## 5 Real-World Application: Government Debt Analysis  
### Dataset Description  
To demonstrate the practical efficacy of our Hamming diversification index methodology, we apply our framework to the Comparative Political Data Set (CPDS) spanning from 1960 to 2022. This comprehensive dataset, curated by [39], provides a robust foundation for analyzing temporal patterns in economic indicators across multiple countries over an extended period.  
The CPDS dataset contains  
* **Temporal Coverage**: 63 years of annual observations (1960-2022);
* **Geographic Scope**: 36 developed economies;
* **Feature Dimensions**: 335 variables covering political, economic, and social indicators;
* **Primary Variable**: Government debt as percentage of GDP ( debt_hist_).  
Government debt trajectories, for instance, provide valuable insights into fiscal policy effectiveness, crisis responses, and long-term sustainability patterns [17; 40]. However, traditional econometric approaches often struggle to capture the categorical nature of policy regimes and the discrete transitions between different fiscal states that characterize real-world policy evolution [18]. For our analysis, we selected eight representative countries that demonstrate diverse fiscal trajectories and economic philosophies, enabling comprehensive evaluation across different debt-to-GDP categories as identified in the empirical literature [17; 41]:  
**High-Debt Trajectory Countries**:
* **United States**: Post-2008 financial crisis debt accumulation, with debt-to-GDP ratio reaching approximately 133% by recent estimates [17], reflecting extensive stimulus policies and structural fiscal challenges;
* **Japan**: Sustained exceptionally high debt levels exceeding 250% of GDP, primarily driven by demographic challenges and prolonged economic stagnation following the 1990s asset price bubble collapse [42];
* **United Kingdom**: Variable debt patterns significantly influenced by economic cycles, financial sector developments, and Brexit-related uncertainties [41];
* **France**: Gradual debt increases reflecting comprehensive welfare state policies and counter-cyclical fiscal responses, consistent with continental European fiscal approaches [18];
* **Germany**: Moderate debt levels maintained through institutional fiscal discipline, particularly following reunification adjustments and European fiscal coordination mechanisms.  
**Fiscally Conservative Countries**:
* **Denmark**: Consistent fiscal discipline achieved through structural reforms and adherence to European stability frameworks, maintaining debt levels well below the 60% GDP threshold established by the Stability and Growth Pact;
* **Switzerland**: Traditional low-debt approach supported by constitutional fiscal rules and decentralized fiscal governance structures, with debt-to-GDP ratio around 32% [41];
* **Norway**: Resource-wealth management through sovereign wealth fund mechanisms, enabling counter-cyclical fiscal policies while maintaining relatively low net debt positions despite gross debt levels around 55% of GDP [43].  
This balanced selection enables comprehensive evaluation of our methodology across different economic models and fiscal philosophies, ensuring robust testing of the Hamming diversification index across diverse evolutionary trajectories. The country selection reflects the empirical literature on fiscal policy variations, incorporating both high-debt economies experiencing fiscal stress and conservative fiscal regimes maintaining sustainable debt dynamics [17; 18].