Cover Image
close this bookAgricultural Growth Linkages in Sub-Saharan Africa - Research Report 107 (IFPRI, 1998, 152 p.)
View the document(introduction...)
View the documentForeword
View the documentAcknowledgments
View the documentSummary
View the documentCHAPTER 1. - Introduction
View the documentCHAPTER 2. - Concepts, Prior Work, and Issues Pertaining to Agricultural Growth Linkages
View the documentCHAPTER 3. - Methodology and Overview of Case Studies
View the documentCHAPTER 4. - North to South in Burkina Faso
View the documentCHAPTER 5. - Southwestern Niger
View the documentCHAPTER 6. - The Senegalese Groundnut Basin
View the documentCHAPTER 7. - Eastern Province, Zambia and Gazaland District, Zimbabwe
View the documentCHAPTER 8. - Conclusions
View the documentBibliography

CHAPTER 3. - Methodology and Overview of Case Studies

The growth linkages approach introduced in the previous chapter investigates the conditions under which additions to income from sales of rural goods and services have multiplied effects through respending of the income on local products that would not otherwise have been produced. To ascertain the extent of these multiplier effects, it is necessary first to determine how people use additions to their incomes and then to distinguish the purchases that are net additions to regional income. Identification of the sectors that have the highest multiplied effects on regional income indicates where development investment has the highest potential return in overall growth.

The methodology for assessing these issues is detailed in this chapter. Since the examples used to illustrate the model are specific to the country cases that follow, the chapter begins with an overview of the country cases and data. A description of the approach for categorizing goods and services by sector and tradability follows, as well as a discussion of the implications of the existence of nontradable goods and services on growth. The final sections explain the estimation of marginal and average household budget shares and the growth multipliers.

Country Case Studies

This research uses existing household-level panel data sets that were collected by IFPRI in collaboration with various African institutions. These data sets have been jointly analyzed with these institutions in other fora but not in the way done here. This report also draws on insights from substantial household-level work by Christopher Delgado, Jane Hopkins, Valerie Kelly, and Peter Hazell with various collaborators on other projects concerning income diversification of rural households and the extent and determinants of regional agricultural trade in the areas concerned. The household data cover weekly or biweekly panels for one full year, during 1984/85 for Burkina Faso, 1989/90 for Niger and Senegal, 1985/86 for Zambia, and 1987/88 for Zimbabwe.2 Characteristics of the study zones and samples are summarized in Table 4 and the details of previous collaborations are discussed further in the sources referenced in the table.

2Unlike the other four case studies, the Zimbabwe study did not involve panel cost-route data, and the scope of analysis for detailed expenditure analysis is less. It therefore could not be used for MBS or growth multiplier analysis. However, it is used in the same chapter as the Zambia results to offer a comparison of average expenditure behavior and to better explain the differences in expenditure behavior of commercial farmers and communal-area smallholders.

The present study covers diverse sites, with annual rainfall ranging from 300 to 1,200 millimeters, average household sizes ranging from 6 to 11 adult-equivalents, and labor-land ratios ranging from 0.20 to 0.91 hectares per capita. A particular advantage of this type of multicountry study is that it permits observation of locational differences in average income levels. Differences in the years of the survey and the difficulty of finding appropriate exchange rates for comparison of the West African franc zone (CFA) countries to Zambia in the periods considered complicate comparisons of income levels across countries. A rough idea is given by the last column of Table 4, which lists average sample total expenditures per capita divided by the average local consumer price of the major cereal crop in the year of survey. Generally, the Zambia sample seems to have distinctly higher purchasing power for food than the Sahelian sample, although it is probable that the Zambians' physical access to imported consumer items, such as many manufactured goods, was distinctly lower, due to foreign exchange difficulties in Zambia at the time.

The Senegal sample, which includes agricultural zones of both high and low potential, is better off on average than the samples studied in other countries. Senegal has a relatively high gross national product (GNP) per capita in Sahelian terms, at US$656 per capita in 1989, compared with US$292 for Niger and US$313 for Burkina Faso. The comparable figures for Zambia and Zimbabwe are US$396 and US$654, respectively (World Bank 1992). However, purchasing power differs substantially between the two zones studied in Senegal. The central Groundnut Basin, closer to Dakar, has higher purchasing power on average than the more remote southeastern Groundnut Basin, where purchasing power is closer to that of the other West African countries studied.

