Nonparametric estimation of triangular simultaneous equations models under weak identification

• 成果类型: Article
• 署名作者: Han, Sukjin
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE975
• 发表日期: 2020
• 页码: 161-202
• 关键词: Triangular models; nonparametric identification; weak identification; weak instruments; series estimation; regularization; concurvity; C13; C14; C36

摘要

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 as concurvity, which motivates the introduction of a regularization scheme. The paper proposes a penalized series estimation method to alleviate the effects of weak instruments and shows that it achieves desirable asymptotic properties. A data-driven procedure is proposed for the choice of the penalization parameter. The findings of this paper provide useful implications for empirical work. To illustrate them, Monte Carlo results are presented and an empirical example is given in which the effect of class size on test scores is estimated nonparametrically.