## 1. Semi-parametric estimations

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---

### Methodology and estimators
- Estimated cross-sectional model: GR_i = β_0 + X_i β + f(PC_i) + ε_i with f(·) approximated by a penalized spline smoother (Wand, 2005).
- Differencing procedure: Yatchew (2003) method used for semi-parametric estimation.
- Panel estimation methods:
  - System GMM of Arellano and Bover (1995) and Blundell and Bond (1998).
  - Two-step Arellano and Bond (1991) procedure with Windmeijer (2005) finite sample correction for robust standard errors.
  - All available lags used as instruments; results robust to using up to 4 lags.
- Statistical diagnostics:
  - OLS regressions support inclusion of PC^2.
  - Hansen tests of overidentifying restrictions never reject the null in reported panel regressions.
  - First-order autocorrelation rejected; most models do not reject no second-order autocorrelation (exception: AR2 marginally significant in one specification, p−value = 0.09).
  - High p-values of the OID test noted; reducing number of lags yields similar results with slightly lower OID values.

### Semi-parametric cross-sectional findings
- Semi-parametric smooth indicates GDP growth reaches a maximum when credit to the private sector (PC) = 76% of GDP.
- Semi-parametric fit is concave and non-monotone; quadratic functional form approximates the semi-parametric fit well.
- At very low PC (PC < 10% of GDP) the relationship is fairly flat.
- Sample includes 24 LDCs, total 136 observations; restricting to LDCs yields no statistically significant relationship; dropping LDCs strengthens results.

### Panel regression results and "vanishing effect"
- Baseline linear-panel (System GMM, 5-year spells):
  - Positive and significant correlation between log(financial depth) and growth in earlier samples (e.g., 1960-1995: point estimate = 1.9).
  - Coefficients decline and become statistically insignificant in more recent periods (1960-2005, 1960-2010) — the documented "vanishing effect".
- Role of sample composition and nonlinearity:
  - Cross-country average PC: 36% of GDP in 1985 → 55% of GDP in 2005.
  - Share of countries with PC > 90% of GDP: 4% → 22% over same period.
  - Increased share of large-PC observations amplifies downward bias in misspecified linear models if the true relationship is non-monotone.
- Quadratic-panel results (PC and PC^2 included):
  - Both linear and quadratic terms statistically significant across samples.
  - Marginal effect of financial depth becomes negative at PC levels (last row of Table 5):
    - 1960-1995 and 1960-2000: 140% of GDP.
    - 1960-2005: 100% of GDP.
    - 1960-2010: 90% of GDP.
  - Using more recent data lowers the threshold and yields more precise estimates of the quadratic term.
- Marginal-effect descriptive points (Figure 4 / Table 5 column 4):
  - Positive effect no longer statistically significant when PC = 42% of GDP (more than 30% of observations above this).
  - Effect becomes negative when PC = 90% of GDP (11% of observations above this).
  - Negative and statistically significant when PC = 113% of GDP (6% of observations above this).
- Country counts (as of 2006):
  - 64 countries above 50% threshold.
  - 27 countries above 90% threshold.
  - 17 countries above 113% threshold.
  - Countries above 110% threshold include: Iceland, the United States, Ireland, the United Kingdom, Spain, and Portugal (Greece noted as an exception).

### Semi-parametric panel fit and thresholds
- Semi-parametric panel estimator confirms concave, non-monotone relationship; semi-parametric maximum at PC = 76% of GDP.
- Thresholds from Table 5 (1960-2010, last three columns) range between 69% and 90% of GDP.
- Conclusion: panel data suggest a concave, non-monotone relationship between PC and GDP growth, well approximated by a quadratic.

### Ten-year growth spells and forecast performance
- Ten-year (10-year) growth spells (Table 6):
  - Quadratic specification: coefficients significant in both 1960-2000 and 1960-2010 samples.
  - Point estimates indicate marginal effect becomes negative when PC is between 80% and 90% of GDP.
  - SLM test supports non-monotonic relationship.
- Out-of-sample forecasting:
  - Quadratic model estimated 1960-2005 forecasts 2005-2010 growth better than linear model (MSE = 5.6 vs MSE = 6.4).
  - Using 1960-2000 estimates to forecast 2005-2010: MSE (linear) = 9.4; MSE (quadratic) = 6.3.
  - Quadratic model without controls (1960-2005 → 2005-2010) MSE = 5.7, outperforming linear full-controls model MSE = 6.4.

### Robustness checks
- Excluding countries with PC > 165% of GDP (six countries) yields similar results; threshold changes (example: becomes 69% of GDP).
- Excluding USA, Iceland, Spain, Ireland — results robust.
- Winsorizing dependent variable (drop top/bottom 1%) — results robust.
- Semi-parametric, quadratic, cross-sectional, panel, and industry-level approaches all show consistent threshold findings.

---

### Volatility, crises, and heterogeneity

- Hypothesized channels for negative returns to financial depth:
  - Rapid credit growth increases macroeconomic volatility or crisis probability.
  - Heterogeneity: benefits of large financial sectors depend on institutional and regulatory frameworks.

- Volatility measures:
  - Volatility defined as within-country standard deviation of annual output growth for each five-year period.
  - High-volatility dummy HVOL = 1 if volatility > sample average = 3.5, = 0 otherwise.

- Volatility-augmented results:
  - Augmenting baseline with HVOL: volatility negatively correlated with growth (reproducing Ramey and Ramey (1995)).
  - Linear and quadratic PC terms remain statistically significant; marginal effect becomes negative when PC > 74% of GDP (point estimate).
  - Heterogeneous coefficients by volatility (system GMM):
    - Low-volatility periods: positive and statistically significant effect when PC < 40% of GDP; becomes negative at 70% of GDP; negative and statistically significant at 110% of GDP.
    - High-volatility periods: effect of PC never statistically significant.
  - Interpretation: financial depth has no positive impact on output growth in periods of high economic volatility; non-monotone relationship is not driven solely by higher macro volatility in large-financial-sector observations.

- Banking crises interactions (BKCR dummy from Laeven and Valencia (2010), sample starts 1970):
  - Banking crises negatively correlated with GDP growth.
  - Controlling for crises increases threshold for negative marginal effect of PC to 105% of GDP.
  - Interacted terms (PC×BKCR, PC2×BKCR) insignificant; point estimates indicate:
    - Marginal effect negative at 80% of GDP in tranquil periods.
    - Marginal effect negative at 110% of GDP in crisis periods.
  - Marginal-effect plots:
    - Tranquil periods: positive and significant when PC < 60% of GDP; negative at 80% of GDP; negative and statistically significant at 180% of GDP.
    - Crisis periods: effect of PC never statistically significant.

