CHAPTER 2. - Concepts, Prior Work, and Issues Pertaining to Agricultural Growth Linkages

As a concept, agricultural growth linkages has a long tradition in the literature seeking to assess the role of agriculture in economic development. It grew out of the search for ways to promote the industrialization of poor, agrarian societies. Over time, the concept has become more formalized. Debates have also increasingly tended to focus on the likely magnitudes of a few key parameters that tend to drive numerical solutions in simplified quantitative models. This chapter will review the concept and its formalization, but only briefly look at ways that it can be made much more complicated. Instead, the emphasis will be on the underlying issues and simple insights that can be gleaned from pursuing this kind of research and their significance for development strategy.

Agricultural Linkages to Overall Growth in Closed and Open Economies

In the tradition of Hirschman's (1958) work in Latin America, early studies on economic linkages between industries or sectors, focused only on production linkages. These were classified as "backward" and "forward" linkages arising from any new production activity. The demand for inputs derived from the new activity are the backward linkages; for example, new net demand for logs arising from establishment of a sawmill. New productive activities that arise as a result of having a new intermediate product on the market are the forward linkages. For example, the increased output of boards from the sawmill (or decreases in the price of boards) would stimulate the construction industry.

Agricultural growth was thought not to have strong backward and forward production linkages. It stimulated little new demand for intermediate inputs or new investment in downstream activities. This led to the conclusion that encouraging agriculture was not a high priority for fostering growth in developing countries. Hirschman (1958) argued that public investment should be directed toward nonagricultural sectors, which typically have greater production linkages to the overall economy, resulting in higher multiplier effects (Hazell and R 1983). An "anti-agriculture" mindset was undoubtedly also encouraged by the elasticity pessimism debate of the time concerning agricultural exports (Prebisch 1959). This held that the demand of the developing countries for the manufactured exports of the developed countries would grow much faster than the demand of the developed countries for the agricultural commodity exports of the developing countries, leading to declining terms of trade for agricultural exporters. Perhaps a general Malthusian concern with diminishing marginal productivity in agriculture also was a factor.

Furthermore, Hirschman espoused the "unbalanced growth" hypothesis, whereby the essence of development strategy was to stimulate production in those areas, typically industrial, thought to exhibit high backward and forward linkages (that is, "growth poles"). In relatively open, small economies, pressure on the prices of food and other wage goods from growth of employment in tradable sectors can be met through increased imports of the things workers wish to consume. Thus, no particular importance was attached to having domestic agricultural output grow at the same rate as nonagricultural output.

The case for agriculture as a motor for overall growth is enhanced by focusing on the impact that growth in the agricultural sector has on incomes and hence on rural demand for consumer goods and services from outside the agricultural sector, particularly when the economy in question is largely closed to trade. Inspired by the experience of India during the Green Revolution, with a large, relatively closed economy, Mellor (1966) and Adelman and Morris (1973) pointed out that although production linkages from the agricultural sector (especially subsistence agriculture) may in fact be weak, having little direct effect on growth outside of agriculture, consumption linkages from the agricultural sector clearly do have major indirect effects on the rest of the economy.

The argument hinges on the view that economic development in a closed economy is a process of balanced growth between agriculture and nonagriculture (see also Nurkse 1953). Growth in one sector is quickly choked off if consumption and production of intermediate goods are inelastic. For example, industrial growth from the transfer of capital and labor out of agriculture is choked off if demand for extra food arising from extra wage income is not met with increased food production. Resulting food price increases are quickly translated into demand for higher wages, which shrink industrial profit ratios. Conversely, food production growth will quickly lead to declining producer incomes if employment, and thus food demand, is not rising fast enough to absorb the additional food produced without a drastic reduction in prices.

In Mellor's view, in addition to the marginal propensity of landlords to invest agricultural profits in nonagricultural ventures, the overall intersectoral impact of growth in food production depends on how much of the extra wage income is spent on labor-intensive, nonagricultural goods and services, and how much is spent on the increased food production itself or leaks out into savings or imports. Respending on food is in fact a "leakage" from the growth multiplier in the original concept of linkages, since it occurs at the expense of new spending on nonagricultural products.

If the combined leakages away from intersectoral resource flows (understood in the early literature as transfers between agriculture and nonagriculture) are low, the net respending effect of the initial growth in incomes on aggregate income could be almost as great as the original income stimulus. In South Asia, the original income stimulus was Green Revolution technical change in rice and wheat that increased employment and landlord profits. Farmers and laborers spent increased incomes on both food and nonagricultural goods, and landlords invested in labor-intensive nonagricultural enterprises. Migration out of agriculture and lower food prices completed the elements necessary to effectively transfer resources from agriculture to nonagriculture, which grew in tandem in the late 1960s and 1970s (Mellor 1976).

Rapid urbanization and the swelling numbers of urban unemployed received great attention in the 1960s and 1970s and were central to the formulation of the linkages paradigm. The perceived need was to find a way to create jobs both outside agriculture and outside cities; this led to a focus on growth processes that would boost demand for rural nonagricultural activities. The linkages literature of the 1970s and early 1980s stresses the advantages of creating demand in rural areas for locally produced nonfood goods and services, hence the increased focus on regional linkages (Mellor 1976; Bell and Hazell 1980).

Siamwalla (1982) sought to refocus the linkages debates along the lines of emergent trade theory, at the time that the latter was gaining the high ground in development theory more generally. His main contribution was to point out that leakages from net additions to rural demand occur not only when expenditures are on imported goods, but also when incremental expenditures are on exportables (Hazell 1984). New local purchases of locally produced goods that otherwise could have been exported from the zone in question do not add to net effective rural demand, although such indirect effects do presumably create some additional value added for local traders.

Thus, the relevant categorization of expenditure for Siamwalla is tradable versus nontradable, without regard to geographic or sectoral (agriculture/nonagriculture) considerations. Only new expenditure on nontradables has the potential to create additional local income, since they are the only goods in this model that are demand-constrained. It is inherent in the notion of tradables for price-taking countries that they are constrained by their supply conditions, facing highly elastic demand (for exportables) or supply (for importables) from a larger external market.

