Spectral Theory of Value and Actual Economies: Controllability, Effective Demand, and Cycles (Evolutionary Economics and Social Complexity Science, 24)

This book develops a unified treatment of the income distribution–capital–value problems with respect to actual economies, and then gradually turns to the issues of effective demand and capitalist accumulation fluctuations from both political economy and economic policy perspectives. That treatment, on the one hand, places produced means of production, positive profits, and capital accumulation at the centre of the analysis and, on the other hand, is analytically based on the modern control theory. Hence, the authors’ investigation is concerned with input–output representations of actual single and joint production, heterogeneous labour, and open economies; zeroes in on the characteristic value distributions of the system matrices; and, finally, derives meaningful theoretical results consistent with the empirical evidence, and vice versa. The main topics addressed are the uncontrollable/unobservable aspects of the real-world economies, the powerful low-order spectral approximationsand reconstructions of the inter-industry structure of production–value–distributive variables relationships, the critical-constructive appraisal of both “mainstream” and “radical” theories of value, the matrix demand multipliers and demand-switching policies in heterogeneous capital worlds, and the circular inter-actions amongst income distribution, effective demand, accumulation, and technical conditions of production. Written on the occasion of the 60th anniversary of the publication of both Piero Sraffa’s Production of Commodities by Means of Commodities and Rudolf E. Kalman’s paper “On the general theory of control systems”, this book provides a consistent and comprehensive framework for theoretical, empirical, and economic policy research. Preface and Acknowledgements Contents About the Authors Chapter 1: Empirical Input-Output Representations and Transmutations of Actual Economies 1.1 Introduction 1.2 The Supply and Use Tables 1.3 The Symmetric Input-Output Tables 1.4 Conversion of Supply and Use Tables into Symmetric Input-Output Tables 1.4.1 Methods Converting Supply and Use Tables into Product-by-Product Symmetric Input-Output Tables 1.4.1.1 The Product Technology Assumption 1.4.1.2 The Industry Technology Assumption 1.4.1.3 The By-Product Method 1.4.1.4 Mixed Technology Assumptions 1.4.1.5 The Transfer Method 1.4.1.6 The ESA Method 1.4.1.7 The Lump-Sum Method 1.4.1.8 The Redefinition Method 1.4.2 Methods Converting Supply and Use Tables into Industry-by-Industry Symmetric Input-Output Tables 1.4.2.1 The Fixed Industry Sales Assumption 1.4.2.2 The Fixed Product Sales Assumption 1.4.3 Evaluation of the Conversion Methods 1.5 The von Neumann-Sraffa-Based Approach 1.6 Concluding Remarks References Chapter 2: Controllability, Observability and Spectral Post-Construction of the Value Theory 2.1 Introduction 2.2 Two Different System Representations 2.2.1 State Variable Representation 2.2.1.1 Axiomatization 2.2.1.2 Strictly Equivalent Representations and Diagonalization 2.2.1.3 Equilibrium and Stability 2.2.1.4 Controllability and Observability 2.2.1.5 Almost Uncontrollability and Unobservability 2.2.2 Transfer Function Representation 2.2.3 State Variable Versus Transfer Function Representation 2.2.4 Numerical Examples 2.3 he Sraffian Representation of Linear Economies 2.3.1 The Stationary Value and Quantity Systems 2.3.2 Controllability and Observability of Sraffian Economies 2.3.3 Traditional Versus Sraffian Value Theories 2.3.4 The Spectral Post-Construction of the National Value Theory 2.4 Synopsis and Final Remarks Appendix: Additional Examples References Chapter 3: The Capital Theory