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Instrument-free estimation of triangular equation systems with the trigmm command

Author

Listed:
  • Heejun Lee

    (Brown University)

  • Arthur Lewbel

    (Boston College)

  • Susanne M. Schennach

    (Brown University)

  • Linqi Zhang

    (Chinese University of Hong Kong)

Abstract

In this article, we introduce trigmm, a package designed to estimate the parameters of triangular two-equation systems without the need for instrumental variables. The trigmm command leverages the identification conditions proposed by Lewbel, Schennach, and Zhang (2024, Journal of Business and Economic Statis- tics 42: 14–25), enabling instrument-free identification primarily through the non- Gaussianity assumption of error variables. We also introduce the trigmmset com- mand, which provides bounds on the parameters based on the set identification re- sults from the same article even without the non-Gaussianity assumption, offering complementary analyses alongside the trigmm command. Estimation is performed by integrating these moment conditions with Stata’s built-in generalized method of moments (gmm) framework. The package’s functionality is demonstrated through an empirical application.

Suggested Citation

  • Heejun Lee & Arthur Lewbel & Susanne M. Schennach & Linqi Zhang, 2026. "Instrument-free estimation of triangular equation systems with the trigmm command," Stata Journal, StataCorp LLC, vol. 26(1), pages 68-89, March.
    • Handle: RePEc:tsj:stataj:v:26:y:2026:i:1:p:68-89
    DOI: 10.1177/1536867X261425780
    Note: to access software from within Stata, net describe http://www.stata-journal.com/software/sj26-1/st0797/
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