Marital Shopping and Epidemic AIDS

Transcription

1 Marital Shopping and Epidemic AIDS Jeremy R. Magruder August 8, 2007 Abstract The high prevalence rates of HIV in much of Africa seem especially striking when considered alongside the very consistently estimated, very low transmission rate of the virus. A variety of epidemiological stories exist to explain this discrepancy; some suggest the importance of a core group who engage in high levels of riskiness; others advocate the importance of concurrent relationships and sexual networks; still others suggest that high prevalences of other sexually transmitted infections increase HIV transmission e ciency. None of these stories, however, can by themselves explain the very steep pro le of deaths by age observed among women in South Africa, which reveals that nearly all women who will ever be infected are infected by age 30 or so. In this paper, I adapt Jovanovic s (1979) model of job turnover into a model of relationship turnover, and show that searching for a partner with a good match quality generates exactly the timing needed to turn a very brief window of high infectiousness described in the medical literature into high prevalence rates in other words, simple dating behavior is in itself su cient to create an epidemic. Using DHS data, I construct the age-pro le of deaths suggested by this model, and nd that it ts the actual deaths data very well. Model predictions are compared to reported sexual behavior in South Africa, HIV prevalence in Kenya, and prevalence of gonorrhea in the US, nding a good t. 1 Introduction The costs in terms of human life and welfare of the African HIV/AIDS epidemic are highly publicized and enormous. In 2004, 25,400,000 Africans were living with HIV, and another 2.3 million died of AIDS(UNAIDS 2004). Antenatal prevalence in Botswana and Swaziland approaches 40%. These numbers seem especially striking when considered alongside the very consistently estimated, very low transmission rates of HIV in Africa and elsewhere ( per sexual contact, or 8-12% per year of a partnership (e.g. Gray et al 2001, Quinn et al 200, Fideli et al 2001)). Yet for all of these stark numbers, economists have rarely turned to understanding the behavioral underpinnings of such an epidemic. Indeed, only one behavioral paradigm exists within the economics literature: speci ed by Philipson and Posner (1993) and Kremer (1996), this model suggests that individuals 1

2 have preferences over sexual risk or variety, and that a core group of individuals preferring high risk drive the epidemic. Outside of a core group behavioral-optimization framework, two other leading hypotheses exist: Morris and Kretzschmar (1997) claim that the speed of the epidemic can only be the result of concurrency in partners; others (including Oster 2005) suggest that greater prevalence of other sexually transmitted diseases increase transmission rates within Africa. Data on HIV incidence and prevalence is far less complete than would be desirable. Antenatal data is subject to selection bias, and population surveys tend to have very high (and surely nonrandom) refusal rates. However, in South Africa, death rates are collected and reported quite completely ( gures 1 and 2, as reported in ASSA 2005). Since 1996, the onset of AIDS is apparent in both the women s and men s death rates. Equally apparent is a striking age-trend: recalling that HIV/AIDS takes on average nine years to kill without treatment, the extremely sharp peak among females suggests that most women who will ever be infected are infected by age 30 or so. Noting that the median age at rst marriage of women in South Africa is 25 is akin to noting that nearly all HIV-positive women were infected when single or shortly after marriage. In fact, the observation that young people are far more likely to contract sexually transmitted disease is not unique to HIV or to Africa. Whether Gonorrhea or Chlamydia in the US (CDC 2005), Human Papilloma Virus in Costa Rica (Castle et al 2005), or Herpes Simplex Virus-2 throughout the world (Smith and Robinson 2002), the young are consistently the population who contract STDs. However, the suggested HIV age-infection pro le is very di erent than one based on sexually-transmitted disease risk. Though there is mixed evidence on the role of non-ulcerative STDs for HIV transmission, it is widely believed that ulcerative sexually transmitted diseases play a much larger role (e.g. Fleming and Wasserheit 1999) (and non-ulcerative diseases may have no e ect at all, see Quinn et al 2000 and Gray et al 2001). The most prevalent ulcerative STD in Africa and the world is Herpes Simplex Virus -2 (e.g. Chen et al 2000, Wawer et al 1999). Therefore, if STD risk alone is explaining the elevated HIV spread in Africa, we would expect to see similar trends in HSV-2 Prevalence by Age and HIV infection. Figures 3 and 4 (Smith and Robinson 2002) reveal that prevalence is highest among older people (as one might expect for a disease which is incurable and non-fatal), so from STDs alone older men and women should be at an elevated risk of HIV contraction, not a much lower one. STDs do not serve as a stand alone story for HIV in Africa; rather, they increase the need for an accompanying behavioral story to both explain the 2

