Adaptive test of conditional moment inequalities

Chetverikov, Denis

doi:10.1920/wp.cem.2012.3612

Cited by 68 publications

(120 citation statements)

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“…First, our paper does not cover conditional moment restrictions (cf. Shi (2013), Chernozhukov, Lee, andRosen (2013), Armstrong (2014), andChetverikov (2013)). Second, alternative asymptotic frameworks like those in Andrews and Barwick (2012) and Romano, Shaikh, and Wolf (2014) may provide a better asymptotic approximation for the type of problems we study in this paper.…”

Section: Discussionmentioning

confidence: 99%

Inference for subvectors and other functions of partially identified parameters in moment inequality models

Bugni

Canay²,

Shi

2017

Quantitative Economics

125

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This paper introduces a bootstrap-based inference method for functions of the parameter vector in a moment (in)equality model. These functions are restricted to be linear for two-sided testing problems, but may be nonlinear for one-sided testing problems. In the most common case, this function selects a subvector of the parameter, such as a single component. The new inference method we propose controls asymptotic size uniformly over a large class of data distributions and improves upon the two existing methods that deliver uniform size control for this type of problem: projection-based and subsampling inference. Relative to projection-based procedures, our method presents three advantages: (i) it weakly dominates in terms of finite sample power, (ii) it strictly dominates in terms of asymptotic power, and (iii) it is typically less computationally demanding. Relative to subsampling, our method presents two advantages: (i) it strictly dominates in terms of asymptotic power (for reasonable choices of subsample size), and (ii) it appears to be less sensitive to the choice of its tuning parameter than subsampling is to the choice of subsample size.

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Section: Discussionmentioning

confidence: 99%

Inference for subvectors and other functions of partially identified parameters in moment inequality models

Bugni

Canay²,

Shi

2017

Quantitative Economics

125

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“…With discrete conditioning variables, identi…ed sets can be expressed using unconditional moment inequalities, and inference may be conducted as in Chernozhukov, Hong, and Tamer (2007), Beresteanu and Molinari (2008), Romano and Shaikh (2008a,b), Rosen (2008), Andrews and Guggenberger (2009), Andrews and Soares (2010), Andrews and Jia-Barwick (2010), Bugni (2010), Canay (2010), or Romano, Shaikh, andWolf (2014). With continuous conditioning variables inference using conditional moment inequalities can be performed, see for example Andrews and Shi (2013a,b), Chernozhukov, Lee, and Rosen (2013), Lee, Song, and Whang (2013a,b), Armstrong(2011a,b), andChetverikov (2011).…”

Section: Resultsmentioning

confidence: 99%

Characterizations of identified sets delivered by structural econometric models

Chesher¹,

Rosen²

2016

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This paper develops characterizations of identi…ed sets of structures and structural features for complete and incomplete models involving continuous or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can arise when there are multiple sources of heterogeneity, censored or discrete endogenous variables, or inequality restrictions on functions of observed and unobserved variables. The models generalize the class of incomplete instrumental variable (IV) models in which unobserved variables are single-valued functions of observed variables. Thus the models are referred to as Generalized IV (GIV) models, but there are important cases in which instrumental variable restrictions play no signi…cant role. Building on a de…nition of observational equivalence for incomplete models the development uses results from random set theory which guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case-by-case proofs of sharpness. The use of random sets de…ned on the space of unobserved variables allows identi…cation analysis under mean and quantile independence restrictions on the distributions of unobserved variables conditional on exogenous variables as well as under a full independence This paper is a revised version of a paper initially circulated as CeMMAP working paper CWP43/13 under the title "Generalized Instrumental Variable Models." We thank Federico Bugni, Matt Masten, and Francesca Molinari for detailed comments and discussion. We have bene…tted from discussion with participants at seminar and conference presentations given at uVa Amsterdam, Boston College, Boston University, Cornell, Chicago, Paris School of Economics, Vanderbilt, the April 2013 conference on Mathematical Statistics of Partially Identi…ed Objects at Oberwolfach, the 2013 Cowles summer econometrics conference, the 2014 Asia meeting of the Econometric Society in Taipei, the 2014 China meeting of the Econometric Society in Xiamen, the Harvard-MIT econometrics workshop, Yale, Virginia, Georgetown, Maryland, Johns Hopkins, Toulouse School of Economics, Oxford, Duke, UIUC, Reading, NUS Singapore, and Surrey. Both authors gratefully acknowedlge …nancial support from the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP). Adam Rosen gratefully acknowledges …nancial support from a British Academy mid-career Fellowship, and from the European Research Council (ERC) grants ERC-2009-StG-240910-ROMETA and ERC-2012-StG-312474. y Address: Andrew Chesher, Department of Economics, University College London, Gower Street, London WC1E 6BT, andrew.chesher@ucl.ac.uk.z Address: Adam Rosen, Department of Economics, University College London, Gower Street, London WC1E 6BT, adam.rosen@ucl.ac.uk. 1 restriction. The results are used to develop sharp bounds on the distribution of valuations in an incomplete model of English auctions, improving on the pointw...

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“…See Nikitin (1995) and Bickel, Ritov, and Stoker (2006) for a general discussion. It would be interesting to consider a multiscale version of our test based on a range of bandwidths to see if it achieves adaptive rate-optimality against a sequence of smooth alternatives along the lines of Armstrong and Chan (2013) and Chetverikov (2011).…”

Section: Discussionmentioning

confidence: 99%

“…1 Researches on conditional moment inequalities include Andrews and Shi (2013), Andrews and Shi (2014), Armstrong (2011a), Armstrong (2011b), Armstrong and Chan (2013), Chernozhukov, Lee, and Rosen (2013), Chetverikov (2011), Fan and Park (2014), Khan and Tamer (2009), Kim (2009), Lee, Song, and Whang (2013), Menzel (2014), and Ponomareva (2010), among others. In contrast, this paper's approach naturally covers a wide class of inequality restrictions among nonparametric functions that the moment inequality framework does not (or at least is cumbersome to) apply.…”

Section: Introductionmentioning

confidence: 99%

Testing for a general class of functional inequalities

Lee¹,

Song²,

Whang³

2014

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Abstract. In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version of L p functionals of kernel-type estimators (1 ≤ p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on nonparametric bootstrap applied to kernel-based test statistics, with an option of estimating "contact sets." We provide regularity conditions under which the bootstrap test is asymptotically valid uniformly over a large class of distributions, including the cases that the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality.

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Adaptive test of conditional moment inequalities

Cited by 68 publications

References 48 publications

Inference for subvectors and other functions of partially identified parameters in moment inequality models

Inference for subvectors and other functions of partially identified parameters in moment inequality models

Characterizations of identified sets delivered by structural econometric models

Testing for a general class of functional inequalities

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