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---

### I. Introduction — core questions and approach
- Research question: Can simply exceeding a critical tax-to-GDP threshold bring about an accelerated trajectory of economic growth and development in a country?
- Methodological advances:
  - Re-estimate tax threshold using regression discontinuity (Card, Mas and Rothstein, 2008 approach as used by Gaspar, Jaramillo and Wingender (2016b) — GJW).
  - Conduct event studies leveraging Callaway and Sant’Anna (2021) difference-in-differences advances to exploit within-country variation and interpret crossing the threshold as a treatment.
  - Construct a richer dataset (WoRLD-based) and collect additional institutional development indicators (financial development, government effectiveness, governance, legal institutions) and macro-fiscal variables (government expenditure, investment, debt).
- Sample and period:
  - 150 non-natural-resource-rich countries.
  - Time coverage from 1965 to 2019.

### II. Main empirical findings
- Existence and magnitude of a tax tipping point:
  - Re-estimated tax–to-GDP tipping point at 10 percent (grid-search peaks roughly at 10 percent across 3, 5, 7, and 10-year horizons; 10-year estimate reported as 10.35 percent).
  - This estimate is almost three percentage points below GJW’s estimate, attributed to upward revisions in nominal GDP series since GJW leading to downward shifts in tax ratios.
  - Cumulative GDP growth over 10 years increases by around 10 percentage points when the tax-to-GDP ratio is raised above 10 percent.
- Magnitude of annual growth effects:
  - Crossing the tax-to-GDP threshold lifts annual growth by about 1 percentage point a year over a decade on average.
  - Episodes with sustainable increases above the threshold show growth acceleration reaching 2 percentage points a year.
  - Comparison: the 2 percentage point sustained acceleration is comparable to previously documented dramatic surges (up to 2.5 points annually for eight years).
- Channels and co-movements:
  - Total investment and government expenditure rise when the tax ratio crosses the threshold.
  - Parallel improvements observed in financial development and government effectiveness when tax increases are sustained.
  - Government expenditure increases by 2 percent of GDP for at least a decade following durable crossings.
  - Investment shows a significant increase of 1 percent of GDP the year after crossing, with noisy further increases to 2 percent of GDP in subsequent years.
- Heterogeneity:
  - Growth benefits accrue mainly to countries that raise their tax-to-GDP ratio sustainably and well above the threshold and where increases are associated with improvements in financial development and government effectiveness.
  - Countries that revert below the threshold experience short-lived and statistically insignificant increases in economic growth, and do not show institutional improvements.

### III. Data: tax series, construction choices, and dataset coverage
- Preferred measure:
  - Tax-to-GDP excluding social security contributions (SSCs), consistent with IMF Government Finance Statistics Manual 2014.
  - Where available, use general government level measures rather than central government only.
- Source datasets combined (preference order and coverage):
  - 1. WoRLD — IMF surveillance — 1980-2022 — 193 countries — 5,392 observations.
  - 2. OECD — Member submissions — 1965-2022 — 36 countries — 1,719 observations.
  - 3. WEO — IMF surveillance — 1962-2023 — 196 countries — 5,408 observations.
  - 4. GRD — Various secondary sources — 1980-2022 — 193 countries — 6,650 observations.
  - 5. GFS 1986 — IMF surveillance — 1970-2002 — 157 countries — 2,967 observations.
- Constructed series composition (selected figures):
  - Overall: 150 countries, 6,273 observations, WoRLD (%) = 61.0, Spliced (%) = 37.4, Interpolated (%) = 0.4.
  - 1965-1975: 75 countries, 391 observations, WoRLD (%) = 0.0, Spliced (%) = 97.4, Interpolated (%) = 0.3.
  - 2005-2015: 150 countries, 1,500 observations, WoRLD (%) = 96.5, Spliced (%) = 2.1, Interpolated (%) = 0.0.
  - 2015-2019: 150 countries, 750 observations, WoRLD (%) = 98.7, Spliced (%) = 0.0, Interpolated (%) = 0.0.
- Sample exclusions:
  - Drop countries identified as resource-rich in WoRLD or with natural resource rents exceeding 30 percent of GDP on average.
  - Zimbabwe dropped due to hyperinflation.
- Correlations and revisions:
  - Pairwise correlation coefficients of constructed series with underlying datasets at least 0.98 except GFS 1986.
  - Correlation with GJW series is 0.96 overall; 0.95 among spliced observations.
  - New tax-to-GDP ratios are on average substantially lower than in GJW due primarily to upward revisions to historical nominal GDP.
- Stylized facts:
  - Distribution of tax-to-GDP in constructed series: median = 16 percent; 25th percentile = 10.6 percent; 75th percentile = 22.1 percent.
  - Distribution of annual per capita real GDP growth: median = 2.4 percent; mean = 2.2 percent.
  - Average tax-to-GDP increased slowly over time: since 1980 average increased from around 15 percent to nearly 19 percent.
  - Cross-sectional association: a 10-percentage point increase in the tax-to-GDP ratio is associated with more than a doubling of real income per capita (using most recent observation per country).

### IV. Empirical approach, event study design, and robustness
- Regression discontinuity search:
  - Two-step procedure: (1) grid search for tipping point γ maximizing R-squared of parsimonious model; (2) estimate growth effect including f(tax − γ) and covariates.
  - Grid search over tax-to-GDP values between 5 and 30 percent; drop observations with tax-to-GDP below 5 percent or above 40 percent.
  - Statistical testing follows Hansen (1999); bootstrap of individual test statistics 1,000 times used for critical values and p-values.
- Estimated tipping points (Table 4):
  - 3-year 9.87
  - 5-year 9.85
  - 7-year 10.12
  - 10-year 10.35
  - 95% no-rejection regions reported for each horizon (e.g., 10-year [9.94; 10.56]).
  - p-values = 0.00 for all horizons; F1 Statistics: 3-year 69.23, 5-year 82.09, 7-year 84.97, 10-year 77.58.
- Event study design:
  - Baseline threshold used for event study: 10.35 percent (10-year horizon).
  - Dynamic DiD with Callaway and Sant’Anna (2021) estimator; coefficients βk capture effects from 11 years before to 15 years after crossing; normalization β−1 = 0.
  - Exclude 82 countries that are above the threshold throughout the estimation period; control group uses 2,901 observations from always-below and not-yet-treated countries.
  - Robust and asymptotic standard errors estimated using Influence Functions; alternative standard errors via multiplicative WildBootstrap used in robustness checks.
- Event study key robustness and sensitivity checks:
  - Trimmed sample excluding anomalous pre- or post-crossing years reduces sample from 2,901 to 2,710 observations; results broadly unchanged.
  - Placebo thresholds (0.5 increments around 10.35) show no other threshold with statistically significant growth impact.
  - Polynomial order sensitivity: alternative polynomials reported; more parsimonious polynomials yield larger point estimates; fourth-order polynomial chosen for main results.
  - Local linear regression bandwidth 1.72 yields a local linear point estimate example of 7.5 percent (compared with 10.7 percent when fourth-order polynomial is used).
  - Causal Random Forest and bootstrap confirm detectable inflection points in 10–15 percent range though less precise.

### V. Event study empirical results and dynamics around first crossing
- Regression-discontinuity coefficients on Tax-to-GDP threshold (10.35 percent) for 10-year growth (Columns 1–7): 0.107*, 0.113**, 0.103**, 0.104**, 0.103**, 0.075, 0.074.
  - Associated standard errors sequence: 0.0559 0.0522 0.0504 0.0506 0.0503 0.0484 0.0494.
  - Observations by specification: 4,470; 4,470; 4,470; 4,470; 4,447; 3,926; 3,903.
  - R-squared sequence: 0.04, 0.1, 0.107, 0.109, 0.103, 0.15, 0.157.
- Tax-ratio dynamics around crossing (43-country continuous 7-year window):
  - Three years prior Mean 8.01; Two years prior Mean 8.49; One year prior Mean 9.35; Threshold year Mean 11.16; One year after Mean 11.43; Two years after Mean 10.96; Three years after Mean 11.02.
  - Median change in tax ratio around crossing is 2 percentage points; average change from 8 percent to 11 percent over three years.
  - About one quarter (about ten countries among the 43) fall back below the threshold in the year after crossing.
- GDP dynamics:
  - No significant pre-trends in log GDP per capita prior to crossing.
  - Significant increase in GDP per capita from one to eleven years after crossing; implied added 10 percentage points growth per decade consistent with RDD.
  - Beyond eleven years estimates become imprecise though effects often continue to grow.
- Institutional and governance dynamics:
  - Financial development accelerates when tax ratio rises above the threshold; magnitude after ten years: almost 10 percent of the standard deviation of the index.
  - Government effectiveness shows significant continuous improvement after crossing; magnitude after ten years equal to 30 percent of the standard deviation of the indicator.
  - Legal structures and property rights improve slowly, with significant acceleration only after ten years (magnitude after ten years equal to 15 percent of the standard deviation).
  - Governance/corruption measures show absence of pre-trends and continuous decline in corruption after crossing, but improvements often insignificant; Bayesian Corruption Index improvement after ten years equals 5 percent of its standard deviation.
- Macroeconomic and fiscal impacts:
  - Government expenditure increases by 2 percent of GDP for at least a decade.
  - No significant change in the primary balance.
  - No significant change in the debt-to-GDP ratio.
  - Public investment shows a large and sustainable increase in the first four years following a sustained crossing, peaking at almost 2 percent of GDP (sample average public investment = 4.6 percent).

