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NBER WORKING PAPER SERIES AN EQUILIBRIUM MODEL OF THE AFRICAN HIV/AIDS EPIDEMIC Jeremy Greenwood Philipp Kircher Cezar Santos Michèle Tertilt Working Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA April 2013 We thank Pascaline Dupas and seminar audiences at the 2009 SED Meetings in Istanbul, the 2009 SITE workshop, the 2009 LACEA/LAMES Meetings, the NBER Growth Conference in San Francisco 2010, the University of Wisconsin,World Bank, University of Frankfurt, University of Mannheim, University of Konstanz,Washington University in St. Louis, University of Texas at Austin, and the University of Zürich for helpful comments. Financial support from NSF grant SES , ERC grant SH , and the Alfred P. Sloan Foundation is gratefully acknowledged. Last but not least, Olga Itenberg and Vera Molitor provided excellent research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications by Jeremy Greenwood, Philipp Kircher, Cezar Santos, and Michèle Tertilt. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including notice, is given to the source. An Equilibrium Model of the African HIV/AIDS Epidemic Jeremy Greenwood, Philipp Kircher, Cezar Santos, and Michèle Tertilt NBER Working Paper No April 2013 JEL No. E0,I1,J12,O55 ABSTRACT Eleven percent of the Malawian population is HIV infected. Eighteen percent of sexual encounters are casual. A condom is used one quarter of the time. A choice-theoretic general equilibrium search model is constructed to analyze the Malawian epidemic. In the developed framework, people select between different sexual practices while knowing the inherent risk. The analysis suggests that the efficacy of public policy depends upon the induced behavioral changes and general equilibrium effects that are typically absent in epidemiological studies and small-scale field experiments. For some interventions (some forms of promoting condoms or marriage), the quantitative exercise suggests that these effects may increase HIV prevalence, while for others (such as male circumcision or increased incomes) they strengthen the effectiveness of the intervention. The underlying channels giving rise to these effects are discussed in detail. Jeremy Greenwood Department of Economics University of Pennsylvania 3718 Locust Walk McNeil Building, Rm 160 Philadelphia, PA and NBER Philipp Kircher Department of Economics University of Edingburgh 30 Buccleuch Place, Edinburgh, EH8 9JT, UK Cezar Santos Department of Economics University of Mannheim L7, Mannheim Germany Michèle Tertilt Department of Economics University of Mannheim L7, Mannheim Germany and NBER 1 Introduction HIV/AIDS is a major cause of death, currently killing about 2 million people worldwide each year. The number of new infections is even higher than 2 million, suggesting an even more severe problem in the future. The most affected continent is Africa, which hosts about two thirds of all HIV/AIDS infected people. Within Africa most transmissions occur through heterosexual sex. Furthermore, the majority of the HIV-positive population is female, compared to less than one third in most developed countries. The current analysis spotlights one part of Africa: The Republic of Malawi. Malawi has a relatively high HIV/AIDS rate and the prevalence for women is higher than for men. 1 It also has very good data related to HIV/AIDS and sexual behavior. So, the facts are clear. Traditionally, two approaches have been taken to studying the transmission of HIV/AIDS in Africa, viz epidemiological studies and field experiments. 2 Epidemiological studies are sophisticated in their treatment of equilibrium but usually lack a feedback loop that captures behavioral responses. Field-experiments are often on a small scale and do not readily allow for the assessment of general equilibrium effects. The current paper advocates the use of choice-theoretic general equilibrium modelling as an additional tool for studying the African HIV/AIDS epidemic. First, the main benefit that economics can bring to the field of epidemiology is homo economicus. Here the assumption is that humans pick their sexual behavior on the basis of a rational benefit/cost calculation. This assumption allows one to study the potential behavioral responses of individuals with respect to particular policies (e.g., adjustments in the number of casual relationships prior to marriage in response to changes in transmission risk). Second, at the heart of the HIV/AIDS epidemic is an externality, the transmission of a virus. General equilibrium modelling is well suited for the study of externalities. One can analyze how individual shifts in behavior feed back on each other in equilibrium (e.g., if the rate of infection for some individuals rise, then the rate of infections for their partners may increase in turn, etc.). Thus, the great advantage of choice-theoretic equi- 1 Section 2 is devoted to providing background on the Malawian HIV/AIDS epidemic. 2 A detailed review of the literature is contained in Section librium modelling is the joint assessment of both behavioral change and equilibrium adjustment in response to proposed policy interventions. Nothing is for free, of course. Some abstractions are needed to operationalize choice-theoretic equilibrium modelling that may render it less rich along some dimensions. As such, choice-theoretic equilibrium modelling complements the above two existing approaches to the study of disease transmission. A choice-theoretic general equilibrium search model is built here to study the Malawian HIV/AIDS epidemic. Despite the fact that computational general equilibrium models have made great progress in recent decades, there is essentially no application to the field of disease transmission (except for few purely theoretical studies that form the basis of departure for this analysis but are too stylized to be directly mapped to data; see the review in the next section). The first applied general equilibrium framework to be used for this purpose is developed here. The constructed model has three main ingredients. First, individuals make rational choices about risky sexual behavior. In contrast to most of the literature (discussed below), the model explicitly models three important margins of risky behavior. Individuals choose the frequency of sex, whether to get married or engage in casual sex, and whether to use a condom or not. These margins allow people to choose those types of behavior that are thought to be the most important factors in disease