Online Resource 1 Home Front: Post-Deployment Mental Health and Divorces Brighita Negrusa and Sebastian Negrusa

Construction of the Analytic Data Set

Over our period of analysis, between March 1999 and June 2010, about 450,000 individuals joined the Army active-duty component. About 27 % of these individuals were married when they joined, and the rest were single. We keep only the individuals who married after they entered service to ensure that at the time of marriage both spouses are aware they are becoming a military family and thus form appropriate expectations regarding their gains from marriage. We drop all entrants who were single at enlistment and who were not yet married as of June 2010, the end of our observation period. We therefore retain all single Army soldiers who entered service after March 1999 and got married in service at some point until June 2010. This represents a number of 245,261 individuals (224,484 enlisted personnel and 20,777 officers).

Further, we drop the observations that do not correspond to the soldiers’ first marriage. Because the PDHA was first administered in 2003, we exclude all soldiers who deployed exclusively between 1999 and 2003, given that they do not have PDHA information. Also, we drop an additional 95,575 deploying enlisted members who do not have PDHA information. We also exclude the enlisted personnel who have PDHA information only from the time they were single

(i.e., 19,205 individuals) as well as individuals with missing values for key analysis variables

(about 60,000 individuals). Next, to make sure we are not capturing the effect of any prior trauma from before marriage, we exclude 2,959 enlisted personnel who report post-deployment

PTSD symptoms prior to marriage.

One potential issue with keeping only deployed soldiers that have a completed PDHA form may be that Army soldiers who complete the form are a nonrepresentative sample of

1 deploying soldiers. However, as shown in Table S1, which presents means of the demographic characteristics of both PDHA and non-PDHA completers, this does not appear to be the case.

The individuals in the pooled sample have virtually the same means by race, gender and education. Also, they look the same by ability scores (AFQT) and by distribution across military occupations (not shown). This is consistent with Hoge et al. (2006), who also showed that across observable characteristics deployed Army service members that have no PDHA forms are very similar to their counterparts with PDHA forms. Across the sample of PDHA completers and the pooled sample, the difference in the fraction of divorces and in the time-varying characteristics

(e.g., years married and cumulative time deployed) are not due to inherent dissimilarities but rather to the fact that for some individuals, the first deployment that is accompanied by a PDHA form does not coincide with their first deployment. Thus, PDHA completers are simply observed, on average, a few months later in marriage, which means that the estimates obtained from the sample of PDHA completers remain representative for the entire sample of deploying soldiers.

Figure S1 shows a list of variables used in the empirical analysis, grouped in three categories: time-invariant variables, time-varying variables (updated quarterly) and post- deployment variables coming from the PDHA and PDHRA forms.

Potential Endogeneity of PTSD Symptoms and Divorces

We acknowledge the possibility that unobservable factors that make an individual more likely to have PTSD symptoms can also increase the probability of divorce after deployments. It is possible that omitted variables (e.g., childhood adversity, family history of mental health problems or other individual vulnerabilities) could increase both the likelihood of PTSD

2 symptoms and the probability of subsequent divorce. If so, the estimates of PTSD symptoms obtained from our discrete hazard models are overestimated and cannot be interpreted as unequivocally causal. However, we believe that the unique features of our longitudinal data and approach, and our focus on a mental health problem that is unlikely to be driven by pre- dispositional characteristics, help mitigate this concern.

Nonetheless, to account for the potential endogeneity of PTSD symptoms, we estimated instrumental variable models in which we instrument for PTSD symptoms. In order for an instrument to be valid, it must be correlated with PTSD symptoms, but uncorrelated with divorce. The natural candidates for valid instruments are variables that provide information on combat exposure; and, to the extent that PTSD symptoms are the result of trauma and shock, another set of likely instruments are variables containing information on whether the soldier visited the sick bay during deployment, and the number of visits in sick call.

In Table S2 we present estimates from two-stage least squares (2SLS) models, along with statistics on endogeneity tests (Wu-Hausman), partial R2, and tests of overidentifying restrictions.

In the IV Models 1 through 5, respectively, we use as instrumental variables number of visits in sick call and combat exposure; whether visited sick call and combat exposure; sick call, combat exposure and an interaction term between the two; sick call, combat exposure and an interaction term between the two plus the number of visits; and number of visits, combat exposure, and an interaction term between the two. Estimating the 2SLS models at different points in time after the deployment end date (6, 12, and 18 months), we observe that the IV estimates of PTSD symptoms are positive and, in most cases, statistically significant. However, the magnitude of the coefficients and standard errors relative to those of the OLS estimates show that the IV estimates should be viewed with caution, given that their validity relies on the choice of instrument.

3 First, based on the endogeneity tests reported in Table S2, the PTSD symptoms variable cannot be unequivocally treated as endogenous. In fact, we can never reject the null hypothesis of PTSD symptoms being exogenous at the 5 % significance level or lower. Assuming however, that PTSD symptoms are endogenous, the instruments we use have positive, large, and highly significant coefficients in the first-stage regression, but the R2 is always lower than 0.1 (not shown), and the partial R2 values associated with the instruments are also very small. This is equivalent to a case of weak instruments. A direct consequence of the small partial R2 values is the very large standard errors in the IV models, relative to the standard errors from the OLS models. More importantly, the very small partial R2 values make the IV estimates vulnerable to even slight correlations between the errors and the instruments, resulting in great losses of precision. This problem may arise even in the case of large data sets and it does not disappear with the inclusion of additional instruments (Bound et al. 1995). The Bassman test for overidentification indicates that the instruments are valid in most cases, but some of the excluded instruments may not be exogenous for some models, thus making the IV estimates inconsistent.

