Studies in the Economics of Uncertainty

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 Department of Economics Dallas, Texas 75275-0496 U.S.A. Tae Kun Seo Department of Economics Dallas, Texas 75275-0496 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 developed 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 University of Montreal, Canada Mary S. Broske Oklahoma State University Georges Dionne University of Montreal, Canada Peter C. Fishburn AT&T Bell Laboratories J. Horen U.S. Sprint Communications Takao Itagaki University of Tsukuba, Japan Donald W. Katzner University of Massachusetts, Amherst Richard Kihlstrom University of Pennsylvania Yoram Kroll Hebrew University, Jerusalem Haim Levy Hebrew University and University of Florida Daniel McFadden Massachusetts Institute of Technology Jack Meyer Michigan State University John W. Pratt Harvard University William R. Russell Tae Kun Sea G. Alex Whitmore McGill University, Canada Sam Y. Wu University of Iowa

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 competition, diversification, international trade under uncertainty, and the theory of multinational 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 of Economic Behavior (Addison-Wesley, 1971) and have come away much the better for it. Since Joe's arrival at 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, mathematical economics and the economics of uncertainty. The department's research productivity 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 uncovered. 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 Dallas. Texas Editors