Moving and Marriage in the US Military

#JHR_Threads "Making Big Decisions: The Impact of Moves on Marriage Among US Personnel" by Susan Payne Carter and Abigail Wozniak

“Making Big Decisions: The Impact of Moves on Marriage Among US Personnel" by Susan Payne Carter and Abigail Wozniak, 2021, Journal of Human Resources, forthcoming. (URL)


Growing up, I had several classmates who had just moved to town because one of their parents was employed in the military. These kids would one day show up to school, stay a few years, and then move when their parent had been reassigned somewhere else.

These types of military moves, I would later learn, were both sort of expected and sort of unpredictable for the family. They knew the moves were coming but didn’t know quite when. The timing of that move, in other words, was the random piece. They must have felt as though someone above them was pulling balls from an urn, calling out numbers, and when theirs was called, off they’d go to the next location.

The US Army’s operations and logistics is tasked with the responsibility to allocate its capital and people across its varied needs in the most efficient way possible. That efficiency requires requires maintaining capital’s balanced equilibrium across countless posts and locations. The allocation of these scarce human resources involves moving people from one place to another regardless of whether the worker is in love or not.

Few of us outside the military experience moves in this way. We do not wake up each day wondering if the Universe will flip a coin and if heads tell us it is time to pack up and leave. Most of us outside the Army have agency over such big decisions as moving. But because we choose when and where to move, it is challenging to say what effect those moves will have over our families because so few of us moved randomly.

When I graduated from the University of Tennessee in 1999, my then on-again, off-again girlfriend and I had just broken up. As I had no career ambitions whatsoever, I decided to move to New Orleans to be near family, in search for a new beginning. I had moved, but not randomly. My moving to New Orleans was purposeful.

But one night I dialed the wrong number and accidentally rang my ex-girlfriend’s phone. As fate would have it, we talked for several hours and in May of 2000, we were married. Perhaps the move caused us to marry, or perhaps not marrying caused me to move. It was impossible to say from observing just one person’s life. The post hoc ergo propter hoc fallacy says that just because two things happen in a row does not mean the first thing caused the second. My move to New Orleans had preceded my marriage, but in hindsight it seemed that it had been my belief we were not to be married that had caused me to move in the first place! If I inputted these choices from this brief window of my life into a longitudinal dataset, it would show up as a series of time delimited rows like:

  1. year=1998, move=0, married=0;

  2. year=1999, move=1, married=0;

  3. year=2000, move=1, married=1

With a large enough rectangle of individuals’ moves and marriages, we could run a fixed effects regression of marriage onto lagged moves, but would this regression suggest a causal effect? If strict exogeneity held, then yes, but given the simultaneity of marriage and moves, probably not. So maybe moving causes marriage, maybe marriage causes move, or maybe both are just spuriously tied together through strange and complex non-causal channels. Who can say.

This problem is so uniquely hard to answer because of how big both decisions are. Big decisions cause moves and marriage to become gnarled in endogenous knots tied so tight that not even panel data can disentangle. Neither moves nor marriage are entered into lightly, require comparing and trading off several major life goals and as such, draw upon many of the same scarce resources like time and money. Simple comparisons in marriage rates between movers and non-movers will therefore be profoundly polluted by selection bias, but randomization? Well randomization can always help us tease out the strands of causal chains. Randomization is the hot knife that moves easily through butter no matter how thick and cold it has become.

This substack is about a recent paper by two excellent labor economists who found just such a hot knife. By surgically twisting just that knife just so, they revealed that moving increases the likelihood people will marry even with all these gnarly knots. Today I will explain and give my interpretation of a forthcoming article in the Journal of Human Resources by Susan Payne Carter and Abigail Wozniak, at West Point and the Federal Reserve, respectively. Carter and Wozniak exploit a living laboratory in the United States Army’s logistics and operations to determine if moving changes the decision to marry, and in so doing, helps shed light on which, if any, of our economic models are the most helpful for understanding moves and marriage.

