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 of these assumptions is violated, we provide semiparametrically efficient treatment effect estimators. However, our no-free-lunch theorem highlights the necessity of accurately identifying the violated assumption for consistent treatment effect estimation. Through comparative analyses, we show our framework's superiority over existing data fusion methods. The practical utility of our approach is further exemplified by three real-world case studies, underscoring its potential for widespread application in empirical research.

翻译：实验研究和观测研究常因无法验证的假设而缺乏有效性。我们提出一种双机器学习方法，用于结合实验研究和观测研究，使从业者能够检验假设违规情况并一致地估计处理效应。我们的框架在较温和的假设下检验外部有效性和不可忽略性的违规情况。当仅违反其中一个假设时，我们提供半参数有效的处理效应估计量。然而，我们的“无免费午餐”定理强调了准确识别违规假设对于一致估计处理效应的必要性。通过比较分析，我们展示了该框架相对于现有数据融合方法的优越性。三个真实案例研究进一步例证了该方法的实用价值，突显其在实证研究中的广泛应用潜力。