- Institutional and regulatory heterogeneity:
  - Institutional quality (ICRG): LQOG = 1 when ICRG ≤ 0.5 (median ICRG = 0.51).
    - Main PC and PC^2 show quadratic relationship; marginal negative effect at PC = 70% of GDP.
    - Point estimates suggest marginal effect becomes negative at 60% of GDP in countries with poor institutions.
    - Figure 9 Panel A:
      - High institutional quality: positive and significant when PC < 20% of GDP; negative at 70% of GDP; negative and significant at 95% of GDP.
      - Low institutional quality: PC never statistically significant.
  - Official supervision (LOSI), capital regulation (LKRI), private monitoring (LPMI) interactions:
    - LOSI (weak supervision = 1): in strong supervision marginal negative at PC = 81% of GDP; weak supervision ~ 82% of GDP.
      - Strong supervision: positive and significant when PC < 55% of GDP; negative at 81% of GDP; negative and significant at 105% of GDP.
      - Weak supervision: correlation never statistically significant.
    - LKRI (low capital stringency = 1): point estimates indicate negative correlation begins when PC > 58% of GDP in strict-capital countries and when PC > 105% of GDP in weak-capital countries.
      - Strict capital requirements: negative effect statistically significant when PC > 100% of GDP.
      - Low capital requirements: correlation never statistically significant.
    - LPMI (low private monitoring = 1): marginal negative at PC = 64% of GDP in strong private-monitoring countries and at PC = 77% of GDP in weak private-monitoring countries.
      - Positive relationship never statistically significant in either group; negative part statistically significant in both groups.
  - Overall upshot: multiplicative effects with volatility, crises, or poor institutions/regulation do not eliminate the inverse U-shaped relationship; the threshold remains a robust empirical feature.

---

### Industry-level (Rajan and Zingales style) evidence

- Model: VAGR_{i,j} = SHVA_{i,j} α + EF_j × (PC_i β + PC_i^2 γ) + λ_j + μ_i + ε_{i,j} for 1990-2000.
- Reproducing Rajan and Zingales (1998) with γ = 0: industries more dependent on external finance grow relatively faster in countries with larger financial sectors.
- Introducing quadratic EF×PC^2 term:
  - Both interactive terms statistically significant at 5% with β > 0 and γ < 0.
  - Point estimates suggest financial depth starts having a negative effect on relative industry-level growth when PC reaches 120% of GDP.
- Robustness:
  - Controlling for interaction between external dependence and GDP per capita, and adding interaction with square of GDP per capita, do not change results.
  - Robust regression (Stata rreg) yields similar results; turning point slightly lower at 110% of GDP.
  - Using Rajan and Zingales’s 1980s index strengthens results (β and γ significant at 1%); threshold about 120% of GDP.
- Conclusion: industry-level evidence supports a threshold around 110–120% of GDP above which financial depth reduces industry-level growth.

---

### Key numeric thresholds and descriptive statistics (preserved)
- Semi-parametric maximum: PC = 76% of GDP.
- Cross-sectional/table thresholds and ranges:
  - Table 5 thresholds (1960-2010): 69% to 90% of GDP.
  - Marginal effect negative at PC ≈ 80–100% of GDP in country-level panel regressions; industry-level thresholds ≈ 110–120% of GDP (robust regression gives 110%).
  - PC < 10% of GDP: relationship fairly flat.
- Volatility/sample facts:
  - Volatility sample average = 3.5.
  - Marginal negative effect at PC > 74% of GDP when controlling for volatility.
  - Low-volatility group: positive when PC < 40% of GDP; negative at 70% of GDP; negative and statistically significant at 110% of GDP.
  - Banking-crisis controlled threshold = 105% of GDP; tranquil-period negative at 80% of GDP; negative and statistically significant at 180% of GDP in one plot.
- Institutional/regulatory numeric thresholds:
  - Institutional median ICRG = 0.51; LQOG = 1 when ICRG ≤ 0.5.
  - Institutional threshold: marginal negative at PC = 70% of GDP generally; 60% of GDP in poor-institution countries.
  - LOSI thresholds: 81% (strong supervision), 82% (weak supervision).
  - LKRI thresholds: 58% (strict capital requirements), 105% (weak capital requirements); negative effect statistically significant when PC > 100% in strict regime.
  - LPMI thresholds: 64% (strong private monitoring), 77% (weak private monitoring).
- Country counts (2006): 64 countries above 50% PC; 27 above 90%; 17 above 113%.
- Summary statistics (selected exact entries from Table 11):
  - Cross-sectional PC: N.Obs 690, Mean 0.46, Std. Dev. 0.34, Min 0.04, Max 1.37.
  - Panel PC: N.Obs 9,170, Mean 0.40, Std. Dev. 0.37, Min 0.01, Max 2.70.
  - Cross-sectional GROWTH: N.Obs 691, Mean 1.58, Std. Dev. 1.34, Min -4.20, Max 4.53.
  - Panel GROWTH: N.Obs 9,172, Mean 2.02, Std. Dev. 2.77, Min -21.00, Max 13.86.
  - Industry VA Growth: N.Obs 1,252, Mean 0.041, Std. Dev. 0.115, Min -0.476, Max 1.05.

---

### Policy-relevant conclusions and implications
- Main empirical finding:
  - Positive and robust correlation between financial depth and economic growth in countries with small and intermediate financial sectors.
  - Existence of a threshold (country-level panel regressions: roughly 80–100% of GDP; industry-level evidence: 110–120% of GDP) above which finance starts having a negative effect on economic growth.
- Robustness: finding holds across semi-parametric and quadratic specifications, across panel and industry-level approaches, and controlling for volatility, banking crises, and institutional/regulatory measures.
- Potential mechanisms for negative effects of large financial systems:
  - Increased macroeconomic volatility and higher probability of large economic crashes.
  - Misallocation of resources: credit shifted toward speculative or non-productive uses.
  - Composition of credit: enterprise credit may be growth-promoting while household credit may not be.
  - Non-bank lending and financial innovations (derivatives, originate-and-distribute models) may have different growth impacts than traditional bank lending.
- Policy implications:
  - There can be "too much" finance for growth; larger financial sectors are not always unambiguously better for growth.
  - Linear-only specifications risk understating the changing marginal effect of financial depth as sectors expand (explains "vanishing effect").
  - Monitoring financial depth and considering macroprudential, regulatory, or capital requirement responses may be warranted when PC approaches identified thresholds (roughly 80–100% of GDP country-level; 110–120% industry-level).
  - Tighter capital or regulatory requirements could be welfare-improving if financial depth is beyond the threshold where marginal effect on growth turns negative.

