A Projection Framework for Testing Shape Restrictions That Form Convex Cones

Fang, Zheng; Seo, Juwon

doi:10.3982/ecta17764

Cited by 9 publications

(3 citation statements)

References 83 publications

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“…In fact, our data-driven UCBs for h 0 and its partial derivatives apply to nonparametric regression with non-Gaussian, heteroskedastic errors as a special case. 6 Finally, our work also compliments several recent papers on (non data-driven) estimation and inference for sieve NPIV models with shape constraints; see for example Chetverikov and Wilhelm (2017), Chernozhukov, Newey, and Santos (2015), Blundell et al (2017), Freyberger and Reeves (2019), Zhu (2020), and Fang and Seo (2021). Each of these works assumes a deterministic sequence of sieve tuning parameters satisfying regularity conditions that depend on unknown model features.…”

Section: Introductionmentioning

confidence: 63%

Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities

Chen¹,

Christensen²,

Kankanala³

2021

Preprint

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We introduce computationally simple, data-driven procedures for estimation and inference on a structural function h 0 and its derivatives in nonparametric models using instrumental variables. Our first procedure is a bootstrap-based, data-driven choice of sieve dimension for sieve nonparametric instrumental variables (NPIV) estimators. When implemented with this data-driven choice, sieve NPIV estimators of h 0 and its derivatives are adaptive: they converge at the best possible (i.e., minimax) sup-norm rate, without having to know the smoothness of h 0 , degree of endogeneity of the regressors, or instrument strength. Our second procedure is a data-driven approach for constructing honest and adaptive uniform confidence bands (UCBs) for h 0 and its derivatives. Our data-driven UCBs guarantee coverage for h 0 and its derivatives uniformly over a generic class of data-generating processes (honesty) and contract at, or within a logarithmic factor of, the minimax sup-norm rate (adaptivity). As such, our data-driven UCBs deliver asymptotic efficiency gains relative to UCBs constructed via the usual approach of undersmoothing. In addition, both our procedures apply to nonparametric regression as a special case. We use our procedures to estimate and perform inference on a nonparametric gravity equation for the intensive margin of firm exports and find evidence against common parameterizations of the distribution of unobserved firm productivity.

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Section: Introductionmentioning

confidence: 63%

Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities

Chen¹,

Christensen²,

Kankanala³

2021

Preprint

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“…Following the original version of this paper, Zhu (2019) and Fang and Seo (2019) proposed inference methods for convex restrictions which, while applicable to an important class of problems, rule out inference on nonlinear functionals or tests of certain shape restrictions. Also related is Freyberger and Reeves (2018) who developed uniform inference for functionals under shape restrictions while imposing point identification.…”

Section: Introductionmentioning

confidence: 99%

Constrained Conditional Moment Restriction Models

Chernozhukov

Newey

Santos³

2023

ECTA

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Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper, we provide a general procedure for inference under shape restrictions in identified and partially identified models defined by conditional moment restrictions. Our test statistics and proposed inference methods are based on the minimum of the generalized method of moments (GMM) objective function with and without shape restrictions. Uniformly valid critical values are obtained through a bootstrap procedure that approximates a subset of the true local parameter space. In an empirical analysis of the effect of childbearing on female labor supply, we show that employing shape restrictions in linear instrumental variables (IV) models can lead to shorter confidence regions for both local and average treatment effects. Other applications we discuss include inference for the variability of quantile IV treatment effects and for bounds on average equivalent variation in a demand model with general heterogeneity.

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“…On the other hand, we show in Section 4.4.2 that an important insight in Andrews, Roth, and Pakes (2019) allows us to adapt our methodology to conduct sub‐vector inference in a class of conditional moment inequality models. Our analysis is also conceptually related to work on sub‐vector inference in models involving moment inequalities and to a literature on shape restrictions; see, for example, Romano and Shaikh (2008), Bugni, Canay, and Shi (2017), Kaido, Molinari, and Stoye (2019), Gandhi, Lu, and Shi (2019), Chernozhukov, Newey, and Santos (2015), Zhu (2019), and Fang and Seo (2021). While these procedures are designed for general problems that do not possess the specific structure in (1), they are, as a result, less computationally tractable and/or rely on more demanding and high‐level conditions than the ones we employ.…”

Section: Introductionmentioning

confidence: 99%

Inference for Large‐Scale Linear Systems With Known Coefficients

Fang

Santos²,

Shaikh

et al. 2023

ECTA

Self Cite

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This paper considers the problem of testing whether there exists a non‐negative solution to a possibly under‐determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test that requires solving only linear programs for its implementation, and thus remains computationally feasible in the high‐dimensional applications that motivate our analysis. The asymptotic size of the proposed test is shown to equal at most the nominal level uniformly over a large class of distributions that permits the number of linear equations to grow with the sample size.

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A Projection Framework for Testing Shape Restrictions That Form Convex Cones

Cited by 9 publications

References 83 publications

Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities

Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities

Constrained Conditional Moment Restriction Models

Inference for Large‐Scale Linear Systems With Known Coefficients

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