## _wp16234

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### Research question and main contribution
- Core question: "Is there a minimum tax-to-GDP ratio associated with a significant acceleration in the process of growth and development?"
- Novel approach: investigate the existence of a tipping point in tax-to-GDP levels where small changes around the threshold could generate sharp changes in subsequent GDP growth.
- Empirical scope: contemporary database covering 139 countries and spanning the period 1965-2011.
- Methodological innovation: combines regression discontinuity design methods (Card, Mas and Rothstein (2008)) with the threshold regression framework (Hansen (1999)) to estimate tax tipping points.
- Extension of prior work (Besley and Persson): (i) broader database coverage; (ii) non-linear model to flexibly estimate reduced-form relation between tax levels and subsequent GDP growth.

### Theoretical and conceptual framework
- Conceptual lineage: Schumpeter’s "The Crisis of the Tax State (Schumpeter, 1918)"—state formation and taxation linked via long-run, structural, self-reinforcing dynamics.
- Distinction: taxes versus other government revenues (patrimony, entrepreneurial activity); taxation central to "Tax State" evolution.
- Complementarities: tax capacity, legal capacity, and public administration capacity are complements; feedback loops can yield multiple equilibria.
- Social norms and compliance: tax morale driven by strategic (enforcement) and normative (fairness, public goods provision) considerations; legitimacy and accountability strengthen quasi-voluntary compliance.

### Data and empirical design
- Contemporary database: unbalanced panel of tax-to-GDP and real GDP per capita for 139 countries, 1965–2011.
  - Tax-to-GDP sources combined (in order): OECD; Mansour (2014, 2015); World Economic Outlook; GFSM 1986 Historical Government Finance Statistics; International Centre for Tax and Development’s Government Revenue Dataset.
  - Real GDP per capita source: Penn World Tables 8.1 (Feenstra, Inklaar and Timmer, 2015).
  - Dropped countries where natural resource rents exceed 30 percent on average over sample.
  - Median values reported: real GDP per capita growth median: 1.9% (distribution of average annual growth), tax-to-GDP median: 16.9% (distribution of tax-to-GDP ratios).
- Historical database: unbalanced panel for 30 advanced countries between 1800 and 1980.
  - Tax-to-GDP from International Historical Statistics (Mitchell, 2003); real GDP per capita (GK$ 1990) from Maddison Project 2013.
  - Median values reported: average real GDP per capita growth rate median: 1.6%, tax-to-GDP median: 11.7%.

### Identification challenge and empirical strategy
- Endogeneity issue: joint determination of GDP and tax-to-GDP (e.g., Wagner’s Law).
- Mitigation strategy: focus on local effects around potential tipping points (small changes near threshold) rather than estimating global linear relations.
- Empirical approach: two-step CMR strategy
  - Step 1: search for threshold γ that maximizes R-squared of constrained specification ∆GDPPC_{ct+j} = α_l + β D + ε_{ct} over γ candidates.
  - Step 2: test significance of tipping point using Hansen (1999) bootstrap procedure and recover β via RDD treating γ̂ as known.
- Estimators: fourth-order polynomial (main estimator) and non-parametric estimators; grid search for γ restricted to between 8 and 30 percent of GDP; drop observations with tax-to-GDP below 5 percent and above 40 percent; search over 2,500 quantiles.
- Testing: null H0: β = 0; Hansen bootstrap likelihood ratio statistic F1 = N(S0 − S1)/S1; p-values and critical values obtained via 1000 bootstrap iterations.