Economic theories of marriage

The economics of marriage dates back at least to Gary Becker’s seminal 1970s work. Becker’s work was extremely influential, and led to more models expanding on his core insights. Today we have even more models describing and predicting the purpose and consequence of marriage. Most if not all of these models assume marriages are the product of rational thought caused by forward looking people looking for partners with whom to build a life.

Despite their reputation as a cold bunch, economists are surprisingly deferential to others. This is because our models have trained us to believe that people know best what to do with their own lives and so, whenever possible, are instincts are to trust that voluntary participation will lead to the best outcomes so long as it is guided by sane institutions and level environments. This trust carries over to our models of marriage which tend to lead to a natural conclusion that since people know best when, whether and to whom they should get married, we should probably just let them do it without interference. After all, how likely is it that our interference could lead to a better equilibrium over something as psychologically and economically complex as marriage and love?

This respect for other’s agency can be easily overlooked given all the equations, Greek letters and opaque mathematical symbols. No one would ever accuse Gary Becker of being a romantic if they knew he required love to satisfy first order conditions. In Becker’s theory of marriage, peoples talents and skills created complementarities such that a households production from its economies of scale left each person with more utility than was possible apart. Listen to this beautiful sonnet explaining love and marriage, for instance.

“A person decides to marry when the utility expected from marriage exceeds that expected from remaining single or from additional search for a more suitable mate. Similarly, a married person terminates his (or her) marriage when the utility anticipated from becoming single or marrying someone else exceeds the loss in utility from separation, including losses due to physical separation from one’s children, division of joint assets, legal fees, and so forth. Since many persons are looking for mates a market in marriages is said to exist.”

Influenced by Becker’s classic market model, several economists trained in new game theory tools began to explore issues related to the division of household resources between married partners and children. Nash cooperative bargaining models, as they were called, by Manser and Browne (1980), McElroy and Horne (1981), as well as the noncooperative ones like Lundberg and Pollack (1993), incorporated outside options and bargaining into the theory of marriage. When outside options collided with a person’s exogenous bargaining weights, then each potential spouse had “bargaining power” over the division of utility produced inside the marriage. The more power she possessed, the more household resources she could consume. And if and when her outside options produced expected utility larger than that within the marriage, she would either renegotiate the terms of the marriage, endure the opportunity costs without leaving, or exit the marriage through divorce.

And then there were the search models like the ones economic theorist, Lones Smith at Wisconsin, developed. As Lones and his coauthors say in their 2017 article, “Sorting Through Search and Matching Models in Economics”, people spend a great amount of time trying to find the right match. And so anything which alleviates or increases the frictions associated with marital search is likely to shift both when a person marries and to whom, and sometimes even in surprising ways depending on preferences and participants in the market.

These three models — Becker’s market model, the Nash bargaining models, and the models of search — are some of the most common models economists use when trying to understand such fundamental units of human life like marriage and divorce. Whether any of these models are remotely relevant for understanding real life marriages is another question and one that Carter and Wozniak contribute to in this paper.

Moving’s Effect on Marriage

If we want to know the price elasticity of demand, then we need exogenous changes in relative prices, but what does that even mean? “Exogenously changing prices” describes when a good’s relative price moves for reasons that are cut off from changes in people’s preferences, consumer incomes, the prices of similar and competing goods, the number of buyers in the market, and/or consumers beliefs about future prices. The only time, we think, when prices will change but none of those others is when supply curves change, because when supply shifts, prices change through markets adjusting to a new equilibrium. Events such as increases in input costs can cause supply to shift thus allowing us to trace out the price elasticity of demand as we move up and down a demand curve.

That same basic logic of identification applies to the question of moves’ impact on marriage. If we want to know the impact of moving on marriage, then we need moves to exogenously change. An exogenous move is a move that occurred for unnatural reasons beyond their control, like when one’s military employer tells them it’s time to move.

