英文标题：
《Discordant Relaxations of Misspecified Models》
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作者：
D\\\'esir\\\'e K\\\'edagni and Lixiong Li and Isma\\\"el Mourifi\\\'e
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最新提交年份：
2021
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英文摘要：
  In many set-identified models, it is difficult to obtain a tractable characterization of the identified set. Therefore, empirical works often construct confidence regions based on an outer set of the identified set. Because an outer set is always a superset of the identified set, this practice is often viewed as conservative yet valid. However, this paper shows that, when the model is refuted by the data, a nonempty outer set could deliver conflicting results with another outer set derived from the same underlying model structure, so that the results of outer sets could be misleading in the presence of misspecification. We provide a sufficient condition for the existence of discordant outer sets which covers models characterized by intersection bounds and the Artstein (1983) inequalities. We also derive sufficient conditions for the non-existence of discordant submodels, therefore providing a class of models for which constructing outer sets cannot lead to misleading interpretations. In the case of discordancy, we follow Masten and Poirier (2020) by developing a method to salvage misspecified models, but unlike them we focus on discrete relaxations. We consider all minimum relaxations of a refuted model which restores data-consistency. We find that the union of the identified sets of these minimum relaxations is misspecification-robust and has a new and intuitive empirical interpretation.
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中文摘要：
在许多集识别模型中，很难获得识别集的可处理特征。因此，经验工作通常基于识别集的外部集合构造置信区域。因为外部集合总是已识别集合的超集，所以这种做法通常被视为保守而有效。然而，本文表明，当模型被数据驳斥时，一个非空的外部集可能会产生与来自同一底层模型结构的另一个外部集相冲突的结果，因此外部集的结果可能会在存在错误指定的情况下产生误导。我们给出了不协调外集存在的一个充分条件，该外集覆盖了以交界和Artstein（1983）不等式为特征的模型。我们还推导了不协调子模型不存在的充分条件，因此提供了一类构造外部集不会导致错误解释的模型。在不一致的情况下，我们遵循Masten和Poirier（2020）的方法，开发了一种修复错误指定模型的方法，但与他们不同的是，我们专注于离散松弛。我们考虑了一个被驳斥模型的所有最小松弛，它能恢复数据的一致性。我们发现，这些最小松弛的确定集合的并集是错误规定的稳健的，并且有一个新的直观的经验解释。
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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