Three approaches have dominated development economics research on farm/non-farm linkages: the input-output (I-O) approach, the expenditure system approach and village-wide modelling. CGE modelling techniques have recently been developed to study village and small regional economies, offering a new perspective on the impacts of exogenous income changes on rural economies.
Input/output models
I-O or Leontief models offer a snapshot of linkages across production sectors in national, regional or village economies. The elements in the rows of an I-O matrix represent sales of output from a row sector to other sectors, shown in the columns; that is, forward linkages. The column elements represent backward linkages, purchases of inputs by column sectors from other row sectors. In general, the larger the elements in the row and column for a sector, the larger the sector’s potential to stimulate growth through creation of forward and backward linkages. The extreme case of all zero entries in a Leontief matrix corresponds to an economic enclave devoid of linkages. Leontief multipliers calculated from I-O matrices measure the multiplicative effect of changes in final demand for sectoral outputs when the household sector, investment, government and rest-of-the-world demands are treated as exogenous.
The first studies of farm/non-farm growth linkages were based primarily on input-output models. Hirschman (1958), citing the sparseness of rows and columns corresponding to traditional agriculture in I-O matrices for countries, criticized agriculture for its lack of forward and backward linkages with the rest of the economy. This view was challenged, most notably by Adelman (1984) and Mellor (1976), and the list of potential linkages has been expanded from production to consumption and fiscal linkages. Even if staple production generates few backward and forward production linkages, for example, a change in exogenous demand for staples, such as export, may raise the incomes of staple-producing households. These households may in turn spend their new-found income on goods and services that include agricultural and non-agricultural commodities. Their expenditure demands may thus stimulate a new round of production increases as firms expand their output to satisfy household consumption demands and increasing demand for intermediate inputs. If staple-producing households have expenditure patterns favouring non-agricultural goods, the increased demand for staples may generate important production linkages through household expenditures.
Expenditure-system models
The potential importance of rural households as a source of demand for farm and non-farm goods stimulated the growth of a new literature on farm/non-farm linkages focusing on rural-household expenditure patterns. Mellor (1976) emphasized the importance of consumption linkages in transmitting changes in rural incomes into demand for farm and non-farm goods, tradables and non-tradables. Utilizing an expenditure system approach, Mellor (1976), Hazell and Roell (1983), Rangarajan (1982) and others offer compelling evidence for the existence of farm/non-farm linkages.
The approach used in this “new economics of growth” research generally entails estimating household expenditure functions for various classes of goods - farm and non-farm, tradables and non-tradables. The estimated equations are used to ascertain farm/non-farm linkages by comparing the impacts of changing farm incomes, for example those resulting from a new agricultural technology, on demand for these goods. Hazell and Roell (1983), for example, concluded that in Muda (Malaysia) and Gusau (Nigeria) the share of increments in total household expenditures allocated to foodgrains is lowest in high-income households, and that the share allocated to local non-tradables is highest in these households.
The expenditure system approach has two important limitations. First, it is partial. Estimated marginal propensities to spend income on farm and non-farm goods are used to identify and quantify farm/non-farm linkages. Modelling expenditures by different household groups is a critical first step in modelling potential farm/non-farm linkages. Without data on the production side, however, it is not possible to ascertain whether these potential linkages actually stimulate growth in the local economy, because the local content of locally supplied goods is not known; nor is the local content of household investment demand known. These shortcomings are the basis for Hart’s (1989) critique of Hazel and Roell (1983). Hart argues that Hazel and Roell’s predictions of growth linkages were exaggerated, precisely because they did not take into account these production and investment considerations.
A second limitation of most of the growth-linkage literature is that it generally assumes perfectly elastic supply responses, ruling out price effects in what are essentially Keynesian demand-driven models. This assumption may be valid under some circumstances, such as when under-utilization of local factors makes the supply of farm and non-farm goods highly responsive to changes in demand, with little or no inflationary pressure. Where non-linearities in production and local resource constraints create less than perfectly elastic supply responses, however, fixed-price linear models are likely to exaggerate income and production effects of policy changes (see Taylor 1995; Haggblade, Hammer and Hazell, 1991). CGE models incorporating non-linearities and endogenous prices have been utilized extensively at the national level. These models generally treat rural households as homogeneous, however, and do not take into account the diversification of rural economies, through which many of the most important farm/non-farm linkages are likely to play themselves out. The diversification of rural economies from farm to non-farm activities is one of the most pervasive and far-reaching features of contemporary LDCs. As rural economies become increasingly diverse, farm/non-farm linkages take new forms, with impacts felt increasingly in small and intermediate cities emerging in traditionally agricultural areas instead of in traditional urban centres. There also appears to be a diversification away from traditional crop activities in agricultural households (see Reardon, Delgado and Matlon, 1992; Taylor and Adelman, 1996).