### Main empirical results — contemporary database
- R-squared search:
  - Stable tipping point roughly between 10 and 15 percent of GDP across horizons j = (3, 5, 7, 10) years.
  - Maximum R-squared values low (around 0.01 for 10-year cumulative growth) but series show unique maxima.
- Hansen bootstrap test statistics (Table 2):
  - p-values: 0.000 for 3-year, 5-year, 7-year, and 10-year horizons.
  - F1 statistics: 17.8 (3-year), 26.2 (5-year), 30.9 (7-year), 30.8 (10-year).
  - Critical values (10%): 2.8 (3-year), 3.2 (5-year), 2.7 (7-year), 2.6 (10-year).
  - Critical values (5%): 4.2 (3-year), 4.7 (5-year), 4.1 (7-year), 3.8 (10-year).
  - Critical values (1%): 6.6 (3-year), 7.5 (5-year), 6.9 (7-year), 5.7 (10-year).
- Estimated tax-to-GDP thresholds (first-step procedure):
  - 3-year: 12.88
  - 5-year: 12.42
  - 7-year: 12.45
  - 10-year: 12.88
- Confidence intervals ("No-rejection region"):
  - 95%:
    - 3-year: [11.56; 14.01]
    - 5-year: [11.70; 13.38]
    - 7-year: [11.60; 13.05]
    - 10-year: [11.62; 13.41]
  - 99%:
    - 3-year: [9.94; 14.19]
    - 5-year: [11.40; 13.78]
    - 7-year: [10.91; 13.51]
    - 10-year: [11.33; 13.97]
- Impact of crossing 12.88 percent tipping point (graphical and dynamic findings):
  - Countries immediately left of 12.88 percent: grow by around 20 to 25 percent in real terms over 10 years (around 2 percent annually).
  - Countries immediately right of 12.88 percent: grow by more than 30 percent over 10 years (2.8 percent annually).
  - Difference between just-right and just-left:
    - 12.36 percent after 10 years.
    - 16.85 percent 15 years later.
  - Interpretation: crossing the tax threshold adds about one percent to real annual GDP per capita growth for the next 10 to 15 years.
- Regression discontinuity estimates (dependent variable = 10-year cumulative GDP per capita growth; indicator = 1 if tax level > 12.88 percent):
  - Tax-to-GDP threshold coefficient estimates (standard errors):
    - Column (1): 12.355* (6.651)
    - Column (2): 6.864** (3.060)
    - Column (3): 7.450** (3.017) — preferred specification (includes initial real GDP per capita)
    - Column (4): 7.283** (3.018)
    - Column (5): 6.852** (3.081)
    - Column (6): 6.963** (3.054)
    - Column (7): 7.717** (2.967)
  - Selected control coefficients:
    - GDP per capita: -3.127*** (0.538); -2.972*** (0.610) where included.
    - Openness: 7.644*** (2.762); 4.388* (2.474).
  - Observations: 3189 (all columns).
  - R-squared, overall: 0.023 (col 1); 0.691 (col 2); 0.739 (col 3); 0.701 (col 4); 0.691 (col 5); 0.692 (col 6); 0.742 (col 7).
  - R-squared, within: (col 2) 0.132; (col 3) 0.266; (col 4) 0.159; (col 5) 0.132; (col 6) 0.135; (col 7) 0.275.
- Robustness:
  - Adding country and year fixed effects reduces the estimated impact (e.g., from 12.36 percent to 6.86 percent).
  - Preferred specification (column (3)) yields a threshold effect of 7.45 percent.
  - Results robust to alternative bootstrap methods and inclusion of initial GDP per capita.
  - Cluster-robust Wald test yields tipping point significant at the 10 percent level at all horizons.
- Pre-trend assessment:
  - No detectable systematic pre-trend for countries around the threshold prior to observation year 0.
  - Joint test of pre-treatment coefficients: p-value = 0.23.

### Treatment of social security contributions
- Main analysis excludes social security contributions from tax revenue (per IMF’s 2014 Government Finance Statistics Manual).
- Including social security contributions:
  - Yields lower tipping-point estimates and more variation across horizons.
  - At the 10-year horizon, social security–inclusive series yield a tipping point at 12.0 percent of GDP.
  - For countries around 12.88 percent, social security contributions make up around 10 percent of tax revenues.
  - Using social security–inclusive taxes and tipping point 12.0 percent: effect on subsequent growth is negligible and statistically insignificant.
  - Defining inclusive tipping point as 12.88 percent plus social security contributions recovers main estimate of effect on subsequent GDP growth.
- Conclusion: adding social security contributions does not provide additional information on location and effect of tax tipping points.

### Historical database results (30 advanced economies, 1800–1980)
- Estimated threshold (first-step procedure): 12.65 for 3-, 5-, 7-, and 10-year horizons.
- Confidence intervals ("No-rejection region"):
  - 95%:
    - 3-year: [12.51; 12.81]
    - 5-year: [11.37; 12.85]
    - 7-year: [12.25; 12.84]
    - 10-year: [12.24; 12.82]
  - 99%:
    - 3-year: [11.24; 12.94]
    - 5-year: [11.28; 14.07]
    - 7-year: [12.17; 13.72]
    - 10-year: [12.17; 12.85]
- Graphical and dynamic findings:
  - Figure 14: sharp increase in average cumulative GDP per capita growth rates just above 12.65 percent.
  - Figure 15: after 10 years cumulative effect ~16 percent; after 15 years estimated long-run effect ~25 percent higher cumulative growth for countries immediately right vs. left of threshold.
  - 90 percent confidence bands are large and include 16.85 percent value from contemporary database.
- Regression estimates (dependent variable = 10-year cumulative GDP per capita growth; observations = 1593):
  - Tax-to-GDP indicator coefficients (standard errors):
    - Column (1): 15.957** (7.189) — no country or year FE
    - Column (2): 5.440 (6.515) — with country and year FE
    - Column (3): 2.535 (5.714) — with country and year FE and GDP per capita
  - GDP per capita coefficient (col 3): -14.139*** (2.847).
  - R-squared, overall: 0.084 (col 1); 0.655 (col 2); 0.655 (col 3).
  - R-squared, within: 0.436 (col 2); 0.585 (col 3).
- Robustness:
  - Including country and year fixed effects reduces the estimated effect substantially (e.g., 15.957** → 5.440) and renders it not statistically different from zero in column (2).
  - Adding initial GDP per capita further reduces point estimate to 2.535 and not statistically significant.
  - Historical panel highly unbalanced, reducing precision when year fixed effects are included.

