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# The Global Effort to Eradicate Rinderpest - International Food Policy ...

The Global Effort to Eradicate Rinderpest - International Food Policy ...

## 11. CONCLUSIONS

ANNEX: TECHNICAL DETAILS OF SAM MULTIPLIER ANALYSIS Overview of SAM Multiplier Analysis Input-output (I-O) models have a storied history in economic analysis. The basis of I-O analysis is the input-output table, in which economywide transactions of productive sectors are recorded (at varying levels of aggregation, depending on data availability). The rows of an input-output table represent the sales or income generated by one sector from other sectors, while the columns detail the payments or purchases made by a sector to other sectors. Input-output tables also contain information on the valueadded generated in an economy (this typically includes salary and tax payments) and final demand resulting from household consumption, investment, government spending, and net exports (Miller and Blair 1985; Sadoulet and de Janvry 1995). SAMs expand upon this information by specifying different types of factor accounts and households that interact in the economy. In many cases, household accounts are disaggregated spatially (urban and rural or by specific regions in the country) and by income class (poor and rich at a minimum, with some SAMs elaborating on income quartiles or deciles) (Kiringai et al. 2006). Input-output tables can be used to detail the linkages between productive sectors in the economy and to assess how changes in final demand influence each sector. One means by which to do this is through the calculation of I-O multipliers. Define A to be the matrix of fixed input-output coefficients from productive sectors. The elements of the A matrix, aij, are the technical coefficients of sector i’s use of input j and are calculated by dividing the ij-th entry of the input-output table by output in sector j. Let X be the vector of final demand and y the vector of output for sectors 1 through n. Then, the I-O table can be rewritten in matrix form as Ay + X = y, or (I-A)y = X. To obtain output multipliers, one needs to solve the previous equation with respect to y, which provides the standard Leontief inverse matrix, that is: y � (I � A) �1 X (1) In equation (1), the multiplier matrix, (I-A) -1 , details the total change in output in sector j resulting from a change in final demand for the output of that sector (Miller and Blair 1985). The total output multiplier (in other words, the direct and indirect effects on other sectors) is computed using the column sum of the aij terms. Income and employment multipliers can also be determined through a like process. The income multiplier from a change in final demand in sector j is the sum of the product of the household income received from all productive activities and the technical coefficient, aij, meaning: n H j � � an �1,ia ij (2) i�1 Income multipliers can be transformed such that they measure the effect of a change in payments to households; these are termed “Type I” multipliers and are obtained by dividing equation (2) by a household’s income from sector j. Employment multipliers are analogous to income multipliers, but involve the technical coefficients for labor rather than households. One often finds in the literature mention of “Type II” multipliers; these refer to multipliers in which households (or labor) are endogenized into the A-matrix and thus tend to lead to larger multipliers than Type I multipliers. SAM multipliers treat factors of production and households as endogenous accounts and are part of the A matrix above. Consequently, SAM multipliers tend to be larger than conventional I-O multipliers (Sadoulet and de Janvry 1995). As noted above, changes in the output of a sector arise from exogenous changes in final demand, which can come from an increase in export demand, government spending, or private investment. Consequently, the impact of the PARC program on the broader economy in a given country can be estimated simply by deriving Leontief multipliers and multiplying these by the expenditure from the 49

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