SAM models
SAM models are designed to capture the complex interlinkages among production, institutions - including households - and the outside world. SAMs provide a starting point for village economy-wide analysis. They are a useful expository device for portraying the structure of rural economies, and they are the basic data input for SAM multiplier and general-equilibrium modelling (Taylor and Adelman, 1996). They summarize and neatly illustrate flows of inputs, output and income between food production and other productive sectors in an economy, flows of income between production activities and households, channelling of household incomes into consumption and investments and exchange of goods and factors between an economy and the rest of the world. The great strengths of the SAM are its comprehensiveness and flexibility in adapting to diverse institutional settings and economic structures and in providing an accounting framework to address diverse policy and planning issues.
Village SAM models
In theory, a SAM can be developed for any economy, from the world to a village to an individual household. The first application of SAMs to village economic analysis appears in Adelman, Taylor and Vogel (1988). Since then a number of other village SAM studies have been carried out (see for example Lewis and Thorbecke, 1992; Subramanian and Sadoulet, 1990; Parikh and Thorbecke, 1994). The village social accounting framework, like its national counterpart, is a form of double-entry accounting. It presents accounting entries in income and product accounts and in input-output production accounts as debit and credit entries in income balance sheets of institutions and activities. Activities may include farm and non-farm production, or any disaggregation of the two. Institutions in SAMs typically include different household groups, governments and the rest of the world. In the context of economy-wide modelling, institutions are categories of economic actors. It is assumed, of course, that all members of a given category of actors interact in a similar manner with other categories and activities in a village.
Entries in a SAM include:
intermediate input demands between production sectors (the Leontief matrix is contained within the SAM);
income or value-added paid by production sectors to different types of labour such as men or women, educated or non-educated or different ethnic groups, land or capital;
distribution of labour or capital income across different household groups;
distribution of household group expenditures across savings, consumption of domestically produced goods and services, and imports.
A government account collects income from activities and households and redirects it within the system to government demand for goods and services, transfers to production activities or household groups, saves it, or uses it to pay foreign institutions for imported goods and services or to repay debts.
The total product of each activity must be allocated to some use inside or outside the economy, such as intermediate demand, consumption, investment, government demand or exports. Gross receipts of each activity must be allocated to some entity inside or outside the system, including purchases of inputs from other activities, payments to labour and capital, imports, taxes and savings. A salient characteristic of SAMs, derived from double-entry accounting, is that equality must be maintained between the sum of expenditures - the column total - and the sum of revenues - the row total - for every account in the system.
Village SAMs have the same conceptual framework as national SAMs, but they depart from national SAMs in specific ways related to the unique nature of village economies and institutions. Some examples of village production activities include subsistence food production, wood gathering, export crop production, handicrafts, traditional healing and religious activity in a temple or mosque. Examples of village institutions are households grouped by land holdings or base-period calorie intake, compounds grouped by compound landholdings, internal and international migrants and village schools. The rest of the world in village models includes the regional and national economies outside the village and the world economy, which does not share the same currency as the village. Examples include marketing cooperatives, plantations, weekly markets, nearby centres or towns, labour commuting and domestic and foreign migrant labour markets. For a village, the rest of the world includes regional and national governments.
One conceptual departure of the village SAM from the national SAM is that rest-of-the-world subaccounts of village SAMs do not necessarily balance. A regional or national government, for example, may be a net surplus appropriator or a net subsidizer of a village. Remittances to village households from migrants abroad through a foreign account may not necessarily be used to purchase goods from abroad, but may be used to purchase goods produced in the village or brought into the village from regional or national markets. Methodologically, these inconsistencies are addressed through the use of entries representing payments between rest-of-the-world accounts or through aggregation, for example by combining some rest-of-the-world accounts, the sum of whose transactions with the village must balance. Another departure of village SAMs from national SAMs is that in village SAMs, non-monetary transactions are typically important. These non-monetary transactions include production for own consumption, labour exchanges or labour lending, interlinked factor markets, interlinked factor and non-factor-input markets and access to commons.
