THE INDEX-NUMBER PROBLEM AND ITS SOLUTION

Transcription

1 THE INDEX-NUMBER PROBLEM AND ITS SOLUTION

2 By the same author THE EXCHANGE STABILITY PROBLEM SYSTEMS OF SOCIAL ACCOUNTS *NATIONAL ACCOUNTS ANALYSIS *Also published by Macmillan

3 THE INDEX-NUMBER PROBLEM AND ITS SOLUTION G. Stuvel Emeritus Fellow ofall Souls College, Oxford M MACMILLAN

4 G. Stuvel 1989 Softcover reprint of the hardcover 1st edition 1989 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright Act 1956 (as amended), or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 33-4 Alfred Place, London WClE 7DP. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. First published 1989 Published by THE MACMILLAN PRESS LTD Houndrnills, Basingstoke, Hampshire RG21 2XS and London Companies and representatives throughout the world British Library Cataloguing in Publication Data Stuvel, G. (Gerhard), The index-number problem and its solution. 1. Econometrics. Indices I. Title 330'. 028 ISBN ISBN (ebook) DOI /

5 'Each maker of index-numbers is free to retain his conviction that his own plan is the very best. I only ask him to think it possible that others may not be entirely mistaken.' (F.Y. Edgeworth in The Economic Journal, 1925, p. 388)

6 Contents Preface PART I BINARY COMPARISONS 1 The Problem 2 The Traditional Approach 3 The Analytical Approach 4 Properties and Tests PART II MULTIPLE COMPARISONS 5 Indirect and Chain Indices 6 Other Transitive Indices PART III MISCELLANEOUS NOTES Irving Fisher's Search for the Ideal Index Number Banerjee's Factorial Index Numbers The Comparative Proportionality Test Von Bortkiewicz Formulae The Relation between Ps and PF Notes and References Bibliography Index ix vii

7 Preface Index numbers of price and quantity such as the retail price index, the index of industrial production and the indices to be found in national accounts publications have become more and more important in the afterwar years. They affect wage negotiations, are used in econometric models that assist in forecasting and economic policymaking, and lately have begun to playa part in the index-linking of government loans, rent agreements, etc. With their growing importance it has also become increasingly important that they should be free of bias. Unfortunately, however, the index-number formulae that are most often used, those of Laspeyres and Paasche, are known to produce biased measures of price and volume change. In the old days the use of these formulae could readily be excused because the effort required to eliminate the element of bias, which was judged to be small, would have been very costly in terms of the excessive computing burden it would have entailed. But thanks to the rapid advance in computing technology that is no longer so. Thus, as the need for more appropriate indices of price and quantity is beginning to make itself felt, the possibility of filling this need at comparatively little extra cost has in many cases become a reality. It is the object of this study to ascertain what formulae, old or new, should ideally be used in the construction of those index numbers which might eventually replace the ones in current use, bearing in mind the purposes these index numbers are designed to serve and the limitations set by data availability. The systematic search for these formulae has led me to introduce a few new ones, which in my opinion recommend themselves because of their capacity to bring the index-number problem, i.e. the problem of assigning appropriate measures of price and quantity change to commodity aggregates, as near to a solution as one could possibly hope for. Oxford G. SruVEL ix