Going to War and Going to College: Estimation Strategy

Going to War and Going to College: Estimation StrategyIII. Estimation Strategy
To estimate the causal effect of veteran service and the associated availability of educational benefits through the G.I. Bill on collegiate attainment, we focus on two measures of collegiate attainment: years of college completed (0-4) and receipt of baccalaureate degree measured by 16 years of completed schooling. Let
Edij = aj + P ij Vij + e j
where Edij represents the educational attainment of individual i in cohort j, Vj is an indicator variable equal to 1 if the individual served in World War II, and eij is an error term. Conceptually, aj represents the mean educational attainment for randomly selected individuals from cohort j under the assumption that the individual did not serve in the military, while fy- represents the effect of military service for individual i in cohort j. Note that we are allowing the coefficient on Vj to vary across individuals – there is no reason to believe that service during the war would effect all of those that served in the same way.
Some individuals would have received a college education regardless of service, others would not have attended regardless of service. For both of these populations pij = 0. On the other hand, some who would not have otherwise attended college, may have been encouraged to attend college by the generous benefits available. For this population, the effect is positive and bij > 0 . Stated in this way it should be clear that fa represents the partial equilibrium effect of service of individual i — fa represents the impact on post secondary educational attainment of switching the ith individual’s veteran status, holding the veteran status of other individuals constant. To understand the (partial equilibrium) impact of the war on educational attainment we are interested in estimating b ° E(bij | Vij = 1) – what in the program evaluation literature has been referred to as the effect of treatment on the treated.
One can imagine various strategies to estimate b. The simplest approach is to simply compare mean educational attainment between veterans and nonveterans for a cohort of individuals:

Formule 1

The term in the square brackets represents the difference in the propensity to go to college of those that did and did not serve in the military. As long as selection into the military is nonrandom, this term is unlikely to be 0. In fact, given the nature of the exemptions from the draft that existed during World War II, we would expect that for the cohorts that served in World War II, the term in brackets would be positive. As a result, the simple comparison between those who did and did not serve will exaggerate the causal effect of service on educational attainment (E(faj) > b ).