Input-Output Analysis :Foundations and Extensions

Publication subTitle :Foundations and Extensions

Author: Ronald E. Miller; Peter D. Blair  

Publisher: Cambridge University Press‎

Publication year: 2009

E-ISBN: 9780511590207

P-ISBN(Paperback): 9780521517133

Subject: F224 经济数学方法

Keyword: 计量经济学Econometrics

Language: ENG

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Input-Output Analysis

Description

This edition of Ronald Miller and Peter Blair's classic textbook is an essential reference for students and scholars in the input-output research and applications community. The book has been fully revised and updated to reflect important developments in the field since its original publication. New topics covered include SAMs (and extended input-output models) and their connection to input-output data, structural decomposition analysis (SDA), multiplier decompositions, identifying important coefficients, and international input-output models. A major new feature of this edition is that it is also supported by an accompanying website with solutions to all problems, wide-ranging real-world data sets, and appendices with further information for more advanced readers. Input-Output Analysis is an ideal introduction to the subject for advanced undergraduate and graduate students in a wide variety of fields, including economics, regional science, regional economics, city, regional and urban planning, environmental planning, public policy analysis and public management.

Chapter

Example 2: Changed Base Year Prices

2.6.5 Applications

2.6.6 The Price Model based on Physical Data

Introduction of Prices

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

2.7 Summary

Appendix 2.1 The Relationship between Approaches I and II

A2.1.1 Approach I

A2.1.2 Approach II

Appendix 2.2 The Hawkins--Simon Conditions

Problems

References

3 Input–Output Models at the Regional Level

3.1 Introduction

3.2 Single-Region Models

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

3.4.5 The US MRIO Models

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

3.5.2 Numerical Example

3.6 The Spatial Scale of Regional Models

3.7 Summary

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

Problems

References

4 Organization of Basic Data for Input–Output Models

4.1 Introduction

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

Approximation Method I

Approximation Method II

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

4.10 Summary

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

Problems

References

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

5.1 Introduction

5.1.1 The Use Matrix

5.1.2 The Make Matrix

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

Using D

Using C

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

Transactions Matrices

Total Requirements Matrices

5.5.2 Industry Technology

Direct Requirements Matrices

Total Requirements Matrices

5.5.3 Making a Model Choice

Which Model to Choose?

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

5.8 Summary

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

A5.2.1 The Problem

3 X 3 Example

4 X 4 Example

5 X 5 Example (from Almon, 2000)

A5.2.2 Approaches to Elimination of Negative Elements

A5.2.3 Results of the Iterative Procedure

3 X 3 Example

4 X 4 Example

5 X 5 Example

Problems

References

6 Multipliers in the Input–Output Model

6.1 Introduction

6.2 General Structure of Multiplier Analysis

6.2.1 Output Multipliers

Simple Output Multipliers

Total 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

Income Multipliers

Type I and Type II Income Multipliers

Relationship Between Simple and Total Income Multipliers or Between Type I and Type II Income Multipliers

Which Multiplier to Use?

Even More Income Multipliers

Physical Employment Multipliers

6.2.3 Value-Added Multipliers

6.2.4 Matrix Representations

6.2.5 Summary

6.3 Multipliers in Regional Models

6.3.1 Regional Multipliers

6.3.2 Interregional Input–Output Multipliers

Intraregional Effects

Interregional Effects

National Effects

Sectoral Effects

More Than Two Regions

6.3.3 Multiregional Input–Output Multipliers

Intraregional Effects

Interregional Effects

National Effects

Sectoral Effects

Final Demand for Goods Made in a Particular Region

More Than Two Regions

6.4 Miyazawa Multipliers

6.4.1 Disaggregated Household Income Groups

6.4.2 Miyazawa's Derivation

6.4.3 Numerical Example

6.4.4 Adding a Spatial Dimension

6.5 Gross and Net Multipliers in Input–Output Models

6.5.1 Introduction

6.5.2 Multipliers in the Net Input–Output Model

Numerical Example

6.5.3 Additional Multiplier Variants

(Indirect Effects)/(Direct Effects)

``Growth Equalized'' Multipliers

Another Kind of Net Multiplier

6.6 Multipliers and Elasticities

6.6.1 Output Elasticity

6.6.2 Output-to-Output Multipliers and Elasticities

Direct Effects

Total Effects

6.7 Multiplier Decompositions

6.7.1 Fundamentals

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

6.8 Summary

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

Problems

References

7 Nonsurvey and Partial-Survey Methods: Fundamentals

7.1 Introduction

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

Other Summary Measures

Data for the US Economy

7.2.2 Constant versus Current Prices

7.2.3 Stability of Regional Coefficients

7.2.4 Summary

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

7.4.1 The RAS Technique

7.4.2 Example of the RAS Procedure

7.4.3 Updating Coefficients vs. Transactions

Numerical Illustration

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

7.5 Summary

Appendix 7.1 RAS as a Solution to the Constrained Minimum Information Distance Problem

