By Warren C. Sanderson and Molly E. Hellmuth

1. Namibia Demographic Model

The Namibia demographic model was constructed as part of the project to provide information about what would happen to the population of Namibia, which is severely affected by HIV/AIDS, under various scenarios. For example, the model allows policy makers to determine the consequences of alternatives such as a successful program that reduces the riskiness of sexual behavior or a government program to provide HIV/AIDS medication to those in need. In these uncertain times, this kind of information can make the difference between policies that help and policies that do not.

The philosophy behind all our models is that they should be as simple as possible, consistent with staying close to the data and capturing the major structural features of the phenomenon.

Categories

The population is divided (1) by age (100 ages from 0 through 99+); (2) by sex (female and male); (3) by education (primary and below, secondary, tertiary); (4) by HIV status (HIV negative; HIV positive, asymptomatic, and not on medication; HIV positive, asymptomatic, and on medication; and AIDS, i.e., symptomatic); (5) by number of years since HIV infection (15 categories from infected this year to infected 14 or more years, for people who are HIV positive, asymptomatic, and not on medication); (6) by sexual behavior risk group (not at risk, sometimes at risk); and (7) by onset of sexual activity (for young women and men).

Data on the initial population by age, sex, and education are taken from the 1991 Census of Namibia. Initial data on HIV prevalence by age for females are derived from the 1994 and 1998 Sentinel Surveillance Surveys after adjustment for geographical representativeness. There are no prevalence data for men. Before they can be used, the aggregate prevalence rates have to be adjusted for the relationship between education, fertility, and HIV prevalence and for the effect of HIV on fertility. Because there are no prevalence rate data on men, their incidence rates will be determined based on the incidence rates for females. The relationship between the incidence rates of men and women five years younger than they are is under the control of the user.

Forecasting the Non-HIV/AIDS Population

There has been a great deal written about population forecasting and we need not repeat it here. The non-HIV/AIDS population is projected using the standard cohort component approach. This involves forecasting the total fertility rate by education, life expectancy at birth by education, and migration rates. The time profile of total fertility rates by education and the time profile of life expectancy at birth are both under the control of the user. In the present version of the model, international migration is ignored. The time paths of the total fertility rates and the life expectancies at birth appear in the programs as lookup functions.

Forecasting HIV/AIDS Incidence and Prevalence Rates

The most difficult part of the program is the determination of the HIV incidence rates. This is done by adjusting prevalence rates for two years. In the case of Namibia, these are 1994 and 1998. Given consistent prevalence rates by age at these two dates, it is possible to estimate incidence rates. With incidence rates and prevalence rates, it is possible to estimate a set of age-specific prevalence-incidence relationship equations. This process requires a set of constants that can be specified by the user.

Three constants are required. One specifies the heterogeneity in the riskiness of sexual behavior. Another represents the manner in which those at risk interact with those not at risk. The third specifies the reduction in infectibility due to the use of medication. All appear on the relevant screen.

Forecasting the Number of New Infections

Once the initial prevalence rates and the prevalence-incidence relationships are determined for each single year of age (for 15 through 49 for women), we can compute age-specific incidence rates. Multiplying the number of women at risk of becoming infected at each age with the incidence rate yields the number of newly infected women at each age.

Forecasting the Number with Symptoms and the Number on Medication

The distribution of durations between infection and symptoms is assumed to be normal with a mean and standard deviation determined by the user. The mean can change over time in a way that users can control. The change in the mean duration to the onset of symptoms is also a lookup function and appears on the relevant screen.

With the onset of symptoms there are two possibilities: either the woman begins receiving medication or she does not. The user controls the probability that a newly symptomatic woman begins medication. If the woman begins medication, she is transferred into the status of being HIV positive, asymptomatic, and on medication. Otherwise she is transferred into the symptomatic category. In each year, a woman on medication has a probability of remaining on medication and a probability of becoming symptomatic. This probability is set by the user and can be found on the appropriate screen. Once a woman enters the symptomatic category, there is only one exit, death. The probability that a symptomatic woman dies each year is determined by the user.