3 age-pattern of their spread and to further explain why those at the ages of greatest risk from STD prevalence are not contracting HIV. This paper commences by arguing that existing behavioral models are challenged by the agedeath pro le in South Africa. In contrast, I examine the temporal variation in HIV infectiousness to suggest an alternate behavioral model which remains consistent with the medical literature and these patterns of deaths by age. Adapting Jovanovic s (1979) classic model of job turnover into one of relationship turnover, I argue that search and matching behavior gives relationships exactly the timing needed to transform a brief period of high infectiousness during early infection into epidemic levels of HIV. Using DHS data to explore marital patterns and model predictions on the relationship-pro le of infection, a deaths-by-age pro le is generated which looks similar to that observed in South Africa for both women and men. Behavioral implications of both the matching model and the taste based model are compared to data, and a model selection test prefers the matching model to the preference-based one. I examine the alternate hypothesis of changing coital frequencies with age, and nd little evidence to support it. Model predictions are extended to micro data on HIV prevalence in Kenya and the di erent biological and cultural context of gonorrhea transmission in the United States, also nding a good t. Finally, public health implications of the matching model are considered. 2 Behavioral Epidemiology of HIV and the Role of Marriage The dominant behavioral paradigm in the economics literature attributes the spread of HIV to heterogeneous preferences, interpreted in two di erent ways. Phillipson and Posner (1993) assume a demand curve for risky sex drives the epidemic. Kremer s (1996) model expands upon theirs, suggesting that rather than preferring risky sex, individuals are heterogeneous in tastes for sexual variety. The heterogeneous preferences model has some surprising implications: Kremer demonstrates that, under some parameterizations, if everyone would engage in more frequent sexual encounters, high-risk individuals wouldn t match with each other often enough to sustain an epidemic, and the epidemic would die out. While heterogeneity in preferences doubtless determines some aspects of sexual behavior, static preferences are hard-pressed to generate the steep decline of risk evident in gure 1 (and one similar to what has been observed in Uganda and the 3

4 Democratic Republic of the Congo (Sewankambo et al (2000) and Pictet et al (1998)). This pro le exhibits high risk over early ages many people are infected within the rst few years of sexual activity. However, at later ages, few are infected. Since the preference model has no implications for changing behavior with age, a risk-pro le must exist where some people are exposed to very high risk (these are the individuals who are quickly infected), some are exposed to very low risk (these individuals escape infection and represent the safe group at older ages) and few can exist in between them (or else they would be still be being infected at older ages). I show in the appendix that in fact these requirements are quite extreme. To t the age-death distribution well, it is important that the high risk types are at nearly biologically maximal risk levels, the low risk types are at approximately zero risk (and encompasses the vast majority of the population), and the middle risk group is small relative to the high risk group. If, in contrast, the middle of the distribution of risk preferences is larger than the right tail, preferences provide a poor approximation to the age-death pro le. This case appears to be quite likely if the distribution of risk choices is similar to the distribution of numbers of sexual partners per year reported by adolescents in Cape Town (presented in columns 2 and 4 of table 8). However, even if preferences could generate this age-deaths pro le in the long run, an additional characteristic of the HIV epidemic in South Africa challenges the ability of static preferences to generate this age pro le. That is, as revealed in Figures 1 and 2, the South African HIV epidemic is in it s infancy the death rate in 2004 was still climing quite quickly, and HIV was hard to observe in the death statistics as recently as As I show in the appendix, if risk is a recent phenomenon, so that older risky individuals were spared in their youth, the age-death distribution looks far di erent from the observed one regardless of preferences. This is logical: in the static preferences model, when HIV is rst introduced, all age groups are equally at risk including the elderly. Rather, what seems to have occured in South Africa is that, from the beginning, women over 30 and men over 35 or 40 have been relatively safe, suggesting that some aspect of behavior has changed even by fairly young ages. Whatever behaviors have led to the AIDS epidemic in South Africa, they have always been behaviors performed primarily by the young, who happen also to be unmarried. Upon re ection, it is surprising that marriage is fairly rarely discussed in the epidemiological literature on the spread of HIV. This represents some divide with the popular press; for example, 4

5 after New York Times Columnist Nicholas Kristof interviews several African women who are certain that their husbands have other girlfriends, he writes 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 (2005). However, as the age-death pro le reveals, if in delities are driving HIV, these in delities are stopping a few years after marriage, so in particular most women have little risk of infection from the often-demonized extra-marital behaviors of African men. The deaths pro le indicates that married individuals choose behaviors which expose their partners to little risk of new HIV infections. Using the Four cities survey in Kisumu, Kenya; Ndola, Zambia; Yaounde, Cameroon; and Cotonou, Benin, some work has been done on the role of marriage in HIV infection. Because men are asked about the marital status of their partners, Glynn et al (2001) are able to determine prevalence rates among women by age and marital status and partners of married versus unmarried women by age and marital status. Building on this, Clark(2004) nds that young women (aged 15-19) who are married are much more likely to test HIV-positive than those who are not, though the point estimate remains loses signi cance after conditioning on age and other covariates. Examining reports of sexual behavior, she concludes that early marriage increases risky behavior among young women and puts them at greater risk. Another interpretation would be that unmarried individuals di er from married individuals in that they never have found a marriage-worthy partner; in particular, they may di er as to the level of e ort that they ve put into such a search. In this case, those who undergo this process early di er only in the age at which they expose themselves to this risk from those who delay marriage. Glynn et al (2001), trying to understand why young women have a much higher prevalence of HIV than young men, observe that lifetime prevalences remain much lower among women who report being virgins at marriage, inspiring her to suggest that much of the HIV in women is acquired before marriage. Getting married appears to be dangerous but staying married may be relatively safe. Indeed, this is the result found by Bongaarts (2006) who discovers that married individuals have higher infection rates, but that this result is due to the fact that they have been sexually active longer a year spent single and sexually active is riskier than a year spent married. 5

