Paul Cahu
email: pcahu@worldbank.org

Falilou Fall
email: falilou.fall@univ-paris1.fr

Accounting for the E¤ects of AIDS on Growth in Sub-Saharan Africa

Keywords: Health, AIDS epidemic, Human Capital, Growth, Sub-Saharan Africa JEL Classi…cation: I10, J11, O15, O40, O55

In this paper, we, …rst, perform a quantitative assessment of the impact of the HIV/AIDS epidemic on growth. Second, we precisely account for the e¤ects of the epidemic on income per capita through human and physical capital accumulations, population and labor force. That is, we disentangle the e¤ect on the di¤erent sources of short and long run growth. Using a dynamic panel of 46 Sub-Saharan African countries over the period 1981-2007, we show that HIV/AIDS has negative, signi…cant and long-lasting e¤ects on demography and growth. According to the estimates presented, GDP per working age population will be 12% lower in the longrun for the average African country than it should be if the epidemic had not spread out. However, the impact is huge for the countries experiencing a high prevalence rate. To tackle the endogeneity issue of HIV/AIDS, we provide a new series of HIV prevalence rate build from the estimation of the propagation dynamic of the epidemic.

Introduction

The UNAIDS 2008 "Report on the global AIDS epidemic" states that there were an estimated 33 million people living with AIDS in 2007 in the World. Sub-Saharan Africa remains the most heavily a¤ected by HIV, accounting for 67% of all people living with HIV and for 72% of AIDS related deaths in 2007. In some countries, as Botswana, Lesotho and South Africa, HIV prevalence rate among pregnant women attending clinics is more than 30%. In Sub-Saharan Africa alone, the epidemic has orphaned nearly 12 million children under 18.

The dramatic humanitarian impact of the epidemic is largely recognized and has drawn most of the attention. This has helpfully mobilized the international community to set up powerful instruments and large …nancial funds to slow down the propagation of the epidemic and treat infected people. Thanks to these e¤orts, promising results have been reached, but enduring challenges remain.

Indeed the epidemic is likely to have very long lasting e¤ects. The UNAIDS report declares that "the natural age distribution in many national populations in Sub-Saharan Africa has been dramatically skewed by HIV with potentially perilous consequences for the transfer of knowledge and values from one generation to the next". This declaration underlines some of the di¤erent channels through which the epidemic can a¤ect growth: short run and long run impact, e¤ects on population dynamics and on education.

In this paper, we, …rst, perform a quantitative assessment of the impact of the HIV/AIDS epidemic on growth. Second, we precisely account for the e¤ects of the epidemic on income per capita through education, physical capital, population and labor force. That is, we disentangle the e¤ect on the di¤erent sources of short and long run growth. Such an exercise may shed some light on the need to tackle the multidimensional impact of the epidemic.

The social and economic consequences of such epidemic are huge. Families are broken, sometimes with an important number of orphans. The burden, in families providing health care for infected people is heavy, and has consequences on savings and investment. It also have large e¤ects on public policies as it diverts resources to health care from others under satis…ed needs.

However, the assessments of the economic impact of the epidemic are very contradictory. In one hand, [START_REF] Bonnel | HIV/AIDS: Does it increase or decrease growth in Africa?[END_REF], Bell, Devarajan, and Gerbach (2003), [START_REF] Mcdonald | AIDS and economic growth: A human capital approach[END_REF], and [START_REF] Papageorgiou | What do we know about the impact of AIDS on cross-country income so far?[END_REF] …nd some evidence of a negative e¤ect of the epidemic. In the other hand, …rst estimation by [START_REF] Bloom | Does the AIDS epidemic threaten economic growth[END_REF] in a cross-country perspective found no evidence that AIDS impedes growth. [START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF] have also found a statistically insigni…cant e¤ect of the HIV epidemic on growth.

Assessing the macroeconomic impacts of the HIV/AIDS epidemics is a very challenging exercise. There have been many reservations made on macroeconomic cross-country regressions. Durlauf, Jonhson and Temple (2005) provide an extensive review of the limitations and progress on the econometrics of growth. Most of the reservations comes from the lack of appropriate data and model uncertainty used to analyze growth. Therefore, they underline the necessity to draw lessons from these analysis with cautious. They also point out the di¢ culty to …nd out valid instruments in panel growth regressions. However, they …nd promising the strategy followed by [START_REF] Tavares | How democracy a¤ects growth[END_REF], which consisted on estimating the e¤ects of democracy on the long run determinants of growth (human capital accumulation, physical capital accumulation or government expenditures) in order to net out its e¤ect on growth.

Recently, [START_REF] Weil | Accounting for the e¤ect of health on economic growth[END_REF] used microeconomics estimates of the e¤ect of health on individual outcomes to construct macroeconomic estimates of the proximate e¤ect of health on GDP per capita. This approach allows to circumvent the endogeneity bias encountered in structural estimates of growth determinant.

Our strategy is inspired by [START_REF] Weil | Accounting for the e¤ect of health on economic growth[END_REF] accounting strategy 1 . We use instrumental variables, including circumcision rate as [START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF] to estimate the independent propagation dynamic of the epidemic, and then we construct a HIV prevalence series. These two complementary steps normally allow us to eliminate or reduce the endogenous bias problem.

Conceptually our approach is similar to the one done by [START_REF] Ashraf | When does improving health raise GDP?[END_REF]. The reasoning is to estimate the impact of a variable of interest and to substract its impact in reference to the potential output the economy would reach without the shock due to the variable of interest. Moreover, their simulations of the impact of eradicating malaria or tuberculosis depict a very instructive functioning of the dynamic e¤ects of epidemic disease directly and indirectly through education, life expectancy and productivity. As HIV/AIDS combines the distinctive patterns of these two diseases, that is hitting either the working adult age population and the young, their exercise help to explain its potential cumulative huge e¤ects.

Our estimates show that for the average Sub-Saharan African countries, at the peak, the total e¤ect of HIV/AIDS on growth is a reduction by 6% of income per capita; the e¤ect through education account for 2.4%, the e¤ect through physical capital account for 2%, the residual e¤ect which account for the reduction of labour participation and technological progress account 1.5%, and the counterbalancing positive e¤ect through capital intensity accounts for less than 0.1%. As the e¤ects pile up, in the long run the cumulative permanent e¤ect is a 12% loss in the level of GDP per capita.

Our results emphasize the necessity to tackle the impact of the epidemic not only through its prevention and the treatment of infected people, but also on human capital and physical capital accumulation.

The paper is organized as follows. Section 2 discusses the controversial literature and presents our conceptual framework. Section 3 presents the data sources and the construction of the independent HIV prevalence series. Section 4 is the econometric assessment of the impact of HIV/AIDS on per capita income and on the determinants of growth. Section 5 presents the accounting exercise we perform and the results. Section 6 discusses our results by comparing them to the literature and concludes.

The conceptual framework and controversial issues

This section presents the theoretical framework and the controversial issues in the disentanglement of the e¤ects of HIV/AIDS on growth. Although there is no doubt that AIDS is a plague for Sub-Saharan African countries, the patterns of the economic outcomes is very controversial.

A non consensual literature

An evidence di¢ cult to show Several studies have tried to estimate the total e¤ect of AIDS on growth. Early estimates by [START_REF] Over | The macroeconomic impact of AIDS in Sub-Saharan Africa[END_REF] and [START_REF] Cuddington | Assessing the impact of AIDS on the growth path of the Malawian economy[END_REF] …nd evidence of a negative e¤ect of AIDS on growth. But these estimates su¤er from a lack of appropriate data. [START_REF] Bloom | Does the AIDS epidemic threaten economic growth[END_REF] run cross-country regressions of GDP per capita growth on HIV/AIDS prevalence and found no e¤ect. However, their studies have been criticized because they used limited data2 . More recently, [START_REF] Mcdonald | AIDS and economic growth: A human capital approach[END_REF] provide new estimates of the e¤ect of AIDS on growth through its impact on health capital. Their study, based on data from 1984 to 1999, relies on the estimation of a Solow-augmented model. Using a panel estimation method applied to cross-country economic growth, they found a strong and signi…cant negative e¤ect of AIDS on growth. While, [START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF] show that there is no e¤ect of the epidemics on growth of African countries. Corrigan, Glomm, and Mendez (2005) show calibration results that imply large negative e¤ects of the epidemic on growth.

A room for a positive or negative impact There are several channels through which the AIDS epidemic can potentially harm economic growth3 . First, as AIDS decreases life expectancy, it reduces the incentives to invest or accumulate physical or human capital. Moreover, as noted by [START_REF] Corrigan | AIDS crisis and growth[END_REF], to the extent that AIDS is more prevalent among highly skilled workers and that highly skilled labor is complementary to capital, the AIDS epidemic can lower the returns on investment and, in turn, savings and capital accumulation. In the same line, potentially large medical costs to treat HIV can divert private or public resources from education investment or capital accumulation. In addition to that, a decrease in life expectancy will reduce individuals or …rms investment in education or training, reducing therefore workers productivity. Second, the disease may eventually hamper schools enrollment and the quality of education4 . The presence of a large generation of orphans, specially in the context of African economies where the government can not compensate for missing parents, may induce a decrease in human capital investment. Finally, the disease can hamper the productivity of infected people, thus lowering average productivity. The disease could reduce the productivity of healthy people as well, as they may devote some of their time taking care of their sick relatives. All these e¤ects, lower investment in physical and human capital, and productivity slowdown, may contribute cumulatively to a negative impact of HIV/AIDS on income.

