Theory and Practice of International Trade Linkage Models

Theory and Practice of International Trade Linkage Models

ADVANCED STUDIES IN THEORETICAL AND APPLIED ECONOMETRICS VOLUME 9 Managing Editors: J.P. Ancot, Nethetlands Economic Institute, Rotterdam, The Netherlands A.J. Hughes Hallett, University of Newcastle, U.K. Editorial Board: G. Adams, University of Pennsylvania, Philadelphia, U.S.A. P. Balestra, University of Geneva, Switzerland M.G. Dagenais, University of Montreal, Canada D. Kendrick, University of Texas, Austin, U.S.A. J. Paelinck, Netherlands Economic Institute, Rotterdam, The Netherlands R.S. Pindyck, Sloane School of Management, Massachusetts Institute of Technology, Cambridge, U.S.A. H. Theil, University of Florida, Gainsville, U.S.A. W. Welfe, University of Lodz, Poland For a complete list of volumes in this series see final page of this volume.

Theory and Practice of International Trade Linkage Models by Alexander Italianer 1986 MARTINUS NIJHOFF PUBLISHERS a member of the KLUWER ACADEMIC PUBLISHERS GROUP DORDRECHT I BOSTON I LANCASTER

Distributors for the United States and Canada: Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, MA 02061, USA for the UK and Ireland: Kluwer Academic Publishers, MTP Press Limited, Falcon House, Queen Square, Lancaster LAI 1RN, UK for all other countries: Kluwer Academic Publishers Group, Distribution Center, P.O. Box 322, 3300 AH Dordrecht, The Netherlands Library of Congress Cataloging in Publication Data Italianer, Alexander. Theory and practice of international trade linkage models. (Advanced studies of theoretical and applies economics ; 9) Bibliography: p. Includes indexes. 1. Commerce--Econornetric models. I. Title. II. Series. HF1008.185 1986 582'.0724 86-21804 ISBN -13: 978-94-010-8491-8 e-isbn-13 :978-94-009-4472-5 DOl: 10.1007/978-94-009-4472-5 Copyright 1986 by Martinus Nijhoff Publishers, Dordrecht. Softcover reprint of the hardcover 1st edition 1986 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 publishers, Martinus Nijhoff Publishers, P.O. Box 163, 3300 AD Dordrecht, The Netherlands.

PREFACE This book was mainly written while I stayed at the Catholic University of Louvain. Professor Anton P. Barten was the one who did not only give me a warm welcome in Louvain, but also supported my research with most valuable comments and constructive criticisms. In addition I benefitted from discussions with Erik Schokkaert, Denis de Crombrugghe and Jo Baras on various subjects, such as the small-sample correction of Chapter 9. The arduous task of transferring my neat handwriting into a readable typescript was excellently taken care of by Brs. E. Crabbe and notably Brs. F. Duij sens, even after working hours. Mrs. A. Molders prevented me of making serious abuse of the English language. My admiration for Carien, finally, is an exponential function of the patience and enthusiasm with which she supported my research. Chapter I is a general introduction to the subject of linkage models, and it contains few mathematical elaborations. Chapters 2 to 4 use more, but elementary, mathematics, and treat several aspects related to the derivation, interpretation and estimation of linkage models. Chapter 2 deals vii tll the theory of import allocation models, Chapter J treats the problem of defining and interpreting elasticities of substitution, while Chapter 4 is concerned with the econometric problems related to the estimation of multivariate models with linear restrictions, such as import allocation models. The core of the study is formed by the derivation, estimation and testing of a new (import) allocation model based on the CRESH aggregator function, in Chapters 5, 8 and 9 respectively. Chapters 6 and 7 describe the estimation method and the data corresponding to t;lis model and therefore serve as background information. Chapter ;0, finally, contains a summary and conclusions.

CONTENTS Page Preface v CHAPTER 1 : THE LINKAGE SYSTEM 1.1 INTRODUCTION 1.2 SOME CONVENTIONS 1.3 ELEMENTS OF A WORLD TRADE LINKAGE MODEL 1.3.1 Data framework 1.3.2 Conceptual aspects 1.4 METHODS OF TRADE LINKAGE 1.4.1 Global and bilateral linkage 1.4.2 Total and import-export allocation 1.4.3 Consistent and inconsistent linkage 1.4.4 Estimation-consistent linkage and simulationconsistent linkage \.4.5 Methodological problems 1.4.6 The choice of a linkage model 1.5 A SLUICE 1.5.1 Summary 1.5.2 Outline of the rest of the study 1.5.3 The hypotheses 5 7 7 13 24 24 27 29 31 32 33 15 :;s 39 Footnotes to Chapter 1 46

- vii - CHAPTER 2 : IMPORT ALLOCATION MODELS 2.1 INTRODUCTION 2.2 THEORETICAL CONSIDERATIONS 2.2.1 The aggregator function 2.2.2 Separability 2.2.3 The aggregation problem 2.2.4 The adding-up condition 2.3 EMPIRICAL MODELS 2.3.1 The CES model 2.3.2 Other models 2.4 SUMMARY AND CONCLUDING REMARKS 50 51 51 53 55 63 69 69 80 82 Footnotes to Chapter 2 84 CHAPTER 3 : ON THE USE OF ELASTICITIES OF SUBSTITUTION 3.1 INTRODUCTION 8 ~ 3.2 BASIC DEFINITIONS 88 3.2.1 Notation 88 3.2.2 The two-factor case 90 3.2.3 Multifactor elasticities of substitution 94 3.3 THE NATURE OF THE EXPERIMENT 102 3.3.1 Constant output (constrained cost minimization) 102 3.3.2 Constant cost (constrained output maximization) 104 3.3.3 Constant marginal cost (profit maximization) 105