6 3 The Transmission of HIV Longitudinal studies in Uganda and Zambia have o ered the best look at HIV infectiousness in Africa. By following sero-dischordant couples (where one member is HIV-positive and the other is HIV-negative) through time, medical researchers are able to observe infection rates per year, or with survey follow-ups, per contact. The studies in the Rakai district, Uganda, are particularly compelling as participants report minimal condom use despite counselling. Here, average infection rates of about 12% per partnership year (PPY) have been observed (Gray et al 2001, Quinn et al 2000), which corresponds to an approximately 1 in 1000 infection rate per contact. Transmission in Lusaka, Zambia, where high condom usage was reported, was observed to be somewhat less (8% PPY) (Fideli et al 2001). These rates (8-12%) aren t very much di erent from those observed in the US and Europe (5-10% PPY), and estimated per-contact rates are identical, inspiring Gray to note greater infectivity of predominant HIV-1 viral subtypes is unlikely to account for the explosive HIV-1 epidemic in sub-saharan Africa (2001). Transmission rates in Africa look similar to those in the US and Europe, yet prevalence rates look nothing alike. While per-partnership-year transmission rates are useful for understanding average transmission patterns, they do not describe within-individual or between-individual heterogeneity in infectiousness, and there is a great deal of evidence that both are quite important for HIV. Gray et al (2001), Quinn et al (2000), and Fideli et al (2001) all nd viral load in the blood plasma has a very large e ect in predicting HIV transmission in the African setting, con rming studies from the US which have found the same result (e.g. Lee et al (1996), Ragni et al (1998), Pedraza et al (1999)). That is, some individuals have much higher viral load than others, and it is precisely these individuals who are most likely to infect their partners. Moreover, as viral load in genital secretions has been shown to be correlated with blood viral load but not perfectly aligned (Pilcher et al 2004) with what looks something like classical measurement error, these estimates may be subject to attenuation bias, meaning viral load may be even more important than the authors conclude. In terms of viral load, we can divide a person s HIV infection into three broad periods. First, acute infection lasts for the rst two to three months. The body has not yet developed an immune response to HIV, and viral load soars to huge levels. 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 6

7 system starts to lose the battle, viral load climbs again, AIDS breaks out shortly and within a year or so the individual dies without medical intervention (e.g. Katzenstein (2003) for a review). People in the longitudinal studies described above are largely in these second and third phases, and individuals in the third phase are unwell enough that high coital frequencies seem unlikely, which is why low transmission rates are consistently observed. Though brief, acute infection may be extremely important for the spread of the HIV epidemic. Pilcher et al (2004) note that infectiousness may be 10 times as high in this period as in mature infection, a number con rmed empirically by Wawer et al (2005). Yerly et al (2001), in a study in Switzerland, perform very speci c analysis on the RNA of di erent individuals HIV in Switzerland and is able to trace clusters of infections. Dealing with under a tenth of estimated new infections over four years, they are still able to trace a third of them into speci c clusters of outbreaks, where individuals were infected with very similar strands of the virus in the same few months in the same area. As they have only a small percentage of total infections, they can t observe some clusters, so attributing a third of the infections to acute infection-based outbreaks is an underestimate. Koopman et al (1997), considering the homosexual HIV epidemic in San Francisco, build an epidemiological model where individuals enter and exit periods of high partner turnover versus low turnover, and match non-randomly with other individuals in the same turnover bracket. Since high-turnover individuals match with other high-turnover individuals, the probability of matching with someone who just contracted HIV (and therefore is in acute infection) is relatively high. In his simulations, if acute infection is shut down, HIV dies out, whereas with acute infection it reaches epidemic prevalence levels. My model can be seen as a behavioral adaptation of his insight, using risk parameters more tting to the heterosexual epidemic in Africa. 4 Model Individuals live for T periods. Each period, individual i receives utility ij + q j from a match with partner j; :where ij is distributed according to F () : q j is the observable component of quality, and ij is unobservable. She faces a choice at the end of the period: to stay with partner j or to draw partner j 0 ; with whom ij 0 is unknown but q j 0 is known. Match quality evolves stochastically according to H () : Individuals match assortitatively on the q j ; in practice, this observed element 7

