Marital Shopping and Epidemic AIDS

Abstract

Introduction

A well-established consensus within the medical literature indicates that the average transmission rate of HIV is extremely low, on the order of 1 in 1,000 per sex act (e.g., Fideli et al. 2001; Gray et al. 2001; Quinn et al. 2000), or 8%–12% per partner-year. Despite this, antenatal prevalence is 40% in Botswana and 25% in South Africa, suggesting that many have been afflicted by this extremely unlikely event. Unsurprisingly, social scientists, epidemiologists, and the popular press have each weighed in on what sorts of behavior could yield such an outcome, with behavioral explanations ranging from heterogeneous preferences for risk (Kremer 1996) to networks of concurrent sexual partners (Morris and Kretzschmar 1997) to unfaithful husbands (Kristof 2005). An implicit criterion in evaluating each of these models is that high HIV prevalence can be obtained despite low transmission rates.

In this article, I ask which of these explanations could explain a majority of infections, and propose that the age-profile of infection represents a second useful criterion in assessing behavioral models of HIV. Death registries in South Africa reveal a strong age trend: HIV infection risk declines sharply after age 30 for women (and after age 35 for men). I open this article by discussing the age profile of infection, and illustrate that this decline in risk occurs too early in life to be explained simply by changing preferences with age, at least if these preferences are correlated with reported coital frequencies or pregnancy rates. I then argue that we can parse most existing behavioral HIV models into those that predict increasing risks with age and those that suggest age-independence (although a spurious decline with age may be generated by the absorbing nature of HIV infection). Intuitively, the sharp decline in risk levels with age seems unlikely to be generated by behavior for which risk is age-independent or age-increasing; as a formal test, I calibrate a flexible model of age-independent heterogeneous risk and find that this class of models does not fit the age-death profile in South Africa well, suggesting that age-independent models do not explain how most people contract HIV.¹ Because these models dominate age-increasing risk in terms of fitting the observed age profile of HIV infection, rejecting age-independent models rules out this latter class of models as well.

Instead, the age-death profile prefers a model of decreasing risk, with risks of new infection declining at around age 30 for women (shortly after the median age of first marriage). This age profile, combined with an empirical trend that longer marital tenures are associated with reduced infection risks, suggests that the process of becoming married may be dangerous. This article is the first to show that a simple search and matching model of serial monogamy is capable of generating high prevalence with relatively few partners because short periods of high partner turnover coincide with a brief window of high infectiousness immediately following infection. That is, epidemic AIDS is possible even when the majority of individuals do not engage in high-risk behaviors. I then argue that a matching model of spousal search fits three additional empirical trends in the data. First, the model generates an age-death profile fitting that observed in South Africa across the duration of the epidemic well for both women and men—a close fit that is robust to a large variety of parametric assumptions. Second, the model closely predicts both the level and intertemporal variation in the annual number of partners that young adults report. Third, it suggests that spending a long time single should be associated with risk, but that the correlation between premarital sexual behavior and HIV should be eliminated for women who have been married for several years, a trend that is confirmed empirically across Africa. Finally, I evaluate the public health implications of “marital shopping” as an important vector for the spread of HIV by examining policies of transmission rate reductions, short-term condom usage, and antiretroviral (ARV) treatment. Short-term condom use is found to be the most effective of these strategies, and it eliminates the potential of spousal search to create an HIV epidemic when combined with the lower transmission rates found in the United States and Europe.

HIV in South Africa

Much of the data that could be used to learn about covariates of HIV infection is suspect. Antenatal prevalence data is subject to selection bias, population survey data often have high refusal rates, and cause of death statistics may be rigged. Changes in overall death rates in areas where the epidemic hit suddenly and recently, however, are immune to these concerns. Figure 1 presents deaths by age and gender observed in South Africa, where death registration is relatively complete (Dorrington et al. 2001; Statistics South Africa 2005). Epidemic AIDS is a recent phenomenon in South Africa, where antenatal prevalence was about 1% in 1990 (RSA 2008; U.S. Census Bureau 2006). This is reflected in the bottom line of each panel of the figure, which shows a relatively flat deaths-by-age profile in 1996. The top line, in contrast, tells a different story. By 2002, the number of 30- to 40-year-old women who died had more than tripled in six years. There is a much slighter increase in deaths for 40- to 45-year-old women; and by age 50, the death rate looks very similar to the historical one. For men, the age-death profile also peaks, although this happens five years later and the decline is less sharp. If we knew the precise time path of prevalence in South Africa, we could infer at precisely which age infection risk peaks. We don’t; however, an approximation can be found by subtracting 10 years from the death rates, given that individuals survive, on average, about 10 years after infection. This approximation suggests that women are at greatly reduced risks of infection after age 30.²

Epidemiological Models of HIV and Age

The fact that women in South Africa face risks that decline quickly with age could be driven by several factors that are unrelated to spousal search. First, this correlation could be driven by some biological factor of HIV transmission that is correlated with age. Second, it could be a consequence of changes in sexual risk that take place as adults age. Third, it could be the direct outcome of an existing behavioral epidemiological model.

