial debt significant and positive only under FE when time-fixed effects are not included.
    - Insignificant in all other estimations (with or without time dummies).
    - High debt interaction (initial debt*Dum_90) significant only under FE without time-fixed effects.
- Summary from growth accounting:
  - Adverse effects of initial debt on growth largely reflect slowdown in labor productivity growth mainly due to reduced investment and slower growth of capital per worker.

### Concluding remarks (selected)
- Large sovereign debts may discourage capital accumulation and reduce economic growth via higher long-term interest rates, higher future distortionary taxation, higher inflation, greater uncertainty, and macroeconomic volatility.
- If growth is reduced, fiscal sustainability issues are likely to be exacerbated with further adverse consequences.
- This paper provides empirical evidence on the impact of high initial debt on subsequent growth for a panel of advanced and emerging market economies over the period of 1970– (text ends at supplied content).

*Source: _wp10174 - 0.18 percent to 0.25 percent per year. In contrast, the coefficients of population size are (PDF).*

### 2007. Methodologically, the paper builds on the large empirical literature on the determinants

### _wp10174 - 2007. Methodologically, the paper builds on the large empirical literature on the determinants

### Methodology
- Builds on the empirical literature on determinants of long-term growth and literature on high external debts (crowding out, debt overhang).
- Empirical estimation employs a variety of econometric techniques and explicitly addresses:
  - reverse causality, endogeneity, outliers,
  - nonlinearities and threshold effects.
- Uses growth accounting framework to explore channels (factor accumulation versus factor productivity) through which government debt may influence growth.
- Dynamic panel estimation uses a two-step system GMM (SGMM) with Windmeijer’s finite-sample correction for the two-step covariance matrix.
- Significance notation and test interpretation:
  - Levels of significance: *** 1 percent, ** 5 percent, * 10 percent.
  - Arellano-Bond AR(2) test: null = first-differenced errors exhibit no second-order serial correlation.
  - Hansen J-statistic: null = instruments are not correlated with residuals.

### Main empirical findings
- Average estimated effect of initial government debt on subsequent growth:
  - On average, a 10 percentage point increase in the initial debt-to-GDP ratio is associated with a slowdown in annual real per capita GDP growth of around 0.2 percentage points per year.
  - Impact is smaller in advanced economies: around 0.15 (percentage points per year).
- Evidence of nonlinearity / threshold:
  - Only high (above 90 percent of GDP) levels of debt have a significant negative effect on growth in some specifications.
- Investment channel:
  - On average, a 10 percentage point increase in initial debt is associated with a decline of investment by about 0.4 percentage points of GDP, with a larger impact in emerging economies.
- Growth accounting results:
  - Adverse effect largely reflects a slowdown in labor productivity growth, mainly due to reduced investment and slower growth of the capital stock per worker.
- Robustness:
  - Various robustness checks (period, sample, parsimonious specifications, additional variables, interaction terms, subsamples) yield largely similar results, though statistical significance varies across specifications.

### Selected regression coefficients and diagnostics (examples from tables)
- Table 1 (Baseline Panel Regression—1970–2007, sample: Advanced and Emerging Economies; Dependent variable: Real per Capita GDP Growth):
  - Government debt, initial: -0.026*** (BE), -0.020*** (Pooled OLS), -0.019*** (FE), -0.029*** (SGMM), -0.018*** (Pooled OLS with time fixed effects), -0.004 (FE with time fixed effects), -0.020** (SGMM with time fixed effects).
  - Initial per capita real GDP: -2.616*** (BE), -2.257*** (Pooled OLS), -3.598*** (FE), -2.555*** (SGMM), -2.187***, -4.506***, -2.823*** (various specifications).
  - Initial years of schooling: 4.246*** (BE), 2.965*** (Pooled OLS), 5.622*** (FE), 4.333* (SGMM) (examples).
  - Fiscal deficit: 0.012 (BE), -0.048*** (Pooled OLS), -0.051*** (FE), -0.056*** (SGMM).
  - Banking crisis: -1.143 (BE), -0.819** (Pooled OLS), -0.782*** (FE), -1.196* (SGMM).
  - Number of observations in Table 1 regressions: 166 (each column).
  - R2 examples reported: 0.78, 0.55, 0.4, 0.66, 0.60 (across specifications).
  - Arellano-Bond AR(2) test p-values reported in Table 1: 0.64 (column example), 0.12 (another example).
  - Hansen J-statistics (p-values) examples: 0.28, 0.26.