### Major findings and interpretation
- Contemporary dataset (139 countries, 1965–2011) first-step tipping point ≈ 12.88 percent tax-to-GDP.
- Preferred contemporary specification: a country just above 12.88 percent has real GDP per capita around 7.5 percent larger after 10 years than an otherwise similar country just below it.
- Historical database (30 advanced economies, 1800–1980) tipping point ≈ 12.65 percent tax-to-GDP, close to contemporary estimate.
- Coincidence of thresholds across databases suggests a common threshold near 12 ¾ percent of GDP.
- Economic magnitude: crossing threshold associated with sustained cumulative gains (e.g., 12.36 percent after 10 years; ~16–25 percent at 15 years depending on sample).
- Statistical significance: contemporary first-step threshold highly significant (Hansen bootstrap p-values = 0.000); estimated growth effects attenuate and sometimes lose statistical significance when country and year fixed effects and initial GDP per capita are included, especially in the historical sample.
- Robustness caveats: smaller historical sample size and unbalanced panel limit statistical definitiveness; tax-to-GDP ratios are volatile and context-dependent.

### Policy implications
- The estimated threshold likely associated with shifts in social norms of compliance and improvements in state capacity.
- For low-revenue countries, aiming for tax-to-GDP levels around 15 percent is consistent with evidence and standard recommendations given the identified tipping point near 12 ¾ percent.
- Strengthening tax capacity up to and beyond the threshold may support sustained increases in real GDP per capita over several years.

### Key statistics and methodological details (preserved exactly)
- Contemporary dataset: 139 countries from 1965 to 2011.
- Contemporary tipping point: 12.88 percent (tax-to-GDP).
- Historical database: 30 advanced economies from 1800 to 1980.
- Historical tipping point: 12.65 percent (tax-to-GDP).
- Preferred specification growth effect: 7.5 percent larger real GDP per capita after 10 years for a country just above the threshold.
- Recommended target for low tax-to-GDP countries: about 15 percent.
- Significance markers: * p<10%, ** p<5%, *** p<1%.
- Polynomial used: fourth-order polynomial in tax-to-GDP with intercept shift at the estimated tax-to-GDP threshold.
- Standard errors: clustered at the country level.
- Appendix figures: local linear regression fit separately on either side of 12.88 using an Epanechnikov kernel and a bandwidth of 1.5; a global fourth-order polynomial also shown.
- Table A1 threshold used: 12.88 percent tax-to-GDP for tipping-point crossings.
- Table A3 threshold used: 12.65 percent revenue-to-GDP for tipping-point crossings.
- Grid search bounds: γ searched between 8 and 30 percent of GDP; observations with tax-to-GDP below 5 percent and above 40 percent dropped; search over 2,500 quantiles.
- Bootstrap iterations for Hansen test and confidence regions: 1000.

*Source: _wp16234 - References*

### References _______________________________________________________________________________________ 31

### _wp16234 - References

### Research question and main contribution
- Core question: "Is there a minimum tax-to-GDP ratio associated with a significant acceleration in the process of growth and development?"
- Novel approach: investigate the existence of a tipping point in tax-to-GDP levels where small changes around the threshold could generate sharp changes in subsequent GDP growth.
- Empirical scope: uses a "novel contemporary database covering 139 countries and spanning the period 1965-2011."
- Methodological innovation: combines regression discontinuity design methods (Card, Mas and Rothstein (2008)) with the threshold regression framework (Hansen (1999)) to provide new estimates of tax tipping points.
- Extends earlier work by Besley and Persson (2011, 2013, 2014a, 2014b) by:
  - (i) relying on a much broader database, both in coverage of countries and years; and
  - (ii) using a non-linear model to flexibly estimate the reduced-form relation between tax levels and subsequent GDP growth.

### Theoretical and conceptual framework
- Conceptual lineage: follows Joseph Schumpeter’s perspective in "The Crisis of the Tax State (Schumpeter, 1918)" emphasizing close linkage between state formation and taxation and the importance of long-run, structural, self-reinforcing dynamics (economic, social, and political).
- Distinction emphasized: taxes versus other forms of government revenue—dependence on revenues from patrimony or entrepreneurial activity is characteristic of an earlier stage of Public Finance development, while taxation plays a central role in the "Tax State" evolution.

### Data and empirical design
- Primary datasets:
  - Contemporary database: 139 countries, 1965-2011.
  - Historical database: described later in the paper (sectioning indicated).
- Focus of analysis: tax revenues (tax-to-GDP ratios) rather than other revenue sources, because other sources (natural resources, foreign aid) are not closely related to economic development in prior evidence.
  - Cited evidence: Arezki et al. (2011) and IMF (2015) on resource-rich countries’ poor economic performance relative to non-resource-rich countries.
  - Foreign aid: no consensus; reference to Edwards (2014) for overview.

### Identification challenge and strategy
- Endogeneity challenge: joint determination of GDP and tax-to-GDP ratios (e.g., Wagner’s Law—rising demand for public services implying higher expenditure-to-GDP and, marginally, higher tax-to-GDP).
- Mitigation strategy: focus on local effects around potential tipping points—how small changes in taxes near a tipping point affect subsequent growth—rather than estimating global linear relations.
- Robustness: local results reported as robust when controlling for the potential endogeneity of taxes.

### Structure of the paper (as presented)
- Section II: selective literature review on taxation and economic development; intuition on how small changes in taxes can lead to large changes in GDP.
- Section III: description of compilation of the two databases—the contemporary database and the historical database.
- Figures and tables inventory (selected):
  - Figures include: Complementarities in State Capacity; Tax Capacity, Social Norms, and Accountability; Tax to GDP and Income Levels; Tax Capacity and Legal Capacity, 2012; Tax Capacity and Public Administration Capacity, 2012; databases’ observation counts and distributions; multiple analyses of tax tipping points and their impacts across horizons and over time.
  - Tables include: Sources for Tax-to-GDP data; Testing for Statistical Significance of Tax Thresholds; Estimated Tax-to-GDP Thresholds; Estimating Growth Effects; Estimating Tax Revenue-to-GDP Thresholds, Historical Database; Estimating Growth Effects, Historical Database.
  - Appendix figures A1–A3: Impact of a Tax Threshold on 3-year, 5-year, and 7-year Cumulative Growth.
  - Appendix tables A1–A3: Tipping Point Crossing (Contemporary and Historical Databases) and Summary Statistics, Historical Database.

*Source: _wp16234 - References*

### Section IV explains the methodology used and the empirical results obtained. Section V

### _wp16234 - Section IV explains the methodology used and the empirical results obtained. Section V

### II. TAXATION AND ECONOMIC DEVELOPMENT
- Literature streams:
  - Development → tax system: countries with higher share of agriculture and lower share of imports-to-GDP tend to have lower taxation (Tanzi (1992); Burgess and Stern (1993)).
  - Link between taxation and formal finance: firms evade taxes by using cash where financial sector value is modest (Gordon and Li (2009)); firm size enables third-party enforcement in more developed countries (Kleven, Kreiner, and Saez (2009)); large informal sectors are hard to tax (Joshi et al. (2014)); informality motivated by desire to avoid taxes (La Porta and Shleifer (2014)).
  - Access to non-tax revenue associated with lower taxation: a 1 percent increase in natural resource rents share of total government income → 1.4 percent lower share of taxation in GDP (Jensen (2011)); negative association between foreign aid and domestic tax revenues, particularly in low-income and weak-institutions countries (Benedek et al. (2014)).
  - Tax system → economy: taxation spent on public goods/investments can raise productivity (Barro (1990)); well-designed tax systems can minimize efficiency losses and raise GDP growth in endogenous-growth models (Barro and Sala-i-Martin (1992)). In sub-Saharan Africa, instability of tax revenue reduces public investment (Ebeke and Ehrhart (2011)). Stricter tax enforcement can reduce bribe demands and encourage market entry (Seidel and Thum (2015)).
  - Political/institutional factors and state capacity (Besley and Persson (2011, 2013, 2014a, 2014b)):
    - State capacity comprises: (i) fiscal capacity (tax collection, enforcement); (ii) legal capacity (contracts, property rights); (iii) collective capacity (public goods).
    - Determinants common across dimensions: war, ethnic homogeneity, political stability, constraints on executive correlate with fiscal and legal capacity.
- Complementarities and feedbacks:
  - Tax capacity, legal capacity, and public administration capacity are complements; improvements in one require investment in others and are positively correlated; feedback loops can yield multiple equilibria (Besley and Persson (2013)).
  - Strength of tax capacity depends on social norms of compliance: effectiveness and trustworthiness of government → legitimacy → quasi-voluntary compliance (Kiser and Levi (2015); Levi (1988)); compliance driven by strategic (probability of being caught, punishment) and normative (fairness, public goods provision) considerations. Tax morale and compliance culture noted (Gordon (1989); Posner (2000); Torgler (2007)). Demand for accountable and transparent government linked to higher compliance (Moore (2007); Brautigam et al. (2008); Ross (2004)).
- Growth accelerations and tax tipping point:
  - Crossing the tax-to-GDP tipping point associated with higher average annual growth rates by about 0.75 ppa over 10 years compared to countries that remain below the tipping point. This effect is important though smaller than the largest growth acceleration episodes (e.g., Hausman et al. (2005) consider 2.5 ppa sustained over 8 years).

