短面板中随机系数的矩

中文摘要 AI 辅助

我们研究短线性面板中随机系数矩的识别与估计，允许异质系数的数量超过每个单位观测到的方程数量。在矩齐性条件下，不同的回归变量历史对同一矩向量施加约束。我们基于回归变量支撑生成的行空间，给出这些约束识别给定阶数矩的充要条件。结果表明，即使无法恢复任何个体的系数，矩也可能被识别；对于两个满行秩历史，我们给出其行空间重叠导致的独立约束损失的精确值。当支撑条件不成立时，我们确立了所维护模型中的非识别性，并刻画了这些条件矩隐含的尖锐识别集。在二阶下，识别集由半正定协方差约束确定，且相对于结果与回归变量的联合分布也是尖锐的。在支撑条件下，加权最小距离估计量服从根N渐近正态分布；在条件非退化下， oracle广义逆加权可达到Chamberlain（1987）针对所维护条件矩模型的效率边界。

英文摘要

We study identification and estimation of moments of random coefficients in short linear panels, allowing the number of heterogeneous coefficients to exceed the number of equations observed for each unit. Under moment homogeneity, different regressor histories impose restrictions on the same moment vector. We give necessary and sufficient conditions for these restrictions to identify moments of a given order, stated in terms of the row spaces generated by the regressor support. The results show that moments may be identified even when the coefficients cannot be recovered for any individual, and, for two full-row-rank histories, give the exact loss of independent restrictions caused by overlap of their row spaces. When the support condition fails, we establish nonidentification in the maintained model and characterize the sharp identified set implied by these conditional moments. At second order, the identified set is determined by positive-semidefinite covariance restrictions and is also sharp relative to the full joint distribution of outcomes and regressors. Under the support condition, weighted minimum-distance estimators are root-$N$ asymptotically normal; under conditional nondegeneracy, oracle generalized-inverse weighting attains the Chamberlain (1987) efficiency bound for the maintained conditional-moment model.

发表机构

• McMaster University（麦克马斯特大学）
• University of Arizona（亚利桑那大学）

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