Inference on Causal and Structural Parameters using Many Moment Inequalities

By Victor Chernozhukov, D. Chetverikov, Kengo Kato. The Review of Economic Studies, 2013

127 citations recorded by the source corpus.

This article 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 analyse various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (1) the union bound combined with a moderate deviation inequality for self-normalized sums, (2) the multiplier and empirical bootstraps, and (3) two-step and three-step variants of (1) and (2) 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.

Subfields: Management Science and Operations Research, Marketing, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/80ac7e0cf70a2c9ab52a7676277bd159bcfd1433

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Citations in the corpus

Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, methodology): “ a growing literature on high-dimensional Gaussian approximation (Chernozhukov et al. (2013), Chernozhukov et al. (2014), Chernozhukov et al. (2015), Chernozhukov et al. (2017b), Zhang and Wu (2017), Chernozhukov et al. (2019a), Chernozhukov et al. (2019b)) by allowing for a panel setting with obser”
High-dimensional central limit theorems by Stein’s method (2020, background): “…random vectors, many articles have been devoted to the development of this subject: For example, see Chernozhukov, Chetverikov and Kato (2017a), Chernozhukov et al. (2019) for generalization to normal approximation on hyperrectangles and improvements of the error bound, Chen (2018), Chen and…”