### VI. Heterogeneity: short-lived versus sustained crossings
- Sample split of 43 countries (7-year window):
  - Short-lived crossings: 21 countries, tax ratios above threshold less than 75% of the time in the 15 years after crossing.
  - Sustained crossings: 22 countries, tax ratios above threshold more than 75% of the time in the 15 years after crossing.
- Summary contrasts (selected means):
  - Threshold crossing year Mean: short-lived 10.98 (SD 0.85); sustained 11.33 (SD 1.18).
  - One year after Mean: short-lived 11.02 (SD 2.48); sustained 11.81 (SD 0.85).
  - Three years after Mean: short-lived 10.08 (SD 1.25); sustained 11.92 (SD 1.38).
- Outcomes by sub-sample:
  - Short-lived crossings:
    - Tax ratios return to initial levels within a few years.
    - GDP per capita initially increases slightly but insignificantly and remains mostly unchanged over 15 years.
    - No improvement in financial development or government effectiveness.
    - No significant change in public investment.
  - Sustained crossings:
    - Tax ratios increase steadily beyond initial rise, by up to 5 percent of GDP after 12 years.
    - GDP per capita increases continuously and significantly, with annual growth higher by almost 2 percentage points for 10 years compared with control group.
    - Significant improvements in financial development and government effectiveness.
    - Public investment increases substantially in the first four years, peaking near 2 percent of GDP.

### VII. Theoretical interpretation — simple dynamic model
- Core model elements:
  - Fiscal capacity captured by tax-to-GDP ratio s.
  - Institutional capacity bundled in stock variable z.
  - Production per capita f(z), institutional capacity law of motion: ż = s * f(z) * (1 − g) − δz * z + εz.
  - Tax ratio law of motion: ṡ = h(z) − δs * s + εs.
- Dynamics and equilibria:
  - Phase diagram yields two stable equilibria: low-s/low-z/low-production and high-s/high-z/high-production, separated by an unstable saddle path (tipping point).
  - Large enough combined shocks to s and z can move a country from low to high equilibrium; small or imbalanced shocks revert to the low equilibrium.
- Implication:
  - Durable transitions require either a sufficiently large tax increase or tax increases coupled with institutional improvements to cross the saddle path.

### VIII. Robustness checks and alternative methods
- Continuity in density test around tipping point:
  - Non-randomized approximate sign test (Bugni and Canay, 2020): cannot reject continuity (p-value 0.22).
- Causal Random Forest bootstrap results (Table A6):
  - Horizon 3: Tipping point 13.3, CI Lower 7.3, CI Upper 18.6.
  - Horizon 5: Tipping point 14.3, CI Lower 7.3, CI Upper 19.0.
  - Horizon 7: Tipping point 14.6, CI Lower 7.4, CI Upper 18.3.
  - Horizon 10: Tipping point 13.8, CI Lower 6.9, CI Upper 18.9.
- Polynomial and threshold sensitivity:
  - Regression discontinuity with alternative polynomial orders yields coefficients (first-row examples) 0.132**, 0.127**, 0.107*, 0.091*, 0.075, 0.078, 0.075 with corresponding standard errors 0.054, 0.059, 0.056, 0.055, 0.056, 0.058, 0.059.
  - Alternative threshold deviations produce varied coefficients (Table A5) and confirm main result centered on the 10.35 percent threshold.

### IX. Conclusions and policy-relevant implications
- Empirical conclusions:
  - A robust tax tipping point around 10 percent of GDP is identified (event study benchmark 10.35 percent).
  - Durable crossings of the tax threshold are associated with an increase in per capita GDP of about 20 percentage points over a dozen years in sustained episodes; in the full sample durable crossings drive average growth gains of about 10 percentage points over 10 years.
  - Short-lived crossings do not deliver growth benefits or institutional improvements.
  - Durable crossings are linked to improvements in financial development, government effectiveness, and public investment.
- Policy implications:
  - Revenue mobilization should aim to durably raise tax-to-GDP ratios above the identified tipping region rather than temporary or one-off increases.
  - Tax increases should be accompanied by institutional reforms and investments in public goods to sustain transitions to higher-growth equilibria.
  - Recognize that optimal tax levels depend on national circumstances; the tipping-point evidence indicates a minimum threshold for possible accelerated growth rather than a universal prescription.

*International Monetary Fund — State Capacity, Growth and Institutions: Taxing for Takeoff — Working Paper No. WP/2025/203 (excerpts from the provided PDF).*

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

### wpiea2025203-source-pdf - References .............................................................................................................

### I. Introduction — core questions and approach
- Research question: Can simply exceeding a critical tax-to-GDP threshold bring about an accelerated trajectory of economic growth and development in a country?
- Methodological advances:
  - Re-estimate tax threshold using regression discontinuity (Card, Mas and Rothstein, 2008 approach as used by Gaspar, Jaramillo and Wingender (2016b) — GJW).
  - Conduct event studies leveraging Callaway and Sant’Anna (2021) difference-in-differences advances to exploit within-country variation and interpret crossing the threshold as a treatment.
  - Construct a richer dataset (WoRLD-based) and collect additional institutional development indicators (financial development, government effectiveness, governance, legal institutions) and macro-fiscal variables (government expenditure, investment, debt).
- Sample and period highlighted in the Introduction:
  - 150 non-natural-resource-rich countries.
  - Time coverage from 1965 to 2019 (dataset leverages WoRLD to construct tax-to-GDP ratios for more countries and over a longer period).

### II. Main empirical findings
- Existence and magnitude of a tax tipping point:
  - Re-estimated tax–to-GDP tipping point at 10 percent.
  - This estimate is almost three percentage points below GJW’s estimate, attributed to upward revisions in nominal GDP series since GJW leading to downward shifts in tax ratios.
  - Cumulative GDP growth over 10 years increases by around 10 percentage points when the tax-to-GDP ratio is raised above 10 percent.
  - Event studies show growth trends are not statistically different between countries about to cross the estimated tax threshold and those that stay below, strengthening causal interpretation.
- Heterogeneity and requirements for sustained growth gains:
  - Growth benefits accrue mainly to countries that raise their tax-to-GDP ratio sustainably and well above the threshold and where increases are associated with improvements in financial development and government effectiveness.
  - On average, countries crossing the tipping point experience sizeable increases in tax ratios; for durable cases tax-to-GDP continues to increase steadily above the threshold, by five percentage points after a dozen years.
  - Countries that revert below the threshold experience short-lived and statistically insignificant increases in economic growth, and do not show improvements in financial development and government effectiveness.
- Magnitude of annual growth effects:
  - Crossing the tax-to-GDP threshold lifts annual growth by about 1 percentage point a year over a decade on average.
  - Focusing on episodes with sustainable increases above the threshold, the growth acceleration reaches 2 percentage points.
  - Comparison: this 2 percentage point sustained acceleration is comparable to dramatic surges documented elsewhere (up to 2.5 points annually for eight years).
- Associated channels and co-movements:
  - Investment and public goods are important channels: total investment and government expenditure rise when the tax ratio crosses the threshold, alongside growing tax revenues.
  - Parallel improvements are observed in financial development and government effectiveness when the tax ratio increases sustainably.
- Theoretical interpretation:
  - A poverty trap model with complementarity between taxation and institutional capacity rationalizes empirical findings.
  - Model produces two stable equilibria: low tax-to-GDP/low institutional capacity/low production and a high-tax/high-capacity/high-production equilibrium with a tipping point between them.
  - Large enough jumps in tax ratio (and concomitant institutional improvements) can move a country from the low to the high equilibrium; smaller or non-accompanied jumps revert to the low equilibrium.

### III. Data: tax series, construction choices, and dataset coverage
- Preferred measure:
  - Tax-to-GDP excluding social security contributions (SSCs), consistent with IMF Government Finance Statistics Manual 2014.
  - Where available, use general government level measures rather than central government only.
  - SSCs are manually excluded from total tax revenues when necessary (SSCs are counted in total tax revenues in OECD data).
- Datasets combined to create historical tax-to-GDP series (Table 1 overview):
  - 1. WoRLD — IMF surveillance — 1980-2022 — 193 — 5392
  - 2. OECD — Member submissions — 1965-2022 — 36 — 1719
  - 3. WEO — IMF surveillance — 1962-2023 — 196 — 5408
  - 4. GRD — Various secondary sources — 1980-2022 — 193 — 6650
- Dataset construction notes:
  - The new dataset leverages WoRLD, allowing tax-to-GDP ratios for 150 non-natural-resource-rich countries and extended temporal coverage.
  - Revisions in nominal GDP (denominator) since prior work (GJW) explain some downward shifts in tax ratios and the lower re-estimated tipping point.