Biological Correlates of Age

For the age trend in infection observed in South Africa to be a suitable criterion to evaluate behavioral models, it must not be determined by a biological component. Other sexually transmitted infections (STIs) increase the transmission risk of HIV (e.g., Oster 2005), which may have age implications. In fact, the observation that young people are far more likely to contract sexually transmitted disease is not unique to HIV nor to Africa. Whether gonorrhea or chlamydia in the United States (CDC 2005), human papilloma virus (HPV) in Costa Rica (Castle et al. 2005), or herpes simplex virus type 2 (HSV-2) throughout the world (Smith and Robinson 2002), the young are consistently the population who contract sexually transmitted diseases (STDs). Despite this observation, the presence of other STDs actually suggests an age-increasing risk profile for HIV infection. There is mixed evidence on whether non-ulcerative STDs affect HIV transmission at all, and it is widely believed that ulcerative STDs play a much larger role (e.g., Fleming and Wasserheit 1999). The most prevalent ulcerative STD in Africa and the world is HSV-2 (e.g., Chen et al. 2000; Wawer et al. 1999). Therefore, the HIV risks that are induced by other STDs should follow the age profile of HSV-2. Because HSV-2 is incurable and nonfatal, the highest prevalence is among the old, as documented empirically across Africa in Smith and Robinson (2002). Thus, STDs as risk factors suggest that older men and women should be at an elevated risk of HIV infection, not a much lower one.

Age-Changing Preferences

A second possibility is that this age trend is an immediate outcome of age-changing preferences about coital frequencies. Although 30 seems a very young age for a sharp decrease in preferences about coital frequency, two forms of evidence are available to evaluate this possibility, both available in the 1998 South African Demographic and Health Survey (DHS). The first is self-reported sexual behavior, which is presented in Panel A of Table 1. For all potential coital frequencies, we see reported sexual behavior increasing until age 40, after which it remains higher than the reported behavior of women in their 20s, which are the ages that the death profile tells us involve peak HIV risk.

However, sexual behavior data is notoriously difficult to measure, and women in particular have been shown to misreport badly (Gersovitz et al. 1998). Therefore, we may be concerned that these differences simply reflect differences in reporting bias, and pregnancy may be preferred as a biomarker. Panel B of Table 1 reports pregnancy rates by age. Indeed, pregnancy rates decline after age 30, as reported in column 1. However, natural declines in fecundity also begin around age 30 (Te Velde and Pearson 2002). Table 1 shows births per year divided by the probability of conception for that age found in two studies: Templeton et al. (1996) and van Noord-Zaadstra et al. (1991).³ As Panel B of Table 1 shows, the actual births per year fall between what the two estimates would predict if sexual behavior remained constant, at least for women younger than 40. These data do not support the hypothesis that women’s age-specific preferences about coital frequency are insulating them from their husbands’ behavior at older ages, nor that women begin to prefer lower coital frequencies at an early age.⁴

Existing Behavioral Epidemiological Models of HIV

Because average HIV infectiousness is so low, models that achieve high HIV prevalence with feasible amounts of sexual behavior often rely on fundamental heterogeneity between individuals. The class of models that has dominated the economics literature revolves around individuals having heterogeneous preferences of sexual risk or variety (e.g., Kremer 1996; Philipson and Posner 1993). In Kremer’s specification, heterogeneous individuals optimize a rate of partner change. A high-risk group seeks out many partners, lower-risk individuals occasionally search for new partners, and partnerships form at random. High-risk individuals are overrepresented in the pool of available partners because of their greater frequency of partner search, increasing the chances of drawing a partner with above population-average risk.

This model belongs to the class of age-independent risk models. Although different individuals prefer different risk levels and some may be likely to become infected earlier in life than others, any uninfected individual will face an identical probability of infection in each period that she remains uninfected. Another age-independent model emphasizes sexual networks of concurrent partners (Morris and Kretzschmar 1997). After HIV is introduced to a network, it can spread quickly throughout the network, exposing all members to high risk. As such, all members of a network are exposed to very similar risk levels, regardless of age. Presumably, individuals are heterogeneous with respect to the size and turnover rate of their networks, so we may expect this model to produce very similar age predictions to the preference-based model.⁵

Can an age-independent risk model with heterogeneous types generate an age-death profile like that of South Africa? In principle, a two-type model might: high-risk types become quickly infected and die out while still young, while low-risk types remain safe. However, this sort of explanation makes two extreme assumptions. First, there are no middle-risk types, who likely survive their youth and continue to be stochastically infected later in life; second, the epidemic is in its steady state. Self-reports of the number of sexual partners in the last year from 14- to 22-year-olds in South Africa, although subject to the concerns discussed in the previous section, seem to contradict the first assumption. As reported in columns 2 and 4 of Table 2, young adults in South Africa report a triangular distribution of annual partners, with the majority being low risk. More importantly, epidemic stability is necessary because this age-independent explanation revolves around the high-risk older women having already attrited from the population, which would not have happened at the onset of the epidemic (as in the case of South Africa).

