## _wp13244 — 1. Descriptive Statistics; selected results and appendices

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### Overview and objectives
- Objective: estimate tax capacity (the maximum level of tax revenue a country can achieve) and tax effort (the ratio between actual revenue and tax capacity) for 113 countries.
- Approach: panel stochastic tax frontier following Pessino and Fenochietto (2010) with extensions for natural-resource dependent countries and sensitivity checks.
- Sample composition:
  - Base sample: 96 non-natural resource dependent countries.
  - Extended sample: 96 + 17 resource-dependent economies (countries with revenue from natural resources greater than specified thresholds in the analysis).
- Time coverage: panel dataset covers 1991–2012 (data availability varies by country).

### Main methodology — stochastic tax frontier and inefficiency specifications
- Core model (panel stochastic frontier):
  - y_it = α + β' x_it + v_it - u_it
  - y_it: log tax revenue to GDP ratio for country i at time t.
  - x_it: vector of determinants; β: parameters; v_it: symmetric noise; u_it: non-negative inefficiency.
- Tax effort (TE): ratio between actual tax revenue and stochastic frontier tax revenue; TE ∈ [0,1]; predicted using Jondrow et al. (1982) conditional expectation.
- Distributional/inefficiency variants:
  - Half normal (Hn): u ~ truncated normal with zero mean and variance σ_u^2.
  - Truncated normal (TN): allows mean μ ≠ 0.
  - Time-varying inefficiency (Battese and Coelli 1992): u_it = u_i * exp[η*(t-T)], with η decay parameter.
- Estimation: maximum likelihood (ML) for panel stochastic frontier models.
- Heterogeneity handling:
  - TNH model: truncated normal heterogeneous in mean and decay inefficiency, g(zit) = exp(η′zit), μi = μ0 + μ1′wi.
  - Mundlak Random Effects Model (MREM) used to control unobserved heterogeneity by including means of explanatory variables.

### Determinants used and expected signs (reduced-form Ltot specification)
- Ltot = f(LGDt, TRt, AVAt, PEt, GINIt; CPIt; LCORt; OILt; GOVt)
- Variable definitions and expected signs:
  - Ltot: log of tax and pension contributions revenue as percent of GDP.
  - LGD: log GDP per capita (PPP 2005). Expected: positive.
  - LGD2: lgd squared. Expected: negative (non-linear elasticity).
  - TR: trade (imports + exports % of GDP). Expected: positive.
  - AVA: agriculture value added % of GDP. Expected: negative.
  - PE: public expenditure on education % of GDP. Expected: positive.
  - GINI: income distribution inequality. Expected: positive (better distribution facilitates collection).
  - CPI: percent change of consumer price index (inflation). Expected: negative.
  - Lcor: log of corruption perception index. Expected: negative (higher corruption → higher inefficiency).
  - GOV: dummy (1 = general government consolidated revenue; 0 = central government only).

### Key estimation results (selected parameter estimates from Table 2 and model diagnostics)
- Three models estimated for pooled sample: HN (Battese-Coelli Half Normal), TN (Battese-Coelli Truncated Normal), TNH (Truncated Normal Heterogeneous in Mean and Decay).
- Reported coefficients and standard errors (preserved exactly as presented):
  - Constant: -1.38619*** (0.312); -1.43757*** (0.324); -1.98777*** (0.295)
  - LGD: 1.0177*** (0.069); 1.03354*** (0.072); 1.15868*** (0.070)
  - AVA: -.00207*** (0.000); -.00213*** (0.000); -.00364*** (0.001)
  - PE: .03000*** (0.002); .03003*** (0.002); .03113*** (0.002)
  - TR: .00059*** (0.000); .00062*** (0.000); .00111*** (0.000)
  - GINI: -.00717*** (0.001); -.00726*** (0.001); -.00857*** (0.001)
  - GOV: .25867*** (0.022); .25498*** (0.023); .16669*** (0.042)
  - LGD2: -.05229*** (0.004); -.05321*** (0.004); -.05904*** (0.004)
  - (TNH only) Constant (heterogeneity term): .26038*** (0.097); .66064*** (0.120)
  - (TNH only) Lcor: -.31809** (0.126)
  - Lambda 1/: 4.2025*** (0.023); 3.00723*** (0.045); 2.75871*** (0.041)
  - Sigma (u) 1/: .41954*** (0.008); .30019*** (0.004); .27891*** (0.003)
  - Eta 2/: .01074*** (0.001); .01030*** (0.001)
  - CPI: 0.00100 (0.001) [not statistically significant per text]
  - Log-likelihood: 1097.36; 1123.02; 1110.2
- Statistical note: ***, **, * indicate significance at 1%, 5%, 10% levels respectively. All coefficients except CPI are statistically significant at 5 percent and have expected signs.

### Empirical findings and interpretation
- Confirmed determinant relationships:
  - Positive correlates of tax capacity/effort: LGD (per capita GDP), PE (education spending), TR (trade openness).
  - Negative correlates: AVA (agriculture share), GINI (income inequality), Lcor (corruption), CPI (inflation) — CPI exception on statistical significance.
- Lambda and inefficiency:
  - Large lambda values indicate a substantial inefficiency component relative to noise (e.g., Lambda 1/: 4.2025***; 3.00723***; 2.75871*** across models).
- Policy interpretation:
  - Identifying the gap between actual revenue and tax capacity indicates scope for revenue increases through improved collection and policy changes before introducing new taxes.
  - The model cannot fully disentangle inefficiency-driven gaps (e.g., evasion) from policy-choice-driven gaps (e.g., exemptions, low statutory rates) without more granular data.