Employees of the US Army are reassigned by the Army’s visible hand. When the Army decides when to move a person, that person moves. It doesn’t matter if they’re training for a marathon, catching up on the latest episode of Only Murders in the Building, just started a new campaign at their friends’ dungeons and dragons group, or on their second date with a cute girl they met at the gym. When the Army tells an employee it’s time to move, then it’s time to move. US Army employees’ courtship and love lives are not constraints when seeking to maximize its own Lagrangean.

This is precisely what Carter and Wozniak claim is the case within the US Army. The Army does not make its human resource allocation decisions based on love or even work opportunities, but rather the need to plug in holes across the world. The authors quote from Army human resources policy which reads:

“[T]he primary considerations in reassigning a Soldier shall be the Soldier’s current qualifications and ability to fill a valid requirement. Other factors such as availability, volunteer status, TOS [time on station, or current posting length], and other criteria shall be secondary.”

If the Army is moving its personnel exogenously, then moves are as good as random, at least with regards to employees’ ordinary decisions to enter into marriage. Given such unique changes in moves, we could compare the marriage rates of movers to non-movers to calculate the causal effect of moves on marriage. The elimination of the selection bias associated with movers is what the hot knife of randomization buys us. It is no wonder that so many labor economists spend large chunks of their careers both studying the military’s operations and using its idiosyncratic features for causal inference (see here, here, here and here).

Summarizing Essentials in Army Dataset

Susan Carter is West Point faculty and that gives her access to administrative records on over 180,000 Army personnel. She and Wozniak use a subsample that records both an employee’s total number of moves as well as their marital status at any time. Some basic information about the average characteristics of these individuals is listed in Table 2 below. The majority of their data are males in their mid-20s. Most are White and 76% have a high school degree only. Sixty-nine percent have ever been deployed and when they were, they were deployed for on average 10 months. The total number of years in service is 8 and the total number of moves was 0.58 at the time the data was collected.

Table 2 also records basic facts about the marriage outcomes of Army personnel. For instance, conditional on not being married when they entered the Army, 55% are now married, 53% remain married at their fifth year, and the age at which they married was 23. Only 9% had dissolved their marriage conditional on having been ever married during the 5 years under the authors’ consideration.

Since randomization is so key to identification in this study, the authors spend some time showing that moves are indeed quasi-random. There are several ways one might go about checking if moves are indeed random. One way that I like is to simply ask people whose jobs it is to know these sorts of things. Carter and Wozniak are clearly well versed in those sorts of institutional details and their writing conveys confidence that indeed Army human resource allocations are invariant to the love lives of its employees.

But a second way one might go about checking for randomization is to create a “balance table” in which covariate values are compared across the distribution of the treatment variable itself (i.e., moves). Since moves is cardinal, and not binary, the authors instead run several regressions with and without employee covariates to check whether their regression models’ predictive power improves when more variables are included. Table 3 shows the results from that type of statistical logic and our focus should be on the R squared listed in the third row from the bottom of the table. Notice that this statistic does not change much when the authors include employee covariates, even though these covariates are significant. Thus the authors conclude that the conditional randomization assumption is reasonably holding in their data.

Econometric methodology

Daniel McFadden once said that a good way to go about econometrics is to look for natural experiments and use statistical models to clean up the stuff nature left messy for us. The cleaner the original natural experiment had been in the first place, the less cleaning you need to do afterwards. Carter and Wozniak do not need much hardware to clean up any mess because conditional physical randomization within their data does most of the cleaning for them.

Table 4 contains their “main results”. I put that in square quotes to note to junior faculty and students that a “main results” table is very common when structuring an applied micro paper. It’s the a table that functions as both an end in itself (the main results) as well as a paradigm through which all subsequent tables (like heterogeneity analysis) will be interpreted. Their main results table has three panels, each panel on a distinct yet similar measure of marriage — were they ever married conditional on not being married originally, were they married after 5 years also conditionally, and were they married after 5 years unconditionally. Each of the models include demographic controls which are listed in the footnotes. Stars correspond to statistical significance, and robust standard errors are displayed in parenthesis. The econometric model is a simple linear probability model estimated with OLS.

