Input-Output Analysis Foundations and Extensions

Transcription

1 Input-Output Analysis Foundations and Extensions Second Edition Ronald E. Miller and Peter D. Blair Hi X$P CAMBRIDGE UNIVERSITY PRESS

2 List of Figures List of Tables Preface page xxii xxiv xxix 1 Introduction and Overview Introduction Input-Output Analysis: The Basic Framework Outline for this Text Internet Website and Text Locations of Real Datasets 8 References 9 2 Foundations of Input-Output Analysis Introduction Notation and Fundamental Relationships Input-Output Transactions and National Accounts Production Functions and the Input-Output Model An Illustration of Input-Output Calculations Numerical Example: Hypothetical Figures-Approach I 21 Impacts on Industry Outputs 21 Other Impacts Numerical Example: Hypothetical Figures - Approach II Numerical Example: Mathematical Observations Numerical Example: The US 2003 Data The Power Series Approximation of (I A) ~* Open Models and Closed Models The Price Model Overview Physical vs. Monetary Transactions The Price Model based on Monetary Data 43

3 vi Contents Summary Appendix 2.1 A2.1.1 A2.1.2 Appendix 2.2 Problems References Numerical Examples Using the Price Model based on Monetary Data Example 1: Base Year Prices Example 2: Changed Base Year Prices Applications The Price Model based on Physical Data Introduction of Prices Relationship between A and C Numerical Examples Using the Price Model based on Physical Data Example 1: Base Year Prices Example 2: Changed Base Year Prices The Quantity Model based on Physical Data A Basic National Income Identity The Relationship between Approaches I and II Approach I Approach II The Hawkins-Simon Conditions Input-Output Modeis at the Regional Level 3.1 Introduction 3.2 Single Region Models National Coefficients Regional Coefficients Closing a Regional Model with respect to Households Many-Region Models: The Interregional Approach Basic Structure of Two-Region Interregional Input-Output Models Interregional Feedbacks in the Two-Region Model Numerical Example: Hypothetical Two-Region Interregional Case Interregional Models with more than Two Regions Implementation of the IRIO Model Many-Region Models: The Multiregional Approach The Regional Tables The Interregional Tables The Multiregional Model Numerical Example: Hypothetical Two-Region Multiregional Case

4 Vll The US MRIO Models Numerical Example: The Chinese Multiregional Model for The Balanced Regional Model Structure of the Balanced Regional Model Numerical Example The Spatial Scale of Regional Models Summary 106 Appendix 3.1 Basic Relationships in the Multiregional Input-Output Model 107 Appendix 3.2 Sectoral and Regional Aggregation in the 2000 Chinese Multiregional Model 109 Appendix 3.3 The Balanced Regional Model and the Inverse of a Partitioned (I - A) Matrix 110 Problems 111 References Organization of Basic Data for Input-Output Models Introduction Observations on Ad Hoc Survey-Based Input-Output Tables Observations on Common Methods for Generating Input-Output Tables A System of National Economic Accounts The Circular Flow of Income and Consumer Expenditure Savings and Investment Adding Overseas Transactions: Imports, Exports, and Other Transactions The Government Sector The Consolidated Balance Statement for National Accounts Expressing Net Worth National Income and Product Accounting Conventions Assembling Input-Output Accounts: The US Case Additional Considerations Secondary Production: Method of Reallocation 140 Example I: Reallocation of Secondary Production Secondary Production: Commodity-by-Industry Accounting 142 Example 2: Commodity-by-Industry Accounts Reconciling with the National Accounts Producers' and Consumers' Prices 144 Example 3: Trade and Transportation Margins Accounting for Imports and Exports 149 Example 4: Competitive and Noncompetitive Imports 149

5 V1U Contents Removing Competitive Imports from Total Transactions Tables 150 Approximation Method I 151 Approximation Method II 151 Example 5: Import Scrubbing 152 Implications of the Estimating Assumptions Adjustments for Inventory Change Adjustments for Scrap Valuation and Double Deflation 157 Example 6: Double Deflation The Aggregation Problem: Level of Detail in Input-Output Tables The Aggregation Matrix 161 Example 7: Sectoral Aggregation Measures of Aggregation Bias Summary 168 Appendix 4.1 Spatial Aggregation in IRIO and MRIO Models 168 A4.1.1 Spatial Aggregation of IRIO Models 168 A4.1.2 Spatial Aggregation of MRIO Models 172 Problems 176 References The Commodity-by-Industry Approach in Input-Output Models Introduction The Use Matrix The Make Matrix The Basic Accounting Relationships Technology and Total Requirements Matrices in the Commodity-Industry Approach Industry Source of Commodity Outputs Commodity Composition of Industry Outputs Generating Total Requirements Matrices 189 Using D 190 Using C "Industry-Based" Technology "Commodity-Based" Technology Direct Requirements (Technical Coefficients) Matrices Derived from Basic Data Total Requirements Matrices 196 Approach I: Starting with Technical Coefficients 196 Approach II: Avoiding C _1 in Commodity Technology Cases 198 Is Singularity Likely to be a Problem in Real-World Models? Numerical Examples of Alternative Direct and Total Requirements Matrices 201

