Nonparametric Comparative Statics and Stability

by Hale, Douglas

• ISBN13: 9780691006901
• ISBN10: 0691006903
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Princeton Univ Pr

Summary

The authors, leading researchers in the fields of mathematical economics and methodology, present the first comprehensive synthesis of literature on qualitative and other nonparametric techniques, which are important elements of comparative statics and stability analysis in economic theory. The topics covered show how to assess the comparative statics and stability of economic models without a precise quantitative knowledge of all model components. Applications of the analysis range from determining refutable hypotheses from theory to auditing the solutions of large, computer-based systems. This book discusses in depth the methodology involved in a nonparametric analysis of many neoclassical economic models. Constituting a virtually self-contained manual on such analysis, it provides detailed derivation of necessary and sufficient conditions for the existence of restrictive comparative statics and stability results for a range of specified models. Further, algorithms for applying certain of these conditions are given, with examples, as well as the underlying mathematical approach taken. A large body of research is unified covering issues that have been dealt with piecemeal in scattered but important journal articles by the authors and others. The book will prove invaluable to mathematical economists, mathematicians specializing in matrix or graph theory, applied economists working with large-scale economic models, and advanced students of economics.

Author Biography

Douglas Hale is a senior researcher at the U.S. Department of Energy.

Table of Contents

Preface ix
Nonparametric Analysis	p. 3
Introduction	p. 3
Quantitative Analysis	p. 4
Nonparametric Analysis	p. 6
An Example	p. 8
Organization of the Book	p. 11
Qualitative Comparative Statics and Stability	p. 13
Introduction	p. 13
Sign Solvability-Background	p. 13
The Algorithmic Approach to Strong Sign Solvability	p. 15
The Algebraic Approach to Sign Solvability	p. 20
Sign Stability	p. 27
Potential Stability	p. 36
Conclusions	p. 38
Appendix	p. 40
Information and Invertibility	p. 49
Introduction	p. 49
An Algebraic Analysis of Qualitative Invertibility	p. 50
The Elimination Principle	p. 56
Categorizing Information	p. 60
The Invertibility of Matrices with Ranked Entries	p. 63
The Invertibility of Matrices with Entries Specified within Given Intervals	p. 81
Summary of the Algebraic Method	p. 85
Stability	p. 86
Applications in Qualitative Comparative Statics	p. 92
Introduction	p. 92
Algorithmic Principles	p. 93
A Qualitative Analysis of the Oil Market Simulation Model	p. 98
A Qualitative Analysis of the Oil and Gas Supply Model	p. 104
Klein's Model	p. 1 117
Summary	p. 121
The Maximization Hypothesis	p. 122
Introduction	p. 122
Unconstrained Maximization	p. 122
Application: Profit-Maximizing Choices of Inputs by a Competitive Firm	p. 134
Constrained Maximization	p. 136
Application: Minimizing the Cost of Production	p. 141
Advanced Topics in Matrix Analysis	p. 143
The Correspondence Principle	p. 150
Introduction	p. 150
An Example	p. 152
Stability and Sign Solvability	p. 157
GM-Matrices	p. 161
Scope of the Correspondence Principle	p. 165
Interpretation	p. 168
The Competitive Equilibrium: Comparative Statics	p. 170
Introduction	p. 170
A Competitive Economy	p. 171
Some Historical Comments	p. 174
Restatement of Sign Solvability	p. 176
Sign Solvability under Walras's Law	p. 180
Sign Solvability under Walras's Law and Homogeneity	p. 196
The Competitive Equilibrium: Stability206
Introduction	p. 206
Stability under Walras's Law and Homogeneity	p. 208
Notes	p. 223
Bibliography	p. 227
Name Index	p. 239
Subject Index	p. 241
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