Forecasting the Number of Deaths Due to HIV/AIDS

The only deaths due to HIV/AIDS are those of people in the symptomatic (AIDS) category. Deaths of HIV positive, but asymptomatic women are due to other causes. The number of deaths is the product of the number of women in the symptomatic (AIDS) category and the user-specified annual death rate. This death rate is not age specific.

2. Namibia Economic Model

The Namibia economic model is what economists call a CGE or computable general equilibrium model. The term "general equilibrium" is sometimes misunderstood to imply that the economy being studied is without distortions, rigidities or disequilibria. In fact, "general equilibrium" models can be used to investigate all sorts of economies from those that are heavily distorted to those that come close to the economists' view of perfect competition.

We have designed the Namibia model to be simple, but yet to incorporate the main features of the Namibia economy. In the following we discuss the economy's production structure, the determination of wages and returns to capital, the structure of demand and savings, the important role played by the Government of Namibia in the economy, and the determination of investment flows.

When the model is run in the Vensim® Model Reader, the screens will guide the user.

Production and Output Prices

The economy is aggregated into three sectors: non-agricultural exports (NAE), non-tradables (NT), and agriculture and agriculture-based manufacturing (AG). The NAE and NT sectors are represented at the upper-most level by Cobb-Douglas production functions in value-added, imports, and intermediate goods purchased from the other sectors. Value-added is represented by a nested constant elasticity of substitution production functions in skilled labor, unskilled labor, and capital. The agricultural sector, AG, is modeled using a Cobb-Douglas production function with inputs of skilled labor, unskilled labor, capital, imports, and intermediate goods purchased from the NT and the AG sectors.

Non-agricultural exports include diamonds, other mining products, tourism, and manufacturing exports. The non-tradable sector includes a wide variety of activities from construction to health care. The agriculture sector includes the output of commercial and non-commercial farms, fisheries, and all manufacturing based primarily on agricultural inputs.

The advantage of the nested constant elasticity of substitution form is that skilled labor and capital can be made complementary inputs, while the aggregate of the two can be substitutable for unskilled labor. This is the situation commonly found in developing countries.

The price and the quantity of NAE output are assumed to be determined exogenously by international conditions. This is certainly true about diamonds, Namibia's main export. The price and the quantity of NT output are both assumed to be determined endogenously. The price of AG output is assumed to be determined exogenously, while the quantity is endogenous. AG exports are the difference between AG production and domestic AG consumption.

Output and input demands in the NT and AG sectors are determined using the assumption of profit maximization. Output in the NAE sector is determined exogenously. Given the output level, inputs are determined so as to minimize the cost of production.

Determination of Wages and Returns to Capital

The supply of skilled labor is assumed to be exogenous and determined from the Namibia demographic model. The wage rate of skilled labor is determined so that the demand for labor at that wage rate is equal to the exogenous supply. The wage rate of unskilled labor is not assumed to clear the market for unskilled labor, allowing unemployment of unskilled labor to exist. In the NT sector, skilled and unskilled wage rates are equal to the respective values of their marginal products.

In Namibia, holding skill level constant, wages in the NAE sector are assumed to be the same as in the NT sector. The user can change this assumption and specify a constant sectoral wage rate ratio. The model also includes a constant ratio of skilled to unskilled wages in the NAE and NT sectors. The wage rate of skilled workers in the AG sector (mainly for people in agriculture-based manufacturing) are assumed to be the same as those in the NAE and NT sectors. Unskilled wage rates, however, are assumed to be different. The ratio of the unskilled wage rate in AG to those in the NAE and NT sectors is set by the user.

In the NT and AG sectors, the earnings of each unit of capital are equal to the value of the marginal product of that capital. In the NAE sector, the return to each unit of capital is determined as a residual, given the price of output, the quantity of output, the prices of the other inputs, the quantities of the other inputs, and the initial stock of capital.