- Table 6 (Impact on Real per Capita GDP Growth of a 10 Percent Increase in the Debt-to-GDP Ratio):
  - Initial Debt Ratios (in percent of GDP), sample averages:
    - <30: 15.8
    - 30-60: 45.1
    - 60-90: 70.3
    - >90: 111.9
  - Regression coefficient, average 1/:
    - <30: 0.022
    - 30-60: -0.025
    - 60-90: -0.023
    - >90: -0.017
  - Growth impact of 10 percent increase in Debt/GDP from sample average 2/:
    - <30: 0.04
    - 30-60: -0.11
    - 60-90: -0.16
    - >90: -0.19
  - Notes:
    - 1/ Average of the estimates (from BE, OLS, SGMM) on coefficients of interaction terms between initial debt-to-GDP and dummy variables for four debt categories for 1970-2007. Coefficients of low debt level (initial debt*Dum_30) are not statistically different from zero in some specifications; statistical significance varies across estimations.
    - 2/ Growth impact of 10 percent increase in debt ratio = regression coefficient (Row 2) × 10 percent of the sample average debt ratios (Row 1).

- Table 7 (Growth Accounts and Panel Regression: Advanced and Emerging Economies):
  - Dependent variable examples and government debt coefficients:
    - Growth of output per worker: Government debt, initial = -0.019** (BE), -0.013** (Pooled OLS), -0.002 (FE), -0.022** (SGMM).
    - Growth of TFP: Government debt, initial = -0.008 (BE), -0.005 (Pooled OLS), -0.003 (FE), -0.011 (SGMM) (examples across columns).
    - Growth of capital stock per worker: Government debt, initial = -0.029* (BE), -0.022** (Pooled OLS), -0.021** (FE), -0.053*** (SGMM) (examples).
  - Number of observations: 159 (each column set).
  - R2 examples: 0.73, 0.53, 0.46, 0.8, 0.52, 0.42, 0.37, 0.36, 0.55.
  - Arellano-Bond AR(2) test p-values examples: 0.16, 0.94, 0.11.
  - Hansen J-statistics (p-values) examples: 0.24, 0.48, 0.40.

- Table 8 (Panel Regression on Investment: Advanced and Emerging Economies; Dependent variable: Domestic Investment percent of GDP, averaged over five-year period):
  - Government debt, initial: -0.099** (BE), -0.051* (Pooled OLS), -0.062*** (FE), -0.038* (SGMM).
  - Lagged dependent variable (investment): 0.828*** (BE), 0.797*** (Pooled OLS) as examples.
  - Initial per capita real GDP: 2.369 (BE), 10.074*** (Pooled OLS), 7.516** (FE).
  - Number of observations: 166 (BE/OLS/FE); 159 (SGMM columns).
  - R2 examples: 0.59, 0.60, 0.57.
  - Arellano-Bond AR(2) test p-values for Table 8 SGMM columns: 0.99, 0.99.
  - Hansen J-statistics (p-values): 0.42, 0.41.

### Policy implications and recommendations
- Findings underline the need to:
  - Take measures to not just stabilize public debts but to place them on a downward trajectory in the medium and long term.
  - Pay attention to debt levels above identified thresholds (notably above 90 percent of GDP in some specifications) where negative growth effects are more likely to be significant.
- Emphasize the investment channel: reducing excessive public debt may help support higher investment and faster capital per worker growth, which in turn can support labor productivity and real per capita GDP growth.