6 ix Direct Requirements Matrices Total Requirements Matrices 202 Commodity-Demand Driven Models 202 Industry-Demand Driven Models Negative Elements in the Commodity-Industry Framework Commodity Technology 203 Direct Requirements Matrices 203 Transactions Matrices 205 Total Requirements Matrices Industry Technology 207 Direct Requirements Matrices 207 Total Requirements Matrices Making a Model Choice 208 Which Model to Choose? 208 Dealing with Negative Values Nonsquare Commodity-Industry Systems Commodity Technology Industry Technology 212 Direct Requirements Matrices 212 Total Requirements Matrices Mixed Technology in the Commodity-Industry Framework Commodity Technology in Vi Industry Technology in Vi Numerical Examples with Mixed Technology Assumptions 219 Example 1: Commodity Technology in\\ 219 Example 2: Industry Technology in Vi Additional Mixed Technology Variants Summary 222 Appendix 5.1 Alternative Approaches to the Derivation of Transactions Matrices 223 A5.1.1 Industry Technology 224 Commodity-by-Commodity Requirements 224 Industry-by-Industry Requirements 225 A5.1.2 Commodity Technology 226 Commodity-by-Commodity Requirements 226 Industry-by-Industry Requirements 228 Appendix 5.2 Elimination of Negatives in Commodity Technology Models 229 A5.2.1 The Problem 229 3x3 Example 229 4x4 Example 229 5x5 Example (from Almon, 2000) 230

7 A5.2.2 Approaches to Elimination of Negative Elements 230 A5.2.3 Results of the Iterative Procedure 234 3x3 Example 234 4x4 Example 234 5x5 Example 235 Problems 237 References 240 Multipliers in the Input-Output Model Introduction General Structure of Multiplier Analysis Output Multipliers 245 Simple Output Multipliers 245 Total Output Multipliers 247 Example: The US Input-Output Model for Output Multipliers in Commodity Industry Models 249 Commodity-Demand-Driven Models 249 Industry-Demand-Driven Models Income/Employment Multipliers 250 Income Multipliers 250 Type I and Type II Income Multipliers 252 Relationship Between Simple and Total Income Multipliers or Between Type I and Type II Income Multipliers 253 Which Multiplier to Use? 254 Even More Income Multipliers 255 Physical Employment Multipliers Value-Added Multipliers Matrix Representations Summary Multipliers in Regional Models Regional Multipliers Interregional Input-Output Multipliers 261 Intraregional Effects 261 Interregional Effects 262 National Effects 263 Sectoral Effects 263 More Than Two Regions Multiregional Input-Output Multipliers 264 Intraregional Effects 266 Interregional Effects 267 National Effects 267 Sectoral Effects 267

8 xi Final Demand for Goods Made in a Particular Region 267 More Than Two Regions Miyazawa Multipliers Disaggregated Household Income Groups Miyazawa's Derivation Numerical Example Adding a Spatial Dimension Gross and Net Multipliers in Input-Output Models Introduction Multipliers in the Net Input-Output Model 278 Numerical Example Additional Multiplier Variants 280 (Indirect Effects)/(Direct Effects) 280 "Growth Equalized" Multipliers 281 Another Kind of Net Multiplier Multipliers and Elasticities Output Elasticity Output-to-Output Multipliers and Elasticities 283 Direct Effects 283 Total Effects Multiplier Decompositions Fundamentals Decompositions in an Interregional Context Stone's Additive Decomposition A Note on Interregional Feedbacks Numerical Illustration Summary 294 Appendix 6.1 The Equivalence of Total Household Income Multipliers and die Elements in the Bottom Row of (I Ä) Appendix 6.2 Relationship Between Type I and Type II Income Multipliers 296 Problems 297 References 299 Nonsurvey and Partial-Survey Methods: Fundamentals Introduction The Question of Stability of Input-Output Data Stability of National Coefficients 304 Comparisons of Direct-Input Coefficients 305 Comparisons of Leontief Inverse Matrices 305 Other Summary Measures 307 Data for the US Economy 307

