Multisector Models

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Multisector Models


Economists use models to understand different aspects of the economy. A multisector model is used primarily to study the allocation of resources across different economic activities. A multisector model, however, has more uses than simply the study of the distribution of resources. Some of the most exciting work being done with multisector models is in the economic theory of growth and development. This work originates in the observation that as an economy grows its production activities and employment shares move from agriculture to industry and services, with services eventually claiming the vast majority of the countrys employment potential. So, if economists can understand what causes these shifts in sectoral employment shares, they might understand what makes countries grow; conversely, if they can understand what makes countries grow, they might understand how the workforce allocates its time across economic sectors.

What is an economic sector? The United Nations has produced a system of activity classificationsthe ISIC (International Standard Industrial Classifications), designed to help classify economic sectors across countries in a comparable way. Using the ISIC, one can define sectors as one-digit, two-digit, three-digit, and so on, depending on the detail required. For example, agriculture, industry, and services are one-digit sectors, whereas textiles and vehicle manufacture are two of the many two-digit sectors within manufacturing.

Economists, however, find that a more useful way of defining a sector draws from the objectives of the multisector model in hand. Examples of multisector models can be found in the fields of economic growth, development economics, labor economics, international trade, spatial (geography) economics, business cycles, and others. In each case, the definition of the sector may differ, and the challenge facing the applied economist is to find the correspondence between the way the sector is defined in the model and the ISIC classification. For example, a multisector model may define sectors according to whether the goods produced within a sector are primary, secondary, or tertiary; agricultural, industrial, or service goods; tradable or nontradable; and public or private. In addition to matching the sectors in the model to the ISIC classification, for other purposes a multisector model may define sectors according to whether the goods are traditional or modern, rural or urban, produced in a formal or informal business environment, and produced at home or in the market.

Multisector models in economic development have added to our knowledge of how an economy leaves the stagnant agricultural state and enters modern growth. An important example is the multisector model by Gary Hansen and Edward Prescott (2002). Their model has a traditional sector and a modern sector. Both sectors produce the same goods but with different technologies. Land is a fixed factor that is used only in the traditional sector but not in the modern sector. Modern technology has a higher rate of productivity growth than traditional technology. Both technologies have diminishing marginal return to their inputs. Hansen and Prescott show that, initially, resources are devoted only into the traditional sector, but as the technology of the modern sector improves, more resources shift into it.

A related class of multisector models has enriched our understanding of the declining share of agriculture, the rise and fall of industry, and the rising share of services observed in most countries that have experienced modern growth. L. Rachel Ngai and Christopher Pissarides (2007) show that when sectors produce goods that are complements of each other, resources move from the sector with high productivity growth to the sector with low productivity growth. Since agricultural and manufacturing sectors experience, on average, faster productivity growth than the services sector, resources are shifted away from agriculture and into manufacturing and services. As the agriculture sector shrinks, eventually resources also shift away from manufacturing and into service production.

So far, the examples of what defines a multisector model are based mainly on technology, but there are other definitions, such as those that are based on preferences and institutions. Addressing the same issue of the decline in agriculture and the rise of services, Piyabha Kongsamut, Sergio Rebelo, and Danyang Xie (2001) present a multisector model that is based on preferences. In their model, agriculture produces an inferior good and services a luxury good; then, as incomes rise, demand shifts from agriculture to services. As a result, resources shift from agricultural to service production.

A third class of multisector models relies on an institutional definition. One class of institution-based multisector models is motivated by the fact that official statistics only report formal market activities. However, there are plenty of studies that show that a large fraction of resources is allocated to informal activities and activities at home. These studies are based on the time-use surveys conducted by individual countries, such as the United Kingdom and the United States, and on a cross-country survey conducted by the World Bank. The production activities at home and in the informal sector can all potentially be produced in the formal market sector, which will then enter the official statistics. The economic activities at home include child care, cooking, cleaning, and so on. If the child is sent to a day-care center, its care will be recorded as part of GDP (gross domestic product). Home production is substantial in most of the time-use surveys. For example, it took up as much time as market production in the United States during the 1990s. The economic activities in the informal sector in general refer to activities that evade government regulation, including tax evasion. This is a more common phenomenon in developing countries.

There are many reasons why economists care about whether a certain activity is done in the formal market sector or in the informal or home sector. Two intuitive and important reasons concern accurate measurement of economic activity and the formulation and implementation of public policies that will increase social welfare. Knowing what fraction of the economys resources are devoted to the formal market sector is important for understanding and interpreting measured GDP, especially when comparisons are made across countries. Second and perhaps more importantly, it might have different policy implications not only for welfare but also for measured economic activities.

A good example is the multisector model by Stephen Parente, Richard Rogerson, and Randall Wright (2000). In their model, goods can be produced in the nonmarket sector or in the market sector. They show that distortionary policy that affects capital accumulation has a larger impact on measured GDP in their multisector model than in the usual one-sector model. This improves our understanding of the reasons that cross-country income differences are so large. Models with home and market sectors are also used for explaining the dynamics of labor supply. Taxes on the market sector play an important role in these models as they shift production from the formal market to the home or informal sector.

SEE ALSO Economic Model; Input-Output Matrix; Models and Modeling; Social Accounting Matrix; Structural Transformation; Two-Sector Models


Hansen, Gary D., and Edward C. Prescott. 2002. Malthus to Solow. American Economic Review 92 (4): 12051217.

Kongsamut, Piyabha, Sergio Rebelo, and Danyang Xie. 2001. Beyond Balanced Growth. Review of Economic Studies 68 (4): 869882.

Ngai, L. Rachel, and Christopher A. Pissarides. 2007. Structural Change in a Multisector Model of Growth. American Economic Review 97 (1): 429443.

Parente, Stephen L., Richard Rogerson, and Randall Wright. 2000. Homework in Development Economics: Household Production and the Wealth of Nations. Journal of Political Economy 108 (4): 680687.

Liwa Rachel Ngai