### Countries’ tax effort and tax capacity (selected country figures preserved exactly)
- Tax effort predictions computed under HN, TN, TNH and tax capacity derived as tax and social contributions divided by tax effort (TNH tax capacity shown).
- Representative country entries (as in Table 3):
  - 1 Albania 2011 Total Revenue 22.878 Per capita GDP 861.10 TN tax effort 0.740 Half Normal 0.730 TNH 0.683 Tax capacity 33.7
  - 2 Argentina 2011 Total Revenue 34.715 Per capita GDP 5501.40 TN tax effort 0.670 Half Normal 0.670 TNH 0.665 Tax capacity 52.2
  - 5 Austria 2011 Total Revenue 42.136 Per capita GDP 35353.00 TN tax effort 0.980 Half Normal 0.970 TNH 0.934 Tax capacity 45.2
  - 77 Singapore 2011 Total Revenue 14.153 Per capita GDP 3591.10 TN tax effort 0.430 Half Normal 0.420 TNH 0.30 Tax capacity 46.8
  - 93 UnitedStates 2011 Total Revenue 24.542 Per capita GDP 2486.00 TN tax effort 0.710 Half Normal 0.710 TNH 0.68 Tax capacity 36.0
  - 96 Zambia 2012 Total Revenue 16.614 Per capita GDP 75.50 TN tax effort 0.980 Half Normal 0.970 TNH 0.98 Tax capacity 16.9
- Stylized patterns:
  - Many European high-income countries (Austria, Belgium, Denmark, Finland, France, Italy, Sweden) have tax efforts > 90 percent (near capacity).
  - Asia-Pacific region shows lower tax effort (examples: Singapore 0.33 TNH; Korea 0.49; Japan 0.53; Indonesia 0.43); policy choices such as low VAT rates contribute.
  - Some low per-capita-GDP countries operate near tax capacity (examples: Mali, Namibia, Senegal, Zambia), sometimes due to large mining activity collected from concentrated taxpayers.
- Noted VAT rates in source (preserved):
  - Panama 7 percent; Paraguay 10 percent; Singapore VAT between 3 percent (1994) and 7 percent (2011); Japan 5 percent in 2011; Korea 10 percent in 2011.

### Regional and income-level descriptive statistics (selected figures preserved)
- Table 1 selected descriptive statistics:
  - TOT: Mean 25.0 Std.Dev. 11.3 Minimum 4.45 Maximum 51.2
  - GDP: Mean 14232.7 Std.Dev. 13649.5 Minimum 372.67 Maximum 4113.9
  - GINI: Mean 38.0 Std.Dev. 9.0 Minimum 24.7 Maximum 67.4
  - COR: Mean 3.2 Std.Dev. 1.4 Minimum 0.5 Maximum 6.0
  - TR: Mean 82.45 Std.Dev. 51.41 Minimum 3.24 Maximum 260.5
  - AVA: Mean 12.7 Std.Dev. 12.6 Minimum 0.16 Maximum 65.1
  - CPI: Mean 6.8 Std.Dev. 11.4 Minimum -8.21 Maximum 183.3
  - PE: Mean 4.5 Std.Dev. 1.5 Minimum 1.3 Maximum 9.5
  - GOV: Mean 0.60 Std.Dev. 0.50 Minimum 0.0 Maximum 1.0
  - lgd: Mean 8.9 Std.Dev. 1.35 Minimum 5.9 Maximum 11.2
  - lcor: Mean 1.1 Std.Dev. 0.5 Minimum -0.7 Maximum 1.8
  - ltot: Mean 3.1 Std.Dev. 0.51 Minimum 1.5 Maximum 3.9
  - lgd2: Mean 281.12 Std.Dev. 22.73 Minimum 35.1 Maximum 125.7
- Table 4 (Countries’ Tax Effort by Level of Development) preserved rows:
  - Low Income: Countries 64; Average Total Revenue 21.47; Per-capita GDP, PPP 2005 752.3; Tax Effort 0.652; Tax Capacity 26.0
  - Middle Income: Countries 49; Average Total Revenue 29.01; Per-capita GDP, PPP 2005 8785.4; Tax Effort 0.64; Tax Capacity 37.3
  - High Income: Countries 18; Average Total Revenue 87.46? 8458.7; Tax Effort 0.76; Tax Capacity 45.1
  - Note: table irregularities preserved exactly as presented in source.

### Natural-resource dependent countries — results and implications
- Inclusion criteria and approach:
  - Earlier practice excluded countries with natural resource revenue > 30 percent of total tax revenue.
  - Current extension includes 17 countries with resource revenue > 25 percent of tax + resource revenue (average 2000–11).
  - For resource-dependent countries analysis considers non-resources tax revenue as percent of non-natural-resources product; dummy variable Oil distinguishes resource-dependent countries.
- Sample effects and inefficiency:
  - For the sample including 17 natural resource countries, lambda is larger ("λi ... larger than 6.4 and statistically significant"), implying a larger inefficiency component than in non-resource sample.
- Representative country tax effort (as reported):
  - Kuwait: tax effort 0.05 (THN model).
  - Saudi Arabia: tax effort 0.07 (THN model).
  - Papua New Guinea: tax effort 0.97 (TNH model).
  - Bolivia: tax effort 0.88 (TNH model).
- Aggregate note: non-hydrocarbon tax revenues for the 17-country group average about 27.6 percent of total revenues (tax and oil revenues).
- Policy implication: for many natural-resource dependent countries total revenue potential depends on reserves and production; institutional improvements and tax-administration capacity matter for non-resource tax mobilization.