9 7.2.2 Constant versus Current Prices Stability of Regional Coefficients Summary Updating and Projecting Coefficients: Trends, Marginal Coefficients and Best Practice Methods Trends and Extrapolation Marginal Input Coefficients "Best Practice" Firms Updating and Projecting Coefficients: The RAS Approach and Hybrid Methods The RAS Technique Example of the RAS Procedure Updating Coefficients vs. Transactions 327 Numerical Illustration An Economic Interpretation of the RAS Procedure Incorporating Additional Exogenous Information in an RAS Calculation Modified Example: One Coefficient Known in Advance Hybrid Models: RAS with Additional Information The Constrained Optimization Context Infeasible Problems Summary 336 Appendix 7.1 RAS as a Solution to the Constrained Minimum Information Distance Problem 337 Problems 338 References 343 Nonsurvey and Partial-Survey Methods: Extensions Introduction Location Quotients and Related Techniques Simple Location Quotients Purchases-Only Location Quotients Cross-Industry Quotients The Semilogarithmic Quotient and its Variants, FLQandAFLQ Supply-Demand Pool Approaches Fabrication Effects Regional Purchase Coefficients "Community" Input-Output Models Summary RAS in a Regional Setting Numerical Illustration 361

10 xiii 8.5 Exchanging Coefficients Matrices Estimating Interregional Hows Gravity Model Formulations Two-Region Interregional Models Two-Region Logic with more than Two Regions Estimating Commodity Inflows to a Substate Region Additional Studies 371 Commodity Flows among US States 371 An Optimization Model for Interregional Flows Hybrid Methods Generation of Regional Input-Output Tables (GRIT) Double-Entry Bi-Regional Input-Output Tables (DEBRIOT) The Multiregional Input-Output Model for China, 2000 (CMRIO) International Input-Output Models Introduction Asian International Input-Output Tables "Hybrid" Many-Region Models for the EC China-Japan "Transnational Interregional" Input-Output (THO) Model, Chinese Exports to Japan for Intermediate Demand 381 Applications Leontief's World Model The Reconciliation Issue Summary 386 Appendix 8.1 Geographical Classifications in the World Input-Output Model 387 Problems 387 References Energy Input-Output Analysis Introduction Early Approaches to Energy Input-Output Analysis Contemporary Energy Input-Output Analysis Overview Concepts of Energy Input-Output Analysis The Basic Formulation The Total Energy Requirements Matrix 404 Example 9.1: Two-Sector Illustration of Hybrid Units Input-Output Analysis 407 Example 9.2: Generalization to Several Energy Types The Hybrid Units Formulation and Energy Conservation Conditions 410

11 XIV Contents Example 9.2: Generalization to Several Energy Types (Revisited) Further Methodological Considerations Adjusting for Energy Conversion Efficiencies 412 Example 9.3: Adjusting for Energy Conversion Efficiencies Accounting for Imports Commodity-by-Industry Energy Models Applications Net Energy Analysis 414 Example 9.4: Net Energy Analysis Energy Cost of Goods and Services Impacts of New Energy Technologies An Energy Tax Energy and Structural Change Energy Input-Output and Econometrics Other Applications Summary 427 Appendix 9.1 Earlier Formulation of Energy Input-Output Models 428 A9.1.1 Introduction 428 A9.1.2 Illustration of the Implications of the Traditional Approach 430 Example 9.5: Energy Input-Output Alternative Formulation 430 Example 9.6: Energy Input-Output Example (Revised) 431 Extensions of Example A9.1.3 General Limitations of the Alternative Formulation 437 Problems 437 References Environmental Input-Output Analysis Introduction Basic Considerations Generalized Input-Output Analysis: Basic Framework Accounting for Pollution Impacts Generalized Impacts 447 Example 10.1: Generalized Input-Output Analysis Summary: Generalized Input-Output Formulations 451 Case I: Impact Analysis Form 451 Case II: Planning Form Generalized Input-Output Analysis: Extensions of the Planning Approach Linear Programming: A Brief Introduction by Means of the Leontief Model Multiple Objectives 457

