Posterior Average Effects

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.

经济学家通常致力于基于不可观测变量的分布估计各类均值，例如个体固定效应的矩，或是离散选择模型（discrete choice models）中的平均偏效应。针对这类量化指标，我们提出并研究了后验平均效应（posterior average effects，PAE），其遵循经验贝叶斯（empirical Bayes）与收缩估计方法的思路，基于样本条件化计算均值。尽管收缩估计在预测任务中的应用价值已得到充分证实，但目前仍缺乏针对后验条件化方法用于估计总体均值的理论依据。我们证明，在不可观测变量的参数分布存在多种形式设定错误（misspecification）的场景下，PAE具备最小的最坏情况设定误差（worst-case specification error）。此外，我们还提出了一种后验条件化信息量测度，用于量化PAE相较于基于参数模型的估计量（parametric model-based estimators）的最坏情况设定误差。作为示例，我们汇报了美国邻里效应分布、以及收入动态模型中永久性与暂时性收入成分分布的PAE估计结果。