Working Paper: NBER ID: w24477
Authors: Patrick M. Kline; Christopher R. Walters
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.
Keywords: Local Average Treatment Effect; Instrumental Variables; Heckit Model; Causal Estimation
JEL Codes: C01; C26; C31; C52
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Differences between structural and IV estimates arise from disagreements about the target parameter (C36) | Structural and IV estimates (C26) |
| Equivalence of structural and IV estimates holds in cases of two-sided noncompliance (C36) | Structural estimates and IV estimates (C26) |
| Divergence occurs when likelihood is maximized on the boundary of the structural parameter space (C62) | Structural estimates and IV estimates (C26) |
| Equivalence fails under certain conditions when noncompliance is present (C52) | Structural estimates and IV estimates (C26) |
| Estimation of overidentified models results in LATE estimates that differ from those derived from IV (C26) | LATE estimates and IV estimates (C26) |
| Parametric estimators of LATE derived from latent threshold crossing models (C24) | Estimates obtained from IV estimators (C26) |