An empirical analysis of worldwide impunity

The paper examines impunity—the absence of punishment for legal violations—as a pervasive phenomenon that undermines justice, trust in institutions, and the rule of law, and can perpetuate inequality, corruption, and violence. The authors argue that impunity levels vary across countries in line with socioeconomic conditions, institutional performance, and cultural factors. Given the difficulty of drawing causal inferences from observational data with potential unobserved confounding, the study adopts a predictive approach. The research question is how to predict expected levels of impunity from a set of economic and social development indicators and use these expectations to classify countries as over- or underperformers relative to their contexts. The study posits that, as countries develop, institutions become more effective and impersonal, reducing impunity. The work aligns conceptually with Modernization Theory (e.g., Rostow’s stages), but does not aim to test it. Instead, it operationalizes seven development-related dimensions to predict a doubly bounded impunity index and compares observed and expected levels to identify countries whose impunity is lower or higher than predicted, highlighting notable cases like the Nordic countries (lower than expected) and the United States (higher than expected).

The study situates impunity within broader literatures on rule of law, corruption, and modernization. Prior work links economic development and long-term exposure to democracy with lower corruption (Treisman 2000), and highlights impunity’s social costs (Snyder and Vinjamuri 2003). Modernization Theory and Rostow’s stages suggest that industrialization, urbanization, and technological progress strengthen institutions, enhance rule of law, reduce corruption, and thereby decrease impunity (Inglehart and Welzel 2005; Rostow 1990). The authors also reference evidence on Protestant influence and institutional quality (La Porta et al. 1999; Treisman 2000). Methodologically, they draw on the beta regression literature for bounded outcomes (Ferrari and Cribari-Neto 2004; Cribari-Neto and Zeileis 2010; Douma and Weedon 2019; Smithson and Merkle 2014) and residual diagnostics (Espinheira et al. 2007). Additional contextual works address inequality and political influence (Bartels 2016) and public sphere dynamics (Habermas 1989). The paper leverages these literatures as conceptual background while focusing on predictive modeling rather than causal testing.

Study design: Cross-sectional predictive modeling of impunity across 119 countries (n=119). The response is a doubly bounded index in (0,1), motivating beta regression with varying precision.

Outcome: Impunity Index = 1 − World Justice Project (WJP) Rule of Law Index (2023). Higher values denote higher impunity. The measure correlates highly (0.9434) with the Atlas of Impunity index.

Predictors (seven dimensions of socioeconomic development):

• Economic Freedom Index (2022), The Heritage Foundation.
• Gini Index of income inequality (2015), IndexMundi.
• Health expenditure (% of GDP, 2020), World Bank/WHO.
• Human Development Index (HDI, 2019), Our World in Data.
• GDP per capita (thousands of USD, 2018), World Bank.
• Press Freedom Index (0–100, 2023), Reporters Without Borders.
• Democracy Quality Index (0–1, 2020), Democracy Matrix (V-Dem based).

Descriptive statistics of Impunity Index: min 0.10, max 0.69, mean 0.4447, median 0.49, SD 0.1488, skewness 0.6174, kurtosis 2.3343; Q1 0.335, Q3 0.55. Top five by lowest impunity: Denmark (0.10), Norway (0.11), Finland (0.13), Sweden (0.15), Germany (0.17). Worst five: Cambodia (0.69), DR Congo (0.66), Haiti (0.66), Cameroon (0.65), Egypt (0.65).

Modeling framework: Beta regression for bounded responses Y_i ~ Beta(μ_i, φ_i) with E[Y_i] = μ_i and Var[Y_i] = μ_i(1−μ_i)/(1+φ_i). Two linked submodels:

• Mean submodel with probit link: Φ^{-1}(μ_i) = linear predictor in covariates, including interactions.
• Precision submodel with square-root link: sqrt(φ_i) = linear predictor (intercept plus one covariate).

Model selection: Implemented in R (betareg package). Considered alternative link choices, untransformed and transformed regressors, and interactions. Two-step selection: (1) retain models having all residuals within half-normal simulated envelopes (100 simulations with 2.5%/97.5% bands), significant regressors at 5% in both submodels, and no pattern in precision vs mean linear predictor plots; (2) compare retained models via AIC, BIC, and Nagelkerke’s pseudo-R², choosing the best.

Selected specification: Mean (probit) submodel included Economic Freedom (x2), Gini (x3), HDI (x15), the interaction HDI × Health Expenditure (x15×x16), and the interaction Democracy Quality × Press Freedom (x17×x18). Precision (sqrt link) included an intercept and one covariate; γ2 was significant. Estimated precisions ranged roughly from 25 to 167.

Estimation and inference: Maximum likelihood via Newton/quasi-Newton optimization. Assessed significance with z-tests and likelihood ratio tests; checked multicollinearity via VIF (max 2.9199). Goodness of fit: AIC = −383.4993, BIC = −361.2663, pseudo-R² = 0.9079. Residual diagnostics: all residuals within simulated envelopes, supporting correct specification. Gini was marginally significant at 5%; removing it produced envelope violations, so it was retained.

Nordic indicator extension: Added a dummy for Denmark, Finland, Norway, Sweden to assess systematic overperformance. Dummy significant at 1% (coefficient −0.1761). Including it reduced average predicted impunity for the Nordics from 0.1530 to 0.1236 (~20% reduction). Gini’s significance dropped below 5% but remained significant at 10%; diagnostics remained satisfactory.

Elasticity analysis: Derived analytic expressions for elasticities of mean impunity with respect to each regressor and computed them under three scenarios reflecting less developed (high Gini; low other covariates), median, and more developed (low Gini; high other covariates) settings. Also bootstrapped standard errors for selected elasticity points (B = 1000 resamples).