However, there is still a room for a positive impact of AIDS/HIV epidemic on growth. The positive e¤ect of AIDS on growth may occur through two closed mechanisms. The …rst one is the capital deepening e¤ect occurring with the loss of working age population caused by epidemics as emphasized by [START_REF] Young | In Sorrow to bring forth children : fertility admidst the plaque of HIV[END_REF]. Indeed, the short-run e¤ect of the epidemic with the huge number of death of adult persons is, in a context or scarcity of capital, to increase the capital to worker ratio, and therefore induces an increase of productivity and growth. The second one is a long run e¤ect depending on the impact of AIDS/HIV on fertility rate and ultimately on population growth. As emphasized by [START_REF] Young | The Gift of the dying: the tragedy of AIDS and the welfare of future African generations[END_REF], the AIDS/HIV epidemic with the adult mortality, the HIV infant mortality and the endogenous decreasing e¤ect on fertility will lead to a lower population growth rate. [START_REF] Young | The Gift of the dying: the tragedy of AIDS and the welfare of future African generations[END_REF] argues that the positive e¤ects of lower population growth are strong enough to o¤set the most pessimistic forecast of human capital losses, and therefore will bring about extra resources that will raise the per capita welfare of future generations.

A disputed issue : the impact on population growth through fertility A long run positive e¤ect of AIDS/HIV on growth depends ultimately on its impact on fertility. Theoretically, the impact can be either positive or negative. The …rst round e¤ect of AIDS/HIV on fertility is negative coming from the direct biological impact of the disease, which lowers the fecundity of infected women. fecundity is reduced by HIV infection due to higher rate of miscarriage and stillbirth. There is an important and convergent literature con…rming this negative direct e¤ect5 . For instance, [START_REF] Juhn | HIV and fertility in Africa: …rst evidence from population based surveys[END_REF] …nd that being infected with HIV reduces births last year by approximately 21 percent.

The second round e¤ect depends on behavioral response of individuals either infected and non infected. Thus, this behavioral response can o¤set or increase the negative …rst round e¤ect, since it aggregates sexual behavior changes of all the women's population. As indicated by [START_REF] Young | The Gift of the dying: the tragedy of AIDS and the welfare of future African generations[END_REF], the rationals for a decrease of the fertility due to behavioral changes come directly from a reduction of the willingness to engage in unprotected sex, and indirectly, from the increase of wages due to scarcity of labor, which increase the opportunity cost of having a baby for women. However, the behavioral response of noninfected women may be to increase fertility, mitigating then the diseases'negative impacts on population. It follows from the link between mortality and fertility as exhibited by the historical pattern of demographic transition. There is no consensus on the impact of AIDS/HIV on fertility and individual behavioral response to the epidemic6 . [START_REF] Young | The Gift of the dying: the tragedy of AIDS and the welfare of future African generations[END_REF] …nd that the HIV epidemic is lowering fertility in Sub-Saharan Africa. Kalemli-Ozcan (2009) using a restricted period of data (1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998) …nd that the e¤ect of HIV prevalence on fertility is positive for South Africa. Ultimately, [START_REF] Forston | HIV/AIDS and Fertility[END_REF] and [START_REF] Fink | HIV and fertility: Long-term Evidence from Sub-Saharan Africa[END_REF] suggest that the AIDS/HIV epidemic had very little impact on fertility and is unlikely to have a signi…cant e¤ect on population size.

The theoretical model

We will denote N the working age population, L the equivalent number of full-time workers in the economy, K the aggregate stock of physical capital, S the average number of years of schooling among the workers, h the HIV prevalence rate and Y the total GDP. We consider an extended Solow-type growth model with both human and physical capital. The aggregate output is:

Y t = F (A t ; K t ; L t ; S t ) = A t K t L 1 t e (1 )St (1)
where 0 < < 1. Total factor productivity A t varies with time and can be a¤ected by exogenous shocks such as civil con ‡icts for instance. This framework allows to take into account the e¤ects of the epidemic on the di¤erent sources of growth mentioned above. [START_REF] Mcdonald | AIDS and economic growth: A human capital approach[END_REF] consider a Solow augmented model that integrates directly health as a variable of the production function. In our speci…cation, health is rather embedded in labor force participation and a¤ects capital accumulation as well7 .

In the long-run, fertility and thus the gross growth rate of population n may be endogenous as well. However, the changes in fertility is unlikely to have large e¤ects on per adult income in the long-run. Indeed, although the change in fertility could a¤ect the magnitude of the e¤ects of HIV/AIDS on growth it is unlikely to modify their directions.

As infected adults have a shorter life expectancy, we model the net increase of the adult population as:

N t = N t 1 1 + n vh t 1 (2)
Labour participation is supposed to be reduced by the epidemic. We assume therefore:

L t = N t (1 uh t ) (3)
We assume that physical capital depreciates at a constant rate and we introduce Inv the investment rate:

K t = (1 )K t 1 + Inv(h)Y t (4)
Therefore the evolution of per adult income y = ln Y N , the variable we are interested in, only depends of the dynamics of the working age population n t = ln(N t ), the labour force participation rate l t = ln(L t ) ln(N t ), the lagged physical stock of capital k t 1 = ln(K t 1 ), the investment rate inv t = ln(Inv t ) and the average years of schooling S t :

y(h) = ln(A t ) + l t (h) + k t (k t 1 ; inv t ; y t ; n t ) l t n t + S t (5)
To investigate how the epidemic a¤ects the per capita income through the di¤erent channels, let us note xt the value the variable x t would have taken if there had been no epidemic.

The various e¤ects of the epidemic on per capita income can be derived from the changes in the di¤erent factors x induced by the epidemic, x t = x t xt . The derivative of the production function gives:

y t = (1 ) l t + ( k t n t ) + (1 ) S t (6)
As the accumulation equation of physical capital is linear, we have to use a log-linear approximation at the …rst order to replace k t . Introducing g the long-run growth rate of the economy8 :

k t K t K t 1 1 + g k t 1 + 1 1 1 + g ( inv t + y t + n t ) (7)
Denoting K = 1 1+g , we could rearrange the equation ( 6) into four components:

y t = K 1 (1 K ) ( k t 1 n t ) + (1 K ) 1 (1 K ) inv t + 0 S t + 1 1 (1 K ) l t
(8) The …rst term measures the positive impact of the diminution of the labour force on per capita capital. The second and the third account for the e¤ects of the disease on investment in both physical capital and human capital. The last one expresses the negative e¤ect of HIV/AIDS on labour market participation. As the above system is linear, we know that there is a set of column matrix fA i g t i=1 such that:

y t = ỹt + t X i=1 A i 0 B B @ inv i S i n i l i 1 C C A (9)

The accounting strategy

One may think to estimate the e¤ects of HIV/AIDS on growth by looking separately at the e¤ects on each components of the equation ( 9), that are investment, schooling, working age population and labour participation. The total e¤ect of the epidemic on the per capita income would be:

y t = t X i=1 A inv i inv i h + A S i S i h + A n i n i h + A l i l i h h i (10)
However, only the …rst three multipliers, if signi…cant, are likely to be measured directly using regressions. The last term however cannot be measured directly, as there is no available data on participation or on worked hours in most Sub-Saharan African countries.

A second strategy could be to estimate directly for the set of countries fig the following equation, where h i t is the epidemic's prevalence rate:

y i t = ỹi t + h i t + " i t ( 11
)
This strategy is relevant only if the e¤ects of the epidemic on capital accumulation have already materialized. If this is not yet the case, such an estimation is likely to underestimate the total e¤ects of the epidemic, by capturing only the short-term e¤ects, that are linked to labor participation.

To assert the relevance of this method, we have to calculate a posteriori the e¤ects of the epidemic on both human and physical capital in order to assess whether or not the impact have already been substantial.

To measure all the e¤ects of HIV/AIDS on growth both in the short and long-term, we propose in this paper the following strategy:

(i) In a …rst step, we estimate directly the e¤ect of the epidemic on productivity.

(ii) In a second step, we estimate separately the e¤ects of the disease on investment, education and the working age population by running the following regressions, where x is one of these variables:

x i t = xi t + x h i t + " i t (12)
To do so, we use control variables to instrument the unknown series xi t .

(iii) Using the equation ( 10) and the previously estimated multipliers x i h , we will calculate the evolution of the output per adult one should have observed if the epidemic has only in ‡uenced education, investment or the total adult population. If the sum of these three components represents a substantial part of the total e¤ect estimated in the …rst step, then the regression (11) is unlikely to underestimate the total e¤ect of the epidemic.

(iv) If the method appears to be valid, we …nally estimate the remaining e¤ect of HIV/AIDS, which is the impact on labour participation, by substracting the e¤ects on education, investment and demography obtained from the direct estimation.

Common empirical framework

To run the previous regressions, one has to …nd satisfactory determinants of the variables zt being fx t ; y t ; y t g. Let us assume that:

zi t = z zi t 1 + K X k=1 z k Control ik t 1 + u z i + z t + " zi t (13)
where z i t is the dependent variable z at time t in the country i, u i is the …xed e¤ect of the country i, t is the year …xed e¤ect and "CONTROL k " represents the control variables.

To assess the e¤ects of AIDS on demographic, education and macroeconomic variables, we therefore run the following panel within regressions with country and yearly …xed e¤ects:

z i t = z z i t 1 + z h i t 1 + K X k=1 z k Control ik t 1 + u z i + z t + " zi t ( 14
)
The …xed e¤ects take into account the heterogeneity between countries in terms of infrastructure, wealth or religion as well as the impact of global shocks such as crop or oil prices. To take into account autocorrelation problems we run GLS regressions with country …xed e¤ects and with clustered errors within countries. To limit the issue of potential endogeneity of the HIV and other control variables, we only introduce lagged variables at the right hand side of equation ( 14). This estimation strategy is consistent with the one followed by [START_REF] Mcdonald | AIDS and economic growth: A human capital approach[END_REF] and [START_REF] Kalemli-Ozcan | Reversal" of the demographic transition and economic development: evidence from Africa[END_REF].

Dealing with endogeneity

There are several good reasons to suspect that HIV prevalence could be a¤ected by economic activity. If this variable were partially endogenous, simple estimations would be biased. Indeed higher growth could attract migrants or fasten urbanization and facilitate the di¤usion of the disease, making then HIV increase with growth. Urbanization could also a¤ect social control over sexual behaviors and contribute to the spread of the epidemic. It has also been claimed that industrialization, especially mining activities, could favor prostitution and in turn the spread of HIV. Otherwise, countries growing faster may also allocate more resources to health and treatments, reducing the mortality of HIV infected people. However, longer life expectancy of sick people induces higher prevalence rate among the population. To deal with endogeneity, we may think to instrument the series of HIV prevalence rate by external series.

