Econometric issues in hedonic price indices: the case of...

Applied Economics, 2010, 42, 1973–1994

Econometric issues in hedonic priceindices: the case of internet serviceproviders

Kam Yua,* and Marc Prud’hommeb

aDepartment of Economics, Lakehead University, 955 Oliver Road,Thunder Bay, Ontanio, P7B 5EI CanadabStatistics Canada, Prices Division, Ottawa, Ontario, Canada

Researchers in hedonic studies frequently encounter the problems of thechoice of functional forms, the use of pooled regression using timedummies vs period to period regression, and the unit of measurementof the product. This article examines these issues through the studyof Internet service providers in Canada from 1993 to 2000. A series of testsare employed to evaluate the best procedure. We find that the commonlyused log-linear equation with period to period regression and hourly ratecharged gives a robust result compared with the more flexible translogfunction. The quality-adjusted price index declines at about 15% per year.

I. Introduction

Changes in quality of the product poses a difficultyin price measurement. If the quality changes areneglected, the resulting price index will be biased.Many statistical agencies use the matched modelapproach to address this problem. It involvesmatching products of identical quality betweentwo periods and comparing their prices. For thisreason new products in the current period orproducts that exist in the base period, but areobsolete in the current period are not included inthe sample. This can become a problem if thequality is changing at a fast pace as in personalcomputers and Internet services. Therefore, pricesindices using the matched method can also bebiased. The hedonic approach has been successfullyapplied to accommodate for quality change indurable goods. It allows for the effect of qualitychange of the goods or services by estimating theshadow (implicit) prices of objectively observablecharacteristics using regression analysis.

In this article, we examine a series of practical issuesfacing practitioners of hedonic studies. These includethe choice of functional form and the use of timedummy variables in pooled regressions vs. singleperiod analysis. Moreover, in the service sector, thedefinition of a product and its unit of measurement aresometimes not as clear cut as a merchandize good.

In the last 10 years, development in telecommuni-cation technology has been growing at a fast pace.The popularity of personal computers and therapid expansion of the Internet have been hailed bysome as a third technological revolution afterthe agricultural revolution in medieval times andthe industrial revolution that began the modernera. Equity values of the so-called e-commercecompanies rose to astonishing levels before therecent stock market collapse. One small set of keyplayers in this transition period are Internet serviceproviders (ISP), which can be defined as ‘companiesor organizations that act as gateways throughwhich businesses, individuals and organizations canaccess the World Wide Web’ (Hillary and Baldwin,

*Corresponding author. E-mail: [email protected]

Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online ! 2010 Taylor & Francis 1973http://www.informaworld.com

DOI: 10.1080/00036840701748995

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1999, 36). Canadians, among others, are on theforefront of this information technology revolution.Expenditures on Internet services have been increas-ing at an exponential rate. For example, averageexpenditure per household on Internet service was$14 or 0.04% of total consumption in 1996.1 In 1997it increased to $29 or 0.08% of total consumption,and in 1998 the expenditure was $48 or 0.13%.2

Eurostat recommends the inclusion of any newproduct in the CPI if it represents at least 0.1%of total consumption.3 From the above data, thisthreshold was crossed in 1998. It is expected that theexpenditure share of Internet services will maintainthe upward trend in the following several years beforeit starts to level off.

The organization of the article is as follows.In Section II, we look at Internet services in Canadafrom the demand side and the supply side. A briefdiscussion of the theoretical foundations for thehedonic method is included in Section III. Section IVdiscusses how we collected the data and tables somedescriptive statistics. Then in Section V, we presentthe various functional forms employed in this studyand finally, we present our empirical findings. We alsocompare the hedonic price indices with the conven-tional matched model index. Recommendations onthe methodology for the regular production of theprice index are provided in the concluding Section VI.

