Partial Identification with Multiple Nonlinear Measurements of a Latent Regressor
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潜在解释变量具有多个非线性测量时的部分识别
- 研究问题
- 当解释变量只能通过多个带噪声且可能非线性的指标观测时，如何协调指标差异、固定潜在尺度并限定结构回归系数的范围？
- 方法与思路
- 作者要求共识测量函数线性，并限制各来源相对斜率的曲率差异，构造闭式识别区间，结合分割工具辅助回归与置信区间。
- 材料陈述的贡献
- 摘要称，识别区间不受未知来源载荷影响，宽度具有二阶性质；至少四个测量可估计曲率界，并将方法用于 AI 暴露指标协调。
- 阅读关注点
- 应核对共识尺度归一化与曲率限制的依据、测量数量要求、边界处一致覆盖，以及剔除不同构念指标的事前规则。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；完整条件与系数单位未说明，作者明确将应用解释为测量协调而非因果效应。
原文摘要
We study linear regression when the regressor is latent and observed only through multiple noisy measurements, each a smooth but possibly nonlinear function of the latent variable. The problem is acute in the measurement of occupational exposure to artificial intelligence, where competing scores yield downstream estimates that differ by a factor of eleven. A regression on any single measurement recovers a source-specific coefficient rather than the structural one. We fix the latent scale by requiring the consensus measurement function to be linear and bound the remaining curvature heterogeneity across sources relative to slope. Under this bound, the structural coefficient lies in a closed-form interval centered at a symmetric cross-source estimator. The interval is invariant to unknown source loadings, and its half-width is second order in the curvature bound and sharp to the same order. With at least four measurements, the bound is estimable from the joint distribution of the sources through a split-instrument auxiliary regression, and Imbens-Manski confidence intervals with the Stoye critical value attain uniform coverage over the curvature class, including at the point-identified boundary. The application matches six exposure measures to an American Community Survey panel of 8.88 million person-year observations for 2015 to 2024. The post-2022 employment coefficient changes sign between the language-model measures and the Webb patent-text measure, and an ex ante factor-analytic rule separates the Webb measure as a distinct construct. The five retained sources yield a loading-invariant consensus coefficient of -0.239, with a partial-identification half-width of 1.23 percent of the point estimate, or 1.88 percent at the one-sided 95 percent upper bound on the curvature. We read the application as measurement reconciliation rather than as a causal estimate of AI displacement.