### Sensitivity analysis and robustness checks
- Exclusion tests and impacts on tax effort:
  - Excluding three highest per-capita GDP countries (Luxemburg, Norway, Singapore): average tax effort changes 1.3 percent (maximum change 5.6 percent; minimum 0.01 percent). Example: Guyana tax effort changes from 0.73 to 0.67 (maximum difference 5.6 percent).
  - Excluding three lowest per-capita GDP countries (Malawi, Mozambique, Niger): average change in tax effort 0.4 percent.
  - Increasing GINI by 15 percent for all countries and increasing CPI and TR by 30 percent for six randomly selected countries (Armenia, Cameroon, France, Latvia, the Philippines, Uruguay) did not have a significant impact on tax effort estimates.
  - Tax effort of the 96 non-natural resource countries does not change significantly whether estimated alone or with the 17 natural resource countries included.
  - Excluding Chile, Norway, and Peru (significant but <25 percent natural resource revenue) did not change outputs significantly.
- MREM (Mundlak Random Effects Model) results (selected estimates preserved):
  - Constant: -2.6669 (St. Error 2.0250)
  - LGD: 1.4189 *** (St. Error 0.1499)
  - AVA: -0.0036 *** (St. Error 0.0013)
  - PE: 0.0265 *** (St. Error 0.0044)
  - TR: 0.0011 *** (St. Error 0.0002)
  - GINI: -0.0060 *** (St. Error 0.0016)
  - GOV: 0.2650 *** (St. Error 0.0585)
  - LGD^2: -0.0732 *** (St. Error 0.0084)
  - Lambda 1/: 6.3094 *** (St. Error 0.0502)
  - Sigma (u) 1/: 0.7129 *** (St. Error 0.0502)
- MREM implications:
  - MREM improves tax capacity estimates for specific countries.
  - For countries with the lowest per capita GDP and for some natural-resource-dependent economies, MREM reduces estimated tax capacity (i.e., TNH capacity may only be achievable in the long term).

### Appendix — variable definitions and data sources (selected)
- Ltot: log of sum of tax and pension contributions revenue as percent of GDP. Source: World Economic Outlook and official websites. Gov dummy flags consolidated (Gov=1) vs central only (Gov=0).
- Lgd: log GDP per capita, PPP constant 2005. Source: World Bank WDI.
- Lgd2: lgd squared.
- TR: trade (imports + exports) as percent of GDP. Source: WDI.
- AVA: agriculture value added % of GDP. Source: WDI.
- PE: public expenditure on education % of GDP. Sources: WDI and FAD statistics.
- GINI: GINI coefficient. Source: WDI.
- CPI: percentage change of consumption price index. Source: WDI.
- Lcor: log of the corruption perception index. Source: Transparency International.
- Data/caveats:
  - Private-administered social security collections excluded; government-collected social security included (affects comparability for countries such as the USA and Chile).
  - Reporting heterogeneity addressed via Gov dummy.
  - Appendix provides country-level observations and model estimate outputs (Mundlak REM, HN, TN, TNH) per country (not reproduced here beyond selected examples).

*Source: _wp13244 — excerpts from 1. Descriptive Statistics; 19. Methodology and results; 32. Natural-resource countries; Appendix 1. Variables and Data Source.*

### 1. Descriptive Statistics ..............................................................................................

### _wp13244 - 1. Descriptive Statistics ..............................................................................................

### Overview
- Objective: estimate tax capacity (the maximum level of tax revenue a country can achieve) and tax effort (the ratio between actual revenue and tax capacity) for 113 countries.
- Approach: stochastic tax frontier for panel data following the econometric model used by Pessino and Fenochietto (2010), extended to include natural-resource dependent countries and sensitivity checks.
- Sample composition: first for 96 non-natural resource dependent countries, then with the addition of 17 resource-dependent economies (countries with revenue from natural resources greater than specified thresholds in the analysis).

### Sample, Scope, and Data Notes
- Number of countries analyzed: 113.
- Resource-dependent inclusion criteria discussed:
  - Previous analysis excluded countries with revenue from natural resources representing more than 30 percent of total tax revenue.
  - Current extension includes 17 countries where revenue from natural resources represents more than 25 percent of total revenue (taxes plus revenue from natural resources excluding non tax-revenue and grants).
  - For resource-dependent countries, the analysis considers only non-resources tax revenue as percent of non-natural resources product.
- Sensitivity analysis: model runs without a group of countries and with alternative values for certain variables; reported that these changes do not have a significant impact on results.