*Italic: Source: _wp10174 - 2007. Methodologically, the paper builds on the large empirical literature on the determinants (PDF chapter/section).*

### Appendix 1. Econometric Methodologies: BE, FE, and SGMM

### Appendix 1. Econometric Methodologies: BE, FE, and SGMM

### Econometric estimators described
- Baseline regression (time-fixed effects ηt dropped for simplicity):
  - yi,t – yi,t-τ = α yi,t-τ + Xi,t-τ β + γ Zi,t-τ + νi + εi,t    (Equation 1)
- Between estimator (BE):
  - Applies OLS to time-averaged equation: viiiii ZXyyyεγβα +++++=− −−−−1,1,1,1,,
  - Upper bar denotes averages across time periods (up to eight periods), e.g., Xi,τ−1,...,t Ti /.
- Fixed effects estimator (FE):
  - Applies OLS to within-transformed (demeaned) version of Equation 1:
    - )()()()()()( ,1,,1,,1,,1,,,,itiitiitiitiitititi ZZXXyyyyyyεεγβα ττττ −+−+−+−=−−−−−−−−−−−− (demeaned form)
- Dynamic panel GMM (generalized method of moments) — setup:
  - Rewrite Equation (1) as yi,t = (1+α) yi,t-τ + Xi,t-τ β + γ Zi,t-τ + νi + εit.
  - For simplicity let Xi,t-τ include initial debt Zi,t-τ and let t denote the 5-year time period.
  - Then yi,t = λ yi,t-1 + Xi,t-1 β + νi + εi,t, t=1,2,...,T (T=8 in our data).

### Assumptions for dynamic panel GMM
- Assumption 1 (error components):
  - E(νi)=E(εit)=E(νi εit)=0
- Assumption 2 (serially uncorrelated shocks):
  - E(εit εis)=0, for t≠s
- Assumption 3 (predetermined initial conditions):
  - E(yi1 εit)=E(Xi1 εit)=0, for t=2,...,T
- Assumption 4 (for SGMM additional moments):
  - E(Δyi2 vi)=E(ΔXi2 vi)=0

### Difference GMM (DGMM) — instruments and moments
- DGMM uses first-differencing to eliminate νi:
  - Example for t=3: yi3 − yi2 = λ(yi2 − yi1) + (Xi2 − Xi1) β + (εi3 − εi2)
- Valid instruments in DGMM:
  - Lagged levels yi1 and Xi1 are valid IVs for Δyi2 and ΔXi2 because E(yi1 Δεi3)=E(Xi1 Δεi3)=0 (follows from Assumption 3)
- General moment conditions exploited by DGMM:
  - E(yit−s Δεit)=0 and E(Xit−s Δεit)=0 for all t=3,..,T; s≥2

### System GMM (SGMM) — added moments and efficiency
- SGMM exploits moment conditions for both first-differenced and level equations under Assumption 4:
  - Additional moments: E(Δyis (vi + εiT))=0 and E(ΔXis (vi + εiT))=0, s=2,...,T-1
- Advantages of SGMM relative to DGMM:
  - Gains efficiency and reduces finite sample bias by using additional valid moment conditions (see Bond (2002) and Roodman (2006) for further discussion)

