Contributions to Statistics€¦ · Foreword In his “Prime ricerche sulla rivoluzione dei prezzi...

Contributions to Statistics

For further volumes:http://www.springer.com/series/2912

Luigi Biggeri · Guido FerrariEditors

Price Indexesin Time and Space

Methods and Practice

EditorsProfessor Luigi BiggeriUniversity of FlorenceViale Morgagni 5950134 [email protected]

Professor Guido FerrariUniversity of FlorenceViale Morgagni 5950134 [email protected] University of China59 Zhongguancun StreetBeijing 100872China

ISBN 978-3-7908-2139-0 e-ISBN 978-3-7908-2140-6DOI 10.1007/978-3-7908-2140-6Springer Heidelberg Dordrecht London New York

Library of Congress Control Number: 2009940050

© Springer-Verlag Berlin Heidelberg 2010This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violationsare liable to prosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are exempt from the relevant protectivelaws and regulations and therefore free for general use.

Cover design: Integra Software Services Pvt. Ltd., Pondicherry

Printed on acid-free paper

Physica-Verlag is a brand of SpringerSpringer is part of Springer Science+Business Media (www.springer.com)

Foreword

In his “Prime ricerche sulla rivoluzione dei prezzi in Firenze”∗ (1939), GiuseppeParenti, by Fernand Braudel regarded as an author who “se classait, d’entrée dejeu et sans discussion possible, à la hauteur même d’Earl Jefferson Hamilton. . ..”begins his opening lines with a description/definition of the price revolution whichtook place in the XVI in Europe as “that extraordinary enhancement of all things thatoccurred in European countries around the second half of the XVI; revolution in thetrue meaning of the word, as not only, like any strong price increase, it modified thewealth distribution process and changed the relative position of the various socialcategories and of the different functions of the economic activity, but affected too, ina way that was not enough studied yet, the relative evolution of the various nationaleconomies, and finally, . . .. . .. . .., certainly contributed to the birth, or at least tothe dissemination, of the new naturalistic economic ideas, from which the economicscience would have sprung”. Definition that can be taken as the founding metaphorof this volume.

The ideal stimulus represented by Parenti’s work may have opened the way tothe now long standing tradition which links the research activity of the Departmentof Statistics of the University of Florence to price index numbers problems, con-cretized in the many works produced by its researchers and in the organizationof the International Seminar on “Improving the Quality of Price Indices” held inFlorence in 1995 under the joint auspices of the Department of Statistics itself andof Eurostat. This seminar can be viewed as a milestone for the research project on“Price Indexes in Time and Space” granted by the Italian Ministry of University(MIUR), which disembogued into the International Workshop on price indexesheld in September 2008 at the Department of Statistics, and of which this volumeconstitutes the printed voice.

The work carried out by scholars, researchers, national and international organ-isms and institutions committed to the analysis of price index numbers theory andpractice and price indexes production is too vast to be accounted for and discussedin this book. And, after all, such an exercise would go beyond its objectives.

∗In “Studi di storia dei prezzi”, cared of the Dipartimento di Statistica dell’Universitá di Firenzeand of the “Fondation de la maison des sciences de l’homme, Paris”, Ann Arbor, 1981.

v

vi Foreword

We will therefore restrain ourselves to stress some points.To begin with, a general remark is in order: both the interest of researchers and

scholars and the attention and work of the statistical offices and organizations inthe twentieth century was basically focussed on time indexes, more specifically ontime price indexes and even more specifically, on Consumer Price Indexes (CPIs),particularly in the early stages of the journey.

Even Irving Fisher, in his classic volume “The Making of Index Numbers” (1922)discussed index numbers as synonymous of time (price) indexes, with no mentionto possible space extension of the concept.

Furthermore, and to quote another prominent scholar and Nobel Prize winner,Ragnar Frisch in his fundamental article “Annual Survey of General EconomicTheory: The Problem of Index Numbers” (Econometrica, 1936) claims “. . .willbe confined to those (index numbers) whose object is to measure some sort ofpurchasing power”. Here the expression “purchasing power” refers to time only.

Parallel to this main trend of thought, although shifted in time, and under theboost of very concrete motivations dictated by the needs for making internationalcomparisons of income and Gross Domestic Product (GDP), Irving B. Kravis,Alan Heston and Robert Summers enlivened the United Nations InternationalComparison Project (ICP) in 1968 by publishing the first volume of the series on“International Comparisons of Real Product and Purchasing Power”, reporting theresearch work the objective of which was to develop a comprehensive and reliablesystem of estimates of real GDP and the purchasing power of currencies based upondetailed price comparisons among countries.

This was probably the first time that the space purchasing power terminology andmeaning, and therefore, the space CPI concept and the related purchasing powerparity (PPP) definition appeared.

Official international statistical agencies, such as the United Nations StatisticalDivision (UNSD), the OECD, and Eurostat started working on the subject, in theframework of the ICP while continuing to be interested in, and producing time priceindexes.

The National Statistical Offices (NSOs) did not follow that trend and continuedto elaborate essentially time price indexes, namely time CPIs.

As a consequence, the two aspects of the same question continued to be treatedand approached in parallel and their duality was somewhat, if not totally, ignored.

This volume intends to somehow bridge this gap, as is obvious from its title“Price Indexes in Time and Space”.

If the measurement of time inflation and, subsequently as above said, of spaceprice comparison has been a first and fundamental concern, other problems appeareddownstage as well, claiming for their own adequate place.

Such is, firstly, the question of the space comparability of time CPIs, which hasopened the way to the studies on harmonized price CPIs and their elaboration.

Secondly, great importance has increasingly been taken by price indexes otherthan the CPIs: wholesale, production, international trade price indexes and so on.

Again, noteworthy significance has been gained by price indexes utilized asNational Accounts (NA) deflators, as well as those in the financial field.