This analysis suggests the importance of four interrelated factors for agriculture to have major extra benefits for overall growth (beyond the growth of tradable agriculture itself) in the present day conceptualization of agricultural growth linkages in Africa. First, there is the obvious but occasionally neglected condition that agriculture must account for a large share of aggregate employment, such that the problem is worth worrying about. The corollary is that no approach to growth can ignore the possibility of agricultural growth linkages if agriculture plays a large role in the economy.

Second, agricultural growth benefits that are widespread will be especially effective at capturing the growth opportunity offered by linkages by allowing the effective demand for goods and services of a broad base of rural people to increase. The potential for an initial income shock to produce new employment depends on the initial distribution of income and who gets the increments to income.

Third, consumption patterns of the direct beneficiaries of agricultural growth must be such that large shares of increments to income are spent on labor-intensive local non-tradable goods and services, stimulating demand for sectors that employ large numbers of rural people outside the agricultural tradables sector. The corollary to this is that the more open a local economy is to trade, all else being equal, the lower the estimated growth multipliers will be. This is not an argument against openness, since the ability to have a growth impulse in the first place is dependent on having a dynamic tradables sector, and a more open economy is likely to have a higher equilibrium level of income. It does point out, however, that growth multiplier effects - the extra growth from using underutilized resources - are likely to be especially important where preconditions such as high transport costs or other structural factors isolate local economies from outside sources of effective demand for local products. In other words, indirect (or consumption) growth linkages are more likely to be of major importance where a major share of the local economy consists of the production and consumption of nontradables.

The key issue is the propensity of rural households to consume nontradable goods and services out of additional income. Thus, even in the case of relatively closed economies, consumption patterns skewed toward tradables in those economies will, all else being equal, reduce growth multipliers.

Fourth, there must be a supply of underused local resources. The Asian literature pioneered by Johnston and Mellor (1961) assumes that net extra demand for local non-agricultural goods and services is fully transmitted into increased production of these items, primarily because of underutilized factors such as labor. However, if the supply of nontradables is inelastic, perhaps because of labor or capital constraints or high transaction costs, then costs of production will quickly rise with expanded demand, and the additional growth in production of local goods and services stemming from the respending of agricultural incomes will be less than would be the case if the supply of local nontradables was more elastic (Haggblade, Hammer, and Hazell 1991).

In sum, growth that only benefits either a small number of large farmers or a relatively small agricultural sector would presumably not have big rural consumption linkages for locally produced goods and services, the production of which would provide a great deal of local employment. On the other hand, growth that stimulates the incomes of large numbers of small farmers is likely to provoke widespread increased demand for local consumer goods and services. The more these goods are demand-constrained by nature (nontradables), the greater the growth impact. Finally, the net additional impact of these demand increases on production growth, and thus on rural employment and further spending, will depend on the elasticity of supply of nontradable goods and services, which in turn is principally dependent on the elasticity of supply of labor. Most empirical estimation of consumption growth multipliers to date has been done with Asian data, with few applications to Africa. Very little has been done in Latin America. The next section briefly reviews the quantitative literature from Asia and Africa that models agricultural growth multipliers.

Earlier Estimates of Agricultural Growth Multipliers

Although the concept of agricultural growth linkages goes back at least to the 1950s - drawing on Ricardo in the early 19th century and Keynes in the early 20th - quantitative estimation of multipliers incorporating consumption as well as production demand is relatively recent. Peter Hazell and Steven Haggblade have been key contributors in this regard. Much of the existing literature on modeling agricultural multipliers is reviewed by Haggblade, Hazell, and Brown (1989) and Haggblade, Hammer, and Hazell (1991). The present report draws heavily on those sources and others to summarize the magnitudes of multipliers that have been estimated to date. All such multipliers are the result of normative rather than positive analysis.

Rangarajan (1982) constructs a macroeconomic model that incorporates linkages in production, savings, and investment demand to examine historical data in India during 1961-72. In this model, national income is determined by both agricultural and industrial output. Agricultural outputs, both foodgrains and nonfood-grains are determined exogenously; hence the main variable to be determined is industrial output. He estimates multipliers of 1.5 for industrial output and 1.7 for national income. This implies that an initial 1 percent increase in agricultural growth will lead to an additional 0.5 percent increase in industrial output and an additional 0.7 percent increase in overall national income.

Rangarajan (1982) also examines production and consumption linkages separately to determine the significance of each. He finds that production linkages in India are weak. Only 13 percent of total agricultural output went to nonagricultural sectors as inputs. Also, a 1 rupee increase in final demand for agricultural output increases manufacturing output by 0.09 rupee, while a similar increase in the final demand for manufactured goods increases agricultural output by 0.26 rupee.

The estimated demand linkages suggest that increases in agricultural income have significant positive effects on the demand for rural and urban nonfood products. The savings and investment linkages show that agricultural income also has a positive effect on both household and government savings (Rangarajan 1982).

Bell and Hazell (1980) and Bell, Hazell, and Slade (1982) develop variants of the semi-input-output model in their study of the effects of technological change in irrigation in the Muda River region of northwest Malaysia. They estimate a multiplier of 1.80 for the local nonagricultural economy. This is interpreted as an additional increase of $0.80 of nonagricultural income, generated through indirect spending linkages, for every dollar generated directly by a given project in the agricultural sector. The model is extended to incorporate a three-sector trade focus in Haggblade and Hazell (1989).

The models and multipliers used in these and other agricultural growth multiplier studies are reviewed in Haggblade, Hammer, and Hazell (1991). They illustrate that a vital feature of most of the models employed up to the time of their writing was the assumption that the supply of nontradables is perfectly elastic, with output constrained by effective demand. Hence the models are "fixed-price" models (that is, the price of nontradables is constant), which have the merit of being relatively tractable and not too far out of accord with the reality of underemployed labor in countries such as India.

