Angrist Imbens and Rubin 1996 — Identification of Causal Effects Using Instrumental Variables

Summary

This paper bridges the econometric structural equation tradition and the Rubin Causal Model (RCM) by embedding instrumental variables (IV) within a potential outcomes framework. The central result is that, under five explicit assumptions, the IV estimand identifies the Local Average Treatment Effect (LATE) — the average causal effect only for compliers, the subpopulation whose treatment status is actually changed by the instrument. Without these assumptions, the IV estimand is merely a ratio of two reduced-form effects with no causal interpretation. The paper applies the framework to estimate the effect of Vietnam-era military service on civilian mortality using the draft lottery as an instrument.

Key Claims

• The IV estimand $= E[\text{causal effect of } Z \text{ on } Y] / E[\text{causal effect of } Z \text{ on } D]$; under the five assumptions this ratio identifies $\text{LATE} = E[Y(1) - Y(0) \mid D(1) - D(0) = 1]$.
• Four compliance types partition the population given any binary instrument: compliers ($D(0)=0, D(1)=1$), never-takers ($D(0)=D(1)=0$), always-takers ($D(0)=D(1)=1$), and defiers ($D(0)=1, D(1)=0$). Monotonicity rules out defiers.
• The old econometric assumption "instrument uncorrelated with disturbances" conflates two distinct assumptions — the exclusion restriction and ignorable assignment — that can fail for different reasons and should be assessed separately.
• Violations of the exclusion restriction bias IV by $E[\text{direct } Z \to Y \text{ for noncompliers}] \times (\text{noncomplier odds})$; violations of monotonicity bias IV by the defier share $\times$ the complier-defier treatment effect difference. Both biases shrink as the instrument strengthens.
• Application: Vietnam draft lottery $\to$ military service $\to$ civilian mortality 1974–1983. IV estimate for men born 1950: military service raises 10-year mortality by $+0.56$ percentage points (pp) ($\approx 25\%$). But a schooling-lottery connection (men with low random sequence number (RSN) stayed in school longer) could account for nearly all the estimated effect via the exclusion restriction.

Concepts Introduced or Extended

• Local Average Treatment Effect
• Instrumental Variables
• Intention-to-Treat Analysis
• Rubin Causal Model

Entities Mentioned

• Joshua Angrist
• Guido Imbens
• Donald Rubin

Quotes

"Without these assumptions, the IV estimand is simply the ratio of intention-to-treat causal estimands with no interpretation as an average causal effect."

"Pooling these assumptions into the single assumption of zero correlation between instruments and disturbances has led to confusion about the essence of the identifying assumptions and hinders assessment and communication of the plausibility of the underlying model."

"We call this the Local Average Treatment Effect (LATE)."

My Take

The foundational paper for modern IV interpretation. Before Angrist, Imbens, and Rubin (AIR) 1996, IV was used routinely but economists could not say precisely for whom the estimate was causal. AIR answered: it is the compliers — those whose treatment changed because of the instrument — and it provided the language (compliers, never-takers, always-takers, defiers) that every subsequent natural-experiment paper uses. Every IV paper in this wiki reports a LATE defined by this framework, whether or not it cites AIR 1996 by name. The Vietnam draft application is unusually honest: the authors themselves work out how a schooling-deferment channel could almost entirely eliminate their estimate, modeling the sensitivity rather than burying it.