77572 HIV Pandemic, Medical Brain Drain, and Economic Development in Sub-Saharan Africa ´ de Alok Bhargava and Fre ´ ric Docquier Country-level longitudinal data at three-year intervals over 1990– 2004 are used to analyze the factors affecting emigration of physicians from Sub-Saharan countries and the effects of this medical brain drain on life expectancy and number of deaths due to AIDS. Data are compiled on emigrating African physicians from 16 receiving Organisation for Economic Co-operation and Development (OECD) countries. A comprehensive longitudinal database is developed by merging the medical brain drain variables with recent data on HIV prevalence rates, public health expenditures, phys- icians’ wages, and economic and demographic variables. A triangular system of equations is estimated in a random effects framework using �ve time observations for medical brain drain rates, life expectancy, and number of deaths due to AIDS, taking into account the interdependence of these variables. Lower wages and higher HIV prevalence rates are strongly associated with the brain drain of physicians from Sub- Saharan African to OECD countries. In countries in which the HIV prevalence rate exceeds 3 percent, a doubling of the medical brain drain rate is associated with a 20 percent increase in adult deaths from AIDS; medical brain drain does not appear to affect life expectancy. These �ndings underscore the need to improve economic con- ditions for physicians in order to retain physicians in Sub-Saharan Africa, especially as antiretroviral treatment becomes more widely available. JEL codes: C33, C5, F22, I12, O11, O55. The AIDS pandemic in Sub-Saharan Africa is affecting all dimensions of social and economic life. In many countries, gains in life expectancy achieved over the past several decades have been wiped out. Reductions in life expectancy are Alok Bhargava (corresponding author) is Professor of Economics at the University of Houston; his email address is bhargava@uh.edu. Fre ´ ric Docquier is a research associate at the National Fund for ´ de Economic Research and professor of economics at the Universite ´ Catholique de Louvain; his email address is frederic.docquier@uclouvain.be. The authors thank C. Ozden, M. Schiff, and A. Winters, of the World Bank, for encouragement and the International Migration and Development Research Program for research support. They also thank P. Ghys and K. Stanecki, of UNAIDS; L.J. Johnson and A. Wittrup, of the International Labour Organization; T. Tan-Torres and N. Van de Maele, of the WHO; and statistical and medical agencies in 16 OECD countries for help in obtaining the data used in the analysis. This article bene�ted from the helpful comments of three reviewers and the journal editor. The article is dedicated to the memory of Enid M. Fogel, who inspired many economists by her warmth and who devoted herself to improving the lives of young people. THE WORLD BANK ECONOMIC REVIEW, VOL. 22, NO. 2, pp. 345 –366 doi:10.1093/wber/lhn005 Advance Access Publication May 15, 2008 # The Author 2008. Published by Oxford University Press on behalf of the International Bank for Reconstruction and Development / THE WORLD BANK. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org 345 346 THE WORLD BANK ECONOMIC REVIEW detrimental at the macroeconomic level, because they reduce economic growth (Bhargava and others 2001). At the micro level, early parental deaths have created the enormous problem of AIDS orphans (USAID, UNICEF, and UNAIDS 2003; Subbarao and Coury 2004). Orphaned children have lower levels of psychological well-being and school attendance, which is critical for learning and for increasing awareness of HIV transmission routes (Bhargava 2005b). Informed policy formulation to deal with these problems requires ana- lyses of data at the micro and macro levels. The formulation of policies in the wake of the HIV/AIDS pandemic is complex and would bene�t from research on broader biomedical and social science issues. For example, the World Health Organization (WHO) advocates antiretroviral treatment provided by public clinics for patients in HIV/AIDS Stage 4 or with a CD4 cell (type of white blood cell) count below 200 (Gutierrez and others 2004). Studies on the effects of antiretroviral treatment on productivity of undernourished populations can provide insights leading to enhanced treatment strategies. In a similar vein, a recent report by Physicians for Human Rights (2004) emphasizes the need for Sub-Saharan African countries to invest more in training physicians and nurses. The training of additional healthcare staff is hampered by low tertiary enrollment rates in Sub-Saharan African countries; the region could bene�t from strategies such as training its physicians in Asia (Bhargava 2005a). Individual-level surveys in six African countries indicate that more than half of all physicians would like to emigrate to developed countries, in search of better working conditions and more comfortable lifestyles (Awases and others 2003). Very large proportions of healthcare staff—38 percent in Ghana, 45 percent in Cameroon, 49 in Senegal, 58 percent in South Africa and Zimbabwe, 62 percent in Uganda—report being “stressed� by caring for HIV/ AIDS patients. The risks associated with caring for HIV/AIDS patients and the possibility of children of healthcare staff contracting HIV as they enter adoles- cence may exacerbate medical brain drain (Awases and others 2003; Bhargava 2005a). Higher HIV prevalence rates can create a vicious circle, by increasing emigration of physicians and nurses, which can in turn increase deaths from AIDS and the numbers of orphaned children. The trends underlying the international migration of skilled and unskilled labor are complex and reflect several aspects of labor supply and