transmission: having sex often, with many different people, and not using a condom. Alternatively, people can engage in relatively safe behavior by being abstinent, getting married, or at least by using a condom. When making these choices, individuals take the riskiness of each type of activity into account. Second, beliefs about the riskiness of various forms of sexual activity are formed rationally. In the analysis a person s past sexual history is private information. Still, the fact that someone desires a casual sexual encounter involving no condom, say, as opposed to seeking a long-term one, may signal something about his past sexual behavior. In particular, it may indicate a proclivity to engage in risky behavior. Hence, in the analysis, people form rational forecasts about the likelihood of a partner having HIV/AIDS based upon the type of relationship that they are seeking. A person can then forecast the odds of getting HIV/AIDS 2 if s/he engages in a particular type of relationship. An individual s choice about what type of sexual activity to engage in may be influenced by his or her belief about their own health. People assess their odds of having HIV/AIDS rationally using Bayes rule. They understand how various sexual activities affect their future health, which influences their current decisions about which type of sexual behavior to engage in. People who believe that they have HIV/AIDS may be more likely to participate in risky behavior than those that do not because they think that they have little to lose. This channel will worsen the health of participants seeking short-term unprotected sex and amplify the risk of a relationship with them. Third, the analysis is general equilibrium in nature. There are markets or meeting places for the different types of sexual activities. People have differing tastes over various types of relationships and search accordingly on the various markets to fulfill their desires. They can choose how intensively to search for a partner on a particular market (or abstain by not searching). They do this recognizing that some of these meeting places will be riskier than others. For example, a short-term relationship using a condom is safer than one that does not. Yet, condoms may fail and hence are not perfectly safe. The model embeds the well-document fact of monetary transfers within relationships. Each market is characterized by a transfer that one of the partners makes to the other. These transfers depend on the number of men relative to the number of women that seek a particular type of relationship, and equilibrate the two sides of the market. For example, in the absence of transfers there may be more men desiring casual unprotected sex than women. To attract women towards this risky activity, men may have to make some form of transfer payment. The market structure eliminates any joint decision problem between partners about whether or not to use a condom. They have the same desires when choosing the same market. The constructed model is then tuned to fit aspects of the Malawian data. In particular, it is calibrated to match the HIV/AIDS rates for men and women, the fraction of sexual relationships that are short term, the fraction of short-term sexual encounters that use a condom, and the fraction of deaths that arise from HIV/AIDS. The model s ability to match some non-targeted lifecycle observations is then examined. These include the profile by age of a sympton-free person s be- 3 lief about being HIV/AIDS infected, the HIV/AIDS infection rate by age, and the likelihood of a casual sexual encounter by age. The model does very well at matching the data along these dimensions. Last, some policy experiments are conducted. To name some, policies are examined such as male circumcision, which some believe reduces the risk of HIV/AIDS transmission from females to males, the promotion of condom use in casual sex, and income transfers to females. Earlier purely theoretical work (discussed in the following literature section) focused on reductions in transmission risk and emphasized that it can lead to higher overall prevalence because people could get excessively risky. The quantitative part of this study does not confirm that behavioral adjustments fully negate the positive effects of reduced transmission risk. Nevertheless, it is important to account for behavioral adjustments and equilibrium effects as they do strongly affect the predicted effectiveness. To show this, we explicitly simulate epidemiological studies (which ignore behavioral adjustments) and small scale field experiments (which ignore equilibrium effects) within our model. As an example, focus on the treatment of other sexually transmitted diseases (STDs) which reduces the transmission risk. The effectiveness of this policy is over-predicted (by around 30%) by the epidemiological model and under-predicted (by around 80%) by the field experiment. For other policies the behavioral responses are larger, and indicate the possibility of negating the positive primary effect. For example, the rate of HIV/AIDS displays a hump-shaped relationship in the psychic pleasure that people get from sex using condoms. This study also showcases channels beyond the simple effect that some agents increase their risky sexual activity. For example, some forms of promoting longterm relationships seem to raise HIV prevalence because some risky people now join the previously safe haven of marriage. While their move towards marriage is usually seen as a reduction in their own risky behavior, it increases the infection risk for their marriage partners who previously had a higher chance of finding a safe match. Such a change in the mixing patterns seriously affects the effectiveness of the policy. For other interventions such one-sided reduction in transmission risk (e.g., male circumcision) or increases in income (especially for women) the behavioral adjustment and equilibrium effects magnify the efficacy of the policy: Especially women react strongly to higher incomes, which makes 4 them substantially less willing to engage in risky activities. These changes feed back on the men leading to a virtuous feedback loop. Overall, this research program aims to develop tools to aid researchers and practitioners in their attempts to think through the various channels that are present in different interventions, and highlights areas where further and more in-depth research should be conducted to assess with more confidence the magnitude of these channels. The remainder of this paper is organized as follows. The next subsection discusses the relation to the literature on HIV/AIDS. Section 2 provides background information on sexual behavior and HIV/AIDS in Malawi. Section 3 sets up the economic environment and defines the equilibrium. Section 4 describes the benchmark parametrization of the model. Section 5 presents the results of the policy experiments, as well as additional relevant literature. Section 6 offers some concluding remarks. 