### II.B. Tipping points: mechanism
- Rationale:
  - Multiple equilibria arise with strategic complementarities (Card et al. (2008)); small changes in initial conditions can produce large outcome changes (tipping points).
  - Shift in social norms can move country from low tax compliance equilibrium to high tax compliance equilibrium (Traxler (2010)).
- Channels for virtuous cycle after exceeding tipping point:
  - Greater tax compliance enlarges tax base → reduces marginal cost of public funds → enables more spending on state capacity building.
  - Increased cooperation and trust facilitate agglomeration effects and formal market participation.
  - Larger taxpayer pool increases accountability → improves governance → decreases corruption → reduces market entry barriers (Murphy, Schleifer, and Vishny (1993)).
- Empirical strategy:
  - Apply regression discontinuity design (RDD) to tax-to-GDP levels vs. subsequent GDP growth to detect discontinuous jumps in growth near tax-to-GDP levels (Card et al. (2008) approach).

### II.C. Stylized facts
- Cross-sectional and long-run evidence:
  - Figure 3: positive relationship between tax-to-GDP and real GDP per capita (2012 cross-section and historical time-series for 30 countries back to 1800).
  - Figure 4: higher tax-to-GDP correlates with stronger protection of property rights (Fraser Institute indicator) and higher regulatory quality (Worldwide Governance Indicators).
  - Figure 5: higher tax-to-GDP correlates with lower corruption (Transparency International index) and stronger budget institutions (Public Investment Management Efficiency (PIE-X) index).

### III. DATA
- Databases used:
  - Contemporary database: unbalanced panel of tax-to-GDP and real GDP per capita for 139 countries from 1965 to 2011.
    - Tax-to-GDP sources combined in order when available: (1) OECD; (2) Mansour (2014, 2015) for sub-Saharan African and MENA countries; (3) World Economic Outlook; (4) GFSM 1986 Historical Government Finance Statistics; (5) International Centre for Tax and Development’s Government Revenue Dataset. Splicing used to combine sources.
    - Table 1: Tax-to-GDP (all sources) 1965-2011 139; 1- OECD 1965-2011 47; 2- Mansour (2014, 2015) 1980-2011 38; 3- World Economic Outlook 1985-2011 77; 4- GFSM 1986 Historical Government Finance Statistics 1970-2002 70; 4- The International Centre for Tax and Development 1980-2010 40.
    - Real GDP per capita at constant national prices from Penn World Tables 8.1 (Feenstra, Inklaar and Timmer, 2015).
    - Dropped countries where natural resource rents exceed 30 percent on average over sample.
    - Figure 6: number of observations on tax-to-GDP by year for advanced and developing countries.
    - Figure 7: distribution of tax-to-GDP and average annual real per capita GDP growth rates across contemporary database. Median values shown: real GDP per capita growth median: 1.9% (distribution of average annual growth), tax-to-GDP median: 16.9% (distribution of tax-to-GDP ratios), and elsewhere median: 1.6% and 11.7% in other panels.
  - Historical database: unbalanced panel for 30 advanced countries between 1800 and 1980.
    - Tax-to-GDP from International Historical Statistics (Mitchell, 2003); real GDP per capita (GK$ 1990) from Maddison Project 2013.
    - Figure 8: number of observations on tax-to-GDP by year; Figure 9: distributions. Median listed: average real GDP per capita growth rate median: 1.6%, tax-to-GDP median: 11.7%.
    - Countries listed: Australia, Austria, Belgium, Canada, Chile, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Israel, Italy, Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Slovenia, Ireland, Spain, Sweden, Switzerland, United Kingdom, United States.
- Notes:
  - IMF’s World Revenue Longitudinal Data set (WoRLD) offers similar compilation; results identical when using WoRLD (note: WoRLD data available at http://data.imf.org/revenues in source).