We conclude that even if some degree of endogeneity of PTSD symptoms exists, finding better instruments presents serious challenges for the current study, and should be the topic of future research.

Interestingly, the OLS estimates are of the same order of magnitude as the discrete hazard estimates, showing an increase in the probability of divorce by about 15 % to 20 % among soldiers with post-deployment PTSD symptoms. However, the models in Table S2 do not account for the right censoring and do not make use of the longitudinal aspect of the data, as is the case with our discrete hazard models.

4 Another strategy to account for unobserved heterogeneity is to estimate discrete hazard models with frailty. However, when attempting to estimate such models, often the iteration algorithm fails to converge, which may be an indication that the variance of unobservable characteristics is degenerate (e.g., Jenkins 1995). In fact, in the few cases for which the algorithm did converge, the estimates were similar to the ones from the model without frailty; and more importantly, the estimate on the variance of unobservable factors was virtually zero. Along with the findings from our exploratory IV analysis, we interpret this as an additional indication that the effects of PTSD symptoms on divorce we estimate in the main model are unlikely to be affected by unobserved individual characteristics.

Other Mental Health Measures

Finally, using the two other measures of mental health symptoms, we estimate that those returning from deployment with depression symptoms or who screen positive for “any mental health concern” have higher divorce hazards relative to those without such symptoms, as reported in Table S3. Although the coefficient on depression is likely to reflect a combination between post-deployment depression symptoms and individual pre-dispositional variables, it provides additional support to the general hypothesis that post-deployment mental health problems affect the stability of military marriages. Because the “any mental concern” is defined by including both PTSD and depression symptoms, the coefficient on that variable is always larger than the coefficients on PTSD or depression symptoms.

5 Figure S1 Variables Used in the Empirical Analysis

6 Table S1 Summary Statistics on Demographic and Deployment Variables for PDHA and Non-PDHA Completers Enlisted Officers

Demographic Variables

Divorces 0.063 0.055

Years married 2.5 3.1

Years married at divorce or exit 2.8 3.4

Age at marriage 23.1 25.6

Number of children 1.0 0.7

Female 0.103 0.136

Hispanic 0.120 0.054

Black 0.182 0.090

No high school diploma 0.018 --

High school diploma 0.940 0.008

Some college 0.019 0.001

College 0.021 0.991

Post-Deployment Variables

Months deployed 13.7 14.1

Months deployed at divorce or exit 14.5 15.3

Observations 461,425 56,324 Individuals 91,271 9,885

7 Table S2 OLS and IV Estimates of PTSD Symptoms – Enlisted personnel

OLS IV (1) IV (2) IV (3) IV (4) IV (5) 6 months post-deployment PTSD (longitudinal) 0.005* 0.007 0.012 0.011 0.018 -0.000 (0.002) (0.022) (0.022) (0.022) (0.020) (0.020)

N 56,267 56,267 56,267 56,267 56,267 56,267 R-sq 0.020 0.020 0.020 0.020 0.020 0.020

Wu-Hausman (p-value) -- 0.906 0.739 0.783 0.497 0.800 Partial R-sq -- 0.013 0.012 0.012 0.015 0.015 Bassman test (p-value) -- 0.019 0.001 0.004 0.009 0.061 12 months post-deployment 0.011** PTSD (longitudinal) 0.044 0.071** 0.066** 0.054** 0.048* * (0.003) (0.029) (0.031) (0.032) (0.028) (0.028)

N 46,399 46,399 46,399 46,399 46,399 46,399 R-sq 0.027 0.025 0.020 0.021 0.023 0.024

Wu-Hausman (p-value) -- 0.237 0.059 0.080 0.114 0.182 Partial R-sq -- 0.013 0.011 0.011 0.014 0.014 Bassman test (p-value) -- 0.334 0.024 0.047 0.073 0.073 18 months post-deployment PTSD (longitudinal) 0.009** 0.080** 0.089** 0.090** 0.085** 0.079** (0.004) (0.041) (0.044) (0.044) (0.040) (0.041)

N 38,347 38,347 38,347 38,347 38,347 38,347 R-sq 0.027 0.019 0.017 0.017 0.018 0.019

Wu-Hausman (p-value) -- 0.079 0.073 0.067 0.055 0.079 Partial R-sq -- 0.010 0.008 0.008 0.010 0.010 Bassman test (p-value) -- 0.655 0.475 0.673 0.834 0.903

Note: Model 1 uses number of visits and combat exposure as IVs, model 2 uses sick call and combat exposure as IVs, model 3 uses sick call, combat exposure and interaction between sick call and combat exposure as IVs, Model 4 uses all IVs from Model 3 plus the number of visits, and Model 5 uses visits, combat exposure and interaction between the two as IVs.

8 Table S3 Screening Positive for Various Mental Health Symptoms and Divorce – Enlisted personnel

Enlisted Officers (1) (2) (3) (4) (5) (6)

Deployed 1.931*** 1.939*** 1.917*** 0.594** 0.646** 0.555* (0.121) (0.121) (0.121) (0.293) (0.293) (0.293)

PTSD 0.195*** 0.535*** (0.040) (0.138)

Depression 0.111*** 0.437*** (0.032) (0.114)

Any Mental Concern 0.237*** 0.786*** (0.033) (0.112)

Observations 360,012 360,012 360,012 48,086 48,086 48,086

Note: *, ** and ***: significant at 10%, 5% and 1%. Regressions include the variables described in Section 3.

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