Structure of Income, Demand, and Savings

In all three sectors, incomes are earned by skilled workers, unskilled workers, and capital. Income flows are aggregated across sectors. What remains are the aggregate incomes of skilled workers, unskilled workers, and capital. Some income goes to pay taxes. What remains can be used to buy the outputs of the NT sector, the AG sector, and imports, or it can be saved. The allocations of the three after-tax earnings to the four possible alternatives are made using three separate extended linear expenditure systems (ELES).

The Role of the Government

The Government of Namibia plays a number of crucial roles in the economy. It provides critical services such as education and health care. It invests in infrastructure, and it varies its level of spending so as to achieve macroeconomic balance. The Government is both a producer of services and a consumer of them. There is only one NT production function, so Government-produced services are not distinguished from other NT outputs. The model distinguishes between Government consumption (including education and health care) and Government investment. It does not subdivide Government consumption by activity, although this would be an easy extension to make. When the Government consumes and invests, it spends money on the outputs of the NT sector and on imports. The proportions spent on NT outputs and imports is different for Government consumption and investment.

Government revenues come from two main sources: (1) taxes and royalties, and (2) tariff revenues. Namibia is a member of SACU, the Southern African Customs Union, which collects all tariff revenue for all of its member countries and then allocates that revenue back to the member countries. Tariff revenue will significantly decrease in the future due to Namibia's international agreements and the EU-South African Free Trade Agreement. The model distinguishes between the two sources of income and allows the tariff rate to change over time. In the model tax rates can differ by sector, but do not change over time. The incorporation of time varying tax rates would be an easy extension. In this version, the model uses the same tax rate of value-added in all three sectors.

Namibia has committed itself to a policy of one-to-one conversion between the Namibian dollar and the South African rand. Therefore, the Government of Namibia cannot let the rate of inflation in Namibia differ significantly from the rate of inflation in South Africa. The Government of Namibia normally runs a budget deficit. It faces two constraints on how large a deficit it can run. First, it cannot run such a large deficit that it generates inflation relative to South Africa. Second, it cannot continually run deficits that endanger the ability of the country to repay its foreign debt. Our model takes these two constraints into account. In the model, the rate of increase in Government spending changes each year depending on the previous year's growth rate of nominal income, on the previous year's rate of relative inflation, and on the last year's ratio of the deficit to nominal gross domestic product. The sensitivities of changes in Government spending to the relative rate of inflation and to the relative size of the deficit are parameters that may be changed by the user.

Investment

The fraction of capital income saved and invested depends on the profitability of the NAE and the NT sectors. Returns experienced in those sectors in 1991 are taken as a benchmark. When returns exceed the benchmarks, investment rates increase and vice versa. The sensitivity of investment to profitability is set by the user.

3. Namibia Water Model Description

The water model is designed to provide forecasts of future regional water supply and demand for Namibia, in order to determine the sustainability of the water supply under various forecasts of economic, population, and climate changes. There are two models for Namibia, one for the specific case of Windhoek and one for the Socio-Ecological Region level [1].

Figure 1 shows a schematic of the water model. The water model breaks the region of interest down into the pertinent watersheds that contribute water to the surface and groundwater supply. The water that is available to consumers is the surface water runoff that is captured by surface infrastructure, or the groundwater recharge that allows sustainable abstraction. This water is then available as supply for the end users, or demand centers.

Figure 1: Water Model Schematic

3.1. Namibia SER Water Supply and Demand Model

The Socio-Ecological Regions (SERs) are shown in Figure 2.

Figure 2: Socio-Ecological Regions

There are 17 major hydrologic basins that were aggregated into macro basins from sub-basin maps (ALCOM, FAO) and delimited for analysis. These basins are shown in Figure 3.

