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Inference in Nonparametric Instrumental Variables With Partial Identification
Author(s) -
Santos Andres
Publication year - 2012
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta7493
Subject(s) - nonparametric statistics , instrumental variable , test statistic , mathematics , statistical hypothesis testing , statistic , identification (biology) , inference , econometrics , monte carlo method , statistics , set (abstract data type) , computer science , artificial intelligence , botany , biology , programming language
This paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework. We construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction. The same test statistic can be employed under identification, in which case the hypothesis is whether the true model satisfies the posited property. An almost sure consistent bootstrap procedure is provided for obtaining critical values. Possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set. As an illustration we obtain confidence intervals for the level and slope of Brazilian fuel Engel curves. A Monte Carlo study examines finite sample performance.