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Input-Output Models Inter-Industry Structure URBPL 5/6020, University of Utah Pam Perlich Input - Output Analysis † Wassily Leontief created the model † He first published it in 1965 † He received a Nobel Prize in 1973 for this work † A review of his work is in the March 1999 Survey of Current Business Input Output Models † Capture inter-industry transactions: „ Industries use the products of other industries to produce their own products „ For example - automobile producers use steel, glass, rubber, and plastic products to produce automobiles „ Outputs from one industry become inputs to another „ When you buy a car, you affect the demand for glass, plastic, steel, etc Input-Output Model Logic Steel Glass Tires Plastic Other Components Input-Output Model Logic Steel Glass Tires Plastic Automobile Factory Other Components Input-Output Model Logic Steel Glass Tires Plastic Automobile Factory Other Components Required Inputs for Auto Production Steel Glass Tires Plastic Others Components Required Inputs for Auto Production Steel A B C Glass Tires Plastic A B C A B C A B C Others Components A B C Required Inputs for Primary Suppliers to Auto Production (Second Round Effects) Required Inputs for Auto Production Steel A B C Glass Tires Plastic A B C A B C A B C Others Components A B C Required Inputs for Primary Suppliers to Auto Production (Second Round Effects) Etc – I-O model accounts for all rounds of spending Regional Purchase Coefficients † For any industry in a region, the required inputs will come from two sources: Other industries within the region Other industries outside the region ‰ A set of regional purchase (or regional trade) coefficients makes this translation • Results in a reduction of economic impact as purchases are made out-of-region Table 4.4 Industry-output multipliers (with households endogenous) Source: Schaffer, page 27 http://www.rri.wvu.edu/WebBook/Schaffer/chap04.html Additional Export (Final Demand) of $1 of Manufacturing Î Additional $1.67 Purchases from Industries on the Left (Table Includes: Direct + Indirect) Source: Schaffer, page 27 http://www.rri.wvu.edu/WebBook/Schaffer/chap04.html Total Requirements (Households Exogenous) (Table Includes: Direct + Indirect) Source: Schaffer, page 28 http://www.rri.wvu.edu/WebBook/Schaffer/chap04.html A Comparison of Output Multipliers Under Different Household Assumptions (Table Includes: Direct + Indirect) Source: Schaffer, page 28 http://www.rri.wvu.edu/WebBook/Schaffer/chap04.html Multipliers - Effects † Direct Effect – Direct Sales † Indirect Effect – Interindustry Purchases (A Matrix adjusted for regional purchase coefficients) † Induced – Household sector is included Multipliers – Types I and II † Type I: Closed on industries (no households) † Type II: Closed on households (households are included) Multiplier Transformations † Output – Use only Type I multipliers † Employment – Transform by using employment to output ratios (Assumes the average is the marginal) † Income – Transform by using household income to output ratios (Assumes the average is the marginal) BEA Produces I-O Models † The Bureau of Economic Analysis „ Generates the data used to build these input output models † This data is the basis of our national income accounts - Gross Domestic Product, etc „ Builds RIMS (Regional Input-Output Modeling System), which is housed in the Regional Program of the Bureau of Economic Analysis † IO models are used at the regional and national levels Final Demand Multipliers for Food Products Machinery Industry From RIMSII Handbook, www.bea.gov Final Demand Multipliers for Food Products Machinery Industry Increase in final demand for Food Products Machinery = $ million Î $15,000 increase in output of Farm products, ag., for., & f.s Î $1.0393 million increase in output of Indus mach & equip Î $1.0112 million increase in output of all other industries Total output in the economic area increases by $2.06555 million Final Demand Multipliers for Food Products Machinery Industry Increase in final demand for Food Products Machinery = $ million Î $3,600 increase in earnings of Farm products, ag., for., & f.s Î $307,200 increase in earnings of Indus mach & equip Î $298,300 increase in earnings of all other industries Total earnings in the economic areas increases by $609,100 Final Demand Multipliers for Food Products Machinery Industry Increase in final demand for Food Products Machinery = $ million Î 2846 increase in employment of Farm products, ag., for., & f.s Î 9.8743 increase in employment of Indus mach & equip Î 14.1743 increase in employment of all other industries Total employment in the economic areas increases by 24.3332 jobs Export of Regionally Produced Goods & Services Î Economic Impacts Regional Economy CUSTOMERS OUTSIDE THE REGION Injection of Income $$$$$ Basic Sector Econ Base vs I-O Models † Econ Base „ Basic „ NonBasic NonBasic Sector † Input Output „ Many industries „ Interindustry purchases Export of Regionally Produced Goods & Services Î Economic Impacts Regional Economy CUSTOMERS OUTSIDE THE REGION Injection of Income $$$$$ Basic Sector NonBasic Sector Econ Base vs I-O Models † Definition of Direct Economic Impact is Same † Estimation of Indirect and Induced Differ [...]