II. Internet Services in Canada

Due to the growth in demand for Internet services,the number of providers has been increasing drama-tically. In 1994, there were 5100 ISPs in Canada.By 1999, there were over 1000 firms of various sizes,ranging from small companies providing services tosmall rural communities to large phone and cablecompanies covering all major residential areasin Canada. A number of surveys have been carriedout to study the market structure on the productionside. A brief discussion of the most recent surveycarried out by Statistics Canada for IndustryCanada in 1997 is provided here.4 With a healthyresponse rate of 60% (389 out of 675), the surveyfound that the industry consists of hundreds of smallcompanies generating relatively little revenue(5$50 000 annually) and a handful of big dominatingcorporations. A total of 30% of the firms in the

survey take in 36% of the total revenue and the top21% of the firms generate 80% of the revenue. Theselarge companies consist of mainly local phonecompanies, long distance phone companies, cablecompanies and large providers from the US. Profitsare on the whole positive, but most small firms arelosing money. Therefore, we expect to see moremarket consolidation in future years. Recently,it appears that broadband Internet connections suchas cable modem and digital subscriber lines aresurging in popularity. These high speed connectionsoffer dedicated Internet access at an unprecedentedspeed up to 100 times faster than a regular dial-upservice (Staihr, 2000). One estimate predicts that by2002 more than half of the households that haveInternet access will have broadband connection(Brethour, 2000).

On the consumer side, Statistics Canada hascarried out the Household Internet Use Surveysince 1997 on a yearly basis (Dickinson and Ellison,2000). In 1999, 41.8% of Canadian households wereregular users of the Internet compared to 35.9%in 1998 and 29.4% in 1997. The penetration rate forthose with access from home has increased substan-tially from 16% in 1997 to 28.7% in 1999. Othermodes of connection include, in 1999, workplaces(21.9%), schools (14.9%) and public libraries (4.5%).Of those respondents using their computers fromhome, 91.7% use them for e-mails, while 84.7%use them for general browsing. Other usage includesplaying games (42.7%), engaging in chat groups(26.2%), electronic banking (27.7%), purchasing(19%), downloading music (27.1%) and education/training (32%). Higher income households (top 25%)are nearly four times more likely than lowerincome households (bottom 25%) to be connected.Usage also depends on education level, age, childrenat home and provinces (Alberta, BC and Ontariohave the highest usage rates while Quebec andNewfoundland have the lowest).

III. The Hedonic Method: TheoreticalFoundations

In this section, we examine the relationships of qualitychange with the concept of a constant utility priceindex, commonly known as a cost of living index.The matched model is in fact what Pollak (1983) calls

1All figures in Canadian funds unless otherwise stated.2 See Statistics Canada (1996, 1997, 1998).3 See Bascher and Lacroix (1999).4 See Hillary and Baldwin (1999) and Khanna (1999).

1974 K. Yu and M. Prud’homme


the goods approach, in which each variety is treatedas an separate good. For the hedonicmethod, there areat least three separate classes of economic theoriesavailable as justifications for the method. We shalldiscuss each class briefly in this section.5 Our ultimategoal is to justify the use of a hedonic index as a proxyfor a true cost of living index.

Household production

In this theory, the consumer is supposed to use marketgoods x! (x1 , . . . , xm) to ‘produce’ household com-modities z! (z1 , . . . , zn) for consumption. The house-hold production function F(x, z)! 0 is assumed to beneoclassical. Household utility u depends on z only,u!U(z). The household faces the budget constraint

y !X

pixi, i ! 1, . . . ,m

The essence of the model is a two-stage optimiza-tion process. In the first stage, the householdminimizes costs given the qualities of z to beproduced:

C"p, z# ! minX

pixi : F"x, z# ! 0n o

where p is the price vector for x and C(p, z) is the costfunction dual to the production function F. In thesecond stage the household maximizes utility subjectto the budget constraint:

V"p, y# ! maxfU"z# : y $ C"p, z#g

where y is the total consumption expenditureor income and V(p, y) is the indirect utility function.The expenditure function dual to V is

E"p, u# ! minfC"p, z# : U"z# $ ug

Denote u0!V(p0, y0) as the base period utilitylevel, the constant utility price index in period t isdefined as

Pt !E"pt, u0#E"p0, u0#

%

Lancaster (1971) assumes that F is a Leontief(linear) production function and calls the feasible setof all z the characteristics space.

Suppose there is a quality change from period 0to period t for market good xi. This implies that the

production function Ft changes in period t. Asa consequence the cost function Ct, the indirectutility function Vt and the expenditure function Et inperiod t also change. A Laspeyres-type price index isa local linear approximation in the form (Muellbauer,1974)

PLt !