Other structural differences of note between the sample countries are the relative openness of the economies and the relative importance of agriculture in national income. In 1989, imports as a share of GDP were highest in Zambia, at 34 percent, compared with 32 percent in Senegal, 29 percent in Burkina Faso, 28 percent in Zimbabwe, and 22 percent in Niger (World Bank 1992). Liquid fuel consumption per capita in 1989 also provides an indicator of the degree of transport infrastructure and internal trade: in Senegal the figure was 139 kilograms, compared with 69 kilograms in Zimbabwe, 59 kilograms in Zambia, 26 kilograms in Niger, and 20 kilograms in Burkina Faso. Agriculture accounted for more than 30 percent of GDP in Burkina Faso and Niger in the same year, just over 20 percent in Senegal, and about 12 percent in Zambia and Zimbabwe (World Bank 1992).

Table 4 - Characteristics of samples and study zones

Country, year, zone

Number of households

Average rainfall

Average number of persons/household

Adult equivalents/household

Land cultivated/capita

Income from

Total expenditure in cereal equivalentsd

Own farma

Local manufacturesb

Local servicesc




(kilograms per capita)

Burkina Faso, 1984/85





























Niger, 1989/90




















Senegal, 1989/90

Southeastern Groundnut



700 1,000








Central Groundnut Basin


500 700








Zambia, 1985/86




850 1,050
















Zimbabwe, 1987/88




< 800









< 1,200







Sources: Country chapters and other reports from the same data as follows: Burkina Faso, Senegal, and Niger: Reardon, Delgado, and Matlon 1992; Kelly et al. 1993; Hopkins and Reardon 1993; Zambia: Celis, Milimo, and Wanmali 1991; Jha and Hojjati 1993; Zimbabwe: Wanmali and Zamchiya 1992.

Notes: n.a. indicates not available.

aValue of crop and livestock products from own farm (excludes gathering).

bLocal manufactured goods (excludes processed foods).

cFood preparation, commerce, transport, construction, wage income from work on someone else's farm, and other services. Agricultural wages arc of minor importance here.

dConsumption expenditure only, deflated by the local consumer price of white sorghum in Burkina Faso, millet in Niger, and the central Groundnut Basin of Senegal, a weighted average of consumer millet and sorghum prices in the southeastern Groundnut Basin of Senegal, and the producer price of white maize in Zambia. The use of producer prices raises the cereal-equivalent estimate of absolute income.

In sum, on a national basis, Senegal is the most open and internally well articulated of the sample countries. Niger is relatively less open and its internal trade is limited. Burkina Faso is more open but has even less internal trade. Zambia exhibits a relatively high degree of openness and a good level of internal trade, while Zimbabwe is less open but relatively high in internal trade.

Both the Senegal and Niger samples were observed during above-average harvest years, whereas the Burkina Faso sample was observed during an extremely bad drought year, following on two other drought years. This helps explain the especially low purchasing power estimate for that country in cereal equivalents. Cereal prices were very high in the survey year. The Zambia data came from a very good harvest year, when the study zone had a year to recover from the devastating drought of the early 1980s.

Sectoral and Tradability Classification of Goods and Services

As discussed in Chapter 2, the expected magnitude of growth multipliers depends to a large extent on the assumptions about demand constraints included in the sectoral classification of goods and services into tradables and nontradables.

Since farmers in Africa typically earn half their income from activities other than the production of crops and livestock, it is misleading to define "farm" and "nonfarm" by location. In fact, farm households are also rural nonfarm households, especially in West Africa (Hopkins, Kelly, and Delgado 1994). Because rural nonfarm activity is primarily carried out on the farms, rather than in market towns as in South Asia and Southern Africa, events in West Africa that stimulate spending on nonfarm goods and services will lead to widespread income growth for farm people in rural areas. Furthermore, since the gains from increased nonfarm activity accrue to households that are also engaged in farming, nonfarm activity increases farm liquidity and spreads income risk. Thus, classifying goods into farm and nonfarm sectors, rather than into food/nonfood or rural/urban categories (which tend to be interpreted as farm and nonfarm in drawing policy conclusions), better captures the reality of the linkages between the farm and nonfarm sectors, at least in West Africa.

