Appendix A

We develop a model of matching on the marriage market that has implications for the effect of deployment shocks on marital stability, and for the selection of couples entering into marriage (Becker, 1973; Becker, Landes and Michael, 1977).

Marriage formation and dissolution

We assume marriage is the outcome of a matching process in a frictionless marriage market and that in equilibrium there is stable matching. The equilibrium is characterized by the relative number of marriageable men and women. Utility is transferable, implying that couples maximize total surplus in equilibrium. Upon marriage, spouses form expectations regarding the value of the match. Let denote women’s contribution to marital gains.[1] Men’s contribution to the match has a common component, an idiosyncratic component and a random component: for civilian men, and for military men. We assume the random component has a zero mean and that the expected marital surplus must be positive for marriage to occur. In the case of military men, we assume for simplicity that the random component is a deployment-related shock.[2] The expected surplus at marriage is for civilians, and for military couples.

If is zero, the family accurately anticipated the deployment experience and there are no changes in the divorce probability. When the deployment experience is different from what was anticipated at marriage, the couple may divorce if The divorce probability of a military couple is: , where is the density function of . Due to the additivity of the elements in the marital surplus, the change in the divorce probability due to can be viewed as a revision in , or as a change toward a policy posture entailing longer deployments such that decreases. [3][4]

Marriage market equilibrium

Given continuous, overlapping distributions of marriage match value and an interior solution in which some but not all civilian and military men marry, the marriage market equilibrium requires positive surplus and equal surplus at the margin between civilian and military marriages:

, for all civilian marriages

, for all military marriages

, at the margin between civilian and military marriages.

The last military man to marry has a that we refer to as . In equilibrium, the number of married military men is , where is the density of , over the continuous interval The number of single military men is and the average deployment-related divorce probability is

.

An unanticipated change in deployments: The case of 9/11

After 9/11, we allow for a term that diminishes the value of the military match, such that the marital surplus of a military couple becomes . The change in deployments is a “regime” change, decreasing the marital surplus’ common component .[5] The probability of divorce for military men married before 9/11 and deployed after 9/11 divorce is , which is always higher than .[6] The average divorce probability, as a result of post 9/11 deployments, in the population married before 9/11 is .

The effect of the deployment shock on the divorce risk among these cohorts is >0. This difference is fully identifiable empirically, because is unanticipated, and thus unrelated to . In these cohorts, the effect of the deployment shock on divorce has a causal interpretation because the effect comes exclusively through the effect of on .

The deployment shock also affects couples that form after 9/11; the surplus of all military couples drops by , so some single military men previously preferred by women get replaced in the ranking by civilians. In the new equilibrium, must hold, with and . The marital surplus of the marginal couple in the new equilibrium is smaller than that of the marginal couple before 9/11. A decrease in affects the margin and changes to , which is smaller than , since . The military men for whom falls in , corresponding to military men in the interval , do not get married, as they cannot generate a marital surplus as large as that for civilian men for whom take values in the interval . The new number of single military men is.

Appendix B

Table B.1. Effect of Time Deployed During First-Term of Duty on Divorce and Reenlistment

Divorce / Reenlistment
Months deployed / 0.008*** / -0.001***
(0.000) / (0.000)
Female / 0.156*** / -0.124***
(0.007) / (0.000)
Black / -0.025*** / 0.101***
(0.003) / (0.003)
Hispanic / -0.013*** / 0.017***
(0.003) / (0.003)
High school dropout / -0.020*** / --
(0.007)
Some college / 0.043*** / --
(0.006)
College / 0.046*** / --
(0.009)
Years in military / 0.022*** / --
(0.001)
Rank 1-3 / -- / -0.457***
(0.002)
Rho / -0.104***
(0.028)
Observations / 275,003

NOTE: Models include the set of controls described in Section II. Standard errors in parentheses; * p<0.10, ** p<0.05, *** p<0.01.

[1] For simplicity we assume that all women are the same and are civilian and that the realized value of is the same as its expected value at the time of marriage.

[2]An explicit modeling of non-deployment shocks is straightforward, but it does not change the main implications of the model.

[3] The civilian couple’s idiosyncratic component captures the impact of spousal absences on the marital surplus, such that a future downward revision of may also lead to divorce.

[4] It may be the case that when the common component of the military couple decreases, service members leave the military and become civilians in order to avoid divorce. We do not model explicitly this possibility. However, we find empirical evidence to the contrary (See Section V and the Appendix).

[5] Given we allow for the term to enter additively in the marital surplus, it is irrelevant if the change in post 9/11 deployments affects the common or the idiosyncratic component. Moreover, even if the negative change affects some service members more than others, i.e., even if varies by individual, the qualitative results of the model remain the same.

[6] The result follows from writing as: .