Nonparametric Estimation of Triangular Simultaneous Equations Models under Weak Identification

Sukjin Han

No 140414, Department of Economics Working Papers from The University of Texas at Austin, Department of Economics

Abstract: This paper analyzes the problem of weak instruments on identification, estimation, and inference in a simple nonparametric model of a triangular system. The paper derives a necessary and sufficient rank condition for identification, based on which weak identification is established. Then nonparametric weak instruments are defined as a sequence of reduced form functions where the associated rank shrinks to zero. The problem of weak instruments is characterized to be similar to the ill-posed inverse problem, which motivates the introduction of a regularization scheme. The paper proposes a penalized series estimation method to alleviate the effects of weak instruments. The rate of convergence of the resulting estimator is given, and it is shown that weak instruments slow down the rate and penalization derives a faster rate. Consistency and asymptotic normality results are also derived. Monte Carlo results are presented, and an empirical example is given, where the effect of class size on test scores is estimated nonparametrically.

Keywords: Triangular models; nonparametric identification; weak identification; weak instruments; series estimation; inverse problem; regularization; concurvity. (search for similar items in EconPapers)
JEL-codes: C13 C14 C36 (search for similar items in EconPapers)
Pages: 75 pages
Date: 2012-06, Revised 2014-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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https://sites.google.com/site/universs01/mypdf/NPweakIV_040814_all.pdf First version, 2014 (application/pdf)

Related works:
Journal Article: Nonparametric estimation of triangular simultaneous equations models under weak identification (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:tex:wpaper:140414

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