---

### Appendix 2. Debt and Growth: An Analytical Perspective for the United States

- Framework and key parameters:
  - Cobb-Douglas production with full crowding out premise: each dollar of debt crowds out one dollar of capital in the long run (Elmendorf and Mankiw, 1999).
  - Historical capital income share ≈ one-third.
  - Capital-output ratio in the United States ≈ 3.7 in 2008.
  - Implied marginal product of capital (MPK) ≈ 9 percent.
    - Elmendorf and Mankiw (1999) estimate MPK = 9.5 percent; Caselli and Feyrer (2007) report MPK = 0.114 in developed countries.
- Quantitative illustration:
  - An increase in net debt-to-GDP ratio of 40 percent over the next five years ≈ increase in net debt of around $6,450bn (in real terms based on the projection of 2  percent average growth of real GDP).
  - Under full crowding out, output would decline by about 4.4 percent in total (MPK × decrease in capital stock as percent of initial real GDP).
  - This is approximately equivalent to a growth slowdown of around 0.8 percent total; or 0.2 percent per year on average for a 10 percent of GDP increase in government debt (assuming the output decline mostly occurs in the following five-year period).
- Caveats and mitigating factors (implying above is an upper bound):
  - Open-economy capital inflows partly offset crowding out.
  - Private saving may rise in response to higher public debt (Ricardian argument).
  - Using conservative adjustments from Gale and Orzag (2003) — private saving increases equal to 20 percent of fall in government saving and foreign saving inflow equal to 25 percent of decrease in national saving — output decline would be 2.6 percent in total instead of 4.4 percent.
  - Endogenous growth externalities: capital accumulation stimulates technological change; crowding out could reduce productivity growth.
  - Increased uncertainty and crisis vulnerability associated with high government debt may further discourage investment and growth.
- Interpretation:
  - The analytical result provides a first approximation of debt’s impact on growth but is likely on the upper end due to the mitigating factors above.

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### Appendix 3. Growth Accounting

- Production function and decomposition:
  - Cobb-Douglas: Y = A K^α (H L)^{1−α}, with α = capital income share; K = physical capital; L = labor; H = human capital; A = TFP.
  - Per worker: y = A k^α H^{1−α}, where y = Y/L and k = K/L.
  - Growth decomposition:
    - ṙy = ṙA + α ṙk + (1−α) ṙH
      - Shown as )./)(1()/(//HHkkAAyy ˙˙˙˙ αα−++=
- Income shares and empirical choices:
  - Most studies assume constant income shares across time and space.
  - Evidence: labor income shares most estimated lie between 0.6 and 0.8; average = 0.65 (Bernanke and Gürkaynak, 2001).
  - Paper tried both fixed labor share of 0.65 and actual income shares from Gollin (2002) and Bernanke and Gürkaynak (2001); results very similar.
- Data construction:
  - TFP dataset constructed for 1970–2007.
  - National income and labor force data: Penn World Table (PWT) version 6.3 (Heston et al., 2009).
  - Human capital (H) — labor quality index:
    - Average years of schooling (E) from Barro and Lee (2000); years for 2005 and 2007 obtained by extrapolation.
    - H = exp(φ(E)) where φ(E) is piecewise linear:
      - slope = 0.134 for E ≤ 4
      - slope = 0.101 for 4 < E ≤ 8
      - slope = 0.068 for 8 < E
    - Rationale: returns to one extra year of education vary: sub-Saharan Africa ≈ 13.4 percent; world average = 10.1 percent; OECD average = 6.8 percent (Psacharopulos, 1994).
- Capital stock estimation:
  - Perpetual inventory method: Kt = (1−δ) Kt−1 + It
  - Investment It from PWT 6.3 as real aggregate investment in PPP.
  - Initial capital stock (e.g., year 1950) estimated as I1950/(g + δ) where g is average compound growth rate between 1950 and 1960; δ = 0.06 assumed.
  - Adjust capital stocks for portion of residential capital not directly related to production:
    - For 63 countries PWT 5.6 provides residential capital per worker as fraction of nonresidential capital per worker; use average ratio of nonresidential to total capital to impute nonresidential capital.
    - For remaining countries assume nonresidential capital is two-thirds of total capital (≈ average value 0.69).
- Validation:
  - Batteries of consistency checks suggest TFP growth estimates are reasonable.