...From the Tire Producer’s Perspective Tire Factory From the Tire Producer’s Perspective Individual Consumers Tire Factory FINAL DEMAND FOR TIRES From the Tire Producer’s Perspective Individual Consumers Tire Factory FINAL DEMAND FOR TIRES School Districts Trucking Companies Automobile Factory INTERMEDIATE DEMAND FOR TIRES Simplified Circular Flow View of The Economy Simplified Circular Flow View of... Economy $$ Consumption Spending (Yi) Goods & Services Households Households buy the output of business: final demand or Yi Businesses Simplified Circular Flow View of The Economy $$ Consumption Spending (Yi) Goods & Services Households Businesses Labor $$ Wages & Salaries Households buy the output of business: final demand or Yi Households sell labor & other inputs to business as inputs to production... (output of industry i sold to industry j) Demand For Industry i n xi = ∑ xij + Yi j=1 xi : output of industry i xij : output of industry i sold to industry j Yi : output of industry i sold to final demand Interindustry Demand xij = aij × xj xj : output of industry j xij : output of industry i sold to industry j aij : input output coefficient 0 ≤ aij ≤ 1 This is industry j’s demand for industry i s product... production Simplified Circular Flow View of The Economy $$ Consumption Spending (Yi) Goods & Services Households Businesses Businesses Labor $$ Wages & Salaries Households buy the output of business: final demand or Yi Households sell labor & other inputs to business as inputs to production Businesses purchase from other businesses to produce their own goods / services This is intermediate demand or xij (output... reaction of additional purchases in the region known as the multiplier effect This is known as an economic impact Economic Impacts † Result from the export of regionally produced goods and services † This generates “new money” for the region † It increases the size of the regional economy beyond what it would have been in the absence of the export sale Regional Purchase Coefficients † For any industry... Generalization in Matrix Form (I- A) × x = Y [ (I- A) -1 ] × (I- A) × x = (I- A) × Y Pre-multiply both sides by (I- A)-1 -1 Generaliza tion in Matrix Form (I- A) × x = Y [ (I- A) -1 ] × (I- A) × x = (I- A) × Y Reduces to I I × x = (I- A) × Y -1 -1 Generalization in Matrix Form (I- A) × x = Y [ (I- A) -1 ] × (I- A) × x = (I- A) × Y I × x = (I- A) × Y -1 Reduces to x x = (I- A) × Y -1 -1 Generalization in Matrix Form (I- A)... [ (I- A) -1 ] × (I- A) × x = (I- A) × Y -1 I × x = (I- A) × Y -1 x = (I- A) × Y -1 nx1 nxn Dimensions allow multiplication nx1 Intermediate Demand X −Y = Z Z : Intermediate Y is final Demand X is total Demand Impact Analysis Δx = (I - A) × ΔY -1 Impact of a change in the final demand on production The change in final demand is an export of regionally produced goods and services This sets off a chain reaction... Regional Purchase Coefficients † For any industry in a region, the required inputs will come from two sources: 1 Other industries within the region 2 Other industries outside the region ‰ A set of regional purchase (or regional trade) coefficients makes this translation • Results in a reduction of economic impact as purchases are made out-of-region ... product It is directly proportionate to the output of industry j Total Demand xi = n ∑x + Yi ij j =1 Substitute: xi = n ∑ (a ij xij = aij × xj × xj ) + Yi j =1 Rearrange xi − n ∑ (a j =1 ij × xj ) = Yi Total Demand xi = n ∑x ij j =1 + Yi Total Demand xi = n ∑x ij + Yi j =1 Substitute: xij = aij × xj Total Demand xi = n ∑x + Yi ij j =1 Substitute: xi = n ∑ (a j =1 ij xij = aij × xj × xj ) + Yi Total Demand... = Y 4 Matrix Form Four Industry Case (1 − a11) -a 21 -a 31 -a 41 -a12 (1 − a 22 ) -a 32 -a 42 -a13 -a 23 (1 − a33) -a 43 -a14 -a14 • -a 34 (1 − a 44 ) x1 y1 x2 y 2 = x3 y 3 x4 y 4 The A-Matrix OUTPUTS INPUTS a11 a 21 a 31 a 41 a12 a 22 a 32 a 42 a13 a 23 a 33 a 43 a14 a 24 a 34 a 44 a43 : This is the number of units of industry 4 product required as input to produce 1 unit of industry 3 output Rearrange