SAM multiplier models
To move from the village SAM as an accounting framework to a village model first requires assumptions about the behaviour of village actors and the specification of production functions. The SAM summarizes transaction flows among economic actors in the village. In designing village models, the simplest assumption is that the responses of village actors to income changes are strictly proportional to the total level of activity in each account - that is, the column totals in the SAM. This means that on the expenditure side, marginal expenditures by village institutions equal average shares derived from the SAM; on the production side there is a fixed input-output technology. These assumptions are restrictive but necessary to estimate fixed-price village SAM multipliers (described below), which are analogous to the Leontief multiplier in input-output analysis. These multipliers are the basis for the SAM policy experiments in Adelman, Taylor and Vogel (1988), Golan (1990), Subramanian and Sadoulet (1990), Lewis and Thorbecke (1992), Ralston (1992) and Parikh and Thorbecke (1996).
Constructing a village model also requires specifying which accounts in the village SAM are endogenous and which are exogenous. This choice is critical in modelling the impact of change on village economies, because the modeler is strictly speaking free to change only exogenous variables and model parameters. The endogenous accounts in the model capture the responses of village economic actors to changes in the exogenous accounts or in parameters. In village models, the logical choices for exogenous accounts are the government and the rest of the world. If the village capital market is fully integrated with outside capital markets, it may be treated as exogenous as well. In most LDC rural areas, however, capital markets are local at best, with the result that local savings constrain investments. In this case, capital markets should be included in the endogenous SAM accounts. Capital is treated as endogenous in all five of our village models for Mexico.
The village multiplier matrix contains estimated total direct and indirect effects of exogenous income injections on the endogenous accounts in the village SAM. The village Leontief multiplier is one component of the village SAM multiplier. The SAM multiplier, however, also captures expenditure linkages induced by changes in production activities through their effect on institutional incomes in the village. These expenditure linkages are typically stronger than production linkages in village SAM models.
Linkages between production and factors, between factors and households and between households and production shape the impact of exogenous changes on a village economy. The village multiplier consists of multiple rounds of feedback among subaccounts in the village SAM. Each new injection of income into a SAM subaccount first swirls around the local subsystem of accounts and is then transmitted to other subsystems of the SAM. This process continues as part of the new income generates a derived demand for goods and services or induces a redistribution of income flows within the village, while some leaks out.
The major strength of SAM multiplier models for estimating farm/non-farm linkages is that they integrate the I-O and expenditure-system approaches into a single model that captures production linkages, consumption linkages and interactions between the two. They thus offer a much more comprehensive and potentially reliable means to identify and estimate the importance of farm/non-farm linkages. Both the I-O and expenditure system approaches may be viewed as representing special cases of SAMs. Leontief multipliers are one component of SAM multipliers, because they ignore consumption linkages operating through the household sector. Multipliers obtained from expenditure-system estimates may be viewed as another component of SAM multipliers, in which production-side linkages are ignored.
Despite its strengths, the village SAM multiplier has the same basic limitations as its national counterpart, although some of these are less important in the village context. First, it is a fixed-price model. In a perfect neoclassical village economy, all transactions are for goods and services whose prices are determined by markets outside the village; but because the neoclassical village is assumed to be a completely open economy, the SAM village income multiplier of an exogenous income change is always unitary. An actual village is characterized by market imperfections that may cause village prices to diverge from market prices outside the village. In simulations using village SAMs, the critical questions are whether prices vary in response to exogenous changes and whether variations in price induce changes in the SAM share matrix. In general, the fewer the local resource and technological constraints on production, the stronger the case for using SAM multiplier models.
A second limitation of SAM multiplier models, related to the first, is the assumption that supply is perfectly elastic; that is, SAM models assume a Keynesian, demand-driven system. Even if supply response is elastic in the long term, it may in some cases be inelastic in the short term; crop production, especially for perennials, is a case in point. One way to incorporate inelastic supply response into SAM multiplier models is to impose constraints on production in the form of a perfectly inelastic supply response in some sectors, as in the second and third experiments described below; see Subramanian and Sadoulet (1990) and Lewis and Thorbecke (1992), or beyond predetermined output levels (Parikh and Thorbecke, 1994).
Third, SAM multiplier models assume that production utilizes linear, fixed-proportion technologies and that average and marginal expenditure propensities are the same. The second assumption can be relaxed by incorporating marginal rather than average shares into the SAM expenditure shares matrix prior to calculating the multiplier matrix. These marginal budget shares may be obtained from econometric expenditure-system estimates.