### Main Methodology: Stochastic Tax Frontier
- Core model (panel stochastic frontier) expressed as:
  - y_it = α + β' x_it + v_it - u_it
  - y_it represents the log tax revenue to GDP ratio for country i at time t.
  - x_it is the vector of variables affecting tax revenue for country i at time t.
  - β is a vector of unknown parameters.
  - v_it is statistical noise (symmetric distribution, e.g., normal; can be positive or negative).
  - u_it represents inefficiency (non-negative), associated with country-specific factors preventing attainment of tax capacity.
- Tax effort (TE) defined as the ratio between actual tax revenue and the corresponding stochastic frontier tax revenue (tax capacity); TE takes values between zero and one, with expressions provided in the Box 1 formulation.
- Distributional assumptions for u_it discussed:
  - Half normal (Hn) model: u distributed as truncated version of a normal with zero mean and variance σ_u^2.
  - Truncated normal (TN) model: relaxes half-normal by allowing mean μ ≠ 0.
- Time-varying inefficiency variant (Battese and Coelli 1992) parametrization:
  - u_it = u_i * exp[η*(t-T)], where T corresponds to the last time period in each panel and η is the decay parameter to be estimated.
- Estimation method: maximum likelihood (ML) is employed for panel stochastic frontier estimation.

### Determinants and Empirical Insights from Literature Reviewed
- Commonly found determinants of tax revenues and tax capacity across literature:
  - Positive correlates: per capita GDP (proxy for development), trade openness, level of education.
  - Negative correlates: inflation, income distribution (GINI), difficulty of tax collection, corruption.
  - Sectoral composition matters: higher share of agriculture associated with lower taxability relative to industry.
- Empirical references summarized:
  - Lotz and Mors (1967): per capita GNP and trade as explanatory variables for international tax ratio.
  - Gupta (2007): dynamic panel finding per capita GDP, share of agriculture in GDP, trade openness, and foreign aid significantly affect tax revenues.
  - Davoodi and Grigorian (2007): institutional quality and informal activity important for tax revenue performance.
  - Keen and Simone (2004) and Baunsgaard and Keen (2010): trade liberalization and customs improvements can increase revenue; relationship between trade and revenue is positive for high and middle income countries and weaker for low income countries.
  - Pessino and Fenochietto (2010): positive relationship between tax capacity and development, trade, and education; negative relationship with inflation, income distribution, collection difficulty, and corruption; introduced stochastic tax frontier with time-varying inefficiency and two disturbance terms.

### Estimation Strategy and Model Variants
- Panel frontier estimation rationale:
  - Panel data expected to provide better efficiency estimates than single cross-section; allows investigation of changes in technical efficiencies and tax capacity over time.
  - If u_it and v_it independent over time and across countries, pooled cross-section frontier models apply (e.g., normal-half normal model via ML).
- Distributional/model choices and references:
  - Normal-half normal model: Aigner, Lovell and Schmidt (1977).
  - Truncated normal model: Stevenson (1980).
  - Gamma model: Greene (1990).
  - Log-likelihood forms referenced in Kumbhakar and Lovell (2000).
  - Preference for truncated-normal distribution suggested (Coelli and others, 2005), but ultimately an empirical decision; both half normal and truncated normal specifications are estimated.
- Time-invariant vs time-varying inefficiency:
  - Time-invariant models are restrictive.
  - Battese and Coelli (1992) time-varying decay model allows inefficiency to change over time and is estimated in a random effects framework using ML.
  - Prediction of technical efficiencies uses conditional expectation given observable residuals (Jondrow et al., 1982).

### Observed Heterogeneity and Environmental Variables
- Two approaches to include observable environmental variables:
  1. Two-stage approach (Pitt and Lee, 1981): estimate frontier omitting environmental variables, predict efficiencies, then regress predicted efficiencies on environmental variables. Risk: omission of environmental variables in first stage biases frontier parameter estimates and predicted efficiencies.
  2. Direct inclusion of environmental variables in the stochastic component or in the mean of the inefficiency distribution (Battese and Coelli framework).
- General heterogeneity model formulation cited:
  - y_it = β′ x_it + v_it – u_it
  - u_it = g(z_u_it) |U_i|, U_i ~ N[μ_i, σ_u^2], μ_i = μ_0 + μ_1′ w_i
  - w_i are variables that influence mean inefficiency; v ~ N[0, σ_v^2].
- Examples of environmental variables discussed: inflation, corruption, degree of government regulation, and other exogenous factors that influence collection capacity from outside the tax-collection technology.

### Key Technical and Policy-Relevant Points (from the text)
- Policy relevance: identifying how far actual revenue is from tax capacity helps determine scope for increasing tax revenue before implementing new taxes or raising existing ones.
- The stochastic frontier approach differs conceptually from OLS: OLS assumes technical efficiency for all countries; stochastic frontier includes inefficiency term u_it allowing cross-country differences in attainment of tax capacity.
- The model cannot disentangle the gap attributable to inefficiency (e.g., evasion) versus policy choices (e.g., tax legislation, exemptions) without more granular data (effective tax rates, tax bases, measures of evasion and collection inefficiencies), which are largely unavailable for most countries and years.
- Sensitivity analysis reported: running the model without certain country groups and varying selected variables did not significantly change results (specific sensitivity outcomes and numerical results are presented elsewhere in the full chapter).