Foreword vii

This volume, and the underlying research project, reflect the above points.Indeed, the logic that has driven us has been that of stressing the close duality oftime and space frames, the most advanced methodologies of statistical approach,also with extensive reference to the axiomatic approach and with emphasis on CPIs,both in time, basically as inflation measures and as time deflators of NA aggre-gates, and in space, again as (spatial) inflation measures or PPPs and as space GDPdeflators, keeping in mind the problems of basket choice, weighting and integration-harmonization. All this, with a perspective as general as possible, which accounts forthe highly relevant questions of the elaboration, use and validity of the sub-indexes,for the implications in the financial field and, last but not least, for the practicalproblems of construction and dissemination of the indexes. That is to say:

– the CPIs theory, the time-space background and the analysis of the time-spaceintegration-harmonization;

– the space CPIs, the PPPs and the international comparisons of GDP;– the time CPIs used as sub-indexes;– the time indexes used as NA deflators;– the price indexes in the financial field.

All the above confirms, we believe, that the subject of price index numbers retainsits fascination and utility, despite the elapsing of time. If anything, it seems tostrengthen all its virtues, due to the needs that the new theoretical and practicaleconomic challenges entail.

As a matter of fact, a price index is a tool as simple as it is powerful and usefulwhich does not cease to unfold its attractiveness and the many uses one can makeof it.

It is the will to stress and emphasize once more the meaning and the effectivenessof price index numbers and to recover their whole potential in a comprehensiveframework that has supported our endeavour and the related work.

The papers in this book deal with all the above topics in an effort to discuss themand afford some contribution to the theoretical debate as well as to the methodologyand practice of elaboration.

An old Chinese saying warns: “you can dig a seventy-two-feet-deep well withhard work, but if you do not find water it is as if you had not worked at all”.

We hope we found some water.

Firenze, December 2009 Luigi BiggeriGuido Ferrari

Contents

Part I Consumer Price Indexes Time-Space Integration

Are Integration and Comparison Between CPIs and PPPs Feasible? . . 3Luigi Biggeri and Tiziana Laureti

Retrospective Approximations of Superlative Price Indexes forYears Where Expenditure Data Is Unavailable . . . . . . . . . . . . . . 25Jan de Haan, Bert M. Balk, and Carsten Boldsen Hansen

Harmonized Cross Region and Cross Country CPI Time-SpaceIntegration in the Euro-Zone . . . . . . . . . . . . . . . . . . . . . . . . 43Guido Ferrari, Tiziana Laureti, and José Mondéjar Jiménez

Part II Consumer Price Indexes in Space

Modelling Spatially Correlated Error Structures in theTime-Space Extrapolation of Purchasing Power Parities . . . . . . . . . 63Alicia N. Rambaldi, D.S. Prasada Rao and K. Renuka Ganegodage

Price Indexes across Space and Time and the StochasticProperties of Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Matteo M. Pelagatti

Intra-National Price Level Differentials: The Italian Experience . . . . 115Rita De Carli

Part III Subindexes

Consumer Price Indexes: An Analysis of Heterogeneity AcrossSub-Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Raffaele Santioni, Isabella Carbonaro, and Margherita Carlucci

Price Dispersion: The Case of “Pasta” . . . . . . . . . . . . . . . . . . . 151Isabella Carbonaro, Raffaele Santioni, and Margherita Carlucci

Measuring the Production of Non-Market Services . . . . . . . . . . . . 167Paul Schreyer

ix

x Contents

Part IV Price Indexes in National Accounts

Total Factor Productivity Surpluses and Purchasing PowerTransfers: An Application to the Italian Economy . . . . . . . . . . . . 191Giorgio Garau, Patrizio Lecca, and Lucia Schirru

Jointly Consistent Price and Quantity Comparisons and theGeo-Logarithmic Family of Price Indexes . . . . . . . . . . . . . . . . . 207Marco Fattore

Part V Price Indexes in Financial Markets

Common Trends in Financial Markets . . . . . . . . . . . . . . . . . . . 225Giuseppe Cavaliere and Michele Costa

An Application of Index Numbers Theory to Interest Rates . . . . . . . 239Javier Huerga

Sector Price Indexes in Financial Markets: Methodological Issues . . . 249Michele Costa and Luca De Angelis

Contributors

Bert M. Balk Rotterdam School of Management, Erasmus University, Rotterdam,and Statistics, Netherlands, [email protected]

Luigi Biggeri Istat, Rome, Italy; University of Firenze, Firenze, Italy,[email protected]

Carsten Boldsen Hansen United Nations Economic Commission for Europe,Geneva, Switzerland, [email protected]

Isabella Carbonaro DET, University of Rome Tor Vergata, Italy,[email protected]

Margherita Carlucci Department of Economics, Sapienza University of Rome,Italy, [email protected]

Giuseppe Cavaliere Dipartimento di Scienze Statistiche, Universita’ di Bologna,Italy, [email protected]

Michele Costa Dipartimento di Scienze Statistiche, Universita’ di Bologna, Italy,[email protected]

Luca De Angelis Dipartimento di Scienze Statistiche, Universita’ di Bologna,Italy, [email protected]

Rita De Carli ISTAT, Rome, Italy, [email protected]

Marco Fattore Dipartimento di Metodi Quantitativi per le Scienze Economiche edAziendali, Università degli Studi di Milano - Bicocca, Via Bicocca degliArcimboldi 1, 20126 – Milano, Italy, [email protected]

Guido Ferrari Dipartimento di Statistica, Università di Firenze, Firenze, Italy,[email protected], and Renmin University of China, PRC

K. Renuka Ganegodage School of Economics, The University of Queensland, StLucia 4072, Australia, [email protected]

Giorgio Garau DEIR, University of Sassari, Sassari, Italy, [email protected]

xi

xii Contributors

Javier Huerga European Central Bank, Frankfurt am Main, Germany,[email protected]

José Mondéjar Jiménez Facultad de Ciencias Sociales de Cuenca, UCLM, Spain,[email protected]

Tiziana Laureti Department of Statistics and Mathematics for EconomicResearch, University of Naples “Parthenope”, Naples, Italy,[email protected]

Patrizio Lecca Department of Economics, University of Strathclyde, Glasgow,UK, [email protected]

Matteo M. Pelagatti Dipartimento di Statistica, Università degli Studi diMilano-Bicocca, Via Bicocca degli Arcimboldi, 8, I-20126, Milano,[email protected]

Alicia N. Rambaldi School of Economics, The University of Queensland, StLucia 4072, Australia, [email protected]

D.S. Prasada Rao School of Economics, The University of Queensland, St Lucia4072, Australia, [email protected]

Raffaele Santioni Bank of Italy, Economic Research Unit, Rome, Italy,[email protected]

Lucia Schirru DEIR, University of Sassari, Sassari, Italy,[email protected]

Paul Schreyer OECD Statistics Directorate, Paris Cedex 16, France,[email protected]

Jan de Haan Statistics Netherlands, Division of Macro-Economic Statistics andDissemination, JM Voorburg, The Netherlands, [email protected]

Part IConsumer Price IndexesTime-Space Integration

Are Integration and Comparison BetweenCPIs and PPPs Feasible?

