A standard framework for
village general equilibrium
modelling

Hans Lofgren

Introduction

This chapter describers a standard computable general equilibrium (CGE) framework for evaluating the impact of economic ‘shocks’ - policy changes and exogenous events - on production, trade, and household welfare in a village economy. This framework makes it possible to incorporate considerable detail on how households’ welfare, incomes and expenditures are influenced by changes in technologies and markets, giving it an important role in a project that aims at a better understanding of the impact of the globalization on the well-being of farmers and other households in African villages.

Since the first applications in the mid-1970s, CGE models have become widely used in policy analysis in developing countries. While most models are for single countries, the underlying general equilibrium approach is applicable at different aggregation levels that range from households to small geographical areas within a country, individual countries, and further on to the whole world. In recent years, a growing number of models have been applied to analyse policy questions for regions within a country, including agriculture-focused village-level studies.^[14]

IFPRI has developed a standard CGE model written in the GAMS (General Algebraic Modelling System) software with the aim of making CGE analysis more cost effective and more accessible to a wider group of analysts.^[15] Since its introduction in 2001, the model has been applied to a large number of countries. This is largely due to two features of the computer code, both of which are relevant to the current project: separation of the model from the database, making it easy to apply the model in new settings; and facilitation of choice among alternative assumptions on how factor markets and macro constraints operate.

In this chapter, we will present a version of the standard model that has been adapted for village-level analysis. Compared to the original model, the changes are relatively few, demonstrating a high degree of commonality across CGE applications at different levels of aggregation. The changes that have been introduced provide additional options for the functioning of the government and factor markets. In addition, the fact that a village does not have a separate currency with an exchange rate has implications for how the interactions of the village with the surrounding economy are balanced. It is also important to note that, in a village model (and in the rest of this chapter), the terms ‘foreign’ and ‘rest of world’ refer to all other regions, inside or outside the country in which the village is located. Similarly, ‘exports’ and ‘imports’ refer to trade with the rest of world, be it inside or outside the country.

This is work in progress - it is likely that additional modifications (for example in the treatment of producer technology) will be introduced in light of the specific questions that will be addressed, the content of the quantitative databases, and qualitative information about the structure of the village economies.^[16]

Database

A social accounting matrix (SAM) is the main component of the database for the village model. The construction of village SAMs will also be a major component of the research activities of this project.^[17] Tables 9a and 9b display the stylized structure of a village SAM that could be applied to the model. Like other SAMs, this one is a square matrix that for a period of time (typically one year) accounts for the economy-wide circular flow of incomes and payments. The cells represent payments from the column to the row account. The SAM summarizes the structure of an economy, its internal and external links, and the roles of different actors and sectors. Its disaggregation is flexible and depends on data availability and the purposes for which the SAM is to be used. The households may be classified on the basis of their incomes sources or other socio-economic characteristics.

In addition to a SAM, the village model requires elasticity data (for production, consumption, and trade). It is preferable (but not necessary) to have data on physical factor quantities (especially for land and labour).

Model structure

The model is written as a set of simultaneous equations, many of which are non-linear. There is no objective function. The equations define the behaviour of the different actors. In part, this behaviour follows simple rules captured by fixed coefficients (for example, tax rates). For production and consumption decisions, behaviour is captured by non-linear, first-order optimality conditions of profit and utility maximization. The equations also include a set of constraints that have to be satisfied by the system as a whole but that are not necessarily considered by any individual actor. These ‘system constraints’ define equilibrium in markets for factors and commodities as well as macroeconomic aggregates (balances for savings-investment, the government, and the current account of the rest of the world).

The standard model is characterized by flexible disaggregation, pre-programmed alternative rules for clearing factor markets and macroeconomic accounts, transactions costs, and household home consumption. Transactions costs, which may be high and a source of significant welfare losses in developing country settings, are incurred when commodities are marketed (with separate treatments for exports, imports, and local sales of local output), leading to gaps between supply and demand prices. Home-consumed outputs are demanded at supply (farm- or factory-gate) prices. All other commodities (local output and imports) enter markets and are demanded at prices that include transactions costs. The inclusion in the model of home consumption and (often high) transactions costs allows the model to capture economic shocks on the poor.

Figure 1. Structure of Payment Flows in the Standard CGE model.

Figure 1 provides a simplified picture of the links between the major building blocks of the model. The disaggregation of activities, (representative) households, factors, and commodities - the blocks on the left side and in the middle of the figure - is determined by the disaggregation of the SAM. The arrows represent payment flows. With the exception of taxes, transfers, and savings, the model also includes ‘real’ flows (a factor service or a commodity) that go in the opposite direction.

Table 9a Initial section of the basic structure of village SAM for standard CGE model

Table 9b Second section of the basic structure of village SAM for standard CGE model

The activities (which carry out production) allocate their income, earned from output sales, to intermediate inputs and factors. The producers are assumed to maximize profits subject to prices and a nested technology in two levels. At the top of the nest, output is a Leontief or constant elasticity of substitution (CES) function of aggregates of value-added and intermediate inputs. At the bottom, aggregate value-added is a CES function of primary factors, whereas the aggregate intermediate input is a Leontief function of disaggregated intermediate inputs. Each activity produces one or more commodities, and any commodity may be produced by more than one activity. The model thus supports disaggregation of production activities (for example by farm size or land category) that permits analysis of ‘livelihood strategies’ by different groups of producers - an important issue in the analysis of distributional issues.

