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Input–Output Analysis

The new edition of Ronald Miller and Peter Blair’s classictextbook is an essential reference for students and scholarsin the input–output research and applications community. Thebook has been fully revised and updated to reflect importantdevelopments in the field since its original publication. Newtopics covered include social accounting matrices (SAMs) (andextended input–output models) and their connection to input–output data, structural decomposition analysis (SDA), multiplierdecompositions, identifying important coefficients, and interna-tional input–output models. A new feature of this edition is thatit is also supported by an accompanying website with solutionsto all problems, a sampling of real-world data sets, and supple-mental appendices with further information for more advancedreaders.

Input–Output Analysis is an ideal introduction to the subjectfor advanced undergraduate and graduate students in a wide vari-ety of fields, including economics, regional science, regionaleconomics, city, regional and urban planning, environmentalplanning, public policy analysis, and public management.

ronald e. miller is Emeritus Professor of Regional Scienceat the University of Pennsylvania, Philadelphia.

peter d. blair is Executive Director of the Division on Engi-neering and Physical Sciences at the National Academy ofSciences, Washington, DC.

www.cambridge.org© Cambridge University Press

Cambridge University Press978-0-521-51713-3 - Input-Output Analysis: Foundations and Extensions, Second EditionRonald E. Miller and Peter D. BlairFrontmatterMore information

http://www.cambridge.org/9780521517133

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Input–Output AnalysisFoundations and Extensions

Second Edition

Ronald E. Miller

and

Peter D. Blair






cambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town, Singapore,São Paulo, Delhi

Cambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York

www.cambridge.orgInformation on this title: www.cambridge.org/9780521739023

© Ronald E. Miller and Peter D. Blair 2009

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.

First edition published by Prentice Hall 1985

Printed in the United Kingdom at the University Press, Cambridge

A catalog record for this publication is available from the British Library

Library of Congress Cataloguing in Publication DataMiller, Ronald E.

Input-output analysis: foundations and extensions / Ronald E. Miller andPeter D. Blair. – 2nd ed.

p. cm.ISBN 978-0-521-51713-3 (hardback) 1. Input-output analysis.I. Blair, Peter D. II. Title.

HB142.M55 2009339.2′3–dc22

2009008470

ISBN 978-0-521-51713-3 hardbackISBN 978-0-521-73902-3 paperback

Cambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication, and does not guarantee that any content on suchwebsites is, or will remain, accurate or appropriate.






Contents

List of Figures page xxii

List of Tables xxiv

Preface xxix

1 Introduction and Overview 11.1 Introduction 11.2 Input–Output Analysis: The Basic Framework 21.3 Outline for this Text 31.4 Internet Website and Text Locations of Real Datasets 8References 9

2 Foundations of Input–Output Analysis 102.1 Introduction 102.2 Notation and Fundamental Relationships 10

2.2.1 Input–Output Transactions and National Accounts 132.2.2 Production Functions and the Input–Output Model 15

2.3 An Illustration of Input–Output Calculations 212.3.1 Numerical Example: Hypothetical Figures – Approach I 21

Impacts on Industry Outputs 21Other Impacts 24

2.3.2 Numerical Example: Hypothetical Figures – Approach II 262.3.3 Numerical Example: Mathematical Observations 272.3.4 Numerical Example: The US 2003 Data 29

2.4 The Power Series Approximation of (I − A)−1 312.5 Open Models and Closed Models 342.6 The Price Model 41

2.6.1 Overview 412.6.2 Physical vs. Monetary Transactions 422.6.3 The Price Model based on Monetary Data 43

v






vi Contents

2.6.4 Numerical Examples Using the Price Model basedon Monetary Data 44Example 1: Base Year Prices 44Example 2: Changed Base Year Prices 45

2.6.5 Applications 462.6.6 The Price Model based on Physical Data 47

Introduction of Prices 48Relationship between A and C 49

2.6.7 Numerical Examples Using the Price Model based onPhysical Data 50Example 1: Base Year Prices 50Example 2: Changed Base Year Prices 51

2.6.8 The Quantity Model based on Physical Data 512.6.9 A Basic National Income Identity 53

2.7 Summary 53Appendix 2.1 The Relationship between Approaches I and II 54

A2.1.1 Approach I 54A2.1.2 Approach II 55

Appendix 2.2 The Hawkins–Simon Conditions 58Problems 62References 66

3 Input–Output Models at the Regional Level 693.1 Introduction 693.2 Single-Region Models 70

3.2.1 National Coefficients 703.2.2 Regional Coefficients 723.2.3 Closing a Regional Model with respect to Households 74

3.3 Many-Region Models: The Interregional Approach 763.3.1 Basic Structure of Two-Region Interregional Input–Output

Models 773.3.2 Interregional Feedbacks in the Two-Region Model 803.3.3 Numerical Example: Hypothetical Two-Region Interregional

Case 823.3.4 Interregional Models with more than Two Regions 863.3.5 Implementation of the IRIO Model 87

3.4 Many-Region Models: The Multiregional Approach 873.4.1 The Regional Tables 873.4.2 The Interregional Tables 893.4.3 The Multiregional Model 913.4.4 Numerical Example: Hypothetical Two-Region

Multiregional Case 93






Contents vii

3.4.5 The US MRIO Models 963.4.6 Numerical Example: The Chinese Multiregional

Model for 2000 973.5 The Balanced Regional Model 101

3.5.1 Structure of the Balanced Regional Model 1013.5.2 Numerical Example 104

3.6 The Spatial Scale of Regional Models 1053.7 Summary 106Appendix 3.1 Basic Relationships in the Multiregional Input–Output

Model 107Appendix 3.2 Sectoral and Regional Aggregation in the 2000 Chinese

Multiregional Model 109Appendix 3.3 The Balanced Regional Model and the Inverse of a

Partitioned (I − A) Matrix 110Problems 111References 115

4 Organization of Basic Data for Input–Output Models 1194.1 Introduction 1194.2 Observations on Ad Hoc Survey-Based Input–Output Tables 1194.3 Observations on Common Methods for Generating

Input–Output Tables 1204.4 A System of National Economic Accounts 121

4.4.1 The Circular Flow of Income and Consumer Expenditure 1224.4.2 Savings and Investment 1234.4.3 Adding Overseas Transactions: Imports, Exports, and Other

Transactions 1264.4.4 The Government Sector 1274.4.5 The Consolidated Balance Statement for National Accounts 1284.4.6 Expressing Net Worth 131