Age-Independent Model Calibration

To evaluate whether an age-independent model is capable of generating the age-death profile observed in South Africa, I calibrate a model with up to three types. Each type is indexed by an annual risk level so that one is at high risk, one is at low risk, and one is at negligible risk. It can be shown in a similar calibration (results available from the author) that if the majority of at-risk people are the low-risk type, only a bad fit can be generated in the steady state. Here, I illustrate that the epidemic is too young in South Africa to generate an age-death profile like the one observed, regardless of the distribution of these three types. Let ρ_g(y) be the infection risk of group g in year y, f_g be the fraction of individuals who belong to group g, X(k) be the survival rate into sexual activity at age k, and S(t) be the survival rate t years after infection. Then, the number of deaths at age a would be

where POP is the population of reproductive-aged women in South Africa who are at some risk of infection. POP is a free parameter, which I choose so that the peaks of the two distributions are equal. To ensure that the high-risk and low-risk groups are different, I allow ρ₁ to reach a peak incidence of between 0 and .2 (.2 is the highest considered because this is the annual risk from unprotected sexual activity with an infected spouse among highly sexually active young couples (Gray et al. 2001)); while I restrict ρ₂ to be between 0 and .02 to create a low-risk group. A level of 2% per year is high for “low” risk; it creates more than a 50% lifetime chance of infection. I further assume that ρ_g(y) increases linearly from the first year of the epidemic (t₀) until it reaches peak risk, at which point it remains at that level until 2002.⁶ This creates a vector of four parameters (ρ₁, ρ₂, f₁,t₀), which are free in this model; I then evaluate the best possible fit of this age-independent risks model by choosing these parameters to minimize sums of squared deviations between the actual deaths data and that suggested by the model. I further examine the epidemic at a variety of ages. A 15-year time frame is about right for South Africa in 2002, given that antenatal prevalence rates were about 1% in 1990 (RSA 2008; U.S. Census Bureau 2006).

Figure 2 shows that a 35-year-old epidemic can fit the age-death profile quite well: the intuition holds that if everyone at risk is at high risk, the risky die while young, leaving behind low-risk people who will reach old age. However, in the early stages of the infection, a heterogeneous-risk model cannot fit the profile. In fact, around year 15, the highest risk is among the oldest groups, in contrast to what we observe in the data. In other words, if people belong to one of three risk types, and those risk types remain relatively constant over lifetimes, then no matter how much risk each of those types contain, or what fraction of the population belongs to each of those types, we should observe far more older people being infected in early-stage epidemics than we actually observe in South Africa. The reason for this is simple and is not driven by the stylized assumptions that make this calibration tractable: at the onset of an epidemic, older individuals of all risk levels are being exposed for the first time. Therefore, if risks are independent of age, the first cohort exposed includes risky people of all ages and should feature deaths at all age groups. In South Africa, the epidemic is simply too new for an age-independent risk model to be a strong candidate explanation for most infections.

Marriage as a Risk Factor

Given that age-independent models of heterogeneous risk are unable to generate South Africa’s decline in risk with age, we can be certain that age-increasing models are poor approximations to the behaviors by which most people contract HIV. As argued earlier, this suggests that the presence of other sexually transmitted diseases do not serve as a stand-alone story for the age-death profile in South Africa. Another theory that suggests age-increasing risks is the possibility that men bring HIV risk into marriage through extramarital affairs. Kristof (2005) argued this case, writing that, “The stark reality is that what kills young women [in Africa] is not promiscuity, but marriage. Indeed, just about the deadliest thing a woman in Southern Africa can do is get married.” However, because older (and, more often, married) women are even safer in South Africa than they would be if marriage had a neutral effect on risk, we can rule out the “cheating husbands” theory as being the explanation for most women becoming infected.

This theory is so pervasive that it is worth reviewing the evidence that has led to it. Clearly, some risk is associated with a long-term partnership, for both men and women (De Walque 2007). However, a lack of long-run panel data, combined with mortality-related attrition and low HIV transmission rates, has left us without a good sense of how that risk compares with the risks of premarital behaviors. Much of the evidence on extramarital risk has come through anecdotal and ethnographic channels, which are hard-pressed to answer questions of relative magnitudes. Even if a large fraction of adults have extramarital partners, risks may be low if the existence of a spouse prevents high-frequency sex with these partners. Empirical evidence on marital risk has been mixed, with Clark (2004) finding that married teenage girls have higher prevalence than their unmarried peers and concluding that marriage is risky. In contrast, Bongaarts (2006) found that marriage is less risky than being sexually active and single, and Glynn et al. (2001) documented that married women who avoided premarital sex have lower prevalence of HIV than their married peers who did not.

The idea that married women may have higher HIV prevalence than unmarried women is consistent with the idea that a year of marriage might be less risky than a year of being sexually active and single if the process of becoming married is dangerous yet staying married is relatively safe. Individual-level data with HIV status are not publicly available for South Africa, preventing a direct examination of this hypothesis. However, in all the high-prevalence countries with publicly available DHS data including serostatus, suggestive evidence exists that it is indeed the process of becoming married that garners risk. If becoming married carries much risk, then we should observe surviving couples being more likely to test jointly negative if they have been married for long enough that preexisting infections should have resulted in death. In Online Resource 1, I show that monogamous couples who have been married for at least 10 years are substantially (and statistically significantly in every DHS country available, save Lesotho) more likely to test jointly negative than couples who have been married 0–5 years. This trend is robust to flexible age and spousal age controls and in some cases, represents truly substantial risk reductions. Across Africa, there is evidence that the process of becoming married, but not being married, is risky.