### IV. Additional empirical and robustness elements (overview)
- Methods and robustness:
  - Re-estimation of tipping point using regression discontinuity in the spirit of GJW.
  - Event studies exploiting quasi-experimental threshold discontinuity with Callaway and Sant’Anna (2021) methods to capture within-country dynamics.
  - Robustness checks documented include grid searches for tipping point candidates, bootstrap point estimates and confidence intervals, trimmed-sample event studies, and alternative polynomials and threshold values in regression discontinuity estimations (figures and tables referenced in the Appendix).
- Empirical patterns documented around threshold crossings:
  - Institutional development indicators (financial development, government effectiveness, legal framework, governance) rise in parallel with revenue mobilization in transformational episodes.
  - No pre-trends in institutional indicators prior to revenue mobilization, consistent with a development trap below the tipping point.

*International Monetary Fund — State Capacity, Growth and Institutions: Taxing for Takeoff — References and Appendix material summarized from the provided PDF content.*

### 5. GFS 1986IMF surveillance 1970-2002 157 2967

### 5. GFS 1986IMF surveillance 1970-2002 157 2967

### Data construction and sources
- Five source datasets combined and spliced to construct a single tax-to-GDP series, preference order: (1) WoRLD; (2) OECD; (3) WEO; (4) GRD; (5) GFS 1986.
- Splicing method: when combining overlapping series, use observed growth rates to cast backwards or forwards tax revenue from the preferred data source.
- For data gaps less than five years, linear interpolation is used in select cases.
- Ad-hoc revisions applied in anomalous cases (e.g., abrupt unexplained tax revenue changes), including changing the preferred underlying data series.
- WoRLD noted as the complete successor to Mansour (2014, 2015) used in GJW.
- All code for dataset construction will be made available upon request.

### Sample exclusions and coverage
- Countries with significant natural resource rents excluded: drop countries identified as resource-rich in WoRLD or with natural resource rents exceeding 30 percent of GDP (as measured in the World Development Indicators) on average.
- Zimbabwe also dropped due to hyperinflation distorting macro aggregates.
- Constructed tax-to-GDP series covers 150 countries over the period 1965-2019.
- The panel is unbalanced, with an average of just under 42 observations per country.

### Constructed series composition (Table 2 summary)
- Overall: 150 countries, 6,273 observations, WoRLD (%) = 61.0, Spliced (%) = 37.4, Interpolated (%) = 0.4.
- 1965-1975: 75 countries, 391 observations, WoRLD (%) = 0.0, Spliced (%) = 97.4, Interpolated (%) = 0.3.
- 1975-1985: 108 countries, 927 observations, WoRLD (%) = 8.2, Spliced (%) = 90.7, Interpolated (%) = 1.3.
- 1985-1995: 142 countries, 1,230 observations, WoRLD (%) = 33.7, Spliced (%) = 64.6, Interpolated (%) = 0.8.
- 1995-2005: 150 countries, 1,475 observations, WoRLD (%) = 77.8, Spliced (%) = 20.3, Interpolated (%) = 0.2.
- 2005-2015: 150 countries, 1,500 observations, WoRLD (%) = 96.5, Spliced (%) = 2.1, Interpolated (%) = 0.0.
- 2015-2019: 150 countries, 750 observations, WoRLD (%) = 98.7, Spliced (%) = 0.0, Interpolated (%) = 0.0.

### Comparison with prior series and GDP revisions
- Constructed series highly correlated with each underlying dataset, pairwise correlation coefficient at least 0.98 with respect to each source dataset except GFS 1986.
- Correlation coefficient with respect to the series of GJW is 0.96.
- Correlation with series of GJW among spliced observations is 0.95.
- Tax-to-GDP ratios in the new data are on average substantially lower than in GJW, primarily due to revisions to historical nominal GDP data (many countries updated national accounting standards/practices, disproportionately upwards revising historical nominal GDP).
- Result: tax-to-GDP figures mechanically revised downwards relative to prior series; gap clearest where GJW tax-to-GDP was in the range of 10 to 18 percent.

### Development indicators and other datasets used
- Real GDP per capita: Penn World Tables (PWT version 10.01), real GDP at constant 2017 national prices in 2017 USD and population; cumulative real GDP growth per capita measured over different horizons.
- Financial Development: Svirydzenka (2016) Financial Development Indexes (FDI-FI, FDI-FM, FDI-FD); covers 149 countries from 1980 to 2019; standardized to mean zero and standard deviation one.
  - Robustness check: standardized “Private credit by deposit money banks to GDP (%)” from World Bank Global Financial Development Database covers all years back to 1965 and all countries.
- Government Effectiveness: World Bank World Governance Indicators (WGI) Government Effectiveness index; normalized to mean zero and standard deviation one; covers all countries in sample from 1996.
  - WGI available in 1996, 1998, 2000 and annually from 2002 onwards; linear interpolation applied for 1997, 1999, and 2001.
- Legal Structure and Rule of Law: Fraser Institute’s index of Legal Structure and Security of Property Rights; aggregates five indicators (range 0-10); chain-linked for consistency; standardized; covers 138 countries from 1970 to 2019.
  - Twelve countries not covered: Antigua and Barbuda, Aruba, Dominica, Grenada, Hong Kong SAR, Macao SAR, Maldives, St. Kitts and Nevis, St. Lucia, St. Vincent and the Grenadines, São Tomé and Príncipe, and Uzbekistan.
- Governance / Corruption: Sherppa Ghent University’s Bayesian Corruption Indicator (BCI) covers 147 countries from 1984 (three missing: Aruba, Hong Kong SAR, Macao SAR); Varieties of Democracy (V-Dem) Public Sector Corruption Index (PSCI) covers 139 countries and spans entire sample; PSCI log-transformed and standardized.
  - V-Dem missing countries: Antigua and Barbuda, Aruba, The Bahamas, Belize, Dominica, Grenada, Hong Kong SAR, Macao SAR, St. Kitts and Nevis, St. Lucia, and St. Vincent and the Grenadines.
- Public finance and investment variables:
  - Government expenditure, primary balance, and gross debt (percent of GDP) from Public Finances in Modern History database.
  - General government and total investment (gross fixed capital formation) from IMF Investment and Capital Stock Dataset (IMF 2021); both in percent of GDP.

### Stylized facts
- Distribution of tax-to-GDP in constructed series: median = 16 percent; 25th percentile = 10.6 percent; 75th percentile = 22.1 percent.
- Distribution of annual per capita real GDP growth: median = 2.4 percent; mean = 2.2 percent (right-panel excludes outliers at approximately the 5th and 95th percentiles).
- Average tax-to-GDP increased slowly over time in the sample: since 1980 (about 100 countries covered), average tax-to-GDP increased from around 15 percent to nearly 19 percent.
- GDP-weighted global tax revenues remained flat over time, implying increases in tax-to-GDP concentrated in smaller economies on average.
- Cross-sectional association: a 10-percentage point increase in the tax-to-GDP ratio is associated with more than a doubling of real income per capita (using the most recent observation per country).
- Higher tax revenues are associated with better outcomes on legal structure and property rights, government effectiveness, financial development, and lower corruption (associations not interpreted as causal in the text).

### Empirical approach — searching for a tax tipping point
- Methodology: regression discontinuity approach of GJW, drawing on Card, Mas and Rothstein (2008); two-step procedure:
  1. Search for a candidate tipping point γ by modeling subsequent cumulative per capita GDP growth as a function of tax-to-GDP allowing a discontinuity at unknown γ. In practice, parsimonious model: ΔGDPPC_{c,t+j} = α + β D_{c,t} + ε_{c,t}, where D_{c,t} ≡ 1(tax_{c,t} > γ).
  2. Taking γ as known from step 1, estimate ΔGDPPC_{c,t+j} = α + β D_{c,t} + f(tax_{c,t} − γ) + X_{c,t} ρ + ε_{c,t}, including covariates and fixed effects.
- Grid search procedure:
  - Search over tax-to-GDP values between 5 and 30 percent.
  - Drop observations with tax-to-GDP below 5 percent or above 40 percent.
  - Select γ̂ that maximizes R-squared of the parsimonious model (Equation (2)).
- Statistical testing: use approach outlined in Hansen (1999) to test for the existence of a tax tipping point, accounting for non-standard properties of γ̂.
- Second-step interpretation:
  - β̂ indicates additional economic growth in countries above the tipping point compared to those just below.
  - Procedure performed for growth horizons of 3, 5, 7 and 10 years.
  - Robustness checks include different covariates, different functional forms for f(.), and placebo tests using arbitrary thresholds above and below estimated tipping point.
- Identification and interpretation notes:
  - The rule determining “treatment” (tipping point) is data-determined in the first step.
  - Tax-to-GDP is endogenous with respect to GDP, but focusing on local effects (small changes around threshold) reduces endogeneity concerns.
  - Causal interpretation hinges on comparability of observations on either side of the estimated threshold and on treatment being determined by exogenous variation in realized tax revenues.
  - Dynamic event-study approaches are used to control for country-specific growth trajectories and to ensure pre-trend differences do not drive results.