*Source: _wp12161 (IMF working paper chapter "1. Semi-parametric estimations").*

### 1. Semi-parametric estimations ............................................................................. 11

### 1. Semi-parametric estimations ............................................................................. 11

### B. Panel Regressions ................................................................................................... 12
- Listed as a subsection following "Semi-parametric estimations".

### 1. Semi-parametric estimations ............................................................................. 16
- Appears again as a subsection heading on page 16.

### III. Volatility, Crises, and Heterogeneity ............................................................................ 16
- Major theme addressing volatility, crises, and heterogeneity.

### IV. Industry-Level Data ...................................................................................................... 21
- Major theme addressing industry-level data.

### V. Conclusions ................................................................................................................... 22
- Conclusions section.

### References ........................................................................................................................... 25
- Reference list.

### Tables
- 1. Cross-Country OLS Regressions .................................................................................. 30
- 2. Cross-Country OLS Regressions .................................................................................. 31
- 3. Tests for an inverse U-shape ......................................................................................... 32
- 4. Panel Estimations .......................................................................................................... 33
- 5. Panel Estimations .......................................................................................................... 34
- 6. Panel Estimations: 10-year Growth Episodes  .............................................................. 35
- 7. Volatility and Banking Crises  ...................................................................................... 36
- 8. Institutional Quality and Bank Regulation and Supervision......................................... 37
- 9. Rajan and Zingales Estimations  ................................................................................... 38
- 10. Data Description and Sources  ...................................................................................... 39
- 11. Summary Statistics  ....................................................................................................... 40

### Figures
- 1. Marginal Effect Using Cross-Country Data ................................................................. 41
- 2. Semi-Parametric Regressions  ...................................................................................... 42
- 3. Credit to the Private Sector  .......................................................................................... 43
- 4. Marginal Effect Using Panel Data  ............................................................................... 44
- 5. Countries with Large Financial Sectors (2006)  ........................................................... 45
- 6. Semi-Parametric Regressions using Panel Data ........................................................... 46
- 7. The Marginal Effect of Credit to the Private Sector with High and Low Output 
  Volatility ....................................................................................................................... 47

*Source: _wp12161 - 1. Semi-parametric estimations ............................................................................. 11*

### 8. The Marginal Effect of Credit to the Private Sector during Tranquil and C

### 8. The Marginal Effect of Credit to the Private Sector during Tranquil and Crisis Periods

### Introduction and framing
- Reexamines the relationship between financial depth (measured as credit to the private sector as a share of GDP) and economic growth.
- Reproduces standard result: at intermediate levels of financial depth there is a positive relationship between the size of the financial system and economic growth.
- Presents evidence for a non-monotonic (inverted-U) relationship: at high levels of financial depth, more finance is associated with less growth.
- Motives and literature:
  - Builds on Goldsmith (1969), King and Levine (1993), Levine and Zervos (1998), Levine, Loayza, and Beck (2000), Beck, Levine, and Loayza (2000), Rajan and Zingales (1998).
  - Cites work raising concerns: Demetriades and Hussein (1996); Arestis and Demetriades (1997); Demetriades and Law (2006); Rousseau and Wachtel (2002, 2011); Rajan (2005); Gennaioli, Shleifer, and Vishny (2010); Easterly, Islam, and Stiglitz (2000).
  - Motivates testing for a threshold above which financial depth may have negative social returns and increase volatility and crisis risk.

### Key empirical findings (country-level)
- Main threshold result:
  - The marginal effect of financial depth on output growth becomes negative when credit to the private sector reaches 80-100% of GDP.
- Cross-sectional regression results:
  - Using a quadratic specification with credit to the private sector (PC) and PC^2, the linear term is positive and the quadratic term is negative, indicating concavity.
  - Financial depth starts yielding negative returns at:
    - 83% of GDP (column 2, Table 1).
    - 82% of GDP (column 4, Table 1 for 1970-2005).
  - Figure 1 (based on column 6, Table 1) highlights:
    - Positive effect no longer statistically significant when credit reaches 70% of GDP (about 40% of observations in column 6 are above this threshold).
    - Effect becomes negative and statistically significant when credit is greater than 110% of GDP (7% of observations in column 6 are above this threshold).
- Sample and periods:
  - Data cover the period 1960-2010; regressions estimated for different sub-periods (e.g., 1970-2000, 1970-2005, 1970-2010, 1980-2010, 1990-2010).
  - Reproduces Beck and Levine (2004) style specification for comparability, with deviations described (use of total credit to the private sector extended by deposit banks and other financial institutions).
- Vanishing effect explanation:
  - A linear specification that omits a quadratic term biases estimates downward as credit grows over time.
  - If credit grows at rate g (xt+1 = (1+g) xt), the omitted-variable bias increases over time by a factor 1+g, explaining the "vanishing effect" found in recent data (Rousseau and Wachtel, 2011).

### Robustness, tests, and methods
- Measures and data choices:
  - Financial depth measured as total credit to the private sector extended by deposit banks and other financial institutions (rather than only deposit banks).
  - Stock market turnover previously used but constrained coverage; primary focus here is credit to the private sector.
  - Controls included in regressions: log of initial GDP per capita, initial stock of human capital accumulation, trade openness, inflation, and ratio of government expenditures to GDP.
- Statistical evidence for inverted-U:
  - Lind and Mehlum (2011) test for inverted-U (Sasabuchi-Lind-Mehlum, SLM test) applied to the quadratic specification y = PC α + PC^2 β + Z γ + u.
  - SLM test rejects the null of non-inverted-U for estimates reported (column 2, Table 1), consistent with an inverted-U relationship.
  - Fieller interval reported: relationship not statistically significant when PC ranges between 65% and 124% of GDP (last row, Table 3).
- Robustness to alternative samples and specifications:
  - Results robust across different sub-periods and estimators (simple cross-sectional, panel regressions, semi-parametric estimators) and at country-level and industry-level.
  - Finding that marginal effect becomes negative at 80-100% of GDP is consistent across methods and datasets.
  - Robustness checks include controls for macroeconomic volatility, banking crises, and institutional quality (detailed in later sections of the paper).

### Interpretation and implications
- Consistency with other literature:
  - Threshold similar to Easterly, Islam, and Stiglitz (2000) who find output volatility increases when credit reaches 100% of GDP.
  - Links to literature on volatility and growth (Ramey and Ramey, 1995) and persistence of negative output shocks (Cerra and Saxena, 2008).
- Policy-relevant insight:
  - Evidence suggests there can be "too much" finance: beyond thresholds in the range roughly 80-100% of GDP credit to the private sector, marginal effects on growth turn negative.
  - Linear-only specifications may understate or make the effect of financial depth "vanish" as financial sectors grow.
  - Monitoring financial depth and implementing macroprudential or regulatory measures may be warranted where credit to the private sector approaches identified thresholds (80-100% of GDP), given associated increases in volatility and crisis risk.
- Relation to talent allocation and social returns:
  - A large financial sector may lead to suboptimal allocation of talent and lower social returns relative to private returns (Tobin, 1984; Rajan, 2010; Crotty, 2009; Deidda, 2006).