### IV. EMPIRICAL APPROACH
#### A. Methodology
- Model:
  - Cumulative GDP per capita growth ∆GDPPC_{ct+j} modeled as function of tax-to-GDP tax_{ct}, allowing discontinuity at unknown threshold γ, with covariates X_{ct}, country fixed effects θ_c, year fixed effects δ_t. Formulation given in Equation (1) with left and right functions f_l(.) and f_r(.).
  - ∆GDPPC_{ct+j} = (GDPPC_{ct+j} − GDPPC_{ct−1})/GDPPC_{ct−1}.
  - Compact form (Equation (2)): ∆GDPPC_{ct+j} = α_l + β D + f(tax_{ct} − γ) + X_{ct} ρ + θ_c + δ_t + ε_{ct}, where β ≡ α_r − α_l, D ≡ 1(tax_{ct} > γ).
- Estimation strategy:
  - Two-step approach from Card, Mas and Rothstein (2008) (CMR):
    1. Estimate structural break: find γ that maximizes R-squared of constrained specification (Equation (2′): ∆GDPPC_{ct+j} = α_l + β D + ε_{ct}), searching γ over candidate values.
    2. Test statistical significance of tipping point using Hansen (1999) bootstrap procedure for non-standard threshold estimators; then recover β via RDD estimator treating γ̂ as known.
  - Use both parametric (fourth order polynomial in tax-to-GDP) and non-parametric estimators in main analysis; main estimator relies on fourth order polynomial.
  - Focus is on local discrete change in GDP growth (α_r − α_l) rather than global functional form.
  - For power and parsimony, first-step search ignores covariates and fixed effects, approximating f(.) by constant.
- Testing procedure:
  - Null H0: β = 0.
  - Hansen (1999) bootstrap likelihood ratio test statistic F1 = N(S0 − S1)/S1 where S0 and S1 are sum of squared residuals under null and alternative; p-value from bootstrapped iterations.
  - Grid search for γ restricted to between 8 and 30 percent of GDP (roughly 5th and 95th percentiles). Drop observations with tax-to-GDP below 5 percent and above 40 percent. Search over 2,500 quantiles.
  - Note: conventional tests can over-reject; use Hansen (1999) approach to account for non-standard distributions. Alternative procedures (CMR split-sample) not feasible due to limited observations.

#### B. Results based on the contemporary database
- R-squared search (Figure 10):
  - Estimating Equation (2′) across thresholds between 8 and 30 percent of GDP and horizons j = (3, 5, 7, 10) years yields low maximum R-squared (around 0.01 for 10-year cumulative growth) but shows a stable tipping point roughly between 10 and 15 percent of GDP at all horizons.
  - Series show unique maxima; threshold candidate is stable across horizons.
- Statistical tests (Table 2):
  - Hansen test statistic p-values: 0.000 for 3-year, 5-year, 7-year, and 10-year horizons (i.e., strongly significant well below the one percent level).
  - F1 statistic values: 17.8 (3-year), 26.2 (5-year), 30.9 (7-year), 30.8 (10-year).
  - Critical values (10%): 2.8 (3-year), 3.2 (5-year), 2.7 (7-year), 2.6 (10-year).
  - Critical values (5%): 4.2 (3-year), 4.7 (5-year), 4.1 (7-year), 3.8 (10-year).
  - Critical values (1%): 6.6 (3-year), 7.5 (5-year), 6.9 (7-year), 5.7 (10-year).
  - Note: p-values and critical values obtained via 1000 bootstrap iterations.
- Estimated tipping point precision:
  - Point estimates of tax threshold are stable across horizons.
  - Example: tax-to-GDP threshold at the 10-year horizon has point estimate 12.88 percent with 99 percent confidence interval from 11.33 percent of GDP to 13.97 percent.
- Robustness notes:
  - Results robust to alternative bootstrap methods and inclusion of GDP per capita in initial year.
  - Using lower-order polynomials produces somewhat lower estimates of effect of crossing tipping point (results available upon request).
  - Cluster-robust Wald test yields tipping point significant at the 10 percent level at all horizons.

*Source: IMF working paper content provided in the input PDF excerpt.*

### 2.65 percentage points wide. The confidence intervals are somewhat wider for shorter time

### _wp16234 - 2.65 percentage points wide. The confidence intervals are somewhat wider for shorter time horizons.

### Estimated tax-to-GDP thresholds (contemporary database)
- Tax-to-GDP threshold (dependent variable: GDP per capita cumulative growth)
  - 3-year: 12.88
  - 5-year: 12.42
  - 7-year: 12.45
  - 10-year: 12.88
- Confidence intervals ("No-rejection region")
  - 95%:
    - 3-year: [11.56; 14.01]
    - 5-year: [11.70; 13.38]
    - 7-year: [11.60; 13.05]
    - 10-year: [11.62; 13.41]
  - 99%:
    - 3-year: [9.94; 14.19]
    - 5-year: [11.40; 13.78]
    - 7-year: [10.91; 13.51]
    - 10-year: [11.33; 13.97]

### Impact of crossing the estimated threshold on growth (contemporary database)
- Graphical and sample-based findings
  - Countries immediately to the left of the 12.88 percent tipping point:
    - Grow by around 20 to 25 percent in real terms over 10 years (around 2 percent annually).
  - Countries immediately to the right of the threshold:
    - Grow by more than 30 percent over 10 years (2.8 percent annually).
  - Relationship is noisier at the bottom of the tax-to-GDP distribution; smoother just above the threshold with a slight negative slope beyond 15 percent of GDP.
- Dynamic effects over time (Figure 12 / Equation (2))
  - Difference between countries just left vs. just right of the tipping point:
    - 12.36 percent after 10 years.
    - 16.85 percent 15 years later.
  - Interpretation: crossing the tax threshold adds about one percent to real annual GDP per capita growth for the next 10 to 15 years.
- Pre-trend assessment
  - No detectable systematic pre-trend for countries around the threshold prior to observation year 0.
  - Joint test of the null that all pre-treatment coefficients are zero: p-value = 0.23.

