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Identification of a Triangular Two Equation System Without Instruments

Author

Listed:
  • Arthur Lewbel

    (Boston College)

  • Susanne M. Schennach

    (Brown University)

  • Linqi Zhang

    (Boston College)

Abstract
We show that a standard linear triangular two equation system can be point identified, without the use of instruments or any other side information. We find that the only case where the model is not point identified is when a latent variable that causes endogeneity is normally distributed. In this non-identified case, we derive the sharp identified set. We apply our results to Acemoglu and Johnson’s (2007) model of life expectancy and GDP, obtaining point identification and comparable estimates to theirs, without using their (or any other) instrument.

Suggested Citation

  • Arthur Lewbel & Susanne M. Schennach & Linqi Zhang, 2020. "Identification of a Triangular Two Equation System Without Instruments," Boston College Working Papers in Economics 1022, Boston College Department of Economics, revised 15 Dec 2022.
    • Handle: RePEc:boc:bocoec:1022
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    Cited by:

    1. Geert Mesters & Piotr Zwiernik, 2022. "Non-Independent Components Analysis," Working Papers 1358, Barcelona School of Economics.

    More about this item

    Keywords

    Returns to schooling; identification; triangular system; Kotlarski; deconvolution;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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