However the epidemic feature of HIV/AIDS induces that prevalence rates are highly autocorrelated. They di¤er across time and from a country to another less because of initial conditions but rather because of particularities a¤ecting the speed of di¤usion of the disease. Therefore …nding an exogenous series directly explaining the level of the epidemic within a country is di¢ cult. It is more relevant to seek rather instruments explaining the speed of di¤usion of the epidemic within a country.

Our strategy to tackle potential endogeneity issues is therefore to build a series of HIV prevalence rate from a theoretical dynamic equation where the speed of propagation of the disease is instrumented. The dynamic of the epidemic is derived from a theoretical model of propagation of HIV presented in the next section.

The data: sources, building and robustness

The data are from several international institutions and cover 46 countries of Sub-Saharan Africa on a yearly basis from 1970 to 2007. Data on HIV/AIDS epidemic are brought from three di¤erent sources:

The UNAIDS ( 2003) epidemiological fact sheets provide raw data on HIV prevalence among pregnant women in rural or urban areas for most countries between 1987 and 2003. The methodology used is consistent over time and countries. However, it is likely to overestimate the extent of the epidemic among the labor force, as young adults are more likely to be infected by HIV. Moreover, as data were collected only on speci…c surveillance site, which could vary across time, these data are volatile and were not collected each year.

The fact sheets[?] report also AIDS cases during the 80s and the early 90s. Collected data are less volatile but may underestimate the extent of the epidemic, as AIDS was not clearly identi…ed as a speci…c disease in the 80s.

Eventually the UNAIDS has recently released estimates of HIV prevalence among the adult population from 1990 to 2007. The UNAIDS used available data9 to calibrate model-based simulations of the spread of the epidemic. This source provides therefore smoother series.

Unfortunately, using only one of these sources to run empirical estimate is not su¢cient to identify the e¤ects of HIV/AIDS on growth. First, because treatments and even diagnosis were poor before the 90s, then the disease, although less frequent, were likely to a¤ect more productivity and fertility at that time. Second, the volatility of growth is substantial in African countries, because of con ‡icts, commodity prices volatility and weather hazard. Thus, long series are necessary to identify a convincing e¤ect of HIV/AIDS on growth. Furthermore as the epidemic a¤ected a limited share of the population in most African countries, the thought e¤ect of HIV/AIDS on growth is likely to remain small in the short-run. To obtain robust results, we build three di¤erent estimates of HIV prevalence rate. The …rst two series are based on UNAIDS data, the last one is our own construction.

HIV prevalence estimates using prevalence among pregnant women

The data on HIV prevalence among pregnant women (hpw) have not been collected on a yearly basis. To build a comprehensive dataset, one can …rst use the correlation between urban and rural prevalence (hpwr) within a country to "predict" the national data. To build comparative data mostly between 1982 and 1990, one can use the correlation between AIDS case (Case) and HIV prevalence among women in urban areas (hpwu). AIDS cases were probably less underreported in urban areas, where health facilities are larger and better endowed.

The following equation, where u i is a country …x e¤ect, is estimated, using GLS regressions, to predict the missing data for HIV prevalence rate among pregnant women in rural area.

hpwr i t = r hpwr i t 1 + r hpwr i t+1 + r hpwu i t + u i + " i t (15)
Table A1 in appendix gives the correlations between HIV prevalence rate among pregnant women in rural areas and urban areas. It gives the coe¢ cient used to predict HIV prevalence rate among pregnant women in rural areas. AIDS cases do not appear to be a good predictor of HIV prevalence rate in rural areas. The number of observations predicted using each regression is indicated in the last row "# predict". Predictions are calculated using the equation ( 15) and assuming that " i t = 0. The di¤erent estimations of the table A1 are used to project HIV prevalence according to available data.

The following equation is used to estimate HIV prevalence rate among pregnant women in urban areas, using the same method. Results are reported in the table A2 in appendix.

hpwu i t = u hpwu i t 1 + u hpwu i t+1 + u hpwr i t + u Case i t 1 + u i + " i t ( 16
)
HIV prevalence rate among pregnant women in total population is …nally calculated as a weighting average of HIV prevalence rate among pregnant women in rural and urban population. However, pregnant women prevalence rates are available between 1987 and 2002 only. To complete the data set between 198210 and 1987, one can use reported AIDS cases and prevalence rate among the whole population (see table A3 in appendix).

ln(hpw

i t ) = a ln(Case i t ) + u i + " i t (17)
This is the …rst series of prevalence rate.

Extension of UNAIDS estimates

UNAIDS estimates are not available for several countries in the early 90s. We use the lower and upper bound estimates to rebuild a main projection (see in appendix table A3, columns 4, 5 and 6).

ln(hiv t ) = a l ln(hiv l t ) + a u ln(hiv u t ) + ln(h 0 )

As linear HIV estimates are likely to be negative for numerous countries before 1990, we run an exponential regression model (see table A3).

ln(hiv t ) = ln(hiv t+1 ) + a 0 ln(Case t ) ln(Case t+1 ) + ln(h 0 )

HIV prevalence data are projected backward using equation ( 19). But such a projection is not possible for countries that do not have estimates of HIV prevalence around 1990. Prevalence was indeed not su¢ ciently high to require the collection of data on AIDS in those countries. We use directly AIDS cases as a proxy of prevalence and run the regression (20) on countries with low prevalence rate, (see last column of table A3).

h t = c 1 Case t + c 2 Case 2 t + c 0 for h t < 0:02 (20)
This gives the UNAIDS series reconstructed for the early 80's.

Building a new series of HIV prevalence rate based on propagation dynamics

As HIV prevalence series are evolving substantially across time, it is unlikely to …nd exogenous series allowing to instrument directly the pro…les of the epidemic in several countries. Indeed [START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF] managed to instrument HIV prevalence only in a cross-section of countries, but did not provide instrumented time series.

Our approach is to estimate the propagation dynamic of the epidemics from exogenous variables and variables very poorly correlated to growth11 . We consider that the spread of propagation of HIV in a given country and the initial conditions are endogenous. We use therefore several variables arguably independent from growth as instruments. We proceed in three steps. First, we instrument the initial extent of the epidemic (initial conditions) using mostly geographical variables such as the distance to Congo Dem. Rep. (as Oster 2009). Second, we instrument (using a panel-data regression) the spread of propagation of the epidemic using mostly circumcisions rates, religion and road network. Although those variables are quite stable in time they do vary a little (except for circumcision rates because we only have one data for each country). Third, we simulate "instrumented"HIV prevalence pro…le for each country, starting from the "instrumented"initial infection, and using the estimated coe¢ cient for our instruments. It is a projection of the speed of propagation of the epidemics.

As the values of the instruments varies from one country to another, the speed of propagation di¤ers and as a consequence, the pro…les are di¤erent. It is worth noting that as the propagation equation is quadratic, the long-term value of the prevalence (as well as the peak value) also depend on each country conditions. For instance, countries with more Muslims will experience lower HIV prevalence rate in the long-run according to our model.

Estimation of the propagation dynamics of AIDS

We build a simple dynamic model of epidemic propagation (see appendix for a full presentation). The model rests on the marital status of people (single or married), their health status (infected and non infected) and their location (which city). It allows mobility of people from one city to another. Combining these elements, we can deduce the following dynamic of HIV prevalence among the total population. A linear trend is allowed to take into account the global evolution of the HIV/AIDS epidemic.

h t+1 h t = 1 ( ; ; ; a ; ; m)h t 2 ( ; ; ; a ; ; m)h 2 t + 3 t + 4 (21)
To identify this equation, we introduce the following instrumental variables :

The share of unprotected intercourse can depend on time as people become more aware of the disease as HIV spreads across the continent. It may also decrease with the heterogeneity of the population as people might be more cautious with someone they do not know; it is measured by fractionalization indicators12 .

The probability of being contaminated by an unprotected intercourse has been proved to be lower for circumcised men 13 . We therefore introduce the share of circumcised men in the population as an instrument of the speed of propagation.

Geographic mobility can be instrumented using the extent and the quality of the road network. We use the current number of kilometers of roads divided by the number of inhabitants in the country in 198014 and the share of paved roads for continental countries 15 . Mobility indicators are expected to increase prevalence.

The di¤erential of mortality between healthy and sick people may be impacted by civil con ‡icts and wars.

We use the proportion of Muslims as an instrument of the share of faithful people.

The rate of mixed unions, m could be also in ‡uenced by population fractionalization.

These instruments are poorly correlated with growth, which allows to treat them as good candidates as exogenous variables (see table 1).

h i t = h i t 1 + 0 1 Z i t 1 h i t 1 + 0 2 Z i t 1 (h i t 1 ) 2 + T t + 0 + i t ( 22
)
The results are reported in table 2 below. 0:58

(6:1)
ethnic hiv 1 0:18

(5:3) 0:17

(13:5) 0:18

(14:3)
mus hiv 1 0:02

(0:3)
circum hiv 1 0:06

(2:6) 0:06

(2:7) 0:05

(2:3)
civc hiv 1 0:11

(5:7) 0:12

(5:9) 0:12

(6:4)
civd hiv 1 0:09

(2:5) 0:11

(7:1)
0:11

(7:3)
t hiv 1 0:01 indicate respectively signi…cance at the 5%, 1% and 0.1% level.

