Chapter
Example 2: Changed Base Year Prices
2.6.6 The Price Model based on Physical Data
Relationship between A and C
2.6.7 Numerical Examples Using the Price Model based on Physical Data
Example 1: Base Year Prices
Example 2: Changed Base Year Prices
2.6.8 The Quantity Model based on Physical Data
2.6.9 A Basic National Income Identity
Appendix 2.1 The Relationship between Approaches I and II
Appendix 2.2 The Hawkins--Simon Conditions
3 Input–Output Models at the Regional Level
3.2.1 National Coefficients
3.2.2 Regional Coefficients
3.2.3 Closing a Regional Model with respect to Households
3.3 Many-Region Models: The Interregional Approach
3.3.1 Basic Structure of Two-Region Interregional Input–Output Models
3.3.2 Interregional Feedbacks in the Two-Region Model
3.3.3 Numerical Example: Hypothetical Two-Region Interregional Case
3.3.4 Interregional Models with more than Two Regions
3.3.5 Implementation of the IRIO Model
3.4 Many-Region Models: The Multiregional Approach
3.4.1 The Regional Tables
3.4.2 The Interregional Tables
3.4.3 The Multiregional Model
3.4.4 Numerical Example: Hypothetical Two-Region Multiregional Case
3.4.6 Numerical Example: The Chinese Multiregional Model for 2000
3.5 The Balanced Regional Model
3.5.1 Structure of the Balanced Regional Model
3.6 The Spatial Scale of Regional Models
Appendix 3.1 Basic Relationships in the Multiregional Input–Output Model
Appendix 3.2 Sectoral and Regional Aggregation in the 2000 Chinese Multiregional Model
Appendix 3.3 The Balanced Regional Model and the Inverse of a Partitioned (I−A) Matrix
4 Organization of Basic Data for Input–Output Models
4.2 Observations on Ad Hoc Survey-Based Input–Output Tables
4.3 Observations on Common Methods for Generating Input–Output Tables
4.4 A System of National Economic Accounts
4.4.1 The Circular Flow of Income and Consumer Expenditure
4.4.2 Savings and Investment
4.4.3 Adding Overseas Transactions: Imports, Exports, and Other Transactions
4.4.4 The Government Sector
4.4.5 The Consolidated Balance Statement for National Accounts
4.4.6 Expressing Net Worth
4.5 National Income and Product Accounting Conventions
4.6 Assembling Input–Output Accounts: The US Case
4.7 Additional Considerations
4.7.1 Secondary Production: Method of Reallocation
Example 1: Reallocation of Secondary Production
4.7.2 Secondary Production: Commodity-by-Industry Accounting
Example 2: Commodity-by-Industry Accounts
4.7.3 Reconciling with the National Accounts
4.7.4 Producers' and Consumers' Prices
Example 3: Trade and Transportation Margins
4.7.5 Accounting for Imports and Exports
Example 4: Competitive and Noncompetitive Imports
4.7.6 Removing Competitive Imports from Total Transactions Tables
Example 5: Import Scrubbing
Implications of the Estimating Assumptions
4.7.7 Adjustments for Inventory Change
4.7.8 Adjustments for Scrap
4.8 Valuation and Double Deflation
Example 6: Double Deflation
4.9 The Aggregation Problem: Level of Detail in Input–Output Tables
4.9.1 The Aggregation Matrix
Example 7: Sectoral Aggregation
4.9.2 Measures of Aggregation Bias
Appendix 4.1 Spatial Aggregation in IRIO and MRIO Models
A4.1.1 Spatial Aggregation of IRIO Models
A4.1.2 Spatial Aggregation of MRIO Models
5 The Commodity-by-Industry Approach in Input–Output Models
5.2 The Basic Accounting Relationships
5.3 Technology and Total Requirement Matrices in the Commodity–Industry Approach
5.3.1 Industry Source of Commodity Outputs
5.3.2 Commodity Composition of Industry Outputs
5.3.3 Generating Total Requirements Matrices
5.3.4 ``Industry-Based'' Technology
5.3.5 ``Commodity-Based'' Technology
5.3.6 Direct Requirements (Technical Coefficients) Matrices Derived from Basic Data
5.3.7 Total Requirements Matrices
Approach I: Starting with Technical Coefficients
Approach II: Avoiding C-1 in Commodity Technology Cases
Is Singularity Likely to be a Problem in Real-World Models?