Luigi Biggeri and Tiziana Laureti

1 Introduction

The importance of integration and comparison between the Consumer Price Indices(CPIs) and the Purchasing Power Parities (PPPs) has been widely discussed inliterature (Heston, 1996; Rao, 2001a; ILO/IMF/OECD/UNECE/Eurostat & TheWorld Bank, 2004; Ferrari, Laureti, & Mostacci, 2005), and recognised in two crit-ical reviews of ICP (International Comparison Program) and PPP computation byinternational organisations (Castles, 1997; Ryten, 1998) as well.

A more integrated approach to CPI and PPP for household consumption isrequired in order to: (i) explore the feasibility of integrating the PPP activities withthe streamlined activities of the National Statistical Offices (NSOs) for the com-pilation of CPIs; (ii) examine the relationship between the PPPs for internationalcomparisons with the evolution of CPIs in the countries in question. Integrationand comparison are very advantageous both among different countries and differentareas or cities within a country (ILO/IMF/OECD/UNECE/Eurostat & The WorldBank, 2004).

Over the last decades there has been very little harmonization of the activities andsurveys of NSOs involved in both CPI and PPP work while the need for comparisonsof CPIs and PPPs depends on the possibility of providing complete matrices oftemporal-spatial price differences (ILO/IMF/OECD/UNECE/Eurostat & The WorldBank, 2004) which can be used for a better comprehension of the factors whichinfluence price levels and their changes in different countries.

Therefore the feasibility of integration and comparison between CPIs and PPPs isan important issue which we will deal with in this paper considering only householdconsumption aggregates and binary comparisons between two areas or countries.

Firstly, in Section 2 we will examine the integration issues considering the con-tent of the different consumption baskets, which can be used for computing theCPIs in two countries and the PPPs between these countries, in order to verify the

L. Biggeri (B)Istat, Rome, Italy University of Firenze, Firenze, Italye-mail: [email protected]

3L. Biggeri, G. Ferrari (eds.), Price Indexes in Time and Space, Contributions toStatistics, DOI 10.1007/978-3-7908-2140-6_1, C© Springer-Verlag Berlin Heidelberg 2010

4 L. Biggeri and T. Laureti

overlapping of the baskets, to identify a basis for integrating the price and expen-diture share data for the CPI and PPP computation and to compare these resultsin a consistent space-time comparison of consumer prices. The potential problemsand benefits that may arise from developing an integrated approach to collect thenecessary information are also specified.

However, the integration approach may be hampered by using the “identity prod-ucts principle” which is commonly applied for the calculation of PPPs and canseriously influence the representativeness of the PPP product list of the consump-tion baskets in different countries or regions within a country, and negatively affectthe comparisons between PPPs and CPIs. For these reasons it is also advisable toinclude less comparable products in the PPP baskets.

Section 3 illustrates a simple statistical approach for investigating the advantageof broadening the definition of comparability in order to include additional productsin the PPP calculation, in terms of coverage and representativeness of the computedPPPs and to evaluate the importance of different factors which affect the results ofthe computations.

Regarding the comparison between CPIs and PPPs it is also important to examinehow the changes in consumer price levels over time in the two countries (computedby the CPIs) affect the movements over time of the PPPs calculated for householdconsumption.

It is not possible to totally integrate and link the commonly computed CPIs andPPPs and to carry out a direct comparison for the time being, because these indicesdiffer in the basket of products and services in question and in the formulae used.

Section 4 illustrates a methodological approach based on the decomposition ofthe formulae in order to approximately evaluate the economic factors which explainthe divergences between the CPIs of the two countries from time t−1 to time t,and the movement of the PPPs concerning the two countries in the same period.

Finally, the concluding remarks in Section 5 explain how to carry out the inte-gration of data collection and increase the comparability of CPIs and PPPs and thenunderline the usefulness of the methods suggested. Lastly, a huge organisational andcostly effort by the NSOs is required in order to obtain the amount of data to be col-lected and estimated at least in a benchmark year for achieving the desired results.

2 Integration of CPIs and PPPs

CPIs and PPPs share conceptual similarities. CPIs measure changes in price levels ofproducts and services over time within a country, whereas PPPs measure differencesin price levels across countries or regions within a country. Therefore, CPIs andPPPs refer respectively to time and spatial dimension of price differences. However,the results obtained are different according to the baskets of goods and servicesconsidered and formulae used.

In order to analyse the possible integration of CPI and PPP activities, Rao (2001a)discussed the issue of optimizing the flow of data from CPI to PPP and presented a

Are Integration and Comparison Between CPIs and PPPs Feasible? 5

figure of the intersection of price data sets at a national level of a generic country,in order to verify the comparisons of sets of products and services between CPI andPPP lists within the country.

Bearing in mind the aims of this paper and considering two different countries,we are interested both in the integration of the price data collection for calculatingthe two indices and in the comparison between CPIs and the change in the level ofPPPs. Therefore, also the CPIs of the two countries should be comparable.

In the following sub-sections, we will analyse the comparison of the CPI basketsof products in the two countries in question, then the comparison of the differentbaskets used for calculating the CPIs and PPPs in the two countries, and finally thepotential problems and benefits involved in developing an integrated approach forcollecting the required information.

2.1 The Comparison of CPI Baskets in the Two Countries

With the aim of comparing the items included in the CPI baskets of two countries,it may be necessary to divide the products and services included in the baskets intotwo parts: non-comparable and comparable items (with at least a minimum degreeof comparability). In this way it is possible to verify the degree of overlapping ofthe sets of elementary items (products and services) representative of the elementaryhousehold expenditure aggregate, included in the consumption baskets used for theCPI calculations. The items priced in different countries could be identical or quitedifferent depending on the heterogeneity level of the two countries concerning thepopulation’s consumption behaviour.