*Source: 8. The Marginal Effect of Credit to the Private Sector during Tranquil and Crisis Periods (excerpt)._wp12161 - 8. The Marginal Effect of Credit to the Private Sector during Tranquil and C*

### 1.    Semi-parametric estimations

### 1. Semi-parametric estimations

### Methodology
- Use of differencing procedure suggested by Yatchew (2003).
- Functional space approximated with a penalized spline smoother (Wand, 2005).
- Estimated model: GR_i = β_0 + X_i β + f(PC_i) + ε_i.
- For panel regressions: GMM system estimator of Arellano and Bover (1995) and Blundell and Bond (1998); two-step procedure of Arellano and Bond (1991); robust standard errors using Windmeijer (2005) finite sample correction.
- Instruments: all available lags used as instruments (results robust to using up to 4 lags).

### Semi-parametric cross-sectional findings
- Semi-parametric smooth indicates GDP growth reaches a maximum when credit to the private sector (PC) is at 76% of GDP.
- The quadratic fit from Table 1 approximates the semi-parametric fit well.
- Conclusion: cross-sectional data suggest a non-monotonic, concave relationship between private credit and GDP growth; a quadratic functional form approximates this non-linear relationship effectively.

### Statistical diagnostics (cross-country / general)
- OLS regressions support inclusion of the square of credit to the private sector.
- Hansen tests of overidentifying restrictions never reject the null in panel regressions reported.
- Regressions reject null of no first order autocorrelation; most models do not reject null of no second order autocorrelation (exception: column 4, AR2 marginally significant with a p−value of 0.09).
- Note: high p-values of the OID test suggest potential overfitting; reducing the number of lags yields similar results with slightly lower OID test values.

---

### B. Panel Regressions — main results and interpretation

### Baseline linear-panel results (Table 4 summary)
- Column 1 (1960-1995): positive and statistically significant correlation between log(financial depth) and economic growth; point estimate = 1.9 (close to Beck and Levine range 1.7–2.2).
- Column 2 (1960-2000): positive and statistically significant correlation, coefficient about one-third of column 1 and less precisely estimated.
- Columns 3 and 4 (1960-2005 and 1960-2010): coefficients smaller and no longer statistically significant.
- Same pattern holds when using level of credit to the private sector over GDP (last four columns): correlation decreases with more recent data and is not statistically significant for 1960-2005 and 1960-2010.
- Interpretation: "vanishing effect" of financial deepening documented by Rousseau and Wachtel (2011) — correlation between financial depth and growth weakens when adding more recent data.

### Role of sample composition and nonlinearity
- Cross-country average of credit to the private sector: 36% of GDP in 1985 → 55% of GDP in 2005.
- Share of countries with private credit > 90% of GDP: 4% → 22% over same period.
- Columns 1 and 5 of Table 4 include 27 observations (5% of total) with PC > 90% of GDP; columns 4 and 8 include 99 observations (11% of total) with PC > 90% of GDP.
- If true relationship is non-monotone, increased share of large-financial-sector observations amplifies downward bias in misspecified linear models, explaining low/insignificant coefficients in later-period regressions.

### Quadratic-panel results (Table 5 summary)
- Augmenting model with square of credit to the private sector: both linear and quadratic terms always statistically significant.
- Marginal effect becomes negative at these PC levels (last row of Table 5):
  - 1960-1995 and 1960-2000: 140% of GDP.
  - 1960-2005: 100% of GDP.
  - 1960-2010: 90% of GDP.
- Using more recent data lowers the threshold and yields more precise estimates of the quadratic term — consistent with amplified downward bias when models omit nonlinearity.

### Marginal effect and thresholds (Figure 4 / descriptive points)
- Positive effect of financial depth no longer statistically significant when PC reaches 42% of GDP (more than 30% of observations in column 4 regression are above this threshold).
- Effect becomes negative when PC is at 90% of GDP (11% of observations in column 4 are above this threshold).
- Negative and statistically significant when PC reaches 113% of GDP (6% of observations in column 4 are above this threshold).

### Country counts as of 2006 (data completeness year)
- 64 countries above the 50% threshold.
- 27 countries above the 90% threshold.
- 17 countries above the 113% threshold.
- Countries above the 110% threshold include: Iceland, the United States, Ireland, the United Kingdom, Spain, and Portugal (Greece is an exception: relatively small financial sector but severe public finance problems).

### Robustness checks (Table 5 additional columns)
- Column 5: excluding countries with PC > 165% of GDP (six countries) — results similar; threshold now 69% of GDP where marginal effect becomes negative.
- Column 6: excluding United States, Iceland, Spain, and Ireland — results robust.
- Column 7: excluding top and bottom 1% of distribution of dependent variable (drop average 5-year growth < -10% and > 11%) — results robust.

---

### C. Longer growth spells and additional panel specifications

### Ten-year growth spells (Table 6 summary)
- Linear specification:
  - 1960-2000 (column 1): credit to the private sector significantly correlated with growth.
  - 1960-2010 (column 2): correlation no longer statistically significant (specification tests suggest possible problems with exclusion restrictions).
- Quadratic specification (columns 3 and 4): coefficients statistically significant in both sub-periods.
  - Point estimates indicate marginal effect of financial depth becomes negative when PC is between 80% and 90% of GDP.
- SLM test supports hypothesis of a non-monotonic relationship (column 5 of Table 3).

### Out-of-sample forecasting performance
- Quadratic model of column 3 in Table 5 (estimated 1960-2005) forecasts 2005-2010 GDP growth better than linear model of column 7 of Table 4:
  - MSE (quadratic 1960-2005 → forecast 2005-2010) = 5.6.
  - MSE (linear 1960-2005 → forecast 2005-2010) = 6.4.
- Using model estimated over 1960-2000 to forecast 2005-2010:
  - MSE (linear) = 9.4.
  - MSE (quadratic) = 6.3.
- Note: quadratic model without controls yields MSE = 5.7 when using 1960-2005 to forecast 2005-2010, outperforming the linear model with full controls used in Table 4 (MSE = 6.4).