Simulation of the new series of HIV prevalence rate using the estimation of the propagation mechanism

We proceed in two steps to build a new series. First, the HIV prevalence rate is estimated for every country in 1990, which is the …rst date for which UNAIDS data is available. As prevalence rate are very small in most countries at this date, we use an exponential regression 16 . We take as instruments the share of the population being Muslims (muslims), the share of the population being catholic (catho), the distance D from the main city of the country to Lodja, the city located at the center of the Democratic Republic of Congo 17 , 16 Indeed, linear estimates of HIV prevalence rate would be negative for a large number of countries. We impute the minimal value of 0.001 for the prevalence rate when actual UNAIDS estimates are below 0.01. 17 As Democratic Republic of Congo is supposed to be the epicenter of the epicemic. the rate of circumcised male (circum) and (isl) for islands. The results of this estimation are given in equation ( 23) below.

ln h i 1990 = 1:3 (3:2) ln D i 2:2 (3:9) musl i (1 Isl i ) 14:2 (4:6)
Isl i 1:2

(2:3) circ i 2:5

(3:4) catho i +11:9

(3:8) + i
(23) To obtain an unbiased estimation of the prevalence rate in 1990, one should take into account the variance of the error term . Denoting Z i 0 the vectors of instruments used in equation 23 and 0 the vector of estimated parameters, we have:

ĥi 1990 = E[h i 1990 ] = E[e 0 0 Z i 0 + i ] = e 0 0 Z i 0 E[e i ] = exp V ar[ i ] 2 e 0 0 Z i 0 (24)
which gives the estimation of HIV prevalence rate in 1990 for each country.

Second, the estimation of the propagation dynamic of HIV prevalence, given by table 2, is used to build the series forward, starting from the 1990 estimates and assuming null residuals. Therefore, this series does not contain any value of the actual series h i t . It is strictly constructed from the values of the instruments. The forward-looking series departing from 1990 is given by:

ĥi t = ĥi t 1 + 0 1 Z i t 1 ĥi t 1 + 0 2 Z i t 1 ( ĥi t 1 ) 2 + T t + 0 if t > 1990 ( 25
)
This process is reproduced backward using the reverse of the equation 22 to project the prevalence before 1990:

ĥi t 1 = ĥi t 0 T t 1 + 0 1 Z i t 1 + 0 2 Z i t 1 h i t if t < 1991 (26)
The following graph plots the average of HIV prevalence across Sub-Saharan Africa for each year and for the three di¤erent series, as well as the Oster's (2009) estimates. It appears that those series di¤er both by their level and dynamic. Our instrumentedsimulated series becomes higher than expected since the early 2000 and stabilizes at a higher level. This gap could be explained by a change in behavior, that has not be taken into account by our instruments 18 . See …gure 6 in appendix for the comparison between our instrumented series and the UNAIDS one for a set of countries.

It is worth noting that our instrumented-simulated series, thought that it is not based on observed AIDS cases, it compares fairly to UNAIDS and Oster series. It expands these series either in terms of the number of countries covered and of time-span. It allows us to perform our accounting exercise going back from early stage of the epidemics.

Sources of other data

Infant mortality data are available on a …ve-year average basis in the United Nations World Urbanization Prospects. We compute annual data from this source using linear projections. Fertility, life expectancy and demographic data, such as working age population 19 or urbanization are published on a yearly basis in the World Development 2007). This dataset contains annual observations of con ‡icts about all members of the international system, as de…ned by [START_REF] Gleditsch | Interstate system membership: A revised list of independent states since 1816[END_REF]), between 1946and 2006. Data on Muslims and catholic are compiled using several sources such as census data from the UN, household surveys data from the Demographic and health surveys and the CIA fact book. Fractionalization data are from [START_REF] Alesina | Fractionalization[END_REF]. Circumcision rates are provided by [START_REF] Williams | The Potential Impact of Male Circumcision on HIV in Sub-Saharan Africa[END_REF]. All measures of HIV/AIDS used in the following are prevalence rates. 4 The e¤ects of HIV/AIDS on growth

Estimation of the direct e¤ect of HIV/AIDS on productivity growth

A direct way to grasp the e¤ect of HIV/AIDS on growth is to include the epidemic prevalence rate among the regressors. Following equation ( 14) which gives the common empirical framework for the di¤erent estimations, we run the following regression, where Y stands for the GDP, L for the working age population, HIV for the HIV prevalence rate and cc and cw respectively indicate the occurrence of a civil con ‡ict or a civil war20 :

ln Y i t L i t = ln Y i t 1 L i t 1 + HIV i t 1 + c Cv i t + w cw i t + u i + t + " i t (27)
By de…nition the ratio of GDP to working age population is a measure of the productivity per worker, therefore we will use indi¤erently growth or productivity growth. Table 4 below reports the di¤erent results. Recall that HIV denote the HIV prevalence rate from UNAIDS completed following the methodology described in section 3.2. HWP is the HIV prevalence rate among pregnant women constructed as described in section 3.1 with UNAIDS estimates of prevalence rate in rural and urban zone. And, HIVinst is the series we constructed completely following the model described in section 3.3 using instrumental variables. Civil wars and civil con ‡icts are always negative and signi…cant at least at the 1% level. Additional controls are regional (Northern, Western and Eastern Africa) year …xed e¤ects. Breush and Pagan test rejects homoscedasticity in all con…gurations. y indicates that the Hausman test con…rms the relevance of country …xed e¤ects.

Table 4 indicates that the lagged growth is the most important determinant and civil con ‡icts and wars have the expected negative and signi…cant impact. It is worth noting that the e¤ect of HIV prevalence on growth is neither identi…ed nor signi…cant when both civil disorders variables and yearly …xed e¤ects are not added. This result underlines the necessity to control for the sources of volatility of growth in the short-run.

These estimates are robust to the introduction of regional year …xed e¤ect and the use of any measure of HIV prevalence. We did not use Oster's prevalence series in our estimates due to its restriction to a fewer number of countries and time-span.

The epidemic prevalence rate has a negative and signi…cant impact on growth. The results are not sensitive to the series used. The magnitude of the coe¢ cient remains similar when using the series built directly from the UNAIDS estimates or the one constructed from the raw data on prevalence among pregnant women.

Moreover, the impact is similar when using the simulated series. As by construction this series is supposed to be more exogenous, the endogeneity bias appears to be limited. Finally, the results is not sensitive to the period (see line Period) of estimation.

Recalling equation ( 27), we can calculate e y t , that is the dynamic of the logarithm of GDP per working age adult if HIV prevalence had remained null till the early 1980s.

e y i t = g y i t 1 + c Cv i t + w cw i t + u i + t + " i t (28)
By substracting eq. ( 28) from equation ( 27), we can obtain the dynamic of the "AIDS gap", y t , which is the di¤erence between the actual level of GDP per adult and the would be GDP per adult if they were no HIV/AIDS.

y i t = y i t e y i t = y i t + HIV i t (29)
In the short-run, the e¤ect of HIV/AIDS on productivity is limited. A 1 point increase in prevalence rate induces a 0.13 point reduction of GDP per working age adult. But this negative e¤ect cumulates over time and the "AIDS gap" becomes much larger. In the long-run, the e¤ect of a permanent increase of HIV prevalence h on GDP per working age adult is:

lim t!1 y t = 1 lim t!1 HIV t (30)
Using the second regression (column 2, Period 81-07), a 1 point increase in prevalence induces indeed a 2.75 reduction in productivity in the long-run. Although likely to be negative, the magnitude of the e¤ect remains nevertheless uncertain. Assuming that the distribution of the parameters and is normal, there is no easy analytical expression of the distribution of the ratio 1 . Therefore, we use Monte-Carlo simulations to compute its distribution21 . Figure 2 shows the distribution of the long-run e¤ect of a 1 point HIV prevalence increase on productivity. A 1 point increase in HIV prevalence induces in average a 2.75 point decrease in GDP per working age adult. In the long-run, this means that the e¤ect of HIV/AIDS on growth goes far beyond the diminution of the labour force22 . This estimate is approximately half of what [START_REF] Bonnel | HIV/AIDS: Does it increase or decrease growth in Africa?[END_REF] obtained. And, it appears to be large compared to McDonald and Roberts's (2003) 23 . However, their method is likely to underestimate the e¤ects of HIV/AIDS on growth for two reasons. First, they do not take into account the e¤ects of health on both physical and human capital accumulation24 . Second, they measured the effects of HIV/AIDS on growth indirectly using infant mortality as a proxy of workers's health capital. But contrary to other endemic diseases such as malaria, HIV is well known to hit disproportionately adults, as the main source of infection is unprotected sexual intercourse. Our estimate is also approximately twice lower than Papageorgiou and Stoytcheva's25 .

To gauge the e¤ect of the epidemics on the di¤erent channels considered in section 1, we investigate its direct e¤ect on the di¤erent variables that determine short and long run growth.

Estimation of the e¤ects of HIV/AIDS on the sources of growth 4.2.1 E¤ects of HIV/AIDS on working age population

The direct e¤ect of the epidemic is to reduce life expectancy and demographic growth. Estimation of those straightforward e¤ects of the epidemic reported in the table 5 con…rm that all the presented measures of HIV prevalence are in the relevant interval. The e¤ects appear to be negative and signi…cant either on life expectancy or on working age population.

E¤ects of HIV/AIDS on human capital

To assess the e¤ects of the epidemic on human capital, we, …rst, estimate the e¤ect on primary and secondary school enrollment rate, and second we compute the total e¤ect on the stock of human capital.

Determining the e¤ects of HIV/AIDS on enrollment rates requires also some work on the data. Indeed enrollment rates are reported by the World Bank on a …ve-year basis before the late 1990s for most of the African Sub-Saharan countries. Moreover, even on a …ve-year basis, data are not available for the same years across countries. To solve that problem, we propose two methods.

