Inference on causal and structural parameters using many moment inequalities
利用大量矩不等式推断因果与结构参数AI 解读 ↓
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利用大量矩不等式推断因果与结构参数
- 研究问题
- 当矩不等式数量远超样本量时，如何对因果与结构参数构造有效检验，并处理统计量相关性及不等式的信息差异？
- 方法与思路
- 作者使用学生化统计量的最大值，比较联合界、乘子与经验 bootstrap 临界值，并构造筛除不具或弱具信息不等式的多步程序。
- 材料陈述的贡献
- 摘要称，在相应条件下尺寸误差随样本量多项式下降，可容许指数级不等式数量且不限制统计量相关结构，并扩展至依赖数据。
- 阅读关注点
- 应核对维度增长与矩条件、不等式筛选规则及其有效性，以及补充材料中块乘子 bootstrap 所需的混合条件。
- 阅读边界
- 所据为 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未列完整条件，对相关结构不加限制不等于无需其他分布条件。
原文摘要
This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters, a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of $p$ Studentized (or $t$-type) inequality-specific statistics, and analyze various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (i) the union bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier and empirical bootstraps, and (iii) two-step and three-step variants of (i) and (ii) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in $n$ while allowing for $p$ being much larger than $n$, indeed $p$ can be of order $\exp (n^{c})$ for some $c > 0$. Importantly, all these results hold without any restriction on the correlation structure between $p$ Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions.