A Python Framework For Analyzing Dependent-Variable Laws Of Large Numbers Convergence: Testing Sectoral Surplus Value Rate Uniformity

This paper develops a comprehensive Python framework for analyzing the convergence of sectoral surplus value rates through multiple approaches to the Law of Large Numbers (LLN), specifically addressing dependent-variable scenarios. We implement and compare three distinct methodologies: triangular arrays, weighted sums with dependent variables, and mixingale processes, each offering unique insights into different aspects of convergence behavior. Our framework incorporates flexible convergence thresholds, detailed difference analysis, and sophisticated Excel reporting capabilities. The results reveal a complex pattern of sectoral convergence. While traditional approaches (triangular arrays and mixingale processes) indicate persistent sectoral differences, the weighted sums method, which explicitly accounts for inter-sectoral correlations, shows evidence of convergence at certain thresholds. This divergence in results suggests the existence of what we term “network uniformity” - a phenomenon where sectors, while maintaining individual characteristics, exhibit systematic convergence patterns when their interconnections are properly weighted. Our findings challenge conventional interpretations of sectoral rate uniformity, suggesting that modern economies might exhibit more sophisticated forms of convergence than traditionally theorized. The framework demonstrates that understanding sectoral relationships, rather than individual sector behaviors, is crucial for accurate economic analysis. These results have significant implications for economic policy and forecasting, particularly in highly interconnected modern economies. Additionally, the study provides methodological insights for analyzing dependent-variable scenarios in economic research, offering a robust computational approach for testing economic theories of sectoral behavior.