First, we run yearly regressions on existing data x i t using …ve-year lagged variables. When the …ve-year lagged …gure x i t 5 is not available, we use instead d x i t 5 the closest lagged available data within the …ve-year span. This projected lagged value is de…ned as:

d x i t 5 = 8 < : x i t 5 if x i t 5 is de…ned x i t s if s 2 [1; 4] and x i t s is de…ned (31)
Second, we use linear projection to complete the series. Let us consider the variable x i t which values are known only for t 2 K = ft k g. The projected series e x i t is therefore de…ne as:

e x i t = 8 < : x i t if t 2 K t k+1 t t k+1 t k x i t k + t t k t k+1 t k x i t k+1 if t 2]t k ; t k+1 [ (32)
E¤ects of AIDS on primary school enrollment We use our empirical framework (see equation 14) to identify the e¤ects of HIV/AIDS on school enrollment rates. We introduce also, F oreign Aid, the share of total aid and assistance into GDP as a control variable. The …rst regression run is, denoting P GE the total26 primary gross rate of enrollment as:

P GE i t = p \ P GE i t 5 + p HIV i t 1 + c cc i t + w cw i t + a Aid i t 1 + u i + t + " i t (33)
Because of the lack of yearly data before 1990, the number of observations is limited.

Regression results are reported in table 6. The equation estimated using projected data is the following.

P GE i t = p P GE i t 1 + p HIV i t 1 + c cc i t + w cw i t + a Aid i t 1 + u i + t + " i t ( 34
)
The epidemic seems to have a negative impact on gross primary enrollment. Although multipliers and standards errors vary widely with the speci…cation, the correlation is signi-…cantly negative using both raw (P GE) and projected ( ] P GE) data. Moreover, estimates obtained using either the UNAIDS or our constructed series are similar. Additional controls are year …xed e¤ects (YFE), linear yearly trend and regional yearly trend. z Estimates remain similar and signi…cant when using rather a yearly trend.

Deriving from equations 33 and 34, we can compute the long run e¤ect of a permanent rise of HIV prevalence on primary school as:

lim t!1 P GE t HIV = p 1 p ( 35
)
Computing this …gure with the coe¢ cients of the …rst and …fth regressions (columns 1 and 5 in table 6) yields that a 1 point permanent increase of HIV prevalence induces a fall of respectively 1 and 6 points of the primary school enrollment rate in the long-run.

The impact of the epidemic on schooling, although uncertain, appears to be very large.

Given the uncertainty on the model, we will assume in the following that:

lim t!1 P GE t HIV 3 (36)
E¤ects of AIDS on secondary school enrollment rate We follow the same methodology to estimate the e¤ects of HIV/AIDS on the secondary school enrollment rate, except that we control for the evolution of the primary school enrollment rate. The estimated equation of the impact of HIV prevalence rate on secondary school enrollment rate is :

SN E i t = s SN E i t 1 + P N E i t 1 + s HIV i t 1 + c cc i t + w cw i t + u i + t + " i t ( 37
)
Regression results are reported in table 7 below. The negative e¤ect of HIV on secondary school enrollment is less pronounced than for primary education. There is no signi…cant e¤ect of HIV prevalence when using the raw data. However when using projected data, HIV seems to have a negative e¤ect on secondary school. But the uncertainty of such e¤ect remains large. There is no signi…cant e¤ect using our instrumented measure. As the instrumented measure di¤ers from the UNAIDS one mostly for the recent years, this may suggest that it is still too early to assert the consequences of HIV on secondary education. HIV 1 0:02

(0:0) 0:07
(2:2) 0:07

(2:2) 0:10

(2:2)
HIV inst 1 0:05 indicate respectively signi…cance at the 10%, 5%, 1% and 0.1% level. T-values reported between brackets are calculated by clustering errors by country. Breush and Pagan test rejects homoscedasticity in all con…gurations y indicates that the Hausman test con…rms the relevance of country …xed e¤ects. Additional controls are year …xed e¤ects, linear yearly trend and regional yearly trend. z Estimates remain similar and no signi…cant when using other time speci…cations.

(0:2) 0:07 (1:9)
To assess the impact of the epidemic on secondary enrollment, one has to take into account the direct e¤ect, and the indirect one, through the diminution of primary school enrollment rate. The derivative of from our linear speci…cation in equation 37, the total e¤ect of HIV on secondary education is given by

SGE t HIV = s SGE t 1 HIV + P GE t 1 HIV s (38)
Therefore, in the long-run, the total e¤ect of HIV/AIDS on secondary enrollment rates becomes:

lim t!1 SGE t HIV = s 1 s 1 s p 1 p (39)
As before, the evaluation of the multiplier depends of the model. Given the uncertainty, we choose:

s 1 s 0:9 (40)
Taking the coe¢ cients of the third regression (column 3, table 9) gives that, a 1 point increase of the HIV prevalence induces a permanent fall of 2.4 point of the secondary school enrollment rate. However, taking the maximal estimates of both p and s would lead to a far larger multiplier, about 4.8. The impact of HIV/AIDS on the investment in human capital may therefore be really high in the long-run.

Assessing the long-run e¤ect of AIDS on human capital We consider the average schooling years as the proxy of human capital. To assess the e¤ects of HIV/AIDS on human capital, one has to transform the variations in enrollment rates into variations in the average schooling years. Theoretically, one can link enrollment rate and schooling years, if the average number of completed grades (D j ) by level j = fp; sg is known, as follows:

S = D p P N E + D s SN E (41)
However, the D j …gures are not precisely known and could also vary across time, as educational system betters. A crude approximation could be to assume that D j = D j 2 where D j is the o¢ cial duration of the level j. To test the sensitivity of such an hypothesis, we use the available (although scarce) data on the years of schooling. [START_REF] Barro | International data on educational attainment: Updates and Implications[END_REF] report such …gures for 30 countries between 1985 and 2000. To this dataset, we add recent estimates for 42 countries, using household survey data27 . Three speci…cations are used to regress years of schooling on gross enrollment rate. A more convincing regression would have to introduce lagged value of the years of schooling. However, there is not enough data to obtain signi…cant estimates of the e¤ects of enrollment on schooling using this speci…cation. Because there is only a few years for each country, we do not introduce either country or years …xed e¤ects. The regression is therefore:

S i t = b p P GE i t 5 + b s ŜGE i t + S 0 + " i t ( 42
)
This equation is estimated using a within regression:

S i t = 1:55 (3:6)
P GE i t 5 + 5:84

(8:0) ŜGE i t + +0:51 (1:6)
+ " i t , adj:R 2 = 0:32 , # obs. = 149

According to those results, a 1 point increase of HIV prevalence would induce a reduction of average human capital by 0.18 years of schooling. Thus, considering that an additional year of schooling increases productivity by about 7% as ln(Y =L) S 0:07 , a 1 point increase of HIV prevalence would diminish productivity through human capital by approximately 1.3 point. Therefore approximately 45% of the long-run e¤ect of HIV/AIDS on growth could be due to a permanent reduction of human capital.

E¤ects of HIV/AIDS on physical capital

As there is no data on physical capital stocks at the national level, we consider rather the e¤ects of the epidemic on investment. The e¤ects of HIV/AIDS on physical capital can indeed be approximated knowing the marginal e¤ects of the epidemic on the investment rate.

Impact of AIDS on investment Investment rates can be computed using GDP and gross capital formation both in current or constant US$. We use the same framework (the theoretical background model and equation 14) to assess the e¤ects of HIV/AIDS on investment. We denote inv the investment rate computed as the ratio of the annual gross capital formation to GDP. In the following regressions, civil con ‡icts appears to be never signi…cant. Therefore, we only present the regressions without this variable. However, we introduce the openness to trade ratio, open28 , and the share of foreign direct investment in the GDP, f di. Using both current and lagged values of those indicators allows to capture both short and medium run e¤ects of openness to trade. Indeed investment is likely to be pro-cyclical and to overreact in the short-run to foreign activity.

ln(inv

i t ) = k ln(inv i t 1 ) + k HIV i t 1 + o open i t + o 1 open i t 1 + f f di i t + f 1 f di i t 1 (44) + w cw i t + u i + t + " i t
Regressions results are reported in table 8. Regressions indicate that HIV prevalence has also a negative impact on investment. As physical investment reacts more quickly than education investment, the negative e¤ects of HIV/AIDS on physical capital a¤ect the economy more rapidly. This e¤ect although large varies however with the speci…cation.

Estimates depend of the measures and are only signi…cant at the 10% level when using the pregnant women prevalence rate and the instrumented measure of HIV prevalence. This seems to indicate that if HIV is likely to dampen investment, its e¤ect may depend on country speci…c conditions. One may think consequently that the adverse e¤ect of the epidemic on physical capital accumulation might be mitigated, at least to some extent.

Impact of AIDS on physical capital

To calibrate precisely the e¤ect of the epidemic on productivity, one should estimate a Solow-type growth model. However, the lack of long-series for both human and physical capital has prevented such an exercise29 . To assess the long-run e¤ect of HIV/AIDS, let us recall the capital accumulation equation 4, from which we can deduce:

K t Y t = 1 1 + g K t 1 Y t 1 + Inv t ) lim t!1 K t Y t = lim t!1 Inv t 1 1 1+g (45)
As a consequence, we have in the long-run:

K t / Y t Inv t ) @ ln(K) @HIV = d ln(Y ) dHIV + @ ln(Inv) @HIV (46)
This allows to deduce the e¤ect of HIV/AIDS on GDP through physical capital accumulation @ ln(Y )

@HIV K : @ ln(Y ) @HIV K = @ ln(Y =N ) @ ln(K) @ ln(K) @h = k 1 k 1 (47)
As argued above, the parameter has not been estimated. We use here the historical average of the investment rate as a proxy of , that is @ ln(Y ) @ ln(K) = 0:2 . With such a value for , the long-run e¤ect of a permanent 1 point rise of HIV prevalence on productivity through capital accumulation is about -0.9 when using the estimates of the …rst regression (column 1 table 8). Choosing a of 0.3 would increase this estimation up to -1.3. Therefore, physical capital accumulation explains approximately one third of the total e¤ect of HIV/AIDS on productivity. x indicates that the regression has been run using the investment rate in constant (2000) US$ rather than current US$. Because of BP test rejection, no country …xed e¤ects were added.