One of the more theoretically satisfactory yet easily computed fixed-price multipliers is derived by Hazell (1984) from the semi-input-output model of Bell and Hazell (1980). It measures increases in income as a result of an exogenous shock to agriculture, via technological change or outside investment, causing the output of nontradables to increase. Assuming that the amount of intermediate inputs used per unit of tradable output does not change as a result of the initial increase in tradable output (Haggblade, Hammer, and Hazell 1991), the multiplier (M) can be written

(1)

where

a_nn, a_nt = the share of nontradable intermediate inputs in nontradable and tradable output, respectively (between 0 and 1),

a_tn, a_tt = the share of tradable intermediate inputs in nontradable and tradable output, respectively (between 0 and 1),

v_n = a constant with a value equal to 1 - a_tn - a_nn, the share of value added in gross output of the nontradables sector,

v_t = same as v_n, for tradables, with value equal to 1 - a_tt -a_nt,

b_n = marginal propensity to consume nontradables, and

s = leakage, a constant proportion of total income (savings and tax rate).

Hazell's (1984) simplified version of this multiplier assumes that a_nn = a_nt = a_n, (intermediate demand for nontradables) and v_n = v_t = v (value-added shares). The multiplier then becomes

(2)

As Haggblade, Hammer, and Hazell (1991) point out, this simplified multiplier can be easily estimated using values for the marginal budget share (MBS) for nontradable goods in household expenditure (b_n), the ratio of nontradable intermediates to gross output in total production (a_n), and the ratio of value added to gross output in total production (v). Like all fixed-price models, the model assumes that tradables are supply constrained and that nontradables are perfectly elastic in supply. It encompasses the effects of both consumption and production linkages in the economy. The effects of production linkages alone can be easily derived by setting b_n = 0.

Using the simplified model and data from Bell, Hazell, and Slade (1982), Hazell (1984) estimates a multiplier of 1.82 for the Muda River region, which is very close to the one estimated by Bell, Hazell, and Slade (1982) for this same region (1.80).

Hazell and Haggblade (1990) compare the results of a cross-sectional econometric analysis, using data from local states and districts in India, with those of a semi-input-output model fitted on national input-output data, to examine rural-urban growth linkages. The estimates from the cross-sectional econometric analysis show that on average for the whole of India an increase in agricultural income of 100 rupees will generate an additional 64 rupees in rural nonagricultural income. In high-productivity areas (Punjab and Haryana), an equivalent increase in agricultural income will generate an additional 93 rupees, and in low-productivity areas (Madhya Pradesh and Bihar), it will generate only an additional 46 rupees. Infrastructure proves to be a significant determinant of the agricultural growth multiplier. Hazell and Haggblade also find some evidence that higher consumption linkages account for the larger multipliers in the high-productivity areas.

The use of the semi-input-output model with aggregate national data allows the estimation of changes in total national demand for nonagricultural products and thus results in a significantly larger multiplier than the cross-sectional analysis estimates derived from state and district data (Hazell and Haggblade 1990). The national model estimates that for every increase of 100 rupees in agricultural income, an additional 135 rupees will be generated by the multiplier effect. This stems from both the more comprehensive "net" for observing linkages effects implicit in the data themselves and a more restricted definition of what is tradable outside of the zone of analysis.

The results from the Indian analysis by Hazell and Haggblade indicate that a greater proportion of the overall multiplier is attributable to consumption linkages than to interindustry production linkages (Hazell and Haggblade 1990, 44, Table 16). The share of the total agricultural growth multiplier calculated by the simplified semi-input-output method attributable to consumption linkages alone is 90 percent for Sierra Leone, 84 percent for the Muda River in Malaysia, and 56 percent for Oklahoma (Haggblade, Hammer, and Hazell 1991). This supports the widely accepted view that production linkages in agriculture are relatively weak (Hazell and R 1983). It also reinforces Mellor's (1966,1976,1986) argument that including consumption linkages in the analysis gives a more comprehensive assessment of the magnitude of linkages in the agricultural sector (Hazell and R 1983; Bell, Hazell, and Slade 1982).

Hazell, Ramasamy, and Rajagopalan (1991) estimate the indirect effects generated by an income-increasing technological change in agriculture. They calculate the change in value-added relative to an initial change in gross output, using a regional input-output model. For North Arcot, India, they report that an increase in agricultural income of 1 rupee will generate an additional 0.87 rupee in nonagricultural income. They also report that production linkages account for 50 percent of the multiplier effects in North Arcot, which is high relative to other studies, perhaps owing to the ongoing technological change observed in North Arcot.

Hazell and R (1983) conduct a comparative analysis of linkages in the Muda River region of Malaysia and Gusau, Nigeria. They too provide evidence of weaker consumption linkages in Gusau than Muda River, which would lead to smaller agricultural multipliers. In keeping with the assumptions made in the Asian literature, they assume that most nonagricultural items are not traded and that most agricultural items are traded.

Hazell and R (1983) find that 75 percent of the average budget share (ABS) in Gusau is accounted for by locally and home-produced foods, compared with 46 percent in Muda (Table 1). The average household in Muda also spends 62 percent of any incremental income (marginal budget share, or MBS) on nonfoods and nearly two-thirds of these are locally produced. In Gusau, these shares are 24 percent with less than half being locally produced. Hazell and R's "Asian" assumptions about sectoral tradability lead to a commodity breakdown that allocates 59 percent of increments to rural spending to tradables and 41 percent to nontradables in Muda, and 68 percent to tradables and 32 percent to nontradables in Gusau. Thus, increments to expenditure in Muda were thought to have a greater stimulative effect on demand for nontradables than those in Gusau.

Table 1 - Consumption parameters affecting growth linkages in Malaysia and Nigeria

Commodities			Muda, Malaysia	Gusau, Nigeria
			(percent)
Nonfoods
	Average budget share		33	19
	Marginal budget share		62	24
Locally produced nonfoods
	Average budget share		18	8
	Marginal budget share		37	11
Locally and home produced foods
	Average budget share		46	75
Nontradables
	Average budget share		24	25
	Marginal budget share
		Whole sample	41	32
		Lowest per capita expenditure decile	24	27
		Highest per capita expenditure decile	55	36
Nontradables including coarse grains
	Average budget share		n.a.	70
	Marginal budget share
		Whole sample	n.a.	64
		Lowest per capita expenditure decile	n.a.	78
		Highest per capita expenditure decile	n.a.	62

Source: Hazell and R 1983.