Figure 3: Modeled waterbasins

Water from these basins is distributed to demand nodes by use of information about surface water supply infrastructure and groundwater recharge rates. There is a macro reservoir for each SER center, which represents the total storage available for the SER. Similarly, the sustainable level of recharge which can be extracted for human consumption was modeled for each basin and then summed over the SER it supplies.

The connection of the water models to the population and development models occurs on both the water supply and demand sides. On the water demand side, population size, GDP per capita, and sectoral GDP drive the water use of the domestic, industrial, institutional, mining, energy, agricultural and livestock consumers. Domestic water use changes as a result of incomes (GDP per capita), urbanization, and population size. Industrial, Energy and Institutional water demands are linearly related to the total industrial and commercial output, which changes with each population scenario. The water demands for irrigation are unequally distributed throughout the year, depending on the growing cycle of crops. On average, 15,000 cubic meters per hectare are used every year, which means that irrigation technology is rather inefficient. The growth of water use in mining is driven by changes in the exports economic sector. Livestock water use changes as a result of changes in livestock production, which may grow or decline depending on the economic demand.

Scenario Options

The following scenario options can be run:

1. Time Scale: The model may be run at the monthly or yearly time scale, which allows the user to consider seasonal effects of water supply.
2. Start Time: Changing this value allows the user to consider scenario choices under different climate conditions. Since we do not know what future precipitation or temperature will be, the user may pick a number between 0 and 970 to choose a future climate [2].
3. Climate Change: This allows the user to run the model with future climate change assumptions incorporated. The Hadley Center Global Circulation Model produced predictions in future variations of precipitation and temperature by month. Set to 1 if you would like to consider the effects of climate change.
4. Demand Side: Set this value to 1 if you would like to consider conservation measures in water consumption. This scenario reduces future industrial water consumption by changing the efficiency of water consumption over time. It reduces domestic water consumption by assuming zero growth in low and high income per capita domestic water use.
5. Percent Efficient: To consider the effects of higher water use efficiency in industrial use, please modify the Efficiency variable to incorporate the percentage of reduction in water use. This will gradually become more efficient as we move from 2002 to 2021.

3.2. Windhoek Water Supply and Demand Model

As Windhoek continues to grow as a result of urbanization, so will the city's water needs. The infrastructure of the existing water supply system as well as possible new sources were modeled. Figure 2 shows the existing infrastructure for Windhoek.

Figure 4: Existing infrastructure for Windhoek

Windhoek currently gets its water supply from the following surface sources: Omatako, Von Bach, and Swakoppoort Dams. Current and future groundwater supplies include the Windhoek, Grootfontein, Goblentz and Tsumeb aquifers. The Gammams reclamation works recycles a portion of Windhoek's wastewater and was also included..

The groundwater sources in the north are not yet connected as a supply source to Windhoek and are subject to local demands. Von Bach Dam will receive water directly from a water transfer canal from the northern groundwater sources. These additional northern groundwater sources were not explicitly modeled; however, the user can make assumptions of how much water can be sustainably transferred to Windhoek. The current estimate is 3 million cubic meters per year (MCM/a) (personal communication, Martin Harris, NAMWater).

Von Bach Dam is the main driver of the surface supply system for Windhoek because it has the best storage characteristics. Storage characteristics are important because evaporation is the biggest consumer of the water supply. The operating rules for the three dam systems and the groundwater transfer to Windhoek were adapted from CAWMP Interim Phase (Volume 1 - Systems Analysis):

