The fact that the intergenerational income elasticity (IGE)—the workhorse measure of economic mobility—is defined in terms of the geometric mean of children’s income generates serious methodological problems. This has led to a call to replace it with the IGE of the expectation, which requires developing the methodological knowledge necessary to estimate the latter with short-run measures of income. This article contributes to this aim. The author advances a “bracketing strategy” for the set estimation of the IGE of the expectation that is equivalent to that used to set estimate (rather than point estimate) the conventional IGE with estimates obtained with the ordinary least squares and instrumental variable (IV) estimators. The proposed bracketing strategy couples estimates generated with the Poisson pseudo–maximum likelihood estimator and a generalized method of moments IV estimator of the Poisson or exponential regression model. The author develops a generalized error-in-variables model for the IV estimation of the IGE of the expectation and compares it with the corresponding model underlying the IV estimation of the conventional IGE. By considering both bracketing strategies from the perspective of the partial-identification approach to inference, the author specifies how to construct confidence intervals for the IGEs, in particular when the upper bound is estimated more than once with different sets of instruments. Finally, using data from the Panel Study of Income Dynamics, the author shows that the bracketing strategies work as expected and assesses the information they generate and how this information varies across instruments and short-run measures of parental income. Three computer programs made available as companions to the article make the set estimation of IGEs, and statistical inference, very simple endeavors.

中文翻译：

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代际收入弹性、工具变量估计和括号策略

代际收入弹性（IGE）——经济流动性的主要衡量标准——是根据儿童收入的几何平均数来定义的，这一事实产生了严重的方法论问题。这导致人们呼吁用预期的 IGE 取代它，这需要发展必要的方法论知识，以用短期收入衡量指标估计后者。本文有助于实现这一目标。作者提出了一种“括号策略”，用于期望的 IGE 的集合估计，该策略等效于用于设置估计（而不是点估计）的常规 IGE，其中使用普通最小二乘法和工具变量 (IV) 获得的估计估计器。所提出的括号策略将使用泊松伪最大似然估计量生成的估计值和泊松或指数回归模型的矩 IV 估计量的广义方法结合起来。作者为期望的 IGE 的 IV 估计开发了一个广义的变量误差模型，并将其与作为常规 IGE 的 IV 估计基础的相应模型进行了比较。通过从推理的部分识别方法的角度考虑这两种括号策略，作者指定了如何构建 IGE 的置信区间，特别是当使用不同的工具集多次估计上限时。最后，使用收入动态小组研究的数据，作者表明，括号法按预期工作，并评估了它们生成的信息以及这些信息在不同工具和短期父母收入指标之间的差异。随文章一起提供的三个计算机程序使 IGE 的集合估计和统计推断变得非常简单。