*Source: _wp13244 - 1. Descriptive Statistics (excerpt provided).*

### 19.      First, this paper estimates countries’ tax effort and capacity by using Battese

### _wp13244 - 19.      First, this paper estimates countries’ tax effort and capacity by using Battese

### Methodology: stochastic frontier and inefficiency specifications
- Two primary estimation strategies:
  - Battese and Coelli’s original formulation without heterogeneity with base specification g(zit) = exp[-η(t – T)] (columns I and II of Table 3).
  - More general formulation with g(zit) = exp(η′zit) and mean of the truncated normal depending on observable covariates μi = μ0 + μ1′wi (column III of Table 3), where z variables influence time-varying inefficiency and wi variables mean time-invariant inefficiency.
- Three frontier model specifications estimated for pooled sample:
  - C I = Battese Coelli - Half Normal (HN)
  - C II = Battese Coelli - Truncated Normal (TN)
  - C III = Truncated Normal Heterogeneous in Mean and Decay Inefficiency (TNH)
- Inefficiency measured via lambda (λi = σui / σvi); large λi (larger than 2.8 and statistically significant) implies a large inefficiency component relative to noise.

### Variables and data
- Panel dataset: 113 countries covering 1991–2012 (data availability varies by country).
- Reduced-form specification:
  - Ltot = (lgd, NTR, TR, AVA, PE, GINI; CPI; lcor; Oil, Gov) = f(LGDt, TRt, AVAt, PEt, GINIt; CPIt; LCORt; OILt; GOVt)
- Definitions and expected signs:
  - Ltot: log of the sum of tax and pension contributions revenue collected by central and sub national governments as percent of GDP.
  - Lgd: log GDP per capita (PPP constant 2005). Expected coefficient: positive.
  - Lgd2: lgd squared to capture non-linear elasticity. Expected sign: negative.
  - TR: trade (imports plus exports as percent of GDP). Expected sign: positive.
  - AVA: value added of agriculture as percent of GDP. Expected sign: negative.
  - PE: public expenditure on education as percent of GDP. Expected sign: positive.
  - GINI: income distribution inequality. Expected sign: positive (better distribution facilitates collection and compliance).
  - CPI: percentage change of consumer price index (inflation). Expected sign: negative (printing money associated with negative efficiency); empirical results discussed below.
  - Lcor: log of corruption perception index (represents inefficiencies in tax collection). Expected sign: negative.
  - GOV: dummy distinguishing general government revenue (54 countries) from central government revenue (42 countries).

### Main estimation results (Table 2: Parameters of the Stochastic Frontier Tax Function, Maximum Likelihood)
- Reported coefficients and standard errors (three models: HN, TN, TNH):
  - Constant: -1.38619*** (0.312); -1.43757*** (0.324); -1.98777*** (0.295)
  - LGD: 1.0177*** (0.069); 1.03354*** (0.072); 1.15868*** (0.070)
  - AVA: -.00207*** (0.000); -.00213*** (0.000); -.00364*** (0.001)
  - PE: .03000*** (0.002); .03003*** (0.002); .03113*** (0.002)
  - TR: .00059*** (0.000); .00062*** (0.000); .00111*** (0.000)
  - GINI: -.00717*** (0.001); -.00726*** (0.001); -.00857*** (0.001)
  - GOV: .25867*** (0.022); .25498*** (0.023); .16669*** (0.042)
  - LGD2: -.05229*** (0.004); -.05321*** (0.004); -.05904*** (0.004)
  - (TNH only) Constant (heterogeneity term): .26038*** (0.097); .66064*** (0.120) [table shows two constants for heterogeneity? preserved as presented]
  - Lcor (TNH only): -.31809** (0.126)
  - Lambda 1/: 4.2025*** (0.023); 3.00723*** (0.045); 2.75871*** (0.041)
  - Sigma (u) 1/: .41954*** (0.008); .30019*** (0.004); .27891*** (0.003)
  - Eta 2/: .01074*** (0.001); .01030*** (0.001)
  - CPI: 0.00100 (0.001) [not statistically significant per text]
  - Log-likelihood: 1097.36; 1123.02; 1110.2
- Statistical notes: ***, **, * indicate significance at 1%, 5%, 10% levels respectively. All coefficients except CPI are statistically significant at 5 percent and have expected signs.

### Interpretation of coefficients and inefficiency determinants
- Per capita GDP (LGD) and public expenditure on education (PE) are positively associated with being near tax capacity (higher tax effort).
- AVA (agriculture share), GINI, and corruption (Lcor) have inverse relationships with tax capacity and tax effort (negative signs).
- In TNH model:
  - Corruption index (measured 0.5 high to 6 low): negative coefficient on mean inefficiency → higher Lcor (less corruption) associated with lower inefficiency.
  - CPI (inflation) increases inefficiency: positive sign implies higher inflation associated with higher inefficiency (decay parameter).