5.4 Numerical Examples of Alternative Direct and Total Requirements Matrices
5.4.1 Direct Requirements Matrices
5.4.2 Total Requirements Matrices
Commodity-Demand-Driven Models
5.5 Negative Elements in the Commodity–Industry Framework
5.5.1 Commodity Technology
Direct Requirements Matrices
Total Requirements Matrices
5.5.2 Industry Technology
Direct Requirements Matrices
Total Requirements Matrices
5.5.3 Making a Model Choice
Dealing with Negative Values
5.6 Nonsquare Commodity–Industry Systems
5.6.1 Commodity Technology
5.6.2 Industry Technology
Direct Requirements Matrices
Total Requirements Matrices
5.7 Mixed Technology in the Commodity–Industry Framework
5.7.1 Commodity Technology in V1
5.7.2 Industry Technology in V1
5.7.3 Numerical Examples with Mixed Technology Assumptions
Example 1: Commodity Technology in V1
Example 2: Industry Technology in V1
5.7.4 Additional Mixed Technology Variants
Appendix 5.1 Alternative Approaches to the Derivation of Transactions Matrices
A5.1.1 Industry Technology
Commodity-by-Commodity Requirements
Industry-by-Industry Requirements
A5.1.2 Commodity Technology
Commodity-by-Commodity Requirements
Industry-by-Industry Requirements
Appendix 5.2 Elimination of Negative sin Commodity Technology Models
5 X 5 Example (from Almon, 2000)
A5.2.2 Approaches to Elimination of Negative Elements
A5.2.3 Results of the Iterative Procedure
6 Multipliers in the Input–Output Model
6.2 General Structure of Multiplier Analysis
Simple Output Multipliers
Example: The US Input–Output Model for 2003
Output Multipliers in Commodity–Industry Models
Commodity-Demand-Driven Models
Industry-Demand-Driven Models
6.2.2 Income/Employment Multipliers
Type I and Type II Income Multipliers
Relationship Between Simple and Total Income Multipliers or Between Type I and Type II Income Multipliers
Even More Income Multipliers
Physical Employment Multipliers
6.2.3 Value-Added Multipliers
6.2.4 Matrix Representations
6.3 Multipliers in Regional Models
6.3.1 Regional Multipliers
6.3.2 Interregional Input–Output Multipliers
6.3.3 Multiregional Input–Output Multipliers
Final Demand for Goods Made in a Particular Region
6.4.1 Disaggregated Household Income Groups
6.4.2 Miyazawa's Derivation
6.4.4 Adding a Spatial Dimension
6.5 Gross and Net Multipliers in Input–Output Models
6.5.2 Multipliers in the Net Input–Output Model
6.5.3 Additional Multiplier Variants
(Indirect Effects)/(Direct Effects)
``Growth Equalized'' Multipliers
Another Kind of Net Multiplier
6.6 Multipliers and Elasticities
6.6.2 Output-to-Output Multipliers and Elasticities
6.7 Multiplier Decompositions
6.7.2 Decompositions in an Interregional Context
6.7.3 Stone's Additive Decomposition
6.7.4 A Note on Interregional Feedbacks
6.7.5 Numerical Illustration
Appendix 6.1 The Equivalence of Total Household Income Multipliers and the Elements in the Bottom Row of (I-)-1
Appendix 6.2 Relationship Between Type I and Type II Income Multipliers
7 Nonsurvey and Partial-Survey Methods: Fundamentals
7.2 The Question of Stability of Input–Output Data
7.2.1 Stability of National Coefficients
Comparisons of Direct-Input Coefficients
Comparisons of Leontief Inverse Matrices
7.2.2 Constant versus Current Prices
7.2.3 Stability of Regional Coefficients
7.3 Updating and Projecting Coefficients: Trends, Marginal Coefficients,and Best Practice Methods
7.3.1 Trends and Extrapolation
7.3.2 Marginal Input Coefficients
7.3.3 ``Best Practice'' Firms
