Examining the Distributional Effects of Military Service on Earnings: A Test of Initial Dominance

Abstract

Existing empirical evidence suggests that the effects of Vietnam veteran status on earnings in the decadeand-a-half following service may be concentrated in the lower tail of the earnings distribution. Motivated by this evidence, we develop a formal statistical procedure that is specifically designed to test for lower tail dominance in the distributions of earnings. When applied to the same data as in previous studies, the test reveals that the distribution of earnings for veterans is indeed dominated by the distribution of earnings for nonveterans up to $12,600 (in 1978 dollars), thereby indicating that there was higher social welfare and lower poverty experienced by nonveterans in the decade-and-a-half following military service.

Exploring skill distribution tails through stochastic dominance

“…Given the cumulative distribution functions (CDFs) F and G, Bennett and Zitikis (2013) state the following hypotheses for their test of initial dominance:…”

“…In order to implement the test, Bennett and Zitikis (2013) suggest the following suitably scaled estimator: where m and n are the sample sizes of CDFs G m (x) and F n (x) and x m,n is the estimated point maximal point of initial dominance (MPID) where the distributions cross for the first time. Bennett and Zitikis (2013) estimate x m,n as a function of the tuning parameter 𝛿 m,n > 0, and suggest 𝛿 m,n = 𝜅((m + n)∕(mn)) 1∕2−𝜖 with 𝜅 = 10 −6 and 𝜖 = 0.01 as a practical choice for this parameter. This is also the parameter choice used in this paper as changes to the parameter values in line with those presented in the Bennett and Zitikis (2013) paper did not lead to significant changes in results.…”

“…Bennett and Zitikis (2013) estimate x m,n as a function of the tuning parameter 𝛿 m,n > 0, and suggest 𝛿 m,n = 𝜅((m + n)∕(mn)) 1∕2−𝜖 with 𝜅 = 10 −6 and 𝜖 = 0.01 as a practical choice for this parameter. This is also the parameter choice used in this paper as changes to the parameter values in line with those presented in the Bennett and Zitikis (2013) paper did not lead to significant changes in results. Furthermore, in order to calculate critical values, Bennett and Zitikis (2013) use a pooled bootstrap method that closely follows Barrett and Donald (2003).…”

“…The Bennett and Zitikis (2013) test of initial dominance lends itself well for the investigation in this paper as it is designed to test for stochastic dominance up until the first crossing point of two distributions. Hence, it can be used in this instance to determine the crossing point of the distributions in each tail, and to test whether or not there is dominance in the tails which would indicate thicker tails in large cities.…”

“…The early and multiple crossing points in the right tail are a consequence of wage top-coding in the utilized data. Thus, the test of initial dominance by Bennett and Zitikis (2013) in its current form is not well-suited for investigating the upper tail when data is top-coded.…”