### Countries’ tax effort and tax capacity (estimates and country rankings)
- Tax effort predicted using Jondrow et al. (1982) formula on observable v_it - u_it.
- Table 3 reports for 96 countries (alphabetical): Total revenue (tax and social contributions as percent of GDP), Per capita GDP PPP 2005, Tax Effort under Half Normal, TN, and TNH, and Tax Capacity under TNH (Tax capacity defined as tax and social contributions divided by tax effort).
- Representative country figures preserved exactly from Table 3 (selected entries shown as in source):
  - 1 Albania 2011 Total Revenue 22.878 Per capita GDP 861.10 TN tax effort 0.740 Half Normal 0.730 TNH 0.683 Tax capacity 33.7
  - 2 Argentina 2011 Total Revenue 34.715 Per capita GDP 5501.40 TN tax effort 0.670 Half Normal 0.670 TNH 0.665 Tax capacity 52.2
  - 5 Austria 2011 Total Revenue 42.136 Per capita GDP 35353.00 TN tax effort 0.980 Half Normal 0.970 TNH 0.934 Tax capacity 45.2
  - 77 Singapore 2011 Total Revenue 14.153 Per capita GDP 3591.10 TN tax effort 0.430 Half Normal 0.420 TNH 0.30 Tax capacity 46.8
  - 93 UnitedStates 2011 Total Revenue 24.542 Per capita GDP 2486.00 TN tax effort 0.710 Half Normal 0.710 TNH 0.68 Tax capacity 36.0
  - 96 Zambia 2012 Total Revenue 16.614 Per capita GDP 75.50 TN tax effort 0.980 Half Normal 0.970 TNH 0.98 Tax capacity 16.9
- Textual findings from Table 3 and Figure 1:
  - Countries’ tax effort under the three models (HN, TN, TNH) are similar.
  - Many European high-income countries (Austria, Belgium, Denmark, Finland, France, Italy, Sweden) have tax efforts higher than 90 percent and are near tax capacity.
  - Asia and Pacific region exhibits the lowest level of tax effort, driven in part by Singapore (0.33 TNH), Korea (0.49), Japan (0.53), and Indonesia (0.43).
  - Some low per-capita-GDP countries operate near tax capacity (examples: Mali, Namibia, Senegal, Zambia), sometimes due to large mining activity collected from easily-controllable large companies.
- Specific country observations:
  - Large exemptions and low tax rates explain low tax effort in some developing countries: Guatemala TNH 0.46; Panama TNH 0.47; Paraguay TNH 0.51.
  - VAT standard rates noted in source: Panama 7 percent; Paraguay 10 percent; Singapore VAT between 3 percent (1994) and 7 percent (2011); Japan 5 percent in 2011; Korea 10 percent in 2011.

### Regional and income-level summary statistics (preserved from source)
- Table 1 selected descriptive statistics (as presented):
  - TOT: Mean 25.0 Std.Dev. 11.3 Minimum 4.45 Maximum 51.2
  - GDP: Mean 14232.7 Std.Dev. 13649.5 Minimum 372.67 Maximum 4113.9
  - GINI: Mean 38.0 Std.Dev. 9.0 Minimum 24.7 Maximum 67.4
  - COR: Mean 3.2 Std.Dev. 1.4 Minimum 0.5 Maximum 6.0
  - TR: Mean 82.45 Std.Dev. 51.41 Minimum 3.24 Maximum 260.5
  - AVA: Mean 12.7 Std.Dev. 12.6 Minimum 0.16 Maximum 65.1
  - CPI: Mean 6.8 Std.Dev. 11.4 Minimum -8.21 Maximum 183.3
  - PE: Mean 4.5 Std.Dev. 1.5 Minimum 1.3 Maximum 9.5
  - GOV: Mean 0.60 Std.Dev. 0.50 Minimum 0.0 Maximum 1.0
  - lgd: Mean 8.9 Std.Dev. 1.35 Minimum 5.9 Maximum 11.2
  - lcor: Mean 1.1 Std.Dev. 0.5 Minimum -0.7 Maximum 1.8
  - ltot: Mean 3.1 Std.Dev. 0.51 Minimum 1.5 Maximum 3.9
  - lgd2: Mean 281.12 Std.Dev. 22.73 Minimum 35.1 Maximum 125.7
- Table 4 (Countries’ Tax Effort by Level of Development) preserved rows:
  - Low Income: Countries 64; Average Total Revenue 21.47; Per-capita GDP, PPP 2005 752.3; Tax Effort 0.652; Tax Capacity 26.0
  - Middle Income: Countries 49; Average Total Revenue 29.01; Per-capita GDP, PPP 2005 8785.4; Tax Effort 0.64; Tax Capacity 37.3
  - High Income: Countries 18; Average Total Revenue 87.46? [table cell as presented] 8458.7; Tax Effort 0.76; Tax Capacity 45.1
  - Note: preserve tabular irregularities exactly as shown in source.

### Tax effort in natural resource economies
- Natural-resource dependent countries can have very large resource revenue shares (examples from source):
  - Libya 2012: resource revenue 72.5 percent of aggregate cited.
  - Kuwait 2011: resource revenue 52.7 percent of aggregate cited.
- High natural resource revenue shares make comparisons of tax capacity with non-resource countries difficult.
- For countries where resource revenue is large, total tax capacity often depends on reserves and production levels rather than variables used for non-resource countries.
- Previous practice excluded countries where natural resource revenue represented more than 30 percent of total tax revenue; current analysis adds a group of 17 countries where resource revenue represents more than 25 percent of tax plus natural resource revenue on average in 2000–11.
- For these resource-dependent countries, a dummy variable (oil) distinguishes those with resource revenue > 25 percent; for these countries only tax revenue (excluding oil and mining sector revenue) considered as percent of non-natural-resources product.