The impact of local income growth on further local growth through the alleviation of local demand constraints depends not only on consumption responses to income growth, but also on whether goods are in fact demand-constrained. By definition, as argued in Chapter 2, only nontradables are demand constrained. Therefore, treating a nontradable good as a tradable leads to an underestimation of the amount of additional growth that can be had through linkage effects. This is because increased demand for tradables, by definition, leads to additional imports (if the good is typically imported to the region), or to decreased exports (if the good is typically exported from the region) rather than new local production. Nontradables, on the other hand, cannot be exported or imported, by definition. Thus, any increased demand must be met by new local production (or increased prices), which creates additional growth in the local economy. Likewise, to the extent that nonfarm goods are misclassified as farm goods, the ability of increased cash crop or livestock income to provide a demand stimulus for the nonfarm economy is underestimated.

By common definition, services in Africa are treated as nontradables, since the service is always performed locally and cannot be exported or imported. In practice, it is not easy to determine whether goods are nontradable from their physical characteristics alone. Nontradability of goods derives from the combination of high transport costs with production costs that are neither low enough to justify exports nor high enough to allow profitable imports. They are rarely traded and are not good substitutes for ones that are. It is often easier to observe the defining characteristic of nontradables: that their domestic prices are not well correlated with import prices, prices of importables, or prices in markets outside the zone of interest. Regardless of how tradability is defined, its application in the classification of goods requires the definition of what is inside the zone of interest and what is outside; the latter is the external reference market. The zone of interest is the area within which benefits are measured and where they may be expected to occur. This zone is referred to here as the "catchment area," a term that expresses the spatial notion, inherent in linkages work, of a geographic zone within which the production of nontradables occurs.

In practice, the country research teams arrived at their classifications subjectively, after much team discussion and visual inspection of price trends over time, when there were doubts. Depending on the country data available, goods consumed and produced by the sample were classified as tradables or nontradables at different levels of disaggregation, ranging from 950 individual items in Niger to two dozen composite groups of goods in Burkina Faso. These were then aggregated into about two dozen goods and services groups, each with a consistent tradability characteristic at the national level.

Because of the sensitivity of growth multiplier results to the choice of trading space, a further procedure was adopted for the West African cases, where trading zones for specific commodities are relatively well defined. An effort was made to re-classify goods from the national definition of nontradables and tradables to alternative definitions, first, with respect to the borders of a local village and then to regional borders, encompassing all of West Africa.

The three alternative definitions of catchment area - local, national, and regional - correspond to a progressively more distant reference market. The local catchment area implicit in Asian studies of agricultural growth linkages is formalized here in the African cases as an area within an approximately 100 kilometer radius of the study site, from which those goods designated as tradables are traded. National tradability means that the national catchment area trades with outside markets, and regional tradability implies that a good is traded on world markets or is a good substitute for one that is. This approach is less feasible for the data sets considered in the Southern African cases; therefore tradability assumptions for Zambia and Zimbabwe are tested for key commodity groups on a more ad hoc basis.

It should be noted that conceptual rigor requires choosing one set of tradability assumptions and sticking with them. As the size of the nontradables sector increases with an expanding catchment area, the elasticity of the sector must fall (de Janvry 1994). Furthermore, using the same level of initial income growth with two different catchment area sizes implies different assumptions about the initial rate of growth in. tradables, since the size of the tradables sector shrinks as the catchment area grows (de Janvry 1994). Therefore, the approach adopted here is to stick with the familiar national definition. The research team also feels most confident about these classifications. Results from the application of local and regional definitions are reported primarily as a guide to the sensitivity of results to tradability assumptions, although it should always be borne in mind that they cannot be directly compared, since they embody different assumptions for the same goods.

In sum, nontradables, using the national definition of tradability, are items for which national supply is equal to national demand; they are rarely if ever traded to or from points outside of national markets, and they are not close substitutes for items that are. Increases in demand for these nontradables in the national catchment area will lead to increased national production of these items, provided that production rigidities or policy interventions do not make their supply perfectly inelastic with respect to price. The more elastic the national supply for nontradables, all else being equal, the greater the increase in local production and incomes from the demand stimulus.

As suggested in Chapter 2, more elaborate models incorporating social accounting matrices capture interindustry linkages better for catchment areas larger than the local one. However, the data needs and assumptions required make this an onerous task for the study areas observed, without sufficient payoff in strategic insights gained. For the rest of the report, unless specifically identified otherwise, results and insights are reported using the national definition of tradability, even though this unfortunately ignores the impact of transport costs within countries.

