Abstract：
Estimates of the impact of body mass index and obesity on health and labor market outcomes often use instrumental variables estimation (IV) to mitigate bias due to endogeneity. When these studies rely on survey data that include self- or proxy-reported height and weight, there is non-classical measurement error due to the tendency of individuals to under-report their own weight. Mean reverting errors in weight do not cause IV to be asymptotically biased per se, but may result in bias if instruments are correlated with additive error in weight. We demonstrate the conditions under which IV is biased when there is non-classical measurement error and derive bounds for this bias conditional on instrument strength and the severity of mean-reverting error. We show that improvements in instrument relevance alone cannot eliminate IV bias, but reducing the correlation between weight and reporting error mitigates the bias. A solution we consider is regression calibration (RC) of endogenous variables with external validation data. In simulations, we find IV estimation paired with RC can produce consistent estimates when correctly specified. Even when RC fails to match the covariance structure of reporting error, there is still a reduction in asymptotic bias.
摘要：
体重指数和肥胖对健康和劳动力市场结果的影响的估计通常使用工具变量估计（IV）来减轻由于内生性造成的偏差。当这些研究依赖于包括自我或代理报告的身高和体重在内的调查数据时，由于个人倾向于低估自己的体重，因此存在非经典测量误差。权重的平均回复误差不会导致IV本身渐近偏置，但如果仪器与重量的加性误差相关，可能会导致偏差。我们证明了存在非经典测量误差时IV有偏差的条件，并以仪器强度和均值回复误差的严重程度为条件得出该偏差的界限。我们证明，单靠仪器相关性的改进不能消除IV偏差，但是降低权重和报告错误之间的相关性可以减轻偏差。我们考虑的解决方案是使用外部验证数据对内生变量进行回归校准（RC）。在模拟中,我们发现，如果正确指定，与RC配对的IV估计可以产生一致的估计。即使RC无法匹配报告错误的协方差结构，渐近偏差仍然有所减少。