Considering Fig. 1, where the CPI baskets of the two countries l and J are rep-resented, composed by Nj and Nl items respectively, it is clear that there are fewerproblems in finding an overlapping area when fairly similar or homogeneous coun-tries are being compared in terms of consumption markets and behaviour. In thiscase, it is possible that Nj = Nl i.e. the total number of products included in the twoCPI baskets of each country in question could be identical. Moreover the character-istics of the products chosen for computing the CPIs and the elementary expenditure

J

. . l

1,...,=lk litem k N

itemkl

1,...,k nl=

itemJk

1,..., Jk n=

1,...,Jitem k Ni=k

Fig. 1 Comparison of CPIbaskets in the two countries,j and l


aggregates could be similar in the two countries. On the other hand, when com-parisons involve countries that are fairly heterogeneous, the overlapping area willdecrease.

The problem of identifying identical or similar products in the two countriescan be related to the different number of items whose prices are to be collectedfor computing the CPIs in the two countries (Nj �= Nl). Moreover, the definitionand the identification of the elementary aggregates and products in the basket, andin particular the methods and practices used for price data collection, can greatlydiffer in the two countries according to the local situation of consumption, the dif-ferences in the consumer markets, the statistical infrastructures and the availableresources.

However, even if the number of the products is the same (Nj = Nl), the physicaland economic characteristics of the products and services which are used for calcu-lating the CPIs can be different in the two countries due to the different patterns ofconsumption.

Therefore, the outer sets in Fig. 1 consist of nj and nl products and services(or groups of products and services) which are typical or characteristic regardingthe consumption behaviour in country j and l respectively. These items should beconsidered separately in the outer sets since they have different price determiningcharacteristics or technical parameters, and cannot be used directly for calculatingcomparable CPIs in the two countries.

It is worth noting that the above theoretical framework for comparing differentconsumption baskets is not applied from a practical point of view because the NSOof a certain country when computing national CPIs does not usually consider thecomparability of the items included in that country’s consumption basket with thoseincluded in the consumption basket of the other country in question.

The main components of CPIs are the data on prices of a large range of prod-ucts and services representative of the consumption baskets of households and theinformation on weights associated with the various product categories reflecting theimportance attached to different items.

The collection of prices and the expenditure weights are based on a classifi-cation of goods and services obtained by using a standard system such as theClassification of Individual Consumption according to Purpose (COICOP), or sim-ilar national classifications. The lowest level of product classification at whichexpenditure weights are available is used for identifying the elementary aggregateindices to be progressively aggregated to the total household expenditure level inorder to obtain the general total CPI.

Within the elementary aggregate, considered as strata sample, the sample itemsto be included in the CPI computation are chosen considering the criteria of rep-resentativeness in terms both of the importance of all the products included in theelementary aggregate concerning consumption expenditure and their evolution ofprice changes over time. The elementary price index is computed using only pricedata, meaning that the index is estimated without using any weights within theelementary aggregate.


In this context, it is obvious that the items included in the CPI baskets of twocountries can be quite different and it is not easy to compare these CPIs if no speci-fication of the characteristics of products and services is given in order to harmonisethe computation of the CPIs.

For this purpose the European HICPs (Harmonised Indices of ConsumerPrices) are computed (ILO/IMF/OECD/UNECE/Eurostat & The World Bank, 2004,Annex 1) to measure inflation on a comparable basis taking into account differencesin national definitions. They are based on the prices of goods and services availablefor purchase in the economic territory of each EU Member State for the purpose ofdirectly satisfying consumer needs. The definitions of prices to be collected and ofthe groups of products and services to be considered are harmonised and agreed on.

The European HICPs are classified according to the four-digit categories or sub-categories of the COICOP-HICP, which is the classification that has been adaptedto the needs of HICPs, in order to have groups of products that are approximatelycomparable in terms of the specific items which must satisfy the same groups ofconsumers’ need.

HICPs must also be based on appropriate sampling procedures, taking intoaccount the national diversity of products and prices and among other things theyillustrate what national consumer price indices have in common among the var-ious countries. Three important sampling dimensions are considered: the itemdimension, the outlet dimension and the regional dimension.

Therefore, the comparability criteria used in the HICPs is quite “weak” interms of comparability of single products since in the HICP calculation therepresentativeness criteria is the most important aspect.

2.2 The Comparison of CPI and PPI Baskets in Two Countries

Considering the above theoretical comparison of the CPI baskets in two countries(Fig. 1), the comparison between CPI and PPP baskets can only refer to the over-lapping set of items, and in this case products are defined according to the need ofcomputing adequate PPPs at elementary level. The computation of PPPs and thefeasibility of the integration between CPI and PPP activities require the evaluationof the degree of comparability of the products in order to measure the price dif-ferential between the two countries in question and the corresponding definition ofthe representative products used for computing the elementary price indices for CPIestimation. For this purpose Fig. 1 can be modified as shown in Fig. 2.

By following the definitions of comparability and representativeness discussedin Biggeri, De Carli and Laureti (2008), we must underline that for computing PPPsthe shaded overlapping area �j,l includes only njl identical products with the samecharacteristics and are therefore strictly comparable but with different systems ofweights in the two countries (j and l). The prices of these products can be and areusually used for calculating PPPs between the two countries.


J

.

. l

lj

ϖj,l

∈ϖjitem jk

1,...,=k nj,

+j l ,

+j l

=item J item l

∈ϖjl = 1,...,njlif k k

itemlk ∈ϖl

1,..., lk n=

kitemJ itemlk=

1, ...,k njl+=if k ∈ϖj,l

+

⎧⎪⎨⎩

⎧⎪⎨⎩

ϖϖ ϖ

ϖ

k k

Fig. 2 Comparison of CPI and PPP baskets in two countries

The PPPs are computed at level of Basic Heading (BH) which consists of a fairlyhomogeneous group of items showing a low dispersion of price ratios. The basicheading level is normally the lowest level of aggregation for which expenditure dataare available; therefore the PPPs at this level are computed without using weightsfor the individual items (Hill, 1997). The basic heading level may be consideredsimilar to the elementary level used in CPI calculation. For the aggregation of priceevolution and price differences above the elementary level or basic heading level,the expenditure share weights are common requirements for both CPIs and PPPs(Balk, 1996, 2001; Diewert, 1993).