4.5 National Income and Product Accounting Conventions 1334.6 Assembling Input–Output Accounts: The US Case 1344.7 Additional Considerations 137

4.7.1 Secondary Production: Method of Reallocation 140Example 1: Reallocation of Secondary Production 141

4.7.2 Secondary Production: Commodity-by-Industry Accounting 142Example 2: Commodity-by-Industry Accounts 142

4.7.3 Reconciling with the National Accounts 1434.7.4 Producers’ and Consumers’ Prices 144

Example 3: Trade and Transportation Margins 1464.7.5 Accounting for Imports and Exports 149

Example 4: Competitive and Noncompetitive Imports 149






viii Contents

4.7.6 Removing Competitive Imports from Total TransactionsTables 150Approximation Method I 151Approximation Method II 151Example 5: Import Scrubbing 152Implications of the Estimating Assumptions 154

4.7.7 Adjustments for Inventory Change 1574.7.8 Adjustments for Scrap 157

4.8 Valuation and Double Deflation 157Example 6: Double Deflation 159

4.9 The Aggregation Problem: Level of Detail in Input–Output Tables 1604.9.1 The Aggregation Matrix 161

Example 7: Sectoral Aggregation 1624.9.2 Measures of Aggregation Bias 165

4.10 Summary 168Appendix 4.1 Spatial Aggregation in IRIO and MRIO Models 168

A4.1.1 Spatial Aggregation of IRIO Models 168A4.1.2 Spatial Aggregation of MRIO Models 172

Problems 176References 180

5 The Commodity-by-Industry Approach in Input–Output Models 1845.1 Introduction 184

5.1.1 The Use Matrix 1855.1.2 The Make Matrix 186

5.2 The Basic Accounting Relationships 1875.3 Technology and Total Requirements Matrices in the

Commodity–Industry Approach 1885.3.1 Industry Source of Commodity Outputs 1895.3.2 Commodity Composition of Industry Outputs 1895.3.3 Generating Total Requirements Matrices 189

Using D 190Using C 191

5.3.4 “Industry-Based” Technology 1925.3.5 “Commodity-Based” Technology 1935.3.6 Direct Requirements (Technical Coefficients) Matrices

Derived from Basic Data 1955.3.7 Total Requirements Matrices 196

Approach I: Starting with Technical Coefficients 196Approach II: Avoiding C−1 in Commodity Technology Cases 198Is Singularity Likely to be a Problem in Real-World Models? 199

5.4 Numerical Examples of Alternative Direct and Total RequirementsMatrices 201






Contents ix

5.4.1 Direct Requirements Matrices 2025.4.2 Total Requirements Matrices 202

Commodity-Demand Driven Models 202Industry-Demand Driven Models 202

5.5 Negative Elements in the Commodity–Industry Framework 2035.5.1 Commodity Technology 203

Direct Requirements Matrices 203Transactions Matrices 205Total Requirements Matrices 206

5.5.2 Industry Technology 207Direct Requirements Matrices 207Total Requirements Matrices 207

5.5.3 Making a Model Choice 208Which Model to Choose? 208Dealing with Negative Values 209

5.6 Nonsquare Commodity–Industry Systems 2115.6.1 Commodity Technology 2115.6.2 Industry Technology 212

Direct Requirements Matrices 212Total Requirements Matrices 213

5.7 Mixed Technology in the Commodity–Industry Framework 2135.7.1 Commodity Technology in V1 2165.7.2 Industry Technology in V1 2185.7.3 Numerical Examples with Mixed Technology

Assumptions 219Example 1: Commodity Technology in V1 219Example 2: Industry Technology in V1 220

5.7.4 Additional Mixed Technology Variants 2205.8 Summary 222Appendix 5.1 Alternative Approaches to the Derivation of Transactions

Matrices 223A5.1.1 Industry Technology 224

Commodity-by-Commodity Requirements 224Industry-by-Industry Requirements 225

A5.1.2 Commodity Technology 226Commodity-by-Commodity Requirements 226Industry-by-Industry Requirements 228

Appendix 5.2 Elimination of Negatives in Commodity TechnologyModels 229

A5.2.1 The Problem 2293 × 3 Example 2294 × 4 Example 2295 × 5 Example (from Almon, 2000) 230






x Contents

A5.2.2 Approaches to Elimination of Negative Elements 230A5.2.3 Results of the Iterative Procedure 234

3 × 3 Example 2344 × 4 Example 2345 × 5 Example 235


6 Multipliers in the Input–Output Model 2436.1 Introduction 2436.2 General Structure of Multiplier Analysis 244

6.2.1 Output Multipliers 245Simple Output Multipliers 245Total Output Multipliers 247Example: The US Input–Output Model for 2003 248Output Multipliers in Commodity–Industry Models 249Commodity-Demand-Driven Models 249Industry-Demand-Driven Models 250

6.2.2 Income/Employment Multipliers 250Income Multipliers 250Type I and Type II Income Multipliers 252Relationship Between Simple and Total Income Multipliers orBetween Type I and Type II Income Multipliers 253Which Multiplier to Use? 254Even More Income Multipliers 255Physical Employment Multipliers 255

6.2.3 Value-Added Multipliers 2566.2.4 Matrix Representations 2566.2.5 Summary 257

6.3 Multipliers in Regional Models 2596.3.1 Regional Multipliers 2596.3.2 Interregional Input–Output Multipliers 261

Intraregional Effects 261Interregional Effects 262National Effects 263Sectoral Effects 263More Than Two Regions 264

6.3.3 Multiregional Input–Output Multipliers 264Intraregional Effects 266Interregional Effects 267National Effects 267Sectoral Effects 267






Contents xi

Final Demand for Goods Made in a Particular Region 267More Than Two Regions 268

6.4 Miyazawa Multipliers 2716.4.1 Disaggregated Household Income Groups 2716.4.2 Miyazawa’s Derivation 2736.4.3 Numerical Example 2756.4.4 Adding a Spatial Dimension 276

6.5 Gross and Net Multipliers in Input–Output Models 2786.5.1 Introduction 2786.5.2 Multipliers in the Net Input–Output Model 278

Numerical Example 2806.5.3 Additional Multiplier Variants 280

(Indirect Effects)/(Direct Effects) 280“Growth Equalized” Multipliers 281Another Kind of Net Multiplier 282