Computing the long run dynamic e¤ects of the epidemic on growth

The epidemic a¤ects productivity through four di¤erent channels: the demography, physical and human capital and labor participation/technical change30 , as pointed out by the following equation:

d ln(Y =N ) dHIV = @ ln(Y =N ) @ ln(N )
@ ln(N ) @HIV + @ ln(Y =N ) @ ln(K) @ ln(K) @HIV + @ ln(Y =N ) @S @S @HIV (48)

+ @ ln(Y =N ) @ ln(L)
@ ln(L) @HIV To calculate the e¤ects of HIV/AIDS on the di¤erent components, we derive from equation ( 14) the cumulated e¤ects of the epidemic on the variables z i t as z i t :

z i t = z i t e z i t = z z i t 1 + z HIV t ; z = fk; S; l; ng (49)
We have estimated so far the three …rst components and the total e¤ect. As it is not possible to estimate the impact of HIV/AIDS on labor participation/technological change because of the lack of data, we will calculate this latter e¤ect by substracting the three …rst one to the total e¤ect. Recalling equation 7, the e¤ect of HIV on productivity through labor participation/technological change is indeed:

@ ln(Y =N ) @HIV L = l t = y t ( k t n t ) (1 ) S t (50)
The evolution of the working age population a¤ects the GDP per adult through two opposite channels. On one hand, the diminution of the population, all other things remaining equal, increases physical capital per worker. On the other hand, the reduction of the size of the economy gradually reduces the level of investment and the stock of capital. In a Solow-type model, output per adult does not depend on the size of the population in the long-run. Therefore, the net e¤ect of demography is null in the long-run. To disentangle the e¤ects of demography and capital, let us de…ne K t the level the stock of capital would reach if it were not a¤ected by the evolution of the adult population. From equation 8, we can obtain the dynamic of K t :

k t = K t K t = K k t 1 + (1 K )( inv t + y t ) (51)
The net e¤ect of the demography on productivity is:

@ ln(Y =N ) @HIV N = ( k t k t n t ) (52)
Consequently, the e¤ect of HIV on productivity through physical capital becomes:

@ ln(Y =N ) @HIV K = k t (53)

Illustration with an average country of the composition of the HIV/AIDS e¤ects

We then can compute the dynamic e¤ects of HIV/AIDS on the logarithm of per adult income through the four di¤erent channels. To illustrate the results we consider the average country which endures the average HIV prevalence of the all 46 African Sub-Saharan countries for which data are available. Between 1980 and 2010, AIDS would have already reduce GDP per worker by about 8.0 points. By comparison, the cumulated e¤ects of civil con ‡icts and wars in Sub-Saharan Africa between 1980 and 2010 would have been a reduction in per worker GDP about 17 points in average31 .

For the same average country, the decomposition of HIV/AIDS e¤ects on the GDP per capita growth rate is illustrated by the …gure 4 below. It appears that the HIV/AIDS e¤ect has already reached its peak around the year 2000. The long-term e¤ects of HIV on growth, although huge, may be compensated by increased e¤orts in education and capital markets.

Decomposition of the e¤ects of the epidemics on several countries

As an illustrative exercise, when we apply these estimated e¤ects to the prevalence rate of speci…c countries, the impact appears to be very important for high prevalence rate countries. The e¤ects of the epidemic on several Sub-Saharan African countries is presented in …gure 5 below. The e¤ects on the growth rate of the countries (South Africa and Lesotho) with high prevalence rate are huge. The cost has been higher than 2 points of growth during the last decade for Lesotho. For countries with a median HIV prevalence rate (Tanzania and Kenya for instance), the epidemic has cost between 0.5 and 0.75 point of growth each year. The economic impact of such an epidemic is therefore strong and heavily persistent. Although the epidemic has already caused great damages to the hit countries, most of them will continue to experience lower growth because of it for several decades. Nevertheless, as most of the long-term e¤ect of HIV/AIDS on growth go through physical and capital accumulation, public policies aiming to increase both investment and education enrollment rate might mitigate the burden of the epidemic.

Figures 7 and8 in appendix plot the e¤ects of HIV/AIDS on the di¤erent components of growth for the same countries. The cumulated cost of AIDS, the "AIDS gap"appears to be huge, especially for the Southern countries. Although dramatic these estimates are lower than most of the projections based on models simulations.

Discussion and conclusion

The relationship between HIV/AIDS and growth is likely to be bidirectional. Therefore, it is very challenging, in a macroeconomic framework, to disentangle the exact impact of HIV/AIDS on growth. We tried to do so in a simple and comprehensive way. To tackle the endogeneity issue, we built a series of HIV prevalence rate using instrumental variables. Although some of the instruments we use could not be arguably considered fully exogenous, they appear to be poorly correlated with growth in Sub-Saharan Africa (see table 1). We use nevertheless geographical variables and circumcision rates, which is seen more and more as a good instrument of risk infection in the literature, see Forston (2009b) and[START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF][START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF]. Our methodology allows us to build a HIV prevalence rate series which compares fairly with both [START_REF] Oster | Estimating HIV prevalence and incidence in Africa from mortality data[END_REF] and UNAIDS series 32 .

It is worth noting that our "instrumented"series does not incorporate actual UNAIDS estimates and has been dynamically simulated only using instrumental variables.

Based on our HIV prevalence rate series, our estimates show that the epidemics has a signi…cant and negative direct e¤ect on growth (see table 6). To assess the robustness of our estimates to measurement error in the data, we show the results using the UNAIDS series, the HIV prevalence rate among pregnant women. The direct e¤ect of HIV/AIDS is negative and signi…cant and this result holds whatever the time period considered, the measure of HIV used and the con…guration of the regression. In the short run, the impact of the epidemics appears to be limited. A 1 point increase of the HIV prevalence induces a 0.13 point decrease of GDP per working age adult the following year. In the long run however, the (permanent) e¤ect is much larger, a 1 point increase in prevalence causing a reduction of GDP per worker about 2.75 points. Using a Monte Carlo simulation, we showed that the e¤ect of HIV/AIDS is negative and statistically signi…cant at the 5% level.

Our estimate stand between [START_REF] Bonnel | HIV/AIDS: Does it increase or decrease growth in Africa?[END_REF], who regressed growth from 1990-97 on AIDS in 1994-97 for approximately 80 developing countries and …nd a negative and statistically signi…cant e¤ect, and McDonnald and Roberts's (2006), who in a dynamic panel regressions …nd that each point of HIV prevalence rate lowers per capita income by 0.59 percent. Our estimate are also consistent with the studies based on theoretical models simulations, as [START_REF] Arndt | The Macro implications of HIV/AIDS in South Africa: A preliminary assessment[END_REF], [START_REF] Kambou | The economic impact of AIDS in an African Country: simulations with a CGE Model of Cameroon[END_REF] and [START_REF] Sackey | Lesotho: the development impact of HIV/AIDS -Selected issues and options[END_REF][START_REF] Sackey | Swaziland: selected development impact of HIV/AIDS[END_REF][START_REF] Sackey | Namibia: selected development impact of HIV/AIDS[END_REF].

To gauge precisely the impact of the HIV/AIDS epidemics on short run and long run growth, we performed an accounting exercise of the epidemics e¤ects on the di¤erent determinants of growth: demography, human capital accumulation and physical capital accumulation. Our results exhibit a highly signi…cant negative e¤ect of HIV/AIDS on life expectancy. The impact on working age population is negative and signi…cant but the magnitude is much lower. These results are consistent with the literature (see for instance [START_REF] Werker | Male circumcision and AIDS: the macroeconomic impact of a health crisis[END_REF]. As pointed by [START_REF] Young | The Gift of the dying: the tragedy of AIDS and the welfare of future African generations[END_REF], the reduction of working population in a context of capital scarcity may increase the total welfare. However, our computations show that although the capital intensity e¤ect is positive in the short run, its magnitude is very limited, a 1 point rise in prevalence induces a rise in the yearly growth rate of the GDP per worker less than 0.1 percent. This capital intensity e¤ect remains very small in the medium run and vanishes after 45 years, about two generations of workers. We did not report the results of our estimations of the impact of the epidemic on fertility. A converging literature …nd that either the impact is very small (Forston 2009b;[START_REF] Kalemli-Ozcan | HIV and Fertility Revisited[END_REF][START_REF] Fink | HIV and fertility: Long-term Evidence from Sub-Saharan Africa[END_REF] or is not signi…cant [START_REF] Boucekkine | How do epidemics induce behavioral changes?[END_REF]). Hence, we do not take into account this impact when considering the impact on demography.

The second channel we evaluate is the impact of the epidemics on human capital accumulation. Our estimations show a negative and signi…cant impact of the HIV prevalence rate on primary school enrollment rate either using raw data (5 years interval) or projected annual data. A 1 point permanent increase of the HIV prevalence rate causes a one point decrease in primary school enrollment rate in the long run. The estimated impact is much higher when using annual data. However, the epidemics appears to have a limited negative e¤ect on secondary school enrollment rate (see table 7). Only the estimations using the projected annual data exhibit signi…cant e¤ect. In the long run, a 1 point permanent increase of HIV prevalence rate induces a permanent fall of 2.4 points of the secondary school enrollment rate.

From these estimates, we derive the impact of the epidemic on the average years of schooling, our human capital variable. According to our results, a 1 point increase in HIV prevalence would induce a reduction in average human capital about 0.18 years of schooling. These results are comparable with [START_REF] Forston | Mortality risk and human capital investment: The impact of HIV/AIDS in Sub-Saharan Africa[END_REF], who estimated the relationship between regional HIV prevalence rate and the educational outcomes of successive birth cohorts in …fteen Sub-Saharan African countries. Using data from the Demographic and Health Surveys (DHS), she found that in areas with prevalence rate of ten percent, the post-1980 birth cohorts completed about 0.5 fewer years of schooling than pre-1980 cohorts. Her results con…rm that HIV/AIDS is likely to have a negative impact on education.

From our estimates, we computed that a 1 point increase in HIV prevalence would diminish productivity through human capital by approximately 1.3 point in the long-run. Therefore, the human capital reduction accounts for more than 45% of the total long-run e¤ect of HIV/AIDS on growth.