However, the choice of the items (products and services) to be included in theBH follows different criteria (OECD-Eurostat, 2006; World Bank, 2007).

The main principle used in PPP computation in developing a product list requiresa selection of “identical products” for the two countries. Identical products ensurethat there are no quality issues in the measurement of the PPPs and the results onlyprovide a measure of price differences. However, this is the most contentious issuein constructing PPPs, because the use of the identity principle can have seriousimplications for the representativeness of the product list of the consumption basketsin different countries.1

Therefore, referring to Fig. 2 and considering the BHs, the degree of the represen-tativeness of items in the overlapping area �j,l can be different in the two countriescompared. In fact, since the patterns of consumption can greatly differ in these twocountries, products that are representative and easily found in country j may notbe easily found in l, due to differences in supply conditions, income levels, taste,climate, customs, etc. From a practical point of view it is evident that the strict com-parability of products, obtained through a detailed specification, leads to PPPs forwhich it is possible to measure pure price differences. At the same time, this strict

1There are several operational procedures used by international organizations in order to deal withthese problems (see among others, Kravis, Kenessey, & Heston, 1975, and more recently Rao,2001b)


comparability will lower the degree of coverage in terms of products consideredand of the general representativeness of a given product in different countries, (andeven within a country); therefore the real consumption basket of these countries canbe inadequately represented. In this case, the overall accuracy and reliability of thecalculated PPPs will be affected.

The two overlapping sets of goods and services marked �+j,l contain n+

jl lesscomparable items, whose prices are used for the computation of CPIs but usuallynot for PPP calculation. However, they could also be used for calculating PPPs byusing a broader definition of comparability or by applying adjustments for qualitydifferences.

The inclusion of the less comparable products in countries j and l for the com-putation of PPPs will increase the degree of coverage and probably the degree ofrepresentativeness of the comparison. However the calculated PPPs may correspondto different products, thus reflecting both pure price differences and the differentrepresentativeness of the selected products in the different countries.

As already mentioned, the outer sets marked �j and �l consist of some goodsand services (nj and nl) which are typical (or characteristic) of the consumptionbehaviour in countries j and l respectively. Two products included in the outer areascannot be considered comparable for PPP purposes, even if we use a broader def-inition of comparability, because consumers may be willing to pay more for oneproduct than another.2 Moreover, these products may not be on sale in one of thetwo countries and vice-versa.

The number of typical products in each country is usually different (nj �= nl)although in some cases it can be the same in both countries (nj = nl). It is clear thatthe higher the number of typical products, the larger the outer areas will be.

As shown in Fig. 2 the total number of the items in the CPI basket in each countryis obtained as the sum of the items included in the different subsets of productsclassified according to the imputed degree of comparability. For example, in countryj the total number of products priced for CPI calculations is expressed as Nj = njl +n+

jl +nj. Similarly, the number of items in country l is expressed as Nl = njl+n+jl +nl.

2.3 Problems and Benefits Involved in Developing an IntegratedApproach for the Collection of the Necessary Informationfor CPIs and PPPs

The calculation of PPPs and standard CPIs is based on similar data requirements.From a practical point of view at present it clear that the definitions of the products

2When a characteristic is price determining the absence or presence of that characteristic will affectthe price that consumers are prepared to pay for the product. There are several examples of pricedetermining characteristics (Word Bank, ICP handbook, 2007). For example, the possession, orabsence, of air conditioning will usually affect the price of an automobile. Consumers in mostcountries will pay more to obtain it. The size of a packet of rice is price determining as consumerswill pay more for a kilo than half a kilo.


to be used for PPP computation may be quite different from the definitions of theproducts used for the computation of CPIs and in any case the price data collectionfollows different criteria for the computation of the two indices. Even if we referto the overlapping area of identical products of CPI and PPP baskets (as in Fig. 2),the same item in the two baskets can be considered identical in theory but not inpractice, since the definition of the products and services in the CPI computation isnot usually well specified in terms of their characteristics.

There are several problems concerning the integration of data collection3 for bothCPIs and PPPs. On one hand it is necessary to evaluate the comparability of productsand identify the identical products in the two countries, meaning that we must verifythe characteristics and the quality of the products chosen for the CPIs and PPPs. Onthe other hand, it is also essential to verify whether the products priced in differentcountries are “representative” of their consumption within the basic headings ornot. A related problem is whether the coverage of the products priced is adequate4

concerning the basic heading to which they belong.There are two different approaches for verifying these conditions, which do not

necessarily exclude each other.The first approach consists in analysing the definition of each item used for each

CPI elementary aggregate and comparing it with the similar item used for the BH inthe PPP computation. This analysis has been implemented in some experiments invarious countries (see for example, Bretell and Gardiner, 2002; Wingfield, Fenwick& Smith, 2005; Aten, 2005, 2006; Melser & Hill, 2005) and also in Italy in order tocompute the PPPs at regional level within the country (De Carli, 2008). The resultsindicate that these analyses can be very difficult and time-consuming to implement.It is often necessary to review the definitions of the items whose prices are collectedfor the CPIs while in other cases it is necessary to implement specific surveys (forexample for clothing, footwear and furniture) in order to obtain adequate price datafor PPPs which are coherent with the identity product principle. Moreover, if it isnot possible to find the items with the same strictly comparable definitions, methodsof spatial quality adjustment must be used in order to compare the products andservices of the two countries.

This approach may guarantee the strict comparability of more items includedboth in CPIs and PPPs, but does not provide any information on the representative-ness and coverage of the PPP item list, which represents the consumption baskets indifferent countries. In order to solve this problem, it is necessary to collect data onexpenditure weights for the products and services belonging to each elementary andBH aggregate. However at present the elementary aggregates and BHs are the low-est level aggregate for which expenditure data are available. Therefore, in order tocarry out specific analyses to assess the degree of representativeness and coverage

3As far as some useful initiatives that could provide a framework for a practical integrated approachfor the integration of PPP and CPI work are concerned we refer to the suggestions of other men-tioned authors and, in particular, to the ILO manual which mentions two core strategies to do it:the “Use of characteristics approach” and “linking approach to international comparisons”.4These issues are currently being researched, and Rao (2001b) offer a modified approach thatattached weights proportional to coverage and representativeness.


of PPPs the expenditure weight data within the elementary aggregates should becollected or evaluated, at least in a benchmark year.