Spousal Search

The process that leads to marriage has changed substantially in sub-Saharan Africa over the past 50 years, just as it has elsewhere in the developing world. A large body of research has emphasized globally that traditional, kinship-based marital institutions are being replaced by Western notions of courtship, wherein individuals must identify for themselves suitable partners to marry (e.g., Ghimire et al. 2006 and Thornton et al. 1994; for African examples, see Mukiza-Gapere and Ntozi 1995; and also Smith 2000). Recent research has more directly emphasized the parallels between Western notions of courtship and premarital behaviors in Africa, where researchers have documented that young people engage in sexual relationships as part of a search for long-term monogamous relationships with psychologically compatible partners (Clark et al. 2010) and that the likelihood of marriage is important in the choice of sexual behavior among premarital partners (Clark et al. 2009).⁷

Model

The process of searching for a compatible spouse, where compatibility is hard to observe, can be easily understood through adapting Jovanovic’s (1979) classic model of job turnover. The idea is simple: if there is some unobserved and unpredictable component to the quality of a relationship between two people, then individuals need to “try out” a relationship to learn its quality. After a person learns the quality of a current relationship, she can compare that quality against how well she could expect to do by ending that relationship and looking for a new partner. Formally, suppose that individuals live for T periods. Each period, individual i receives utility from a match with partner j, where . q_j is the observable component of quality that is known before the relationship, and θ_ij is match-specific and unobservable. She faces a choice at the end of the period: to stay with partner j or to draw partner j′, with whom is unknown but q_j′ is known.⁸ Match quality evolves stochastically according to H(θ). Individuals match assortatively on the q_j. In practice, this observed element drops out of the optimization problem because it is constant among any mutually acceptable suitor. Therefore, each individual solves the dynamic programming problem with Bellman equations:

where β is the discount rate, and is the random variable representing next year’s match quality with partner j.

To solve this model, individuals solve backward. In the penultimate period, each person faces a choice between staying with her current partner (for whom θ_ij is known, and can be predicted with some accuracy) or finding a new one. Therefore, she stays with the current relationship if or if her current relationship is better in expected value than she might expect to do by drawing a new one. Otherwise, she ends her current relationship and finds a new partner, indexed j′, from whom she receives match-specific utility in her last period of life. The previous period, the choice is slightly more complicated; here, she stays if the expected value of the current relationship—including the option value of being able to end that relationship in the following period—is larger than the expected value of a new relationship, again considering the possibility that that relationship could be terminated after one period. Iterating back to the first period leads to the well-known solution for search models, wherein optimal behavior is to form a sequence of reservation qualities, , where individuals stay in any relationship where . In this specification, so that as individuals age, reservation qualities lower. This means that the probability of a good relationship turning sour enough to dissolve after a certain age becomes low, creating “marriage” behavior. In my preferred specification, match evolution is slow, so that the first period provides a fairly accurate measure of the quality of a relationship; this evolution rate creates behavior that mimics the observed nine-year time span from sexual initiation until marriage in South Africa. This evolution can be interpreted as truly evolving utility from a partner or as a learning process. In any matching model, a large fraction of relationships are rejected immediately because reservation qualities are always bounded below by the expectation of the quality of a new match. As a result, individuals have clusters of several short relationships in between a few much longer ones; this will have disastrous consequences for the HIV epidemic. I define marriage as occurring at the date when a person begins to match with her (ex post) last partner. Men and women match randomly with someone else who is actively searching for a new partner. After 20 years, individuals quit searching, with a payoff of 10 years’ worth of utility at the current match quality.⁹ Men and women are identical in this model; this assumption is supported by de Walque (2007), who observed that in a large fraction of couples, only one is infected, equally often the woman as the man.

Integrating HIV Into the Matching Model

The average rate of infection per partnership-year (PPY) has been documented through longitudinal studies in Uganda and Zambia. By following serodiscordant couples (in which only one member is HIV positive) through time, medical researchers observe transmission rates. The studies in Rakai, Uganda, are particularly compelling because their participants report minimal condom use despite counseling. These studies estimate average infection rates of about 12% PPY (Gray et al. 2001; Quinn et al. 2000), which corresponds to an infection rate per contact of approximately 1 in 1,000. Transmission in Lusaka, Zambia, where higher condom use was reported, was lower at 8% PPY (Fideli et al. 2001).

However, the average infection rate may not be a sufficient statistic to understand the dynamics of HIV transmission. PPY rates do not describe within-individual or between-individual heterogeneity in infectiousness, and there is substantial evidence that both are important for HIV. Many studies (e.g., Gray et al. 2001; Pedraza et al. 1999; Quinn et al. 2000) have documented the correlation between viral load and infectiousness. In terms of viral load, we can divide a person’s HIV infection into three broad periods. First, acute infection lasts for the first two to three months, during which the body has not developed an immune response to HIV and viral load is high. In this period, HIV may be 10 times as infectious as it will be later (Pilcher et al. 2004; Wawer et al. 2005). Next, in latent infection (the next eight years or so), the body’s immune response keeps viral load extremely low. Finally, the body’s immune system starts to fail at containing the virus, and the infection becomes mature. Starting about two years before death, viral loads begin climbing. As viral loads increase, AIDS breaks out, causing death within about one year without medical intervention (e.g., Katzenstein 2003). People in the longitudinal studies described earlier are primarily in the second phase of infection, which is why low average transmission rates are consistently observed. In the epidemiological model most similar to this one, Koopman et al. (1997) assumed that individuals transition randomly between high- and low-turnover states and match nonrandomly with others in the same state. Considering infection among homosexuals in the United States, and assuming very risky behavior, they found that shutting down acute infection may end the epidemic entirely.¹⁰

Therefore, it is important to take into account the dynamics of HIV infection. I specify that if an individual of gender g matches with a partner who is in phase k of infection, that person faces probability of infection. After becoming infected, individuals die according to the survival function published in UNAIDS (2004). Two years before death, individuals enter mature infection (following Wawer et al. 2005). I do not allow individuals whose partners have died from HIV to find a new match unless they would have resumed searching from the relationship’s evolution in any event. In each cohort, a small percentage (δ) enter already infected with HIV, with δ/6 entering in acute infection.¹¹ This consistent injection of HIV can be interpreted as infection from all sexual behaviors other than spousal search. Individuals who are initially infected do not behave differently from other individuals.