8 drops out of any individual s optimization problem as it is constant among any mutually acceptable suitor. Therefore, each individual solves the dynamic programming problem with Bellman equations V t ( ij ) = max ij + q i + E V t+1 0 ij jij ; E ij 0 + q i + V t+1 0 ij fstay;leaveg 0 where is the discount rate. As is well known, the solution to this problem is a sequence of reservation qualities, t, t =@t 0; and where individuals stay in any relationship where ij > t : Individuals in this model usually have a series of very short relationships in between a few longer-term boyfriends and girlfriends. As they age, reservation qualities lower so that the probability of a good relationship turning sour enough to dissolve after a certain age becomes low. In my preferred speci cation, match evolution is slow, so that the rst period provides a fairly accurate measure of the quality of a relationship. This evolution can be interpreted as truly evolving utility from a partner or as a learning process where the initial signal is much more informative than subsequent ones. I de ne marriage as occurring at the date when a person begins to match with his (ex post) last partner. Every four months, a new cohort enters. who is actively searching for a new partner. Men and women match randomly with someone else After 20 years, individuals quit searching, with a payo of 10 years worth of utility at the current match quality. If an individual of gender g matches with a partner is in acute (latent) infection, they face probability g 1 (g 2 ) of infection. I ignore the last stage of infection, as individuals in this stage are ill and may not be maintaining high coital frequencies despite their greater viral load. Finally, after nine years of infection, I turn o infectiousness for individuals; nine years corresponds to the mean survival length for HIV in Africa. I do not allow individuals whose partners have died from HIV to nd a new match, unless they would have resumed searching from the relationship s evolution in any event. In each cohort, a small percentage () enter already infected with HIV. This consistent injection of HIV allows me to obtain higher prevalences and can be interpreted as infection from all other sources. My preferred interpretation for this injection is that it represents new matches for individuals whose spouses may have died or migrants who nd new partners; however, all other hypothesized sources of HIV infection are included within as well (including intravenous drug use, men who have sex with men, prostitution, in delity, concurrency, etc.). Individuals who are initially infected do 8

9 not behave di erently from other individuals as they would in a core group model. The Data Appendix describes parametric assumptions and shows summary statistics from simulated data. Each period corresponds to a month, and mature transmission rates are similar to those found by Gray et al (2001) for young couples (above average rates are due to the greater coital frequency of young couples) whereas acute transmission rates are similar to those suggested by Pilcher et al (2004) and Wawer et al (2005). The distribution over is chosen for simplicity; changing to other simple distributions alters lifetime numbers of partners and HIV prevalences surprisingly little, as reservation qualities adjust downwards when good matches become more scarce. Men and women are identical in this model, and as such have very similar simulated data; I present only the results for my simulated women. 5 Results Table 1 reveals that marital shopping serves to multiply by roughly a factor of about 7 overall for low levels of ; that is, each inputted infection results in about 6 additional infections on average. Lifetime prevalence rates of the rst 6 and last 6 cohorts are presented to illustrate the speed of the epidemic; within the lifetime of the rst cohort, the prevalence level attains between two-thirds and three-quarters of the prevalence it will ever achieve. Moreover, by the time of the last several cohorts, inputted injection rates are multiplied by a factor of 8 or 9 for low a huge multiplier e ect. Summary statistics are based on 50 simulations. What sort of deaths pro le does my model generate? Let S (t) be the survival rate after t years of infection and I (a; t) be the overall incidence of HIV at age a in time period t. The number of deaths from HIV at age a in year t is given by ax D (a; t) = I (a r; t r) (S (r) S (r + 1)) r=0 The marital shopping model suggests that a sharp change in risk behaviors occurs at time at marriage, so to infer death rates it is convenient to partition individuals into married versus single. That is, if I S (a; t) is the fraction of individuals who are both single and infected at age a and time 9

10 t, and I M (a; t) is the same for married individuals, we have ax D (a; t) = (S (r) S (r + 1)) I S (a r; t r) + I M (a r; t r) r=0 Suppose S (t) is the raw incidence rate for single individuals at time t; or the fraction of single individuals who become infected in that time period. Under the matching model, single individuals all behave the same, and hence are at equal risk, with one caveat. HIV is an absorbing state, and so individuals who have already been infected cannot become infected again. Hence let i S (k; t) represent the risk of becoming infected for an individual who has been sexually active for k years. Moreover, due to HIV s absorbing nature, the raw incidence rate has to be multiplied by the fraction of individuals who can still be infected, that is, (1 s (t)) if s (t) is the single prevalence rate at time t in order to generate the true risk that a single individual faces. Then i s (k; t) = s (t) 1 S (t) ky r=0 1 S (r) 1 S (r) and ax I S (a; t) = i S (k; t) S (a; k) k=0 if S (a; k) is the percentage of women who are single at age a and who have been searching for k years. In the marital shopping model, married individuals face an incidence rate which declines exponentially at the annual transmission probability, : In particular, let i M (; k; t) be the risk of infection for an individual who married years earlier after k years of search in period t: then i M (; k; t) = m (t ) (1 ) 1 ky r=0 1 s (t r) 1 S (t r) where m (t) is the prevalence rate among newlyweds, which is in general di erent from the single prevalence due to the declining reservation quality with age. Hence ax ax I M (a; t) = i M (; k; t) M (a ; k) =0 k=0 10

