On Heckits, Late, and Numerical Equivalence

28 Pages Posted: 12 Apr 2018 Last revised: 20 May 2023

See all articles by Patrick Kline

Patrick Kline

University of California, Berkeley - Department of Economics

Christopher Walters

University of California, Berkeley - Department of Economics

Date Written: April 2018

Abstract

Structural econometric methods are often criticized for being sensitive to functional form assumptions. We study parametric estimators of the local average treatment effect (LATE) derived from a widely used class of latent threshold crossing models and show they yield LATE estimates algebraically equivalent to the instrumental variables (IV) estimator. Our leading example is Heckman’s (1979) two-step (“Heckit”) control function estimator which, with two-sided non-compliance, can be used to compute estimates of a variety of causal parameters. Equivalence with IV is established for a semi-parametric family of control function estimators and shown to hold at interior solutions for a class of maximum likelihood estimators. Our results suggest differences between structural and IV estimates often stem from disagreements about the target parameter rather than from functional form assumptions per se. In cases where equivalence fails, reporting structural estimates of LATE alongside IV provides a simple means of assessing the credibility of structural extrapolation exercises.

Suggested Citation

Kline, Patrick and Walters, Christopher, On Heckits, Late, and Numerical Equivalence (April 2018). NBER Working Paper No. w24477, Available at SSRN: https://ssrn.com/abstract=3158916

Patrick Kline (Contact Author)

University of California, Berkeley - Department of Economics ( email )

508-1 Evans Hall #3880
Berkeley, CA 94720-3880
United States

Christopher Walters

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

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