demand conditions in developing and developed countries (Ozden and Schiff 2006). Emigration of skilled workers in general increases remittances and creates business and infor- mation networks that can enhance economic performance in the countries of origin. The net effects of emigration of physicians and nurses from developing countries are likely to depend on the domestic demand for healthcare services over a long period. The AIDS pandemic makes it dif�cult for Sub-Saharan African countries to withstand attrition of already scarce healthcare workers. The results of numerous household-level studies of HIV/AIDS in Sub-Saharan Africa indicate that factors such as multiple sex partners and Bhargava and Docquier 347 sexually transmitted infections can exacerbate HIV transmission (Caral and Holmes 2001). HIV prevalence rates constructed from individual-level data that take account of survival time after contracting HIV are useful for estimat- ing life expectancy. The effects of medical brain drain on indicators of well-being—such as life expectancy and the number of adult deaths due to AIDS—cannot be investi- gated using data from household surveys; country-level data are needed. Longitudinal data are useful for modeling the relation between HIV prevalence rates and brain drain. Analyses at the country level can provide insights for designing surveys investigating economic and social factors underlying medical brain drain. Variables reflecting medical brain drain are not available for Sub-Saharan African countries. Fortunately, most statistical and medical agencies in receiving countries of the Organisation for Economic Co-operation and Development (OECD) keep longitudinal information on immigration of physicians (infor- mation on nurses is not compiled in the same detailed fashion). Databases such as the World Development Indicators (World Bank 2005) contain limited information on HIV prevalence rates. UNAIDS (2006) recently expanded AIDS-related variables on a longitudinal basis for Sub-Saharan African countries. Data on wages from the International Labour Organization (ILO) (2005) and on public health expenditures from the WHO (2006) can be merged with economic and demographic variables from the World Development Indicators to create a comprehensive longitudinal database. This article estimates medical brain drain rates, the number of adult deaths due to AIDS, and life expectancy for 1990–2004 from longitudinal data. Alternative speci�cations are tested using econometric techniques. The article is structured as follows. Section I briefly describes the data on medical brain drain and other variables. Section II develops the analytical framework for spe- ci�cation of the relations, outlining the likely forms of interdependence among medical brain drain rates, the number of deaths due to AIDS, and life expect- ancy. Section III describes the empirical models, and section IV the econo- metric methods used to estimate and test the models. Section V presents the results from estimating random effects models for medical brain drain rates, the number of adult deaths due to AIDS, and life expectancy for Sub-Saharan African countries at �ve points between 1990 and 2004. Certain exogeneity hypotheses for the variables are tested to assess the validity of the model assumptions. The last section summarizes the article’s main conclusions and identi�es some areas for further research. I . THE DATA This article examines the 16 most important OECD countries (Australia, Austria, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, New Zealand, Norway, Portugal, Sweden, Switzerland, the United Kingdom, and 348 THE WORLD BANK ECONOMIC REVIEW the United States) for which longitudinal data on foreign-born physicians are available. These countries account for 93 percent of skilled immigrants in the OECD (Docquier and Marfouk 2006). The medical brain drain can be evaluated in terms of stocks and rates, following Carrington and Detragiache (1999) and Docquier and Marfouk (2006). The rate of medical brain drain m for country i in time period t can be written as: Mit ð1Þ mit ¼ Pit þ Mit where Mit denotes the stock of physicians from country i working abroad and P denotes the number of physicians working in the home country. Docquier and Bhargava (2007) developed an annual database covering 1991–2004 from data provided by national agencies. For the data extracted from national censuses, two or three data points are usually available; data for the remaining years were interpolated using a log-linear adjustment. Data on the country of quali�cation of immigrants are available from medical associ- ations in Canada, France, New Zealand, Norway, United Kingdom, and the United States; these data cover 73 percent of the sample. When the country of quali�cation could not be determined, data on country of birth were obtained from national censuses and registers in Australia, Austria, Belgium, Denmark, Ireland, and Sweden; these data cover 18 percent of the sample. For countries for which these data were not available (Italy, Germany, Portugal, and Switzerland), emigrants were de�ned according to their citizenship; these data cover 9 percent of the sample.1 The data reveal that medical brain drain rates from 44 Sub-Saharan African countries to 16 OECD countries rose in most countries between 1991 and 2000 (�gure 1). Only Angola, Benin, Burkina Faso, Chad, The Gambia, Ghana, Kenya, Malawi, Mauritania, Mozambique, Niger, Senegal, South Africa, and Uganda experienced declines in medical brain drain over this period. Comprehensive longitudinal data on HIV prevalence rates and the number of adult deaths due to AIDS were recently released by UNAIDS for 1990– 2004 (UNAIDS 2006). They reveal skyrocketing levels of HIV prevalence rates in many countries between 1991 and 2000 (�gure 2). Longitudinal information on government expenditures on health by Sub-Saharan African countries are available for 1996–2004 (WHO 2006). Because of missing observations for 1990–95, average government health expenditures during 1996–2004 are treated as time-invariant variables in the 1. Because the medical brain drain rate is treated as an endogenous variable in the estimation, alternative de�nitions of emigrants are not critical. Moreover, highlighting differences in the de�nitions across OECD countries should promote a more uni�ed approach in the future. Bhargava and Docquier 349 F I G U R E 1. Medical Brain Drain Rates for Sub-Saharan Africa, 1991 and 2000 Source: Docquier and Bhargava 2007. F I G U R E 2. HIV Prevalence Rates in Sub-Saharan Africa, 1991 and 2000 Source: UNAIDS 2006. 