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Set-Valued Control Functions

Sukjin Han, Hiroaki Kaido

arXiv 1 Mar 2024 · Econometrics

arXiv:2403.00347 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

113
references
193
in-text mentions
113
distinct cited
6
self-citations
17,227
main-text words

appendix boundary found by appendix_command · 69% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bertanha, M., M. Luflade, and I. Mourifié (2025) Causal Effects in Matching Mechanisms with Strategically Reported Preferences1.00093100%
2Newey, W. K., J. L. Powell, and F. Vella (1999) Nonparametric Estimation of Triangular Simultaneous Equations Models0.92844100%
3Molchanov, I. and F. Molinari (2018) Random sets in econometrics0.92843100%
4Thornton, R. L (2008) The Demand for, and Impact of, Learning HIV Status0.87452100%
5Manski, C. F. and E. Tamer (2002) Inference on Regressions with Interval Data on a Regressor or Outcome0.8558462%
6Balat, J. F. and S. Han (2023) Multiple treatments with strategic substitutes0.84333100%
7Han, S (2021) Identification in nonparametric models for dynamic treatment effects self0.84333100%
8Heckman, J. J. and E. Vytlacil (2005) Structural Equations, Treatment Effects, and Econometric Policy Evaluation0.84333100%
9Chesher, A. and A. M. Rosen (2017) Generalized instrumental variable models0.8307357%
10Jovanovic, B (1989) Observable implications of models with multiple equilibria0.81142100%

Showing the top 10 of 113 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Universal Inference for Incomplete Discrete Choice Models0.64422
2Identification of Treatment Effects under Limited Exogenous Variation0.40511
3Causal Effects in Matching Mechanisms with Strategically Reported Preferences0.40511
4Policy Relevant Treatment Effects with Multidimensional Unobserved Heterogeneity0.40511
5Endogenous Heteroskedasticity in Linear Models0.40511