Each period corresponds to one month. Latent transmission rates are those measured by Gray et al. (2001) for young couples (slightly above average rates owing to the greater coital frequency of young couples), whereas acute and mature transmission rates follow Pilcher et al. (2004) and Wawer et al. (2005).¹² The distribution over θ is uniform and chosen for simplicity; changing to other simple distributions alters lifetime numbers of partners and HIV prevalence only slightly, since reservation qualities endogenously adjust downward when good matches become more scarce. Men and women are identical in this model, and as such, they have similar simulated data; I present only the results for simulated women.

Simulating the Model

To simulate this model, I first solve the dynamic programming problem numerically (distributional assumptions and summary statistics from the simulated data are given in Online Resource 1). Then, I simulate N men and N women in the first cohort, each of whom randomly draws a partner from the simulated opposite sex and receives a draw of partner quality. At the end of the period, each person decides whether to stay in their relationship or to draw a new one based on the solution of the dynamic programming problem. If both members choose to stay, the relationship match quality evolves, and each member faces the same decision in the subsequent period. If either member chooses to leave, both people receive a new partner from the pool of other individuals who choose to search and a new draw on θ. The outcome of this random process is that individuals stay single for about 8.5 years, which is close to South Africa’s empirical data. (The median South African woman becomes sexually active at 17 and married at 25.) Over the 20 years of sexual activity, the median person has 11 partners. Eleven partners over 20 years is low relative to many epidemiological models, which typically assume that individuals acquire at least 1–2 new partners per year (e.g., Actuarial Society of South Africa (ASSA) 2005; Morris and Kretzschmar 1997; Oster 2005) and sometimes assume many more (e.g., Koopman et al. 1997). Every 10 months, a new cohort of N individuals of each sex enters the pool of searching singles and similarly draws a partner and a match quality. I simulate the model for 40 years; I do not explicitly model homophily in age so that entering cohorts are treated the same as single individuals in existing cohorts (although, of course, their age is different, resulting in a different solution to the search problem). With the entry of the 10th cohort, the HIV epidemic begins, and all living individuals face instantaneous probability δ of contracting HIV.¹³ Following, each new cohort enters with prevalence δ, and HIV transmission occurs as HIV-negative partners of HIV-positive individuals face random draws against the transmission rate. The two sources of randomization in this model are the match process and the HIV epidemic. After the match has been solved, the spread of HIV happens in a way that is computationally quick. All results presented are for 50 realizations of the match, each averaged over 10 realizations of the epidemic.

Results

Table 3 reports the fraction of fully exposed women who will become infected for each δ. Marital shopping acts as a multiplier of 5–7 on inputted infections, so that each percentage point of inputted infections results in about 6% of people becoming infected. In other words, each person who enters the spousal search period infected will cause about 2 to 2.5 other single people to become infected, and all of them go on to infect the person they eventually marry. Thus, if 1% of the population enters the spousal search period infected, we end up with a prevalence rate similar to that in Kenya or Tanzania. With just 3% infected by all sexual behaviors other than spousal search, we are at South Africa’s epidemic prevalence rates. The reason for this is basic behavior generated by matching models (and hence fairly insensitive to parametric assumptions). Individuals have clusters of several very short relationships that are easily rejected in between a few much longer ones. Therefore, when they enter a new relationship, they are likely to have just left another very short one. In turn, this means that they are much more likely to have just been infected, will remain in the acute phase of infection, and hence are more likely to infect their new partner. Prevalence among the first six cohorts reaches 80% of its eventual peak (not presented here). Thus, with a tiny fraction of the population entering the spousal search phase of their lives infected, marital shopping can create an epidemic quickly.

To explore the importance of acute infection, Rows 3 and 4 of Table 3 report prevalence results if the acute infection transmission rate, ρ₁ were 0. The results are strong: acute infection is responsible for a large fraction of the infections caused by spousal search, including about one-third of infections for δ  <  .05. Now, δ is multiplied by 4–5 rather than 5–7, so that each initially infected person causes only about 1 to 1.5 other infections before both people infect their spouses. This thought experiment is interesting for two reasons. First, it supports data from Switzerland (Yerly et al. 2001), which show that more than one-third of infections are attributable to acute infection, and Wawer et al. (2005) demonstrated similar results in Uganda. Second, it is implementable. A policy of wearing condoms for the first three months of each relationship would stop new infections caused by acute infection. While a preference for condoms in short relationships is familiar and intuitive, it represents a sharp divergence from the current message being spread by many non-governmental organizations (NGOs), which promote condom use throughout marriage (e.g., Ali et al. 2004). This policy is evaluated more explicitly later in this article.

Theoretical predictions and data can be used to determine the age profile of infection and death suggested by spousal search with minimal reliance on parametric assumptions. More specifically, matching models imply that infection risk is more or less constant for uninfected single individuals.¹⁴ Among married individuals, in contrast, it declines exponentially. Because no new infections are brought into a marriage, one’s risk at any point in time is the product of the transmission rate, the risk that one’s spouse entered the marriage already infected, the chance that one entered the marriage uninfected, and the probability that it hasn’t yet been contracted from one’s spouse. Similarly, the time path of risk suggests the relative fraction of infections occurring to single and married individuals. The algebraic identities suggested by these predictions are straightforward, if tedious, and are contained in Online Resource 1.