350 THE WORLD BANK ECONOMIC REVIEW econometric modeling. The ILO (2005) provides data on physicians’ wages expressed in terms of average physicians’ wages in the United States (see also Vujicic and others 2004). Data on gross domestic product (GDP) (in 2000 dollars) are from the World Development Indicators (World Bank 2005). Additional information from UNESCO (2004) and the World Bank (2006) were used to reduce the numbers of missing observations. Estimates of the proportion of the labor force with secondary or tertiary education are from Barro and Lee (2001), Docquier and Marfouk (2006), and Cohen and Soto (2007). The variables in the database were averaged to create �ve three-year interval time points over 1990–2004. Alternative data sets were created using two- and four-year averages; the three-year average �gures are used here because of the structure of the data and the stochastic properties of the variables (Bhargava 2001); interpolations of variables such as life expect- ancy can create dif�culties for econometric modeling. A steady increase in HIV prevalence rates and the number of adult deaths due to AIDS is evident from the sample means (table 1). The number of phys- icians emigrating from Sub-Saharan African countries rose between 1990 and 2004, as did medical brain drain rates. Average life expectancy fell about two years between 1991 and 2003. There was an increase over time in net school enrollment rates in primary and secondary education. Physicians’ wages in Sub-Saharan Africa declined slightly relative to physicians’ wages in the United States. I I. A N A LY T I CA L FR A M E WO R K The relations between HIV prevalence rates, medical brain drain, number of adult deaths due to AIDS, and life expectancy estimated using country-level data are of interest to policymakers. The nature of HIV transmission through sexual intercourse and the lags between contracting HIV and the onset of AIDS have important implications for the speci�cation of macroeconometric models that go beyond the usual dif�culties of deducing the effects of disease prevalence rates on aggregate economic indicators. It is even more complex to explain HIV prevalence rates at the country level, where information on the average number of sex partners, the prevalence of sexually transmitted infections, and patterns of migrant labor are unavailable. The effects of HIV prevalence rates on medical brain drain can nevertheless be analyzed, while allowing for the possibility that the HIV prevalence rate is potentially an endogenous variable in the system and may be influenced by medical brain drain. Most rural residents in Sub-Saharan Africa have limited access to basic healthcare, and only a small proportion of people with HIV receive antiretro- viral treatment. The lags between HIV infection and the onset of AIDS are thus likely to depend mainly on the natural rate of disease progression. That T A B L E 1 . Sample Means and Standard Deviations of Selected Variables in Sub-Saharan Africa, 1990–2004 (3-year averages) 1991a 1994 1997 2000 2003 Standard Standard Standard Standard Standard Variable Mean deviation Mean deviation Mean deviation Mean deviation Mean deviation HIV prevalence 2.98 3.72 5.037 5.592 6.594 7.047 7.073 7.907 7.085 8.096 (percent) Number of AIDS 3,960.82 7,777.64 10,253.64 16,672.51 19,713.29 28,002.43 30,245.11 40,974.4 36,963.61 54,538.9 deaths Number of 0.15 0.24 0.15 0.22 0.16 0.24 0.16 0.24 0.16 0.24 physicians per 1,000 population Number of 151.35 528.16 169.10 586.36 188.77 650.39 211.26 687.94 269.75 925.89 physicians emigrating Medical brain 0.09 0.11 0.10 0.12 0.10 0.11 0.10 0.11 0.11 0.12 drainb Life expectancy 50.79 8.21 50.13 8.28 49.36 7.75 48.59 7.88 48.21 8.56 (years) GDP per capita 752.84 1,134.56 749.14 1,179.60 818.13 1,292.17 876.92 1,400.12 906.38 1,415.34 (2000$) GDP per capita 1.67 1.55 1.95 2.13 4.18 8.23 2.81 2.86 3.63 3.74 growth rate (percent) Population 11,536 16,747 12,511 18,310 13,515 19,799 14,539 21,223 15,581 22,692 (thousands) Literacy rate 50.76 19.73 53.73 19.72 56.76 19.62 59.70 19.46 62.57 19.21 (percent of adult population) Bhargava and Docquier (Continued ) 351 TABLE 1. Continued 352 1991a 1994 1997 2000 2003 Standard Standard Standard Standard Standard Variable Mean deviation Mean deviation Mean deviation Mean deviation Mean deviation Primary-school 58.11 25.01 60.20 25.41 61.00 23.31 62.57 20.98 67.00 19.71 enrollment (percent) Secondary-school 19.11 15.95 20.64 17.34 22.06 18.22 23.91 18.72 25.58 18.62 enrollment (percent) Percentage of 13.2 10.2 14.8 11.7 16.0 12.6 17.0 12.9 18.0 13.7 population with secondary or tertiary THE WORLD BANK ECONOMIC REVIEW education Government health 4.32 1.31 4.68 1.42 4.84 1.75 4.87 1.79 4.98 1.75 expenditure (percent of GDP) Physicians’ wages 0.124 0.133 0.104 0.110 0.098 0.106 0.082 0.072 0.083 0.074 in home country/ physicians’ wages in United States Investment 18.98 9.67 20.93 11.19 21.77 13.64 21.36 13.57 20.04 13.45 (percent of GDP) Note: There are at most 47 