In over-identified models, misspecification -- the norm rather than exception -- fundamentally changes what estimators estimate. Different estimators imply different estimands rather than different efficiency for the same target. A review of recent applications of generalized method of moments in the American Economic Review suggests widespread acceptance of this fact: There is little formal specification testing and widespread use of estimators that would be inefficient were the model correct, including the use of "hand-selected" moments and weighting matrices. Motivated by these observations, we review and synthesize recent results on estimation under model misspecification, providing guidelines for transparent and robust empirical research. We also provide a new theoretical result, showing that Hansen's J-statistic measures, asymptotically, the range of estimates achievable at a given standard error. Given the widespread use of inefficient estimators and the resulting researcher degrees of freedom, we thus particularly recommend the broader reporting of J-statistics.

翻译：在过度识别模型中，模型误设——作为常态而非例外——从根本上改变了估计量所估计的对象。不同的估计量对应着不同的估计目标，而非对同一目标的不同估计效率。通过对《美国经济评论》中广义矩方法近期应用案例的回顾，我们发现这一事实已被广泛接受：正式的模型设定检验较为少见，而大量使用的估计量在模型正确时本应是低效的，包括"人工筛选"矩条件和权重矩阵的做法。基于这些观察，我们系统梳理并整合了关于模型误设下估计的最新研究成果，为透明稳健的实证研究提供指导原则。同时，我们提出了一项新的理论结果：Hansen的J统计量在渐近意义上度量了在给定标准误差下可达到的估计值范围。鉴于低效估计量的广泛使用及其带来的研究者自由度问题，我们特别建议更广泛地报告J统计量。