Misspecification in Moment Inequality Models: Back to Moment Equalities?
Misspecification in Moment Inequality Models: Back to Moment Equalities?
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矩不等式模型中的错误指定：回到矩不等式？
DOI：
10.1111/j.1368-423x.2010.00332.x
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
E. Tamer
中科院分区：
文献类型：
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作者：
M. Ponomareva;E. Tamer
考虑线性模型E[y| x] = x 'β其中我们有兴趣了解β，给定y和x上的数据，并且当y是测量的区间时;也就是说，我们观察到（[y' 8 y1]，x）使得P（y ∈ [y '8 y1]）= 1。矩不等式程序使用蕴涵E[y 0| x] ≤ x'β ≤ E[y1| x]。与经典回归模型中的最小二乘法相比，使用基于这些矩不等式的目标函数获得的估计值并不提供对潜在的未观察到的条件均值函数的明确近似。最重要的是，在错误指定下，没有参数β满足所有x值的前述不等式，因此基于这些矩不等式的目标函数的最小值通常是紧的。我们构造了线性模型中β的集合估计，当模型错误指定时，它有一个清晰的解释。这些集合基于矩相等模型。我们说明这些集，并将它们与使用基于矩不等式的方法获得的估计进行比较。除了具有区间结果的线性模型之外，我们还分析了具有单调工具假设（MIV）的二进制缺失数据模型，我们发现当这个假设被错误指定时，边界仍然可以是非空的，并且可以不同于通过最大似然法获得的参数。我们还研究了一个二元离散多均衡博弈。总而言之，矩不等式模型中的误设定与矩相等模型中的误设定不同，因此应注意（1）估计值的tecinterpretation和（2）“识别集”的大小。
Consider the linear model E[y | x] = x'β where one is interested in learning about β given data on y and x and when y is interval measured; that is, we observe ([y'8 y1], x) such that P(y ∈ [y'8 y1]) = 1. Moment inequality procedures use the implication E[y0 | x] ≤ x'β ≤ E[y1 | x]. As compared to least squares in the classical regression model, estimates obtained using an objective function based on these moment inequalities do not provide a clear approximation to the underlying unobserved conditional mean function. Most importantly, under misspecification, it is not unusual that no parameter β satisfies the previous inequalities for all values of x, and hence minima of an objective function based on these moment inequalities are typically tight.We construct set estimates for β in the linear model that have a clear interpretation when the model is misspecified. These sets are based on moment equality models. We illustrate these sets and compare them to estimates obtained using moment inequality-based methods. In addition to the linear model with interval outcomes we also analyse the binary missing data model with a monotone instrument assumption (MIV), we find there that when this assumption is misspecified, bounds can still be non-empty, and can differ from parameters obtained via maximum likelihood. We also examine a bivariate discrete game with multiple equilibria. In sum, misspecification in moment inequality models is of a different flavour than in moment equality models, and so care should be taken with (1) the˙interpretation of the estimates and (2) the size of the ‘identified set’.