• Signs and significance: Holding other factors constant, higher income concentration (Gini) is associated with higher mean impunity; higher economic freedom, GDP per capita, health expenditure, HDI, democracy quality, and press freedom are associated with lower mean impunity. All retained regressors were significant at 5% in the main model; Gini was marginal at 5% but necessary for specification.
• Model fit: Pseudo-R² = 0.9079; AIC = −383.4993; BIC = −361.2663; VIF max = 2.9199; residual diagnostics acceptable. The democracy × press freedom interaction was most influential; removing it reduced pseudo-R² to 0.8521.
• Predicted vs observed: Overall close alignment; 59 countries overperform (observed impunity below predicted) and 60 underperform (above predicted). Notable deviations: • Highest positive residuals (worse than expected): Cambodia (obs 0.69; pred 0.5936; resid 0.0964), United States (0.30; 0.2137; 0.0863), Trinidad and Tobago (0.48; 0.3957; 0.0843), Mexico (0.58; 0.4981; 0.0819), Hungary (0.49; 0.4136; 0.0764). • Lowest residuals (better than expected): Rwanda (0.37; 0.5863; −0.2163), China (0.53; 0.6390; −0.1090), Algeria (0.51; 0.6024; −0.0924), Zimbabwe (0.60; 0.6907; −0.0907), Uzbekistan (0.50; 0.5823; −0.0823).
• United States: Observed impunity lies near the 0.99 quantile of its predicted beta density, implying much higher impunity than expected given its development indicators; approximately 40% above expected.
• Nordic countries: Lower impunity than expected. Including a Nordic dummy reduces their predicted impunity by ~20% on average (from 0.1530 to 0.1236). Quantiles of observed impunity in predicted densities (with dummy): Denmark 0.17, Finland 0.34, Norway 0.72, Sweden 0.78.
• Countries with lowest predicted impunity: Luxembourg, Norway, Ireland, Denmark, Sweden, Netherlands, Finland, Germany, Australia, New Zealand; most Nordic countries both have low predicted and even lower observed impunity (negative residuals), except Netherlands also overperforms among non-Nordics.
• Elasticities (scenario analysis): Only Gini elasticity is positive; all others are negative. Responsiveness is larger in more developed settings. Impact tiers (max absolute elasticities under favorable conditions): • High: Economic freedom and GDP per capita (−1.2), implying a 1% improvement can reduce mean impunity by more than 1%. • Medium: Democracy quality and press freedom (−0.7). • Low: Health expenditure (−0.25) and HDI (−0.14). Press freedom exhibits the largest gap in responsiveness between least and most developed scenarios.
• Nordic vs other developed (scenario 3): Impunity is more responsive to unit percentage improvements in all regressors for Nordic countries; increases in inequality (Gini) raise impunity more sharply there as well.
• Out-of-sample illustration: Predicted expected impunity (no Nordic dummy model): Israel 0.3324, Switzerland 0.1171. Atlas of Impunity values 0.3814 and 0.1327 exceed expectations by about 15% and 13%, suggesting underperformance.
• Bootstrap example (economic freedom at mean = 62): scenario 1 elasticity −0.5388 (SE 0.0911), scenario 2 −0.6203 (SE 0.1008), scenario 3 −0.7566 (SE 0.1162).

The predictive beta regression framework effectively captures how seven dimensions of socioeconomic development map onto expected national impunity levels, enabling a country-specific benchmark for performance assessment. The results support the premise that development—via economic freedom, income, democratic quality, and press freedom—aligns with lower expected impunity, while higher income concentration aligns with higher impunity. The strong fit (pseudo-R² ≈ 0.91) and robust diagnostics lend credibility to the model’s predictive utility. Identifying overperformers (e.g., Nordic countries, Rwanda) and underperformers (e.g., the United States, Cambodia) relative to expected levels provides actionable intelligence for policymakers to investigate structural drivers beyond headline development indicators. Elasticity analyses show that improvements in key domains have larger proportional impacts in more advanced societies, indicating that institutional consolidation amplifies the benefits of reforms (especially press freedom). The Nordic dummy analysis suggests systematic overperformance beyond what measured predictors capture, possibly reflecting additional institutional, cultural, or historical factors. Conversely, the United States’ impunity substantially exceeds expectations, consistent with complex social and institutional dynamics discussed by the authors. Overall, the findings address the research aim by furnishing expected impunity baselines and revealing where countries diverge meaningfully from those baselines.

The study introduces a high-performing predictive framework (beta regression with varying precision) to estimate expected impunity from seven development-related dimensions and to benchmark countries as over- or underperformers relative to their contexts. Key insights are that economic freedom and per capita income are the most influential predictors (highest elasticities), followed by democracy quality and press freedom; HDI and health spending have smaller impacts. Inequality (Gini) increases expected impunity. Nordic countries systematically exhibit lower-than-expected impunity, while the United States displays higher-than-expected levels. Elasticity patterns indicate that reforms yield larger proportional gains in more developed institutional environments. Future research directions include country-specific deep dives to uncover unmeasured factors driving over- or underperformance and exploring additional predictors or temporal dynamics to enhance predictive accuracy.

The analysis is predictive and cross-sectional; it does not establish causal relationships between development indicators and impunity. Results reflect associations conditional on the chosen indices and years (e.g., WJP 2023, Gini 2015, HDI 2019, GDP per capita 2018, etc.), which may introduce temporal misalignment. Some institutional or cultural determinants may be unobserved, as suggested by the Nordic dummy’s significance. The sample covers 119 countries; external validity beyond this set depends on the availability and comparability of predictor data. While model diagnostics were favorable, results remain contingent on specification (e.g., interactions) and the quality of underlying indices and surveys.