*IMF Working Papers — State Capacity, Growth and Institutions: Taxing for Takeoff (authors’ construction).*

### 2. Event Study

### 2. Event Study

### Event study design and purpose
- Complementary to the two-step procedure: uses an event study approach to study dynamics of countries that cross the estimated tax threshold.
- Focuses on the threshold of 10.35 percent estimated for the 10-year growth horizon.
- Takes the existence of a tax tipping point as given and examines dynamics of outcomes around the year a country raises its tax-to-GDP ratio above the threshold.

### Estimation framework
- Implemented using a dynamic Difference-in-Differences (DiD) model. Outcomes 풚
풄풕 include log GDP per capita, the tax ratio, and various development indexes.
- Main estimating equation (notation preserved):
  - 푦
푐,푡
= 훼
푐
+ 훿
푡
+ ∑훽
푘
ퟏ{푡
푐푟표푠푠푖푛푔,푐
+푘=푡}
15
푘=−11
+ 휖
푐,푡
- 훼
푐
: country fixed effect; 훿
푡
: year fixed effect.
- Indicator 1{푡
푐푟표푠푠푖푛푔,푐
+푘=푡} equals 1 for the year that is 푘 years after country c crosses the tax-ratio threshold when 푘>0, or |−푘| years before crossing when 푘<0.
- Coefficients 휷
풌
 capture dynamic impacts for 11 years preceding crossing (k negative), the year of crossing (k=0), and 15 years following (k positive). Normalization imposed: 훽
−1
= 0.
- Robust and asymptotic standard errors estimated using Influence Functions.

### Estimator choice and justification
- All 휷
풌
 coefficients estimated using Callaway and Sant’Anna (2021) estimator.
- Motivation: traditional two-way fixed effects (TWFE) can perform poorly with multiple time periods and variation in treatment timing because TWFE mixes “clean” comparisons and “forbidden” comparisons, which can produce negative weighting and misleading aggregate estimates when treatment effects are heterogeneous.
- Callaway and Sant’Anna (2021) approach:
  - (i) Estimates “clean” comparisons between countries treated from 푡
푐푟표푠푠푖푛푔,푐
 to 푡
푐푟표푠푠푖푛푔,푐
+푘 and countries not yet treated over that same period.
  - (ii) Uses appropriate weights to aggregate these comparisons across 푡
푐푟표푠푠푖푛푔
 into estimators of treatment effects by length of exposure ( 훽
̂
푘
).

### Treatment definition, sample construction, and complications
- Treatment defined as first observed crossing of the tax-to-GDP threshold from below (“first crossing”): country considered “treated” in the first year its tax ratio increases to exceed the threshold and in all subsequent years.
- Exclude 82 countries that are above the tax ratio threshold throughout the estimation period when applying Callaway and Sant’Anna (2021) estimator.
- Control group uses 2,901 observations from countries that are always below the threshold (never treated) and from not-yet-treated countries.
- Some countries exit treatment (tax ratio declines below threshold). Overall trend: share of countries above the threshold increases over time. Only two countries above the threshold at the beginning of the sample end up below the threshold (Central African Republic and Sudan).
- Many countries that start below and end above experience more than one threshold crossing as tax ratios fluctuate before ending above.

### Robustness / trimmed sample
- Trimmed sample excludes initial and final years corresponding to a decline in the tax ratio below the threshold:
  - For countries that start above, fall below, and rise above: exclude all observations before the first year the tax ratio is below the threshold (88 observations).
  - For countries that rise above but end up below: exclude all observations after the last year the tax ratio is above the threshold (97 observations).
- Purpose: reduce number of observations with taxes below threshold in treated groups and taxes above threshold in control group.
- Result: event study on trimmed sample performed on 2,710 observations (down from 2,901 observations corresponding to countries below the threshold at least once).

### Empirical results: Identifying a tax tipping point
- Grid search over threshold values up to 30 percent of GDP estimated Equation (1) for multiple growth horizons (3, 5, 7, and 10 years).
- All four time horizons show quantitatively and qualitatively similar patterns with a clear peak in R-squared at roughly 10 percent of GDP.

Key statistics from statistical tests and threshold estimates:
- Table 3. Tests for Statistical Significance of Tax Tipping Point (p-values and F1 Statistic)
  - p-value: 3-year 0.00, 5-year 0.00, 7-year 0.00, 10-year 0.00
  - F1 Statistic: 3-year 69.23, 5-year 82.09, 7-year 84.97, 10-year 77.58
  - Critical values:
    - 0.10 level: 3-year 2.79, 5-year 2.61, 7-year 2.91, 10-year 3.01
    - 0.05 level: 3-year 3.95, 5-year 3.73, 7-year 3.88, 10-year 4.23
    - 0.01 level: 3-year 6.62, 5-year 6.24, 7-year 8.04, 10-year 7.23
  - Note: Critical values and p-values obtained by bootstrapping individual test statistics 1000 times.

- Table 4. Estimated Tax Tipping Points (Cumulative GDP per-capita growth)
  - Tax-to-GDP threshold estimates:
    - 3-year 9.87
    - 5-year 9.85
    - 7-year 10.12
    - 10-year 10.35
  - Confidence intervals (no-rejection regions):
    - 95%:
      - 3-year [9.50; 10.56]
      - 5-year [9.70; 10.26]
      - 7-year [9.78; 10.55]
      - 10-year [9.94; 10.56]
    - 99%:
      - 3-year [9.26; 10.68]
      - 5-year [9.47; 10.56]
      - 7-year [9.45; 10.56]
      - 10-year [9.78; 10.68]
  - Note: Confidence intervals obtained by the “no-rejection region” method.

- Statistical significance: Estimated tax tipping point thresholds are highly statistically significant across all four growth horizons (p-values = 0.00).

### Comparison with prior work and robustness checks
- Estimated threshold values are considerably below those found in GJW (range 12.4-12.9 percent).
- Restricting the new dataset to be comparable with GJW yields similar grid search results with threshold value estimated to fall within the range of 10.2 to 10.6 percent.
- Conjecture: significant revisions to historical tax-to-GDP data explain the downward shift in estimated thresholds; downward revisions are most common and uniformly downwards for countries with lower tax-to-GDP ratios.
- Alternative method: Causal Random Forest machine learning approach used to look for a structural break in the relationship between growth and tax-to-GDP ratio.
  - Bootstrapping produces a distribution of tax tipping point estimates.
  - Results confirm a tipping point at about the same level, though estimates from this approach are less precise and primarily distributed in a range of 10 to 15 percent of GDP.

*IMF Working Papers — State Capacity, Growth and Institutions: Taxing for Takeoff*

### 10.7 percent when the fourth order polynomial function is used to estimate the global relationship between tax

### Growth Effect from Crossing the Tax Tipping Point (Content Unit)

### Key regression-discontinuity findings on 10-year growth
- Estimated growth effect from crossing the tax-to-GDP threshold (Tax-to-GDP threshold indicator = 1 if tax-to-GDP ratio exceeds 10.35 percent):
  - Column (1)–(7) coefficients on Tax-to-GDP threshold: 0.107*, 0.113**, 0.103**, 0.104**, 0.103**, 0.075, 0.074
  - Associated standard error reported sequence (under Tax-to-GDP threshold row): 0.0559 0.0522 0.0504 0.0506 0.0503 0.0484 0.0494
- Sample and fit statistics:
  - Observations: 4470, 4470, 4470, 4470, 4447, 3926, 3903 (by specification)
  - R-squared: 0.04, 0.1, 0.107, 0.109, 0.103, 0.15, 0.157
- Controls included in regressions: year fixed effects (in most specifications), log(GDP per capita), log(capital per capita), trade openness; human capital index added in some specifications (reduces coefficient sizes slightly and shrinks sample).
- Estimation details:
  - Coefficients come from a fourth-order polynomial in tax-to-GDP fully interacted with the tax-to-GDP threshold and year fixed effects (not shown).
  - Standard errors clustered at the country level.
  - Significance notation: * means p<10%, ** p<5%, *** p<1%.
- Comparison with prior work:
  - Results are in the same range as GJW, who estimated a 12.4 percent gain over 10 years in their basic specification and 7.5 percent in their preferred specification.