countries in the sample at each time point. a Based on medical brain drain rates in 1991 and 1992. b Ratio of number of physicians from Sub-Saharan Africa working in 16 OECD countries to the number of physicians working in Sub-Saharan and OECD countries. Source: Docquier and Bhargava 2007. Bhargava and Docquier 353 progression is accelerated by poor nutritional status, including anemia (Belperio and Rhew 2004). Survival time for individuals contracting HIV in Sub-Saharan Africa is about 10 years (Jaffar and others 2004). These biological aspects are useful for interpreting empirical evidence from analyses of country- level data. Medical brain drain should increase the number of adult deaths due to AIDS, especially among urban populations that receive some form of medical care. However, a 15-year period may not be long enough to observe the adverse effects of medical brain drain on HIV prevalence rates or on life expectancy, which is already low in Sub-Saharan Africa. It is useful to outline the pathways through which HIV prevalence can depress economic activity. In developed countries, where antiretroviral treat- ment is widely available, high HIV prevalence rates may not signi�cantly reduce productivity. By contrast, in developing countries AIDS-related work absenteeism is likely to be common. The effects of HIV prevalence rates on aggregate indicators of economic activity may be dampened somewhat by the fact that many people in Sub-Saharan Africa are engaged in household tasks and work on their own farms; when they fall ill, other household members can step in to perform their tasks (Bhargava 1997). Thus while the effects of HIV prevalence rates on GDP growth rates may not be evident, reductions in life expectancy due to HIV/AIDS can hamper economic growth (Bhargava and others 2001). The relations among HIV prevalence, medical brain drain, the number of adult deaths caused by AIDS, and life expectancy can be embodied in a tri- angular system of equations. First, one can specify a model for medical brain drain that is likely to be affected by physicians’ wages, GDP levels, and HIV prevalence rates, which increase the risks in the work environment. Second, HIV prevalence rates and medical brain drain are likely to increase the number of adult deaths due to AIDS and reduce life expectancy. Longitudinal data are available at �ve time points for estimating econometric models for the out- comes medical brain drain rates, number of adult deaths due to AIDS, and life expectancy; the simultaneous equation system is a “block triangular� system (the triangular system of equations contains longitudinal observations that are themselves triangular in form because of time orderings; see equation (8) below). Appropriate techniques for ef�ciently estimating all the equations simul- taneously are not available in the econometrics literature. Instead, each model can be estimated separately using longitudinal estimation methods that take into account the potential endogeneity of variables such as HIV prevalence rates. The models for medical brain drain rates, number of adult deaths due to AIDS, and life expectancy should be dynamic in nature, because past realization of these variables is critical for explaining their current levels. 354 THE WORLD BANK ECONOMIC REVIEW III. THE EMPIRICAL MODELS The �rst equation in the simultaneous equations system is the model for the rate of medical brain drain. It is given by ð2Þ Logistic ðmedical brain drain rateÞit ¼ a0 þ a1 lnð physicians wage=USA ratioÞit þ a2 lnðschool enrollment secondaryÞit þ a3 lnðGDP per capitaÞit þ a4 lnðHIV prevalence rateÞit þ a5 Logistic ðmedical brain drain rateÞitÀ1 þ u1it ði ¼ 1; . . . ; N ; t ¼ 2; 3; 4; 5Þ Transforming the variables into logs is generally useful; the initial obser- vations on medical brain drain rate as well as the lagged dependent variables are treated as endogenous variable in the system (that is, correlated with the errors u1it) (Anderson and Hsiao 1981; Bhargava and Sargan 1983). The HIV prevalence rate is treated as an endogenous variable, and exogeneity assump- tions are tested using likelihood ratio tests. A dynamic model for HIV prevalence rate is estimated to investigate possible reverse causality (the possibility that higher medical brain drain rates predict higher HIV prevalence). Four-year averages at three time points are used in spe- ci�cation 4 to assess the robustness of the results from analyzing three-year averages. The errors, u1it’s, can be decomposed in a random effects fashion as ð3Þ u1it ¼ di þ vit where the di terms are country-speci�c random effects that are distributed with zero mean and �nite variance, and the vit terms are independently distributed random variables with zero mean and �nite variance. Equation (3) is a special case of the assumption invoked in the empirical modeling that the variance- covariance matrix of u1it is an unrestricted positive de�nite matrix (Bhargava and Sargan 1983). The empirical models for the number of adult deaths due to AIDS and for life expectancy are similar. The model for the number of deaths due to AIDS is written as lnðnumber of adult deaths due to AIDSÞit ¼ b0 þ b1 lnð populationÞi þ b2 lnð proportion of labor force with secondary or tertiary educationÞit ð4Þ þ b3 lnðGDP per capitaÞit þ b4 lnðHIV prevalence rateÞit þ b5 lnðmedical brain drain rateÞit þ b6 lnðdeaths due to AIDSÞitÀ1 þ u2it ði ¼ 1; . . . ; N ; t ¼ 2; 3; 4; 5Þ: Bhargava and Docquier 355 In equation (4), the country’s entire population is accounted for, and medical brain drain and HIV prevalence rates are treated as endogenous vari- ables. An interaction term between HIV prevalence and medical brain drain rates is included in an extended version of the model (speci�cation 2, table 3). In view of the lags between contracting HIV and