Heckman 1996 — Identification of Causal Effects Using Instrumental Variables Comment

Summary

Published as a comment on Angrist, Imbens, and Rubin (AIR; 1996) in the same Journal of the American Statistical Association (JASA) issue (Vol. 91, No. 434, pp. 459–462), Heckman argues that the AIR framework reinvents econometric ideas already present in the switching regression and Roy model literature, that the local average treatment effect (LATE) is a "controversial parameter" for an unobservable subpopulation inferior to the mean treatment effect on the treated (ATT), that AIR's full independence assumptions are unnecessarily strong (mean independence suffices for ATT without monotonicity), and that those assumptions impose behavioral restrictions violated in the most-used structural models. He also mounts a specific critique of the Vietnam draft lottery instrument used as the paper's application.

Key Claims

• The "Rubin model" (potential outcomes + the Stable Unit Treatment Value Assumption, SUTVA) is equivalent to the switching regression model (Quandt 1958; Maddala and Nelson 1975), the Roy model (Heckman and Honoré 1990), and competing risks (Cox 1962) — independently invented in econometrics before Rubin (1974).
• Econometric instrumental variables (IV) allow heterogeneous treatment effects without AIR's full independence assumption; ATT is identified under mean independence alone (A-1: $Z \perp \text{mean}(Y_0 \mid X)$; A-2: $Z \perp \text{mean}(D_1 - D_0 \mid X)$) without requiring monotonicity.
• AIR's independence assumptions have implicit behavioral content — they impose Granger noncausality conditions violated in the Roy model, competing risks, and the Gronau-Heckman labor supply model whenever agents have private information about their own gains ("essential heterogeneity").
• The Vietnam draft lottery instrument is questionable on two grounds: (1) high lottery numbers attract volunteers with high perceived private gains, violating A-2; (2) high numbers lead to more job training, potentially violating the exclusion restriction.
• Structural models (Bjorklund and Moffitt 1987; Heckman and Honoré 1989, 1990) identify the full distribution of counterfactual outcomes — not just one LATE at a particular instrument-defined margin.

Concepts Introduced or Extended

• Local Average Treatment Effect — critiques LATE as a parameter for an unobservable subpopulation; ATT (mean treatment effect on the treated) identifies causal effects for an observable group under weaker conditions
• Instrumental Variables — argues AIR conditions have strong behavioral content; presents mean independence (A-1, A-2/A-2', A-3) as sufficient for ATT without monotonicity
• Rubin Causal Model — argues the potential outcomes framework was independently invented in econometrics (switching regression, Roy model) before Rubin (1974)

Entities Mentioned

• James Heckman
• Joshua Angrist
• Guido Imbens
• Donald Rubin

Quotes

"The LATE parameter is a highly controversial parameter since it identifies the mean gain for an unobservable group — the compliers."

"The conditions A-1, A-2 (or A-2'), and A-3 are those already used in the econometrics literature to identify the mean effect of treatment on the treated without requiring any assumptions about the distributions of the unobservables."

"The probability model of Quandt (1958, 1972, 1988) and the switching regression model of Maddala and Nelson (1975) are equivalent to the 'Rubin Model.'"

My Take

Heckman is right on priority (the switching regression predates Rubin's formalization), right that LATE identifies an unobservable subpopulation while ATT targets an observable one, and right that AIR's full independence is stronger than what ATT identification requires. His critique of the draft lottery instrument is well-taken as an external validity concern. The deeper tension is normative: Heckman prefers structurally interpretable parameters (ATT, MTE, full distributions) estimated under explicit behavioral models, while AIR prioritizes assumptions that can be transparently stated and partly tested without a structural model. Both traditions coexist in modern causal inference — AIR won the pedagogical battle, Heckman's marginal treatment effect (MTE) generalization won the methodological one.