11 where M (a ; k) is the percentage of women who married at age after having been single for k years. I assume independence between age of sexual onset and age of marriage; in the South African DHS data these are uncorrelated. Hence if M (a) represents the fraction of individuals who are married at age a, S (a; k) = (1 M (a)) ~ S (k) ; and M (a; k) = M (a) ~ M (k) ; where ~ S (k) ~ M (k) is the proportion of single (married) individuals who have actively searched for k years. Since this is unobservable, I assume it is proportional to the percentage of women who report having had sex for the rst time at age k years earlier: Search intensity while single seems likely to be di erent for currently married individuals in particular, for age-a married individuals, R a 0 ~ M (k) = 1; whereas there is no such implication for ~ S (k) ; so if X (k) is the distribution of individuals who report sexual onset at age k, then I assume that S (a; k) = S (1 M (a)) X (a k) and M (a; k) = M (M (a)) X (a k) : Therefore D (a; t) = ax (S (r) S (r + 1)) r=0 0 S (1 M M (a) P a =0 M (a)) P a k=0 is (k; t) (X (a k) X (a k 1)) + P a k=0 im (; k; t) (X (a k) X (a k 1)) 1 C A Using DHS data, I estimate a Kaplan-Meier survival function out of singlehood for African Women in South Africa, and a similar survival function into sexual activity. For men, for whom there is no South African DHS data, tabulations of percent never married are taken at each age from the September 2001 South African Labour Force Survey, and beginning sexual search is calibrated in two ways: as being identical to the female distribution of coital onset, and as being the female distribution plus ve years (as the average married male is ve years older than his spouse in South Africa). The survival function for HIV is taken from UNAIDS(2002). ; the incidence per year of relationship, is set to.20, similar to Gray s (2001) nding for young couples, and non-aids deaths are taken to be identical to those in Time-paths of single incidence rates, single prevalence rates, and newlywed prevalence rates are simulated with the model, allowing identi cation of everything but S and M. However, from simulations I observe that roughly the same number of infections occur to single people as to married people (this is because most infected people marry and eventually infect someone who is not infected). This identi es S = M ;meaning that I can identify the death rate up to a constant. I identify this constant by setting the peak of 11

12 my death curves equal to the empirical peak this is the only point in the following pictures which is set expressly to t the data. Figures 5 and 6 illustrates the simulated deaths curve alongside the 2002 observed deaths in South Africa, with the peak set equal to that in the deaths data. As the reader can observe, my model slightly overpredicts younger deaths and underpredicts older ones for both women and men; however, the t is very good. Moreover, the shapes of men s and women s death rates are distinguishable; the male marriage pattern is di erent from the female one, and this is re ected in the age-distribution of HIV infection and death. 6 Behavioral evidence Though the marital search model seems to match the age-pro le of deaths quite well, some behavioral justi cation is also in order. A major di erence between the matching model and a tastebased model is the intertemporal correlation in sexual choices. That is, in Kremer s speci cation of the taste-based model, individuals optimize a rate of partner change, so the number of new partners in the previous twelve months should be equal to the number of partners in any sexually active 12 month period (plus or minus one partner because of integer problems). Total partners, then, is the simple multiplication of partners in the last 12 months times sexually active. One may be concerned that individuals reporting one partner in the last 12 months have a rate of partner change far less than 1/year; I nd that assuming these individuals rate of partner change is one per lifetime ts the data far better and use that in my comparisons. The matching model, in contrast, provides no such result. Lifetime number of partners is probabilistic, and is correlated with annual number of partners and years spent single as these are indicators of bad luck in nding a good partner, but far from perfectly. Tables 2 through 5 show kitchen sink regressions of sexual behavior variables which seem likely to be correlated with matching or Kremer s model for men and women, along with results from two sources. Tables 2 and 3 utilize the Cape Area Panel Study, a panel dataset of young adults aged in 2002 who live in the Cape Town Metropolitan Area, for males and females respectively. In 2002, the number of partners from that year was asked, while in 2003 a random subsample was reinterviewed and lifetime number of partners was asked. Very few of these young adults have become married, so although it seems important to the matching model I exclude it from the model selection test 12