the onset of AIDS, lagged HIV prevalence rate is used instead of the current rate in speci�cation 3 (table 3). In speci�cation 4, the medical brain drain rate is replaced by the number of physicians in the home country ( per 1,000 people) and the number working abroad. Although nonlinearities with respect to these variables are taken into account, it is dif�cult to simultaneously address all possible nonli- nearities given the limited number of countries and time periods in the sample. In the model for life expectancy (table 4), speci�cation 2 replaces the medical brain drain rate with the number of physicians in the home country and the number working abroad. Net percentages of school enrollment in primary edu- cation is a regressor in the model for life expectancy, because even a few years of primary education are associated with lower child mortality in Sub-Saharan Africa (Bhargava and Yu 1997). I V. T H E E C O N O M E T R I C F R A M E W O R K The methodology used to estimate dynamic random effects models in which some explanatory variables are endogenous was developed by Bhargava and Sargan (1983) and Bhargava (1991). Let the dynamic model be given by X m X n1 X n ð5Þ yit ¼ zij gj þ x1ijt b j þ x2ijt b j þ ayitÀ1 þ uit j ¼1 j¼1 j¼n1 þ1 where the z terms are time-invariant variables, the x1 terms are exogenous time-varying variables, and the x2 terms are endogenous time-varying vari- ables. In the model for medical brain drain rates, for example, the HIV preva- lence rate is likely to be an endogenous time-varying variable (that is, is included in the x2ijt’s); unobserved factors affecting HIV prevalence rates may be influenced by country-speci�c random effects (di) in equation (2). It is useful to rewrite the dynamic model in a simultaneous equations frame- work by de�ning a reduced form for the initial observations and a system of (T 2 1) structural equations for the remaining time periods (Bhargava and Sargan 1983): X m X T X T ð6Þ yi1 ¼ zij z j þ y jk xijk þ ui1 ði ¼ 1; . . . ; N Þ j¼0 j¼1 k¼1 356 THE WORLD BANK ECONOMIC REVIEW and B Y0 Cz Z0 Cx X0 U0 ð7Þ � þ � þ � ¼ ðT À1ÞÂT T ÂN ðT À1ÞÂðmþ1Þ ð mþ1ÞÂN ðT À1ÞÂnT nT ÂN ðT À1ÞÂN In equations (6) and (7), Y, Z, and X are matrices containing observations on the dependent, time-invariant, and time-varying explanatory variables; dimensions of the matrices are written below the respective symbols. B is a (T – 1)  T lower triangular matrix of coef�cients: ð8Þ Bii ¼ a; Bi;Iþ1 ¼ À1; Bij ¼ 0 otherwise ði ¼ 1; . . . ; T À 1; j ¼ 1; . . . ; T Þ: Matrix Cz contains coef�cients of time-invariant regressors. Matrix Cx con- tains coef�cients of time-varying regressors. Matrix U contains the error terms. The pro�le log-likelihood functions of the model in equation (2) can be opti- mized using a numerical scheme such as E04 JBF from Numerical Algorithm Group (1991). Assuming that the number of countries is large but the number of time observations is �xed, asymptotic standard errors of the parameters are obtained by approximating second derivatives of the function at the maximum. The random effects decomposition in equation (3) can be tested in this frame- work using likelihood ratio tests. Given �ve time observations, under the null hypothesis of the random effects decomposition, the likelihood ratio statistic is distributed for a large N as a chi-squared variable with 12 degrees of freedom. In short panels, it is reasonable to assume that a variable such as the HIV prevalence rates in equation (2) is correlated with the country-speci�c random effects, di:: ð9Þ x2ijt ¼ lj di þ xà 2ijt where x*2ijt is uncorrelated with di, and the di terms are randomly distributed variables with zero mean and �nite variance, as in equation (3). This corre- lation pattern was invoked by Bhargava and Sargan (1983); the advantage in employing equation (9) is that deviations of the x2ijt’s from their time means that ð10Þ xþ 2ijt ¼ x2ijt À x 2ij ðt ¼ 2; . . . ; T ; j ¼ n1 þ 1; . . . ; n; i ¼ 1; . . . ; N Þ where X T ð11Þ x 2ij ¼ x2ijt =T ð j ¼ n1 þ 1; . . . n; i ¼ 1; . . . ; N Þ t ¼1 Bhargava and Docquier 357 can be used as [(T – 1)n2] additional instrumental variables to facilitate identi- �cation and estimation of the parameters. While more general correlation pat- terns between the explanatory variables and errors are possible (Bhargava 1991), the identi�cation conditions may not be met in dynamic models esti- mated from short panels. Exogeneity hypotheses can be tested using likelihood ratio tests. Given �ve time observations, the likelihood ratio statistic for testing correlation between the random effects and time means of HIV prevalence rates in equation (2) is distributed as a chi-squared variable with �ve degrees of freedom. Fixed-effects estimators (with dummy variables for countries) can be used to circumvent certain endogeneity problems, but the rise in the number of parameters that accompanies the increase in sample size leads to the problem of incidental parameters (Neyman and Scott 1948). V. E M P I R I C A L R E S U L T S This section presents the results from estimating random effects models for medical brain drain rates, the number of adult deaths due to AIDS, and life expectancy for Sub-Saharan African countries at �ve time points over the period 1990–2004. Effect on Medical Brain Drain Rates Speci�cation 1 of the model in equation (2) treats the HIV prevalence rate as an exogenous variable; it does not restrict the variance-covariance matrix of the errors in the simple random effects fashion (equation 3) (table 2). The variance-covariance matrix is restricted to be that of the random effects model in speci�cation 2, and the between/within variance ratio and the within var- iance are estimated. Speci�cation 3 treats HIV prevalence rates as an endogen- ous variable that is correlated with