This paper investigates the distribution of public school expenditures across U.S. school districts using a bayesian maximum entropy model. Covering the period 2000-2016, I explore how inter-jurisdictional competition and household choice influence spending patterns within the public education sector, providing a novel empirical treatment of the Tiebout hypothesis within a statistical equilibrium framework. The analysis reveals that these expenditures are characterized by sharply peaked and positively skewed distributions, suggesting significant socioeconomic stratification. Employing Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling, I fit these patterns into a statistical equilibrium model to elucidate the roles of competition, as well as household mobility and arbitrage in shaping the distribution of educational spending. The analysis reveals how the scale parameters associated with competition and household choice critically shape the equilibrium outcomes. The model and analysis offer a statistical basis for shaping policy measures intended to affect distributional outcomes in scenarios characterized by the decentralized provision of local public goods.

翻译：本文采用贝叶斯最大熵模型，研究了美国各学区公共教育支出的分布特征。基于2000-2016年的面板数据，我在统计均衡框架下探讨了跨辖区竞争与家庭选择如何影响公共教育部门的支出模式，并对蒂伯特假说提供了新颖的实证检验。分析表明，这些支出呈现尖峰正偏态分布特征，揭示了显著的社会经济分层现象。通过贝叶斯推断与马尔可夫链蒙特卡洛（MCMC）抽样方法，我将这些分布模式拟合至统计均衡模型，以阐明竞争机制以及家庭流动性与套利行为对教育支出分布的塑造作用。研究进一步揭示了与竞争和家庭选择相关的尺度参数如何关键性地影响均衡结果。该模型与分析为制定旨在影响地方公共物品去中心化供给情境下分配结果的政策措施提供了统计学基础。