An important implication of using a national definition of tradability is that more major consumer items are classified as nontradables, as is the case for millet and sorghum in parts of West Africa. Besides favoring high multipliers, this resuscitates the notion that wage goods play a strategic role in growth for countries subject to high agricultural transport costs to outside markets. Wage goods are items that account for a large share of consumer expenditure, whether or not they are tradable. As the name implies, their prices are closely correlated with wage levels. They acquire long-run strategic importance if their domestic relative prices are largely determined by domestic supply and demand factors, since the same determinants then affect wage levels. For example, if they are nontradables, they do not enter trade because they are bulky, have high transport costs relative to their final value, and no close tradable substitutes.

Surges in domestic demand for nontradable wage goods without close substitutes can raise their relative prices, putting upward pressure on wages relative to output prices and cutting profit margins. This chokes off growth in the tradables sector, unless the supply of wage goods or close substitutes is elastic. This upward pressure tends to be closely correlated with the supply price of labor. More expensive wage goods quickly imply less competitive tradable production.

Summary of Classifications in Country Reports

The detailed data sets used in this report and the field experience acquired in collecting the data allowed the authors to consider the sectoral placement and tradability of specific goods and services in detail. Locally produced food is sometimes equated with the farm sector in computing multipliers. In the Sahelian studies, processed food items such as beer, breads, cakes, processed vegetables, and processed meats are placed in the nonfarm sector, since much of the value added of these items occurs postharvest and is service related. Consumption durables (such as kitchen utensils, furniture, and clothing) and nondurables (such as fuelwood, kerosene, soap, and services) are also classified as nonfarm services. Raw goods that originate on farms, such as unprocessed cereals and pulses, fresh vegetables and fruits, milk, and live animals, are classified as farm goods. Prepared foods that are not packaged for transit (for example, sorghum beer and millet cakes) are local nontradables, as are fresh meat and dairy products.

More items become nontradable at the national level of tradability. Examples would be fruits and vegetables, most prepared foods (such as peanut butter), and some starchy staples, including millet and sorghum in Burkina Faso and Senegal, and cassava, sweet potatoes, and fonio (a wild grain crop of West Africa in the millet family) in all cases. Further examples on the input side include crop by-products used for fodder and domestic varieties of seeds retained for sowing.

Major food staples, such as millet and sorghum in Burkina Faso and Senegal, are classified as nontradables because of their independent price behavior. Adding to this judgment, the interior regions of West Africa cannot import coarse grains from the world market on a consistent basis, at unsubsidized prices, because of high transfer costs. Furthermore, there is a substantial body of evidence, partially reviewed in Chapter 2, suggesting that world market grains such as rice and wheat are not good substitutes for millet and sorghum in the landlocked countries, particularly because their calories are much more expensive.

The issue of the tradability of coarse grains at the national level in Senegal and Burkina Faso depends on whether they are occasionally imported or exported (a rare event), and whether their prices are closely linked to items that are traded. This mainly boils down to whether rice imported from the world market is a good substitute for millet and sorghum. In Senegal, in particular, coarse grains are seldom imported as food. Rice accounts for an especially large share of staple food consumption in Senegal, and most of it is imported from the world market. However, the correlation between retail prices for rice and coarse grains is low. This is only partly the result of policy interventions that stabilize rice prices but not coarse grain prices. Rice prices are fundamentally determined by relatively stable world prices, while local coarse grain prices fluctuate according to local supply and demand, greatly influenced by erratic weather fluctuations. It is probably correct to say that in Senegal, unlike Burkina Faso and Niger, massive rice imports provide an effective ceiling for coarse grain prices, but typically the coarse grains trade at half to two-thirds the price of rice. Substitution will occur at the margin, but the real income penalty of switching to rice is high in a low-income area. Therefore, the elasticity of substitution is low; coarse grain prices have plenty of latitude to fluctuate without inducing additional large stabilizing inflows of rice. Overall, Sahelian millet and sorghum are classified as nontradables with respect to world markets, except for Niger, where an active coarse grains trade with Nigeria suggests that this would be inappropriate.