---

### Appendix 4. Cross-Country Regressions

- Baseline cross-country regression:
  - gyi = α + β Xi + γ Zi + λ Di + εi
    - i = country; α = constant; εi = unobserved error term
    - Xi = vector of economic and financial variables (mostly initial values)
    - Zi = initial gross government debt (percent of GDP)
    - Di = vector of region dummies (OECD, Asia, Latin America, sub-Saharan Africa)
    - gyi = average growth rate of real GDP per capita (percent per annum) over sample period
- OLS results (Appendix Table 2 summary):
  - Sample: all advanced and emerging economies (without >5 million population restriction) for various periods.
  - Columns 1–5: negative relationship between initial government debt (% of GDP) and subsequent per capita GDP growth.
    - Coefficients of initial government debt range from -0.017 to -0.026 (negative and significant at conventional levels except Column 2 for 1985–2007 where insignificant).
    - Interpretation: a 10 percentage point increase in initial debt-to-GDP ratio associated with decline in per capita GDP growth of around 0.17-0.26 percent per year.
  - Columns 6–8 (average level of government debt over periods instead of initial):
    - Coefficients significant at the 5 percent level.
    - Coefficient range from -0.018 to -0.022.
- Parsimonious growth-components regressions (Appendix Table 3 summary):
  - Periods: 1990–2007 and 1995–2007.
  - Growth of output per worker regressions (Columns 1–2):
    - Coefficients of initial debt significant at 5 percent, ranging around -0.019 to -0.24.
  - Regressions for TFP growth (Columns 5–8):
    - Coefficients of initial debt significant at 1 percent.
    - Size of coefficients in TFP growth regressions ≈ two-thirds of that in output per worker regressions.
  - Regressions for growth of capital per worker:
    - Coefficients of initial debt not significant (but negative).
    - Coefficients of average debt significant at 5 percent, suggesting a 10 percent of GDP increase in debt associated with slowdown in growth of capital per worker by about 0.25 percent per year.
- Robustness note:
  - Repeating regressions with largest available sample including developing countries yields similar results; estimated coefficients of initial government debt become slightly smaller, ranging from -0.013 to -0.020.

---

### Appendix 5. Description of Data

- Dependent variables (measured over five-year period in panel or relevant period in cross-country regressions):
  1. Growth of real per capita GDP, PWT6.3 (2009)
  2. Growth of output per worker, PWT6.3 (2009)
  3. TFP growth, constructed using PWT6.3 (2009) and Barro and Lee (2000)
  4. Growth of capital per worker PWT6.3 (2009)
  5. Domestic investment (percent of GDP), PWT6.3 (2009)
  6. Volatility of output (log of standard deviation of annual real GDP growth rates over the five-year period), PWT6.3 (2009)
- Explanatory variables (initial values measured at beginning of each five-year period unless otherwise noted):
  1. Initial real GDP per capita (in log), PWT6.3 (2009)
  2. Initial average years of schooling of population age over 15 (in log), Barro and Lee (2000)
  3. Initial government size (percent of GDP), PWT6.3 (2009)
  4. Initial trade openness (percent of GDP), PWT6.3 (2009)
  5. Initial inflation rate (log of (1+π)), WDI (2009)
  6. Initial financial market depth (liquid liabilities, percent of GDP), WDI 2009
  7. Terms of trade growth (in percent), IMF, WEO 2009
  8. Banking crisis (total number of incidences over five-year period), Reinhart and Reinhart (2008)
  9. Initial population size (in log), PWT6.3 (2009)
  10. Fiscal deficit (percent of GDP), IMF, WEO (2009)
  11. Population growth (in percent), PWT6.3 (2009)
  12. Initial domestic investment (percent of GDP), PWT6.3 (2009)
  13. Fiscal volatility (log of standard deviation of annual growth rates of real general government expenditures over the five-year period), WDI (2009)
  14. Aged-dependency ratio (ratio of population of age over 65 to working population), WDI (2009)
  15. Urbanization, WDI (2009)
  16. Checks and balances, Database of Political Institutions (2009)
  17. Constraints on executive decision-making, Polity IV (2009)
  18. Initial gross government debt (percent of GDP), IMF, WEO (2009)
  19. Average gross government debt (percent of GDP), IMF, WEO (2009)