Using the South African DHS (South Africa Department of Health and ORC Macro 2001), I estimate Kaplan-Meier hazard functions into marriage and into sexual activity to estimate search and marriage behavior, with the assumption that being unmarried but having had sex is reflective of being single and searching.¹⁵ Because the DHS provides data only on women, I estimate the men’s hazard function into marriage by taking means by age of the fraction married from the September 2001 South African Labour Force Survey (Statistics South Africa 2002–2004), and I alternatively assume that the hazard function into sexual activity is the same for men as it is for women, or that it is shifted to five years older because South African men marry, on average, five years later than women. As described earlier, I know the risk profiles for single and married individuals if I know the time path of the epidemic and the relative prevalence rates for newlyweds and singles. Therefore, to construct the age-death profile, I need only the time paths of the prevalence for newlyweds and single people. These are taken from simulations; reassuringly, Figs. 3 and 4 are robust to reasonable changes in both single and married prevalence trends because it is the empirical distributions of singlehood and marriage as well as the theoretical risk predictions that produce the close fit.

Figure 3 presents this comparison. Here, I make the further assumption that the number of deaths by age in 1996 represents the number of non-AIDS deaths in 2002, and I set the peak of simulated AIDS deaths equal to the empirical peak. That is, the height of the curves is rigged; however, that is the only point that is expressly fit, and the shape of my predicted age-death curve is derived from the theory and the data. The fit is very close.¹⁶ I very slightly underpredict older women’s deaths. Because this model assumes perfect monogamy, extramarital sex may create this difference; however, the quantity of infections that this nonmonogamy produces is tiny in comparison with the number of monogamous infections. For men, the data lie between the age death curves created by assuming that men have the same sexual initiation as women and assuming that their sexual initiation is five years older. Still, the fit is overall very close and is distinguishable from the fit for women. Men marry five years later than women and over a broader range of ages, and that is precisely how they die.

There is no reason to expect that the marital shopping model would fit the epidemic only in 2002. Figure 4 estimates the model for every year from 1997 to 2002. For men, I take the average of the predicted results from the two assumptions on sexual initiation. For both men and women and at all years of the epidemic, I find a close fit (once again, only the peak of each year is fixed). Moreover, some of the time dynamics in the age profile of infection are preserved between the model and the data, not least being the age peak from early years, which was absent in the heterogeneous risk model. Regarding the female age-prevalence profile, at the onset of the epidemic, peak deaths occurred in the 25–30 age group, with a similar rate among 30- to 35-year-olds; by 2002, 30- to 35-year-olds experienced more deaths. This is predicted by the marital shopping model.

Marital Shopping or Preferences Over Variety?

In the marital shopping model, people are motivated by the utility payoff of finding a high-quality partner. They undergo search in their youth, which is characterized by brief periods of high partner turnover in between longer periods with a single monogamous partner. Ultimately, they find a high-quality match and they marry. A behaviorally similar model (and one that would generate an identical age-profile construction as that used earlier) would be that individuals prefer to have a high rate of partner turnover in their youth until they exogenously prefer to have a single partner at heterogeneous ages. It is doubtless true that both changing preferences about variety and the presence of a high-quality partner play a role in marriage decisions. A few distinctions are worth noting. First, spousal search generates higher HIV prevalence than a changing preference model with an identical number of partners. This follows because the short periods of high turnover are a major contributor to the potential of spousal search to spread HIV. If partner turnover is relatively uniformly distributed over time, this potential is attenuated. Further, if preferences about variety decline in a smooth and monotonic manner, then the predictions based on age are a worse fit than those created by a spousal search model. The spousal search model presumes that individuals are of constant risk over their ages of singlehood, and already fully explains the number of infections among the very young. Finally, as discussed later in this article, an implication of marital shopping (unlike preferences about variety) is that there should be a high variance in intertemporal choices in sexual partners, which is supported by self-reported sexual behavior data. However, it remains true that a model wherein individuals transition randomly between preferences for high and low rates of partner turnover and exogenously prefer a single partner after a particular age would be behaviorally equivalent to the one presented earlier and hence would have similar predictions.¹⁷ As with any model, this one is indistinguishable in data from behaviorally equivalent, exogenously changing preferences. However, many policy predictions remain similar in either case.

Spousal Search, Sexual Behavior, and Risk

In a spousal search, a large number of partners is simply an indication of bad luck in finding a good match in a given year rather than an indication of underlying preferences. Thus, if this model is relevant, we should observe relatively little serial correlation in number of partners. Moreover, most people will have isolated years when they have several partners, but most years will be spent with a single partner because most time is spent with either a long-term partner or with a spouse. Therefore, a second prediction of spousal search is that most of the time, nearly everyone has only a single partner in a given year.