West African maize is a close substitute for millet and sorghum. It could reasonably be classified as a world tradable in West Africa, as is implicitly the case in Zambia. Yet, while maize is clearly a tradable across national borders within the west and southern African regions, high transport costs relative to value and taste and preference factors make it an unconvincing tradable vis-a-vis the world market. Farmers in Niger trade significant quantities of coarse grains commercially with markets in coastal countries, especially Nigeria. Millet and sorghum are therefore tradables at the national level in Niger. Since the issue of the substitutability of local cereals and non-African maize is unclear (and assuming nontradability could bias the results favorably), maize is also assumed to be a full tradable vis-a-vis world markets in the Niger study. In Niger, consumption of maize from Nigeria is important, and the data are not clear on country of production. However, maize is classified as a nontradable vis-a-vis the world market in Burkina Faso and Senegal.3

3 Some of the maize consumed in the northern zone of the Burkina Faso sample in 1985 was food aid of non-African origin. It would be a mistake, however, to classify items provided on concessional terms as "tradables," since consumers cannot increase their access to these items at will.

At the regional level of tradability, important tradable products consumed in the West African study areas are rice, groundnuts, coffee, tea, wheat, and sugar. Imported or importable nonfood commodities consumed include matches, cigarettes, kerosene, flashlights, batteries, ready-made clothing, bicycles, and radios.

Although most locally produced nonfood goods in the Sahelian study zones are nontradables in the national catchment area, as well as world markets, there are exceptions. In Niger, for example, a number of locally produced nonfarm goods, such as palm-frond woven mats, are exported to Burkina Faso.

In Zambia, on the other hand, many farm commodities and processed foods are tradables, either regional imports or exports. They include roller meal (maize), breakfast meal (maize), white maize, rice, dry groundnuts, livestock, margarine, butter, cooking oil, white sugar, and salt. The predominance of maize and the urban processing of grain in Zambia make it structurally different from the other West African countries in this regard. Like West Africa, however, there is little reason to believe that locally produced nonfood goods and services are exported from the study zone. They are mostly local services that are nontradable by definition. Moreover, many locally produced nonfood goods cannot compete outside the local catchment area because of transport costs.

Analysis of Household Expenditure Patterns

The country case studies estimate rural consumption responses to income changes for disaggregated commodity groups. In these groups, goods are clustered that are either reasonable substitutes for each other or are likely to have similar responses to income changes for some other reason. They are also grouped to maintain consistency on tradability assumptions.

The parameters of interest are the ABS and MBS. ABSs measure the percentage of total household expenditures going to a group of goods. A high percentage suggests that the income response for that group is relatively important. Even if marginal income changes have only a small percentage effect on consumption of a good, the absolute change in quantity demanded is significant.

MBSs measure the percentage of additions to income that are allocated to the group of goods in question. Being the practical equivalent of the marginal propensity to consume a given group, they measure the direct impact of income changes on the consumption of the group of goods in question. Unlike ABSs, which are derived directly from the expenditure data for each subsample of interest, MBSs are based on the coefficients of a demand or income-consumption model that takes into account behavioral factors influencing household expenditures.

An MBS that is lower for a given group of goods than the ABS for the same group implies that the relative importance of that commodity in the consumption basket decreases as income (that is, total expenditure) increases.4 In such cases demand is income inelastic. A nice property of both ABSs and MBSs is that they are additive. A complete classification of goods yields ABSs and MBSs that sum independently to 100 percent. Commodity groups can be aggregated easily from separate estimates of ABSs and MBSs.

4 This is equivalent to saying that the commodity faces inelastic demand with respect to income, since the expenditure elasticity of demand is MBS/ABS In what follows, total household expenditure and income will be used synonymously. This does not alter the conclusions, provided that savings are a constant share of income across households. Even if this assumption is violated, low average savings ratios in rural Africa suggest that any distortion arising from using total expenditures as a conceptual proxy for income is low.

A variant of the Working-Leser model is used to estimate the income-consumption relationship for individual commodities consumed by sample households and to establish how these relationships change as household income changes (see Hazell and R 1983, for a complete description). Use of annualized cross-sectional data helps control for the fact that household expenditures on some goods and services are seasonal, while others (such as clothes and durables) tend to be purchased infrequently or only after the harvest. Using total expenditure (E) as a proxy for income, Engel functions of the following form are estimated:


where Ei is expenditure on commodity i, E is total consumption expenditure, Zj are household characteristic variables, and ai, bi, ci, mij, and lij are constants. This functional form allows for nonlinear relationships between consumption and income. It also controls for household characteristics (for example, farm and family size, education, and wealth) that may affect both the intercept and slope of the Engel function.