---

*Source: _wp12161 - 1.    Semi-parametric estimations (PDF chapter).*

### 1.    Semi-parametric estimations

### 1.    Semi-parametric estimations

### Semi-parametric estimator: shape and thresholds
- Semi-parametric estimator allowing credit to the private sector (PC) to take a general form finds a concave, non-monotone relationship between PC and GDP growth.
- At very low levels of financial depth (PC < 10% of GDP) the relationship is fairly flat.
- Sample includes 24 LDCs, for a total of 136 observations (these are all countries with very low levels of financial depth).
- Restricting analysis to LDCs: relationship (linear or quadratic) is never statistically significant.
- Dropping LDCs from the sample strengthens results.
- Semi-parametric fit (solid black line in Figure 6) shows GDP growth reaches a maximum when PC = 76% of GDP.
- Thresholds from Table 5 (data for 1960-2010, last three columns) range between 69% and 90% of GDP.
- The quadratic fit (solid light line) obtained from Column 7 of Table 5 is a good approximation to the semi-parametric fit.
- Conclusion: panel data suggest a concave, non-monotone relationship between credit to the private sector and GDP growth, well approximated by a quadratic functional form.

### Volatility, crises, and heterogeneity — setup and baseline findings
- Hypothesized channels for negative returns to financial depth include:
  - Rapid credit growth increasing macroeconomic volatility or leading to financial and banking crises.
  - Heterogeneity: large financial sectors beneficial under good institutional/regulatory frameworks, damaging when frameworks are weak.
- Volatility measure: within-country standard deviation of annual output growth for each five-year period.
- High-volatility dummy (HVOL) = 1 if volatility > sample average of 3.5, = 0 otherwise.
- Augmenting baseline model with HVOL:
  - Volatility is negatively correlated with growth (reproducing Ramey and Ramey (1995)).
  - Linear and quadratic terms of PC remain statistically significant.
  - Point estimates indicate marginal effect of financial depth becomes negative when PC surpasses 74% of GDP.

### Heterogeneous effects by volatility
- Estimated model allowing coefficients to differ between low- and high-volatility country-periods (system GMM estimation described).
- Coefficients on PC and PC^2 are statistically significant; interacted terms with HVOL are not statistically significant and have opposite sign to main effects.
- Point estimates: β0 > 0, (β0 + b0) > 0, β1 < 0, (β1 + b1) < 0 → concave relationship in both low- and high-volatility periods, possibly not statistically significant in the high-volatility subsample.
- Marginal-effect plots (Figure 7):
  - Low-volatility periods (left panel): positive and statistically significant effect on GDP growth when PC < 40% of GDP; becomes negative at 70% of GDP; negative and statistically significant at 110% of GDP.
  - High-volatility periods (right panel): effect of PC is never statistically significant.
- Interpretation: financial depth has no positive impact on output growth in periods of high economic volatility; non-monotone relationship is not driven solely by higher macroeconomic volatility in large financial sectors.

### Banking crises interactions
- Banking crisis dummy BKCR = 1 when Laeven and Valencia (2010) signal a crisis; BKCR = 0 in tranquil periods. (Sample starts in 1970 due to data availability.)
- Column 3 (Table 7): banking crises negatively correlated with GDP growth; controlling for crises does not eliminate non-monotonicity, but increases threshold for negative marginal effect of PC to 105% of GDP.
- Interaction (Column 4): main effects significant; interacted terms insignificant, smaller in absolute value, opposite sign.
- Point estimates: marginal effect of PC becomes negative at 80% of GDP in tranquil periods and 110% of GDP in crisis periods.
- Figure 8 plots:
  - Tranquil periods (left panel): positive and statistically significant effect when PC < 60% of GDP; becomes negative at 80% of GDP; negative and statistically significant at 180% of GDP.
  - Crisis periods (right panel): effect of PC never statistically significant.
- Conclusion: controlling for banking crises raises threshold but quadratic relationship remains robust in tranquil periods; macroeconomic volatility and banking crises are not the only explanations for the non-monotone relationship.

### Institutional and regulatory heterogeneity
- Institutional quality: ICRG index of quality of government used to build low-quality-of-government dummy (LQOG = 1 when ICRG ≤ 0.5; median ICRG = 0.51; LQOG = 0 when ICRG > 0.5).
  - Column 1 (Table 8): LQOG positively correlated with GDP growth (unexpected sign) but effect not statistically significant.
  - Main PC and PC^2 show quadratic relationship; marginal effect becomes negative when PC reaches 70% of GDP.
  - Interactive terms insignificant, smaller in absolute value, opposite sign; point estimates suggest marginal effect becomes negative at 60% of GDP in countries with poor institutions.
  - Figure 9 Panel A:
    - High institutional quality: positive and statistically significant effect when PC < 20% of GDP; effect becomes negative at 70% of GDP; negative and statistically significant at 95% of GDP.
    - Low institutional quality: PC is never statistically significant.

- Bank supervision/regulation (Barth et al., 2008 indices), time-invariant variables:
  - LOSI (official bank supervision): LOSI = 1 for weak supervision, 0 for strong, 0.5 for intermediate.
    - Interaction results: only main quadratic effect statistically significant; main linear and interacted effects not statistically significant but consistent with concave relationship (Column 2).
    - Point estimates: in countries with strong official supervision marginal effect becomes negative when PC > 81% of GDP; in countries with low official supervision threshold ~ 82% of GDP.
    - Figure 9 Panel B:
      - Strong supervision: positive and statistically significant when PC < 55% of GDP; becomes negative at 81% of GDP; negative and statistically significant at 105% of GDP.
      - Weak supervision: correlation never statistically significant.
  - LKRI (capital regulatory index): LKRI = 1 for low capital stringency, 0 for high stringency.
    - Interaction results (Column 3): main linear and interacted effects not statistically significant; main quadratic effect negative and statistically significant.
    - Point estimates: negative correlation begins when PC > 58% of GDP in countries with strict capital requirements and when PC > 105% of GDP in countries with weak capital requirements.
    - Figure 9 Panel C:
      - Low capital requirements: correlation never statistically significant.
      - Strict capital requirements: positive correlation never statistically significant; negative effect becomes statistically significant when PC > 100% of GDP.
  - Private monitoring (LP MI): LP MI = 1 for low private monitoring, 0 for high.
    - Interaction results (Column 4): point estimates indicate marginal effect becomes negative when PC = 64% of GDP in countries with strong private monitoring and when PC = 77% of GDP in countries with weak private monitoring.
    - Interacted effects go in same direction as main effect; non-monotone relationship stronger and tighter in countries with low private monitoring.
    - Panel D of Figure 9: positive relationship never statistically significant in either group; negative part statistically significant in both groups.

- Overall upshot: multiplicative effects with macroeconomic volatility, banking crises, or poor institutional/regulatory frameworks do not fundamentally alter the existence of a threshold of financial depth above which credit to the private sector negatively affects economic growth. The inverse U-shaped relationship between financial depth and economic growth remains the most compelling empirical representation of the data and helps account for the "vanishing effect" of finance reported in the literature.