Notes: n.a. indicates not applicable. In the bottom section of the table average and marginal budget shares of nontradables, as reported by Hazell and R (1983), are modified to include millet, sorghum, and maize in the list of nontradables. In Muda this leads to no significant change in values since these cereals are not a significant component in food consumption patterns. Hence, only values for Gusau are reported. Marginal budget shares by per capita expenditure decile are calculated using estimates, also by Hazell and R (1983), for cereals and cereal products, which includes a tradable, rice, as well as millet, sorghum, and maize. In the case of Gusau, where very little rice is consumed, this will only slightly overestimate the marginal budget shares by per capita expenditure decile.

Haggblade, Hazell, and Brown (1987) estimate growth multipliers for Sierra Leone and Nigeria using the data cited and Hazell's simplified version of a semi-input-output model reported in equation (2). Because accurate estimates of the relevant parameters that determine the multiplier were not available, they used rough orders of magnitude for these values. Estimates of the MBS for nontradables in household expenditures (b_n) were derived from data by King and Byerlee (1978) in Sierra Leone. The ratios of nontradable intermediate inputs in nontradable and tradable output (a_nn and a_nt) were estimated using evidence from Botswana (Haggblade 1982) and Sierra Leone (Leidholm and Chuta 1985). The ratio of value added to gross output in total production (v) was estimated based on the rural characteristics of the area (70 percent of rural value added is thought to be derived from agriculture, with v lying in the range of 0.82 to 0.86). Given the values a_nn = a_nt = a_n = 0.10, v = 0.85, and b_n = 0.03, Haggblade, Hazell, and Brown estimate that the multiplier for Sub-Saharan Africa is about 1.5, which is significantly lower than the one in Asia.

A survey of the literature on agricultural-nonagricultural linkages in Africa by Haggblade, Hazell, and Brown (1989) concludes that estimated multipliers are significantly smaller for Africa than those estimated for Asian countries and India. They attribute this variation to differences in climate conditions, undeveloped backward production linkages in Africa, lower population density in Africa, and differences in consumption patterns. Simler (1994) computes an agricultural growth multiplier of 1.66 for Malawi, using field data from 1986/87, with a range of values from 1.41 to 3.08 depending on assumptions.

Dorosh and Haggblade (1993) provide an application of a variant of the fixed-price, semi-input-output model built around a condensed social accounting matrix (SAM) for Madagascar, consisting of six tradable and six nontradable sectors. They estimate that a small increment of value added in agriculture in Madagascar increases overall value added by as much as 2.0 to 2.7 times the initial shock, depending on assumptions made. The authors attribute the greater order of magnitude of these multipliers relative to previous multiplier estimates in Africa to having considered the full national economy, including linkages from expenditures outside the rural region. A selection of multipliers found in the literature is given in Table 2.

Limitations of Fixed-Price Multiplier Models and Some Alternatives

All fixed-price models make three basic assumptions (Haggblade, Hammer, and Hazell 1991). First, regional economic growth is driven primarily by the increased production of tradable goods. Second, production can be adequately modeled as Leontief fixed coefficients technology. Third, prices are constant for both tradable and nontradable goods and services.

The main limitations of the fixed-price model arise from its assumption that regional growth is driven by the production of tradable goods. It ignores both the possible benefits of a major technological breakthrough for nontradables and, because it is a static equilibrium approach, the dynamic aspects of savings and investment.

Table 2 - Agricultural growth multipliers in Africa and Asia

Study	Location	Dollars of total income growth from $1.00 of direct growth in agricultural income
Rangarajan (1982)	India, all	1.70
Bell, Hazell, and Slade (1982)	Malaysia, Muda River region	1.83
Hazell (1984)	Malaysia, Muda River region	1.82
Hazell and Haggblade (1990)	India, all	1.64
	India, Punjab and Haryana	1.93
	India, Madhya Pradesh and Bihar	1.46
Hazell, Ramasamy, and Rajagopalan (1991)	India, North Arcot, and Tamil Nadu	1.83
Haggblade, Hazell, and Brown (1987)	Sierra Leone and Gusau, Nigeria	1.50
Dorosh and Haggblade (1993)	Madagascar	2.0-2.7
Simler (1994)	Malawi	1.66
Haggblade, Hazell, and Brown (1987) assuming millet, sorghum, and maize are nontradables	Nigeria, Gusau	2.81

Notes: All multipliers, except those used by Rangarajan (1982), Dorosh and Haggblade (1993), and Simler (1994), are derived using Hazell's simplified semi-input-output model (Hazell 1984). The multiplier listed for Gusau, Nigeria, is derived by the present authors using the same values for the ratio of nontradable intermediates to gross output in total production (a_n = 0.10) and the ratio of value added to gross output in total production (v = 0.85) used by Haggblade, Hazell, and Brown (1987) to derive the multiplier for Sierra Leone and Nigeria. The marginal budget share for nontradable goods (b_n) in household expenditure is modified to include millet, sorghum, and maize in the group of nontradables. This value, which increases from 0.32 to 0.64, is calculated using the consumption parameters for different goods and services categories estimated by Hazell and R (1983).

The first problem is best dealt with by noting that if such a breakthrough occurs for nontradables, its growth effects will soon be felt: either the former nontradable will become so cheap that it will then be tradable, or resources will flow out of the nontradable to the tradable sector (for example, the acreage planted in a nontradable food grown for self-sufficiency purposes will be reduced once its yields go up, and acreage will go to production of an exportable crop). In either case, growth is captured in the model through an exogenous increase in tradables production and its spin-off effects. Thus the story can be told through a linkage model, with additional explanations of the source of the exogenous growth in tradables.

The second problem is harder to dispose of. Savings are a net leakage in the model, and thus bad for growth. Investment is not considered. There is no easy way around this failure to consider savings and investment except to appeal to the relative absence of a large-scale landowning class in the Latin American or Asian sense in most African countries, and the consequent paucity of investment linkages. In poor and probably more egalitarian rural Africa (relatively speaking and excluding areas of European settlement), the omission of dynamic investment effects may be less bothersome than elsewhere.