To mitigate potential heteroskedasticity problems, the model is estimated in share form. Dividing (1) by E gives,


where Si = Ei/E is the share of commodity i in total expenditure.

The MBSi, ABSi, and expenditure elasticity (xi,) for the ith commodity are


ABSi = Si, and


x = MBSi/ABSi.


The share equations are estimated by ordinary least squares (OLS). Adding up, (Sibi = 1 and Sici = Siai = Simij, = Silij = 0 for all i), is automatically satisfied when the equations are estimated in this way (Hazell and R 1983).

Equation (4) is estimated using OLS for (1) each of four sectors (farm tradables, farm nontradables, nonfarm tradables, and nonfarm nontradables), and (2) each of one-to-two dozen commodity categories, depending on the country (local food and livestock products, for example). MBSs are computed for the overall sample and for sample subgroups by evaluating the coefficients at the sample subgroup means. The coefficients derive from the additive properties of MBSs, which permit estimation of the model parameters for the entire data set but estimation of results for specific strata using subgroup averages of data on the right-hand side.

Rural Growth Multipliers

As discussed in Chapter 2, growth multipliers estimate an upper bound for how much extra net income growth can be had from stimulating the nontradable (demand-constrained) sectors with a stream of new income from the traded sectors. The actual multiplier is a numerical derivation from a regional model that incorporates household demands and intermediate demands between sectors and explicitly models these interrelationships.

The multiplier model employed for the empirical estimation presented in this study is a four-sector variant of the semi-input-output model of Bell and Hazell (1980) and Haggblade and Hazell (1989). The latter study modeled a regional economy with a tradables sector producing agricultural goods, and a nontradables sector producing both agricultural (farm) and nonagricultural (manufactures and services) goods. By splitting the tradables sector, to allow for both agricultural and nonagricultural goods, the model presented here makes it possible to examine the effects of technological change or other supply shiners for both agriculture and nonagriculture on rural growth linkages.

An important qualification of this model is the embedded assumption that the supply of nontradables is perfectly elastic with respect to price. Where this assumption does not hold strictly, some of the estimated multiplier is monetary rather than real: producers of nontradables reap higher unit prices in addition to real income gains from expanded output. The net gain for growth is less than in the case of a perfectly elastic supply of nontradables, since producers' gains come at the expense of other producers and consumers. Multiplier estimates that assume a perfectly elastic supply will exaggerate total growth effects. The specific numerical effects of less than perfectly elastic supply on the multiplier estimates was discussed in Chapter 2 and will be discussed in the country chapters as well as the conclusions.

As in Haggblade and Hazell (1989), household consumption expenditure on farm and nonfarm nontradables is assumed to be linearly related to income, with savings proportional to income, as follows:

Han = a0an + ban (Y-S),


Hmn = a0mn + bmn (Y-S), and





Han = household consumption of farm (a) nontradables (n),

Hmn = household consumption of nonfarm (m) nontradables,

Y = total household income,

S = total savings,

ban = MBS of farm nontradables,

bmn = MBS of nonfarm nontradables,

s = marginal propensity to save, and

a0an, a0mn = constants.

Intermediate demands for farm and nonfarm nontradables are assumed to be proportionate to sectoral gross output. Therefore,

Pan = Tat +aan.mtTmt + aan.anA + aan.mnM,


Pmn = amn.atTat + amn.mtTmt + amn.anA + amn.mnM,



Pan = intermediate demand for farm nontradables,

Pmn = intermediate demand for nonfarm nontradables,

aij = intermediate deliveries from sector i to sector j (per unit of currency), where i = (an, mn) and j = (at, mt, an, mn),

Tat == gross output of farm tradables,

Tmt = gross output of nonfarm tradables,

A = gross output of farm nontradables, and

M = gross output of nonfarm nontradables.

Investment (I) and government (G) demands for nontradables are assumed to be exogenously given as Ian, Imn, Gan, and Gmn Including household, intermediate, investment, and government demands, total outputs of farm and nonfarm nontradables are then

A = Han + Pan + Ian + Gan, and


M = Hmn + Pmn + Imn + Gmn.


