Going to War and Going to College: Primary strategy

The primary strategy we use to try to estimate b is to compare educational attainment across cohorts. To discuss the rational for such an approach we start by assuming a time homogenous environment – i.e. the a’s and the distribution of the b’s are constant across cohorts. Now imagine comparing cohorts across time. Define d Ed as Edij – Ed if . Then:

Formule-2

Given the close to universal service during World War II, this seems like a reasonable assumption. Under this assumption cross cohort changes in educational attainment divided by cross cohort changes in the fraction of the cohort serving identify the average effect of service for the population that would have served in one regime but not in the other – what Imbens and Angrist have referred to as the local average treatment effect (LATE).
In practice it is unrealistic to assume a time homogenous environment. Since the fraction of the population attending college was rising both before and after World War II, it seems natural to assume that the a’s rose over time. To account for such secular changes we include a linear time trend in the analysis. Thus, deviations from a trend identify the effect of veteran status on educational attainment.
Beyond this, it is easy to imagine that the distribution of b’s might change over time. Thus, for example, individuals from cohorts that had, for the most part, started careers before being called to serve would probably be less likely to be induced to attend college than would individuals drawn from cohorts that were called up immediately out of high school. We deal with this issue by, when possible, focusing on comparisons between closely adjacent cohorts. In particular, we focus on cohorts that would have entered military service shortly after turning 18 (or shortly before, if they volunteered). We discuss these issues further in the context of specific estimates.
Our empirical strategy closely follows much recent discussion of the estimation of causal effects. It has long been understood that under suitable assumptions comparisons over time could be used to eliminate selection bias (Heckman and Robb, 1985). Effectively what we are doing is to use cohort dummies to form an instrument for veterans status. The connection between instrumental variables and time aggregation has been noted by various authors (e.g. Angrist (1991), Moifitt (1995)). Condition (4) is exactly analogous to the monotonicity condition discussed by Imbens and Angrist (1994).