For present purposes, the most troubling of the three basic assumptions of fixed-price models is that the supply of nontradable goods and services is perfectly elastic (the "fixed price"). This assumption may be applicable in Asian countries, which are known to have a plentiful supply of labor. In Africa, this assumption raises concern about the existence of the required pool of underemployed nontradable goods and services needed to put in motion the multiplier effect, as discussed in greater detail in a subsequent section. If the assumption of perfect elasticity is relaxed, then the model overestimates the true multiplier.

Price-endogenous models, allowing for upward-sloping supply curves for nontradables, provide better estimates of multiplier effects in situations where the assumption of perfectly elastic supply of nontradable output must be relaxed. These models also impose no functional form on the production function, so one is not restricted to using the restrictive Leontief form (Haggblade, Hammer, and Hazell 1991).

Haggblade, Hammer, and Hazell (1991) estimate multipliers for Sierra Leone, the Muda River, and Oklahoma, to compare the extent of overestimation from fixed-price models. They investigate two possible scenarios. In the first case, both labor and other nontradables are price inelastic. They estimate that the degree of overestimation ranges from 20 to 40 percent. If either labor or "other nontradables" is inelastic, they estimate that the range of overestimation is from 10 to 25 percent. They assume that in Africa all nontradable goods and services are inelastic; therefore, on average, the degree of overestimation will be about 30 percent. In Asia, neither labor nor other nontradables are believed to be inelastic; hence, on average, the degree of overestimation will be 10 percent. Table 3 reports adjusted multipliers, accounting for too rosy a view of the elasticity of the supply of nontradables.

Computable general equilibrium (CGE) models that allow for the simultaneous interaction of price and quantity variables do away with the cumbersome need to model exogenous prices explicitly through behavioral forms, as required by semi-input-output models (Dervis, de Melo, and Robinson 1982). Constructing and running CGE models is now relatively easy with available statistical software packages. However, it typically requires the construction of a SAM, which organizes the underlying data and parameters used in CGE models. Creating a SAM is a lengthy process that requires in-depth access to data sources such as national accounts, input-output tables, and household, enterprise, financial, and labor surveys (Dorosh et al. 1991).

CGE models are not completely lacking in restrictive assumptions either. As for all neoclassical general equilibrium models, they require a set of restrictive equilibrating conditions in order to close the system of equations. Conditions are normally imposed such that excess demands are set to zero through the clearing of markets and full employment of all resources (except labor). Such market clearing assumptions may not always be appropriate for developing countries (Robinson 1989). Yet, the simple fixed-price approach has the merit of producing easily understood indicators as to why, when, and where it is important to increase the elasticity of supply of nontradables to achieve potential added growth that can be had from a given positive income shock to the local economy.

The few empirical estimates of growth multipliers for Africa suggest similarities and important differences for Africa relative to Asia. For both Africa and Asia, consumption-based agricultural growth linkages were four to five times more important to growth than production-based linkages. This suggests that neglecting the consumption side a la Hirschman is severely misleading. In both the African and Asian cases, neglecting growth linkages altogether would lead to underestimation of up to 40 percent of the potential growth that could be had from investment in agriculture. Yet, while the Asian cases suggested multipliers on the order of 1.8 ($0.80 of extra nonagricultural income for each $1.00 of new agricultural income), the two African cases yielded fixed-price multipliers on the order of 1.5.

Table 3 - Fixed-price agricultural growth multipliers in Africa and Asia adjusted for an inelastic supply of nontradables

Study	Location	Dollars of total income growth from $1.00 of direct growth in agricultural income after adjustment
Bell, Hazell, and Slade (1982)	Malaysia, Muda River region	1.65
Hazell (1984)	Malaysia, Muda River region	1.64
Hazell and Haggblade (1990)	India, all	1.48
	India, Punjab and Haryana	1.74
	India, Madhya Pradesh and Bihar	1.31
Hazell, Ramasamy, and Rajagopalan (1991)	India, North Arcot, Tamil Nadu	1.64
Haggblade, Hazell, and Brown (1987)	Sierra Leone and Nigeria	1.05
Haggblade, Hazell, and Brown (1987) assuming millet, sorghum, and maize are nontradables	Nigeria, Gusau	1.97

Notes: Multipliers are adjusted for overestimation as determined by the estimation of price endogenous models in Haggblade, Hammer, and Hazell (1991). In Asian countries they suggest a possible overestimation on the order of 10 percent and in African countries as high as 30 percent. Multipliers are arbitrarily reduced by these assumed degrees of overestimation.

Even so, it is difficult to interpret these numbers as suggesting that the true African multipliers are in fact lower, since the Africa cases were estimated assuming that major expenditure items such as millet and sorghum were tradable. Hazell and R (1983) find that households in Muda have a higher MBS for nontradables than do households in Gusau (see Table 1). Thus, in Gusau, estimated growth linkages turn out to be weaker, since there is a lower marginal propensity to spend on nontradables as they define them, leading to their pessimism about linkages in Africa.

The neglect of noninfinite price elasticities for nontradables in the fixed-price methodology was found to be more of a problem in Africa than Asia. Rectifying this omission in both cases would probably reduce African agricultural growth multipliers relative to the Asian ones. A back-of-the envelope calculation suggests that while the true endogenous price multipliers for the Asian cases studied are probably still on the order of 1.6, since labor is abundant, they would be less than 1.1 in the African cases (Table 3) if the tradability assumptions in Hazell and R (1983) are justified.

These points illustrate three insights for the design of policy-oriented research: (1) the tradability of rural consumer items and the factors influencing this characteristic are central to growth linkages analysis in Africa; (2) the problem of an inelastic supply of nontradables is not a negligible concern in Africa; and (3) the first concern is likely to be far more important to results than the second concern.

The following sections integrate these insights into a broader literature to isolate key structural characteristics of Africa that affect the magnitude of agricultural growth multipliers, with emphasis on what can be done to enhance growth in Africa. Key issues are (1) the degree of openness of rural economies and the tradability of major items consumed and produced there; (2) the allocation of rural consumption expenditures between tradables and nontradables; (3) the pattern of rural income distribution, given that different income groups have different consumption patterns; and (4) evidence on the elasticity of supply of rural nontradables.