1. Transfer water from the Omatako Dam to the Von Bach Dam at a maximum transfer rate of 30 MCM/a, until the Omatako Dam reaches dead storage level.
2. Transfer water from the Swakoppoort Dam to the Von Bach Dam at a maximum transfer rate of 4 MCM/a, until the Swakoppoort Dam reaches a minimum storage level of 6.60 MCM/a. The transfer capacity will increase to 10 MCM/a in 2003. Swakoppoort Dam also supplies Karibib with water.
3. Compute Windhoek's total water demands. The total demand supplied by the Von Bach Dam will be reduced by supplies from the Windhoek aquifer and the Gammaman reclamation plant. Starting in June 2001, the recycled water will have a capacity of 5 MCM/a; the capacity will be linearly increased to 7.5 MCM/a by 2011. Groundwater is taken at an assumed sustainable rate of 2 MCM/a, although this varies with the monthly recharge rate.
4. Northern groundwater sources can be connected as scenarios. Current estimates place the sustainable amount of groundwater that can be transferred from Grootfontien at 3 MCM/a. The other new groundwater sources are not specifically modeled. The Grootfontein node is already connected (transfer capacity 2.4 cubic meters per second). This water is subject to high losses and will be transferred to avoid projected water shortages.
5. Finally, a scenario can be run where water is abstracted from the Okavango River (1.62 cubic meters per second).

The water demands that are modeled for the Windhoek Municipality are Domestic, Industrial, Institutional and Energy. The Domestic demands are driven by Windhoek Population, which is broken into High and Low Income water users. The water use rates for these two categories are allowed to grow as per capita income grows, but will eventually reach a maximum water use saturation level. Industrial, Institutional and Energy consumption is driven by changes in annual GDP in the non-tradables economic sector (described in the Economic Model Description). This is a linear relationship.

Scenario Options

The following variables may be changed or turned on (=1) or off (=0) depending on the choice of the modeler:

1. Time Scale: The model may be run at the monthly or yearly time scale, which allows the user to consider seasonal effects of water supply.
2. Start Time: Changing this value allows the user to consider scenario choices under different climate conditions. Since we do not know what future precipitation or temperature will be, the user may pick a number between 0 and 970 to choose a future climate.
3. Climate Change: This allows the user to run the model with future climate change assumptions incorporated. The Hadley Center Global Circulation Model produced predictions in future variations of precipitation and temperature by month. Set to 1 if you would like to consider the effects of climate change.
4. GW North On: Set this to 1 if you would like to allow Windhoek to receive additional water supplies from the northern groundwater sources.
5. Maximum Northern Groundwater Transfer: Change this value to allow northern groundwater sources to be transferred to Windhoek.
6. Banking On: Change this value to 1 if you would like to consider the effects of water banking. This means that water is transferred to the Windhoek aquifer instead of into the Von Bach Dam, in order to decrease evaporative losses. For this scenario, runoff into the Von Bach Dam is diverted into the Windhoek aquifer at a loss of 25%, if space permits. The pumping capacity is assumed to be 20 MCM/a. The total Windhoek aquifer capacity is 25 MCM/a.
7. Okavango On: Set this value to 1 if you would like to consider the transfer of water from the Okavango River to Windhoek. 8. Demand Side: Set this value to 1 if you would like to consider conservation measures in water consumption. This scenario reduces future industrial water consumption by changing the efficiency of water consumption over time. It reduces domestic water consumption by assuming zero growth in low and high income per capita domestic water use.
8. Percent Efficient: To consider the effects of higher water use efficiency in industrial use, please modify the Efficiency variable to incorporate the percentage of reduction in water use. This will gradually become more efficient as we move from 2002 to 2021. In addition, experienced users may wish to change other variables, such as initial storage capacities or water losses.

In addition, experienced users may wish to change other variables, such as initial storage capacities or water losses.

Endnotes Water Model Description

[1] Molly E. Hellmuth, M., K.M. Strzepek, and D.N.Yates. 2000. Methodological Framework of the Southern African Integrated (SAINT) Model of Water Supply and Demand. Draft available from the author at hellmuth@iiasa.ac.at

[2] The start time is a random number to start the model with a different climate. For instance, if you type in 12, it will take the first month of precipitation (i.e., January, "year 12"). If you type in 780, it will take the first month of precipitation that is found in data series 780. Since we do not know what the future climate will be, auto- and cross-correlated 1000-year monthly data series of precipitation, temperature and vapor pressure were created.