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Generalized Local IV with Unordered Multiple Treatment Levels Identification Efficient Estimation and Testable Implication

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Document pages: 50 pages

Abstract: This paper studies the econometric aspects of the generalized local IVframework defined using the unordered monotonicity condition, whichaccommodates multiple levels of treatment and instrument in programevaluations. The framework is explicitly developed to allow for conditioningcovariates. Nonparametric identification results are obtained for a wide rangeof policy-relevant parameters. Semiparametric efficiency bounds are computedfor these identified structural parameters, including the local averagestructural function and local average structural function on the treated. Twosemiparametric estimators are introduced that achieve efficiency. One is theconditional expectation projection estimator defined through the nonparametricidentification equation. The other is the double debiased machine learningestimator defined through the efficient influence function, which is suitablefor high-dimensional settings. More generally, for parameters implicitlydefined by possibly non-smooth and overidentifying moment conditions, thisstudy provides the calculation for the corresponding semiparametric efficiencybounds and proposes efficient semiparametric GMM estimators again using theefficient influence functions. Then an optimal set of testable implications ofthe model assumption is proposed. Previous results developed for the binarylocal IV model and the multivalued treatment model under unconfoundedness areencompassed as special cases in this more general framework. The theoreticalresults are illustrated by an empirical application investigating the return toschooling across different fields of study, and a Monte Carlo experiment.

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