### Industry-level data (Rajan and Zingales approach)
- Model estimated: VAGR_{i,j} = SHVA_{i,j} α + EF_j × (PC_i β + PC_i^2 γ) + λ_j + μ_i + ε_{i,j}, where:
  - VAGR_{i,j} is real value-added growth in industry j in country i over 1990-2000;
  - SHVA_{i,j} is initial share of value-added of industry j over total industrial value-added in country i;
  - EF_j is Rajan and Zingales (1998) index of external financial dependence for industry j in the 1990s;
  - PC_i is credit to the private sector in country i in the 1990s;
  - λ_j and μ_i are industry and country fixed effects.
- Setting γ = 0 reproduces Rajan and Zingales (1998) result: industries more dependent on external finance have a relative advantage in countries with larger financial sectors (Column 1, Table 9).
- Introducing quadratic term: both interactive terms statistically significant at 5% with β > 0 and γ < 0 (Column 2, Table 9).
  - Point estimates suggest financial depth starts having a negative effect on relative industry-level growth when PC reaches 120% of GDP.
- Robustness checks:
  - Controlling for interaction between external dependence and GDP per capita does not change results (Column 3).
  - Adding interaction with square of GDP per capita does not change results (Column 4).
  - Robust regression (Stata rreg) yields essentially identical results; turning point slightly lower at 110% of GDP (Column 5).
  - Using Rajan and Zingales’s (1998) 1980s index strengthens results (β and γ significant at 1%); threshold still at 120% of GDP (Column 6).
- Conclusion: industry-level evidence supports a threshold (around 110–120% of GDP) above which financial depth reduces industry-level growth.

### Key numeric thresholds and sample facts (preserved)
- PC < 10% of GDP: flat relationship at very low financial depth.
- Sample: 24 LDCs, total 136 observations.
- Semi-parametric maximum: PC = 76% of GDP.
- Table 5 thresholds (1960-2010): 69% to 90% of GDP.
- Volatility sample average: 3.5.
- Marginal negative effect at PC > 74% of GDP (with volatility controlled).
- Low-volatility group: positive when PC < 40% of GDP; negative at 70% of GDP; negative and statistically significant at 110% of GDP.
- Banking-crisis controlled threshold: 105% of GDP.
- Tranquil periods: positive when PC < 60% of GDP; negative at 80% of GDP; negative and statistically significant at 180% of GDP.
- Institutional median ICRG = 0.51; LQOG = 1 when ICRG ≤ 0.5.
- Institutional thresholds: marginal negative at PC = 70% of GDP generally; 60% of GDP in poor-institution countries.
- Official supervision thresholds (LOSI): 81% (strong supervision), 82% (weak supervision).
- Capital regulation thresholds (LKRI): 58% (strict capital requirements), 105% (weak capital requirements); negative effect statistically significant when PC > 100% in strict regime.
- Private monitoring thresholds (LP MI): 64% (strong private monitoring), 77% (weak private monitoring).
- Industry-level threshold: PC ≈ 120% of GDP (robust regression gives 110% of GDP).
- Periods: industry regressions focused on 1990s; comparisons include 1980s index.

### Policy-relevant conclusions and implications
- Main empirical finding: positive and robust correlation between financial depth and economic growth in countries with small and intermediate financial sectors, but a threshold (estimated around 80–100% of GDP in country-level panel regressions; 110–120% in industry-level evidence) above which finance starts having a negative effect on economic growth.
- Robustness: result holds across semi-parametric and quadratic specifications, across panel and industry-level approaches, and controlling for volatility, banking crises, and measures of institutional/regulatory quality.
- Possible mechanisms for negative effects of large financial systems:
  - Increased macroeconomic volatility and higher probability of large economic crashes.
  - Misallocation of resources (including credit toward speculative rather than productive uses).
  - Composition of lending: enterprise credit may be growth-promoting while household credit may not be.
  - Non-bank lending and financial innovations (derivatives, originate-and-distribute) may have differing effects from traditional bank lending.
- Implication for financial regulation debate (e.g., Basel III capital requirements):
  - The assumption that larger financial sectors are always better for growth is questioned.
  - For several countries, smaller financial sectors may be desirable.
  - Tighter capital requirements may not necessarily reduce welfare if financial depth is beyond the threshold where marginal effect on growth is negative.

*Source: IMF working paper chapter "1.    Semi-parametric estimations" (content unit provided).*

### REFERENCES

### _wp12161 - REFERENCES

### Key empirical findings from cross-country OLS and panel regressions
- Table 1 (Cross-Country OLS regressions):
  - LGDP(t-1) coefficients: -0.560***, -0.548***, -0.541***, -0.556***, -0.627***, -0.626*** (robust s.e. in parentheses: (0.210), (0.205), (0.194), (0.182), (0.193), (0.185)).
  - LPC coefficients reported: 0.743**, 0.646*, 0.701** (s.e. (0.354), (0.327), (0.316)).
  - PC coefficients reported: 5.815**, 6.170***, 5.759*** (s.e. (2.354), (2.066), (1.875)).
  - PC2 coefficients reported: -3.503**, -3.753***, -3.275*** (s.e. (1.538), (1.312), (1.130)).
  - LEDU coefficients range: 1.447***, 1.488***, 1.421***, 1.427***, 1.321**, 1.332** (s.e. provided).
  - LINF coefficients include -0.304**, -0.351***, -0.256*, -0.296**, -0.125 (s.e. shown).
  - N. Obs. reported: 666, 666, 666, 636, 3? (table shows sequence "666666666363" — original table layout indicates samples across columns).
  - R2 reported: 0.435, 0.458, 0.412, 0.465, 0.347, 0.398.
  - Period entries include 1970-00, 1970-05, 1970-10.
  - dGR/dPC values shown: 0.8 3? table lists "dGR/dPC=00.830.820.88" (preserve as in source).

- Table 2 (Cross-Country OLS regressions for alternative periods):
  - LGDP(t-1) coefficients: -0.780***, -0.806***, -0.306*, -0.327* (s.e. given).
  - LPC reported: 0.759**, 0.429 (s.e. (0.303), (0.259)).
  - PC: 5.262***, 3.924*** (s.e. (1.947), (1.343)).
  - PC2: -2.633**, -2.028*** (s.e. (1.137), (0.673)).
  - LEDU: 2.010***, 1.975***, 1.043**, 0.993**.
  - LGC coefficients include -0.782, -0.951*, -1.097**, -1.234***.
  - N. Obs.: 868, 697, 97, 97 (presented as "86869797").
  - R2 entries: 0.394, 0.420, 0.243, 0.284.
  - Periods: 1980-10, 1990-10.
  - dGR/dPC shown as "01.000.97" (preserve formatting).