Debate and the Almost Uncontrollability and Unobservability of Actual Economies 3.1 Introduction 3.2 Spectral Decompositions of the Value-Wage-Profit Rate System 3.2.1 Fundamental Forms 3.2.2 Alternative Approximations 3.3 Empirical Evidence 3.3.1 Linear Approximations 3.3.2 Higher-Order Approximations 3.3.3 Controllability Characteristics 3.3.4 Evaluation 3.4 Concluding Remarks References Chapter 4: Value Theory, Joint Production, and International Trade Issues 4.1 Introduction 4.2 Aspects and Implications of Pure Joint Production 4.2.1 Closed Economy 4.2.2 Open Economies 4.3 Sectoral Productivity Changes and the Harrod-Balassa-Samuelson Effect 4.3.1 Relative Prices and Productivity Changes 4.3.2 The Harrod-Balassa-Samuelson Effect 4.4 Synopsis and Final Remarks References Chapter 5: Empirical Pitfalls of the Traditional Value Theory: Joint Production and Actual Economies 5.1 Introduction 5.2 The Analytic Framework 5.2.1 Wage-Profit Rate Curves in Joint Production Economies 5.2.2 Values in Joint Production Economies 5.3 Empirical Investigation 5.3.1 Wage-Profit Rate Curves in Actual Joint Production Economies 5.3.1.1 Monotonicity 5.3.1.2 Curvature 5.3.1.3 Linearity 5.3.1.4 Visual Representation of Wage-Profit Rate Curves 5.3.1.5 Sensitivity Analysis 5.3.2 Values in Actual Joint Production Economies 5.4 Concluding Remarks Appendix: A Note on the Data Data Sources Construction of Variables Denmark Finland France FYROM Germany Greece Hungary Japan Portugal Slovenia Sweden USA References Chapter 6: Time Dilation, Abstract Social-International Labour, and Profit 6.1 Introduction 6.2 On Marx ́s Theory of Profit 6.2.1 The Basic Counter-Argument 6.2.2 Some Extensions 6.2.2.1 Reducibility 6.2.2.2 Heterogeneous Labour 6.2.2.3 Pure Joint Production 6.3 Time Dilations and Abstract Social-International Labour 6.4 Concluding Remarks References Chapter 7: Arguing in Circles: Alternative Value Bases and Actual Economies 7.1 Introduction 7.2 Single Production 7.2.1 The Analytic Framework 7.2.2 Empirical Investigation 7.2.2.1 France 7.2.2.2 Sweden 7.3 Joint Production 7.3.1 The Analytic Framework 7.3.2 Empirical Investigation 7.4 Concluding Remarks Appendix: Data Sources and Construction of Variables References Chapter 8: Capital Theory and Matrix Demand Multipliers in Sraffian Frameworks 8.1 Introduction 8.2 The Matrix Demand Multiplier in the Base Framework 8.3 Autonomous Demand-Transfer Payments Relationships 8.4 Some Extensions 8.4.1 Indirect Taxes and Changes in Income Distribution 8.4.2 Changes in the Technical Production Conditions 8.4.3 Heterogeneous Labour and Open Economy Systems 8.4.4 Pure Joint Production 8.5 Effective Currency Devaluation and Multiplier Effects in the Long-Run 8.5.1 The Single Production Case 8.5.2 The Joint Production Case 8.5.2.1 The Model 8.5.2.2 Joint Versus Single Production 8.5.2.3 Numerical Examples 8.6 Concluding Remarks Appendix 1: On the Eigenvalues of the Matrix of Total Consumption and a Dynamic Multiplier Process Appendix 2: The Formal Similarities Between the Trade-Offs Appendix 3: Closing the System: A Numerical Example Appendix 4: A Post-Keynesian-Sraffian One-Country Model Appendix 5: A Numerical Example for the Joint Production Case References Chapter 9: Effective Demand and Devaluation Policies: Evidence from Input-Output Tables for Eurozone Economies 9.1 Introduction 9.2 Matrix Demand Multipliers in a Joint Production Framework: A Comparative Analysis of the Greek, Spanish and Eurozone Econo... 9.2.1 The Analytic Framework 9.2.2 Main Empirical Results and Evaluation 9.2.3 Conclusions 9.3 Wage versus Currency Devaluation in a Single Production Framework: A Comparative Analysis of the Greek and Italian Economi... 