### Regression discontinuity estimates and robustness (contemporary database; Table 4)
- Table 4: Dependent variable = 10-year cumulative GDP per capita growth; Tax-to-GDP threshold is indicator = 1 if tax level > 12.88 percent of GDP.
- Tax-to-GDP threshold coefficient estimates (standard errors in parentheses)
  - Column (1): 12.355* (6.651)
  - Column (2): 6.864** (3.060)
  - Column (3): 7.450** (3.017)
  - Column (4): 7.283** (3.018)
  - Column (5): 6.852** (3.081)
  - Column (6): 6.963** (3.054)
  - Column (7): 7.717** (2.967)
- Selected control coefficients (standard errors in parentheses)
  - GDP per capita: -3.127*** (0.538); -2.972*** (0.610) [columns where included]
  - Openness: 7.644*** (2.762); 4.388* (2.474)
  - Capital per capita: 2.395 (18.400); -13.893 (16.755)
  - Human capital index: -4.754 (4.170); 0.718 (4.786)
- Fixed effects and fit
  - Country and year FE: No in column (1); Yes in columns (2)–(7)
  - Observations: 3189 (all columns)
  - R-squared, overall:
    - Column (1): 0.023
    - Column (2): 0.691
    - Column (3): 0.739
    - Column (4): 0.701
    - Column (5): 0.691
    - Column (6): 0.692
    - Column (7): 0.742
  - R-squared, within:
    - Column (1): (not applicable)
    - Column (2): 0.132
    - Column (3): 0.266
    - Column (4): 0.159
    - Column (5): 0.132
    - Column (6): 0.135
    - Column (7): 0.275
- Robustness summary
  - Adding country and year fixed effects reduces the estimated impact (e.g., from 12.36 percent to 6.86 percent).
  - Preferred specification (column (3)) including initial real GDP per capita yields a threshold effect of 7.45 percent.
  - Estimates remain broadly similar across specifications and after adding controls, except for degree of openness and human capital in some columns.

### Treatment of social security contributions
- Definition choice
  - Main analysis excludes social security contributions from tax revenue, following the IMF’s 2014 Government Finance Statistics Manual.
  - Rationale: social security contributions are associated with expected future benefits and do not change the net asset position of the government in the same way as taxes.
- Comparisons and sensitivity
  - Including social security contributions yields consistently lower estimates for the tipping point and more variation across horizons.
  - At the 10-year horizon, social security–inclusive series yield a tipping point at 12.0 percent of GDP.
  - For countries with tax levels around 12.88 percent of GDP, social security contributions make up around 10 percent of tax revenues.
  - Using social security–inclusive taxes and a tipping point of 12.0 percent: the effect on subsequent growth is negligible and statistically insignificant.
  - When defining the tipping point for inclusive series as contemporary estimate 12.88 percent plus the level of social security contributions, the main estimate of the effect on subsequent GDP growth is recovered.
- Conclusion: adding social security contributions does not provide additional information on the location and effect of tax tipping points.

### Historical database results (International Historical Statistics)
- Estimated threshold (Table 5)
  - Tax-to-GDP threshold (dependent variable: GDP per capita cumulative growth):
    - 3-year: 12.65
    - 5-year: 12.65
    - 7-year: 12.65
    - 10-year: 12.65
  - Confidence intervals ("No-rejection region")
    - 95%:
      - 3-year: [12.51; 12.81]
      - 5-year: [11.37; 12.85]
      - 7-year: [12.25; 12.84]
      - 10-year: [12.24; 12.82]
    - 99%:
      - 3-year: [11.24; 12.94]
      - 5-year: [11.28; 14.07]
      - 7-year: [12.17; 13.72]
      - 10-year: [12.17; 12.85]
- Graphical and dynamic findings
  - Figure 14 (10-year cumulative growth): sharp increase in average cumulative GDP per capita growth rates just above 12.65 percent.
  - Figure 15 (impact over time): after 10 years the cumulative effect on real GDP per capita growth is around 16 percent; after 15 years estimated long-run effect is around 25 percent higher cumulative growth for countries immediately to the right of the threshold compared to immediately to the left.
  - 90 percent confidence bands are large and include the 16.85 percent value found in the contemporary database.
- Regression estimates and robustness (Table 6)
  - Dependent variable: 10-year cumulative GDP per capita growth; observations = 1593.
  - Tax-to-GDP indicator coefficients (standard errors in parentheses):
    - Column (1): 15.957** (7.189) — no country or year FE
    - Column (2): 5.440 (6.515) — with country and year FE
    - Column (3): 2.535 (5.714) — with country and year FE and GDP per capita
  - GDP per capita coefficient (column (3)): -14.139*** (2.847)
  - R-squared, overall:
    - Column (1): 0.084
    - Column (2): 0.655
    - Column (3): 0.655
  - R-squared, within:
    - Column (2): 0.436
    - Column (3): 0.585
  - Robustness summary:
    - Including country and year fixed effects reduces the estimated effect substantially (e.g., from 15.957** to 5.440) and renders it not statistically different from zero in column (2).
    - Adding initial GDP per capita further reduces the point estimate to around 2.535 and not statistically significant.
    - Historical panel is highly unbalanced, reducing precision when year fixed effects are included.

