Set-Valued Control Functions

Sukjin Han; Hiroaki Kaido

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arXiv · 2403.00347

Set-Valued Control Functions

Sukjin Han·Hiroaki Kaido

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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.

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Sukjin Han, Hiroaki Kaido. 2024-03-01. Set-Valued Control Functions. https://arxiv.org/abs/2403.00347

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