A Test of Non-Identifying Restrictions and Confidence Regions for Partially Identified Parameters

By Alfred Galichon, Marc Henry. 2009

79 citations recorded by the source corpus.

We propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables, which do not necessarily identify the data generating process. The restrictions can be derived from any model of interactions, allowing censoring and multiple equilibria. When the restrictions are parameterized, the test can be inverted to yield confidence regions for partially identified parameters, thereby complementing other proposals, primarily Chernozhukov etÂ al. [Chernozhukov, V., Hong, H., Tamer, E., 2007. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 1243-1285].

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/db4b73531bc230038b5c559fd1b725cd0c3250ac

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Citations in the corpus

PARTIAL IDENTIFICATION OF THE DISTRIBUTION OF TREATMENT EFFECTS AND ITS CONFIDENCE SETS (2009, background): “By following the proof of Theorem 1 in Galichon and Henry (2008), we can show that under conditions stated in the theorem below, ffiffiffiffiffi n1 p ½MnðdÞ MðdÞ ) sup y2Ysup;d Gðy; dÞ; ffiffiffiffin1 p ½mnðdÞ mðdÞ ) inf y2Yinf ;d Gðy; dÞ where fGðy; dÞ : y 2 Ydg is a tight Gaussian process with…”
Set identification via quantile restrictions in short panels (2009, methodology): “He shows how the instrumental variable quantile regression estimator of Chernozhukov and Hansen (2006) ”
Asymptotically exact inference in conditional moment inequality models (2011, background): “The results draw a connection between moment selection, bandwidth selection, irregular identification and nonstandard M-estimation.”
Weighted KS Statistics for Inference on Conditional Moment Inequalities (2011, methodology): “in this paper could be used to construct confidence regions for points in the identified set, as proposed by Imbens and Manski (2004). Local power results for tests satisfying this less stringent requirement would follow from similar arguments.”
Set Identified Linear Models (2011, methodology): “We exhibit a necessary and sufficient condition, a generalization of the usual over-identifying condition à la Sargan, under which the identified set is not empty and the exclusion restrictions are acceptable.”
VALIDITY OF SUBSAMPLING AND “PLUG-IN ASYMPTOTIC” INFERENCE FOR PARAMETERS DEFINED BY MOMENT INEQUALITIES (2009, methodology): “This is true of the methods in Andrews et al. (2004), Pakes et al. (2004), Rosen (2008), and Galichon and Henry (2008).”
Nonparametric Inference Based on Conditional Moment Inequalities (2014, background): “Galichon and Henry (2009) considers a testing problem with an infinite number of unconditional 1This holds because the functions g1(x), ..., gk(x) in (3.1) below, which multiply the moment functions indexed by 1, ..., k, need not be the same.”
Intersection bounds: estimation and inference (2009, background): “1Examples include monotone instrumental variables and the returns to schooling (Manski and Pepper (2000)), English auctions (Haile and Tamer (2003)), the returns to language skills (Gonzalez (2005)), set identification with Tobin regressors (Chernozhukov, Rigobon, and Stoker (2007)), endogeneity wit”