The second approach focuses on the “reconciliation” of the definitions of prod-ucts in the PPP and CPI baskets, using a broader definition of comparability forthe computation of the PPPs (Krijnse-Locker, 1984). In this way a larger numberof items included in the CPI baskets become comparable with those considered inother countries and can be used for the computation of new enlarged PPPs, thusachieving a higher level of comparability between CPIs and PPPs.

In our opinion, it is necessary to go beyond the criteria of identical products cur-rently used for computing PPPs, because the cost of living could be misinterpreted ifthe comparison is based on two identical products which satisfy the same consumerneed but are more frequently purchased in one country than the other and vice versa.

In order to compare the levels of expenditure between two countries for a specificbasket of an elementary aggregate which can fulfil specific consumer demand, it isbetter to refer to the most frequently purchased products in each country since evenif they are not strictly comparable they will certainly represent the products pur-chased in these countries. However, it is important that these products are purchasedby consumers in order to satisfy the same specific needs.

The use of a broader definition of comparability might be achieved by using theStructured Product Descriptions (SPDs) suggested by the ICP Global office of theWorld Bank and used in the 2005 ICP (Diewert, 2008). In fact, SPDs provide theframework for selecting the representative items to be priced. These price move-ments, taken together, can supply a good estimate of the overall change in prices forthe group of similar products as a whole. When completing a SPD, collectors areidentifying a specific product with all its relevant characteristics and distinguishingit from the other products in the same elementary aggregate. These product charac-teristics may be used to specify a particular product to be included in the calculationof CPIs and PPPs.

These product characteristics were used to specify a particular product to beincluded in the calculation PPPs. The SPDs could also be used for collecting productprices in order to construct CPIs thus obtaining a harmonized framework to carryout the comparison among countries. Apart from increasing the number of itemsto be included in the computation, the above mentioned analyses can improve therepresentativeness of the consumption basket of the countries examined. However,disaggregated data concerning expenditure weights within the elementary aggre-gates are necessary for evaluating improvements in representativeness and coverageof the PPPs and in comparability between CPIs and PPPs5.

A successful integration of PPP activity with the CPI compilation depends onto what extent these two activities can be based on a common pool of data andinformation available at a national level and at a territorial level within a country.

Nevertheless, concerning data collection it is clear that for achieving the inte-gration of PPP computation with CPI activities an increased amount of information

5For the international comparisons the integration work also requires the harmonisation of thedefinitions and classifications of products and of the methods for the collection of data.


to be collected and processed during the construction of the CPI is required andtherefore a lot of extra work is necessary (see also Rao, 2001a; ILO/IMF/OECD/UNECE/Eurostat & The World Bank, 2004; Ferrari, Laureti & Mostacci, 2005). Soit is clear that the NSOs and organizations involved in CPI construction must believethat PPP computation and any results from PPPs are a natural extension of currentCPI activities, and produce much more important statistical information on whichpossible economic analysis can be performed.

However, the NSOs must be aware that the integration activities could also resultin tangible benefits as many authors have underlined. In short the potential benefitsare:

• increased coverage in terms of products and share of the household expenditurefor the PPPs;

• improved quality of the PPP estimations in terms of the representativeness of theconsumption baskets of the countries involved;

• increased coherence between the results of PPP and CPI calculations;• possibility for computing the PPPs at reduced intervals of time, taking into

account the high frequency of collection of data for CPI purposes, thus over-coming the difficulties linked to the use of CPIs for the temporal updating of thePPPs;

• improved research on methods for quality adjustment in order to make more com-parable similar products, which could enable us to verify the quality changes overtime and quality differences across countries.

One more important advantage is the possible development of PPPs across differ-ent cities and/or regions within countries. In this case it is easier to make a reliablecomparison and a successful integration of the PPPs and CPIs between two regionswithin a country because the level of homogeneity concerning consumer behaviouris usually higher and the definitions of all the products are more similar.

However, NSOs must evaluate some of the above mentioned benefits, especiallyconcerning the coverage and the quality improvement of the PPP estimations inorder to decide whether it is better to implement the integration of the CPIs andPPPs and more importantly if less comparable products should be included in thePPP computation. Moreover, NSOs must assess the pros and cons in terms of com-parability between CPIs and PPPs. In the following sections we will suggest somestatistical methods for carrying out these evaluations.

3 A Methodological Approach for Deciding whether to IncludeLess Comparable but More Representative Productsin the PPP Calculation

3.1 Inclusion of Less Comparable Products vs Identical Products

In order to understand to what extent it is profitable to include less comparableproducts in the list for the computation of spatial indices, and in particular when


they come from the CPI calculation, we need a method for measuring the effectcaused by their inclusion in the PPP calculation.

On one hand, the inclusion of less comparable products should increase both thecoverage referring to the share of the household expenditure of each set of productsand the representativeness of PPPs referring to the values of the PPPs concerningdifferent sets of products, on the other hand by doing so the degree of comparabilityof the same products will decrease. Therefore, there is a sort of trade-off betweenthe concept of representativeness and comparability.

In order to select the right number of products we will propose a simple methodbased on the calculation of three different indices referring to three different sets ofproducts, already illustrated in Fig. 2 and represented by the overlapping areas �j,l(shaded), the �+

j,l (striped) and the outer areas �j and �l.By following Biggeri, De Carli & Laureti (2008) the three spatial indices are cal-

culated as ratios of the weighted geometric mean prices of the three sets of productsof the two countries in question. The first two indices are called Average Prices’Parities (APPs) to differentiate them from the currently computed PPPs, and thethird is called the Characteristicity Index (CI), because it measures the influence oftypical products of the country’s basket on spatial comparisons.

It is worth noting that all these spatial indices can be calculated by using countryj or country l as the reference country thus obtaining APPs comparing country jto country l or vice-versa. Below only indices, calculated considering country l asreference country, are shown since the results are similar but opposite.