### Empirical conclusions summarized
- Empirical estimates confirm expected signs for nearly all explanatory variables (CPI exception) and robustness across HN, TN, TNH specifications.
- LGD (per capita GDP) and PE (education spending) are strong positive determinants of tax effort.
- AVA (agriculture share), GINI, and corruption are negatively associated with tax capacity and tax effort.
- Large lambda and significant inefficiency term indicate substantial scope for improving revenue collection efficiency in many countries.
- Regional patterns: high-income European countries near tax capacity; Asia-Pacific shows lower tax effort partly due to policy choices (low VAT rates) in some high-income economies; Africa shows heterogeneity with some low-income countries near capacity often due to resource or re-export tax bases.

*Italic: Content derived from _wp13244 - 19.      First, this paper estimates countries’ tax effort and capacity by using Battese (source text provided).*

### 32.      As with the sample of 96 non-natural resource dependent countries, we ran first

### _wp13244 - 32.

### Natural-resource countries: frontier results and tax effort
- Models run: HN, TN, and TNH models for sample including 17 natural resource dependent countries.
- Statistical significance and signs:
  - "All coefficients (except those for CPI and corruption) are statistically significant (different from zero) at 10 percent (at least) and have the expected signs."
- Inefficiency (lambda):
  - "λi, the lambda parameter, is quite large, larger than 6.4 and statistically significant."
  - "By adding the 17 natural resource countries to the initial sample of 96 countries, the value of the lambda parameter is significantly larger than that of the first group of non-natural resource dependent countries, implying a larger inefficiency component in the model."
- Country examples of tax effort (models indicated in source):
  - Kuwait: tax effort 0.05 (THN model).
  - Saudi Arabia: tax effort 0.07 (THN model).
  - Papua New Guinea: tax effort 0.97 (TNH model).
  - Bolivia: tax effort 0.88 (TNH model).
- Contextual notes:
  - "The group of 17 natural resource countries included now in this analysis is very heterogeneous."
  - "In this group of countries, non-hydrocarbon tax revenues account for about 27.6 percent of total revenues on average (tax and oil revenues)."

### Sensitivity analysis
- Exclusion scenarios tested:
  - Without three countries with highest per capita GDP (Luxemburg, Norway, Singapore).
  - Without three countries with lowest per capita GDP (Malawi, Mozambique, Niger).
  - Without three countries with lowest GINI coefficient.
- Outcomes:
  - "Running the model without the three countries with the highest level of per capita GDP, we found that, in average, tax effort changes 1.3 percent (with the maximum change being 5.6 percent and the minimum being 0.01 percent)."
  - "Running the model without the three countries with the lowest per capita GDP, the average change in tax effort is only 0.4 percent."
  - Maximum difference example: Guyana tax effort changes from 0.73 to 0.67 (maximum difference of 5.6 percent).
- Additional tests:
  - Increased GINI by 15 percent for all countries.
  - Randomly selected six countries (Armenia, Cameroon, France, Latvia, the Philippines, Uruguay) and increased CPI and TR by 30 percent.
  - Result: "these changes do not have a significant impact on the estimated tax effort of the 113 countries included in the sample of this study."
- Robustness to sample composition:
  - "Tax effort of the 96 non-natural resource countries does not change significantly when we consider in the estimates only these 96 countries (column VII) or when we run the analysis by including also the 17 natural resource countries (column VII)."
  - Additional check: excluding Chile, Norway, and Peru (significant but <25 percent natural resource revenue) did not change output significantly.

### Unobserved heterogeneity, Mundlak REM (MREM) and implications
- Modeling approach:
  - Paper estimated Battese-Coelli HN and TN models (without heterogeneity), TNH model (including corruption and inflation to capture observable heterogeneity), and a Mundlak version of the Random Effects Model (MREM) to address unobserved heterogeneity.
  - Rationale: TFE and REM can suffer from incidental parameter problem and unobserved variables bias; MREM adds means of explanatory variables to reduce bias and separate inefficiency from unobserved heterogeneity.
- MREM results (Table 8 summary lines preserved from source):
  - Coefficients and lambda under MREM: "all coefficients and lambda are significant and statistically significant (different from zero) at 1 percent and have the expected signs (Table 8)."
  - Reported MREM parameter estimates (from Table 8 excerpt in source):
    - Constant: -2.6669 (St. Error 2.0250)
    - LGD: 1.4189 *** (St. Error 0.1499)
    - AVA: -0.0036 *** (St. Error 0.0013)
    - PE: 0.0265 *** (St. Error 0.0044)
    - TR: 0.0011 *** (St. Error 0.0002)
    - GINI: -0.0060 *** (St. Error 0.0016)
    - GOV: 0.2650 *** (St. Error 0.0585)
    - LGD^2: -0.0732 *** (St. Error 0.0084)
    - Lambda 1/: 6.3094 *** (St. Error 0.0502)
    - Sigma (u) 1/: 0.7129 *** (St. Error 0.0502)
- MREM effects on tax capacity estimates:
  - "In running the MREM, we find that the results change improving tax capacity estimates for some specific countries."
  - "In general, for countries with the lowest level of per capita GDP and for natural resource dependent economies (with low level of revenue) the MREM reduces tax capacity (maximum level of revenue that the country could achieve)."
  - Interpretation: MREM "seems to adequately control for the ‘short term’ tax capacity" of low-income and natural-resource-dependent countries; these countries "could reach the TNH level of tax capacity only in the long term."