Panel A shows the effect of moves on the probability of getting married conditional on not being married before. As moves can be more than 1, the coefficient represents the return to each additional move. For every additional move, the linear probability of marriage rises 0.08. It moves around a little for different samples, but the differences are not likely statistically significant.

As I said earlier, I tend to think of self-selected marriage as more stable than marriages forced upon a couple. Thus any marriages created by moving would, to me, seem less stable than ones formed endogenously if only because the decision to marry is being rushed and I tend to think people are good at managing their own lives without pressure anyway. And so panel B of Table 4 intrigued me because if these marriages induced by moves were, in fact, unstable, I should expect to see a drop off by year 5. But the coefficient on moves is in Panel B is roughly identical to the one in Panel A. Panel C regressions have even people who were married prior to the entry into the Army but results don’t really change.

Table 5 explores these effects in more detail. Panel A shows that being pushed into marriage because of a move cause personnel to marry at younger ages than they would have otherwise Panel B shows that the moves are also causing the personnel to establish families much faster than they would’ve otherwise.

Panel C provides some evidence for my hunch that these marriages are less stable and perhaps suboptimal at the margin, though the effects are admittedly very small. Nonetheless, the linear probability of divorce increases by 0.005 off a mean of 9% suggesting these moves are marginally less stable, but surprisingly to me, not so much as to be of any real consequence probably. Most of these people remain married at the end of the period under consideration (Table 4, Panels B-C).

A good picture is far more effective in causal projects than many people realize. When designed well, a good visualization of your causal results is far more persuasive than a table filled with numbers, asterisks and parentheses. Carter and Wozniak help get their point across with a series of event study plots showing the frequentist probability of marriage along a move in relative event time. Notice how in Figure 2, for instance, the probability of marriage is rising straight through the zero line. In the month before marriage, the probability flattens, followed by a sizable increase in the first month after a move which then decays with time. This figure suggests that moving triggers the marriage probability because the marriage probability is shifting right around the point when the treatment occurs. Thus we have some evidence again that the estimates reported earlier are indeed causal.

Interpretations and Conclusion

Steven Levitt, a professor of economics at the University of Chicago, published recently an article in the Review of Economic Studies entitled “Heads or Tails: The Impact of a Coin Toss on Major Life Decisions and Subsequent Happiness” that examined what happened when you nudged indecisive people to go through on hard decisions. He recruited thousands of such indecisive people and offered to take the decision out of their hand by deciding with a coin flip. Heads, he would suggest they quit the job they said they didn’t like. Tails, he would recommend they stay. Levitt flipped the coins thousands of times and after telling each respondent the result let them go. Much later, he caught back up to them to see how they about life and found two very interesting things. First a large number of people who got heads “complied” with the coin flip, despite it being a major life decision. And of those who went through the hard choice as a result of their coin outcome, there were significant increases in self-reported happiness months later.

While Carter and Wozniak are studying a topic far different from Levitt’s, both papers share in common a somewhat subtle suggestion that humans around major life decisions may not always be capable or willing to do what is perhaps in their own best interest. If people are optimally sorting into marriages when and with whom they want, then any jiggling like inducing sweeping geographic relocations could only make resulting marital assignments weakly worse. They either have no effect, or they cause the marginal marriage to be relatively unstable. Carter and Wozniak, though, find almost no effect on divorce. Moving induces these people to get married sooner than they would’ve, and by all appearances, these marriages have long legs. They remain together up to five years out and have had children together. It would seem that at least over the windows of time and behaviors that these two researchers can observe, these shocks did not create unstable marriages — a finding that will keep me reflecting on some of my core beliefs about marriage and matching for quite some time.

Interview with Susan Carter and Abigail Wozniak

Below is a 30 minute interview I did with Susan and Abigail. Originally Abby was dialing in with her rotary phone and therefore we could not see her, which prompted me to make a joke in which I said it will be interesting to see what Abby was wearing (thinking we would all then laugh when you saw a picture of her phone). About one second passed and I realized that that was not going to sound well to anyone else. I could probably stand to be a bit more indecisive with my jokes going forward.