Tradability, Demand-Constrained Items, and the Sensitivity of Multipliers to the Choice of Trading Space

Other than value added from local trading, incremental local income spent on goods imported to the region does not add any additional income to the area. Potential export proceeds are also forgone when incremental income is spent on goods that could instead have been exported out of the region. Thus, to estimate agricultural growth multipliers, it is necessary to classify all intermediate goods, final goods, and services into nontradable and tradable items. The key difference between the two in the present context is that locally produced nontradables by definition have no market outside the local area. Locally consumed nontradables also have no source of supply from outside the local area. In the present simplified framework, nontradability implies that a good (and all services) is demand constrained. Tradable goods, on the other hand, by definition always have an outside market and an outside source of supply. Their local production is supply constrained.

The Asian growth linkages literature typically defines as "nontradable" those goods, inputs, and services that are neither imported to nor exported from a region around the survey area, usually within 50 to 100 miles of the point of analysis. This literature also implicitly or explicitly views locally produced nonagricultural commodities as being nontradables and locally produced agricultural commodities as being tradables. This practice is consistent with agricultural sectors where the main products are rice, wheat, and poultry. In the Muda study, for example, all locally produced non-foods were classified as nontradable, and the only foods classified as nontradable were dairy products and food preparations. It should be noted that this classification makes for a close congruence between the earlier concern for agricultural versus nonagricultural linkages and the more recent interest in tradables versus nontradables.

The numerical results for multipliers in Hazell and R (1983) and Haggblade, Hazell, and Brown (1987) depend on extending to Africa two key assumptions made in the previous Asian literature. First, the definition of tradability is limited to a small area, the immediate region around Gusau. Second, millet, sorghum, and maize in Gusau are treated as tradables, just like rice in Muda River (and Gusau). It is debatable whether millet and sorghum from Gusau have an export market outside the immediate region of northern Nigeria except in unusual circumstances. These crops are clearly not tradable in the usual sense if the catchment area goes beyond local areas in northern Nigeria. Reclassifying millet, sorghum, and maize as nontradables would almost triple the ABS for nontradables in Gusau and double the MBS. This would bring the estimated agricultural growth multiplier from Gusau to 2.8, considerably larger than the one from Muda! Even allowing for the maximum 40 percent overvaluation from using a fixed-price model, this yields an African growth multiplier of 2.0.

Thus, tradability assumptions for specific goods matter because they incorporate assumptions about whether new demand simply displaces regional exports (or increases regional imports), or whether it has the potential to draw underutilized resources into production for which there would not otherwise be a market. Labor supply insensitivity to price (if true) matters because it indicates whether demand stimulus will be channeled into higher relative prices for nontradables or increased production thereof.

The Elasticity of Supply of Nontradables in Semi-Open Africa and the Issue of Underemployed Resources in Rural Areas

Fixed-price growth multiplier estimates are clearly too high because of the embedded unrealistic assumption of a perfectly elastic supply of nontradables. But how serious is this bias? In the Asian literature referenced here it is customarily ignored, since Asia's high rural population densities are traditionally thought to imply low marginal productivities of labor, hence easy availability of labor for more lucrative new opportunities.

There are at least three reasons to be concerned that the elasticity of supply of rural nontradables is low in Africa. First, rural Africa is usually thought to be labor-constrained in relation to Asia, at least during the peak seasons for cultivating cereals (Eicher and Baker 1992). Second, since nontradables account for large shares of rural activity in the aggregate, it is probable that supply elasticities for the sector as a whole will be much lower than for individual activities (de Janvry 1994). Third, under the usual assumption of full employment of resources, benefits from demand shocks to nontradables would mostly be monetary, rather than net increments to growth, since the output gain in one sector would come in response to an output loss in another (Bigsten and Collier 1995).

Yet the issue is not so clear cut, especially in West Africa. In most of West Africa, national economies are "semi-open," exhibiting many of the characteristics of Asia with respect to the food economy and of Latin America on nonfoods (Delgado 1992). Following Myint (1975), a semi-open economy may be characterized as one where price-taking emerging countries are firmly linked to world trade, yet a large part of the domestic economy remains insulated from the impact of foreign trade because of a high rate of natural trade protection due to remoteness and undeveloped infrastructure. In the present cases, semi-openness can be thought of in terms of a farm sector producing both exportable crops and nontradable foods and mostly nontradable nonfarm services and handicrafts.

In such a stylized economy, farm exportables are potentially supply constrained by factor supplies. However, unlike most farm nontradables, they are also constrained by technology, by infrastructure, and by the reliability of supply of modem inputs such as fertilizer. Nonfarm nontradables are primarily constrained by demand. The effective constraints on farm nontradables have not been well established. However, they are likely to be constrained in production either by factor supplies or by demand. It seems likely that the productive potential for these items (such as millet in Burkina Faso and subsistence food crops in most countries) regularly exceeds effective demand, except in exceptional years.

In the aggregate, the supply of rural nontradables could be elastic either at the expense of farm exportables or, if there are underused farm resources, in equilibrium. The former leads only to monetary, not real, gains, since the initial impetus for linkages by hypothesis comes from the exportable farm sector. Therefore, the key issue for the elasticity of the aggregate supply of nontradables in rural areas in such a stylized economy boils down to the existence in equilibrium of underused resources of labor, land, and capital that can flow into new production of nontradables stimulated by demand shocks.

What evidence is there of underused resources in rural Africa? While this question has not been conclusively studied, strong anecdotal evidence suggests the existence of such resources. There are two main arguments. First, there is the clear existence of seasonal slack periods in rural areas covering much of the year, combined with varying degrees of underutilized land resources (Ruthenberg 1971; Cleave 1974; Delgado and Ranade 1987). This situation is supported in the chapters in this report on Burkina Faso, Niger, and Zambia. Second, the binding constraints on farm exportables are typically those other than the supplies of land and labor that constrain nontradable foods in much of Africa, allowing food production to expand without necessarily causing the export crop production to contract.

