Studies in the Economics of Uncertainty: In Honor of Josef Hadar

232 Pages·1989·7.985 MB·English

by  P. C. Fishburn (auth.), Thomas B. Fomby, Tae Kun Seo (eds.)

Studies in the Economics
of Uncertainty
Josef Hadar
Thomas B. Fomby Tae Kun Sea
Editors
Studies in the
Economics
of Uncertainty
In Honor of Josef Hadar
With 25 Illustrations
Springer Verlag
New York Berlin Heidelberg
London Paris Tokyo Hong Kong
Thomas B. Fomby Tae Kun Seo
Department of Economics Department of Economics
Southern Methodist University Southern Methodist University
Dallas, Texas 75275-0496 Dallas, Texas 75275-0496
U.S.A. U.S.A.
Library of Congress Cataloging-in-Publication Data
Studies in the economics of uncertainty in honor of Josef Hadar/
edited by Thomas B. Fomby and Tae Kun Seo.
p. cm.
ISBN -13: 978-1-4613-8924-8
I. Uncertainty. 2. Stochastic processes. 3.Hadar, Josef.
I. Hadar, Josef. II. Fomby, Thomas B. III. Seo, Tae Kun.
HB615.S78 1989
330'.01'5192-dc20 89-11343
CIP
Printed on acid-free paper
© 1989 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1989
All rights reserved. This work may not be translated or copied in whole or in part without
the written permission ofthe publisher (Springer-Verlag, 175 Fifth Avenue, New York. NY
10010, USA), except for brief excerpts in connection with reviews or scholarly analysis.
Use in connection with any form of information storage and retrieval, electronic adaptation,
computer software, or by similar or dissimilar methodology now known or hereafter devel
oped is forbidden.
The use of general descriptive names, trade names, trademarks, etc. in this publication,
even if the former are not especially identified, is not to be taken as a sign that such names,
as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used
freely by anyone.
Camera-ready copy supplied by authors.
9 8 765 432 I
ISBN -13: 978-1-4613-8924-8 e-ISBN -13: 978-1-4613-8922-4
001: 10.1007/978-1-4613-8922-4
CONTENTS
Contributors .................................... '............................................................. vi
Introduction..................................... . .................... ............ ........ . . . ....... .... ....... vii
PART I: Theory
Stochastic Dominance in Nonlinear Utility Theory
P.C. Fishburn .................................... ......... ......... ..................... .... .... ...... 3
The "Comparative Statics" of the Shackle-Vickers Approach
to Decision-Making in Ignorance
Donald W. Katzner .................................................................................. 21
Stochastic Dominance and Transformations of Random Variables
Jack Meyer .......................... .......................... ..... ....................... .... ...... .... 45
Representative Sets for Stochastic Dominance Rules
W.R. Russell and T.K. Seo ........................................................................ 59
Stochastic Dominance for the Class of Completely Monotonic Utility Functions
G.A. Whitmore ............. ............. ......... ........................ .................. ............ 77
PART II: Estimation and Testing
The Stochastic Dominance Estimation of Default Probability
Mary S. Broske and Haim Levy ................................................................. 91
Testing for Stochastic Dominance
Daniel McFadden .................................................................................... 113
PART III: Applications
Insurance and the Value of Publicly Available Information
Marcel Boyer, Georges Dionne, Richard Kihlstrom ....................................... 137
Vertical Transactions under Uncertainty
J. Horen and S. Y. Wu .............................................................................. 157
Optimal Tariffs and Quotas under Uncertain International Transfer
Takao Itagaki ........................................................................................... 187
Investment, Capital Structure and Cost of Capital: Revisited
Yoram Kroll and Haim Levy ...................................................................... 201
Utility Functions, Interest Rates, and the Demand for Bonds
John W. Pratt ......................................................................................... 225
CONTRIBUTORS
Marcel Boyer Haim Levy
University of Montreal, Canada Hebrew University and University of
Florida
Mary S. Broske
Oklahoma State University Daniel McFadden
Massachusetts Institute of Technology
Georges Dionne
University of Montreal, Canada Jack Meyer
Michigan State University
Peter C. Fishburn
AT&T Bell Laboratories John W. Pratt
Harvard University
J. Horen
U.S. Sprint Communications William R. Russell
Southern Methodist University
Takao Itagaki
University of Tsukuba, Japan Tae Kun Sea
Southern Methodist University
Donald W. Katzner
University of Massachusetts, Amherst G. Alex Whitmore
McGill University, Canada
Richard Kihlstrom
University of Pennsylvania Sam Y. Wu
University of Iowa
Yoram Kroll
Hebrew University, Jerusalem
INTRODUCTION
It is a pleasure to be able to offer the enclosed collection of papers on the economics
of uncertainty, all to honor the contributions of Professor Josef Hadar to his profession,
students, and colleagues. Among his contributions to the profession, Joe along with Bill
Russell, wrote one of the seminal papers on Stochastic Dominance, "Rules for Ordering
Uncertain Prospects," American Economic Review, 59 (1969), 25-34. Thus it seems quite
fitting that the subject of this Festschrift should be "the Economics of Uncertainty." A