the country-speci�c random effects. Speci�cation 4 analyzes four-year averages. These speci�cations yield several important �ndings. First, the likelihood ratio statistic for testing speci�cation 2 against speci�cation 1 is 50.96; it is dis- tributed as a chi-squared variable with 12 degrees of freedom. The test rejects the null hypothesis of simple random effects decomposition (the 5 percent criti- cal level is 21.0). The likelihood ratio statistic for testing the exogeneity of the HIV prevalence rate assumes the value 12.04, which is close to the 5 percent critical limit of 11.10. Thus the null hypothesis is rejected. In view of the close- ness of the statistic to its critical limit, it is perhaps not surprising that the results from speci�cations 1 and 3 are close. The discussion focuses on the results from speci�cation 3. Second, the coef�cient of the variable measuring physicians’ wages in Sub-Saharan African countries as a percentage of physicians’ wages in the United States is signi�cant at the 5 percent level: countries with higher phys- ician wages have lower emigration rates. These �ndings are consistent with the responses of health-care personnel who want to emigrate, among whom large T A B L E 2 . Maximum Likelihood Estimates for Medical Brain Drain from Sub-Saharan African Countries Explained by 358 Socioeconomic Variables and HIV Prevalence Rates, 1990–2004 Speci�cation 1 Speci�cation 2 Speci�cation 3a Speci�cation 4b Standard Standard Standard Standard Explanatory variable Coef�cient error Coef�cient error Coef�cient error Coef�cient error Constant 2 0.465** 0.146 2 0.815** 0.224 2 0.485** 0.151 2 1.055** 0.201 ln(physicians’ wages in home 2 0.036** 0.019 2 0.057** 0.030 2 0.035** 0.019 2 0.066** 0.032 country/physicians’ wages in United States) ln(percent school enrollment 0.115** 0.045 0.236** 0.069 0.124** 0.048 0.248** 0.081 secondary) ln(GDP per capita) 2 0.035 0.033 2 0.102** 0.057 2 0.037 0.034 2 0.085 0.066 ln(HIV prevalence) 0.079** 0.017 0.082** 0.022 0.071** 0.021 0.107** 0.036 Lagged dependent variable 0.921** 0.028 0.811** 0.053 0.914** 0.031 0.769** 0.035 THE WORLD BANK ECONOMIC REVIEW Between/within variance ratio 0.445 0.354 Within variance 0.051 2 (maximized log-likelihood 512.75 461.79 570.55 300.45 function) Chi-squared test for random 50.96** effects decomposition (12 degrees of freedom) Chi-squared test for exogeneity 12.04** of HIV prevalence rate (5 degrees of freedom) Dependent variable: Logistic (medical brain drain rate). **Signi�cant at the 5 percent level. Note: Data on 39 countries, with �ve time observations at 3-year intervals. a HIV prevalence rate is treated as an endogenous variable. b Speci�cation uses 4-year averages at three time points. Source: Authors’ estimation results. Bhargava and Docquier 359 majorities—68 percent in Cameroon, 77 percent in Zimbabwe, 78 percent in South Africa, 84 percent in Uganda, 85 percent in Ghana—report a desire to earn more as a motivation (Awases and others 2003). Third, net enrollment in secondary education is a positive and signi�cant predictor of medical brain drain, with an estimated short-run elasticity of 0.12. This result is not surprising, as higher enrollments in secondary education entail greater expenditures on education; physicians educated in such environ- ments are likely to have better emigration prospects. Fourth, the HIV prevalence rate is a signi�cant predictor of medical brain drain, with the short-run elasticity (0.07) robust across the �rst three speci�ca- tions. Moreover, the coef�cient of the lagged dependent variable is estimated at 0.91 in speci�cation 3, indicating that the long-run impacts of the explanatory variables are about 11 times greater than the short-run coef�cients. Thus the long-run elasticity of the medical brain drain rate with respect to HIV preva- lence is about 0.8. This means that a doubling of the HIV prevalence rate implies an 80 percent increase in the medical brain drain rate in the long run. This is a large effect, with important policy implications, especially given that the average number of physicians per 1,000 people is only 0.15 in Sub-Saharan Africa (see table 1). Furthermore, higher ratios of physicians to the population will be needed as more people with HIV develop AIDS. Fifth, the large estimated coef�cients of the lagged dependent variable suggest that emigration patterns in Sub-Saharan African countries are becom- ing well established, presumably as a result of stable demand from OECD countries for physicians trained in speci�c countries. While speci�cation 2 is rejected in favor of speci�cation 1 by the likelihood ratio test, the estimated between/within variance ratio is not signi�cant in speci�cation 2, possibly because of the relatively small number of countries in the sample. Sixth, the results from speci�cation 4 employing four-year averages are similar to those from speci�cation 1, indicating robustness of the results from three-year averages at �ve time points. In fact, use of four-year averages entails a loss of information, because the data from 2002, 2003, and 2004 cannot be used in speci�cation 4. Finally, a model similar to equation 2 was estimated for HIV prevalence rates with medical brain drain rate as an explanatory variable to investigate possible reverse causality. Coef�cients of medical brain drain rate were not sig- ni�cant in any of the speci�cations, thereby supporting the model formulation and exogeneity assumptions. Effect on Numbers of Adult Deaths Due to AIDS and on Life Expectancy The results for the numbers of adult deaths due to AIDS are shown for four speci�cations (table 3). Speci�cation 2 includes an interaction term between medical brain drain and HIV prevalence rates; this term is included because higher HIV prevalence rates can exacerbate the effects