The first argument runs as follows. Given that labor bottlenecks are a constraint only a few weeks of the year, there is probably some slack in resource use in the system most of the time. Beyond underemployment, labor often migrates seasonally, and nonfarm activity accounts for some time during the dry season (Delgado and Ranade 1987). These resources could probably be used to produce items and alleviate excess demand during the slack periods. That the large amount of nonfarm activity observed on an annual basis in rural Africa is carried out by farmers within their own household compounds suggests that the transaction costs of switching among sectors are also relatively low - certainly lower than having to migrate (Reardon et al. 1994).

Taken together, seasonal slack periods in farm activities and low transaction costs for moving between farm and nonfarm activities suggest that the supply elasticities of nonfarm activities and farm activities that are not seasonally constrained (that is, nonfood farm activities) may potentially be fairly high, even in the aggregate, since there appears to be underused labor and land resources available most of the year. However, since so much of aggregate rural production is accounted for by the nontradable foods that also account for the seasonal labor bottlenecks, it is still reasonable to question whether farm nontradables as a group are price elastic in supply.

The second argument partially addresses this problem and is well supported in the literature. While nontradable food production is primarily a function of the land and labor allocated to its production in Africa, nonfarm exportables are primarily constrained by other factors. Seasonal labor bottlenecks for nonfarm exportables in the main field-crop growing areas of Africa tend to be different than those for the main nontradable foods in the same areas. This fact helps explain the rapid expansion of export cropping on small farms in the 1960s without much apparent loss of previous food production (de Wilde 1967; Ruthenberg 1971; Delgado and McIntire 1982; Delgado and Ranade 1987). Farm exportables in Africa, on the other hand, have tended to be highly dependent on commodity-specific organizations and resources, such as specialized export infrastructure, a reliable supply in rural areas of imported inputs such as fertilizer and pesticides, remedies for specific crop diseases and pests, and so forth (de Wilde 1967; Lele 1975, 1991; Eicher and Baker 1992). Availability of such organizations and resources may also affect food production, but presumably much less for nontradable items such as millet and cassava (grown far away from infrastructure) than for maize and rice, which are clearly tradables in most cases.

If farm exportables and nontradables are not in direct competition with each other at the margin for land and labor, then the existence of underused rural resources is much more plausible. Although arrived at by a different path, this view is in fact compatible with the philosophy of structural adjustment lending in Africa, whereby demand shocks (because of the correction of price distortions toward the farm sector as a whole) will elicit an aggregate supply response from the farm sector (see, for example, Chhibber 1989).

In conclusion on this issue, it is difficult to go beyond the quantitative estimates of a 20 to 40 percent overvaluation of fixed-price multipliers in Africa suggested by Haggblade, Hammer, and Hazell (1991) in speculating about the impact of inelasticity in the supply of nontradables on the true size of growth multipliers. This is primarily because the issue is hard to measure empirically other than through the type of simulations these authors used. This kind of work cannot be redone in the present study. Furthermore, there is plenty of anecdotal evidence suggesting that the problem is not more serious than in Asia, where it typically has been neglected. Therefore a rule of thumb allowing for 30 percent overvaluation will be adopted in interpreting the results, and this is judged to be conservative.

Rural Consumption Patterns and Nontradable Foods in Africa

As already noted, the consumption patterns of beneficiaries of a direct increase in agricultural income are a major determinant of the strength of agricultural growth linkages. The multiplier effect is most significant when incremental income is spent on labor-intensive, locally produced, nontradable goods and services. Infrastructure and regional characteristics in much of Africa are such that a significant range of goods and services fall within nontradables.

Household budget surveys across Africa consistently show basic foods to be the main consumer expenditure item in rural areas. Because the costs of transporting and marketing imports and exports of food are very high, most food consumption is from domestically produced sources. Exports of starchy food staples and livestock products to points outside of Africa are negligible. It can easily cost twice the f.o.b. cost of imported grain in West African ports to transport it to markets in the interior of West Africa (Delgado 1992).

Furthermore, although grain can be imported by African price-taking countries in large quantities at a constant price, imported cereals such as rice and wheat that are consumed by urban dwellers in Africa often are much more expensive calories on a per unit basis than local grain. Since much of the population of West Africa is very poor and grain consumption is sensitive to real income, only a small share of the people can substitute expensive imported grains for local food items. Thus it is not surprising that food staple markets are characterized by prices that vary depending on domestic supply and demand conditions, in a gap between export and import price parities with little or no external trade (Delgado 1991, 1992).

Since starchy food staples represent a large share of explicit or implicit consumer budgets in Africa, it follows that the real price of labor is likely to be closely linked to the price of the main domestic starchy staple. In West Africa, Delgado (1992) finds that internationally nontraded food staples such as millet, sorghum, plantains, and root crops accounted for 20 to 40 percent of total household expenditures in rural areas, and these staples were not well correlated with domestic prices of tradable foods such as rice and wheat. Relative prices for the nontraded food items listed, in terms of tradables in the region typically fluctuate more than 25 percent across years, particularly given the severe weather fluctuations observed in the period concerned. Kyle and Swinnen (1994) report that up to 50 percent of total calories consumed in some Central African countries come from nontradable roots and tubers.

Under these conditions, the price of nontraded food is positively linked in both directions to the price of (nontradable) labor, and both food and labor are nontradables in addition to being nontraded. The implication of this is that factors that shift the supply curve for food nontradables to the right can be expected to shift the supply curve of tradables in the same direction by lowering the costs of production of tradables in terms of nontradables (Delgado 1992).

Having such a high share of food consumption in the nontraded sector in parts of Africa (especially inland West Africa) implies that exogenous rural income growth has great potential to pull underutilized resources into the food sector. Thus, potential growth multipliers are high, even if consumption of locally produced manufactures is low.

Rural Income Distribution and Growth Linkages

Consumption patterns typically change across the income spectrum, and the nontradable content of intermediate inputs and final commodities consumed varies also. Therefore, it is reasonable to wonder whether some segments of the population have persistently higher contributions to growth multipliers. Is multiplier-type growth more likely to be concentrated among lower-income and smaller-sized farm households, or are higher-income, larger-sized farms more conducive to growth linkages?

