标题： 模拟和预测变量背景下的矩不等式 显示英文标题

标题： Moment Inequalities in the Context of Simulated and Predicted Variables

摘要： 本文探讨了模拟矩对基于矩不等式的推断方法性能的影响。常用的参数置信集是准则函数的水平集，其边界点可能以不规则的方式依赖于样本矩。由于这一特性，模拟误差可以以非标准方式影响推断的表现。特别是，由于模拟误差导致的（一阶）偏差可能会残留在置信集的估计边界中。我们通过蒙特卡洛实验表明，模拟误差可以在小样本情况下显著降低置信集的覆盖率概率。当不等式约束的数量很大时，这种大小扭曲尤为严重。这些结果突显了在矩不等式模型中忽略模拟误差导致的抽样变化的危险性。在使用预测变量的矩不等式模型中也出现了类似的问题。我们提出了一种方法来正确校正这些变化，该方法基于正则化参数空间中矩的交集，并且我们证明所提出的方法在理论上和实践中表现良好。 显示英文摘要

摘要： This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in non-standard ways. In particular, a (first-order) bias due to the simulation errors may remain in the estimated boundary of the confidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can significantly reduce the coverage probabilities of confidence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice.