Posterior Average Effects
提出后验平均效应（PAE）方法，用于估计不可观测变量的分布平均值，如个体固定效应或离散选择模型中的平均偏效应，证明其在模型误设下具有最小最坏情况规范误差，并应用于美国邻里效应和收入动态分析。
Economists are often interested in estimating averages with respect to distributions of unobservables, such as moments of individual fixed-effects, or average partial effects in discrete choice models. For such quantities, we propose and study posterior average effects (PAE), where the average is computed conditional on the sample, in the spirit of empirical Bayes and shrinkage methods. While the usefulness of shrinkage for prediction is well-understood, a justification of posterior conditioning to estimate population averages is currently lacking. We show that PAE have minimum worst-case specification error under various forms of misspecification of the parametric distribution of unobservables. In addition, we introduce a measure of informativeness of the posterior conditioning, which quantifies the worst-case specification error of PAE relative to parametric model-based estimators. As illustrations, we report PAE estimates of distributions of neighborhood effects in the U.S., and of permanent and transitory components in a model of income dynamics.