Qualitative and Quantitative Mathematical Economics

Transcription

1 Qualitative and Quantitative Mathematical Economics

2 ADVANCED STUDIES IN THEORETICAL AND APPLIED ECONOMETRICS VOLUME 1 EDITORIAL BOARD P. Balestra, Universite De Geneve, Switzerland M.G. Dagenais, Universite de Montreal, Canada A.J. Hughes Hallett, Erasmus University Rotterdam, The Netherlands J.H.P. Paelinck, Netherlands Economic Institute, The Netherlands R.S. Pindyck, Sloane School of Management, Massachusetts Institute of Technology, Cambridge, United States The Special Scope of the Series The fortress of econometrics has often been laid siege to from one or a few sides only. According to their inspiration or inclination, authors have laid stress on model specification, parametrer estimation, testing and prediction or more generally the use of models (prediction in particular being a rare bird in econometric literature). Special topics, such as errors in the variables, missing observations, multi-dimensional data, time-series analysis, dynamic specification, spatial autocorrelation, were dealt with as and when the need arose. No econometric exercises will ever be complete. Nevertheless, in setting up such an exercise as part of an operational economic investigation, one may reasonably be expected to try and encompass in it as many aspects of econometric modelling as may present themselves. This series is devoted to the publication of work which, as far as possible, addresses all aspects of a "complete econometric modelling" approach; for instance, spatial econometrics or policy optimisation studies which account explicitly for the specification, estimation or analysis of components of those models in the widest sense, including any complementary components from the environment in which the economic model must operate. The very objective of the series may limit its extensions; but as Andre Gide put it (Les faux monnayeurs), "il est bon de suivre sa pente, pourvu que ce soit en montant". All correspondence should be addressed to A.J. Hughes Hallet or to J.H.P. Paelinck at the Erasmus University, PO Box 1738,3000 DR Rotterdam, The Netherlands.

3 Qualitative and Q uanthative Mathematical Economics edited by J. H. P. Paelinck I.'.. I I. I '. u ~ Martinus N ijhoff Publishers The Hague / Boston / London

4 iv Distributors: for the United States and Canada Kluwer Boston, Inc. 190 Old Derby Street Hingham, MA USA for all other countries Kluwer Academic Publishers Group Distribution Center P.O. Box AH Dordrecht The Netherlands library of Congress Cataloging in Publication Data Main entry under title: Qualitative and quantitative mathematical economics. (Advanced studies in theoretical and applied econometrics; v. 1) Contents: Tribute to Luigi Solari / Richard Stone -- The s c i e n work t i fof i Luigi ~ Solari / J.-N. Du Pasquier and E. Rossier -- Econometric model building for the Common Market / A. Barten -- A nonlinear expenditure system: qualitative analysis and experiments with Canadian data / F. Carlevaro -- [etc.} 1. Economics, Mathematical--Addresses, essays, lectures. 2. Econometrics--Addr sses, essays, lectures. 3. Solar:i-, Luigi. I. Solari, Luigi. II. Paelinck, Jean H. P. III. Series. H B ~ ' ISBN-13: AACR2 ISBN-13: : / e-isbn-13: Copyright 1982 by Martinus Nijhoff Publishers, The Hague. Softcover reprint of the hardcover 1st edition 1982 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Martinus Nijhoff Publishers, P.o. Box 566, 2501 CN The Hague, The Netherlands.

5 LUIGI SOLARI { ESSAYS IN MEMORY OF LUIGI SOLARI

6 vii TARLE OF CONTENTS Presentation of the volume J.H.P. Paelinck ix PART I: REFLECTING ON METHODOLOGY 1. Trihute to Luigi Solari 2. The scientific work of Luigi Solari Richard Stone J.-N. Du PasQuier and E. Rossier 3 13 PART II: fmdelling 1. Econometric model builning for the Common }1arket 4. A nonlinear expenditure svstem: Qualitative Analvsis and Experiments with Canadian Data A. Rarten F. Carlevaro PART III: ESTIMATING 5. A general approach for estimating econometric models with incomplete observations 6. Dvnamic misspecification and serial correlation M.G. and D.L. Dagenais A9 P. Balestra 115 PART IV: PROGRAfmING 7. Estimating revealed preferences in models of planning behaviour A. Recent experiences with the Oualiflex Multicriteria method A.J. Hughes Hallett and J.-P. Ancot J.-P. Ancot and J.H.P. Paelinck 14Q 217

7 viii The systematics of symbol use in this book: - Lower-case letters (Latin or Greek) represent scalars - Underlined lower-case letters represent vectors - Matrices are represented by capital letters af - Gradients are noted as ai or a f / a ~ af - Jacobians are noted as ai or a! / a ~

8 PRESENTATION OF THE VOLUME J.H.P. Paelinck, Netherlands Economic Institute and Erasmus University Rotterdam Luigi Solari left us on November 12, 1977, at a moment of his life when he could have given many a contribution to the topics that are presented hereafter in memory of him. Linearly logical, then mathematical economics preceding quantification, and sometimes leading up to more advanced "quantitative" (0-1, or combinatorial) problems, those were the subjects that had his permanent attention; how he worked out his ideas on epistemology is one moving chapter of this book, as it so vividly recalls the person Solari, to whom a well-deserved tribute has been given. Specifying our relationships is a complex though indispensable step in our thinking. Probably no economist starts out in theoretical life by writing down complex equations, be it in terms of functional forms or of variables included. Non-linearities, discontinuities, asymptotes, they all result from previous - sometimes, during the gestation phase, sloppy - thinking. Two chapters are devoted to modelling, one being in a field Luigi liked very much, and to which he has contributed in an original way. Estimating and testing these relationships is considered the econometrician's stronghold, which has to be permanently kept robust against missing data and specification biases; hence two contributions evaluating the cost of our ignorance or misbehaviour. But what would it all be good for if no choices had to be guided by the results of the previous exercises? The volume is concluded by new results in the field of revealed-preference detection and multi-criteria decision processes, both exercises relying heavily on previous econometric results. The final versions of the papers collected together in this volume were contributed in July The responsibility we unhesitatingly took in editing this volume was not only scientific, it had also a deep human dimension: would the volume as such reach the heights on which the person it remembers used to dwell and think? One thing is certain: all contributions have been prepared and

9 x written UP as a token of lasting friendship and esteem for a colleague who honoured the profession, and this additional incentive could only bias them towards relativelv more perfection. Rut as the cartesian Nicolas de }lalebranche once said, "il faut tendre il la?erfection sans jamais v p r ~ t e n Luigi d r e Solari, " ; the humanist, would have wholeheartedlv agreed with him. While this volume was in press we heard of the tragic death of another colleague, Edouard Rossier, of the Department of Econometrics at the University of Geneva. We would like to evoke his memorv together with that of Luigi Solari.