The third component we evaluate is the impact on physical capital accumulation. As already noted there are many channels through which the HIV/AIDS epidemics a¤ect the incentives to invest or accumulate. We control for trade, foreign direct investment and civil wars in our regressions. We found a negative e¤ect signi…cant at the 5% level using UNAIDS estimate, but which is only signi…cant at the 10% level using pregnantwomen HIV prevalence or our "instrumented" series. Building from these estimates, we found that in the long run, the reduction of physical capital accumulation accounts for approximately one third of the long run e¤ect of HIV/AIDS on growth.

According to this accounting exercise, human capital is likely to drive the most important part of the total e¤ect. Physical capital accumulation plays a larger role in the short-run (see …gure 3). Our estimates show that at the peak, around 2002-2003 in average, the total e¤ect of HIV/AIDS is a reduction by 6% of income per capita; the reduction of human capital accounting for 2.4%, the reduction of physical capital accounting for 2%, labor participation (and technological change) accounting for 0.7% and the counterbalancing positive e¤ect through capital intensity account for 0.1%. In the long-run, those e¤ects are approximately double. They are consistent with Santaeulàlia-Llopis's results (2008), based on a population model structured by age-speci…c groups and which takes into account the fertility process, the mortality and the aging process. The modelled economy experiences a development transition path from a Malthusian-agricultural sector to a neoclassical-industrial sector. When this model is calibrated to an African country, incorporating the di¤erent channels through which AIDS a¤ects populations over time (i.e. reshapes the age distribution of the population, reduces population growth and life expectancy due to raising mortality rates of young adults and lower fertility rates), the author found that AIDS epidemic reduces per capita income as much as 12%.

However, [START_REF] Ashraf | When does improving health raise GDP?[END_REF] perform a simulation exercise to explore the economic e¤ects of an exogenous change in population health33 . Their model allows for a direct e¤ect of health on worker productivity , as well as indirect e¤ects that run through schooling, the size and age-structure of the population, capital accumulation, and crowding of …xed natural resources. They show that eradicating speci…c diseases (malaria or tuberculosis) in a typical country in Sub-Saharan Africa would raise GDP per capita by only two percent in the long run. These results are very small compared to ours for HIV/AIDS e¤ects, but the mechanisms their simulation shows are very instructive. First, as the two diseases they consider a¤ect di¤erently the di¤erent categories of the population (workingage adults and school-age population) their e¤ect on capital per worker, productivity of workers and education are di¤erent. As tuberculosis hit more the working-age adults, its eradication causes an immediate decline of capital per worker and has a positive steep e¤ect on productivity of workers. But, the e¤ects on schooling years are small. In contrast, the eradication of malaria brings about a larger, but more delayed decline in capital per worker as the cohort of children who would have died from the disease enter the labor force. As malaria a¤ects less the working age population, its eradication have a delayed e¤ect on productivity, but a more immediate impact on schooling.

HIV/AIDS combines these di¤erent characteristics, it hits sharply the working-age adults, modi…es the age distribution of the population, produces a great number of orphans and therefore brings about a negative impact on education. It combines a stock e¤ect by killing a part of the population and a long lasting e¤ect as a¤ected people can live with the disease during a number of years. Therefore, it is likely that HIV/AIDS adds up the di¤erent indirect e¤ects shown by [START_REF] Ashraf | When does improving health raise GDP?[END_REF].

13

  Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

Figure 1 :

 1 Figure 1: HIV prevalence series by year, average of all Sub-Saharan African countries.

Figure 2 :

 2 Figure 2: Distribution of the e¤ects of a 1 point increase of the prevalence rate

Figure 3 :

 3 Figure 3: E¤ects of HIV/AIDS on the level of GDP per adult in the average Sub-Saharan African country (Simulation using the estimated parameters).

Figure 4 :

 4 Figure 4: E¤ects of HIV/AIDS on GDP per adult annual growth rate in the average Sub-Saharan African country

Figure 5 :

 5 Figure 5: The e¤ects of the epidemics on the growth rate of several countries.

Table 1 :

 1

	Partial Correlations (period 1970-2008)
		growth musl. ethnic island Lodja dis. paved roads
	growth	1.00
	Muslims	-0.02	1.00
	ethnic fraction. -0.09	-0.11	1.00
	island	0.01	-0.07 -0.40	1.00
	Lodja distance	-0.02	0.46	-0.00	0.34	1.00
	paved roads	0.05	0.08	-0.47	0.77	0.44	1.00
	road network	0.02	-0.23 -0.01 -0.11	-0.15	-0.18 1.00
	circumcision	-0.02	0.55	0.42	-0.13	0.26	-0.14 -0.25
	Rewriting equation 21 with the vector of instruments Z i t = (1; ethnic i t ; t; network i t ; paved i t ; muslm i t ; civconf i t ; civwar i t ; circum i t ) and 1 and 2 two vectors of parameters,
	the estimated propagation dynamic is:

Table 2 :

 2 Estimation of the dynamic of HIV prevalence Dep. Var.

		hiv	hiv	hiv
	hiv 1	0:30 (12:3)	0:30 (13:1)	0:333 (16:7)
	paved hiv 1	0:78 (10:8)	0:77 (10:8)	0:75 (10:6)
	network hiv 1	1:60 (3:9)	1:54 (4:1)

Table 3

 3

	: Descriptive statistics
	Variables	# obs. Mean Std. Dev. Min	Max Source
	GDP (constant 2000 US$)	1 662 1483	1933	98 19376 World Bank
	Work. age pop. (thousands)	1 702 5715	8960	36 76656 World Bank
	Fertility	1 726	6.0	1.3 1.9	8.5 World Bank
	Life expectancy at birth	1 727	50.7	7.6 23.6	73.2 World Bank
	Infant Mortality (for 1,000)	1 610 109.6	36.8 14.6 206.4 UN
	HIV preg. women	1 498	0.03	0.061	0 0.417 UN Facts sheets
	HIV	1 778 0.023	0.050	0 0.289 UNAIDS
	Primary enrollment (%)	1 562	77.0	33.2 8.0 179.6 World Bank
	Secondary enrollment (%)	1 536	21.6	18.4 1.1 114.0 World Bank
	Urbanization (%)	1 739	29.0	14.3 2.4	84.1 World Bank
	Civil con ‡ict (occurrence)	1739	0.2	0.2	0	1 UCDP/PRIO
	Civil war (occurrence)	1739	0.2	0.2	0	1 UCDP/PRIO

Notes: Variables are averaged over 1970-2006. Fertility is the total number of children per woman. HIV prevalence is the previously built variable. Enrollment in primary and secondary schools are gross. Urbanization is the share of population in urban areas. See Table

A5

in appendix for partial correlations between variables.

Table 4 :

 4 The e¤ects of AIDS on productivity growth Dep. var. ln(Y =L) ln(Y =L) ln(Y =L) ln(Y =L) ln(Y =L) ln(Y =L) ln(Y =L)

	Method		Withiny Withiny Within	Within	Within Withiny Within
	ln(Y 1 =L 1 )		0:97 (66:9)	0:96 (34:9)	0:95 (68:1)	0:96 (34:0)	0:96 (24:7)	0:96 (35:1)	0:96 (34:0)
	HIV 1		0:14 (2:9)	0:11 (2:4)	0:12 (2:1)	0:15 (2:2)
	HW P 1						0:10 (2:1)
	HIV inst 1							0:13 (2:2)	0:13 (2:0)
	Controls:		Civil con ‡icts & wars, intercept, year and country …xed e¤ects
	Add. controls:	-	-	-	Reg YFE	-	-	Reg YFE
	# obs.		1509	1174	1196	1174	1292	1179	1179
	# countries		45	45	45	45	45	45	45
	Period		70-07	81-07	70-00	81-07	81-04	70-07	81-07
	adj. R 2		0.95	0.94	0.92	0.94	0.94	0.94	0.94
	Notes: ; ;	indicate respectively signi…cance at the 5%, 1% and 0.1% level.
	T-values reported between brackets are calculated by clustering errors by country.

Table 5 :

 5 HIV prevalence rate e¤ects on demographic variables Dep. Var.

		LifeEx	LifeEx	LifeEx	ln(L)	ln(L)	ln(L)
	Method	Withiny	Within Within Withiny Withiny Withiny
	LifeEx 1	0:94 (60:90)	0:98 (49:2)	0:99 (91:3)
	ln(L 1 )				0:96 (57:3)	0:94 (46:7)	0:96 (108:7)
	HIV 1	10:57 (6:6)			0:08 (3:7)
	HP W 1		6:46 (5:6)			0:04 (2:4)
	HIV inst 1			3:93 (2:9)			0:07 (3:7)
	Controls:		Intercept, year and country …xed e¤ects
	Controls:		ln(GDP=L)		Civil con ‡icts and wars
	# obs.	1145	930	1145	1175	957	1180
	# countries	45	43	45	45	45	45
	Period	81-07	81-04	81-07	81-07	81-04	81-07
	adj. R 2	0.98	0.98	0.98	0.99	0.99	0.99
	Notes: ; ;	indicate respectively signi…cance at the 5%, 1% and 0.1% level.
	T-values reported between brackets are calculated by clustering errors by country.
	Breush and Pagan test rejects homoscedasticity in all con…gurations
	y indicates that the Hausman test con…rms the relevance of country …xed e¤ects.

Table 6 :

 6 The impact of HIV/AIDS on primary school enrollment rate indicate respectively signi…cance at the 10%, 5%, 1% and 0.1% level. T-values reported between brackets are calculated by clustering errors by country. Breush and Pagan test rejects homoscedasticity in all con…gurations y indicates that the Hausman test con…rms the relevance of country …xed e¤ects.

