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Index Numbers and Their Relationship with the Economy No. 1 No. ECLAC Methodologies Index numbers and their relationship with the economy Federico Dorin Daniel Perrotti Patricia Goldszier Index numbers and their relationship with the economy and their relationship numbers Index Thank you for your interest in this ECLAC publication ECLAC Publications Please register if you would like to receive information on our editorial products and activities. When you register, you may specify your particular areas of interest and you will gain access to our products in other formats. www.cepal.org/en/publications ublicaciones www.cepal.org/apps Alicia Bárcena Executive Secretary Mario Cimoli Deputy Executive Secretary Raúl García-Buchaca Deputy Executive Secretary for Management and Programme Analysis Rolando Ocampo Chief, Statistics Division Ricardo Pérez Chief, Publications and Web Services Division This publication was prepared by Federico Dorin, Daniel Perrotti and Patricia Goldszier under the auspices of the Statistics Division of the Economic Commission for Latin America and the Caribbean (ECLAC) and the ECLAC office in Washington, D.C. The authors are grateful to Salvador Marconi and Mara Riestra for their detailed reading of the document and valuable comments, and to Pascual Gerstenfeld, Inés Bustillo and Giovanni Savio for their support for its preparation. The views expressed in this document are those of the authors and do not necessarily reflect the views of the Organization. United Nations publication ISBN: 978-92-1-122038-4 (print) ISBN: 978-92-1-004737-1 (pdf) ISBN: 978-92-1-358272-5 (ePub) Sales No.: E.18.II.G.13 LC/PUB.2018/12-P Distribution: G Copyright © United Nations, 2020 All rights reserved Printed at United Nations, Santiago S.19-01059 This publication should be cited as: F. Dorin, D. Perrotti and P. Goldszier, Index numbers and their relationship with the economy, ECLAC Methodologies, No. 1 (LC/PUB.2018/12-P), Santiago, Economic Commission for Latin America and the Caribbean (ECLAC), 2020. Applications for authorization to reproduce this work in whole or in part should be sent to the Economic Commission for Latin America and the Caribbean (ECLAC), Publications and Web Services Division, [email protected]. Member States and their governmental institutions may reproduce this work without prior authorization, but are requested to mention the source and to inform ECLAC of such reproduction. Contents Introduction ................................................................................................................11 Chapter I Direct comparison and choice of an index from the consumer’s standpoint ............13 A. Averages approach ............................................................................................14 1. Simple or elementary indices .....................................................................14 2. Complex indices .........................................................................................15 B. Fixed-basket approach ...................................................................................... 24 1. Laspeyres price index ................................................................................ 25 2. Paasche price index ................................................................................... 26 3. Laspeyres price index and type of mean .................................................... 27 4. Paasche price index and type of mean ...................................................... 28 C. Axiomatic approach .......................................................................................... 32 D. Stochastic approach ......................................................................................... 34 E. Economic approach .......................................................................................... 36 1. The “real” cost of living index...................................................................... 37 2. Choice of a consumption basket ................................................................40 Chapter II Direct comparison and the producer perspective ................................................... 53 Chapter III Indirect comparison and chain-linked indices ..........................................................61 A. Indirect comparison ...........................................................................................61 B. Chain-linked indices .......................................................................................... 63 Chapter IV Purchasing power parity .......................................................................................... 69 A. Law of one price ................................................................................................ 70 B. What is purchasing power parity? ....................................................................... 71 C. What are PPPs used for? ................................................................................... 73 D. Comparing international prices ......................................................................... 73 1. Creation of the baskets of goods and services .......................................... 74 2. Collection and validation of price data ....................................................... 75 3. Collection and validation of data for weighting .......................................... 75 4. Estimating purchasing power parity .......................................................... 76 E. International comparison of volumes over time ................................................. 88 F. International Comparison Program ................................................................... 89 1. Presentation of the Program and background ........................................... 89 2. Information requirements ......................................................................... 90 3. The prices ..................................................................................................91 4. The weights ............................................................................................... 92 5. Other components of GDP ......................................................................... 93 G. Results of the 2011 round of the International Comparison Program .................. 95 Bibliography .............................................................................................................101 4 Contents Economic Commission for Latin America and the Caribbean (ECLAC) Annexes...................................................................................................................107 Annex A1 ...................................................................................................................109 Annex A2 ................................................................................................................... 111 Annex A3 ...................................................................................................................113 Stage 1: Cost minimization at initial prices ........................................................113 Stage 2: Cost minimization at updated prices ...................................................114 Stage 3: Estimating the cost of living ................................................................115 Annex A4 ...................................................................................................................116 1. Definition of the function ...........................................................................116 2. Budget constraint .....................................................................................117 3. Maximizing production: direct and indirect production function ................117 4. Minimization of production costs ..............................................................120 5. Elasticity of substitution between factors ................................................123 Annex A5 ..................................................................................................................126 Annex A6 .................................................................................................................. 127 Annex A7 ..................................................................................................................136 Exercise 1: Calculation of PPP for a basic heading ............................................ 136 Exercise 2: Aggregation of two basic headings ................................................144 Annex A8 ..................................................................................................................146 1. Quaranta tables ........................................................................................146 2. Dikhanov tables ........................................................................................148 3. Reference parities ....................................................................................150 Tables I.1 Hypothetical prices of wine and bread for an exercise to calculate the general price level...................................................................13 I.2 Application of the elementary price index formula to the wine and bread example...........................................................................................15 I.3 Calculation of the price level using the simple arithmetic mean .......................16 I.4 Calculation of the price level using the simple harmonic mean ........................ 17 I.5 Calculation of the price level using the
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