9.3.1 The Analytic Framework 9.3.1.1 Basic Assumptions and Price Equation 9.3.1.2 Wage Devaluation 9.3.1.3 Currency Devaluation Under Complete Wage Indexation 9.3.1.4 Long-Run Trade-Offs 9.3.2 Main Empirical Results and Evaluation 9.3.3 Conclusions 9.4 Final Remarks Appendix 1: Data Sources and Construction of Variables for the Estimation of Demand Multipliers Appendix 2: The Input-Output Structure of the Greek Economy 2005-2010 The System of Indices Results Conclusions Appendix 3: The Arithmetic Means of the Net Output Multipliers as Functions of the Savings Ratios Appendix 4: Data Sources and Construction of Variables for the Estimation of the Effects of Wage and Currency Devaluations Appendix 5: The Long-Run Wage-Profit-Exchange Rates Trade-Offs for the Greek and Italian Economies References Chapter 10: Wrestling with Goodwin ́s Distributive Growth Cycle Modelling: Theory and Empirical Evidence 10.1 Introduction 10.2 Goodwin ́s Original Model 10.3 Goodwin ́s Original Model with a VES Production Function 10.3.1 The Model 10.3.2 The Properties 10.4 Goodwin ́s Disaggregated Models 10.4.1 GDM1: The One-Commodity Case 10.4.2 GDM2: The One-Commodity Case 10.4.3 Goodwins ́s Method of Principal Coordinates 10.4.4 GDM1: The Heterogeneous Capital Case 10.4.5 GDM2: The Heterogeneous Capital Case 10.5 Empirical Testing 10.6 Concluding Remarks Appendix 1: Proofs Appendix 2: The Solution Paths of u1′ and v1′ for the period 1988-1997 References Chapter 11: Marxian Distributive-Effective Demand Dynamics and the ``Law ́ ́ of Rising Profit Rate 11.1 Introduction 11.2 The Goodwin Model with the Bhaduri-Marglin Accumulation Function 11.2.1 The One-Commodity Case 11.2.1.1 The Static Core 11.2.1.2 Dynamization 11.2.1.3 Evidence from Econometric Estimations 11.2.2 The Heterogeneous Capital Case 11.3 Extensions of the One-Commodity Model 11.3.1 CES Production Functions 11.3.2 Commodities Market Disequilibrium 11.4 Technological Change, Profit Rate, and Profit Mass 11.4.1 The ``Law ́ ́ of Rising Profit Rate 11.4.2 Falling Profit Rate with Rising Profit Mass 11.5 Synopsis and Final Remarks References Index This book develops a unified treatment of the income distribution capital value problems with respect to actual economies, and then gradually turns to the issues of effective demand and capitalist accumulation fluctuations from both political economy and economic policy perspectives. That treatment, on the one hand, places produced means of production, positive profits, and capital accumulation at the centre of the analysis and, on the other hand, is analytically based on the modern control theory. Hence, the authors' investigation is concerned with input-output representations of actual single and joint production, heterogeneous labour, and open economies; zeroes in on the characteristic value distributions of the system matrices; and, finally, derives meaningful theoretical results consistent with the empirical evidence, and vice versa. The main topics addressed are the uncontrollable/unobservable aspects of the real-world economies, the powerful low-order spectral approximations and reconstructions of the inter-industry structure of production value distributive variables relationships, the critical-constructive appraisal of both mainstream and radical theories of value, the matrix demand multipliers and demand-switching policies in heterogeneous capital worlds, and the circular inter-actions amongst income distribution, effective demand, accumulation, and technical conditions of production. Written on the occasion of the 60th anniversary of the publication of both Piero Sraffa Production of Commodities by Means of Commodities and Rudolf E. Kalman's paper on the general theory of control systems this book provides a consistent and comprehensive framework for theoretical, empirical, and economic policy research