Problems

References

8 Nonsurvey and Partial-Survey Methods: Extensions

8.1 Introduction

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

8.2.9 Summary

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

8.6.5 Additional Studies

Commodity Flows among US States

Interregional Social Accounts Model (ISAM)

National Interstate Economic Model (NIEMO)

An Optimization Model for Interregional Flows

8.7 Hybrid Methods

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

8.8.1 Introduction

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

8.10 Summary

Appendix 8.1 Geographical Classifications in the World Input–Output Model

Problems

References

9 Energy Input–Output Analysis

9.1 Introduction

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 Applications

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

9.4.4 An Energy Tax

9.4.5 Energy and Structural Change

9.4.6 Energy Input–Output and Econometrics

9.4.7 Other Applications

9.5 Summary

Appendix 9.1 Earlier Formulation of Energy Input–Output Models

A9.1.1 Introduction

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

Problems

References

10 Environmental Input–Output Analysis

10.1 Introduction

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

Case II: Planning 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

Specifying Objectives

Tightly Constrained Problems

Solution Methods

10.4.5 Applications to the Generalized Input–Output Planning Problem

10.4.6 Policy Programming

Impact Analysis Form

Planning Form

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

Economic Subsystem

Ecologic Subsystem

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

10.8 Other Applications

10.9 Summary

Problems

References

11 Social Accounting Matrices

11.1 Introduction

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 SAM Multipliers

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

11.14 Summary

Problems

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

12.1.4 Joint Stability

The Issue

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)

A Ghosh Quantity Model

12.2 Linkages in Input–Output Models

12.2.1 Backward Linkage

12.2.2 Forward Linkage

12.2.3 ``Net'' Backward Linkage

12.2.4 Classifying Backward and Forward Linkage Results

12.2.5 Spatial Linkages

12.2.6 Hypothetical Extraction

Backward Linkage

Forward Linkage

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

Observation 1

Observation 2

Observation 3

12.3.3 ``Inverse-Important'' Coefficients

12.3.4 Numerical Example

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

12.4 Summary

Appendix 12.1 The Sherman–Morrison–Woodbury Formulation

A12.1.1 Introduction

A12.1.2 Application to Leontief Inverses

Problems

References

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

Changes in Final Demand

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

Decomposition of L

Decomposition of A

Numerical Illustration (continued)

13.1.5 Decompositions of Changes in Some Function of x

13.1.6 Summary for …x

13.1.7 SDA in a Multiregional Input--Output (MRIO) Model

13.1.8 Empirical Examples

Washington State

The US Multiregional Model

A Multicountry Model for the European Community (Oosterhaven and van der Linden, 1997)

The European Union

13.2 Mixed Models

13.2.1 Exogenous Specification of One Sector's Output

Rearranging the Basic Equations

13.2.2 An Alternative Approach…

13.2.3 Examples with…

Example 1: f1 = 100,000, f2 = 200,000, x3 = 150,000

Example 2: f1 =f2 =0, x3 = 150,000

Approach I

Approach II

Example 3: f1 = 100,000, f2 = 200,000, x3 = 100,000

Example 4: The Critical Value of x3

Multipliers

13.2.4 Exogenous Specification of…

13.2.5 An Example with…

Example 5 (Example 2 expanded)

Approach I

Approach II

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

Terminal Conditions

Initial Conditions

13.4.3 Numerical Example 1

Terminal Conditions

Initial Conditions

13.4.4 Numerical Example 2

Terminal Conditions

Initial Conditions

13.4.5 ``Dynamic'' Multipliers

13.4.6 Turnpike Growth and Dynamic Models

Example

13.4.7 Alternative Input–Output Dynamics

13.5 Summary

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

Problems

References

14 Additional Topics

14.1 Introduction

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.1 Introduction

A.2 Matrix Operations: Addition and Subtraction

A.2.1 Addition

A.2.2 Subtraction

A.2.3 Equality

A.2.4 The Null Matrix

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.7 Diagonal Matrices

A.8 Summation Vectors

A.9 Matrix Inequalities

A.10 Partitioned Matrices

A.10.1 Multiplying Partitioned Matrices

A.10.2 The Inverse of a Partitioned Matrix

References

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

B.1 Introduction

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

References

Author Index

Subject Index

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