Multiscale adaptive inference on conditional moment inequalities

Armstrong, Timothy B.; Chan, Hock Peng

doi:10.1016/j.jeconom.2016.04.001

Cited by 51 publications

(55 citation statements)

References 31 publications

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“…78 I refer to Andrews and Shi (2013), Chernozhukov, Lee, and Rosen (2013), Lee, Song, and Whang (2013), Armstrong (2014Armstrong ( , 2015, Armstrong and Chan (2016), Chernozhukov, Chetverikov, and Kato (2018), and Chetverikov (2018), for inference methods in the case that the conditioning variables have a continuous distribution.…”

Section: Framework and Scope Of The Discussionmentioning

confidence: 99%

“…;Andrews and Soares (2010);Canay (2010);Andrews and Barwick (2012);Romano, Shaikh, and Wolf (2014), among others, make significant contributions to circumvent these difficulties in the context of a finite number of unconditional moment (in)equalities Andrews and Shi (2013)Chernozhukov, Lee, and Rosen (2013);Lee, Song, and Whang (2013);Armstrong (2014Armstrong ( , 2015;Armstrong and Chan (2016);Chetverikov (2018), among others, make significant contributions to circumvent these difficulties in the context of a finite number of conditional moment (in)equalities (with continuously distributed conditioning variables) Chernozhukov, Chetverikov, and Kato (2018). and study, respectively, the challenging frameworks where the number of moment inequalities grows with sample size and where there is a continuum of conditional moment inequalities.…”

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confidence: 99%

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Econometrics with Partial Identification

Molinari¹

2019

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Econometrics has traditionally revolved around point identification. Much effort has been devoted to finding the weakest set of assumptions that, together with the available data, deliver point identification of population parameters, finite or infinite dimensional that these might be. And point identification has been viewed as a necessary prerequisite for meaningful statistical inference. The research program on partial identification has begun to slowly shift this focus in the early 1990s, gaining momentum over time and developing into a widely researched area of econometrics. Partial identification has forcefully established that much can be learned from the available data and assumptions imposed because of their credibility rather than their ability to yield point identification. Within this paradigm, one obtains a set of values for the parameters of interest which are observationally equivalent given the available data and maintained assumptions. I refer to this set as the parameters' sharp identification region. Econometrics with partial identification is concerned with: (1) obtaining a tractable characterization of the parameters' sharp identification region; (2) providing methods to estimate it; (3) conducting test of hypotheses and making confidence statements about the partially identified parameters. Each of these goals poses challenges that differ from those faced in econometrics with point identification. This chapter discusses these challenges and some of their solution. It reviews advances in partial identification analysis both as applied to learning (functionals of) probability distributions that are well-defined in the absence of models, as well as to learning parameters that are well-defined only in the context of particular models. The chapter highlights a simple organizing principle: the source of the identification problem can often be traced to a collection of random variables that are consistent with the available data and maintained assumptions. This collection may be part of the observed data or be a model implication. In either case, it can be formalized as a random set. Random set theory is then used as a mathematical framework to unify a number of special results and produce a general methodology to conduct econometrics with partial identification.

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Section: Framework and Scope Of The Discussionmentioning

confidence: 99%

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confidence: 99%

Econometrics with Partial Identification

Molinari¹

2019

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“…, the variance of m(Y, Z)w z,h (Z). This is the test statistic used in Armstrong and Chan (2016), up to a minor modification that they use infinite sets Z n and H n . Since they couple the test statistic T with the (1 − α) quantile of the asymptotic distribution of T when E[m(Y, Z)|Z] = 0 almost surely, it follows that the power of their test essentially coincides with that of our one-step bootstrap tests, which can be improved by using our two-step and three-step bootstrap tests.…”

Section: Powermentioning

confidence: 99%

Inference on causal and structural parameters using many moment inequalities

Chernozhukov

Chetverikov

Kato

2018

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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.

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“…Moment inequality selection methods and corresponding methods of inference based on GMM-type estimators are developed in Andrews and Guggenberger (2009), Andrews and Soares (2010) and Andrews and Barwick (2012). Extensions of GMM to conditional moment inequality models have also been considered; see, e.g., Shi (2013, 2014), Armstrong (2014Armstrong ( , 2015, Armstrong and Chan (2016) and Khan and Tamer (2009). Misspeci ed moment inequalities are studied in Ponomareva and Tamer (2011) and Bugni et al (2012).…”

Section: Introductionmentioning

confidence: 99%

GEL-based inference with unconditional moment inequality restrictions

Grant¹,

Smith²

2018

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This paper studies the properties of generalised empirical likelihood (GEL) methods for the estimation of and inference on partially identi ed parameters in models speci ed by unconditional moment inequality constraints. The central result is, as in moment equality condition models, a large sample equivalence between the scaled optimised GEL objective function and that for generalised method of moments (GMM) with weight matrix equal to the inverse of the e cient GMM metric for moment equality restrictions. Consequently, the paper provides a generalisation of results in the extant literature for GMM for the non-diagonal GMM weight matrix setting. The paper demonstrates that GMM in such circumstances delivers a consistent estimator of the identi ed set, i.e., those parameter values that satisfy the moment inequalities, and derives the corresponding rate of convergence. Based on these results the consistency of and rate of convergence for the GEL estimator of the identi ed set are obtained. A number of alternative equivalent GEL criteria are also considered and discussed. The paper proposes simple conservative consistent con dence regions for the identi ed set and the true parameter vector based on both GMM with a non-diagonal weight matrix and GEL. A simulation study examines the e cacy of the non-diagonal GMM and GEL procedures proposed in the paper and compares them with the standard diagonal GMM method.

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Multiscale adaptive inference on conditional moment inequalities

Cited by 51 publications

References 31 publications

Econometrics with Partial Identification

Econometrics with Partial Identification

Inference on causal and structural parameters using many moment inequalities

GEL-based inference with unconditional moment inequality restrictions

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