13 for these young adults. Unfortunately, sample size is small, which creates problems of statistical signi cance in the OLS estimates. In order to create a comparable sample from my simulated data, I use simulated agents with an identical distribution of years of sexual activity as that reported in the CAPS data. Tables 4 and 5 utilize the National Survey of Family Growth (NSFG), an American dataset of men and women aged for males and females. Tobits are used, as for men annual and lifetime partners are right-truncated at 7, and for women lifetime partners are right-truncated at 50. I exclude observations where the relationship between annual and lifetime partners is deterministic, that is, observations where the individual has been sexually active for a year or less or men who have had seven or more partners in the previous year. Column 1 of Tables 2 through 5 report the estimates from the data, while column 3 reports the results from running identical estimation on simulated data from the matching model and column 5 illustrates the theoretical predictions of Kremer s model. For men and women in the US and Cape Town, Kremer s model is resoundingly rejected the coe cient on annual partners interacted with years sexually active is close to zero and tightly estimated for both men and women. However, the data also does not t perfectly with to the simulated matching data; in particular, the coe cient on the marriage dummy is quite di erent. Vuong s (1989) test of model selection with non-nested hypotheses allows us to formalize which of the two models ts the data better. Creating a matched lifetime partners prediction and a Kremer prediction, I run a tobit of actual observed partners on each. That is, I examine the equation Lifeprt i = E m [Lifeprt i jx i ] + cons + " i where E m [Lifeprt] is predicted number of lifetime partners according to model m given data vector X i and " i is normally distributed measurement error. In the case of Kremer s model, X is a su cient statistic for expected lifetime partners, however in the case of the matching model only the linear projection of simulated data onto available explanatory variables is utilized. As much of the variation of the matching model is thrown away, this is likely to bias results against accepting the matching model as a better t. Vuong s test normalizes the ratio of likelihood ratio of these two models to have an asymptotic standard normal distribution, where a number signi cantly greater than zero states that the matching hypothesis ts the data better, while a 13

14 signi cant negative coe cient suggests that the taste-based model is more accurate. Vuong s test provides strong support for the matching model over the taste-based one in both samples and for both genders. Given that both the African and American data prefer the matching model, it is interesting to ask just how similar they are. Tables 6 through 8 run simple tabulations of number of partners in the last year, age at rst intercourse, and marital status for sexually active adolescents. The American data look nearly identical to the African data; indeed, even the di erence in male versus female reporting appears to be quite constant between the two continents. Moreover, the two-type hypothesis which could also generate the steep age-death pro le is also rejected in both datasets, young adults report a continuous distribution of partners. Reported sexual behavior appears to remain remarkably similar across cultures. 7 Epidemiological evidence Another prediction of the marital shopping model is that length spent single should be correlated with HIV infection. That is, a longer time period spent single indicates less luck in nding a lifetime match, and should be correlated with the amount of risk assessed over a lifetime. Bongaarts (2006) discusses cross-country and individual level data from DHS surveys which suggest that both age at marriage and the gap between the age at rst sex and age at marriage are important predictors of HIV infection or prevalence. Similar to Bongaarts analysis, table 9 predicts HIV prevalence at the sample cluster and individual level using the 2003 Kenya DHS survey. Column 1 and 2 reveal that later marriage and earlier sexual onset have similar e ects on HIV prevalence at the sample cluster level and that some characteristic about time spent single is indeed correlated with HIV prevalence at the population level. These results are made more striking by the fact that two other frequent candidates, polygamy and spousal age di erences are not statistically signi cant, though the polygamy coe cient is large and noisy. One concern may be that sex and marriage behaviors have adjusted to accomodate the di erential HIV prevalences in sampling clusters. To correct this, Columns 3 and 4 repeat the analysis using sex and marriage variables for women over 40, for whom these decisions will have been made years earlier prior to the the epidemic.. Once again, singlehood seems to be the primary determining variable. 14

15 A natural extension is to examine whether the correlation is present at the individual level as well as the sampling cluster. Indeed, Columns 5 and 6 reveal that this same characteristic is also correlated at the individual level, conditional on cluster HIV prevalence. However as both the decision to commence sexual activity and the decision to get married are endogenous, we may remain concerned that this the length of singlehood is picking up other correlated omitted variables like preferences. Fortunately, a simple test is available: if singlehood is risky when single, then the e ect of the married-single gap should be strongest over the recently married, as those who have been married longer would have been single when HIV was less prevalent and are likely to be absent from the sample due to premature death if they caught HIV when Single. In contrast, if a long period of singlehood is simply correlated with other risky behaviors, such as preferences, then those who were single for a long time period should still be at risk years after marriage. Figure 9 presents marginal e ects from a probit of HIV prevalence on average cluster HIV prevalence and years of singlehood, where the e ect of singlehood on HIV and the average HIV prevalence are allowed to change by years of marriage. As is apparent, a long singlehood is quite risky for the rst ve years of marriage, and declines slightly in point estimate and remains di erent from zero for the second half-decade. After longer marriage tenures, the point estimate becomes quite small and loses its signi cance (though it becomes noisier as well). Ten years is a logical turning point, as it is the median life expectancy after infection. These results suggest that being single longer is risky in large part due to behaviors which take place when single rather than correlated behaviors which last a lifetime, consistent with the marital shopping model. 8 Other Hypotheses A rst hypothesis is that preferences over coital frequencies change dramatically with age, so that older adults simply prefer to have much less sex and hence face a much lower risk. This might suggest a reason for in delities to cease at older ages, or, if this is a female-only phenomenon, older women may be protected from their husbands extra-marital behaviors if they begin to prefer abstinence. We can test this hypothesis rst by looking at di erences in reported sexual behavior among women and second by looking at pregnancy rates. Table 10 shows mean sexual behavior reports by age group 15

