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The Input- Output Process <br />The input- output model is based on a table of 533 <br />finely detailed industries showing local sales and <br />purchases. The local and state eccrttorny of cacti <br />community is researched so the table can be <br />customized for each community. The basic <br />purchase patterns for local industries are derived <br />fi -orn a similar table for the U.S. economy for 2007 <br />(the latest detailed data available from the U.S, <br />Depadment of Curnmerce }, The table is first <br />reduced to reflect the unique size and industry mix <br />of the local economy, based on data from C ouWy <br />Business patterns and the Regional 1lcvnomie, <br />Information System of the U.S. Department of <br />Commerce. It is then adjusted so that cnly <br />transactions with local businesses are recorded in <br />the inter - industry part of the table. This technique <br />compares supply and demand and estimates th+e <br />additionaJ imparts or exports required to make total <br />supply equal total demand. The resulting table <br />shows the detailed sales and purchase patterns of <br />the local industries. The 533 - industry table is then <br />aggregated to reflect the ,general activities of 32 <br />industries plus local households, creating, a total of <br />33 industries. To trace changes in the economy, <br />each column is converted to shore the diYuet <br />requirements per dollar of gross output for each <br />sector. This direct- requirerrnants table represents the <br />"recipe" for producing the output of each industry. <br />The economic impact figures for Arts & liccortrsmi <br />Prospei rIVwere computed using what is called <br />an "iterative" procedure. This process uses the sum <br />of a power series co approximate thu solution to the <br />economic model. This is what the proxess looks liJke . <br />in matrix algebra: <br />T = IX + ABC + A2X + AI X + .., + An-X. <br />T is the solution, a column vector of changes in <br />each industry's outputs caused by the changes <br />represented in the column vector X. A is the 33 by <br />33 direct - requirements matrix. This equadon.. is used <br />to trace the d ire ul expenditures attributablc to <br />nonprofit ails organizations and their audieenees. A <br />mult.iplicr effect table is produccd that displays the <br />results of this equation, The total column is T, The <br />initial expenditure to be traced is IX (i is the identity <br />matrix, which is operationally equivalent to the <br />number 1 in ordinary algebra). Round I is AX, the <br />result of multiplying the matrix A by the erector X <br />(the ot;tPuts required of each supplier to produce the <br />goods and services purchased in the initial change <br />birder study). Round 2 is A2X, which is the result of <br />multiplying the matrix A by Round I (it answers the <br />carne question applied to Round 1: "What are the <br />outputs required of each supplier to produce the <br />goods and .services purchased in Round 1 of this <br />chain of events ? " ). Each of columns l through 12 in <br />the multiplier effects table represents ,one of the <br />elements in the continuing but diminishing chain or <br />expoDditures on the right side of'ihe equation. Their <br />sum, T, represents the total production required in the <br />local econoiny in response to arts activities, <br />Calculation of the total impact of the nonprofit arts <br />on the outputs of other industries (T) can now be <br />converted to impacts an the final incornes to local <br />residents by multiplying the outputs produced by the <br />ratios of hOrlsehold income to output and <br />employment to output. Thus, the employment impact <br />of changes in outputs due to arts expenditures is <br />calculated by multiplying elements in the column of <br />total outputs by the ratio of crnployrnent to output for <br />the 32 industries in the region, Changes in household <br />incomes, local government rcvcnues, and state <br />goverranertt revenues due to nonprofit arts <br />expenditures are similarly transformed. The same <br />process Is also wed to show the direct nnpact on <br />incornm and revenues associated with the column of <br />direct local expenditures. <br />A comprehensive description of the methodology <br />used to complete the national study is available at <br />iN wtr.America nsFat •TheArts.orgtEcortnmictmpact, <br />20 arts & EOWWmic rarasp -9rrfy W I Arnevicans far the A is <br />