6.6 Multipliers and Elasticities 2836.6.1 Output Elasticity 2836.6.2 Output-to-Output Multipliers and Elasticities 283

Direct Effects 283Total Effects 284

6.7 Multiplier Decompositions 2856.7.1 Fundamentals 2856.7.2 Decompositions in an Interregional Context 2866.7.3 Stone’s Additive Decomposition 2886.7.4 A Note on Interregional Feedbacks 2896.7.5 Numerical Illustration 290

6.8 Summary 294Appendix 6.1 The Equivalence of Total Household Income Multipliers

and the Elements in the Bottom Row of (I − A)−1 295Appendix 6.2 Relationship Between Type I and Type II Income

Multipliers 296Problems 297References 299

7 Nonsurvey and Partial-Survey Methods: Fundamentals 3037.1 Introduction 3037.2 The Question of Stability of Input–Output Data 303

7.2.1 Stability of National Coefficients 304Comparisons of Direct-Input Coefficients 305Comparisons of Leontief Inverse Matrices 305Other Summary Measures 307Data for the US Economy 307






xii Contents

7.2.2 Constant versus Current Prices 3077.2.3 Stability of Regional Coefficients 3097.2.4 Summary 310

7.3 Updating and Projecting Coefficients: Trends, Marginal Coefficientsand Best Practice Methods 3117.3.1 Trends and Extrapolation 3117.3.2 Marginal Input Coefficients 3117.3.3 “Best Practice” Firms 312

7.4 Updating and Projecting Coefficients: The RAS Approachand Hybrid Methods 3137.4.1 The RAS Technique 3137.4.2 Example of the RAS Procedure 3207.4.3 Updating Coefficients vs. Transactions 327

Numerical Illustration 3277.4.4 An Economic Interpretation of the RAS Procedure 3287.4.5 Incorporating Additional Exogenous Information in an RAS

Calculation 3307.4.6 Modified Example: One Coefficient Known in Advance 3317.4.7 Hybrid Models: RAS with Additional Information 3337.4.8 The Constrained Optimization Context 3347.4.9 Infeasible Problems 335

7.5 Summary 336Appendix 7.1 RAS as a Solution to the Constrained Minimum Information

Distance Problem 337Problems 338References 343

8 Nonsurvey and Partial-Survey Methods: Extensions 3478.1 Introduction 3478.2 Location Quotients and Related Techniques 349

8.2.1 Simple Location Quotients 3498.2.2 Purchases-Only Location Quotients 3538.2.3 Cross-Industry Quotients 3538.2.4 The Semilogarithmic Quotient and its Variants,

FLQ and AFLQ 3548.2.5 Supply–Demand Pool Approaches 3568.2.6 Fabrication Effects 3568.2.7 Regional Purchase Coefficients 3578.2.8 “Community” Input–Output Models 3588.2.9 Summary 359

8.3 RAS in a Regional Setting 3608.4 Numerical Illustration 361






Contents xiii

8.5 Exchanging Coefficients Matrices 3638.6 Estimating Interregional Flows 364

8.6.1 Gravity Model Formulations 3658.6.2 Two-Region Interregional Models 3668.6.3 Two-Region Logic with more than Two Regions 3678.6.4 Estimating Commodity Inflows to a Substate Region 3698.6.5 Additional Studies 371

Commodity Flows among US States 371An Optimization Model for Interregional Flows 372

8.7 Hybrid Methods 3738.7.1 Generation of Regional Input–Output Tables (GRIT) 3748.7.2 Double-Entry Bi-Regional Input–Output Tables (DEBRIOT) 3758.7.3 The Multiregional Input–Output Model for China, 2000

(CMRIO) 3778.8 International Input–Output Models 378

8.8.1 Introduction 3788.8.2 Asian International Input–Output Tables 3788.8.3 “Hybrid” Many-Region Models for the EC 3808.8.4 China–Japan “Transnational Interregional” Input–Output

(TIIO) Model, 2000 381Chinese Exports to Japan for Intermediate Demand 381Applications 383

8.8.5 Leontief’s World Model 3838.9 The Reconciliation Issue 3848.10 Summary 386Appendix 8.1 Geographical Classifications in the World Input–Output

Model 387Problems 387References 392

9 Energy Input–Output Analysis 3999.1 Introduction 399

9.1.1 Early Approaches to Energy Input–Output Analysis 4009.1.2 Contemporary Energy Input–Output Analysis 400

9.2 Overview Concepts of Energy Input–Output Analysis 4019.2.1 The Basic Formulation 4039.2.2 The Total Energy Requirements Matrix 404

Example 9.1: Two-Sector Illustration of Hybrid UnitsInput–Output Analysis 407Example 9.2: Generalization to Several Energy Types 408

9.2.3 The Hybrid Units Formulation and Energy ConservationConditions 410






xiv Contents

Example 9.2: Generalization to Several Energy Types(Revisited) 411

9.3 Further Methodological Considerations 4119.3.1 Adjusting for Energy Conversion Efficiencies 412

Example 9.3: Adjusting for Energy Conversion Efficiencies 4129.3.2 Accounting for Imports 4139.3.3 Commodity-by-Industry Energy Models 413

9.4 Applications 4149.4.1 Net Energy Analysis 414

Example 9.4: Net Energy Analysis 4159.4.2 Energy Cost of Goods and Services 4179.4.3 Impacts of New Energy Technologies 4219.4.4 An Energy Tax 4219.4.5 Energy and Structural Change 4219.4.6 Energy Input–Output and Econometrics 4239.4.7 Other Applications 427

9.5 Summary 427Appendix 9.1 Earlier Formulation of Energy Input–Output Models 428

A9.1.1 Introduction 428A9.1.2 Illustration of the Implications of the Traditional Approach 430

Example 9.5: Energy Input–Output Alternative Formulation 430Example 9.6: Energy Input–Output Example (Revised) 431Extensions of Example 9.1 433

A9.1.3 General Limitations of the Alternative Formulation 437Problems 437References 442

10 Environmental Input–Output Analysis 44610.1 Introduction 44610.2 Basic Considerations 44610.3 Generalized Input–Output Analysis: Basic Framework 447

10.3.1 Accounting for Pollution Impacts 44710.3.2 Generalized Impacts 447

Example 10.1: Generalized Input–Output Analysis 44810.3.3 Summary: Generalized Input–Output Formulations 451

Case I: Impact Analysis Form 451Case II: Planning Form 452

10.4 Generalized Input–Output Analysis: Extensions of thePlanning Approach 45210.4.1 Linear Programming: A Brief Introduction by Means of the