7.4 Updating and Projecting Coefficients: The RAS Approachand Hybrid Methods
7.4.2 Example of the RAS Procedure
7.4.3 Updating Coefficients vs. Transactions
7.4.4 An Economic Interpretation of the RAS Procedure
7.4.5 Incorporating Additional Exogenous Information in an RAS Calculation
7.4.6 Modified Example: One Coefficient Known in Advance
7.4.7 Hybrid Models: RAS with Additional Information
7.4.8 The Constrained Optimization Context
7.4.9 Infeasible Problems
Appendix 7.1 RAS as a Solution to the Constrained Minimum Information Distance Problem
8 Nonsurvey and Partial-Survey Methods: Extensions
8.2 Location Quotients and Related Techniques
8.2.1 Simple Location Quotients
8.2.2 Purchases-Only Location Quotients
8.2.3 Cross-Industry Quotients
8.2.4 The Semilogarithmic Quotient and its Variants, FLQ and AFLQ
8.2.5 Supply–Demand Pool Approaches
8.2.6 Fabrication Effects
8.2.7 Regional Purchase Coefficients
8.2.8 ``Community'' Input–Output Models
8.3 RAS in a Regional Setting
8.4 Numerical Illustration
8.5 Exchanging Coefficients Matrices
8.6 Estimating Interregional Flows
8.6.1 Gravity Model Formulations
8.6.2 Two-Region Interregional Models
8.6.3 Two-Region Logic with more than Two Regions
8.6.4 Estimating Commodity Inflows to a Substate Region
Commodity Flows among US States
Interregional Social Accounts Model (ISAM)
National Interstate Economic Model (NIEMO)
An Optimization Model for Interregional Flows
8.7.1 Generation of Regional Input–Output Tables (GRIT)
8.7.2 Double-Entry Bi-Regional Input–Output Tables (DEBRIOT)
8.7.3 The Multiregional Input–Output Model for China, 2000 (CMRIO)
8.8 International Input–Output Models
8.8.2 Asian International Input–Output Tables
8.8.3 ``Hybrid'' Many-Region Models for the EC
8.8.4 China–Japan ``Transnational Interregional'' Input–Output (TIIO) Model, 2000
8.8.5 Leontief's World Model
8.9 The Reconciliation Issue
Appendix 8.1 Geographical Classifications in the World Input–Output Model
9 Energy Input–Output Analysis
9.1.1 Early Approaches to Energy Input–Output Analysis
9.1.2 Contemporary Energy Input–Output Analysis
9.2 Overview Concepts of Energy Input–Output Analysis
9.2.1 The Basic Formulation
9.2.2 The Total Energy Requirements Matrix
Example 9.1: Two-Sector Illustration of Hybrid Units Input–Output Analysis
Example 9.2: Generalization to Several Energy Types
9.2.3 The Hybrid Units Formulation and Energy Conservation Conditions
Example 9.2: Generalization to Several Energy Types (Revisited)
9.3 Further Methodological Considerations
9.3.1 Adjusting for Energy Conversion Efficiencies
Example 9.3: Adjusting for Energy Conversion Efficiencies
9.3.2 Accounting for Imports
9.3.3 Commodity-by-Industry Energy Models
9.4.1 Net Energy Analysis
Example 9.4: Net Energy Analysis
9.4.2 Energy Cost of Goods and Services
9.4.3 Impacts of New Energy Technologies
9.4.5 Energy and Structural Change
9.4.6 Energy Input–Output and Econometrics
Appendix 9.1 Earlier Formulation of Energy Input–Output Models
A9.1.2 Illustration of the Implications of the Traditional Approach
Example 9.5: Energy Input–Output Alternative Formulation
Example 9.6: Energy Input–Output Example (Revised)
Extensions of Example 9.1
A9.1.3 General Limitations of the Alternative Formulation
10 Environmental Input–Output Analysis
10.2 Basic Considerations
10.3 Generalized Input–Output Analysis: Basic Framework
10.3.1 Accounting for Pollution Impacts
10.3.2 Generalized Impacts
