Nonparametric estimation of triangular simultaneous equations models under weak identification

Vincent Han*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
Original languageEnglish
Number of pages42
JournalQuantitative Economics
Issue number1
Early online date1 Jul 2019
Publication statusE-pub ahead of print - 1 Jul 2019

Structured keywords

  • ECON Econometrics


  • Triangular models
  • nonparametric identification
  • weak identification
  • weak instruments
  • series estimation
  • regularization
  • concurvity


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