Leontief Model 45210.4.2 Multiple Objectives 457






Contents xv

10.4.3 Conflicting Objectives and Linear Goal Programming 45710.4.4 Additional Observations 461

Specifying Objectives 461Tightly Constrained Problems 462Solution Methods 462

10.4.5 Applications to the Generalized Input–Output PlanningProblem 463

10.4.6 Policy Programming 469Impact Analysis Form 470Planning Form 470

10.4.7 Ecological Commodities 47310.5 An Augmented Leontief Model 475

10.5.1 Pollution Generation 47510.5.2 Pollution Elimination 478

Example 10.2: Pollution-Activity-Augmented LeontiefModel 479

10.5.3 Existence of Non-negative Solutions 480Example 10.2 (Revisited): Pollution-Activity-AugmentedLeontief Model 482

10.6 Economic–Ecologic Models 48310.6.1 Fully Integrated Models 48310.6.2 Limited Economic–Ecologic Models 484

Economic Subsystem 484Ecologic Subsystem 485Commodity-by-Industry Formulation 485Example 10.3: Limited Economic–Ecologic Models 485

10.7 Pollution Dispersion 48710.7.1 Gaussian Dispersion Models 48710.7.2 Coupling Pollution Dispersion and Input–Output Models 488

Example 10.4: Coupling Input–Output and PollutionDispersion Models 488

10.8 Other Applications 48910.9 Summary 490Problems 490References 494

11 Social Accounting Matrices 49911.1 Introduction 49911.2 Social Accounting Matrices: Background 49911.3 Social Accounting Matrices: Basic Concepts 50111.4 The Households Account 50211.5 The Value-Added Account 504






xvi Contents

11.6 Interindustry Transactions and the Connection to the Input–OutputFramework 504

11.7 Expanding the Social Accounts 50711.8 Additional Social Accounting Variables 50711.9 A “Fully Articulated” SAM 51011.10 SAM Multipliers 513

11.10.1 SAM Multipliers: Basic Structure 51411.10.2 Decomposition of SAM Multipliers 516

Example 11.1: Reduced Form Case 51811.10.3 Multipliers in an Expanded SAM 522

Example 11.2: The Expanded Case 52411.10.4 Additive Multipliers 528

11.11 The Relationship between Input–Output and SAM Multipliers 53011.12 Balancing SAM Accounts 535

11.12.1 Example: Balancing a SAM 53511.12.2 Example: Balancing a SAM with Additional

Information 53611.13 Some Applications of SAMs 53611.14 Summary 537Problems 537References 541

12 Supply-Side Models, Linkages, and Important Coefficients 54312.1 Supply Side Input–Output Models 543

12.1.1 The Early Interpretation 543Numerical Illustration (Hypothetical Data) 546Numerical Application (US Data) 547

12.1.2 Relationships between A and B and between L and G 54712.1.3 Comments on the Early Interpretation 54812.1.4 Joint Stability 549

The Issue 549Conditions under which both A and B will be Stable 551

12.1.5 Reinterpretation as a Price Model 551Connection to the Leontief Price Model (Algebra) 553Connection to the Leontief Price Model (NumericalIllustration) 553A Ghosh Quantity Model 554

12.2 Linkages in Input–Output Models 55512.2.1 Backward Linkage 55612.2.2 Forward Linkage 55812.2.3 “Net” Backward Linkage 55812.2.4 Classifying Backward and Forward Linkage Results 559






Contents xvii

12.2.5 Spatial Linkages 56012.2.6 Hypothetical Extraction 563

Backward Linkage 564Forward Linkage 564

12.2.7 Illustration Using US Data 56512.3 Identifying Important Coefficients 567

12.3.1 Mathematical Background 56812.3.2 Relative Sizes of Elements in the Leontief Inverse 569

Observation 1 569Observation 2 570Observation 3 570

12.3.3 “Inverse-Important” Coefficients 57012.3.4 Numerical Example 57212.3.5 Impacts on Gross Outputs 57312.3.6 Fields of Influence 57812.3.7 Additional Measures of Coefficient Importance 580

Converting Output to Employment, Income, etc. 580Elasticity Coefficient Analysis 581Relative Changes in All Gross Outputs 581Impacts of Changes in more than One Element of theA Matrix 582

12.4 Summary 582Appendix 12.1 The Sherman–Morrison–Woodbury Formulation 582

A12.1.1 Introduction 582A12.1.2 Application to Leontief Inverses 585


13 Structural Decomposition, Mixed and Dynamic Models 59313.1 Structural Decomposition Analysis 593

13.1.1 Initial Decompositions: Changes in Gross Outputs 593Numerical Example 596

13.1.2 Next-Level Decompositions: Digging Deeper into�f and �L 598Additive Decompositions with Products of more than Two Terms 598Changes in Final Demand 599

13.1.3 Numerical Examples 601One Category of Final Demand (p = 1) 601Two Categories of Final Demand (p = 2) 601

13.1.4 Changes in the Direct Inputs Matrix 602Decomposition of �L 602Decomposition of �A 604Numerical Illustration (continued) 605






xviii Contents

13.1.5 Decompositions of Changes in Some Function of x 60613.1.6 Summary for �x 60713.1.7 SDA in a Multiregional Input–Output (MRIO) Model 60713.1.8 Empirical Examples 608

Studies Using National Models 608Studies Using a Single-Region or Connected-RegionModel 615

13.2 Mixed Models 62113.2.1 Exogenous Specification of One Sector’s Output 621

Rearranging the Basic Equations 621“Extracting” the Sector 624

13.2.2 An Alternative Approach When f1, . . ., fn−1 and xn AreExogenously Specified 625

13.2.3 Examples with xn Exogenous 626Example 1: f1 = 100, 000, f2 = 200, 000,x3 = 150, 000 626Example 2: f1 = f2 = 0, x3 = 150, 000 627Example 3: f1 = 100, 000, f2 = 200, 000, x3 = 100, 000 628Example 4: The Critical Value of x3 628Multipliers 629

13.2.4 Exogenous Specification of f1, . . ., fk , xk+1, . . ., xn 62913.2.5 An Example with xn−1 and xn Exogenous 632

Example 5 (Example 2 expanded) 63213.3 New Industry Impacts in the Input–Output Model 633

13.3.1 New Industry: The Final-Demand Approach 63413.3.2 New Industry: Complete Inclusion in the Technical

Coefficients Matrix 63613.3.3 A New Firm in an Existing Industry 63713.3.4 Other Structural Changes 639