12 xv Conflicting Objectives and Linear Goal Programming Additional Observations 461 Specifying Objectives 461 Tightly Constrained Problems 462 Solution Methods Applications to the Generalized Input-Output Planning Problem Policy Programming 469 Impact Analysis Form 470 Planning Form Ecological Commodities An Augmented Leontief Model Pollution Generation Pollution Elimination 478 Example 10.2: Pollution-Activity-Augmented Leontief Model Existence of Non-negative Solutions 480 Example 10.2 (Revisited): Pollution-Activity-Augmented Leontief Model Economic-Ecologic Models Fully Integrated Models Limited Economic-Ecologic Models 484 Economic Subsystem 484 Ecologic Subsystem 485 Commodity-by-Industry Formulation 485 Example 10.3: Limited Economic-Ecologic Models Pollution Dispersion Gaussian Dispersion Models Coupling Pollution Dispersion and Input-Output Models 488 Example 10.4: Coupling Input-Output and Pollution Dispersion Models Other Applications Summary 490 Problems 490 References Social Accounting Matrices Introduction Social Accounting Matrices: Background Social Accounting Matrices: Basic Concepts The Households Account The Value-Added Account 504

13 xvi Contents 11.6 Interindustry Transactions and the Connection to the Input-Output Framework Expanding the Social Accounts Additional Social Accounting Variables A "Fully Articulated" SAM SAM Multipliers SAM Multipliers: Basic Structure Decomposition of SAM Multipliers 516 Example 11.1: Reduced Form Case Multipliers in an Expanded SAM 522 Example 11.2: The Expanded Case Additive Multipliers The Relationship between Input-Output and SAM Multipliers Balancing SAM Accounts Example: Balancing a SAM Example: Balancing a SAM with Additional Information Some Applications of SAMs Summary 537 Problems 537 References Supply-Side Models, Linkages, and Important Coefficients Supply Side Input-Output Models The Early Interpretation 543 Numerical Illustration (Hypothetical Data) 546 Numerical Application ( US Data) Relationships between A and B and between L and G Comments on the Early Interpretation Joint Stability 549 The Issue 549 Conditions under which both A and B will be Stable Reinterpretation as a Price Model 551 Connection to the Leontief Price Model (Algebra) 553 Connection to the Leontief Price Model (Numerical Illustration) 553 A Ghosh Quantity Model Linkages in Input-Output Models Backward Linkage Forward Linkage "Net" Backward Linkage Classifying Backward and Forward Linkage Results 559

14 xvii Spatial Linkages Hypothetical Extraction 563 Backward Linkage 564 Forward Linkage Illustration Using US Data Identifying Important Coefficients Mathematical Background Relative Sizes of Elements in the Leontief Inverse 569 Observation Observation Observation "Inverse-Important" Coefficients Numerical Example Impacts on Gross Outputs Fields of Influence Additional Measures of Coefficient Importance 580 Converting Output to Employment, Income, etc. 580 Elasticity Coefficient Analysis 581 Relative Changes in All Gross Outputs 581 Impacts of Changes in more than One Element of the A Matrix Summary 582 Appendix 12.1 The Sherman-Morrison-Woodbury Formulation 582 A Introduction 582 A Application to Leontief Inverses 585 Problems 585 References Structural Decomposition, Mixed and Dynamic Models Structural Decomposition Analysis Initial Decompositions: Changes in Gross Outputs 593 Numerical Example Next-Level Decompositions: Digging Deeper into Af and AL 598 Additive Decompositions with Products of more than Two Terms 598 Changes in Final Demand Numerical Examples 601 One Category of Final Demand (p = I) 601 Two Categories of Final Demand (p 2) Changes in the Direct Inputs Matrix 602 Decomposition of AL 602 Decomposition of A A 604 Numerical Illustration (continued) 605

15 Decompositions of Changes in Some Function of x Summary for Ax SDA in a Multiregional Input-Output (MRIO) Model Empirical Examples 608 Studies Using National Models 608 Studies Using a Single-Region or Connected-Region Model Mixed Models Exogenous Specification of One Sector's Output 621 Rearranging the Basic Equations 621 "Extracting" the Sector An Alternative Approach When/i,...,/ _i and x Are Exogenously Specified Examples with x n Exogenous 626 Example l:f\ = 100,000,/ 2 = 200,000, jt 3 = 150, Example 2:f\ = / 2 = 0, * 3 = 150, Example 3:f x = 100,000,/ 2 = 200,000, x 3 = 100, Example 4: The Critical Value ofx^ 628 Multipliers Exogenous Specificationof/i,...,/*,x^+i,..-,x An Example with x n -1 and x n Exogenous 632 Example 5 (Example 2 expanded) New Industry Impacts in the Input-Output Model New Industry: The Final-Demand Approach New Industry: Complete Inclusion in the Technical Coefficients Matrix A New Firm in an Existing Industry Other Structural Changes Dynamic Considerations in Input-Output Models General Relationships A Three-Period Example 642 Terminal Conditions 643 Initial Conditions Numerical Example Terminal Conditions 646 Initial Conditions Numerical Example Terminal Conditions 649 Initial Conditions "Dynamic" Multipliers Turnpike Growth and Dynamic Models 651 Example 653