of medical brain drain on adult deaths caused by AIDS. In speci�cation 3, the current HIV prevalence 360 T A B L E 3 . Maximum Likelihood Estimates for Number of Adult Deaths due to AIDS, 1990–2004 Speci�cation 1a Speci�cation 2a Speci�cation 3b Speci�cation 4c Standard Standard Standard Standard Explanatory variable Coef�cient error Coef�cient error Coef�cient error Coef�cient error THE WORLD BANK ECONOMIC REVIEW Constant 2 2.833** 0.422 2 3.412** 0.165 2 5.011** 0.203 3.553** 0.481 ln(population) 0.450** 0.017 0.480** 0.006 0.635** 0.008 ln(proportion of population with 2 0.045 0.027 2 0.005 0.026 0.024 0.016 2 0.114 0.085 secondary or tertiary education) ln(GDP per capita) 2 0.014 0.025 2 0.072** 0.025 2 0.008 0.006 2 0.093** 0.047 ln(HIV prevalence) 0.542** 0.039 0.778** 0.038 0.660** 0.052 ln(HIV prevalence) – 1 0.836** 0.016 ln(medical brain drain rate) 0.095** 0.019 2 0.059** 0.023 2 0.080** 0.020 ln(number of physicians in home 2 0.007 0.173 country/1,000 people) ln(number of physicians abroad) 0.113** 0.035 [ln(number of physicians in home 0.001 0.028 country/1,000 people)]2 [ ln(number of physicians abroad)]2 0.014** 0.006 ln(medical brain drain)  ln(HIV 0.049** 0.008 prevalence) ln(medical brain drain)  ln(HIV 0.061** 0.005 prevalence) – 1 ln(HIV prevalence)  ln (physicians 2 0.032** 0.011 abroad) Lagged dependent variable 0.510** 0.012 0.498** 0.001 0.357** 0.008 0.535** 0.015 2  (maximized log-likelihood 1,243.35 1,258.20 1,282.88 835.39 function) Chi-squared test for exogeneity of 104.03** 116.63** 96.94** medical brain drain and HIV prevalence rates (10 degrees of freedom) Dependent variable: ln(number of adult deaths caused by AIDS). **Signi�cant at the 5 percent level. Note: Data on 39 countries with �ve time observations at 3-year intervals are used in the estimation. a Medical brain drain rate (ratio of number of physicians from Sub-Saharan Africa working in 16 OECD countries to the number of physicians working in Sub-Saharan and OECD countries) and HIV prevalence rates are treated as endogenous variables. b HIV prevalence rate is lagged one period. c Physicians in home country per 1,000 people and physicians abroad are entered as separate variables. Source: Authors’ estimation results. Bhargava and Docquier 361 362 THE WORLD BANK ECONOMIC REVIEW T A B L E 4 . Maximum Likelihood Estimates from Dynamic Random Effects Models for Life Expectancy in Sub-Saharan African Countries Explained by Socioeconomic Variables and HIV Prevalence and Medical Brain Drain Rates, 1990–2004 Speci�cation 1 Speci�cation 2 Standard Standard Explanatory variable Coef�cient error Coef�cient error Constant 1.117** 0.005 1.012** 0.004 ln( government health expenditure as percent 0.040** 0.003 0.029** 0.003 of GDP) ln(percent primary school enrollment) 0.022** 0.009 0.022** 0.002 ln(GDP per capita) 0.001 0.007 0.009** 0.004 ln(HIV prevalence) 2 0.027** 0.003 2 0.026** 0.004 ln(medical brain drain rate) 2 0.005 0.003 ln(physicians in home country, per 1,000 2 0.0001 0.003 people) ln(physicians abroad) 0.0001 0.002 Lagged dependent variable 0.662** 0.002 0.700** 0.001 2  (maximized log-likelihood function) 1558.80 1588.15 Chi-squared test for exogeneity of medical 16.64** 24.46** brain drain rate or physicians abroad (5 degrees of freedom) Dependent variable: ln(life expectancy). **Signi�cant at the 5 percent level. Note: Data on 39 countries with �ve time observations at 3-year intervals in are used in the estimation. The medical brain drain rate (ratio of number of physicians from Sub-Saharan Africa working in 16 OECD countries to the number of physicians working in Sub-Saharan and OECD countries) is treated as an endogenous variable. Source: Authors’ estimation results. rate is replaced by the value lagged one period (that is, three years). Speci�cation 4 replaces the medical brain drain rate with the number of phys- icians in the home country and those working abroad, taking into account some nonlinearities. Constraints on the variance-covariance matrix implied by the random effects decomposition are rejected in all speci�cations. The results in table 3 show the importance of HIV prevalence rates for the number of adult deaths due to AIDS. Although the short-run elasticity from speci�cation 1 is just 0.54, the long-run elasticity is close to 1.0. In view of the lack of antiretroviral treatment for the vast majority of people with HIV during the sample period, it is not surprising to �nd large long-run effects of HIV prevalence rates on adult deaths. In speci�cation 1, the medical brain drain rate is a signi�cant predictor of the number of deaths due to AIDS, with a short-run elasticity of 0.1 and a long-run elasticity of 0.2. Even where antiretroviral treatment is not provided, reduced access to physicians who provide basic care, such as treatment of Bhargava and Docquier 363 tuberculosis and other illnesses that accompany HIV, is likely to exacerbate the progression of the illness. Thus at the aggregate country level, medical brain drain appears to reduce the survival time of people with HIV. In speci�cations 2 and 3, the interaction term medical brain drain and HIV prevalence rates is signi�cant, indicating that the effects of medical brain drain are likely to depend on national HIV prevalence rates. The results from speci�- cations 2 and 3 are close, indicating small differences between using current and lagged HIV prevalence rates. While the effects of medical brain drain rate on the number of deaths due to AIDS become positive after HIV prevalence rates cross the 3 percent threshold, it is dif�cult to precisely estimate the stan- dard errors in nonlinear models with modest sample sizes. Nevertheless, the results in table 3 suggest the importance of devising economic and other incen- tives for reducing medical brain drain as