### Event study dynamics around first threshold crossing
- Baseline threshold used for event study: 10.35 percent tax-to-GDP (10-year horizon estimate).
- GDP dynamics:
  - No significant pre-trends in log GDP per capita between treated and untreated/not-yet-treated countries prior to crossing the threshold.
  - Significant increase in GDP per capita in the years following crossing, especially from one to eleven years after crossing.
  - Beyond eleven years, estimates become imprecise though estimated effects continue to grow.
  - Estimated implied magnitude: an added 10 percentage points growth rate per decade (consistent with RDD findings).
- Tax-ratio dynamics:
  - Crossing the threshold typically follows a large, abrupt change in tax mobilization.
  - Increase in the tax ratio in the 3-year window around crossing (from year −2 to year 1) is estimated to be almost 3 percentage points.
  - For the next 15 years after crossing, the tax ratio fluctuates around the level reached at crossing without a clear upward trend.

### Descriptive statistics for tax-to-GDP around first crossing (Table 6; 43 countries with continuous 7-year window)
- Summary statistics (Mean, SD, First quantile, Median, Third quantile):
  - Three years prior: Mean 8.01; SD 2.11; First quantile 7.3; Median 8.75; Third quantile 9.47
  - Two years prior: Mean 8.49; SD 1.85; First quantile 8.24; Median 9.24; Third quantile 9.51
  - One year prior: Mean 9.35; SD 0.94; First quantile 9.03; Median 9.68; Third quantile 9.99
  - Threshold crossing year: Mean 11.16; SD 1.04; First quantile 10.57; Median 10.85; Third quantile 11.32
  - One year after: Mean 11.43; SD 1.86; First quantile 10.33; Median 11.08; Third quantile 11.97
  - Two years after: Mean 10.96; SD 1.48; First quantile 9.73; Median 11.09; Third quantile 11.96
  - Three years after: Mean 11.02; SD 1.6; First quantile 9.89; Median 11.17; Third quantile 11.99
- Additional sample notes:
  - Analysis focuses on 43 countries with tax ratios observed continuously from 3 years before to 3 years after first crossing.
  - In the full sample, tax ratios increase to cross the threshold in 62 distinct countries.
  - Median change in tax ratio around crossing is 2 percentage points; average change from 8 percent to 11 percent over three years.
  - About one quarter (about ten countries among the 43) have tax ratios that fall back below the threshold in the year after crossing, indicating some crossings are short-lived.

### Dynamics of other development indicators around crossing
- Institutional and financial indicators generally show:
  - No significant pre-trends prior to crossing the threshold.
  - Improvements that begin around the time the tax ratio exceeds the threshold.
- Government effectiveness:
  - Event study shows absence of pre-trend and significant, continuous improvement after crossing.
  - Magnitude after ten years: equal to 30 percent standard deviation of the indicator.
  - Such 10-year improvements occur in less than 20 percent of available observations.
- Financial development:
  - Accelerates when the tax ratio rises above the threshold; no significant difference in the 11 years prior.
  - Magnitude after ten years: large and statistically significant at almost 10 percent of the standard deviation of the index.
  - Alternative indicator (private credit by deposit money banks to GDP) shows similar and clearer results.
  - Decomposition suggests improvements come mostly from financial institutions rather than financial markets.

### Robustness checks and identification tests
- Continuity in density test around tipping point:
  - Non-randomized approximate sign test (Bugni and Canay, 2020): cannot reject continuity (p-value 0.22).
- Polynomial order sensitivity:
  - Alternative polynomial orders reported in Table A4: more parsimonious polynomials yield larger point estimates; higher order polynomials reduce coefficient sizes.
  - Cannot reject that coefficients under alternative polynomials differ from the fourth-order polynomial used in main results.
- Placebo threshold tests:
  - Placebo regressions varying the threshold in 0.5 increments around 10.35 (Table A5): no other threshold shows statistically significant growth impact.
- Local linear regression bandwidth:
  - Bandwidth selected by common mean squared error minimization: 1.72.
  - Local linear regression point estimate example: 7.5 percent (compared with 10.7 percent when fourth-order polynomial is used to estimate global relationship).
- Event study robustness:
  - Alternative Callaway and Sant’Anna (2021) implementation using always-below-threshold countries as control: fewer observations, wider confidence intervals, results broadly the same and significant at 90 percent level except horizons beyond 5 years for GDP.
  - Standard errors estimated via multiplicative wild bootstrap: narrower confidence intervals.
  - Using lower 3-year horizon threshold estimate of 9.87 percent: results essentially unchanged.
  - Defining treatment as last observed crossing: broadly same results, but absence of pre-trends in log GDP per capita is less clear.
  - Trimmed sample excluding years above threshold before first crossing and below threshold after last crossing: findings almost identical; timing of tax ratio increase appears to begin one year earlier in trimmed sample.

*IMF Working Paper content unit: wpiea2025203-source-pdf — material on the growth, tax-to-GDP tipping point, event studies, and robustness checks as presented in the supplied text.*

### Section II.1 and Table A2 for details. Robust and asymptotic standard errors are estimated using Influence Functions.

### Section II.1 and Table A2: Robust and asymptotic standard errors are estimated using Influence Functions.

### Legal structures, property rights, and governance
- Evidence on legal structures and the security of property rights (Panel c in Figure 9) is mixed; there are no significant differences between countries whose tax ratios will cross the threshold and those in the control group before the threshold crossing.
- Estimates point to some slow improvement prior to the crossing, although insignificant.
- After the tax ratio crosses the threshold:
  - Progress along legal structures and property rights is initially slow and only accelerates significantly after ten years.
  - By then, the magnitude of the added increase is equal to 15 percent of the standard deviation of the indicator.
- Governance measures:
  - Estimated effects on the Bayesian Corruption Index (Panel d in Figure 9) and the alternative Public Sector Corruption Index (Figure A6 panel b) strongly suggest the absence of any pre-trends prior to crossing the threshold.
  - Thereafter, estimates suggest a continuous decline in corruption, but the improvement in governance is often insignificant.
  - The improvement after ten years in the Bayesian Corruption Index is small, equal to 5 percent of the standard deviation of the Bayesian Corruption Index.

### Macroeconomic and fiscal impacts
- Higher government revenue immediately translates into higher spending (Panel e in Figure 9).
- Government expenditure increases by 2 percent of GDP for at least a decade.
- Higher revenue and higher spending broadly offset each other and:
  - No significant change is found in the primary balance.
  - No significant change is found in the debt-to-GDP ratio (Figure A6 panels e and f in the appendix).
- Investment dynamics:
  - Noisy estimates suggest that total investment increases.
  - There is at least a significant increase of 1 percent of GDP the year after crossing the threshold.
  - Further insignificant increases to 2 percent of GDP in the years that follow are observed.

### Heterogeneity: short-lived versus sustained increases in the tax ratio
- Sample split (Table 7): 43 countries with observable tax-to-GDP ratios in a 7-year window around the first threshold crossing are divided into two sub-samples:
  - 21 countries with short-lived crossings: tax ratios are above the threshold less than 75% of the time in the 15 years after crossing.
  - 22 countries with sustained crossings: tax ratios are above the threshold more than 75% of the time in the 15 years after crossing.
- Summary statistics from Table 7 (means and dispersion for the two groups):
  - Three years prior
    - Short-lived crossings: Mean 7.93, SD 2.25, First quantile 4.9, Third quantile 10.05
    - Sustained crossings: Mean 8.08, SD 2.02, First quantile 6.22, Third quantile 9.76
  - Two years prior
    - Short-lived crossings: Mean 8.31, SD 2.22, First quantile 6.67, Third quantile 9.79
    - Sustained crossings: Mean 8.67, SD 1.45, First quantile 6.65, Third quantile 9.85
  - One year prior
    - Short-lived crossings: Mean 9.3, SD 0.94, First quantile 7.97, Third quantile 10.05
    - Sustained crossings: Mean 9.39, SD 0.96, First quantile 7.61, Third quantile 10.08
  - Threshold crossing year
    - Short-lived crossings: Mean 10.98, SD 0.85, First quantile 10.38, Third quantile 11.88
    - Sustained crossings: Mean 11.33, SD 1.18, First quantile 10.63, Third quantile 12.19
  - One year after
    - Short-lived crossings: Mean 11.02, SD 2.48, First quantile 9.45, Third quantile 11.84
    - Sustained crossings: Mean 11.81, SD 0.85, First quantile 10.86, Third quantile 12.92
  - Two years after
    - Short-lived crossings: Mean 10.27, SD 1.58, First quantile 8.89, Third quantile 11.96
    - Sustained crossings: Mean 11.62, SD 1.03, First quantile 10.34, Third quantile 12.78
  - Three years after
    - Short-lived crossings: Mean 10.08, SD 1.25, First quantile 8.58, Third quantile 11.6
    - Sustained crossings: Mean 11.92, SD 1.38, First quantile 10.66, Third quantile 12.85
- Outcomes by sub-sample:
  - Short-lived crossings:
    - Tax ratios return to initial levels within a few years after crossing.
    - GDP per capita initially increases slightly but insignificantly and remains mostly unchanged over 15 years after the crossing.
    - Absence of improvement in financial development and government effectiveness.
    - No significant change in public investment around the crossing.
  - Sustained crossings:
    - Tax ratios increase steadily beyond the initial rise, by up to 5 percent of GDP after 12 years.
    - GDP per capita increases continuously and significantly, with annual growth higher by almost 2 percentage points for 10 years compared with the control group.
    - Significant and substantial improvements in financial development and government effectiveness.
    - Legal framework increases in both sub-samples but only significant a decade after the crossing.
    - Decline in corruption is small and insignificant in both sub-samples.
    - Government investment shows a large and sustainable increase in the first four years following a sustained crossing, with a peak that reaches almost 2 percent of GDP.
      - This is notable relative to the sample average public investment of 4.6 percent.