16 xix Alternative Input-Output Dynamics Summary 654 Appendix 13.1 Alternative Decompositions of x = LBf 655 Appendix 13.2 Exogenous Specification of Some Elements of x 656 A The General Case: An n-sector Model with k Endogenous Outputs 656 A The Output-to-Output Multiplier Matrix 658 A The Inverse of a Partitioned (I-A (n) ) Matrix 659 A The Case of k = 2, n = A The Case of k = 1, n = A "Extracting" the Last (n - it) Sectors 662 Problems 663 References Additional Topics Introduction Input-Output and Measuring Economic Productivity Total Factor Productivity Numerical Example: Total Factor Productivity Accounting for Prices References for Section Graph Theory, Structural Path Analysis, and Qualitative Input-Output Analysis (QIOA) References for Section Fundamental Economic Structure (FES) References for Section Input-Output, Econometrics, and Computable General Equilibrium Models The Variable Input-Output Model Regional Input-Output Econometric Models Computable General Equilibrium Models References for Section Additional Resources for Input-Output Extensions and Applications Edited Collections Journal Special Issues Collections of Reprints References for Section Some Concluding Reflections 686

17 xx Contents Appendix A Matrix Algebra for Input-Output Models 688 A.l Introduction 688 A.2 Matrix Operations: Addition and Subtraction 689 A.2.1 Addition 689 A.2.2 Subtraction 689 A.2.3 Equality 689 A.2.4 The Null Matrix 689 A.3 Matrix Operations: Multiplication 689 A.3.1 Multiplication of a Matrix by a Number 689 A.3.2 Multiplication of a Matrix by Another Matrix 689 A.3.3 The Identity Matrix 690 A.4 Matrix Operations: Transposition 691 A.5 Representation of Linear Equation Systems 691 A.6 Matrix Operations: Division 693 A.7 Diagonal Matrices 696 A. 8 Summation Vectors 698 A.9 Matrix Inequalities 698 A. 10 Partitioned Matrices 699 A Multiplying Partitioned Matrices 699 A The Inverse of a Partitioned Matrix 700 References 701 Appendix B Reference Input-Output Tables for the United States ( ) 702 B.l Introduction 702 B.2 Transactions Accounts 703 B.3 Matrices of Technical Coefficients and Total Requirements 715 References for US Input-Output Tables ( ) 722 Appendix C Historical Notes on the Development of Leontief's Input-Output Analysis 724 C.l Conceptual Foundations 724 C.2 Quesnay and the Physiocrats 725 C.3 Mathematical Formalization 728 C.4 Leontief and the "Economy as a Circular Flow" 729 C.5 Development of Input-Output Analysis 731 References 735

18 xxi Author Index 738 Subject Index 746 The Following Supplementary Appendices are Available Online at Web Appendix 5W. 1 Left and Right Inverses in Nonsquare Input-Output Systems A5W.1.1 Introduction A5W.1.2 More Commodities than Industries (m > ri) Numerical Illustration Commodity Technology Industry Technology A5W.1.3 Fewer Commodities than Industries (m < ri) Numerical Illustration Commodity Technology Industry Technology Web Appendix 8W.1 Detailed Results for the Numerical Illustration in Section 8.4 Web Appendix 12W. 1 Hypothetical Extractions with Partitioned Matrices A12W.1.1 Case 1: Complete Extraction of Sector 1 A12W.1.2 Case 2: Extraction of Sector l's Intersectoral Relations A12W.1.3 Case 3: Extraction of Sector l's Intermediate Purchases A12W.1.4 Case 4: Extraction of Sector l's Intermediate Sales A12W.1.5 Case 5: Extraction of Sector l's Intersectoral Intermediate Purchases A12W.1.6 Case 6: Extraction of Sector l's Intersectoral Intermediate Sales A12W.1.7 The Ghosh Model and Some Comparisons Web Appendix 12W.2 Brief History of Leontief Inverses with Errors in the Coefficients of A A12W.2.1 Mathematical Background A12W.2.2 Application of Leontief Inverses Dwyer and Waugh (1953) Evans (1954) West (1982) Sherman-Morrison and Sonis-Hewings