1.1 Relationship to the Literature This appears to be the first quantitative general equilibrium model of disease transmission with purposive decision making. Previous papers are either purely theoretical or do not consider the endogeneity of rational human behavior. In addition, there are purely empirical studies; in particular, a recent literature uses field experiments to study HIV/AIDS prevention policies. The economic literature on disease transmission is small. Philipson and Posner (1993) provide the first economic analysis of HIV/AIDS. Their book gives a great overview of the different aspects involved in treating HIV/AIDS from testing, to regulatory intervention, to medical research and the political economy of treatment. Most of their analysis is verbal, however. Few formal models of risky sexual behavior and HIV /AIDS exist. 3 For tractabil- 3 There is of course a large economic literature on mate selection, starting from Becker (1973). Examples include Burdett and Coles (1997), Shimer and Smith (2000) and Boulier and Rosenzweig (1984). The current paper also connects to the simulation-based analysis of sexual behavior in Greenwood and Guner (2010). However, none of these papers study disease transmission. 5 ity, most of this work has focussed on only one dimension of risky behavior and abstracts from intertemporal considerations of an individual over his lifetime. Most prominently, Kremer (1996) builds a theoretical model where the number of partners is determined endogenously as a choice by rational agents that depends on the prevalence of the disease. The paper focuses on the theoretical implications of such endogeneity and shows that a reduction in the transmission probability can increase the overall prevalence rate because individual agents behave in a more risky fashion. Moreover, it is shown that changes in mixing pattern might be an important channel affecting the overall prevalence rate. To derive these predictions theoretically, the paper abstracts from a number of important issues. People only consider the lifetime probability of contracting HIV/AIDS, but do not care about the exact timing. In particular, people do not update their behavior based on past sexual experience. Condom use is not explicitly modeled, which abstracts from the joint decision problem in using a condom. A distinction between long-term and short-term partners is not made. Finally, the model is a one-gender model that makes the analysis of gender asymmetries in the disease dynamics impossible. The current paper shows how these richer elements can be modeled, and evaluates quantitatively the impact of these various channels for disease transmission, but at the cost of additional complexity. The only other model that explicitly models men and women is Magruder (2011) who develops a Jovanovic (1979) style matching model of marital search to analyze the HIV/AIDS epidemic in South Africa. The idea is that partners enter trial marriages and explore whether or not they are good matches. During this period couples have sex. In his setting, however, there is no decision about whether or not to use a condom during these trial marriages. Also, the analysis is not general equilibrium in nature. The decision about whether to accept or reject a partner is not affected by the prevalence rate of HIV/AIDS in society, or by any beliefs that the individual may have about whether or not s/he has the virus based upon her or his past sexual history. These margins may be important because healthy (young) individuals might self-select into the safety of marriage while those who believe they are infected have less to gain from safety and might opt for more risky alternatives. While the economic literature on disease transmission is small, there is a large 6 literature on disease transmission and specifically HIV/AIDS in epidemiology. The critical difference to the economic literature is that epidemiological models do not model decision-making. 4 In other words, these models do not try to understand why people engage in risky sexual behavior and how this behavior changes in response to changes in the environment. Instead, they take sexual behavior as exogenously given. The assumption that individuals do not change their behavior in response to their environment in particular in response to the overall prevalence of the disease is problematic for human populations. Survey evidence and several empirical studies suggest that people react to a higher presence of HIV/AIDS by adjusting the number of partners, the type of sexual relationships, and the protective measures that they use [Wellings et al. (1994)]. Since economic studies of HIV/AIDS augment epidemiological models with decisionmaking, a brief review of the epidemiological literature is given here. The workhorse epidemiological model of disease transmission is the susceptible-infected (SI) model with random mixing; see, e.g., Anderson and May (1992). In such a model people are in either of two states: infected or susceptible. If a person is infected he transmits the disease to susceptible (non-infected) people until he leaves the sexually active population. In models of HIV/AIDS there is no stage of recovery. 5 In these models people encounter other individuals in the population randomly. Most epidemiological models take the number of encounters, i.e., the number of sexual partners, as exogenously given. An interesting contribution is Kremer and Morcom (1998) who introduce selective mixing into an SI model: Individuals have a higher probability of meeting people like themselves as opposed to others. This idea also features prominently in this paper, but is applied to the type of sexual behavior that a person seeks. For example, an individual that seeks a long-term relationship can search in a way that makes it particularly likely to meet a partner that also seeks a long-term relationship. The special case where people exclusively meet others who are seeking 4 Very recently there have been a few at
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