16 Reported sexual behavior changes very little until age 45, and seems to reach its peak over the age range after most women who will be infected are infected already. Pregnancy rates, illustrated in table 11, decline. However, there is a vast literature documenting a natural decline in fecundity beginning at age 30 or so (e.g. te Velde and Pearson 2002 for a review). Two studies which have examined this are Templeton et al (1996) and van Noord-Zaadstra et al (1991). Templeton considers all in-vitro fertilizations in Britain from , while van Noord-Zaadstra considers all arti cial inseminations in two fertility clinics in the Netherlands during the clinicspeci c period when fresh (rather than frozen) semen was used ( for one clinic, for the other), and restricts analysis to married women whose husbands were azoospermic and who had never previously given birth or received an arti cial insemination. Table 11 shows births per year divided by the probability of conception for that age ( ve-year age group in the Templeton study) estimated from a xed number of cycles of arti cial insemination (the van Noord-Zaadstra study is of women aged only, so the van Noord-Zaadstra adjusted estimates are restricted to this sample). As the table above shows, the actual births per year estimates seem to be in between what the two estimates would predict for women if sexual behavior remained constant, at least for women under 40. Sample sizes are tiny in both studies for women over 40, so these may be unreliable. While the above table cannot speak to individual tastes for variety, if these tastes are correlated with tastes for frequency, then we can say with some con dence that they are not declining with age, at least through age 40. These data do not support the hypothesis that women s age-speci c preferences over 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. Another hypothesis is that concurrency in partners is important for the spread of HIV. Morris and Kretzschmar argue that only sexual networks of concurrent partners can cause explosive HIV epidemics, as opposed to this paper s model of serial monogamy. The age pattern of deaths demands that few new concurrencies are being formed where one of the women in the network is over 30, which suggests that, if concurrency is playing a role, marital status still regulates concurrency so that the formation of new concurrencies is primarily a behavior of single individuals. Slight modi cations of the search could allow multiple partner draws in the same period, or even search behavior where individuals hope to have 2 or 3 or more concurrent partners. Any of these modi cations would explode the marital shopping model to even higher prevalences, without 16

17 detracting from any of the basic conclusions. As the search model shows, concurrency is not a necessary condition for an HIV pandemic. 9 Why Africa? Intuitively, there is nothing about the marital search model which is unique to Africa. Indeed, two arguments have also been made to suggest that there is little about Africa which is idiosyncratic in terms of sexual behavior: rst, other sexually transmitted diseases in di erent continents exhibit similar age-patterns of spread, and second, young people report strikingly similar behavior in America as in Cape Town. An additional test of the model would be to consider whether inputting transmission dynamics of a di erent sexually transmitted disease in a di erent context also provides a good age- t. Unfortunately, transmission probabilities of most sexually transmitted diseases are little understood, and reporting is often subject to hard to predict biases. However gonorrhea in the US provides a good case study. Unlike HIV, gonorrhea is extremely infectious; with transmission probabilities very high for a single contact and approaching 1 for a month-long relationship. Gonnorhea is also a very transient infection, with most people spontaneously recovering without treatment in a few months, or experiencing quicker recovery with an anti-biotic. The marital search model, then, would predict a constant incidence for single, sexually active adults and zero incidence for married adults. Figures 7 and 8 illustrate the predicted versus observed gonnorhea prevalences by age in the US. For both women and men I overpredict prevalences at older ages. Nonetheless, the predictions do exhibit a similar pattern to the data despite the very di erent biological and geographical context. Behavior shared by Western and African cultures appears to drive the spread of sexually transmitted diseases. Why, then, has the US and Europe been spared a pandemic of the scale of that observed in Africa? Undoubtedly many factors play a role: for example, the transmission rate may be lower in the US due to a more circumcised male populace and lower (though still high) herpes prevalences (although average estimated transmission rates aren t a tremendous amount higher in Africa). The quick and strong public health response to the rst few AIDS cases may have encouraged Americans to more frequently use condoms with their short-term relationships (this has been o ered as one of the explanations for the quick drop in gonorrhea prevalence observed in 17