- Table 3 (Tests for an inverse U-shape — Sasabuchi-Lind-Mehlum):
  - Slope at PCmin: 5.50*** (2.22), 5.48*** (1.78), 3.79*** (1.30), 3.61** (1.73), 7.20*** (2.01).
  - Slope at PCmax: -4.33*** (2.32), -3.19*** (1.41), -2.61*** (0.97), -7.27*** (2.38), -16.63*** (4.53).
  - SLM test for inverse U shape statistics: 1.87, 2.26, 2.69, 2.10, 3.60.
  - p-values: 0.03, 0.01, 0.01, 0.02, 0.00.
  - Fieller 90% confidence intervals: [0.65; 1.24], [0.73; 1.11], [0.77; 1.16], [0.18; 1.18], [0.68; 0.97].

- Table 4 (Panel estimations — System GMM, 5-year spells):
  - Selected coefficients (lags): LGDP(t-1) across columns: -0.748*, -0.315, -0.820**, -0.914***, -0.688*, -0.828**, -0.800**, -0.770** (Windmeijer robust s.e. in parentheses).
  - LPC(t-1) values reported: 1.882***, 0.637*, 0.479, 0.353 (s.e. (0.547), (0.368), (0.373), (0.389)).
  - PC(t-1) values: 5.429***, 3.652***, 1.063, 0.072 (s.e. (1.570), (1.239), (0.745), (0.747)).
  - LEDU(t-1) several significant positive coefficients reported (e.g., 2.803***, 2.810***, 2.780***, 2.833***).
  - LGC(t-1) negative and often significant (e.g., -2.833***, -1.888**, -1.978***, -1.920***).
  - LOPEN(t-1) positive in several columns (e.g., 1.138**, 1.618***, 1.590**, 1.615***).
  - AR1 statistics: -3.81, -4.35, -5.04, -5.41, -3.76, -4.44, -4.99, -5.36 with p-value 0.000 for all.
  - AR2 statistics and p-values shown (e.g., AR2 values around -0.35 to -1.71 with p-values reported).
  - OID statistics: 90.2, 110.2, 113.6, 121.5, 85.7, 96.2, 115.0, 126.8 (p-values show e.g., 0.95, 0.78, 1? as printed).
  - N. Obs. sequences: 549, 675, 798, 917, 549, 675, 798, 917.
  - N. Cy.: 107, 127, 131, 133, 107, 127, 131, 133.
  - Period columns include 1960-95, 1960-00, 1960-05, 1960-10.
  - dGR/dPC entries not printed explicitly in the table excerpt.

- Table 5 (Panel estimations — System GMM with PC and PC2):
  - LGDP(t-1) coefficients: -0.713*, -0.751*, -0.767**, -0.728**, -0.579, -0.746**, -0.688**.
  - PC(t-1): 8.724***, 5.427***, 3.646**, 3.628**, 5.074**, 3.655*, 3.128* (s.e. shown).
  - PC2(t-1): -3.026*, -1.975*, -1.774*, -2.021***, -3.666***, -2.264*, -1.755**.
  - LEDU(t-1) positive and often significant across columns.
  - LGC(t-1) negative and often significant (e.g., -2.757***, -2.057***, -1.720***).
  - LOPEN(t-1) positive and significant in many columns (e.g., 1.781***, 1.649***, 1.235***).
  - AR1 and AR2 test statistics reported with p-values, and OID values with p-values.
  - dGR/dPC values across columns listed as "1.44 1.37 1.03 0.90 0.69 0.81 0.89".
  - Notes a–c: a excludes countries where PC was ever larger than 1.65; b excludes USA, IRL, ESP and ISL; c one percent Winsorization of the dependent variable.

- Table 6 (Panel estimations: 10-year growth episodes):
  - PC(t-1) coefficients: 2.832*, 0.540, 6.965**, 7.270*** (s.e. (1.653), (0.991), (2.821), (2.016)).
  - PC2(t-1) coefficients: -3.912**, -4.430*** (s.e. (1.663), (1.181)).
  - LEDU(t-1) values e.g., 1.044, 2.226**, 1.217, 1.571*.
  - LGC(t-1) negative, e.g., -2.375**, -3.159***, -1.398, -2.443**.
  - AR1 and AR2 reported; OID statistics with p-values.
  - N. Obs.: 360, 479, 360, 479. N. Cy.: 127, 133, 127, 133.
  - Periods: 1960-00, 1960-10, 1960-00, 1960-10.
  - dGR/dPC reported as "00.890.82" (preserve as in source).

- Table 7 (Volatility and Banking Crises; System GMM):
  - PC(t-1) coefficients: 2.925*, 2.999**, 3.334*, 3.957** (s.e. (1.640), (1.453), (1.734), (1.859)).
  - PC2(t-1): -1.982**, -2.104**, -1.577*, -2.431** (s.e. given).
  - HVOL coefficient: -1.326***, -1.076** (s.e. (0.288), (0.529)).
  - BKCR coefficient: -1.898***, -2.134** (s.e. (0.448), (0.837)).
  - Interactions PC×HVOL, PC2×HVOL, PC×BKCR, PC2×BKCR reported (some not significant; s.e. shown).
  - LEDU(t-1) positive and significant: 1.570**, 1.726***, 2.155***, 1.871***.
  - LGC(t-1) negative and significant in each column.
  - dGR/dPC baseline values listed: 0.7, 0.71, 1.06, 0.81 (table shows "dGR/dPC=00.740.711.060.81").
  - dGR/dPC when HV or BC equals 0 entries "0.65 1.13" (table shows "dGR/dPC=0 (HV or BC)0.651.13").

- Table 8 (Institutional quality, bank regulation and supervision; System GMM with interactions):
  - PC(t-1) coefficients: 3.443*, 4.505, 2.785, 2.306 (s.e. shown).
  - PC2(t-1): -2.459***, -2.797*, -2.387*, -1.810*.
  - Interactions between PC/PC2 and LQOG, LOSI, LKRI, LPMI reported; cross-terms and main effects have coefficients and s.e. as printed (many not significant).
  - dGR/dPC baseline entries: 0.7, 0.81, 0.58, 0.64 (table shows "dGR/dPC=00.700.810.580.64").
  - dGR/dPC at INT=0 entries: 0.60, 0.82, 1.05, 0.77 (table shows "dGR/dPC=0 INT0.600.821.050.77").

