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Set-Valued Control Functions

Author

Listed:
  • Sukjin Han
  • Hiroaki Kaido

Abstract

The control function approach allows the researcher to identify various causal effects of interest. While powerful, it requires a strong invertibility assumption in the selection process, which limits its applicability. This paper expands the scope of the nonparametric control function approach by allowing the control function to be set-valued and derive sharp bounds on structural parameters. The proposed generalization accommodates a wide range of selection processes involving discrete endogenous variables, random coefficients, treatment selections with interference, and dynamic treatment selections. The framework also applies to partially observed or identified controls that are directly motivated from economic models.

Suggested Citation

  • Sukjin Han & Hiroaki Kaido, 2024. "Set-Valued Control Functions," Papers 2403.00347, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2403.00347
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    References listed on IDEAS

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    3. Newey, Whitney K., 1987. "Efficient estimation of limited dependent variable models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 36(3), pages 231-250, November.
    4. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
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