13.4 Dynamic Considerations in Input–Output Models 63913.4.1 General Relationships 63913.4.2 A Three-Period Example 642

Terminal Conditions 643Initial Conditions 644

13.4.3 Numerical Example 1 645Terminal Conditions 646Initial Conditions 648

13.4.4 Numerical Example 2 649Terminal Conditions 649Initial Conditions 649

13.4.5 “Dynamic” Multipliers 65013.4.6 Turnpike Growth and Dynamic Models 651

Example 653






Contents xix

13.4.7 Alternative Input–Output Dynamics 65313.5 Summary 654Appendix 13.1 Alternative Decompositions of x = LBf 655Appendix 13.2 Exogenous Specification of Some Elements of x 656

A13.2.1 The General Case: An n-sector Model with k EndogenousOutputs 656

A13.2.2 The Output-to-Output Multiplier Matrix 658A13.2.3 The Inverse of a Partitioned (I − A(n)) Matrix 659A13.2.4 The Case of k = 2, n = 3 659A13.2.5 The Case of k = 1, n = 3 660A13.2.6 “Extracting” the Last (n − k) Sectors 662


14 Additional Topics 66914.1 Introduction 66914.2 Input–Output and Measuring Economic Productivity 670

14.2.1 Total Factor Productivity 67014.2.2 Numerical Example: Total Factor Productivity 67214.2.3 Accounting for Prices 67314.2.4 References for Section 14.2 674

14.3 Graph Theory, Structural Path Analysis, and QualitativeInput–Output Analysis (QIOA) 67414.3.1 References for Section 14.3 677

14.4 Fundamental Economic Structure (FES) 67814.4.1 References for Section 14.4 679

14.5 Input–Output, Econometrics, and Computable General EquilibriumModels 67914.5.1 The Variable Input–Output Model 68014.5.2 Regional Input–Output Econometric Models 68114.5.3 Computable General Equilibrium Models 68114.5.4 References for Section 14.5 682

14.6 Additional Resources for Input–Output Extensions andApplications 68314.6.1 Edited Collections 68414.6.2 Journal Special Issues 68514.6.3 Collections of Reprints 68614.6.4 References for Section 14.6 686

14.7 Some Concluding Reflections 686






xx Contents

Appendix A Matrix Algebra for Input–Output Models 688A.1 Introduction 688A.2 Matrix Operations: Addition and Subtraction 689

A.2.1 Addition 689A.2.2 Subtraction 689A.2.3 Equality 689A.2.4 The Null Matrix 689

A.3 Matrix Operations: Multiplication 689A.3.1 Multiplication of a Matrix by a Number 689A.3.2 Multiplication of a Matrix by Another Matrix 689A.3.3 The Identity Matrix 690

A.4 Matrix Operations: Transposition 691A.5 Representation of Linear Equation Systems 691A.6 Matrix Operations: Division 693A.7 Diagonal Matrices 696A.8 Summation Vectors 698A.9 Matrix Inequalities 698A.10 Partitioned Matrices 699

A.10.1 Multiplying Partitioned Matrices 699A.10.2 The Inverse of a Partitioned Matrix 700

References 701

Appendix B Reference Input–Output Tables for the United States(1919–2006) 702

B.1 Introduction 702B.2 Transactions Accounts 703B.3 Matrices of Technical Coefficients and Total Requirements 715References for US Input–Output Tables (1919–2006) 722

Appendix C Historical Notes on the Development of Leontief’sInput–Output Analysis 724

C.1 Conceptual Foundations 724C.2 Quesnay and the Physiocrats 725C.3 Mathematical Formalization 728C.4 Leontief and the “Economy as a Circular Flow” 729C.5 Development of Input–Output Analysis 731References 735






Contents xxi

Author Index 738

Subject Index 746

The Following Supplementary Appendices are Available Online atwww.cambridge.org/millerandblairWeb Appendix 5W.1 Left and Right Inverses in Nonsquare Input–Output

SystemsA5W.1.1 IntroductionA5W.1.2 More Commodities than Industries (m > n)

Numerical IllustrationCommodity TechnologyIndustry Technology

A5W.1.3 Fewer Commodities than Industries (m < n)Numerical IllustrationCommodity TechnologyIndustry Technology

Web Appendix 8W.1 Detailed Results for the Numerical Illustration inSection 8.4

Web Appendix 12W.1 Hypothetical Extractions with Partitioned MatricesA12W.1.1 Case 1: Complete Extraction of Sector 1A12W.1.2 Case 2: Extraction of Sector 1’s Intersectoral RelationsA12W.1.3 Case 3: Extraction of Sector 1’s Intermediate PurchasesA12W.1.4 Case 4: Extraction of Sector 1’s Intermediate SalesA12W.1.5 Case 5: Extraction of Sector 1’s Intersectoral Intermediate

PurchasesA12W.1.6 Case 6: Extraction of Sector 1’s Intersectoral Intermediate

SalesA12W.1.7 The Ghosh Model and Some Comparisons

Web Appendix 12W.2 Brief History of Leontief Inverses with Errors in theCoefficients of AA12W.2.1 Mathematical BackgroundA12W.2.2 Application of Leontief Inverses

Dwyer and Waugh (1953)Evans (1954)West (1982)Sherman-Morrison and Sonis-Hewings






Figures

1.1 Input–Output Transactions Table 32.1a–d Production Functions in Input Space. (a) Linear production function.

(b) Classical production function. (c) Leontief production function.(d) Activity analysis production function. 18

A2.2.1a Solution Space Representation of (A2.2.2); a12 > 0 and a21 > 0 59A2.2.1b Solution Space Representation of (A2.2.2); a21 = 0 60A2.2.1c Solution Space Representation of (A2.2.2); a12 = 0 613.1 Increases in Washington Final Demands Affecting Washington Outputs

via Connecticut 80A3.2.1 Regional Aggregation in the 2000 Chinese Multiregional Model 1094.1 The Circular Flow of Income and Expenditures 1224.2 Circular Flow Example: Point of Departure 1234.3 Introduction of Savings and Investment into the Circular Flow of

