Estimation of Models with Multiple-Valued Explanatory Variables

We study estimation and inference when there are multiple values (“matches”) for the explanatory variables and only one of the matches is the correct one. This problem arises often when two datasets are linked together on the basis of information that does not uniquely identify regressor values. We offer a set of two intuitive conditions which ensure consistent inference using the average of the possible matches in a linear framework. The first condition is the exogeneity of the false match with respect to the regression error. The second condition is a notion of exchangeability between the true and false matches. Conditioning on the observed data, the probability that each match is correct is completely unrestricted. We perform a Monte Carlo study to investigate the estimator's finite-sample performance relative to others proposed in the literature. Finally, we provide an empirical example revisiting a main area of application: the measurement of intergenerational elasticities in income.

我们研究了当解释变量存在多个匹配值，且仅其中一个匹配为正确匹配时的估计与推断问题。当两类数据集基于无法唯一识别回归元取值的信息进行连接时，该问题会频繁出现。我们提出两条直观条件，确保在线性框架下利用所有可能匹配值的均值进行推断时可获得一致估计。第一条条件为错误匹配与回归误差满足外生性；第二条条件为真实匹配与错误匹配间存在可交换性。在观测数据的条件下，每个匹配为正确匹配的概率完全不受限制。我们开展蒙特卡洛研究，对比本文所提估计量与文献中其他估计量的有限样本表现。最后，我们提供一个实证案例，重新审视该方法的核心应用领域之一：代际收入弹性的测算。