As discussed earlier, sexual behavior data are problematic and known to be biased with strong underreporting. It is not clear whether bias changes over time, so it is not clear whether bias could itself account for a low level of serial correlation in the number of partners. The Cape Area Panel Study (CAPS) ¹⁸ (Lam et al. 2006), which is a random sample of 4,758 teens and young adults ages 14–22 in 2002 who live in the Cape Town Metropolitan Area, however, can provide suggestive evidence. Here, I examine the self-reports on the number of sexual partners from the previous 12 months for CAPS respondents who had sex at least once by 2002 and the same respondents three years later in 2005. I then compare the scatterplot of these respondents with that generated by 2,500 observations of simulated data. CAPS respondents are younger than a random selection of simulated adults from the model. Thus, I choose for each simulated observation one of the first five years at random to represent that simulated person’s behavior in 2002 and then compare the number of partners that observation had in that year with the same observation three years later. I then overlay the two scatterplots for easy comparison, weighting each observation so that the sample sizes are identical.

Figure 5 shows the results of this exercise. Here, simulated data are represented by diamonds, actual data are represented by squares, and the size of each point is proportional to the frequency with which it occurs in the data. One deviation from the model is that it does not allow individuals to transition out of sexual activity and a few individuals in CAPS have 0 partners in a year after they have had sex at least once. These observations aside, the fit is quite remarkable. In both CAPS and the simulated data, the overwhelming majority of observations have one partner in 2002, and again one partner three years later in 2005. Also, in both CAPS and the simulated data, substantial fractions have more than one partner in one of the two years; however, it is extremely infrequent to observe individuals who have many partners in both years. The overwhelming majority of individuals with several sexual partners in either one of the two years had only one partner in the other. This is striking, particularly because any models that rely on fundamental heterogeneity would suggest the opposite. That is, if some people simply prefer more variety, one would expect this preference to be serially correlated; however, in practice, reported behavior is not. I also impose a regression line for both simulated and actual data to describe the relationship between partners in 2002 and partners in 2005. The constant term is slightly larger in the simulated data; however, the estimated slopes are both indistinguishable from 0 and from each other. Teens and young adults in Cape Town report sexual behavior that is strikingly similar to that suggested by the marital shopping model.

The model of courtship and marriage developed here would seem appropriate for the United States and Europe, too, and so it would be reassuring if young adults in both contexts reported similar sexual behavior. Columns 1 and 3 of Table 2 report tabulations of numbers of partners in the past year among U.S. adolescents from the National Survey of Family Growth (NSFG; National Center for Health Statistics 2002); columns 2 and 4 report similar calculations for CAPS respondents (all data are described in Online Resource 1). Across cultures, the annual numbers of reported partners appear identical. To the extent that adolescent males are partnering only with adolescent females, we know that one of these two groups is misreporting. Strikingly, even the bias in male versus female reporting appears to be consistent between the two continents.¹⁹

Finally, if spousal search is dangerous, then those who spend a longer time single should be at greater risk of HIV infection. That is, a longer time period spent single indicates less luck in finding a match, and should be positively correlated with the amount of risk borne. Data to test this possibility are not available for South Africa; however, in Online Resource 1, I use DHS data to illustrate that length spent single is correlated with HIV status across Africa, and that it is correlated only for those who have been married recently enough to have survived whatever infections were suffered during their singlehood. That is, a long singlehood is strongly predictive of HIV status for people who have been married less than 10 years but not for individuals who have been married for more than 10 years. This suggests that high risk is created by long singlehood, rather than things like preferences, which may be correlated with singlehood but would persist into marriage. Although those who have been married longer may be an imperfect control group, this analysis represents additional suggestive evidence that spousal search is dangerous.

Policy Discussion

In this article, I consider three policies to reduce the spread of HIV. The first is for individuals to use condoms for the first three months of each relationship. The majority of relationships in this model are short in tenure because most partnerships are quickly found unacceptable; thus, using condoms at the beginning of relationships may prevent transmission from most lifetime partners and would eliminate the role of acute infection. I consider what happens when fraction λ of the population follows this policy. Panel A of Table 4 observes the mean lifetime prevalence across cohorts for a variety of λ, in each case assuming δ = .03, which relates to the South African epidemic.²⁰ For each λ, the overall prevalence is reported and then decomposed into the prevalence for those who follow this strategy and the prevalence for those who do not. The strategy of wearing condoms in short relationships is very effective for those who follow it: in each case, inputted values of δ are multiplied by 3–4.5 for those who follow this strategy and 4–5.5 for those who do not. Strong evidence of externalities emerges; as some individuals protect themselves, epidemic progression is limited, and everyone faces lower risks. Moreover, if everyone uses protection in short relationships, epidemic prevalence falls tremendously: each new infection is responsible for about two additional infections. In a model like this, spouses will almost deterministically become infected, so that each inputted infection now causes about one-half of an additional couple to become infected (rather than 2–2.5 couples in the baseline case).