	Dep. Var.	P GE	P GE	P GE	P GE	P GE	] P GE	] P GE
	Method	Within Withiny Withiny Within Withiny Within	Within
	\ P GE 5	0:42 (7:2)	0:39 (7:6)	0:36 (6:8)	0:44 (7:2)	0:40 (7:5)
	P GE 1						0:97 (97:8)	0:97 (80:0)
	HIV 1	0:67 (3:1)	0:70 (2:7)	0:84 (2:4)			0:18 (4:2)
	HIV inst 1				0:68 (2:6)	0:56 ? (1:8)		0:22 (3:1)
	Controls:	Foreign aid 1 , Civil con ‡icts and wars, intercept, country …xed e¤ects.
	Add controls:	YFE	Trend	R trend	YFE	Trend	YFEz	YFEz
	# obs.	565	565	565	560	560	1432	1123
	# countries	46	46	46	45	45	47	46
	Period	70-07	70-07	70-07	70-07	70-07	81-07	81-07
	adj. R 2	0.51	0.42	0.45	0.50	0.41	0.96	0.95

Notes: ? ; ; ;

Table 7 :

 7 The impact of HIV prevalence rate on secondary school enrollment rate

	Dep. Var.	SGE	SGE	] SGE	] SGE	] SGE	] SGE	] SGE
	Method	Withiny Withiny Withiny Withiny Withiny Withiny Withiny
	\ SGE 5	0:40

Table 8

 8 reported between brackets are calculated by clustering errors by country. y indicates that the Breush and Pagan test rejects homoscedasticity and that Hausman test con…rms the relevance of country …xed e¤ects.

	: The impact of HIV prevalence rate on investment
	Dep. Var.	ln(inv) ln(inv) ln(inv) ln(inv) x	inv	ln(inv) ln(inv)
	Method	Withiny Withiny Within Within Withiny Withiny Withiny
	ln(inv 1 )	0:63 (16:4)	0:63 (13:0)	0:54 (8:0)	0:91 (72:0)		0:59 (7:9)	0:64 (13:0)
	inv 1				0:54 (4:5)
	HIV 1	0:58 (3:0)	0:60 (3:2)	1:01 (2:4)	0:19 ? (1:8)	0:17 (2:2)
	HP W 1						(1:8) 0:23 ?
	HIV inst 1							(1:8) 0:46 ?
	Controls:	Civil wars, open, open 1 , f di and f di 1 , intercept, year …xed e¤ects
	Add. Controls:	Country …xed e¤ects		Country …xed e¤ects
	# obs.	1042	1225	737	794	1046	847	1047
	# countries	45	45	45	36	45	45	45
	Period	81-07	70-07	90-07	81-07	81-07	81-07	81-07
	adj. R 2	0.59	0.62	0.49	0.73	0.51	0.56	0.58
	Notes: ? ; ; ;	indicate respectively signi…cance at the 10%, 5%, 1% and 0.1% level.
	T-values

Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

See Caselli (2005) for a survey of growth accounting analysis.

Indeed, the time period of their estimates(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992) is characterized by a growing, but still limited, AIDS epidemic.

See Boucekkine, Diene and Azomahou (2006) for a survey.

Indeed orphans due to AIDS are less likely to attend school. Moreover, the epidemic has not spared the teachers, increasing pupil-teachers ratios. Also the reduction of household earnings increases opportunity cost. 4 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

See[START_REF] Lewis | The population impact of HIV on fertility in sub-Saharan Africa[END_REF] for a review.

See Oster (2009a) and[START_REF] Oster | Estimating HIV prevalence and incidence in Africa from mortality data[END_REF] for estimates of behavioral changes due to HIV prevalence.

Indeed health is likely to have important e¤ect on growth, see[START_REF] Bhargava | Public policies and the orphans of AIDS in Africa[END_REF]. 5 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

At the …rst order, we do not take into account the impact of the epidemic on the long-run growth rate here. 6 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

Raw data from the epidemiological UNAIDS fact sheets (2003) and also direct estimates of HIV prevalence among the population from household surveys conducted since 2003.

Prevalence rates of HIV are assumed to be null everywhere before 1982. 10 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

See in apendix a full description of the dynamic model of propagation of the epidemics and the fondations of the links between the instrumental variables and AIDS dynamics.

[START_REF] Pongou | A dynamic theory of …delity networks with an application to the spread of HIV/Aids[END_REF] show in a network model the link between ethnic composition of the population and the spread of the HIV/AIDS epidemic. 11 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

See Weiss and all (2000) or[START_REF] Halperin | Male circumcision and HIV infection: 10 years and counting[END_REF] for a survey orGray and alli (2007), for a recent randomized experience in Uganda.

To avoid capturing demographic growth.

Indeed the spread of the epidemics has been dramatically reduced by the isolation of island countries.12 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

Although strong evidence supports such a change in behaviors since 2000, there is unfortunality no relevant data to measure it, which would be available and comparable for all coutries.

The working age population, that is the share of population between 15 and 64 is not available for the Seychelles. We use therefore the total population for this country.

By de…nition, a country experienced a con ‡ict when at least 25 and at most 999 battle-related deaths occured within one year, and a war when at least 1,000 battle-related deaths occured within one year. 16 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

We use a random sample of 10,000 observarions, assuming no correlation between and to plot this distribution. The distributions of and are assumed to be normal and are calibrated using the estimated expectancy and standard deviation of the regression 2 of table 4.

If the epidemic just prevented the infected people to work, one should expect the multiplier to be around 1 in the long-run.

According to their results, a 1 percent increase in HIV prevalence induce a drop of 0.6 points in per capita income in Africa in the long-run.

Bonnel's and our own estimates (see section 4.2) indeed indicate that HIV/AIDS a¤ect signi…cantly both investment rate and school enrollment.

They reported that each AIDS case (over 100,000 people) induced a 0.3-0.4 points decrease of GDP per worker. With an average of 22 cases between 1979 and 2000, the epidemic would have costed during this period between 6.5 and 9.0 points of GDP per worker in Africa versus 4.0 pts according to our estimates.

Both boys and girls. 20 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

See Cahu (2010) for data brought from MICS, DHS and LSMS household surveys.

Openness is computed as the sum of the share of imports and exports into GDP.

From the investment series, we have produced series for physical capital stock assuming constant depreciation rate over time. However, it was not possible to obtain neither plausible nor signi…cant estimates of the marginal elasticity of capital to GDP.

There is no data allowing to disentangle the e¤ects of the epidemic on labor participation (hours worked) and technological change.

We use the same methodology to compute the cumulated e¤ects of wars on growth, by switching civil wars and con ‡icts to HIV prevalence in equation (14). 26 Documents de Travail du Centre d'Economie de la Sorbonne -2011.09

[START_REF] Oster | Estimating HIV prevalence and incidence in Africa from mortality data[END_REF] infers HIV prevalence rate from microeconomic mortality data.

See also[START_REF] Acemoglu | Disease and development : The e¤ect of life expectancy on economic growth[END_REF] for an assessment of the e¤ect of disease on growth through life expectancy.

; indicate respectively signi…cance at the 5% and 0.1% level

Acknowledgments

We are grateful to Jane Fortson, Sebnem Kalemli-Ozcan, Emily Oster, Roland Pongou and David Weil and seminar participants at Paris 1 and OLG days at University of Aix-Marseille for hepful comments. The usual disclaimers applies.

Appendix

A) Appendix related to data building Estimations used to project prevalence among pregnant women in rural area Table A1: Determinant of HIV prevalence among pregnant women in rural area Dep. var.

HIV rural HIV rural HIV rural HIV rural HIV rural Method GLS GLS GLS GLS GLS HIV rural (-1) 0:77 The model relies on the eight following assumptions:

(i) There are two types of individuals in the economy, having two di¤erent sexual behaviors. People of type F (faithful) has only intercourse with her legitimate spouse while type U has several sexual partners. One assumes that the proportion of faithful people is exogenous and equals .

(ii) There is an exogenous fraction m of type-F people who marries randomly a type-U individual.

(iii) At each period, a fraction of the type-U people has unprotected intercourse with another random type-U people. This results in the contamination of the healthy partner with a probability . This probability may vary.

(iv) Moreover, one assumes that every legitimate spouse of an infected type-U individual is also HIV-positive.

(v) As the dynamic of a disease is closely linked to the movement of population, one has to take into account the geographical dimension of the epidemic. Therefore, let us assume that a country is constituted of N cities which are all populated by 1 N of type-U adults. Let us denote i t the HIV prevalence rate of the type-U adults in the city i.

(vi) In addition to that, let us assume that at each period, an exogenous fraction of U-type individuals moves randomly to another city to …nd a sex partner.

(vii) Mortality rates of adults only depends of their HIV-status and are exogenous equalling + and respectively for HIV-positive and HIV-negative people.

(viii) Finally, a new generation of n HIV-negative young appears at the beginning of each period.

By de…nition, F-type people cannot contaminate everyone. Therefore, the dynamic of the epidemic only depends on the dynamic of the disease among the U-type people. According to assumption (ii), the prevalence rate of HIV among type-F people in the city i, F;i = m i . Therefore, the total HIV prevalence in the city i, h i is:

At the end of the period t, the newly infected U-type people A i t living in the city i could have been contaminated in their own city or in other places, either by locals or foreigners. The spread of the infection is an increasing function of the mobility of the sex partners. It also decreases with the spatial variance of the prevalence rate, V ( ).

Dynamic of the epidemic among unfaithful individuals

The following array gives the probabilities of encounters by places and city of origin for a people from the city 1. From this array, one can express the number of people from the city 1 who have been infected during the period t:

For a large number of cities in the country, the dynamic equation becomes:

The total number of new infections is thus at the national level:

One can deduce the dynamic of the prevalence rate among U-type people from the number of infected people:

Introduction of identi…cation variables

Due to population mobility, the variance of HIV prevalence across space has a tendency to decrease with the spread of the epidemic. Thus, we assume the following form for the variance V ( ):

Considering moreover that + << 1 ,we obtain a quadratic equation for HIV among U-type people dynamic. Combining (A1), (A8) and (A9) we can deduce the dynamic of HIV prevalence among the total population. A linear trend is allowed to take into account the global evolution of the HIV/AIDS epidemic.