To complete the model it is necessary to define household income Y. Assuming that value added (vj) is a constant share of gross output in each sector and that all value added accrues to households, then

Y = vatTat + vmtTmt + vanA + vmn,M, (15)


vj = the proportion of value added to gross output from sector j, where j = at, an, mt, and mn.

With income so defined, and using the rate of savings in equation (10), household demands for farm and nonfarm nontradables, equations (8) and (9), can be rewritten as

Han = a0an + ban (1 - s) (vatTat + vmtTmt + vanA + vmnM), and


Hmn = a0mn + bmn (1 - s) (vatTat + vmtTmt + vanA + vmnM).


Household and intermediate nontradables demands, equations (16), (17), (11), and (12), can now be substituted into the total output equations of farm and nonfarm nontradables (13) and (14). Considering the equation for farm nontradables, equations (11) and (16) are substituted into (13) to get

A = a0an + ban (1 - s) (vatTat + vmtTmt + van + vmnM) + aan.atTat + aan.mtTmt + aan.anA + aan.mnM + Ian + Gan.


All terms not involving A or M are gathered into one variable, dan, creating

dan = a0an + ban (1 - s) (vatTat + vmtTmt) + aan.atTat + aan.mtTmt + Ian + Gan.

The total output of farm nontradables is then

A = dan + (1 - s) banvanA + (1 - s) banvmnM + aan.anA + aan.mnM. (19)

Similarly for nonfarm nontradables, equations (12) and (17) are substituted into (14) to get

M = (a0mn, + bmn (1 - s) (vatTat + vmtTmt, + vanA + vmnM) + amn.atTat + amn.mtTmt + amn.anA + amn.mnM + Imn + Gmn.


All terms not involving A or M are gathered into one variable, dmn, creating

dmn = a0mn + bmn (1 - s) (vatTat + vmtTmt) + amn.atTat + amn.mtTmt + Imn + Gmn.

Total output of nonfarm nontradables is then

M = dmn + (1 - s) bmnvanA + (1 - s) bmnvmnM + amn.anA + amn.mnM. (21)

Solving equations (19) and (21) for A and M creates

A = (1/D) [1 - - (1 - s) bmnvmn] dan + (1/D) [ + (1 - s) banvmn] dmn, and


M= (1/D) [ + (1 - s) bmnvan] dan + (1/D) [1- - (1 - s) banvan] dmn,



D = [1 - - (1 - s) banvan] [1 - - (1 - s) bmnvmn] - [ + (1 - s) banvmn] [ + (1 - s) bmnvan].

Equations (22) and (23) specify output of farm nontradables in terms of value added, technology, savings, and MBS parameters.

Two value-added multipliers can now be specified, one measuring the change in regional income resulting from additional sales of tradable farm goods and another measuring the change in regional income resulting from additional sales of tradable nonfarm goods. The first step in calculating these multipliers is to take the derivatives of income, equation (15), with respect to the output of farm tradables (Tat) and the output of nonfarm tradables (Tmt), resulting in

Y/Tat = vat + van A/Tat + vmnM/Tat, and


Y/Tmt = vmt + van A/Tmt + vmnM/Tmt,


The standardized multipliers providing the effects of a dollar increase in gross output of tradables on total regional income are obtained by dividing equations (24) and (25) by the ratio of value added to gross output (vj) by the sector that changed (farm tradables or nonfarm tradables):

(1/vat) (Y/Tat) = 1 + (van/vat) (A/Tat) + (vmn/vat) (M/Tat), and


(1/vmt) (Y/Tmt) = 1 + (van/vmt) (A/Tmt) + (vmn/vmt) (M/Tmt),


These multipliers, equations (26) and (27), have a base value of one dollar, which represents the direct effect of the additional dollar of farm or nonfarm tradables that starts the multiplier process. Two further indirect components appear as well. Equation (26) includes the indirect effects of increased output of farm tradables on regional income through farm nontradables (van/vat) (A/Tat) and nonfarm nontradables (vmn/vat) (M/Tat). Equation (27) includes the indirect effects of increased nonfarm tradables output on regional income through farm nontradables (van/vmt) (A/T) and nonfarm nontradables (vmn/vmt) (M/Tmt).

