Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects

Xiaohong Chen (), Han Hong and Alessandro Tarozzi
Additional contact information
Han Hong: Duke University

No 1644, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We study semiparametric efficiency bounds and efficient estimation of parameters defined through general nonlinear, possibly non-smooth and over-identified moment restrictions, where the sampling information consists of a primary sample and an auxiliary sample. The variables of interest in the moment conditions are not directly observable in the primary data set, but the primary data set contains proxy variables which are correlated with the variables of interest. The auxiliary data set contains information about the conditional distribution of the variables of interest given the proxy variables. Identification is achieved by the assumption that this conditional distribution is the same in both the primary and auxiliary data sets. We provide semiparametric efficiency bounds for both the "verify-out-of-sample" case, where the two samples are independent, and the "verify-in-sample" case, where the auxiliary sample is a subset of the primary sample; and the bounds are derived when the propensity score is unknown, or known, or belongs to a correctly specified parametric family. These efficiency variance bounds indicate that the propensity score is ancillary for the "verify-in-sample" case, but is not ancillary for the "verify-out-of-sample" case. We show that sieve conditional expectation projection based GMM estimators achieve the semiparametric efficiency bounds for all the above mentioned cases, and establish their asymptotic efficiency under mild regularity conditions. Although inverse probability weighting based GMM estimators are also shown to be semiparametrically efficient, they need stronger regularity conditions and clever combinations of nonparametric and parametric estimates of the propensity score to achieve the efficiency bounds for various cases. Our results contribute to the literature on non-classical measurement error models, missing data and treatment effects.

Keywords: Auxiliary data; Measurement error; Missing data; Treatment effect; Semiparametric efficiency bound; GMM; Sieve estimation (search for similar items in EconPapers)
JEL-codes: C1 C3 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2008-03
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Published in Annals of Statistics (2008), 36: 808-843

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/files/pub/d16/d1644.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
Working Paper: Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:1644

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().