---

### Appendix 6. Country List

- Sample: 38 advanced and emerging economies with population over 5 million included in the panel regressions:
  - Australia; Austria; Belgium; Brazil; Canada; Chile; China; Colombia; Czech Republic 1/; Denmark; Egypt; France; Germany; Greece; Hong Kong; Hungary; India; Indonesia; Italy; Japan; Korea; Malaysia; Mexico; Netherlands; Pakistan; Peru; Philippines; Poland; Portugal; Russian Federation 1/; Slovak Republic 1/; South Africa; Spain; Sweden; Switzerland; Turkey; United Kingdom; United States
- Additional note:
  - Eight additional countries available when removing the over-5-million-population restriction: Finland, Iceland, Ireland, Israel, Jordan, Norway, New Zealand, and Singapore.
  - Advanced economies list (subset) includes: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, France, Germany, Greece, Hong Kong, Hungary, Italy, Japan, Korea, Mexico, Netherlands, Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, Turkey, the United Kingdom, and the United States.
  - 1/ Not included in the growth accounting exercise because necessary data in computing TFP are not available.

*Source: Appendix 1–6 of the IMF content unit titled "Appendix 1. Econometric Methodologies: BE, FE, and SGMM" from the supplied PDF.*

### Appendix Table 1. Level of Initial Government Debt, Growth, and Investment, 1970–2007:

### Appendix Table 1. Level of Initial Government Debt, Growth, and Investment, 1970–2007: Countries with a Population of over 5 million

### Average: Real per capita GDP Growth Rate (annualized  percent change over the subsequent 5 years)
- Entire: 5.1, 2.8, 2.7, 2.3, 1.4, 3.1
- Advanced: 3.2, 2.3, 2.2, 1.9, 1.6, 2.4
- Emerging: 6.6, 2.6, 3.7, 3.9, 2.1, 4.7
- Developing: 7.2, 4.5, 2.6, 2.3, 0.7, 3.0

### Average: Output per worker Growth Rate (annualized  percent change over the subsequent 5 years)
- Entire: 4.5, 2.1, 2, 2, 1.0, 2.5
- Advanced: 2.7, 1.7, 1.7, 1.9, 1.6, 2
- Emerging: 6.0, 2.1, 2.6, 3.4, 1.1, 3.7
- Developing: 6.4, 3.6, 1.9, 1.8, 0.2, 2.5

### Average: TFP Growth Rate (annualized  percent change over the subsequent 5 years)
- Entire: 1.5, 0.7, 0.9, 1.4, 0.5, 1.5
- Advanced: 0.8, 0.5, 0.7, 0.9, 0.6, 0.9
- Emerging: 3.2, 1, 1.9, 2.1, 0.5, 3
- Developing: 1.8, 1.3, 0.7, 1.8, -0.2, 1.7

### Average: Capital stock per worker Growth Rate (annualized  percent change over the subsequent 5 years)
- Entire: 4.1, 2.4, 1.8, 1.6, 1.1, 2.1
- Advanced: 3.9, 2, 2.2, 2.2, 2.1, 2.3
- Emerging: 6.9, 1.2, 1.7, 1.5, 1.4, 1.9
- Developing: 1.2, 5.2, 1.0, 1.3, -1, 2

### Average: Domestic Investment ( percent of GDP over the subsequent 5 years)
- Entire: 26.7, 22.7, 20, 16.4, 18.9, 18.1
- Advanced: 32, 26.7, 27.5, 29.4, 27.6, 28.6
- Emerging: 27.4, 15.7, 15.4, 11.4, 14.1, 15.2
- Developing: 18.6, 15.6, 11.1, 9.4, 8.1, 10.8

Notes on Appendix Table 1:
- Initial debts are the government gross debt to GDP (percent) in the first year of each five-year sub-period (i.e., 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005).
- Average growth rates (percent per annum) are over each five-year sub-period (i.e., 1970-74, 1975-79, 1980-84, 1985-89, 1990-94, 1995-99, 2000-04, 2005-07).