10.3.3 Summary: Generalized Input–Output Formulations
Case I: Impact Analysis Form
10.4 Generalized Input–Output Analysis: Extensions of thePlanning Approach
10.4.1 Linear Programming: A Brief Introduction by Means of the Leontief Model
10.4.2 Multiple Objectives
10.4.3 Conflicting Objectives and Linear Goal Programming
10.4.4 Additional Observations
Tightly Constrained Problems
10.4.5 Applications to the Generalized Input–Output Planning Problem
10.4.6 Policy Programming
10.4.7 Ecological Commodities
10.5 An Augmented Leontief Model
10.5.1 Pollution Generation
10.5.2 Pollution Elimination
Example 10.2: Pollution-Activity-Augmented Leontief Model
10.5.3 Existence of Non-negative Solutions
Example 10.2 (Revisited): Pollution-Activity-Augmented Leontief Model
10.6 Economic–Ecologic Models
10.6.1 Fully Integrated Models
10.6.2 Limited Economic–Ecologic Models
Commodity-by-Industry Formulation
Example 10.3: Limited Economic–Ecologic Models
10.7 Pollution Dispersion
10.7.1 Gaussian Dispersion Models
10.7.2 Coupling Pollution Dispersion and Input–Output Models
Example 10.4: Coupling Input–Output and Pollution Dispersion Models
11 Social Accounting Matrices
11.2 Social Accounting Matrices: Background
11.3 Social Accounting Matrices: Basic Concepts
11.4 The Households Account
11.5 The Value-Added Account
11.6 Interindustry Transactions and the Connection to the Input–Output Framework
11.7 Expanding the Social Accounts
11.8 Additional Social Accounting Variables
11.9 A ``Fully Articulated'' SAM
11.10.1 SAM Multipliers: Basic Structure
11.10.2 Decomposition of SAM Multipliers
Example 11.1: Reduced Form Case
11.10.3 Multipliers in an Expanded SAM
Example 11.2: The Expanded Case
11.10.4 Additive Multipliers
11.11 The Relationship between Input–Output and SAM Multipliers
11.12 Balancing SAM Accounts
11.12.1 Example: Balancing a SAM
11.12.2 Example: Balancing a SAM with Additional Information
11.13 Some Applications of SAMs
12 Supply-Side Models, Linkages, and Important Coefficients
12.1 Supply Side Input–Output Models
12.1.1 The Early Interpretation
Numerical Illustration (Hypothetical Data)
Numerical Application (US Data)
12.1.2 Relationships between A and B and between L and G
12.1.3 Comments on the Early Interpretation
Conditions under which both A and B will be Stable
12.1.5 Reinterpretation as a Price Model
Connection to the Leontief Price Model (Algebra)
Connection to the Leontief Price Model (Numerical Illustration)
12.2 Linkages in Input–Output Models
12.2.3 ``Net'' Backward Linkage
12.2.4 Classifying Backward and Forward Linkage Results
12.2.6 Hypothetical Extraction
12.2.7 Illustration Using US Data
12.3 Identifying Important Coefficients
12.3.1 Mathematical Background
12.3.2 Relative Sizes of Elements in the Leontief Inverse
12.3.3 ``Inverse-Important'' Coefficients
12.3.5 Impacts on Gross Outputs
12.3.6 Fields of Influence
12.3.7 Additional Measures of Coefficient Importance
Converting Output to Employment, Income, etc
Elasticity Coefficient Analysis
Relative Changes in All Gross Outputs
Impacts of Changes in more than One Element of the A Matrix
Appendix 12.1 The Sherman–Morrison–Woodbury Formulation
A12.1.2 Application to Leontief Inverses
13 Structural Decomposition, Mixed and Dynamic Models
13.1 Structural Decomposition Analysis
13.1.1 Initial Decompositions: Changes in Gross Outputs
13.1.2 Next-Level Decompositions: Digging Deeper into f and L
Additive Decompositions with Products of more than Two Terms