### Event study estimation and inference
- Graphs (Figure 10) show coefficient estimates from equation (3) with associated 90 percent confidence intervals.
- Coefficients capture effects of having crossed the 10.35 percent tax ratio threshold either −κ years ago for κ<0, or κ years after for κ>0.
- Left-hand side graphs use the sub-sample with tax ratios above the threshold less than 75% of the time in the 15 years after crossing; right-hand side graphs use the sub-sample with tax ratios above the threshold more than 75% of the time in the 15 years after crossing.
- Outcome variables shown include: tax-to-GDP ratio, log GDP per capita, Financial Development Indicator, Government Effectiveness Indicator, Legal Structures and Security of Property Rights, Bayesian Corruption Index, Government Expenditure, and Public Investment.
- Robust and asymptotic standard errors are estimated using Influence Functions (see Section II.1 and Table A2 for details).

### Theoretical interpretation: simple dynamic model
- Model framework:
  - Fiscal capacity is captured by the tax-to-GDP ratio s.
  - Other institutional capacity dimensions are bundled in stock variable z.
  - Production is F(AL,K,Z), homogeneous of degree 1; output per capita is f(z).
  - Institutional capacity law of motion:
    - ż = s * f(z) * (1 − g) − δz * z + εz  (equation (4))
  - Tax ratio law of motion:
    - ṡ = h(z) − δs * s + εs  (equation (5))
- Dynamics:
  - Phase diagram in (z,s) space yields two attractors (stable equilibria A and C) and one unstable saddle path (D).
  - Trajectories:
    - A-to-B-to-C: sufficiently large combined shocks (εz, εs) can move a country onto a path to the high-z high-s equilibrium, with accumulating institutional capacity and increasing output.
    - E-to-A: smaller or imbalanced shocks lead to convergence back to the low-z low-s equilibrium.
- Implications:
  - Successful transitions require either a tax increase sufficiently above the threshold, or a tax increase coupled with improvements in institutional capacity to move above the saddle path.
  - The saddle path is downward sloping: a large positive shock to institutional capacity εz could substitute for a smaller shock to s, but large rapid institutional shocks may be harder to achieve in practice.

### Conclusions and policy-relevant implications
- Empirical findings:
  - A robust tax tipping point of around 10 percent of GDP is identified (the event study references a 10.35 percent threshold).
  - Durable crossings of the tax threshold are associated with an increase in per capita GDP of about 20 percentage points over a dozen years.
  - Short-lived crossings see no subsequent growth benefits; sustained crossings drive an average growth gain of 10 percentage points over 10 years in the full sample of tipping point crossings.
  - Durable crossings are associated with substantial improvements in financial development, government effectiveness, government investment, and legal institutions; gains are concentrated in countries that maintain tax ratios above the tipping point.
- Interpretive reframing:
  - The tax tipping point is best seen as a minimum tax threshold for accelerated growth: a single year above the threshold does not suffice.
  - Large and sustained increases in tax revenues above the tipping point, accompanied by institutional development, are required for accelerated socio-economic growth.
- Policy implications (inferred from the empirical and theoretical results presented):
  - Pursue holistic revenue mobilization that produces tax-to-GDP ratios durably above the tipping point and that is accompanied by institutional reforms.
  - Complement tax increases with investments in public goods and institutional capacity (legal structures, public investment, government effectiveness) to sustain revenue mobilization and enable transitions to higher-growth equilibria.
  - Recognize that optimal tax levels depend on national economic conditions and citizens’ preferences; the paper does not prescribe a single optimal level.

*IMF WORKING PAPERS — Section II.1 and Table A2 (Robust and asymptotic standard errors estimated using Influence Functions).*

### References

### References

### Core literature on tax policy, growth, and state capacity
- Acosta-Ormaechea, S. and Moruzomi, A. (2021). The value-added tax and growth: design matters. International Tax and Public Finance. Volume 28, pages 1211–1241.
- Arnold, J. M., Brys, B., Heady, C., Johansson, Å., Schwellnus, C., & Vartia, L. (2011). Tax policy for economic recovery and growth. Economic Journal, 121, F59–F80.
- Barro, R. J., 1990, “Government spending in a simple model of endogenous growth”, Journal of Political Economy, 98, 103-125.
- Barro, R. J. and X. Sala-i-Martin, 1992, “Public finance models of economic growth”, Review of Economic Studies, 59, 645-661.
- Besley, T. and T. Persson, 2011, Pillars of Prosperity: The Political Economics of Development Clusters. Princeton: Princeton University Press.
- Besley, T. and T. Persson, 2014, “The Causes and Consequences of Development Clusters: State Capacity, Peace and Income”, Annual Review of Economics, 6:927-49.
- Berg, A., Ostry, J. D., & Zettelmeyer, J. (2012). “What makes growth sustained?”, Journal of Development Economics, 98(2), 149-166.
- Hausmann, R., Pritchett, L., & Rodrik, D. (2005), “Growth accelerations”, Journal of Economic Growth, 10(4), 303-329.
- Schumpeter, J.S., 1918, Die Krisis des Steuerstaats, Zeitfragen aus dem Gebiete der Soziologie, 4, Graz and Leipzig: Leuschner & Lubensky, pp. 3-74 also available as chapter 1, The Crisis of the Tax State, in Richard Swedberg (ed.), 1991, The Economics and Sociology of Capitalism / Joseph A Schumpeter, Princeton: Princeton University Press.

### Empirical and methodological references (econometrics, identification, and robustness)
- Azariadis, C. and Stachurski, J., 2005. Poverty traps. Handbook of economic growth, 1, pp.295-384.
- Bugni, F. A., & Canay, I. A. (2021). Testing continuity of a density via g-order statistics in the regression discontinuity design. Journal of Econometrics, 221(1), 138-159.
- Callaway, B. and Sant’Anna, 2021, P. H. Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2):200–230.
- Deville, Jean-Claude. 1999. “Variance estimation for complex statistics and estimators: Linearization and residual techniques.” Survey Methodology 25:193–203.
- Hampel, F.R., 1974. The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69(346), pp.383-393.
- Hansen, B. E. (1999). Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of econometrics, 93(2), 345-368.
- Hansen, B. E. (2000). Sample splitting and threshold estimation. Econometrica, 68(3), 575-603.
- Bugni, F. A., & Canay, I. A. (2021). Testing continuity of a density via g-order statistics in the regression discontinuity design. Journal of Econometrics, 221(1), 138-159.