### Appendix Table 2 — Cross-country Regression: Government Debt and Real per Capita GDP Growth (Advanced and Emerging Economies)
Dependent Variable: Real per Capita GDP Growth

- Regression specifications reported (columns): (1) OLS 1975-2007, (2) OLS 1985-2007, (3) OLS 1990-2007, (4) OLS 1995-2007, (5) OLS 2000-2007, (6) OLS 1990-2007, (7) OLS 1995-2007, (8) OLS 2000-2007.
- Selected estimated coefficients (coefficient (t-statistic)):

  - Initial per capita real GDP:
    - (1) -0.968 (-1.65)
    - (2) -3.383 (-1.68)
    - (3) -2.737** (-3.27)
    - (4) -1.851* (-1.75)
    - (5) -0.902 (-0.89)
    - (6) -1.626* (-1.80)
    - (7) -1.364** (-2.17)
    - (8) -0.828 (-0.98)

  - Initial years of schooling:
    - (1) 3.195*** (5.81)
    - (2) 0.225 (0.14)
    - (3) 2.461* (1.84)
    - (4) 2.15 (1.35)
    - (5) 0.944 (0.56)
    - (6) 1.504 (1.29)
    - (7) 1.962** (2.15)
    - (8) 0.991 (0.71)

  - Initial inflation rate:
    - (1) 10.317*** (13.64)
    - (2) -1.243 (-0.58)
    - (3) 0.228 (0.46)
    - (4) 9.015 (1.59)
    - (5) 1.005 (0.26)
    - (6) -0.07 (-0.29)
    - (7) 2.738* (1.93)
    - (8) 0.766 (0.21)

  - Initial government size:
    - (1) -0.241*** (-8.82)
    - (2) -0.066 (-0.79)
    - (3) -0.043 (-1.05)
    - (4) -0.003 (-0.07)
    - (5) 0.075 (1.57)
    - (6) -0.027 (-0.93)
    - (7) -0.0004 (-0.01)
    - (8) 0.067 (1.46)

  - Initial trade openness:
    - (1) 0.015*** (4.97)
    - (2) 0.011 (0.83)
    - (3) 0.009 (1.97)
    - (4) 0.014** (2.48)
    - (5) 0.004 (0.76)
    - (6) 0.008* (1.83)
    - (7) 0.005 (1.03)
    - (8) 0.003 (0.56)

  - Terms of trade growth:
    - (1) 0.199*** (4.84)
    - (2) -0.045 (-0.19)
    - (3) -0.168 (-0.72)
    - (4) -0.075 (-0.73)
    - (5) 0.078 (0.80)
    - (6) -0.132 (-0.87)
    - (7) -0.076 (-0.91)
    - (8) 0.053 (0.61)

  - Banking crisis:
    - Reported in some columns; e.g., (6) -0.534 (-1.23), (7) -0.417 (-0.89), (8) 0.008 (0.02), (4) -0.049 (-0.16), (5) -0.971* (-1.97), (7) -0.059 (-0.12)

  - Government debt, initial:
    - (1) -0.026*** (-5.98)
    - (2) -0.004 (-0.34)
    - (3) -0.017** (-2.60)
    - (4) -0.024*** (-3.22)
    - (5) -0.019* (-1.73)
    - Government debt, average:
      - reported in select columns as -0.02** (-2.52), -0.022** (-2.81), -0.018** (-2.11)

- Number of Observations by column: 10, 20, 30, 37, 44, 42, 46, 46
- R2 values by column: 0.99, 0.56, 0.74, 0.56, 0.56, 0.53, 0.48, 0.57

Notes on Appendix Table 2:
- Heteroskedasticity consistent t-statistics are in parentheses.
- Levels of significance: *** 1 percent, ** 5 percent, * 10 percent.
- An intercept term and dummies for OECD, Asia, Latin America, and sub-Saharan Africa are included in each regression (not reported).