By only considering the strictly comparable products, which are those includedas identical products in the overlapping area �j,l in Fig. 2, we will calculate thefollowing spatial index:

APP�jll,j =

njl∏

k=1

(pj

k

)wjk

njl∏

k=1

(pl

k

)wlk

(1)

where pjk (wj

k) denotes the price (weight, as share of expenditure) of item specifica-tion k in country j, pl

k (wlk) is the price (weight) of item specification k in country

l ,njl∑

k=1wj

k =njl∑

k=1wl

k = 1 and nij is the number of identical items priced in both

countries.Considering only the less comparable products, which are contained in the two

striped areas �+j,l

in Fig. 2, a second index APP�+

jll,j can be computed as a ratio of the

weighted geometric mean prices:

APP�+

jll,j =

n+j∏

k=1

(+pj

k

)+wjk

n+l∏

k=1

(+plk

)+wlk

(2)


where +pjk (+wj

k) and +plk (+wl

k) are the price (weight) of the less comparable

products priced in country j and l respectively andn+

j∑

k=1

+wjk =

n+l∑

k=1

+wlk = 1.

Finally, by considering the typical products we can calculate the CI as the ratiobetween the weighted geometric average prices of the typical products in the twocountries in question, included in the outer areas �j and �l:

CIl,j =

nj∏

k=1

(∗pj

k

)∗wjk

nl∏

k=1

(∗plk

)∗wlk

(3)

where ∗pjk (∗wj

k) and ∗plk (∗wl

k) are the price (weight) of the characteristic products

in country j and l respectively andnj∑

k=1

∗wjk =

nl∑

k=1

∗wlk = 1.

After having calculated these indices we must check their values so assess if theyare equal or different to 1 and then compare the results.

For example if APP�+

jll,j is equal to 1 it seems that the inclusion of less com-

parable products does not add further information to the comparison of the levelof prices between the two countries compared to the information from the APP�jl

index although it increases the coverage. When as usual the APP�+

jll,j is different to 1,

the inclusion of less comparable products shows a different behaviour of the pricesfor these products in the two countries.

Having established that the second APP index, APP�+

jll,j , is different to 1 we must

compare it to the APP�jll,j index.

By comparing the values of APP�+

jll,j and APP

�jll,j we can assess whether the com-

putation of the APP for the less comparable products adds further information to thecomparison of the level of prices between the two countries.

If the two indices are equal to one another it would be advantageous to computePPPs by using less comparable products because in this way the representativenessand coverage of the computed PPPs are improved.

When the two indices differ we should evaluate the degree of divergence and thetrade-off between comparability and representativity. Moreover in order to includethe right number of products we must consider to what extent the two different setsof products weigh on the total household consumption expenditure in both countries.This can be done by considering the total share of expenditure for those productsincluded in the different countries. The cost for applying quality adjustment meth-ods should also be considered when deciding whether to include less comparableproducts.


The value of the index APP�+

jll,j can be much higher than that of APP

�jll,j meaning

that the calculation of spatial indices based only on identical products do not fullyrepresent the consumption baskets of these countries.

The characteristicity index is not useful for deciding whether to include otherproducts in the PPP calculation since the products on which this index is based areso different and typical of each country that they cannot be considered when com-paring the price level of the two countries. On the other hand, if we are aware ofthe value of the CIl,j and the corresponding weight in terms of consumer expen-diture concerning typical products we can evaluate the loss in terms of the overallrepresentativeness (characteristicity effect). If the typical products of each countryweigh heavily, a direct comparison between the two countries in question would beimpossible.

3.2 Interpretation of the Factors Influencing the PPPs Basedon Products with Different Degree of Comparability

Although the information obtained from the computation and comparison of thethree indices is sufficient for deciding the number of products to be included in thecomputation of the PPPs, this evaluation can be improved by using a decompositiontechnique.

In fact, we can suggest an interesting decomposition of the first two indices whichcan be used to assess the importance of the different factors that affect the value ofbinary spatial indices.

Considering for example the APP�+

jll,j , calculated referring to the less comparable

products, the following decomposition is obtained:

APP�+

jll,j =

n+jl∏

k=1

(+pjk

+plk

)wlk

·n+

jl∏

k=1

(+pjk

)wjk−wl

k(4)

The first factor on the right hand side of (4) represents the Pure Price Effect(PPE), corresponding to a bilateral PPP, using a weighted Jevons index with weightsof country l. The Weight Effect (WE), expressed by the second factor on the righthand side of (4), concerns the impact of the difference in consumption patternin the two countries in question. When the products have a similar degree ofrepresentativeness concerning consumer behaviour, the difference in the weightscorresponding to the item k is close to zero.

By introducing the variables αk = ln

(pj

k

plk

)

and cl,jk =

(wj

k − wlk

), which

express the logarithm of price ratio concerning item k in country j and l andthe difference between the corresponding expenditure weights, respectively (wherek = 1, . . . , n+

jl ), after simple algebra, formula (4) can be equivalently expressed as:


APP�+

jll,j = exp (α) exp

(nij · sα · swl

k· Rwl

k ,α

)× exp

(nij · sln Pj · s

cl, jk

· Rln Pj,cl, j

k

)

(4bis)Thus it is possible to identify the factors that influence the Pure Price Effect,

that is swlk

the standard deviation of the weighing system of the base country l, sα ,the standard deviation of the logarithm of the price ratios, Rwl

k ,α the linear corre-lation coefficient between the log price ratios and the weights of country l . It is

worth noting that exp (α) =n∏

k=1

(pl

k

pjk

)

is the unweighted geometric mean of the

price ratios between country j and l. This index is the Jevons index which is thebest estimator when the log - distribution of price changes is Normal. Therefore,the spatial index and the evaluation of the degree of the influence of the factorsin which it is decomposed depends on the shape of the distribution of the ratiobetween the prices of the products in the baskets of the two countries. As the dis-tribution of the ratios of the price levels in two countries may vary according tothe choice of the reference country, the influence of the shape of the distributionon the spatial indices could cause problems and therefore further analyses may berequired.