Income and Expenditures 1244.4 Introduction of Depreciation into the Circular Flow of Income

and Expenditures 1244.5 Addition of the Rest of World Account 1264.6 Addition of the Government Account 1284.7 Net Worth 1319.1 US Energy Use for 2006 4029.2 Net Energy Analysis 4149.3 Changes in US Energy Consumption: 1972–1985 4239.4 Hudson–Jorgenson Model 42410.1 Two-Sector Leontief Model 45310.2 Input–Output and Linear Programming: Example 10.1 45410.3 Different Values of GNP for Example 10.1 45510.4 Linear Programming Solution 45810.5 Goal Programming Solution: Objective 1 46010.6 Goal Programming Solution: Objective 2 46010.7 Goal Programming Solution: Objective 3 461

xxii






List of Figures xxiii

10.8 Goal Programming Solution: Objective 4 46210.9 Goal Programming Generalized Input–Output Initial Solution 46410.10 Generalized Input–Output Goal Programming: Example 10.1

(Objective 1) 46510.11 Generalized Input–Output Goal Programming: Example 10.1





(Objective 6) 46810.16 Location of Air Pollution Sources and Receptor Points 48911.1 Circular Flow of Income, Expenditure, and Markets 50011.2 Sample Macroeconomy: Problem 11.1 537C.1 François Quesnay’s Tableau Économique 727






Tables

1.1 Illustrative Real Input–Output Data Locations 82.1 Input–Output Table of Interindustry Flows of Goods 132.2 Expanded Flow Table for a Two-Sector Economy 142.3 Flows (zij) for the Hypothetical Example 222.4 Technical Coefficients (the A Matrix) for the Hypothetical Example 222.5 Flows (zij) for the Hypothetical Example Associated with xnew 242.6 Round-by-Round Impacts (in dollars) of f 1

1 = $600 and f 12 = $1500 27

2.7 The 2003 US Domestic Direct Requirements Matrix, A 292.8 The 2003 US Domestic Total Requirements Matrix, L = (I − A)−1 292.9 Input–Output Table of Interindustry Flows with Households Endogenous 352.10 Flows (zij) for Hypothetical Example, with Households Endogenous 382.11 Transactions in Physical Units 422.12 Transactions in Monetary Units 422.13 Transactions in Revised Physical Units 422.14 Transactions in Monetary Terms 432.15 The Leontief Quantity and Price Models 452.16 Transactions for Hypothetical Example with One Primary Input 452.17 Flows in Physical Units 472.18 Transactions in Physical Terms (Germany, 1990) (millions of tons) 522.19 Alternative Input–Output Price and Quantity Models 543.1 Interindustry, Interregional Flows of Goods 773.2 Flow Data for a Hypothetical Two-Region Interregional Case 823.3 Data Needed for Conversion of National to Regional Coefficients via the

Product-Mix Approach 893.4 Interregional Shipments of Commodity i 903.5 Flow Data for a Hypothetical Two-Region Multiregional Case 933.6 Interregional Commodity Shipments for the Hypothetical Two-Region

Multiregional Case 943.7 Chinese Interregional and Intraregional Transactions, 2000 (in �10,000) 983.8 Direct Input Coefficients for the Chinese Multiregional Economy, 2000 99

xxiv






List of Tables xxv

3.9 Leontief Inverse Matrix for the Chinese Multiregional Economy, 2000 1003.10 Region- and Sector-Specific Effects (in �1000) of a �100,000

Increase in Final Demand for Manufacturing Goods, China, 2000 101A3.2.1 Regional Classifications in the 2000 Chinese Multiregional Model 109A3.2.2 Sectoral Aggregation in the 2000 Chinese Multiregional Model 1104.1 Basic National Accounts: Example Economy 1254.2 Basic National Accounts Including Rest of World 1274.3 Basic National Accounts Including the Government Sector 1294.4 Balance Statement for the Basic National Accounts 1304.5 The Basic National Accounts Balance Statement in Matrix Form 1304.6 Matrix of National Accounts Including Net Worth Calculations 1324.7 The Commodity-by-Industry Use Table 1364.8 The Industry-by-Commodity Make Table 1384.9 Consolidated Make and Use Accounts 1394.10 Input–Output Transactions: Example 1 1414.11 Consolidated Input–Output Accounts: Example 2 1434.12 Production Account Allocated to Individual Products and Sectors 1454.13 Industry-by-Commodity Make Matrix: Running Example 1464.14 Consolidated Commodity-by-Industry Input–Output Accounts: Running

Example 1474.15 Example Trade and Transportation Margins: Example 2 1484.16 Domestic Interindustry Transactions: Example 4 1504.17 Modified Interindustry Transactions: Example 4 1504.18 Approximation Methods for Scrubbing Interindustry Transactions of

Competitive Imports: Example 5 1554.19 Double Deflation: Example 6 159A4.1.1 Input Coefficients for the Five-Sector, Three-Region Interregional

Input–Output Table for Japan (1965) 169A4.1.2 Spatial Aggregation of IRIO Models: Results for Japanese IRIO Table 171A4.1.3 Five-Sector, Three-Region Multiregional Input–Output Tables for the

United States (1963) 173A4.1.4 Spatial Aggregation of MRIO Models: Results for US MRIO Model 1755.1 The Use Matrix (U) and Other Data for a Two-Commodity,

Two-Industry Hypothetical Example (in Dollars) 1865.2 The Make Matrix (V) and Other Data for a Two-Commodity,

Two-Industry Hypothetical Example (in Dollars) 1875.3 The Complete Set of Commodity–Industry Data 1875.4 Total Requirements Matrices, Commodity-Demand Driven Models 1975.5 Total Requirements Matrices, Industry-Demand Driven Models 1975.6 Rewritten Forms of Total Requirements Matrices 1995.7 Alternative Classifications, Total Requirements Matrices,

Commodity-Demand Driven Models 209






xxvi List of Tables

5.8 Examples of Negative Elements in Real-World Commodity-TechnologyDirect Requirements Matrices [ AC

(c×c)= BC−1] 210

5.9 A Three-Commodity, Two-Industry Example 2125.10 Share of Secondary Product Output in Total Industry Output (European

Union Countries, 60-sector level) 223A5.2.1 Summary of Two Commodity/Two Industry Results 230A5.2.2 Steps in the Iterative Procedure for the 3 × 3 Example 2355.11 Commodity Final Demands for US 2003 Input–Output Tables 2396.1 Total Requirements Matrices in Commodity–Industry Models 2496.2 Model Closures with Respect to Households 2566.3 Input–Output Multipliers 2586.4 General Multiplier Formulas 2596.5 Leontief Inverse Matrix, L, for the Chinese Multiregional

Economy, 2000 2696.6 Simple Intra- and Interregional Output Multipliers for the Chinese

Multiregional Input–Output System, 2000 2706.7 Sector-Specific Simple Output Multipliers for the Chinese Multiregional