### Conclusions and policy-relevant findings
- Method and scope:
  - Stochastic frontier tax analysis applied to determine tax effort and tax capacity of 113 countries (initially 96 non-natural resource dependent economies).
  - Approach yields comparative predictions of tax effort relative to peers, accounting for economic and institutional characteristics.
- Confirmed relationships:
  - Positive and significant relationships between tax revenue (percent of GDP) and:
    - Level of development (per capita GDP).
    - Trade (imports and exports as percent of GDP).
    - Education (public expenditure on education as percent of GDP).
  - Negative relationships between tax revenue (percent of GDP) and:
    - Inflation (CPI).
    - Income distribution (GINI coefficient).
    - Ease of tax collection (agricultural sector value added as percent of GDP).
    - Corruption.
- Policy-relevant examples and implications:
  - "High levels of exemptions and low tax rates explain, in part, why some developing countries have a low level of tax effort."
    - Implication: for these countries, public choice (tax policy design) is a contributor to the gap between actual revenue and potential revenue.
  - European countries (Austria, Belgium, Denmark, Finland, France, Italy, Sweden) exhibit tax efforts higher than 90 percent and appear near tax capacity, implying limited scope for revenue increases through higher compliance alone.
  - Countries with high per capita GDP but low tax effort:
    - Singapore: tax effort 0.33 (THN model).
    - Korea: tax effort 0.49.
    - Japan: tax effort 0.53.
    - Contributing factor: low VAT rates (examples given: Singapore between 3 percent (1994) and 7 percent (2011); Japan 5 percent in 2011; Korea 10 percent in 2011).
  - Natural resource dependent countries:
    - When included in the sample, the model shows higher inefficiency in establishing or collecting taxes.
    - Non-hydrocarbon tax revenues in this group average about 27.6 percent of total revenues (tax and oil revenues).
    - For many natural resource dependent and the poorest countries, improved institutions (tax administration and customs) and longer-term structural developments are needed for them to reach TNH tax capacity levels.

*Source: Excerpt from _wp13244 - 32.*

### Appendix 1. Variables and Data Source

### _wp13244 - Appendix 1. Variables and Data Source

### Variable definitions and roles
- Ltot: the log of the sum of tax and pension contributions revenue collected by central and sub national governments as percent of GDP.
  - General government revenue was only available for 52 countries; for the remaining 60 countries we used central government revenue.
  - Dummy variable Gov distinguishes reporting type: Gov=1 for countries that report consolidated revenues; Gov=0 for those that report only central government revenues.
  - Caveat: social security revenue collected and administered by private institutions is not included; social security revenue collected by the Government is included. As a consequence, countries such as the USA and Chile, with an important level of private social security collection might be closer to its maximum tax capacity than what the analysis shows.
  - Source: World Economic Outlook and official websites.

- Lgd: the log GDP per capita, purchasing power parity constant 2005.
  - Source: World Bank World Development Indicators (WDI).

- Lgd2: lgd square; included to capture the presumably non-linear elasticity between tax revenue and per capita GDP.

- TR: trade (imports plus exports) as percent of GDP; reflects the degree of openness of an economy.
  - Source: WDI.

- AVA: value added of the agriculture sector as percent of GDP; used to represent how easy (or not) it is to collect taxes.
  - Source: WDI.
  - Footnote 14: Due to political reasons, some countries exempt agricultural products from VAT as well as agricultural producers from the income tax. Moreover, this sector is difficult to control particularly when it is composed of small producers.

- PE: total public expenditure on education as percent of GDP; represents the level of education.
  - Sources: WDI and FAD statistics.
  - Footnote 15: Other variables could reflect better the level of people’s education; however, data sometimes are not available for all countries. On other occasions, some variables are not useful for comparison. For instance, labor force with secondary education (percent of total) was not available for some countries, and secondary education significantly differs among countries.

- GINI coefficient: measures the extent to which the distribution of income among individuals deviates from the equal distribution.
  - Source: WDI.

- CPI: the percentage change of consumption price index.
  - Source: WDI.

- Lcor: the log of the corruption perception index.
  - Rationale: chosen to represent inefficiencies (examples: corruption, weak tax administrations, government ineffectiveness, low enforcement) that can prevent countries from reaching their tax frontier.
  - Source: Transparency International.

### Data and measurement notes
- Revenue concept: Tax and pension contributions revenue are measured as percent of GDP and used to construct Ltot (log of the sum).
- Reporting heterogeneity: A Gov dummy (Gov=1 consolidated; Gov=0 central only) is used to flag countries with different revenue reporting bases.
- Omitted components: Private-administered social security collections are excluded from revenue totals; government-collected social security is included.
- Nonlinear specification: The squared log of per capita GDP (Lgd2) is included to capture non-linearities in the relationship between tax revenue and income per capita.

### Table / dataset structure (as presented in subsequent appendices)
- The Appendix provides country-level observations with variables including:
  - Total Revenue (tax and social contributions as percent of GDP) and Year.
  - Per capita GDP, PPP 2005.
  - Model estimates and measures: Mundlak REM, Half Normal, Truncated Normal, TNH / 2 results for Tax Effort and Tax Capacity.
  - Notes on estimation: 1/ Tax and social contributions as percent of GDP. 2/ Truncated Normal Heterogeneous in Mean and Decay Inefficiency. 3/ Tax capacity (percent of GDP): tax and social contributions divided by tax effort.

*Source: _wp13244 - Appendix 1. Variables and Data Source*

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