Angrist 1990 — Lifetime Earnings and the Vietnam Era Draft Lottery

Summary

Uses Vietnam-era draft lottery random sequence numbers (RSNs) as an instrument for veteran status to estimate the long-run earnings effects of military service, circumventing selection bias in ordinary least squares (OLS) comparisons. Drawing on Social Security Continuous Work History Sample (CWHS) data for earnings and Survey of Income and Program Participation (SIPP)/Defense Manpower Data Center (DMDC) administrative records for veteran status, Angrist introduces Two-Sample instrumental variable (IV) (TSIV) and finds that white veterans born 1950–52 suffered annual earnings losses of $\$1{,}500$–$\$2{,}100$ (1978 dollars) through the early 1980s — roughly $15\%$ below comparable nonveterans — with no significant effect for nonwhites. The earnings gap is well explained by treating military service as displacing approximately two years of civilian labor market experience.

Key Claims

• Draft lottery as natural experiment: Vietnam-era RSNs (1–365) were randomly assigned to birthdates; men with RSN below the induction ceiling ($195$ for the 1970 lottery, $125$ for 1971, $95$ for 1972) were "draft-eligible." Eligibility is by construction uncorrelated with earnings ability or family background, making it a valid instrument for veteran status.
• White veteran earnings penalty: TSIV estimates show white veterans born 1950–52 lost $\$1{,}562$–$\$2{,}094$ per year (1978 dollars) in 1981–84 earnings — approximately $15\%$ below nonveterans — a decade after discharge. Wald estimates by individual cohort-year confirm the direction and magnitude.
• Racial asymmetry is a first-stage story: No significant earnings loss for nonwhites. The lottery first-stage is weaker for nonwhites ($\approx 0.05$–$0.09$ increase in $P(\text{veteran})$ per unit of eligibility vs. $\approx 0.10$–$0.16$ for whites), making IV estimates imprecise, not indicating a zero true effect.
• Loss-of-experience mechanism: Veterans' earnings loss is consistent with having lost $\approx 2$ years of civilian labor market experience. Mincerian experience-earnings profiles fitted via TSIV imply the gap closes around age $50$ (standard error (s.e.) $\approx 16$ years), not immediately — military experience is only a partial substitute for civilian experience.
• Two-Sample IV (TSIV): CWHS contains earnings but no veteran status; SIPP and DMDC administrative records contain veteran status probabilities by lottery number but not earnings. Angrist develops optimal TSIV: treat veteran probability estimates from the second sample as instruments in generalized least squares (GLS) regressions of CWHS earnings on $73$ lottery-number cells per cohort-year. The minimized objective is an overidentification test statistic.
• Overidentification tests pass: Chi-square ($\chi^2$) statistics for model fit are below their degrees of freedom for whites, providing no evidence that lottery numbers affect earnings through channels other than veteran status — supporting the exclusion restriction.
• Draft-avoidance concern addressed: Baskir and Strauss (1978) claim Vietnam-era college enrollment was $6$–$7\%$ above normal due to the draft. Angrist (1989a) micro-data specification tests and the overidentification statistics find no evidence that lottery numbers correlate with covariates other than veteran status, weakening the avoidance-channel concern.

Concepts Introduced or Extended

• Instrumental Variables — Wald estimator formula $\hat{\alpha} = (\bar{y}^e - \bar{y}^n)/(\bar{p}^e - \bar{p}^n)$, where $\bar{y}^e$ and $\bar{y}^n$ are mean earnings for draft-eligible and non-eligible men and $\bar{p}^e$ and $\bar{p}^n$ are their respective veteran rates; TSIV for split-sample designs; lottery-number cells as instrument set
• Natural Experiments — draft lottery as paradigmatic randomized instrument embedded in policy
• Local Average Treatment Effect — "lottery-based estimates identify the effect of military service for those who served in the armed forces" — proto-local average treatment effect (LATE) reasoning; later formalized in Angrist, Imbens, and Rubin (AIR) (1996)

Entities Mentioned

• Joshua Angrist
• Alan Krueger
• Jacob Mincer

Quotes

"Social Security administrative records indicate that in the early 1980s, long after their service in Vietnam was ended, the earnings of white veterans were approximately 15 percent less than the earnings of comparable nonveterans."

"Experience-earnings profiles estimated using Social Security data imply that white veterans suffered an earnings reduction equivalent to the loss of two years civilian labor market experience."

My Take

The draft-lottery design is the cleanest natural experiment in labor economics: randomization was public, mechanical, and pre-announced. The methodological contribution — TSIV combining administrative data sources — was at least as important as the substantive finding. The racial asymmetry is a first-stage weakness problem, not a heterogeneous treatment effect story, though the paper does not formalize this distinction (AIR 1996 would). Angrist already invokes the Wald estimator, discusses treatment heterogeneity and avoidance behavior as threats, and uses overidentification tests — the conceptual apparatus of IV is fully present, only lacking the formal LATE/complier framework. The loss-of-experience explanation remains the consensus interpretation: Vietnam veterans paid an experience tax, not a permanent scarring penalty, consistent with the Angrist and Chen (2011) finding that earnings effects had largely dissipated by age 50.