18 the 1980s, although a contemporaneous anti-gonorrheal campaign confounds analysis). However, the marital search model suggests an additional story. In order to achieve pandemic HIV, the marital search model demands a constant injection of a few percent who have been infected over many years. These few percent may well be the di erence between Africa and elsewhere. Indeed, Epstein (2002) has suggested that the di erence between Southern and Eastern Africa could well be the culture of migratory labor in Southern Africa if migrants undergo a search process both at home and at their worksite, then they would be a perfect example of the injection I describe. 10 Conclusions and Messages for Public Health Campaigns Serial monogamy with high turnover is su cient to create and maintain extremely high prevalence levels, and can blow up infection from other sources to much higher levels. Simple dating can create this behavior, if we believe that there are idiosyncratic, unpredictable components to the quality of a relationship and that individuals prefer spending more time with better matches. The age-pro le of deaths is extremely restrictive as to which explanations for the spread of HIV it will allow; the matching story is one of the few which passes this test. Moreover, the matching story allows acute infection to be important without individuals having extremely high numbers of lifetime partners, supporting empirical evidence on the importance of acute infection. If we shut down acute infection, prevalence rates fall dramatically, as shown in table 12. I remain agnostic about the source of ; so this is una ected in the following estimates. Therefore the di erence between the previous prevalence rates and these rates are underestimates of the e ects of shutting down acute infection since the role of acute infection in the generation of is not changed. For low ; the average inputted infection results in about 3 other infections half the level as previously, and the epidemic does not experience much growth across cohorts as it does when acute infection is present. 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 nd using condoms for 3 months much more palatable than a lifetime of condom usage, and a tremendous amount of risk would be averted. Indeed, this is in contrast to the message adopted by many public health groups, who encourage condom usage throughout marriage. As many individuals doubtless hope to have unprotected sex at some point in their lives, 18

19 it would be truly dangerous if they felt they had to make an always or noth ing choice because they did not understand the relative risks of pre-marital and marital sex. Like any advertising campaign, public health campaigns are targeted at speci c groups. My analysis suggests that the most important group to target is young and single men and women, and the correct message would indicate that single, monogamous relationships carry a great deal of risk, particularly in the rst months. This is in contrast with campaigns whose primary message is to encourage monogamy, or those who blame extreme-risk behaviors or individuals for the spread of HIV. It would be extremely dangerous if individuals believed that monogamy implied safety; in particular, every relationship is monogamous on the rst date, when the probability of acute infection is highest. Moreover, widely-held beliefs demonizing married men for HIV seem inconsistent with the observed deaths pro le; these beliefs suggest HIV is spread through extra-marital behavior and may increase HIV stigma with little empirical basis. An implication falling out of the medical literature is that testing campaigns will be hard to sell. Antibody-based tests are by far the cheapest and those predominantly in use both in Africa and in the United States. These tests cannot pick up acute infection, and therefore misdiagnose HIV when it s at it s most infectious, for the simple reason that the body has not yet developed an immune response. Since more than half of the risk that a person faces with a new partner is caused by acute infection, demanding that a partner get tested before intercourse will not protect the person very much moreover, if a negative result encourages choosing against condoms, then it could actual make sex much more dangerous. If individuals learn from their friends who do demand testing of their partners and nevertheless get infected, we should not be surprised at how little testing has caught on. 19

20 11 Appendix: Sexual Risk Distributions and the Age-Death Curve To nd the best t for the age-death curve for women that can be generated by heterogeneity in preferences over sexual risk or variety, I follow two strategies. In the rst, I assume stability in the HIV epidemic. That is, I allow individuals to belong to two groups, one low risk and one high risk, and then presume that they these groups were subjected to their chosen risk level each year that they remained uninfected, assuming that incidence rates have been constant throughout all age-groups lifetimes. This is clearly an unrealistic assumption for South Africa in 2004 where the epidemic was a recent phenomenon and prevalence rates had been growing quickly; however, it avoids the di culties of assumptions about the timing and speed with which the epidemic struck South Africa. It also is a worst-case" scenario for the rejection of heterogeneous, static preferences as an underlying source of the epidemic, as I illustrate when I relax this assumption below. Then, if g is the annual infection risk of group g, f g the fraction of individuals who belong to group g, X (k) the survival rate into sexual activity at age k; and S (t) the survival rate t years after infection, the number of deaths at age a would be 2X Xa 1 Xa k ( 1) D (a) = P OP (X (k) X (k + 1)) f g 1 g g (S (a ) S (a + 1)) g=1 k=0 =0 where P OP is the population of reproductive-aged women in South Africa who are at some risk of infection. P OP is a free parameter, and as in the matching model I choose P OP so that the peak of the two distributions are equal. This parameter is of independent interest, as it indicates the number of individuals who are at any risk whatsoever. We also know from census data the number of women living in South Africa at this time period. Therefore, the di erence between this estimated number and the population represents the third group, who are at zero risk. Appendix gures 1 through 3 illustrate the age-death pro le generated by thes preferences, where f g and 1 are chosen to t the age-death distribution as best as possible, with 1 restricted to various plausible levels (.2 is the highest considered as this is the annual risk from frequent unprotected sexual activity with a spouse who is infected), and 2 is restricted to be.02. At this rate, about 55% of individuals will be infected within the 40 years considered, so while this does indeed represent a high risk level, it is chosen to be a middle risk level" such that some individuals will eventually 20