Input–Output System, 2000 2716.8 Interrelational Interregional Income Multipliers 2777.1 Values of a11 and a23 at Each Step in the RAS Adjustment Procedure 3237.2 Differences from Row and Column Margins at Each Step in the RAS

Adjustment Procedure 3237.3 Elements in the Diagonal Matrices rk and sk , for k = 1, . . . , 7 3247.4 MAD and MAPE when One Coefficient is Known in Advance in an RAS

Estimate 3328.1 Total Intraregional Intermediate Inputs and Intraregional Output

Multipliers for Region 1 (North China) Calculated from SeveralRegionalization Techniques 362

8.2 Components in the DEBRIOT Approach 3758.3 Structure of the TIIO Model 3818.4 China-to-Japan Intermediate Transactions in TIIO 3829.1 Energy and Dollar Flows: Example 9.1 4079.2 Interindustry Economic Transactions: Example 9.2 (millions of dollars) 4099.3 Energy Flows: Example 9.2 (1015 BTUs) 4099.4 Interindustry Transactions in Hybrid Units: Example 9.3 4129.5 Input–Output Transactions for the US Economy in Hybrid Units (1967) 4169.6 Technical Coefficients: Example 9.4 4189.7 Leontief Inverse: Example 9.4 4199.8 Total Primary Energy Intensities: Example 9.4 4209.9 Power Plant Inputs: Example 9.4 4209.10 Summary of Energy Input–Output Relationships: Initial Formulation 428A9.1.1 Dollar Transactions for Example 9.5 (millions of dollars) 431






List of Tables xxvii

A9.1.2 Energy Flows for Example 9.5 (1015 BTUs) 431A9.1.3 Energy Flows for Example 1 Revised (1015 BTUs) 432A9.1.4 Summary of Energy Input–Output Relationships 433A9.1.5 Energy and Dollar Flows for Example 9.1 (Revised) 435A9.1.6 Implied Energy Prices for Example 9.1 (Revised) 435A9.1.7 Results for Example 9.1 (Revised) 43510.1 Input–Output Transactions (millions of dollars) 44810.2 Direct Impact Coefficients 44810.3 Policy Programming: Composite Scenario Weights 47210.4 Economic–Ecologic Commodity Flows 47410.5 Economic–Ecologic Commodity Flows: Matrix Definitions 47610.6 Pollution-Generation Example: Dollar Transactions 47610.7 Input–Output Transactions: Pollution-Expanded Model Example 47910.8 Basic Structure of Economic–Ecologic Models 48310.9 Limited Commodity-by-Industry Economic–Ecologic Model 48510.10 Economic–Ecologic Models: Example 10.3 48611.1 The Basic National Accounts Balance Statement in Matrix Form 50111.2 (Table 4.5 Revisited) The Basic National Accounts Balance Statement in

Matrix Form: Example 50211.3 The Basic National Accounts Balance Statement in Matrix

Form Expanded to Include the Households Account 50311.4 The Basic National Accounts Balance Statement in Matrix

Form: Example, Expanded to Include the Households Account 50411.5 The Basic National Accounts Balance Statement in Matrix Form Expanded

to Include the Value-Added Account 50511.6 The Basic National Accounts Balance Statement in Matrix Form:

Example, Expanded to Include the Value-Added Account 50511.7 SAM Framework Example: Input–Output Representation 50611.8 SAM Framework Example Using Social Accounting Conventions 50611.9 Input–Output Accounts for Table 11.6 Revisited 50811.10 Expanded Value-Added Accounts 50911.11 Expanded Final-Demand Accounts 50911.12 Sources of Value-Added Income 50911.13 Expanded Input–Output Accounts 51111.14 SAM Representation of Expanded Input–Output Accounts 51211.15 The Basic National Accounts Balance Statement in Matrix

Form Expanded to Include Additional Macro Transactions 51311.16 Expanded National Accounts Balance Statement in Matrix

Form: Example, Expanded to Include Additional Macro Transactions 51311.17 Reduced Form Fully Articulated SAM: Example 11.1 51911.18 Expanded Form Fully Articulated SAM: Example 11.1 52511.19 SAM Framework Example Using Social Accounting Conventions

(revised to include endogenous final demand) 532






xxviii List of Tables

11.20 Comparative Input–Output and SAM Multipliers 53511.21 Unbalanced SAM: Examples 11.12.1 and 11.12.2 53611.22 SAM with Expanded Interindustry Detail for United States, 1988 54012.1 Overview of the Leontief and Ghosh Quantity and Price Models 55512.2 Linkage Measures 55912.3 Classification of Backward and Forward Linkage Results 56012.4 Summary of Spatial/Sectoral Linkage Measures (Two-Region Example) 56212.5 Hypothetical Extraction Linkages 56512.6 Linkage Results, US 2003 Data 56612.7 Classification of Linkage Results, US 2003 Data 56612.8 Hypothetical Extraction Results, US 2003 Data 56612.9 Classification of Hypothetical Extraction Results, US 2003 Data 56712.10 Number of Important Transactions in the 2000 China MRIO Model 56812.11 (lri/xr) × 106 for the 2003 US Seven-Sector Model 57512.12 Percentage Change in x Resulting from �aij = (0.2)aij 57512.13 Upper Threshold on �aij/aij for γ = 1 Percent 57612.14 Average Values in US Total Requirements Matrices 57712.15 Column Sums of |F[i, j]| for Numerical Example 58012.16 Sum of all Elements in |F[i, j]| (‖F‖ = ∑

ij

∣∣ fij∣∣) 580

13.1 Alternative Structural Decompositions 59713.2 Sector-Specific and Economy-Wide Decomposition Results [Equation

(13.7)] 59713.3 Sector-Specific and Economy-Wide Decomposition Results (with

Two-Factor Final-Demand Decomposition Detail) 60213.4 Sector-Specific and Economy-Wide Decomposition Results (with

Three-Factor Final-Demand Decomposition Detail) 60313.5 Sector-Specific and Economy-Wide Decomposition Results (with

Additional Technology and Final-Demand Decomposition Detail) 60613.6 Selected Empirical Structural Decomposition Studies 61213.7 Selected Empirical Structural Decompositions of Changes in Energy

Use or Pollution Emissions 61613.8 SDA Percentage Change Sensitivities 61713.9 Selected Empirical Structural Decompositions at a Regional,

Interregional or Multiregional Level 620A13.1.1 Alternative Decompositions of x = LBf 657B.2 Transactions Accounts 703B.3 Matrices of Technical Coefficients and Total Requirements 715C.1 Selected International Conferences on Input–Output Analysis 733






Preface

We started working on the first edition of this book (Miller and Blair, 1985) in the late1970s. At that time, input–output as an academic topic (outside of Wassily Leontief’sHarvard research group) was a little more than 25 years old – 1952–1979, give ortake a year at either end. We use 1952 because that was when the first author wasintroduced to input–output analysis in a sophomore-year economics class at Harvardtaught by Robert Kuenne, who later claimed that was the first time input–output hadbeen included (anywhere) in an undergraduate economics course.

