Experimental and observational studies often lack validity due to untestable
assumptions. We propose a double machine learning approach to combine
experimental and observational studies, allowing practitioners to test for
assumption violations and estimate treatment effects consistently. Our
framework tests for violations of external validity and ignorability under
milder assumptions. When only one assumption is violated, we provide
semi-parametrically efficient treatment effect estimators. However, our
no-free-lunch theorem highlights the necessity of accurately identifying the
violated assumption for consistent treatment effect estimation. We demonstrate
the applicability of our approach in three real-world case studies,
highlighting its relevance for practical settings.

本文提出了一种双机器学习方法，以结合实验和观测研究，让从业人员能够测试假设的违规情况并一致地估计治疗效果，进而测试外部效度和忽略的可接受性。然而，我们的无免费午餐定理强调了准确识别被违反的假设对于一致的治疗效果估计的必要性。我们在三个实际案例研究中展示了我们的方法的适用性，并突出了其在实际设置中的相关性。