Poor people in both Africa and Asia tend to spend a large share of their incomes and increments to income on basic starchy staples. These goods are produced locally and in most cases are labor-intensive. Higher-income rural households, on the other hand, tend to spend a greater portion of their incremental income on manufactured goods and preferred foods such as dairy products, meats, and fruits. As discussed earlier, the tradability of these items will vary greatly with infrastructure and location.

An early study by King and Byerlee (1978) estimated factor intensity and locational linkages of consumption patterns at various levels of income for a disaggregated set of goods in Sierra Leone. They estimated expenditure elasticities and marginal propensities to consume for each commodity used in the survey. Their results on factor intensities show that labor requirements arising out of consumption decrease as households' incomes increase. This supports the hypothesis that lower-income households consume more labor-intensive goods, and higher-income households consume more capital-intensive and imported goods, though only moderately so. Overall, consumption patterns appear to be relatively homogeneous, largely due to the uniformity of income distribution in Sierra Leone.

King and Byerlee's findings on locational linkages show that the marginal propensity to consume subsistence goods drops as incomes rise, rural consumers spend a greater proportion of their incremental income on rurally produced goods, the marginal propensity to consume products from urban centers is low, and higher-income groups tend to allocate a greater proportion of their income to imported goods than lower-income households do. Households at all income levels have high marginal propensities to consume rurally produced goods, with values falling slightly as incomes rise. Low-income households spend 7 percent more of their incremental income on rurally produced goods and services than high-income households (Hazell and R 1983).

Celis and Bliven (1991) examined consumption linkages in Zambia by estimating Engel function expenditures on various goods and services. Their estimates of marginal changes in budget shares indicate that 75 percent of incremental income went to food and 25 percent went to nonfood. This allocation of incremental expenditure to food did not vary across expenditure quintiles. They also found that improved agricultural technology did modify consumption patterns in favor of nonfood goods and services, which probably stimulated growth in the nonagricultural economy and hence increased multiplier effects.

Consistent with their assumption that cassava, millet, sorghum, and other starchy staples are tradable, and that local manufactures are nontradable, Hazell and R (1983) find that higher-income households in both Muda and Gusau had higher MBSs for nontradables than do lower-income households. Nontradables in Muda are nonagricultural and in Gusau they are agricultural. Consistent with this commodity difference and the usual view of preference changes with increasing incomes, higher-income households in Gusau did not have budget shares as high as low-income households in Muda.

Hazell and R (1983) argue that since low-income groups spend most of their income on foodgrains, which tend to be price-inelastic in supply, tradable income gains by this group may result in the generation of fewer linkages. This is because the magnitude of the true multiplier depends on there being an elastic supply of the goods and services demanded. Finally, the effects on income distribution of raising the incomes of lower-income households are not as significant as suspected, since higher-income households benefit more from multiplier effects through increases in "returns to capital, managerial skills, and skilled labor," which they have in relatively greater abundance. Hazell and R conclude that large-sized farms in their sample had the most desirable spending patterns for multiplied growth.

Growth Linkage Studies and Identification of Rural Growth Bottlenecks

Studies of consumption growth linkages are useful for assessing the strategic consequences of final and intermediate demand patterns. Even though prices do not enter the analysis directly, linkage analysis indicates which sectors are likely to be under price pressure once exogenous growth from the tradable sectors occurs. Furthermore, the greater the level of disaggregation, the more useful it is for this purpose.

The starting point for promoting economic growth in rural areas in almost all African countries is to alleviate supply constraints for agricultural exportables, principally through technological change that permits total factor productivity gains. Interventions to cut the unit costs of distribution of tradables will also improve the competitiveness of African economies. While the supply-side emphasis on the production cost and producer price incentives for exportables has long been accepted on the grounds of comparative advantage, the very important secondary effects that come when incomes from cash cropping are respent have tended to be ignored in the past. In any event, there has been less attention paid in the past 15 years - especially given the lackluster performance of agricultural commodities on world markets during that period - to the importance of improving the unit costs of production and distribution of both agricultural exports and nontradable foods in Africa.

The growth linkages literature shows that growth processes from successful interventions to develop areas of agricultural comparative advantage can be significantly curtailed by an inelastic supply of nontradable inputs, goods, and services. Thus, even if a country has the good fortune to have a breakthrough on the production side for an exportable, production costs will quickly rise if the ensuing demand for labor and inputs meets inelastic supply because increased labor demand has raised the cost of living significantly. This pinpoints one of the most important current areas for research on agricultural development strategy in Africa: the link between prices for the nontradable items that workers in the tradables sector consume and production costs for tradables. Although the present report cannot directly address these price effects, it will show where they are likely to be important.

Rural Economic Growth Strategy in Africa

The discussion in this chapter suggests that earlier studies, such as Hazell and R (1983) and Bigsten and Collier (1995), were premature in downplaying the potential for obtaining multiplied spin-off effects for regional growth, arising from the consumer spending of growing incomes of rural households under commercialization and technological change in Africa. On the contrary, it is suggested here that such spin-off effects are likely to be greatest in remote, poor areas, where the transaction costs of trade are high. Under such conditions, many local products and all local services are constrained by the level of local effective demand. Large parts of many African countries may fit this model well.

As in other parts of the world, economic growth in Africa will need an "engine" - a cut in unit production costs from technological change or a decrease in marketing costs from better infrastructure. The study of agricultural growth linkages will not help identify these engines for specific areas. However, such work does show that if supply-led growth is occurring somewhere in agriculture, if the benefits are widely spread and there are underemployed rural resources, then there is considerable scope for the stimulation of further economic activity that would otherwise be constrained by a lack of solvent local demand. However, unlike the case of Asia in the 1960s, many of the demand-constrained items in rural Africa may come from within the agricultural sector. Thus the growth problem may be less of an issue of how cities will pull the countryside along, as was previously thought, and more of how supply-side measures to start agricultural growth in rural areas can be helped to provide second-round and higher-round effects within agriculture itself. The next chapter lays out a model and a series of case studies for investigating these assertions.