The Causal Question

Does military service affect civilian earnings? The question matters for veterans' policy, conscription debates, and labour economics more broadly. But estimating the causal effect of military service is hard. Those who serve in the military differ from those who do not: they may be healthier, more disciplined, from different socioeconomic backgrounds, or have different civilian labour market prospects. Any OLS comparison of veterans' and non-veterans' wages confounds the effect of service with these pre-existing differences.

Angrist(1990)'s study of the Vietnam-era draft lottery offered a solution of elegant simplicity. By exploiting the lottery's random assignment of draft risk, Angrist constructed an instrumental variable that generated exogenous variation in military service, identifying the causal effect for the subpopulation of compliers — men who served because they were at risk of conscription.

Identification Strategy: The Draft Lottery as Instrument

How the Lottery Worked

Beginning in 1970, the US Selective Service System assigned draft eligibility by conducting a lottery over birth dates. Each birth date in a given cohort was assigned a random lottery number from 1 to 366. Men with numbers below a threshold (which varied by year, typically around 95–195) were classified as draft-eligible and called up for military service. Men with numbers above the threshold were not called.

The lottery numbers were assigned randomly, conditional on birth date, creating the key feature for identification: among men born in a given year, lottery number assignment was independent of ability, family background, health, and all other determinants of civilian earnings. Men with low lottery numbers were no different (on average) from men with high lottery numbers — except that they faced a much higher probability of military service.

The IV Estimator

Angrist used draft eligibility (a binary indicator for having a lottery number below the cutoff) as an instrument for veteran status. Let \(Z_i = 1\) if man \(i\) had a lottery number below the draft threshold, and \(D_i = 1\) if he actually served in the military. The first stage is \[\begin{equation} D_i = \pi_0 + \pi_1 Z_i + \eta_i, \label{eq:firststage} \end{equation}\] and the reduced form (intent-to-treat) is \[\begin{equation} Y_i = \alpha + \rho Z_i + \nu_i, \label{eq:reducedform} \end{equation}\] where \(Y_i\) is log earnings. The 2SLS estimate is \(\hat{\tau}^{\text{IV}} = \hat{\rho} / \hat{\pi}_1\), the ratio of the reduced-form effect to the first-stage effect. Under the LATE framework (Imbens and Angrist(1994)), this identifies the average effect of military service for compliers: men who served because they were draft-eligible but would not have served otherwise.

Instrument Validity

The lottery satisfies the three IV conditions:

1. Relevance. Draft eligibility substantially raised the probability of military service. Angrist reports first-stage estimates showing that draft-eligible men were around 16 percentage points more likely to have served.
2. Exclusion. Lottery numbers were randomly assigned; a man's lottery number plausibly affected his earnings only through its effect on military service, not through any other channel. There is no direct mechanism by which knowing one has a low lottery number (absent actual service) would change earnings.
3. Monotonicity. It is plausible that no man was induced into civilian life by having a high lottery number who would have served with a low number — the "no defiers" assumption holds naturally here.

One potential concern is draft avoidance: men with low lottery numbers had strong incentives to seek college deferments, medical exemptions, or other ways to avoid service. This does not invalidate the instrument — it just means that not all draft-eligible men served — but it reduces the first-stage strength and sharpens the LATE interpretation to men who could not or did not avoid service.

Data

Angrist used two main data sources:

1. Social Security Administration (SSA) earnings records. These provide individual-level annual earnings for cohorts born in 1950–1953. The administrative nature of the data avoids the non-response and measurement error problems that plague survey-based earnings data.
2. Selective Service System records. These contain the lottery number and draft eligibility status for each birth date in each cohort year.

By merging these sources, Angrist constructed a dataset linking each man's lottery number (his instrument) to his long-run civilian earnings — an unusually clean quasi-experimental setup.

Key Findings

Angrist's main results focused on white men born in 1950–1953, for whom the lottery was conducted in 1970–1972:

• The reduced-form (intent-to-treat) effect of draft eligibility on log earnings was negative: draft-eligible white men earned approximately 2.4 log points less than non-eligible men, averaged over the years 1978–1984.
• The first-stage effect was approximately 0.16: draft eligibility raised the probability of military service by 16 percentage points.
• The IV estimate (LATE) therefore implies that military service reduced civilian log earnings of compliers by roughly \(0.024 / 0.16 \approx 0.15\) — approximately 15% — a substantial and long-lasting penalty.

The OLS estimate is actually positive — veterans appear to earn more than non-veterans — reflecting the positive selection of servicemen (they must pass health and aptitude tests). The IV estimate reveals that once selection is removed, the true effect is negative: military service disrupted human capital accumulation and civilian career development.

Angrist found smaller and statistically insignificant effects for Black men — an important heterogeneity result. For Black veterans, military service may have offered access to training, structure, and networks that partially offset the opportunity cost of civilian experience lost.

Limitations and What We Learn

The IV estimate applies to compliers: men who served because of the lottery and would not have served otherwise. This excludes enthusiastic volunteers (always-takers) and determined draft avoiders (never-takers). Whether these results extrapolate to other populations — volunteers, women, or conscripts in different conflicts — is an open question.

The estimates apply to men born 1950–1953, who served during the Vietnam War and re-entered the civilian labour market in the 1970s, a period of economic disruption. The earnings penalty may reflect the specific economic context as much as the general effect of military service.

Angrist focuses on earnings through the early 1980s, roughly a decade after service. Longer-run effects, including the role of the GI Bill's educational benefits, are not fully captured. Subsequent research using similar designs found that the earnings penalty declined over time as veterans caught up through education and re-training.

Military service affected not only earnings but also health and mortality, via combat exposure, stress, and substance use. Hearst et al.(1986) used the draft lottery to show that Vietnam veterans faced higher suicide and accident mortality. Earnings-based welfare comparisons miss these non-market effects.

This study demonstrates the feasibility of using administrative data linked to quasi-random assignment to estimate causal effects of major life events. It shows that selection bias in naive comparisons can be large and in the wrong direction. And it illustrates the LATE framework's power: even when only a minority of the sample is moved by the instrument (compliers), the estimate recovers a meaningful causal quantity for a well-defined group.

The Angrist (1990) paper helped establish the template for modern IV research: a clearly stated instrument, a well-articulated first stage, reduced-form evidence as a transparency check, and 2SLS as the main estimator. It remains a model for how natural experiments can credibly resolve long-standing empirical debates.