### Appendix Table 3 — Growth Accounting and Cross-Country Growth Regression: Advanced and Emerging Economies
- Panels present regressions for three dependent variables: Growth of real output per worker, Growth of TFP, Growth of capital stock per worker.
- Regression specifications reported across columns: (1) OLS 1990-2007, (2) OLS 1995-2007, (3) OLS 1990-2007, (4) OLS 1995-2007, (5) OLS 1990-2007, (6) OLS 1995-2007, (7) OLS 1990-2007, (8) OLS 1995-2007, (9) OLS 1990-2007, (10) OLS 1995-2007, (11) OLS 1990-2007, (12) OLS 1995-2007.

- Selected estimated coefficients (coefficient (t-statistic)):

  - Initial per capita real GDP:
    - (1) -2.387*** (-3.16)
    - (2) -1.419* (-1.67)
    - (3) -1.446 (-1.56)
    - (4) -0.985 (-1.64)
    - (5) -1.982*** (-3.69)
    - (6) -1.161* (-1.92)
    - (7) -1.435** (-2.25)
    - (8) -1.037** (-2.61)
    - (9) -1.183 (-1.26)
    - (10) -0.699 (-0.70)
    - (11) 0.166 (0.16)
    - (12) 0.294 (0.40)

  - Initial years of schooling:
    - (1) 2.564** (2.31)
    - (2) 2.334* (1.68)
    - (3) 1.974* (1.68)
    - (4) 2.343** (2.49)
    - (5) 3.041*** (3.54)
    - (6) 2.317** (2.19)
    - (7) 2.490*** (3.13)
    - (8) 2.535*** (3.89)
    - (9) 0.832 (0.54)
    - (10) 1.342 (0.80)
    - (11) -0.185 (-0.12)
    - (12) 0.731 (0.58)

  - Initial inflation rate:
    - Selected coefficients include (1) 0.611 (1.22), (2) 9.619 (1.56), (5) 0.588* (1.81), (6) 8.304** (2.29), (11) -0.518 (-1.42)

  - Initial government size:
    - Coefficients generally small and not statistically significant across panels; e.g., (1) -0.041 (-0.98), (2) 0.025 (0.67)

  - Initial trade openness:
    - (1) 0.01* (2.09)
    - (2) 0.012** (2.37)
    - (5) 0.010*** (3.62)
    - (6) 0.010*** (3.23)
    - Other columns show smaller or insignificant estimates, including negative coefficients for some capital regressions (e.g., -0.007 (-1.14), -0.009 (-1.56))

  - Terms of trade growth:
    - Coefficients generally small and statistically insignificant across specifications (e.g., -0.001 (-0.01), -0.083 (-0.79), -0.129 (-1.52))

  - Banking crisis:
    - Mixed coefficients; e.g., -0.101 (-0.25), -0.385 (-0.66), 0.373 (1.09), -0.928 (-1.60), -1.312* (-1.68) in one specification for capital stock per worker

  - Government debt, initial:
    - Significant negative coefficients in several specifications:
      - (1) -0.019** (-2.59)
      - (2) -0.024** (-2.56)
      - Other panels report -0.013*** (-3.24), -0.015*** (-2.79)
    - Government debt, average:
      - Reported in some specifications as -0.019** (-2.29), -0.017** (-2.17), -0.009* (-1.67), -0.024** (-2.39), -0.025** (-2.60)

- Number of Observations by relevant groupings: 30, 36, 44, 45 (varies by column)
- R2 values reported across columns range from 0.32 to 0.78 (e.g., 0.72, 0.54, 0.48, 0.45, 0.78, 0.64, 0.52, 0.5, 0.53, 0.32, 0.48, 0.39)

Notes on Appendix Table 3:
- Heteroskedasticity consistent t-statistics are in parentheses.
- Levels of significance: *** 1 percent, ** 5 percent, * 10 percent.
- An intercept term and dummies for OECD, Asia, Latin America, and sub-Saharan Africa are included in each regression (not reported).

*Source: _wp10174 - Appendix Table 1. Level of Initial Government Debt, Growth, and Investment, 1970–2007*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10174.pdf_