The dollar value solutions to equations (26) and (27) include eight values, van, vat, vmn, vmt, (A/Tat), (M/Tat), (A/Tmt), and (M/Tmt). The first four are the ratios of value added to gross output for each of the four types of goods. The second four elements are the indirect effects on total income of additional sales of tradables through their effects on nontradables. These indirect effects occur when changing sales of tradables cause demand for nontradable intermediate inputs to change, and when households employed in producing tradables change their purchases of nontradables because of variation in their incomes. They are found by returning to equations (22) and (23) and taking the derivatives with respect to changes in output of farm and nonfarm tradables.

Beginning with changes in farm tradables and noting that tradables enter only the ds,


= (1/D) [1 - - (1 - s) bmnvmn] dan/Tat

+ (1/D) [ + (1 - s) banvmn] dmn/Tat, and



= (1/D) [ + (1 - s) bmnvan] dan/Tat

+ (1/D) [1 - - (1-s) banvan] dmn/Tat,



dan/Tat = (1 - s) banvat +, and


dmn/Tat = (1 - s) bmnvat +


Substituting equations (30) and (31) into (28), and equations (30) and (31) into (29) results in


= (1/D) [1 - - (1 - s) bmnvmn] [(1 - s) banvat, +]

+ (1/D) [ + (1 - s) banvmn] [(1 - s) bmnvat +], and



= (1/D) [ + (1 - s) bmnvan] [(1 - s) banvat +]

+ (1/D) [1 - - (1 - s) banvan] [(1 - s) bmnvat +].


Similarly, the derivatives of output of farm and nonfarm nontradables with respect to changes in the nonfarm sector are


= (1/D) [1 - -(1 - s) bmnvmn] dan/Tmt

+ (1/D) [ + (1 - s) banvmn] dmn/Tmt, and



= (1/D) [ + (1 - s) bmnvan] dan/Tmt

+ (1/D) [1 - - (1 - s) banvan] dmn/Tmt,



dan/Tmt = (1 - s) banvmt +, and


dmn/Tmt = (1 - s) bmnvmt +


Substituting equations (36) and (37) into (34), and (36) and (37) into (35) results in


= (1/D) [1 - - (1 - s) bmnvmn] [(1-s) banvmt +]

+ (1/D) [ + (1 - s) banvmn] [(1 - s) bmnvmt +], and



= (1/D) [ + (1 - s) bmnvan] [(1 - s) banvmt +]

+ (1/D) [1 - - (1 - s) banvan] [(1 - s) bmnvmt +].


Finally, to obtain expressions for the multiplier for changes in the farm tradables sector in terms of the model parameters, equations (32) and (33) are substituted into (26), producing

(1/vat) (Y/Tat) = 1+(van/vat)

× {(1/D) [1 - - (1 - s) bmnvmn] [(1 - s) banvat +]

+ (1/D) [ + (1 - s) banvmn] [(1 - s) bmnvat +]}

+ (vmn/vat) {(1/D) [ + (1 - s) bmnvan] [(1 - s) banvat +]

+ (1/D) [1 - - (1 - s) banvan] [(1 - s) bmnvat +]}.


To obtain an expression for the multiplier for changes in the nonfarm tradables sector in terms of the model parameters, equations (38) and (39) are substituted into (27), producing

(1/vmt) (Y/Tmt) = 1+(van/vat)

× {(1/D) [1 - - (1 - s) bmnvmn] [(1 - s) banvmt +]

+ (1/D) [ + (1 - s) banvmn] [(1 - s) bmnvmt +]}

+ (vmn/vmt) {(1/D) [ + (1 - s) bmnvan] [(1 - s) banvmt +]

+ (1/D) [1 - - (1 - s) banvan] [(1 - s) bmnvmt +]}.


The multipliers provided by equations (40) and (41) include 17 unknowns: the marginal propensity to save (the ss), four MBSs (the (bs), four ratios of value added to gross output (the vs), and eight values of intermediate deliveries between sectors (the as). The sources of these parameters are discussed in the country chapters.

In summary, the steps required to arrive at the multipliers detailed here are, first, to classify goods by tradability category and by sector (farm or nonfarm); second, to retrieve the marginal propensity to save, sectoral value-added, and intermediate demand parameters from budget data; third, to estimate MBSs for specific commodities that can be aggregated into composite groups of goods defined by sector and catchment size; fourth, to calculate the growth multipliers; and fifth, to recall that numerical estimates may be too high (30 percent, following the discussion in Chapter 2) because of the assumptions about a perfectly elastic supply of nontradables.