- viii - 3.4 A FRAMEWORK FOR ELASTICITIES 3.4.1 One-factor, one-price elasticities of substitution (OOES) 3.4.2 Two-factor, one-price elasticities of substitution (TOES) 3.4.3 Two-factor, two-price ejasticities of substitution (TTES) 3.5 A GENERALISATION OF THE TWO-FACTOR CASE 3.6 SHORT-RUN ELASTICITIES OF SUBST1TUTION 3.7 CONSTANT ELASTICITIES OF SUBSTITUTION 3.8 SUMMARY AND CONCLUDING REMARKS 108 108 109 109 112 114 116 120 Footnotes to Chapter 3 122 CRAPTER 4. MAXIMUM LIKELIHOOD ESTIMATION OF NONLINEAR MODELS WITH LINEAR CONSTRAINTS ON THE FUNCTIONAL FORM 4.1 INTRODUCTION 4.2 CONSTRAINED MODEL AND LOPPED MODEL 4.3 A HOMOSCEDASTIC COVARIANCE MATRIX 4.3.1 The case k=l one constraint 4.3.2 The case ~ 1 more than one constraint 124 127 132 134 143 4.4 A SPECIAL CASE WITH A HETEROSCEDASTIC COVARIANCE MATRIX 150 4.5 SUMMARY AND CONCLUSIONS 154 Footnotes to Chapter 4 157

- ix - CHAPTER 5 : A MODEL WITH PAIRWISE DIFFERING ELASTICITIES OF SUBSTITUTION 5.1 INTRODUCTION 5.2 THE CRESH MODEL WITH CONSTANT RETURNS TO SCALE 5.2.1 The choice for the CRESH function 5.2.2 Definition 5.2.3 First-order conditions 5.2.4 Elasticities of substitution 5.2.5 Second-order conditions 5.3 THREE APPROXIMATIONS 5.3.1 A linearization in levels 5.3.2 A loglinear approximation 5.3.3 A differential approximation 5.4 AN INTERPRETATION AS TOTAL ALLOCATION MODEL 5.5 SUMMARY AND CONCLUSIONS 159 162 162 165 167 172 175 180 180 189 194 205 209 Footnotes to Chapter 5 215 CHAPTER 6 : ECONOMETRIC SPECIFICATION 6.1 INTRODUCTION 6.2 A FURTHER SIMPLIFICATION 6.3 STOCHASTIC SPECIFICATION 6.4 STATIC MODEL WITHOUT TIME TREND 6.5 STATIC MODEL WITH TIME TREND 6.6 DYNAMIC MODEL WITHOUT TIME TREND 6.7 DYNAMIC MODEL WITH TIME TREND 6.8 SUMMARY AND CONCLUDING REMARKS Footnotes to Chapter 6 217 218 221 225 232 234 235 238 239

- x - CHAPTER 7 THE DATA 7.1 INTRODUCTION 7.2 COMPATIBILITY OF CLASSIFICATIONS 7.3 PRICE INDICES; CURRENT AND CONSTANT PRICES 7.4 ANOMALIES 7.5 THE DOMESTIC AGGREGATE 7.6 CONCLUDING REMARKS Appendix 7.A GOODS CLASSIFICATION Appendix 7.B COMPOSITION OF THE ZONES 240 244 247 252 254 256 258 259 Footnotes to Chapter 7 260 CHAPTER 8 : ESTIMATION 8.1 INTRODUCTION 8.2 MODEL CHARACTERISTICS 8.3 THE COVARIANCE MATRIX 8.4 THE AGGREGATE TRADE MODEL 8.4.1 Estimation 8.4.2 Functional forms 8.5 MODELS PER CATEGORY OF GOODS 8.6 SUMMARY AND CONCLUDING REMARKS 261 262 266 272 272 280 284 294 Appendix 8.A DETAILED ESTIMATION RESULTS 296 Footnotes to Chapter 8 308

- xi - CHAPTER 9 : HYPOTHESIS TESTING 9.1 INTRODUCTION 9.2 THE GENERAL TEST PROCEDURE 9.3 WEAK SEPARABILITY 9.4 CLASSIFICATION OF PARTNERS 9.4.1 An analytical example 9.4.2 Test procedure 9.4.3 Test results 9.5 CLASSIFICATION OF GOODS 9.5.1 Test procedure 9.5.2 Test results 9.6 SUMMARY AND CONCLUDING REMARKS 309 312 317 322 323 327 330 333 334 335 340 Appendix 9.A A SMALL-SAMPLE CORRECTION FOR THE LIKELIHOOD RATIO TEST 343 Footnotes to Chapter 9 355 CHAPTER 10 : CONCLUSIONS 10.1 THEORY 10.2 PRACTICE 10.3 SUGGESTIONS FOR FURTHER RESEARCH 356 358 362 REFERENCES AUTHOR INDEX SUBJECT INDEX 365 383 386