HIV prevalence rates cross the 3 percent threshold (average HIV prevalence rates after 1991 in table 1 are above this threshold). The results from speci�cation 4 show that the number of physicians abroad is a signi�cant predictor of the number of adult deaths due to AIDS, while the number of physicians in the home country is not statistically signi�cant. It is dif�cult to precisely estimate the coef�cients in the presence of nonlinearities among explanatory variables using only �ve time observations on 39 countries. The results on life expectancy are presented for two speci�cations (table 4). Speci�cation 2 replaces the medical brain drain rate with the numbers of phys- icians in the home country and those working abroad. The exogeneity hypoth- eses for the medical brain drain rate in speci�cation 1 and for the number of physicians abroad in speci�cation 2 are rejected. Because speci�cation 1 is a special case of speci�cation 2, another likelihood ratio test can be applied to choose between these two speci�cations. Speci�cation 2 is the preferred model in table 4, because the likelihood ratio statistic assumes the value 29.35 and is asymptotically distributed as a chi-squared variable with one degree of freedom. Government health expenditures expressed as a percentage of GDP have positive coef�cients in both speci�cations and are statistically signi�cant. The data on this variable were compiled annually from 1996; the estimation method treated average expenditures as a time-invariant variable. The net enrollment in primary education is also estimated with positive and signi�cant coef�cients in both speci�cations in table 4. This result is not surprising, as school enrollment rates are very low, especially in rural areas of Sub-Saharan African countries, and child survival and life expectancy are likely to increase with education. The fact that the coef�cient of the GDP variable is insigni�cant in speci�cation 1 may seem surprising in view of the relation between GDP levels and life expectancy (Preston 1976). However, the coef�cient of GDP is statistically signi�cant in speci�cation 2, which is a more general formulation. It is also likely that the HIV/AIDS pandemic is driving recent variations in life expectancy in Sub-Saharan Africa. 364 THE WORLD BANK ECONOMIC REVIEW The estimated coef�cients of HIV prevalence rates are signi�cant and negative in both speci�cations shown in table 4. The short-run elasticity of life expectancy with respect to the HIV prevalence rate is 0.02, and the long-run elasticity is 0.07. Thus a doubling of the HIV prevalence rate would reduce life expectancy to 7 percent in the long run. The estimated coef�cient for the medical brain drain rate is negative in speci�cation 1, but not statistically signi�cant. In the long run, the increase in the number of AIDS deaths predicted by the medical brain drain rate also implies lower life expectancy. However, the coef�cients of the numbers of physicians in the home country and abroad are statistically insigni�cant in speci�cation 2 after controlling for population size. The coef�cients of the lagged dependent variables are signi�cant in both speci�cations but lower than those obtained for medical brain drain rates in table 2. This result may be due to the differences in availability of antiretroviral treatment across Sub-Saharan Africa; longitudinal data on the percentages of people with HIV receiving antiretroviral treatment are not available in the databases. Overall, the empirical models for adult deaths due to AIDS and for life expectancy exhibit a triangular form, although the medical brain drain rate is not a signi�cant predictor of life expectancy. It is plausible that a combined variable for the emigration of physicians and nurses (on whom data were not available) might have had greater explanatory power because of the role of nurses in administering treatments. VI. CONCLUSIONS What effect has Sub-Saharan Africa’s AIDS pandemic had on the emigration of physicians? How has the medical brain drain affected life expectancy and the number of adult deaths due to AIDS? Lower physicians’ wages and higher HIV prevalence increase emigration of physicians from Sub-Saharan Africa. Empirical analyses at the country level that take into account country characteristics and unobserved heterogeneity are important for policy formulation. In particular, as is evident from the results here, physicians’ wages and living standards need to be improved to better reflect the workload and risks in high HIV-prevalence environments. Some observers have suggested schemes in which developed countries would compen- sate Sub-Saharan African countries for the loss of their healthcare staff (Bhargava 2005a). Whether or not such schemes are adopted, it is imperative that international agencies implement pilot programs for reducing the emigra- tion of physicians from Sub-Saharan Africa. Such policies would stop the vicious circle of higher HIV prevalence rates leading to increased emigration of physicians, which in turn lowers the quality and quantity of care for AIDS patients, increasing death rates and the numbers of orphaned children. The medical brain drain rate is associated with an increase in the number of adult deaths after HIV prevalence rates cross the 3 percent mark. A doubling of the medical brain drain rate is associated with a 20 percent increase in adult Bhargava and Docquier 365 deaths from AIDS. These �ndings underscore the importance of retaining phys- icians in Sub-Saharan African countries, especially as antiretroviral treatment becomes more widely available. The results from the model for life expectancy show the importance of lower HIV prevalence rates and to some extent higher government expenditures on health. 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