The meaning Input-Output Models

Input–output models are general equilibrium models defined for national or regional economies. They are based on a tableaux of transactions by groups of industries that are referred to as sectors. Pioneered by Wassily Leontief, they build on systems of national accounts that track gross product and gross income and also include measures of intermediate transactions. These models decompose all industrial production in whatever region is being modeled into groupings of industries (sectors) that have distinctive production structures.

Wassily Leontief’s brilliant insight in developing these models was to recognize that economies classified according to these production structures could then be generalized so that the final production measures in national or regional accounts could be mathematically related to measures

of industrial output in particular sectors. Input–output models typically are built around a matrix of transactions.

The sales (or output) of any given sector are distributed as sales to other sectors (intermediate sales) and sales to categories of final demand (consumption, investment, government, and exports to other regions). In any sector, the distribution of sales is paralleled by accounts that describe where a sector purchases the inputs needed to produce its output. These are divided among purchases from other sectors, purchases from sources of value added, and imports from other regions. The grouping of industries into sectors is based on an analysis of the structure of input (purchase) requirements such that each sector has a distinctive input structure.

The transactions matrix in an input–output model is generalized into a system of input coefficients, defined by dividing the purchases in a sector into proportions of total purchases. Through appropriate matrix arithmetic manipulations, these input coefficients can be modified to represent sector-to-sector specific “multipliers.” The multiplier concept is at the heart of input–output models. These multipliers relate levels of sales (output) to levels of final demand in specific pairs of sectors.

Input–output models frequently are specified so that the multiplier measures are expressed in multiple ways such as measures of industrial output, employment, and labor income. Input–output models can be estimated by surveys of national or regional economies. However, they frequently are estimated for regions through nonsurvey approaches and have various degrees of “closure.” In regional applications, it is common to include in the multiplier structure of these models components of the income and final demand accounts that are strongly tied to levels of local production such as personal consumption expenditures and labor income.

Input–output models are conceptually similar to several other widely used models of multipliers, including simple economic base models and regional econometric models. Simple economic base models do not distinguish the magnitude of multipliers of individual sectors; instead, they simply describe total output or employment as a function of export activity. Regional econometric models develop more complex multiplier relations than those found in regional input–output models. They extend the mathematics of these models to deal with temporal patterns in multipliers and provide more sophisticated measures of impact than those provided by input–output models. —William Beyers