Angrist and Chen 2011 — Schooling and the Vietnam-Era GI Bill

Summary

Uses 2000 census data and Vietnam-era draft lottery instruments to estimate the long-run effects of military service on schooling and earnings. White veterans received $\approx 0.33$ more years of schooling than comparable nonveterans — most likely via GI Bill college benefits ($50\%$ of Vietnam-era veterans used the GI Bill for college, the highest rate of any war cohort). By age 50, the earnings penalty documented in Angrist (1990) has vanished; the paper reconciles this with a Mincerian framework showing that the GI Bill schooling gain and the lost-experience penalty approximately cancel on a flat portion of the age-earnings profile.

Key Claims

• GI Bill schooling effect: Two-stage least squares (2SLS) estimates show white Vietnam veterans got $0.33$ more years of schooling than nonveterans, predominantly in college ($+0.26$ years of college, $+5$ percentage points (pp) probability of bachelor's degree (BA)). Effects are similar in magnitude to studies of World War II (WWII) and Korean-era GI Bills (Bound and Turner 2002; Stanley 2003). Draft-avoidance through deferments is ruled out as the primary mechanism: the largest cohort effects are for men born in 1951 and 1952, for whom college deferments were phased out.
• Earnings penalty dissipated by 2000: At age $\approx 48$–$50$, 2SLS estimates of the earnings effect are $-\$517$ (standard error (s.e.) $= \$1{,}240$), statistically indistinguishable from zero. Ordinary least squares (OLS) estimates ($-\$8{,}600$) are far outside the instrumental variable (IV) confidence interval. The earnings loss of $10$–$15\%$ documented for the early 1980s in Angrist (1990) has largely disappeared.
• Mincer reconciliation: The near-zero veteran earnings effect is explained by two offsetting forces. Veterans lost $\delta+\ell \approx 2.3$ years of civilian experience (where $\ell \approx 2$ = years of military service and $\delta \approx 0.33$ = GI Bill–induced schooling years). The earnings cost of lost experience on a flat age-50 profile is approximately offset by the return to GI Bill-funded schooling: $\rho\delta \approx 7\% \times 0.33 \approx 2\%$ (where $\rho$ = return per year of schooling). Because the experience-squared coefficient $\beta_2 \approx 0$ at age 50 (flat profile), equation (6): $\pi \simeq -\beta_1(\delta+\ell) + \rho\delta \approx 0$ (where $\pi$ = total veteran earnings effect and $\beta_1$ = linear experience coefficient).
• IV return to schooling below OLS: IV estimates of the returns to schooling in the 2SLS Mincer equation are $\approx 0.07$ (vs. OLS $\approx 0.12$). The paper offers two explanations: (a) positive ability bias in OLS; (b) GI Bill subsidies induce enrollment from veterans who may have below-average marginal returns, or the nonlinearity of returns across education levels (college vs. secondary).
• Other outcomes: White veterans $5$–$6$ pp more likely to work in the federal government (consistent with veteran hiring preferences); $3$ pp less likely to live in their state of birth; no significant marriage effect. These secondary effects do not explain the null earnings finding.
• Net lifetime cost of conscription: Even accounting for GI Bill schooling gains, present discounted value (PDV) calculations (1972–2000) show conscription reduced veterans' lifetime earnings by about $10\%$ of total. The GI Bill offset roughly $15\%$ of the total lifetime earnings loss — meaningful but far from compensatory.
• Instrument: Both a simple draft-eligibility dummy and an expanded 5zx set (five lottery-number group dummies interacted with year of birth; 15 instruments for the 1950–1952 sample) are used. The 5zx set yields only modest precision gains over the simple eligibility dummy. Over-identification test $p$-values exceed $0.4$, supporting the exclusion restriction.

Concepts Introduced or Extended

• Returns to Schooling — GI Bill subsidy as explanation for IV < OLS return; Mincer framework reconciling early earnings loss with near-zero age-50 effect
• Instrumental Variables — 5zx expanded instrument set; over-identification tests support exclusion restriction
• Natural Experiments — Vietnam draft lottery as instrument; ruling out draft-avoidance deferments as confound

Entities Mentioned

• Joshua Angrist
• David Card
• Alan Krueger
• Jacob Mincer

Quotes

"Our results also suggest that the Vietnam veteran earnings penalty has largely faded. Seen through the lens of a Mincer-style wage equation, the near-zero veteran wage penalty can be explained by the combination of lost experience on a flat portion of the experience profile and the economic return to additional schooling funded by the GI Bill."

"The GI Bill was found to be important but not revolutionary. While many veterans cited the GI Bill as key to their decision to attend college, 60 percent reported that they definitely would have gone to college without GI Bill funding."

My Take

The Mincer reconciliation is the paper's most elegant contribution: it doesn't just document the null earnings finding but explains why the earlier penalty had to disappear, using the structure of the earnings function. The IV return to schooling below OLS ($0.07$ vs. $0.12$) is substantively interesting — it's one of the rare cases where IV < OLS, and the GI Bill subsidy mechanism (low-return marginal compliers) is more credible here than in most contexts because the instrument literally changed the cost of schooling. The main limitation is that the paper cannot cleanly separate GI Bill effects on schooling from other veteran-specific channels (health, job preferences). The $15\%$ offset finding from the lifetime PDV calculation is a useful summary statistic but rests on strong assumptions about experience-profile extrapolation.