In 1962, the first author joined the faculty of the Regional Science Department atthe University of Pennsylvania. He was asked by then department chair Walter Isardto teach the graduate course in linear models for regional analysis; this was to includea strong input–output component. At that time coverage of the topic in texts was to befound primarily in two chapters of Dorfman, Samuelson and Solow (1958), in Cheneryand Clark (1959), in Stone (1961) and in a long chapter on input–output at the regionallevel in Isard et al. (1960); later there were texts by Miernyk (1965), Yan (1969), andRichardson (1972).

The second author of the current text began teaching an applied course coveringextensions of the input–output approach to energy, environmental, and other contem-porary policy issues of the time in that same regional science program at Penn in theearly 1970s, and by the end of that decade the need for a comprehensive and up-to-datetextbook became apparent to us. So the first edition of this book very much reflectedour shared experiences with students (primarily graduate or undergraduate submatric-ulants) in mostly regional science and public policy courses at Penn during the 1960sand 1970s. In addition to the basics (“foundations”), many of the additional topicswe included (“extensions”) reflected our research interests at that time – interregionalfeedbacks for one of us, energy and environmental applications for the other and spatialaggregation in many-region models as a joint interest.

Over the past decade or so it became increasingly and abundantly clear that thetime was ripe for an update/revision. We began to take this notion seriously around2000–2001 – almost an additional 25 years further into the input–output timeline, so

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xxx Preface

the subject was essentially twice as old as when we wrote the first edition. Activity inthe field during that quarter century seems to have exploded. For example:

• The International Input–Output Association (IIOA) was founded (1988).• The IIOA’s journal, Economic Systems Research, began publication (1989).• International conferences were held with increasing frequency and drawing increas-

ing numbers of participants (summarized at the end of Appendix C) and startingrecently, “intermediate” input–output meetings are held in nonconference years,co-organized by the IIOA.

• In 1998 Heinz Kurz, Erik Dietzenbacher and Christian Lager published an editedthree-volume set of almost 1,500 pages that reproduces some 85 significant input–output papers, along with extensive and detailed introductions to each of the volumes(Kurz, Dietzenbacher and Lager, 1998).

These activities are in part a reflection of enormous increases in computer speed andcapacity since the 1950s. The net result is that there is now considerable new materialto be examined, digested and considered for inclusion and explanation.

Accordingly, around the end of 2000 we communicated with about 30 of our input–output colleagues throughout the world, asking for help in finding our way throughthis maze of material. We listed some new topics that we thought should be included(e.g., social accounting matrices or SAMs), some that we might emphasize more (e.g.,commodity-by-industry models), some less (e.g., detailed numerical interregional ormultiregional examples), and we asked for reactions and suggestions. Additionally, wetook into account what we knew of the uses to which the first edition had been put, e.g.,as a text for teaching purposes or desk reference for practitioners and researchers.

As a result, we have added some discussion of:

• SAMs (and extended input–output models) and their connection to input–output data;• Structural decomposition analysis (SDA);• Multiplier decompositions [Miyazawa, additive (Stone), multiplicative (Pyatt and

Round)];• Identifying important coefficients;• International input–output models.

We have expanded discussions of:

• The historical background and context for Leontief’s work;• The connection of input–output accounts and national income and product accounts

(NIPAs);• Commodity-by-industry accounting and models;• Multipliers, including Miyazawa multipliers, net multipliers, elasticity measures, and

output-to-output multipliers;• Location quotients and related techniques for estimating regional technology,

including numerical examples and real-world illustrations;• Energy input–output analysis to include references to econometric extensions;






Preface xxxi

• Environmental applications to include linear programming and multiobjectiveprogramming extensions;

• The hypothetical extraction approach to linkage analysis;• The Ghosh (supply-side) model;• The Leontief price model;• Estimating interregional flows;• Hybrid methods;• Mixed exogenous/endogenous models.

In order to keep the new edition to manageable length, there are topics that had tobe excluded or treated only very briefly; these include:

• Econometric/input–output model connections;• Qualitative input–output analysis;• Recent developments in dynamic input–output modeling;• Discussions and comparisons of alternative working models (e.g., REMI and

IMPLAN in the USA and others elsewhere);• The role and interpretation of eigenvectors and eigenvalues in input–output models.

The historical material on US input–output data has been reworked and updated,especially to reflect the international movement toward commodity-by-industry for-mulations. With the ready accessibility of computing capabilities, we have greatlyexpanded the end-of-chapter problems to include many more realistic examples aswell as some real-world examples and applications. Because of the higher level ofmathematical competence that we see in our potential readers as compared with 20+years ago, we have tried to use more compact matrix representations more extensivelyand whenever possible.

With appreciation we acknowledge many helpful conversations, face-to-face andelectronic, with Takahiro Akita, William Beyers, Faye Duchin, Geoffrey Hewings,Takeo Ihara, Andrew Isserman, Randall Jackson, Louis de Mesnard, Jan Oosterhaven,Karen Polenske, Jeffery Round and Guy West. Anne Carter and Joseph Richter helpedus fill in the historical record of IIOA meetings. Sandra Svaljek and Ivan Rusan atThe Institute of Economics, Zagreb, Croatia, kindly supplied us with a copy of MijoSekulic’s important 1968 article in Ekonomska Analiza, a publication of their Institute.We are grateful to IDE/JETRO (Tokyo), especially Satoshi Inomata, who provided uswith many of their important input–output tables and studies using those tables and toleadership and staff of the US Department of Commerce, Bureau of EconomicAnalysis,especially Mark Planting, who helped us navigate the US input–output tables. Finally,we single out two colleagues with whom we have had almost continuous interaction foryears: Erik Dietzenbacher, with whom we have had literally hundreds of discussionsand from whom we have had as many suggestions, and Michael Lahr who has beena constant source of critical observations and has recommended and helped us trackdown countless important references.






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