### Datasets, indices, and IMF/World Bank resources used or cited
- Feenstra, R., Inklaar, R. and Timmer, M. (2015), "The Next Generation of the Penn World Table." American Economic Review, 105(10), 3150-3182.
- Government Finance Statistics Manual (GFSM). 1986. “Government Finance Statistics Manual 1986.”
- Government Finance Statistics Manual (GFSM). 2014. “Government Finance Statistics Manual 2014.” https://www.imf.org/external/pubs/ft/gfs/manual/2014/gfsfinal.pdf.
- International Monetary Fund. 2021. Investment And Capital Stock Dataset (ICSD) 2021: Manual & FAQ - Estimating Public, Private, And PPP Capital Stocks. Washington, DC. https://infrastructuregovern.imf.org/content/dam/PIMA/Knowledge-Hub/dataset/InvestmentandCapitalStockDatabaseUserManualandFAQ_May2021.pdf
- International Monetary Fund. 2024. World Economic Outlook: Policy Pivot, Rising Threats. Washington, DC. October.
- UNU-WIDER Government Revenue Dataset. Version 2023. https://doi.org/10.35188/UNU-WIDER/GRD-2023.
- Mansour, Mario, Marijn Verhoeven, Fayçal Sawadogo, and Benedict Chu Sheen Tan. 2025. “Methodology and Overview of the IMF’s World Revenue Longitudinal Database.” IMF Technical Notes and Manuals 2025/04. International Monetary Fund, Washington, DC.
- James Gwartney, Robert Lawson, and Ryan Murphy (2024). Economic Freedom Dataset, published in Economic Freedom of the World: 2024 Annual Report. Fraser Institute.
- Kaufmann, Daniel; Kraay, Aart. 2024. The Worldwide Governance Indicators: Methodology and 2024 Update. Policy Research Working Paper; 10952. © World Bank. http://hdl.handle.net/10986/42373
- Pemstein, D., Marquardt, K. L., Tzelgov, E., Wang, Y.-t., Medzihorsky, J., Krusell, J., Miri, F., & von Römer, J. (2023). The v-dem measurement model: Latent variable analysis for crossnational and cross-temporal expert-coded data. Varieties of Democracy Institute Working Paper, 21 (8th Ed)
- Dahlberg, Stefan, Aksel Sundström, Sören Holmberg, Bo Rothstein, Natalia Alvarado Pachon, Cem Mert Dalli, Rafael Lopez Valverde, Victor Saidi Phiri & Lauren Gerber. 2025. The Quality of Government Basic Dataset, Version Jan25. University of Gothenburg: The Quality of Government Institute, https://www.gu.se/en/quality-government doi:10.18157/qogbasjan25
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### Working papers and policy notes on tax capacity and growth
- Gaspar, V., Jaramillo, L., & Wingender, P. (2016a). Political Institutions, State Building and Tax Capacity: Crossing the Tipping Point. IMF Working Paper, WP/16/233.
- Gaspar, V., Jaramillo, L., & Wingender, P. (2016b). Tax Capacity and Growth: Is there a Tipping Point? IMF Working Papers, WP/16/234.
- Benitez, J. C., M. Mansour, M. Pecho & C. Vellutini. Building Tax Capacity in Developing Countries. IMF Staff Discussion Note SDN/2023/006, September 2023, International Monetary Fund, Washington DC.
- Mario Mansour, 2015. "Tax Policy in MENA Countries: Looking Back and Forward," IMF Working Papers 2015/098, International Monetary Fund.
- Choudhary, R., F. U. Ruch & E. Skrok. Taxing for Growth: Revisiting the 15 Percent Threshold. World Bank Policy Research Working Paper No. 10943, 10 July 2024, Washington DC.

### Additional empirical studies on governance, corruption, and financial development
- Mauro, P., Romeu, R., Binder, A. and Zaman, A., 2015. “A modern history of fiscal prudence and profligacy”. Journal of Monetary Economics, 76, pp.55-70.
- Martin Cihák, Asli Demirgüç-Kunt, Erik Feyen, and Ross Levine. 2012. Benchmarking Financial Systems around the World. Policy Research Working Paper 6175, World Bank, Washington, DC.
- Seidel, A., and M. Thum, 2015, “Tax Evasion, Corruption and Market Entry”, Scottish Journal of Political Economy, doi: 10.1111/sjpe.12100.
- Standaert, S. (2015). Divining the level of corruption: A Bayesian state-space approach. Journal of Comparative Economics, 43 (3), 782–803. https://doi.org/10.1016/j.jce.2014.05.007
- Traxler, C., 2010, “Social Norms and Conditional Cooperative Taxpayers”, European Journal of Political Economy, 26 (2010) 89–103.
- Svirydzenka, K., 2016. Introducing a new broad-based index of financial development. International Monetary Fund Working Paper 16/5.

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### Appendix — figures, event-study descriptions, and additional tables

### Figures (event study and robustness)
- Figure A1. Grid Search for Tipping Point on GJW Sample
  - Shows the R-squared from estimating Equation (1) when setting the threshold at different values up to 30 percent of GDP.
  - Series obtained using different growth horizons (3, 5, 7, and 10 years) as the dependent variable.
  - Sample restricted to those used by GJW, but using the newly constructed tax series of this paper.
- Figure A2. The Growth Effect of the Tipping Point at Different Time Horizons
  - Shows regression coefficients for 훽̂ with 90 percent confidence intervals from estimating equation (1’) over different time horizons j.
- Figure A3. Countries With Tax-to-GDP Above Estimated Tipping Points
  - Source: GJW series uses the tax series constructed by Gaspar, Jaramillo and Wingender (2016b) and the tipping point they estimated over a 10-year growth horizon (12.88).
  - New Dataset series uses the tax series constructed in this paper and a threshold of 10.35 based on our 10-year growth horizon estimates.
- Figure A4. Dynamic Effects of Crossing the Tax-Ratio Threshold: Trimmed Sample
  - Panels a–h include: log GDP per capita, Tax-to-GDP ratio, bootstrapped standard errors, use of a 9.87 tax threshold, and last observed crossing.
  - Notes: Coefficient estimates 훽̂k from equation (3) with 90 percent confidence intervals; trimmed sample controls described in section III.2; bootstrapped standard errors using a multiplicative WildBootstrap; unless otherwise specified, robust and asymptotic standard errors estimated using Influence Functions.
- Figure A5. Dynamic Effects of Crossing the Tax-Ratio Threshold: Event Study Robustness Checks
  - Panels a–h mirror Figure A4 robustness checks.
  - Notes: Coefficient estimates 훽̂k from equation (3) with 90 percent confidence intervals; alternative control groups and standard-error procedures described; default use of Influence Functions for robust and asymptotic standard errors.
- Figure A6. Development Indicators Around the Tipping Point: Additional Indicators
  - Panels a–f include: Private Credit by Deposit Money Banks to GDP; Public Sector Corruption Index; Financial Institutions Index; Financial Markets Index; Primary Balance; Public Debt.
  - Notes: Graphs show coefficient estimates 훽̂k from equation (3) and the associated 90 percent confidence interval; coefficients capture effects of having crossed the 10.35 percent tax ratio threshold either −κ years ago for κ<0, or κ years after for κ>0; see Section II.1 and Table A2 for outcome variable details; robust and asymptotic standard errors estimated using Influence Functions.
- Figure A7. Development Indicators Around the Tipping Point: Trimmed Sample Event Study Graphs
  - Panels a–d include: Government Effectiveness; Financial Development Index; Legal Structures and Security of Property Rights; Governance (Bayesian Corruption Index).
  - Notes: Coefficient estimates 훽̂k from equation (3) with 90 percent confidence intervals; outcome variable mapping described in Section II.1 and Table A2; robust and asymptotic standard errors estimated using Influence Functions.
- Figure A8. Development Indicators Long Before the Tipping Point and In the Decade Before
  - Panels a–d include distributions for Government Effectiveness; Financial Development Index; Legal Structures and Security of Property Rights; Governance (Bayesian Corruption Index).
  - Notes: Graphs show distributions for two subsamples: “far from it” (at least a decade away) and “approaching the tipping point” (will cross in 10 years or less).
- Figure A9. Development Indicators Long Before the Tipping Point and In the Decade Before
  - Panels a–d as in Figure A8 but distinguishing “short-lived crossing” (tax ratios above threshold less than 75% of the times in the 15 years after crossing) and “long-lived crossing”.

