世界银行-地方福利的非正态经验贝叶斯预测（英）-2025.4_30页_1mb

Non-Normal Empirical Bayes Prediction of Local Welfare

Problem:
Estimating small-area poverty/income inequality faces challenges from potential violations of normality in error structures. The paper proposes relaxing this assumption.

Key Contributions:

• Uses finite normal mixtures for flexible modeling of error distributions (both area and household components).
• Employs Empirical Bayes estimation under heteroscedasticity.

Findings:

• ELL (non-normal non-Empirical Bayes) and Normal-EB are special cases.
• New method (Non-normal-EB) outperforms both consistently:
  • Reduces RMSE by up to 15-25%.
  • Gains are marginal despite low location effects but always positive.
• Optimal choice depends on:
  • High location effect: Normal-EB (simple stochastically dominant).
  • Low location effect: ELL (ignores spatial correlation).
  • Any setting: Non-normal-EB (robust and easy to use).

Implementation:

• Fits normal mixtures via EM algorithm.
• Easily integrates into standard simulation-based inference frameworks.

Implications:

• Beyond targetting cash transfers, method can aid regressors in empirical analyses.
• Extensible to other non-linear functions of welfare (e.g., Gini inequality).