We develop theoretical foundations for widely used falsification tests for instrumental variable (IV) designs. We characterize these tests as conditional independence tests between negative control variables - proxies for potential threats - and either the IV or the outcome. We find that conventional applications of these falsification tests would flag problems in exogenous IV designs, and propose simple solutions to avoid this. We also propose new falsification tests that incorporate new types of negative control variables or alternative statistical tests. Finally, we illustrate that under stronger assumptions, negative control variables can also be used for bias correction.

翻译：我们为工具变量设计中广泛使用的证伪检验建立了理论基础。我们将这些检验特征化为负对照变量（潜在威胁的代理变量）与工具变量或结果之间的条件独立性检验。研究发现，常规应用这些证伪检验会在外生工具变量设计中标识出问题，并提出了避免此问题的简单解决方案。我们还提出了融合新型负对照变量或替代统计检验的新证伪检验方法。最后，我们论证了在更强假设条件下，负对照变量也可用于偏差校正。