Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions

Xiaohong Chen, Demian Pouzo and James Powell

Journal of Econometrics, 2019, vol. 213, issue 1, 30-53

Abstract: This paper considers estimation and inference for a weighted average derivative (WAD) of a nonparametric quantile instrumental variables regression (NPQIV). NPQIV is a non-separable and nonlinear ill-posed inverse problem, which might be why there is no published work on the asymptotic properties of any estimator of its WAD. We first characterize the semiparametric efficiency bound for a WAD of a NPQIV, which, unfortunately, depends on an unknown conditional derivative operator and hence an unknown degree of ill-posedness, making it difficult to know if the information bound is singular or not. In either case, we propose a penalized sieve generalized empirical likelihood (GEL) estimation and inference procedure, which is based on the unconditional WAD moment restriction and an increasing number of unconditional moments that are implied by the conditional NPQIV restriction, where the unknown quantile function is approximated by a penalized sieve. Under some regularity conditions, we show that the self-normalized penalized sieve GEL estimator of the WAD of a NPQIV is asymptotically standard normal. We also show that the quasi likelihood ratio statistic based on the penalized sieve GEL criterion is asymptotically chi-square distributed regardless of whether or not the information bound is singular.

Keywords: Nonparametric quantile instrumental variables; Weighted average derivatives; Penalized sieve generalized empirical likelihood; Semiparametric efficiency; Chi-square inference (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Working Paper: Penalized Sieve GEL for Weighted Average Derivatives of Nonparametric Quantile IV Regressions (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:213:y:2019:i:1:p:30-53

DOI: 10.1016/j.jeconom.2019.04.004

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