*Italic: Source: content unit _wp16234 - 2.65 percentage points wide. The confidence intervals are somewhat wider for shorter time horizons.*

### 12.65 percent of GDP. GDP per capita taken from the Maddison project expressed in

### _wp16234 - 12.65 percent of GDP. GDP per capita taken from the Maddison project expressed in

### Major findings
- Using a contemporary dataset covering 139 countries from 1965 to 2011, the estimated tax-to-GDP tipping point from the first-step procedure is around 12.88 percent.
- According to the preferred specification in the contemporary sample, a country just above the 12.88 percent threshold will have real GDP per capita around 7.5 percent larger, after 10 years, than an otherwise similar country just below it.
- Using a historical database for 30 advanced economies (up to 1800–1980), the estimated threshold is 12.65 percent of GDP, very close to the contemporary estimate of 12.88 percent.
- The coincidence of thresholds in both databases suggests a common threshold in tax-to-GDP level that may be an invariant feature in the process of development.
- The tipping point effects on subsequent growth in the historical sample are economically relevant but not statistically significant once time and country fixed effects are introduced.

### Methodology
- Two databases used: a novel contemporary database (139 countries, 1965–2011) and a historical database (30 advanced economies, up to 1800–1980).
- Empirical approach draws on CMR and follows a two-step approach:
  - Step 1: find the tipping point and document its statistical significance.
  - Step 2: take the threshold value as if it were known and estimate the impact of crossing the tipping point on growth.
- Coefficients from a fourth-order polynomial in tax-to-GDP with intercept shift at the estimated tax-to-GDP threshold; year and country fixed effects included in preferred specifications (not shown). Standard errors clustered at the country level.
- Robustness checks include alternative specifications and historical sample validation; smaller historical sample size limits full statistical definitiveness.

### Estimated thresholds and impacts
- Contemporary dataset tipping point: 12.88 percent (tax-to-GDP).
- Historical database tipping point: 12.65 percent (tax-to-GDP).
- Estimated impact (preferred contemporary specification): real GDP per capita ~7.5 percent larger after 10 years for a country just above versus just below the 12.88 percent threshold.
- Recommendation interpretation: reasonable to assume a tax-to-GDP tipping point at about 12 ¾ percent of GDP.
- Policy-oriented guidance: findings align with the standard recommendation for countries with low tax-to-GDP levels to aim for levels about 15 percent.

### Robustness and caveats
- Robustness checks using historical data are not fully definitive due to smaller sample size.
- The tipping point in the historical sample is tightly estimated but the threshold impact on subsequent growth loses statistical significance when including time and country fixed effects.
- Tax-to-GDP ratios are volatile; interpretation should account for volatility and context-specific factors such as social norms and state capacity.

### Policy implications and interpretation
- The estimated threshold is likely associated with changes in social norms of behavior and state capacity.
- For low revenue countries, aiming for tax-to-GDP levels around 15 percent is consistent with the evidence and standard recommendations, given the identified tipping point near 12 ¾ percent.
- Strengthening tax capacity up to and beyond the threshold may support sustained increases in real GDP per capita over several years.

### Key statistics and numbers (preserved exactly)
- Contemporary dataset: 139 countries from 1965 to 2011.
- Contemporary tipping point: 12.88 percent (tax-to-GDP).
- Historical database: 30 advanced economies from 1800 to 1980.
- Historical tipping point: 12.65 percent (tax-to-GDP).
- Preferred specification growth effect: 7.5 percent larger real GDP per capita after 10 years for a country just above the threshold.
- Recommended target for low tax-to-GDP countries: about 15 percent.
- Significance markers in regressions: * means p<10%, ** p<5%, *** p<1%.
- Polynomial used: fourth-order polynomial in tax-to-GDP with intercept shift at the estimated tax-to-GDP threshold.
- Clustering: Standard errors clustered at the country level.
- Appendix figures use a local linear regression fit separately on either side of 12.88 using an Epanechnikov kernel and a bandwidth of 1.5; a global fourth-order polynomial is also shown.
- Table A1 threshold used: 12.88 percent tax-to-GDP for tipping-point crossings.
- Table A3 threshold used: 12.65 percent revenue-to-GDP for tipping-point crossings.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16234.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16234.pdf_