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Nonparametric Comparative Statics and Stability

Nonparametric Comparative Statics and Stability

Copyright Date: 1999
Pages: 256
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  • Book Info
    Nonparametric Comparative Statics and Stability
    Book Description:

    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.

    Originally published in 1999.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6503-1
    Subjects: Statistics

Table of Contents

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  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. Preface
    (pp. ix-2)
  4. 1 Nonparametric Analysis
    (pp. 3-12)

    In the early 1950s, the federal government decided to stockpile strategic materials to protect against the possibility of hostilities with the USSR. Planners constructed a massive 400 x 400 input-output model of the U.S. economy, entailing the estimation of a very large number of input-output coefficients, mainly based on data from the 1947 Census of Manufactures, to assess the effects of alternative inventory holdings. After several years of data gathering and analysis, they tested the resulting model, using the final bill of goods for the economy for 1951. Among other findings from that test was that the calculated domestic steel...

  5. 2 Qualitative Comparative Statics and Stability
    (pp. 13-48)

    We begin our analysis with a study of purely qualitative systems, i.e., systems in which theonlyinformation assumed to be available is sign pattern information concerning the entries of the matrixAand the vectorbin (1.4). We first take up the problem of sign solvability. We then investigate sign stability. The appendix to this chapter contains the mathematical results that are necessary for the reader to follow the formal arguments.

    A vectorxdetermined by a system of linear equationsAx=bis said to befully sign solvableif for any matrixBwith the...

  6. 3 Information and Invertibility
    (pp. 49-91)

    The basic issue addressed in this chapter may be summarized as follows:For the linear system Ax = y, how do different states of knowledge about the entries of the matrix A enable conclusions to be reached about characteristics of the matrix A-1 and the stability of A?

    An important matter to resolve in approaching this problem is a determination of what is to be meant by “knowledge about the entries of the matrixA.” Starting with Chapter 5, the applied framework for which the model was developed, i.e., equilibrium or optimization, will be an important source of information about...

  7. 4 Applications in Qualitative Comparative Statics
    (pp. 92-121)

    In this chapter, three rather different models are investigated with respect to their qualitative comparative statics: the Oil Market Simula tion and Oil and Gas Supply models, both developed by the U.S. Department of Energy, and a small macro-economic model sometimes called Klein’s Model I. In each case, the model may be understood to be a system of equations,

    ${f^1}(x,y) = 0,i = 1,2,.,n,$(4.1)

    wherexis ann-vector of variables to be evaluated by solving the model andyis anm-vector of parameters to be given values prior to solving the model. The comparative statics analysis of a model solution is...

  8. 5 The Maximization Hypothesis
    (pp. 122-149)

    Qualitative techniques are useful because theories and models are formulated for a wide range of diverse environments, where quantitative values for parameters are unknown, unreliable, or unstable. Using a qualitatively specified approach permits an investigation into the implications of a theory for a broad class of such environments. In a few exceptional cases, the model does not impose any quantitative or semi-quantitative restrictions on parameter values. For those cases, a “purely qualitative” approach, as described in Chapter 2, is applicable. But in most models, there are restrictions imposed on parameter values by the structure of the model, and these restrictions...

  9. 6 The Correspondence Principle
    (pp. 150-169)

    This chapter deals with Samuelson’s (1947) “correspondence principle” as it applies to qualitative models. The underlying idea is this: Comparative statics analysis in economics and in other fields is concerned with deriving predictive statements about changes in the values of certain endogenous variables in response to changes in the values of certain exogenous variables. For example, economists attempt to predict the change in price of a good that will occur if an excise tax is imposed on it, or the change in Gross Domestic Product (GDP) that will occur if the Federal Reserve increases the money supply. The conceptual apparatus...

  10. 7 The Competitive Equilibrium: Comparative Statics
    (pp. 170-205)

    Equilibrium is a recurring theme in scientific explanation. Observed physical, chemical, ecological, and economic processes are often interpreted as a balance of interacting influences, formally described by equation (1.1) in Chapter 1. Some equilibria are unchanged for finite time periods; others evolve as described by the equilibrium equations. Depending upon context. the equilibrium equations can themselves impose restrictions on how observations can change in response to changes in the environment and over time.

    This chapter and the next show how the equilibrium hypothesis can be exploited to yield definite qualitative conclusions. Our example is the competitive equilibrium. The competitive equilibrium...

  11. 8 The Competitive Equilibrium: Stability
    (pp. 206-222)

    This chapter examines the application of qualitative concepts to the problem of determining the stability of a model. As before, our example is the competitive equilibrium. After restating what is meant by stability in this setting, we examine the implications of Walras‘s law, and homogeneity for identifying qualitatively specified competitive models where stability can be proved.

    In our analysis of the stability properties of the competitive model we employ the Walrasiantâtonnementmechanism as formalized in Arrow and Hurwicz (1958, 1959). Under this mechanism, it is assumed that a “referee” is charged with the job of clearing markets in the...

  12. Notes
    (pp. 223-226)
  13. Bibliography
    (pp. 227-238)
  14. Name Index
    (pp. 239-240)
  15. Subject Index
    (pp. 241-242)