Regional Input-Output ModelsAssumptionsNational input-output tableBalanced Regional Input-Output TablesUnbalanced Regional input-output TableRegional Input-Output TablesInterregional Input-Output tableMultiregional input-output tables—trade matricesCommodity Flow TableMultiregional Input-Output tableMIT OpenCourseWarehttp://ocw.mit.edu 11.481J / 1.284J / ESD.192J Analyzing and Accounting for Regional Economic Growth Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Regional Input-Output Models Xin Li Reference: Karen R. Polenske. 1995. Leontief’s Spatial Economic Analyses, Structural Change and Economic Dynamics 6: 309-318Assumptions • Constant returns to scale • Homogeneous products with no joint production • Constant direct input (technology) coefficient • A demand-driven modelProducing industries National input-output table Purchasing industries FD FD= final demands, including m X m Gross National Product • Personal consumption expenditures • Gross private capital formation • Net inventory change • Net foreign exports • Federal, state and local gov’t purchase VA= Value added, including • Wages and salaries • Rent • Depreciation • Taxes etc. VA Gross National Income m = number of industriesBalanced Regional Input-Output Tables Import Export from to other other regions regions Purchasing industries (+) (-) FD m X m m x 1 m x 1 Sum of each row = sum of each column Assumption: Technology coefficients differ by region VA Producing industries Region 1 m = number of industriesUnbalanced Regional input-output Table Purchasing industries FD • Sum of each row: total consumption only by purchasers within the region. • Sum of each column: total inputm X m requirements of each industry, regardless of the location of production. • Sum of each row ≠ sum of each column VA m = number of industries Region 1 Producing industriesRegional Input-Output Tables Purchasing industries‘ FDFDPurchasing industries‘ FDFDProducing industries m x m Producing industries m x m Region n VAVAVAVARegion 1 Purchasing industries‘ FDFDRegion 2 • For a regional table, the sums of corresponding rows and columns will not necessarily be equal. • The difference is attributable to interregional trade. m = number of industries Producing industries VA VAn = number of regions NationInterregional Input-Output table m x mm x mm x mm x mm x mGNPGNINationalflow tablem x mm x mm x m m x mm x mm x mm x mm x mm x mm x mRegion 1 Region 2 Region n TotalRegion nRegion 2Region 1Total1 1m FD m FD m FD1 m FDTotaloutput1mVA1mVAmVA111mVATotalinputRegionalIO tablesFigure by MIT OpenCourseWare, based on Polenske (1963).Shipping region Multiregional input-output tables— trade matrices Receiving region‘ Receiving region‘ n x n Shipping region n x n Industry m Industry 1 Industry 2 Receiving region Assumption: Technology coefficients are the same for all regions • Sum of each row: For a given industry, total outflows from a region. • Sum of each column: for a given industry, total inflows into a region. • Sum of each row ≠ sum of each column Shipping region n x n • The difference is net foreign export m = number of industries Total n = number of regionsCommodity Flow Table Foreign Foreign export import Total Receiving region (+) (-) output Regional Demand n X n n x 1 n x 1 Shipping region Industry 1 n = number of regionsMultiregional Input-Output table n x nn x nn x nn x nn x nGNPGNINationalflow tablen x nn x nn x n n x nn x nn x nn x nn x nn x nn x nIndustry 1 Industry 2 Industry m TotalIndustry mIndustry 2Industry 1Total1 1m FD m FD m FD1 m FDTotaloutput1mVA1mVAmVA111mVATotalinputMultiregionalIO tablesFigure by MIT OpenCourseWare, based on Polenske
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