Similarly, the Weight Effect is influenced by sln Pj , the standard deviations ofprices of country j,s

cl,jk

, the standard deviation of the difference between the weights

in the two countries compared cj,lk =

(wl

k − wjk

)and R

ln Pj,cl,jk

, the linear correlation

coefficient between the prices and the differences in the corresponding weights.Although it is possible to obtain similar decomposition forms as already men-

tioned (considering country j as the reference country) that give two estimations ofthe effects which differ slightly, the most important aspect is that we obtain sta-tistical measures (standard deviation, central tendency and correlation coefficient)concerning the variability of price changes and the consumers’ behaviour in the twocountries which can be interpretable from a statistical and economic point of view.

On the other hand, the symmetric treatment of countries can be achieved forthe pure price effect and for the weight effect by using a geometric mean of theindices and then by applying a geometric average to the results therefore obtain-ing Törnqvist indices. Considering the PPE calculated by using less comparableproducts we can state that:

TPPEl,j =

√√√√√

n+jl∏

k=1

(+pjk

+plk

)wlk

·n+

jl∏

k=1

(+pjk

+plk

)wjk

TPPEj,l =

√√√√√

n+jl∏

k=1

(+plk

+pjk

)wjk

·n+

jl∏

k=1

(+plk

+pjk

)wlk

where TPPEl,j = 1T PPEj,l


4 Comparison Between the Computed CPIs and PPPs

Considering the comparison between CPIs and PPPs and referring to householdconsumption it is important to examine how the changes in levels of consumer pricesover time in the two countries (computed by the CPIs) affect the movements overtime of the PPPs calculated for the household consumptions.

As already stated, it is not possible to totally integrate and link the currentlycomputed CPIs and PPPs.

Although CPIs are conceptually very similar to PPPs, since their aim is to mea-sure price level differences over time and across space respectively, the formulaeused in the calculations are quite different.

We suggest comparing the CPIs between two countries by considering theLaspeyres type index, which is the formula generally used by most NSOs for theconstruction of CPIs and comparing the PPPs over time by using the formulaepresented above. Following this procedure it is not possible to carry out a directcomparison since the two price indices differ in the formula used and in the basketof goods and services to be included in the calculation. Nevertheless the compari-son can be carried out by decomposing the two different formulae used in time andspace comparisons. By following this decomposition method, considering countryl as the reference country, we can compare CPIs across space, thus measuring andinterpreting the factors which explain the divergences between the CPIs of the twocountries from time t−1 to time t:

t−1Pjt − t−1Pl

t =n∑

k=1

t−1Pjk,t · t−1wj

k −n∑

k=1

t−1Plk,t · t−1wl

k

where t−1Pjk,t = pj

t,k

pjt−1.k

and t−1Plk,t = pl

t,k

plt−1.k

are elementary price indices in area j and

l respectively, t−1wjk and t−1wl

k are the weights, expressed by expenditure shares oncommodity or service k in the base period t−1, relating to country j and country l,and

∑

kt−1wj

k = ∑

kt−1wj

k = 1.

On the other hand, by using a decomposition approach and considering country las the reference country, we can compare APPs (and in a similar way PPEs or PPPs)over time in order to understand the influencing factors, which refer to the variationsfrom time T−1 to time T of the APPs comparing the price levels of two countriescalculated at time t−1 and time t:

APPTl,j

APPT−1l,j

=

njl∏

k=1

(pj,T

k

)wl,Tk

/njl∏

k=1

(pl,T

k

)wl,Tk

njl∏

k=1

(pj,T−1

k

)wl,T−1k

/njl∏

k=1

(pl,T−1

k

)wl,T−1k


4.1 Comparing CPIs Across Space

Considering CPIs calculated in fairly homogeneous countries (for example at terri-torial level across different areas in the same country) it is reasonable to assume thatthe products purchased are the same (number and characteristics) in the two areascompared.6

By using the decomposition methods, suggested in (Biggeri and Giommi, 1987;Biggeri, Brunetti & Laureti, 2008) the divergences between the CPI for countryj, t−1Pj

t, and the CPI for country l as reference country, t−1Plt, for each aggregation

level, can be decomposed as follows7 :

t−1Pjt − t−1Pl

t =∑

kt−1 wl

k

(

t−1Pjk,t − t−1Pl

k,t

)+

∑

kt−1 Pj

k,t ·(

t−1wjk − t−1 wl

k

)(5)

It is clear that a divergence emerging from a comparison between the CPIsreferring to the two countries depends on two main factors:

• the different evolution of the prices of the products and services (elementary priceindex effect ), which is expressed by the first factor on the right hand side.

• the differences regarding the behaviour of consumers in their purchases, that ison the share of the expenditure devoted to the different products and services(weight effect).

By introducing the variables δk =(

rPjk,t − rPl

k,t

)and dk =

(

rwjk − rwl

k

), which

express the difference between the sets of elementary price indices in country jand l and the differences between the expenditure weights respectively, after apply-ing simple algebra, we can identify the various factors which influence the twoeffects8:

rPjt − rPl

t = [δ + (

n · swl · sδ · Rwl,δ

)] + (n · sPj · sd · RPj,d

)(5bis)

The first factor on the right hand side of (5 bis), that is the elementary priceeffect

[δ + (

n · swl · sδ · Rwl,δ

)], is influenced by δ = 1

n

∑

kδk the distance between

the centres of the two distributions of elementary price indices, swl , the standarddeviation of the weights, by sδ the standard deviation of the elementary price index

6If this hypothesis is not satisfied the results of the decomposition are approximate.7We must underline that by applying similar procedures and considering area j as reference area,after some simple algebra, we can obtain four different forms of the decomposition of the CPIdifferences, that give two estimations of the effects which differ slightly (see Biggeri et al. 2008).In actual fact a unique measure of the difference could be achieved but it is irrelevant to the aim ofthis paper so we will leave this issue for further development.8Once again by applying similar procedure we can obtain similar decomposition forms bychanging the reference country. However the results may differ slightly.

Contributions to Statistics€¦ · Foreword In his “Prime ricerche sulla rivoluzione dei prezzi...

Documents

Transcript of Contributions to Statistics€¦ · Foreword In his “Prime ricerche sulla rivoluzione dei prezzi...