A second potential policy is to reduce the transmission rate of HIV, either through reducing the prevalence of STIs (e.g., Oster 2005) or through male circumcision (e.g., Potts et al. 2008). Using the marital shopping model, we can observe the effect of reducing transmission rates on prevalence while remaining agnostic about the best mechanism to achieve such a result. A review of medical studies (presented in Online Resource 1) suggests that transmission in the United States and Europe is on the order of 50%–100% as efficient as in Africa.²¹ I take the midpoint and assume that a 25% transmission rate reduction is accomplishable through biological means. The Western transmission rates rows of Table 4 repeat the marital shopping model but reduce transmission risks in all stages of infection to 75% of the previous levels. The first row indicates what can be expected if transmission rates are reduced by 25% without accompanying behavioral change. In this case, the multiplier changes from between 6 and 7 to just more than 4, or one extra couple being infected. Clearly, this is an effective strategy, about as effective as compelling one-half of individuals to use condoms in their short relationships; which of these approaches is more feasible is an empirical question.²² Table 4 also explores the consequences of reducing transmission rates in parallel with short-term condom use. The results here are strong. In this model, there is basically no way to reduce the multiplier below 2: individuals who enter spousal search already infected will very probably infect their eventual spouse. When the transmission rate is reduced to Western levels and individuals are compelled to use condoms in their short relationships, very few individuals other than spouses ever become infected. If Americans have these transmission rates and follow this strategy of protection in short relationships, it may explain why spousal search does not create an HIV epidemic in the United States despite otherwise similar sexual behavior. Strategies that seek to reduce transmission rates through treatment of sexually transmitted diseases and male circumcision can effectively combat the epidemic, as can short intervals of protected sex, and the pursuit of both strategies in tandem may be tremendously effective.

The third potential policy is ARV treatment for the epidemic. ARV treatment both extends life and reduces transmission rates, creating, in principle, an ambiguous effect on the epidemic and leading to mixed findings in the epidemiological literature (Cohen et al. 2007). Standard medical practice is to treat individuals either just before or at the onset of AIDS; hence, in calibrating, I assume that life is extended for three to seven years in between latent and mature infection, and transmission rates are reduced to between 0% and 50% of that latent infection rate.²³ As Panel B of Table 4 illustrates, ARV treatment has only a limited effect on the epidemic, resulting in at most a 15% reduction in prevalence or potentially a very small increase. The reason for this is simple: by the time people are nearing the end of their HIV infection, they are typically married and no longer accumulating many new partnerships. This suggests that using ARVs to provide a similar window of low infectiousness earlier in the infection’s course may be much more effective, and similar simulations (not presented here) reveal that extending life by reducing infectiousness in the first years of infection may be associated with substantial reductions in epidemic prevalence.²⁴ This heightens the immediacy of current medical studies, which are testing the value of treating HIV-positive individuals long before the onset of AIDS (HPTN 2010). It also highlights the importance of the underlying behavioral modeling: models that do not account for the life history of sexual risk would overstate epidemiological implications of current ARV practice.

Conclusions

Serial monogamy with high turnover is sufficient to create and maintain high prevalence levels and can inflate infection rates from other sources to much higher levels. Simple dating can create this behavior, if there are idiosyncratic, unpredictable components to the quality of a relationship and individuals prefer spending more time with better matches. In contrast with many existing behavioral models that can achieve high prevalence with low transmission rates, the matching model is consistent with the observed age-death profile. Moreover, matching also supports empirical evidence on the importance of acute infection for the HIV epidemic without requiring extremely high numbers of partners.

If individuals use protection in only their short relationships, prevalence rates fall dramatically, with 50% usage being as effective as a reduction in transmission rates to Western levels. This highlights an important choice for public policy: should policy makers emphasize using condoms in new relationships at the cost of using them in older ones? Some individuals may find three months of condom use more palatable than a lifetime of protection, and a tremendous amount of risk would be averted.²⁵ Indeed, this message contrasts strongly with the message adopted by many public health groups, who encourage condom use throughout marriage. As many individuals doubtless hope to have unprotected sex at some point in their lives, it would be dangerous if they felt they had to make an all-or-nothing choice because they did not understand the relative risks of premarital and marital sex. Moreover, when short-term condom use is combined with reduced transmission rates, marital shopping ceases to be an effective mechanism to transmit HIV, suggesting two clear goals for policy. This also suggests that public health campaigns should target young and single men and women, with a message stressing the risks in new relationships.

An implication emerging from the medical literature is that testing campaigns will be hard to sell. Antibody-based tests are by far the cheapest and predominantly in use both in Africa and in the United States. However, these tests cannot detect acute infection because the body has not yet developed an immune response and therefore they misdiagnose HIV when it is most infectious. Because much of the risk that a person faces with a new partner is caused by acute infection, demanding that a partner get tested before intercourse is not fully protective. Moreover, if a negative result encourages choosing against condoms, then it could actually make sex more dangerous. This may pose a major challenge to testing initiatives.

Finally, I show in this article that serially monogamous dating and marriage behavior acts as a multiplier on low prevalence rates from outside sources, and simulated evidence suggests that spousal search could cause 5/6–6/7 of all infections. Another consequence of this multiplier is that small changes in the number of these outside infections can lead to huge differences in the prevalence rate. This article, as well as others (e.g., Oster 2005), has documented the similarity in reports of sexual behavior between Africa and the United States; it has also reemphasized how similar behavior with differences in transmission rates and short-term condom use can explain the different prevalence levels. However, a few pivotal people may well behave differently and become infected through other methods, and both the aggregate statistics that are central to this article and traditional econometric analysis are ill-suited to identifying these small samples, perhaps explaining the divergence between these results and the reports of ethnographers. Respondent-driven sampling methodologies (e.g., Heckathorn 1997) may be an asset in understanding the behavior of this pivotal minority.

Acknowledgments

I am indebted to Fabian Lange, Ethan Ligon, Ted Miguel, Nicoli Nattrass, Emily Oster, Rohini Pande, Claus Portner, Paul Schultz, Jeremy Seekings, Chris Udry, Damien de Walque; and seminar participants at Yale, Berkeley, Harvard, the University of Washington, and the University of Cape Town for many helpful suggestions. All mistakes are naturally my own.

Notes

References