### Additional tables and key statistics
- Table A1. Pairwise Correlations Between Different Tax Series
  - ALL DATA correlation matrix excerpts:
    - New Series: 1.0000
    - GJW with New Series: 0.9584
    - WoRLD with New Series: 0.9966
    - OECD with New Series: 0.9888
    - WEO with New Series: 0.9816
    - GRD with New Series: 0.9861
    - GFS with New Series: 0.8502
  - SPLICED DATA excerpt:
    - New series: 1.0000; correlation with GJW: 0.9455; with WoRLD: 1.0000; with OECD: 0.9828; with WEO: 0.9839; with GRD: 0.9789; with GFS: 0.7956.
  - Note: Authors’ construction. Correlation coefficients use all observations available in each pairwise case.
- Table A2. Summary Statistics - Table of Raw Indicators (selected entries)
  - Financial Development Index (FDI-FD): Years 1980-2019; Countries 149; Obs. 5452; Interpolated (%) 0.0; Scale 0 - 1; Avg. 0.3; SD 0.2.
  - Financial Institutions Index (FDI-FI): Years 1980-2019; Countries 149; Obs. 5452; Interpolated (%) 0.0; Scale 0 - 1; Avg. 0.4; SD 0.2.
  - Financial Markets Index (FDI-FM): Years 1980-2019; Countries 149; Obs. 5452; Interpolated (%) 0.0; Scale 0 - 1; Avg. 0.2; SD 0.2.
  - Private credit by deposit money banks to GDP (%): Years 1965-2019; Countries 149; Obs. 5878; Interpolated (%) 0.8; Scale 0 - 100; Avg. 42.4; SD 35.9.
  - Government Effectiveness Index: Years 1996-2019; Countries 149; Obs. 3538; Interpolated (%) 12; Scale -2.5 – 2.5; Avg. 0.1; SD 1.0.
  - Legal Structure and Security of Property Rights: Years 1970-2019; Countries 138; Obs. 5589; Interpolated (%) 41.9; Scale 0 - 10; Avg. 5.2; SD 1.9.
  - Bayesian Corruption Indicator (BCI): Years 1984-2019; Countries 146; Obs. 4562; Interpolated (%) 0.0; Scale 0 - 100; Avg. 45.6; SD 18.7.
  - Public Sector Corruption Index: Years 1965-2019; Countries 139; Obs. 5846; Interpolated (%) 0.0; Scale 0 - 1; Avg. 0.4; SD 0.3.
  - Total Investment: Years 1965-2019; Countries 149; Obs. 6110; Interpolated (%) 0.0; Scale Avg. 18.7; SD 8.7.
  - Public Investment: Years 1965-2019; Countries 149; Obs. 6110; Interpolated (%) 0.0; Scale Avg. 4.6; SD 3.6.
  - Government expenditure: Years 1965-2019; Countries 149; Obs. 4662; Interpolated (%) 0.0; Scale Avg. 29.5; SD 12.7.
  - Primary Balance: Years 1965-2019; Countries 149; Obs. 4597; Interpolated (%) 0.0; Scale Avg. -0.01; SD 3.74.
  - Government Debt: Years 1965-2019; Countries 149; Obs. 4593; Interpolated (%) 0.0; Scale Avg. 53.13; SD 35.6.
  - Note: Summary statistics for the effective sample of countries with available tax-to-GDP data (6273 observations). * In the analysis these indicators are multiplied by -1 to reflect better governance before standardizing them.
- Table A3. Years in which Countries Crossed the Tax-to-GDP Threshold of 10.35 Percent of GDP from Below
  - Lists country-specific years of crossing (examples):
    - Albania: 1998
    - Antigua and Barbuda: 2000 2006
    - Argentina: 2006
    - Benin: 1981 2007 2019
    - Bhutan: 2000 2002 2009
    - Bolivia: 1986 1992
    - Burkina Faso: 1997 2004
    - Burundi: 1978 1991
    - Cameroon: 1980 2000 2006 2011
    - China: 1997
    - Colombia: 1991
    - Djibouti: (no year listed in snippet)
    - Egypt: (no year listed in snippet)
    - India: 1976 1978
    - Indonesia: 1979 1985 1990 2001 2010
    - Madagascar: 1975 1999 2004 2007 2017
    - Mexico: 1979 2013
    - Pakistan: 2018
    - Panama: 1974 1977 1990 2012
    - Philippines: 1975 1980 1987 1989
    - Rwanda: 2006
    - Sierra Leone: 1978 2016
    - Sri Lanka: 1972 2015
    - Tanzania: 1991 2007
    - Togo: 2006 2011
    - Türkiye: 1977 1981 1990
    - Uganda: 2016
    - Uruguay: 1976
    - Vietnam: 1993 2000
  - Note: Full table lists numerous countries and multiple crossing years where applicable.
- Table A4. Regression Discontinuity Results with Alternative Polynomials
  - Order of polynomial (columns 2 through 8) and Coefficient (first row): 0.132**, 0.127**, 0.107*, 0.091*, 0.075, 0.078, 0.075.
  - Second row (standard errors): 0.054, 0.059, 0.056, 0.055, 0.056, 0.058, 0.059.
  - Note: Table shows results from specification (1) in Table 5 with alternative orders of the polynomial. * means p<10%, ** p<5%, *** p<1%.
- Table A5. Regression Discontinuity Results with Alternative Threshold Values
  - Threshold deviations and Coefficients (first row): -2.0: -0.015; -1.5: -0.447; -1.0: 0.092; -0.5: 0.117; Main: 0.107*; 0.5: 0.046; 1.0: 0.046; 1.5: 0.078; 2.0: 0.192.
  - Second row (standard errors): 0.215, 0.363, 0.189, 0.087, 0.056, 0.059, 0.085, 0.100, 0.134.
  - Note: Table shows results from specification (1) in Table 5 with alternative threshold values; “Main” corresponds to the threshold value in Table 5. * means p<10%, ** p<5%, *** p<1%.

*IMF Working Papers — State Capacity, Growth and Institutions: Taxing for Takeoff — References and Appendix (excerpts as provided).*

### 3. Nominal GDP Revisions and Tax-to-GDP Ratios

### 3. Nominal GDP Revisions and Tax-to-GDP Ratios

### Historical revisions to nominal GDP
- Historical GDP series may be revised over time due to newly available or incorporated data and changes in methodological approaches, including changes in the base year and national accounting practices (e.g., 2008 System of National Accounts (SNA) introduced a broader definition of financial services and a new treatment for the classification of research and development).
- Revisions often increase GDP estimates as more complete and accurate data become available (annual surveys refined, administrative records such as tax data accessible).
- Among 180 countries, 2010 GDP recorded in the April 2025 WEO was:
  - 1.4 percent higher than in the April 2016 WEO at the median
  - 8.3 percent higher at the mean
- Revisions diverge across income levels and regions:
  - Revisions are more common, larger, and more uniformly upwards among low- and lower middle-income countries, with many cases of upwards revisions of 30 percent or more in these groups.
  - Regionally, upwards GDP revisions have the largest effect in sub-Saharan Africa, where most countries’ 2010 GDP estimates increased in the last decade; upwards revisions also occurred in many countries in the rest of the world.
- Upwards revisions in many African countries are attributed to improvements in recording economic activity, implementation of latest standards, and rebasing of GDP sometimes after long gaps.

### Effect on historical tax-to-GDP ratios
- GDP revisions substantially reduce estimated tax-to-GDP in historical data compared to that used in GJW.
- Examples for 2010:
  - Togo: tax-to-GDP in the new series is 9.9 percent, compared to 15.7 percent in GJW, reflecting an upwards revision to nominal GDP of 50 percent.
  - Djibouti: tax-to-GDP decreases from 20.2 percent to 14.8 percent; GDP revised upwards more than 40 percent.
  - Uzbekistan: tax-to-GDP decreases from 20.6 percent to 16.1 percent; GDP revised upwards 28 percent.
- Aggregate differences:
  - Overall, average tax-to-GDP is just over 1 percentage point lower in the new series (Figure A11).
  - Restricting the comparison to the same countries and years across datasets yields an average difference of 1.25pp, indicating the difference is not attributable to different samples.

### Causal Random Forest robustness check for the grid-search tipping point
- Purpose and setup:
  - Used as a robustness check for the grid-search R-squared maximization specification.
  - Implemented a simple Causal Random Forest without covariates to estimate heterogeneous effects of taxation on economic growth, maintaining consistency with the simplicity of the main grid search procedure.
  - Treatment variable: tax-to-GDP ratio, continuous, measured in the initial year of the forward growth window.
  - Outcome variable: future GDP per capita growth calculated over 3, 5, 7, 10, and 15-year horizons.
- Methodology overview:
  - Causal forests extend Random Forests by splitting data to maximize differences in the relationship between an outcome and a treatment variable, enabling estimation of heterogeneous treatment effects (Conditional Average Treatment Effects, CATEs).
  - Applied to panel data sorted by country and year; simplified setup without covariates captures unconditional heterogeneity (variation reflecting random sampling variation rather than differences explained by observed characteristics).
  - To detect the tipping point, LOESS smoothing (Locally Estimated Scatterplot Smoothing) was applied to the scatterplot of estimated treatment effects versus the tax-to-GDP ratio; the tipping point is identified where the smoothed curve shows a clear change in trend.
- Bootstrap stability check:
  - Implemented a nonparametric bootstrap: resampling the data with replacement and re-running the full causal forest and LOESS estimation for each draw.
  - The tipping point was re-estimated in each iteration, yielding an empirical distribution of tipping points to compute confidence intervals.
  - Distributions are based on 1,000 bootstrap replications using LOESS-smoothed treatment effects from causal forest models.
  - The green vertical lines in Figure A12 indicate the 2.5th and 97.5th percentiles, forming a 95% confidence interval around the tipping point estimate.
- Conclusion:
  - The bootstrap results confirm that the tipping points are not artifacts of sampling noise and provide evidence of non-linear effects in the taxation-growth relationship.
  - The non-parametric robustness check shows that—even in a model-free setting—there is a statistically detectable inflection point in the effect of taxation on economic growth.

### Tipping point bootstrap estimates (Table A6)
- Horizon 3: Tipping point 13.3, CI Lower 7.3, CI Upper 18.6
- Horizon 5: Tipping point 14.3, CI Lower 7.3, CI Upper 19.0
- Horizon 7: Tipping point 14.6, CI Lower 7.4, CI Upper 18.3
- Horizon 10: Tipping point 13.8, CI Lower 6.9, CI Upper 18.9

*State Capacity, Growth and Institutions: Taxing for Takeoff — Working Paper No. WP/2025/203*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025203-source-pdf.pdf_