13.1.3 Numerical Examples
One Category of Final Demand (p = 1)
Two Categories of Final Demand (p = 2)
13.1.4 Changes in the Direct Inputs Matrix
Numerical Illustration (continued)
13.1.5 Decompositions of Changes in Some Function of x
13.1.7 SDA in a Multiregional Input--Output (MRIO) Model
13.1.8 Empirical Examples
The US Multiregional Model
A Multicountry Model for the European Community (Oosterhaven and van der Linden, 1997)
13.2.1 Exogenous Specification of One Sector's Output
Rearranging the Basic Equations
13.2.2 An Alternative Approach…
Example 1: f1 = 100,000, f2 = 200,000, x3 = 150,000
Example 2: f1 =f2 =0, x3 = 150,000
Example 3: f1 = 100,000, f2 = 200,000, x3 = 100,000
Example 4: The Critical Value of x3
13.2.4 Exogenous Specification of…
Example 5 (Example 2 expanded)
13.3 New Industry Impacts in the Input–Output Model
13.3.1 New Industry: The Final-Demand Approach
13.3.2 New Industry: Complete Inclusion in the Technical Coefficients Matrix
13.3.3 A New Firm in an Existing Industry
13.3.4 Other Structural Changes
13.4 Dynamic Considerations in Input–Output Models
13.4.1 General Relationships
13.4.2 A Three-Period Example
13.4.3 Numerical Example 1
13.4.4 Numerical Example 2
13.4.5 ``Dynamic'' Multipliers
13.4.6 Turnpike Growth and Dynamic Models
13.4.7 Alternative Input–Output Dynamics
Appendix 13.1 Alternative Decompositions of x=LBf
Appendix 13.2 Exogenous Specification of Some Elements of x
A13.2.1 The General Case: Ann-sector Model with k Endogenous Outputs
A13.2.2 The Output-to-Output Multiplier Matrix
A13.2.3 The Output-to-Output Multiplier Matrix
A13.2.4 The Case of k=2, n=3
A13.2.5 The Case of k=1, n=3
A13.2.6 “Extracting” the Last (n−k) Sectors
14.2 Input–Output and Measuring Economic Productivity
14.2.1 Total Factor Productivity
14.2.2 Numerical Example: Total Factor Productivity
14.2.3 Accounting for Prices
14.2.4 References for Section 14.2
14.3 Graph Theory, Structural Path Analysis, and Qualitative Input–Output Analysis (QIOA)
14.3.1 References for Section 14.3
14.4 Fundamental Economic Structure (FES)
14.4.1 References for Section 14.4
14.5 Input–Output, Econometrics, and Computable General Equilibrium Models
14.5.1 The Variable Input–Output Model
14.5.2 Regional Input–Output Econometric Models
14.5.3 Computable General Equilibrium Models
14.5.4 References for Section 14.5
14.6 Additional Resources for Input–Output Extensions and Applications
14.6.2 Journal Special Issues
14.6.3 Collections of Reprints
14.6.4 References for Section 14.6
14.7 Some Concluding Reflections
Appendix A Matrix Algebra for Input–Output Models
A.2 Matrix Operations: Addition and Subtraction
A.3 Matrix Operations: Multiplication
A.3.1 Multiplication of a Matrix by a Number
A.3.2 Multiplication of a Matrix by another Matrix
A.3.3 The Identity Matrix
A.4 Matrix Operations: Transposition
A.5 Representation of Linear Equation Systems
A.6 Matrix Operations: Division
A.10 Partitioned Matrices
A.10.1 Multiplying Partitioned Matrices
A.10.2 The Inverse of a Partitioned Matrix
Appendix B Reference Input–Output Tables for the United States (1919–2006)
References for US Input–Output Tables (1919–2006)
Appendix C Historical Notes on the Development of Leontief’s Input–Output Analysis
C.1 Conceptual Foundations
C.2 Quesnay and the Physiocrats
C.3 Mathematical Formalization
C.4 Leontief and the ``Economy as a Circular Flow''
C.5 Development of Input–Output Analysis