- Table 9 (Rajan and Zingales industry-level estimations, 1990-2000):
  - SHVA t-1: -2.069**, -2.059**, -2.063**, -2.061**, -0.645, -2.217** (s.e. shown).
  - EF×PC coefficients: 0.0180*, 0.0742**, 0.0696**, 0.0654*, 0.0508** (s.e. listed).
  - EF×PC2 coefficients: -0.0300**, -0.0284**, -0.0265*, -0.0227*.
  - OEF×PC: 0.169*** (s.e. (0.0452)); OEF×PC2: -0.0694*** (s.e. (0.02)).
  - PC thresholds at which marginal effect becomes negative (PC thresh.): 1.237, 1.225, 1.234, 1.119, 1.218.
  - N. Obs.: 1252 (across columns), R-squared values reported: 0.336, 0.338, 0.338, 0.338, 0.433, 0.343.

### Tests, marginal effects, and graphical summaries
- Inverse U-shape evidence:
  - Table 3 reports significant positive slope at PCmin and significant negative slope at PCmax across multiple specifications, SLM test p-values as low as 0.00 and Fieller 90% CIs consistently excluding zero for most specifications (examples: [0.65; 1.24], [0.73; 1.11], [0.77; 1.16], [0.18; 1.18], [0.68; 0.97]).

- Marginal effects dGR/dPC reported at various tables/columns (preserve original formatting when presented):
  - Table 5 dGR/dPC entries (columns): 1.44, 1.37, 1.03, 0.90, 0.69, 0.81, 0.89.
  - Table 6 dGR/dPC entries: "00.890.82".
  - Table 7 dGR/dPC baseline: "00.740.711.060.81"; and under HV or BC: "0.651.13".
  - Table 8 baseline dGR/dPC: "00.700.810.580.64"; INT=0: "0.600.821.050.77".
  - Figure captions indicate plotted marginal effects derived from Table 1 column 6 and Table 5 column 4, semi-parametric fits, and comparisons across volatility, crisis, and institutional/regulatory strata.

- Graphical descriptors (figures in document):
  - Figure 1: "Marginal Effect Using Cross-Country Data" — plots marginal effect from Table 1, column 6.
  - Figure 2: "Semi-Parametric Regressions" — plots relationship between credit to private sector and growth, with 90% confidence intervals and quadratic fit of column 6, Table 1.
  - Figure 3: "Credit to the Private Sector" — evolution of PC mean and median and share of obs with PC>90% and PC>120% across 1960–2010.
  - Figure 4: "Marginal Effect Using Panel Data" — plots marginal effect from Table 5, column 4.
  - Figures 5–9: distributions of PC in 2006, semi-parametric panel fits, and marginal effects under low/high volatility, tranquil/crisis periods, and across institutional/regulatory groupings (as described in captions).

### Data definitions, sources, and summary statistics (selected exact entries)
- Table 10 (Data Description and Sources) — key variable definitions and sources (as stated in source):
  - Growth: "Annual percentage growth rate of GDP at market prices based on constant local currency. Aggregates are based on constant 2000 U.S. dollars. Source: World Bank World Development Indicators (WDI) 2011."
  - PC: "Claims on private sector by deposit money banks and other financial institutions divided by GDP. Source: Beck et al. (November 2010 update) and Beck et al. (2000) when Beck et al. (2010) has missing data (LPC and PC2 are the log and the square of PC)."
  - EDU: "Average years of schooling of males and females above 25 years of age (the regressions use the inverse hyperbolic sine transformation LEDU C= ln(EDU C+√EDU C2+1)). Source: Barro and Lee (2010)."
  - GC, OPEN, INFL definitions and WDI 2011 as source.
  - HVOL: "Dummy variable ... standard deviation of annual GDP growth ... greater than 3.5 %."
  - BKCR: "Dummy variable ... at least one banking crisis. Source: Laeven and Valencia (2010)."
  - LQOG: "Dummy variable ... continuous quality of government index is smaller than 0.5 ... Source: QOG Institute ... icrg-qog variable ... For early periods we set the LQOG variable to be equal to its 1984 value."
  - LOSI, LKRI, LPMI: time-invariant variables based on Barth et al. (2008) indices with imputation procedures described; source details preserved as printed.
  - Industry-level variables: VAGR, SHVA, EF*PC, EF*Y, OEF*PC defined with sources (UNIDO, Eichengreen et al. (2011), Rajan and Zingales (1998)).

- Table 11 (Summary Statistics) — selected exact statistics:
  - Cross-sectional:
    - GROWTH: N.Obs 691, Mean 1.58, Std. Dev. 1.34, Min -4.20, Max 4.53.
    - LGDP: N.Obs 698, Mean 4.31, Std. Dev. 1.57, Min 5.05, Max 10.94.
    - PC: N.Obs 690, Mean 0.46, Std. Dev. 0.34, Min 0.04, Max 1.37.
    - LEDU: N.Obs 691, Mean 1.67, Std. Dev. 0.59, Min -0.30, Max 2.50.
    - LGC: N.Obs 692, Mean 2.68, Std. Dev. 0.30, Min 1.94, Max 3.46.
    - LINF: N.Obs 692, Mean 2.40, Std. Dev. 1.03, Min 1.03, Max 5.84.
    - LOPEN: N.Obs 694, Mean 4.09, Std. Dev. 0.50, Min 3.02, Max 5.36.
  - Panel:
    - GROWTH: N.Obs 9,172, Mean 2.02, Std. Dev. 2.77, Min -21.00, Max 13.86.
    - LGDP: N.Obs 9,177, Mean 7.80, Std. Dev. 1.55, Min 4.61, Max 10.89.
    - PC: N.Obs 9,170, Mean 0.40, Std. Dev. 0.37, Min 0.01, Max 2.70.
    - LEDU: N.Obs 9,172, Mean 2.28, Std. Dev. 0.67, Min 0.27, Max 3.27.
    - LGC: N.Obs 9,172, Mean 2.65, Std. Dev. 0.39, Min 1.17, Max 3.83.
    - LINF: N.Obs 9,172, Mean 2.50, Std. Dev. 1.21, Min -3.56, Max 6.91.
    - LOPEN: N.Obs 9,172, Mean 4.12, Std. Dev. 0.60, Min 2.05, Max 6.08.
  - Industry-level:
    - VA Growth: N.Obs 1,252, Mean 0.041, Std. Dev. 0.115, Min -0.476, Max 1.05.
    - Ext. Dep. ’90s: N.Obs 360, Mean 0.014, Std. Dev. 0.566, Min -1.14, Max 2.43.
    - Ext. Dep. ’80s: N.Obs 360, Mean 0.319, Std. Dev. 0.406, Min -0.45, Max 1.491.

*Source: _wp12161 - REFERENCES (PDF)._

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