search of the literature in any number of subject areas (the theory of the firm, international
trade, portfolio theory, income distribution theory, on and on) will give a clear indication
of the importance of the Stochastic Dominance concept to economics and allied disciplines.
The current papers bear strong witness to the maturity of the subject given its beginnings
only 20 years ago. One can only guess what researchers will be applying the stochastic
dominace principle to in the next 20 years.
Apart from the SD concept, Joe has made contributions in the areas of imperfect com
petition, diversification, international trade under uncertainty, and the theory of multi
national firms. In addition to his advanced research, Joe has made substantial contributions
to the lucid exposition of microeconomic theory. Many graduate students have cut their
microeconomic teeth on his Mathematical Theory ofE conomic Behavior (Addison-Wesley,
1971) and have come away much the better for it.
Since Joe's arrival at Southern Methodist University in 1972, 16 students have had
the distinct honor of writing dissertations under his direction while countless others have
benefitted from his counsel though not writing directly under his supervision. In fact, it is
easy to spot a Hadar dissertation student. He or she is typically walking out of his office
carrying a well marked manuscript that was submitted only the day before. No moss has
ever collected on his students' drafts. Quite understandably Hadar students are known for
their questioning minds, rigor of thought, and precision of written expression.
The department's faculty has greatly benefitted from Joe's collegiality. Joe has been
and continues to be available for consultation on matters involving microeconomics, mathe
matical economics and the economics of uncertainty. The department's research productiv
ity has directly benefitted as a result. Even outside his fields of expertise Joe serves as an
astute sounding board.
If you will indulge an econometrician's story, recently Joe came across a newspaper
article on the new statistical technique called bootstrapping. Once the conversation began,
a few minutes of probing questions followed. The core of the concept was quickly uncov
ered. Joe said, "What if you have an atypical sample to begin with." Point made. It has not
been uncommon to see the collars of seminar speakers become progessively tighter from a
barrage of Hadar questions. All of this was, of course, for the better because the speakers'
papers subsequently became much better for it.
viii
On December 28, 1988 a reception was held in Joe's honor in the Petit Trianon room
of the New York Hilton during the American Economic Association meetings. Several of
the contributors to this Festschrift as well as many of his students and colleagues (past and
present) were in attendance. All agreed that the attention Joe drew was well deserved. Joe,
this volume's contributors, your students, colleagues, and friends thank you.
The editors would especially like to thank Ms. Gloria Jones for her role in putting
together this Festschrift. from being an expert word processor to being a skilled artist.
March 1, 1989 Thomas B. Fomby and Tae Kun Seo
Department of Economics
Southern Methodist University
Dallas. Texas
Editors
PART I
Theory
STOCHASTIC DOMINANCE IN NONLINEAR UTILITY THEORY
P.C. Fishburn
AT&T Bell Laboratories
Murray Hill, NJ 07974
1. Introduction
Stochastic dominance has interested mathematicians for more than
half a century (Karamata, 1932; Hardy, Littlewood and Polya, 1934;
Sherman, 1951; Lehmann, 1955), and its integration into decision theory
began nearly forty years ago (Masse and Morlat, 1953; Allais, 1953a,
1953b; Blackwell and Girshick, 1954; Quirk and Saposnik, 1962; Fish
burn, 1964). However, it was not until a cluster of important papers
on stochastic dominance appeared around 1969-71 (Hadar and Russell,
1969, 1971; Hanoch and Levy, 1969; Whitmore, 1970; Rothschild and
Stiglitz, 1970, 1971) that it emerged as a central topic in economic
decision theory. Hundreds of papers as well as a survey book (Whit
more and Findlay, 1978) and an extensive research bibliography (Bawa,
1982) testify to its popularity.
The vast majority of this literature addresses the use of sto
chastic dominance in expected utility analysis, based on either the
von Neumann-Morgenstern (1944) linear utility theory for decision under
risk or Savage's (1954) theory of subjective probability and linear
utility for decision under uncertainty. Fishburn and Vickson (1978)
summarizes the fundamentals of stochastic dominance in the linear
utility context.
My purpose here is to discuss the role of stochastic dominance in
what I shall refer to as nonlinear utility theories. These theories
are based on the same formulations as the linear utility theories of
von Neumann-Morgenstern and Savage, but they use different utility
models to represent preference between risky prospects or uncertain
acts. with the exception of Allais (1953a, 1953b, 1979), most of the
nonlinear theories arose around 1980. All of them were motivated by
the empirical research of Allais and others, including May (1954),
Ellsberg (1961), Tversky (1969), Lichtenstein and Slovic (1971, 1973),
MacCrimmon and Larsson (1979), and Kahneman and Tversky (1979), which
uncovered systematic violations of the preference axioms that imply the
linear models. For the most part, the preference axioms for the non
linear models are weaker than those for the linear models. Their
3