Given the assumption that they are small relative to the market, producers take prices as given when making their decisions. After meeting home consumption demands, outputs with both exports and village sales are allocated between these two destinations in shares that respond to changes in the ratio between the prices that the producers receive when selling in the village and the prices they receive when selling to the rest of the world. Some commodities may only have exports or only village sales. In markets of the rest of the world, the supplies of exports are absorbed by infinitely elastic demands at fixed prices - the small country (village) assumption. Supplies from local producers and the rest of the world (imports) meet local market demands (for investment, private consumption, government consumption, and intermediate input use). Some commodities may only have imports or only be supplied from local producers. For any commodity for which demand is met by both imports and local products, the ratio between the demand for imports and demand for local output responds to changes in the relative prices of imports and local output that is sold at home. In the markets of the rest of the world, import demand is met by an infinitely elastic supply of imports at fixed prices. In the local markets for products of local origin, flexible prices ensure that the quantities demanded and supplied are equal.

Any factor may be integrated traded with the rest of the world in an integrated market where the net trade quantity clears the market. Such a factor market closure may be particularly important for certain types of labour. Additional mechanisms for the clearing of factor markets have also been pre-programmed. The alternatives cover situations with a market-clearing wage in a situation with fixed (possibly full) employment (the standard neoclassical assumption), unemployment, and different degrees of mobility or segmentation within the market for any given factor.

The factor costs of the producers are passed on as receipts to the household block in shares that reflect endowments. If a factor is imported, a part of the cost is paid to the rest of the world. In a setting with factor exports, part of the income of the factor in question comes from the rest of the world. The household block is defined broadly. Apart from (representative) households, it may also include other nongovernmental institutions, most important one or more ‘enterprises’ (which also may be labelled ‘firms’ or ‘corporations’). In addition to factor incomes, the different entities within the block may receive transfers from the government (which are indexed by the Consumer Price Index, or CPI), the rest of the world (fixed in foreign currency), and other institutions within the household block. These incomes may be spent on savings, direct taxes, transfers to other institutions, and, for the households, consumption. Savings, direct taxes, and transfers are modelled as fixed income shares. Consumption is split across different commodities, both home-consumed and market-purchased, according to LES (Linear Expenditure System) demand functions (derived from utility maximization). Enterprise transfers to households represent distributed profits.

For the government, only village-level expenditures and revenues are covered. The government may receive direct taxes from the households and transfers from the rest of the world. It then spends this income on consumption (typically fixed in real terms), transfers to households, and savings (which are fixed, representing the contribution of the government to village investments). The rest of the world (more specifically the current account of the balance of payments) receives payments for the (factor and commodity) imports of the village, and then spends these earnings on (factor and commodity) exports from the village, on transfers to government activities (representing the contribution of the rest of the world (including the central government) to current government expenditures in the village in excess of revenues from taxes and other sources), and on ‘foreign savings’ (savings from the rest of the world financing part of village investments, corresponding to the current account deficit of the village). Finally, the savings-investment account collects savings from all institutions and uses these to finance local investment.

As noted, the user has the option to choose among a relatively large number of pre-programmed alternative closure rules for the three macroeconomic accounts of the model - the (current) government balance, the balance of the rest of the world, and the savings-investment balance. For single-period welfare analysis in a village setting, the appropriate choice may be to assume that the account-clearing variables are government transfers to the rest of the world (in effect to the central government, a residual given the prior specification of rules for the determination of all other government receipts and expenditures, including government savings), the real exchange rate (given a fixed level for foreign savings), and the savings rates of selected households and enterprises (given rules determining all other savings flows and the need to finance a fixed bundle of investment goods). The fact that the village does not have a separate currency exchange rate does not invalidate the notion that the real exchange rate clears the payments flows between the village and the rest of the world. However, if the exchange rate variable is eliminated (or fixed at unity), a new variable is needed to clear the rest-of-the world balance. This role may be played by the price index for local output sold inside the region. For any given level of export and import prices, a decline in this price index corresponds to a real depreciation (the price of traded commodities increases relative to non-traded commodities); an increase corresponds to a real appreciation.

Applying the model

The basic standard model is used for single-period comparative static analysis, implying that the impact of the shock (or the combination of shocks) that is being simulated is found by comparing the model solutions with and without the shock(s). It is straightforward to simulate a wide range of shocks. In village analysis, important simulations may revolve around changes in export and import prices, technology, and transactions costs. Each model solution provides an extensive set of economic indicators, including GDP (here gross village product), sectoral production and trade volumes, factor employment, consumption and incomes for representative households, commodity prices, and factor wages.

References

Holden, S., Lofgren, H. & Shiferaw, B. 2003. Economic Reforms and Soil Degradation in the Ethiopian Highlands: Analysis with a Village General Equilibrium Model. (mimeo)

Isard, W., Azis, I.J., Drennan, M.P., Miller, R.E., Saltzman, S. & Thorbecke, E. 1998. Methods of Interregional and Regional Analysis, Ashgate Publishing Company, Brookfield.

Lofgren, Hans, Rebecca Lee Harris & Sherman Robinson with assistance from Marcelle Thomas and Moataz El-Said. 2002. A Standard Computable General Equilibrium (CGE) Model in GAMS. Microcomputers in Policy Research, Vol. 5. International Food Policy Research Institute Washington D.C. (also available at www.ifpri.org).

Lofgren, H., Robinson, S. & El-Said, M. 2003. Poverty and Inequality Analysis in a General Equilibrium Framework: The Representative Household Approach. Forthcoming as Chapter 15 in Bourguignon F. and Pereira da Silva, A.L. (eds), Toolkit for Evaluating the Poverty and Distributional Impact of Economic Policies.

Robinson, S., Cattaneo, A. & El-Said, M. 2001. Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods. Economic Systems Research,. 13 (1):47-64.

Taylor, J. E. & Adelman, I. 1996. Village Economies: The Design, Estimation, and Use of Villagewide Economic Models. Cambridge University Press, New York..