Village CGEs
Village CGE (VCGE) models overcome these limitations. They combine the strengths of microeconomic household-farm models (see Barnum and Squire, 1979; Singh, Squire and Strauss, 1986) with those of SAM-based, village-wide models. Although both SAM and VCGE models use village or mini-regional SAMs as their data base, VCGEs capture price effects, nonlinearities in household-farm responses to policy changes and the implications of family resource constraints on production elasticities. Household-farm models are useful for estimating the effects of policy changes on production and consumption in individual households. They do not capture production and expenditure linkages among households, however, and recursive household-farm models ignore market imperfections, which can play an important role in household-farm economies (see de Janvry, Fafchamps and Sadoulet, 1991). These include factor-market imperfections caused by the high cost of separating management from labour on household farms (see Lopez, 1986; Bardhan, 1988). Household-farm micromodels also ignore general-equilibrium feedback effects (see Braverman and Hammer, 1986). As demonstrated above, village SAM models reveal income linkages among households that play an important role in shaping the impacts of policies on village incomes. In the fourth section of this chapter a microregion CGE is utilized to explore the impacts of exogenous income changes on the village-town microregion - that is replicating with a CGE the experiments in the third section of the chapter that use a SAM multiplier approach.
Structure of the village/town CGE model
The microregional CGE is centred on a household farm of the type prevalent in rural Mexico, engaged in maize production and a portfolio of other economic activities, including migration. The model captures production and expenditure linkages within villages, between villages and a nearby town and between the village/town microregion and the rest of Mexico, including household consumption and production demand for manufactured goods. Migration from Mexico to the United States and internal migration are modelled explicitly as a function of the returns to migration and the returns to family labour in the village/town microregion. The model consists of five blocks of equations for each of the village and town economies, linked by commodity and factor markets. The five equation blocks are a household-farm production block, a household-farm income block, an expenditure block, a set of general equilibrium closure equations and a price block.
In the town and each of the villages, household-farm production includes four production activities and one commercial sector that serves to import goods into the village from the town or the rest of Mexico or into the town from the villages or the rest of Mexico. Production in each of the sectors is carried out using two variable factors - family labour and hired labour - and two fixed factors - physical capital and land. In contrast to the traditional neoclassical household-farm model, it is not assumed that family and hired labour are perfect substitutes.
Household-farms are assumed to maximize utility defined by consumption goods and leisure. On the production side, this implies maximizing net farm income from the five production activities, given market prices for output and either market or shadow prices for factors of production and intermediate inputs. Endogenous shadow prices include family wages, which equal the marginal utility of leisure divided by the marginal utility of income. Physical capital and land inputs are fixed in the short term, but family and hired labour are variable inputs.
The household-farm sector in our model consists of three groups: commercial, subsistence and net-buyer households. Commercial households are net-surplus producers of agricultural goods. Subsistence households engage in crop production for their own use but typically supplement this with income from non-crop production, wage labour or migration. Net-buyer households have minimal or no involvement in crop production. Household-farm income is the sum of wage income, capital, land and family-labour value-added from household-farm production activities and migrant remittances. Migration from Mexico to the United States and internal migration are a function of the differential between average migrant remittances specific to household groups and the shadow price of family labour in village production activities. The expenditure block includes the consumption demand for village and town products and manufactured goods produced elsewhere in Mexico, leisure, savings, including investments in physical and human capital such as schooling, taxes and some household-to-household transfers.
The general-equilibrium closure equations include village/town market-clearing conditions for factors and goods, a savings/investment balance and a trade-balance equation. For goods and factors for which the village/town economy is a price-taker in regional markets, that is village/town tradables, the market-clearing conditions determine net village/town marketed surplus. For non-tradables, they determine local prices. The savings/investment balance constrains investments in physical and human capital to be self-financed, that is out of local savings. The trade equation constrains the value of village/town exports of goods and factors to equal the value of village/town imports, minus net borrowing from outside the local economy - a village/town analogue to foreign savings in national CGE models. It represents the redundant equation in our village/town CGE system.
Prices of village/town tradables are fixed, determined by regional markets or government policy. Prices of non-tradables are determined by interaction of local supply and demand. Family wages adjust to ensure that family time allocated to production activities, migration and leisure equals total family time allocations. The price of land is also endogenous, because it is assumed to be fixed and equal to its marginal value product in village/town production activities.