Pni!1 !itzi0Pni!1 !i0zi0

where !it! @Ct/@zit is the shadow marginal cost of zitin period t.6 Similarly a Paasche-type price indexformula can be obtained.

Simple repackaging

In the simple repackaging case the utility functionof a representative consumer is

u ! U"x1, . . . , xm, b# ! U"x, b#

where b is a quality index of x1.7 In the base period,

b! 1. The expenditure function can be written as

E"p, u, b# ! minX

pixi : U"x, b# $ un o

We want to seek a p1* such that

E"p&1, p2, . . . , pm, u, 1# ! E"p1, . . . , pm, u, b# "1#

Note that if b! 1 then p1*! p1, i.e. no quality changeimplies no price adjustment. Simple repackagingmeans that @p&1=@b is independent of x2 , . . . , xm.This is true if and only if

U"x, b# ! F"g"x1, b#, x2, . . . , xm# "2#

that is, b is weakly separable from x2 , . . . ,xm. If thiscondition is not satisfied, then it may be appropriateto adjust the prices of other goods. For instance,if improvement in the quality of new refrigerators willmake ice cream more enjoyable, then it is appropriateto adjust the price of ice cream instead of the priceof refrigerators. Most empirical studies on hedonicprice indices implicitly assume the above separabilitycondition so that a subindex can be constructed withthe product’s own characteristics. Muellbauer (1974)argues that since b is a parameter in the utilityfunction, it should be stable over the medium term atleast. This is in contrast to yearly regression in thehedonic method,8 where parameters change discretelyfrom year to year. In high-tech sectors like computers

5 For details see Pollak (1983) and Triplett (1987).6Muellbauer (1974, p. 988) also shows that the semilog hedonic model is not compatible with the household productionframework. The proof relies on the incompatibility of a function being in additive form and at the same time in multiplicativeform. But since

Pni!1 !itzi0 is only a linear approximation, we cannot conclude that it is incompatible with a multiplicative

form.7 See Fisher and Shell (1972).8Yearly regression will be discussed in specification tests for structural change.

Econometric issues in hedonic price indices 1975


and Internet services, however, the technology isdeveloping so fast that consumers’ preferences andexpectations also change rapidly. Therefore, it maybe necessary to use yearly regression in these cases.

Assume that the consumer buys only one unit ofgood 1 (x1! 1) and let b! f(z) where z ! "z1, . . . , zk#is a vector of characteristics of good 1. This meansthat b is an overall quality index of the product. Also,we group all the other goods x2, . . . , xm into oneaggregate good X with price pX. Then the utilityfunction in (2) can be redefined as

u ! U"q"z#,X# "3#

where q(z)! g(1, f(z)). Now (1) can be written as

E"p&1, pX, u, 1# ! E"1, pX, u, f"z## "4#

where we have normalized p1! 1. The hedonic priceof good 1 is implicitly defined in (4) as

p&1 ! !"z, pX, u# "5#

Using a linear approximation for the marginal rate ofsubstitution for q(z) and X, Diewert (2001) derives ahedonic price equation similar to (5), which isindependent of u and separable in pX and z:

p&1 ! apXf"z#

where a is a positive constant. The hedonic equationin (5) only considers the consumer side. In the nextsection, we will look at the producer side as well. Thehedonic price function is then a result of marketequilibrium.

Implicit markets

Rosen (1974) uses spatial models to interpret hedonicregression in a market equilibrium framework.Products with different characteristics are treatedas product differentiation in pure competition. Theregression equation is the locus of equilibrium pointswhere the demand curves of different consumersintersect with the supply curves of different suppliers.On the consumer side, the utility function is inthe form of (3), i.e. u!U(q(z), X), assumed to bestrictly concave, increasing and differentiable. Theprice of the aggregate good X is set to unity and theprice of the hedonic good is assumed to depend onits characteristics, p! h(z), where h is usually calleda hedonic function. The budget constraint faced by aconsumer with income y is then X' h(z)! y. Definea value function "(z, u, y)! " implicitly according to

U"q"z#, y( "# ! u

Conditional on income and a utility level, " is theconsumer’s willingness to pay for the hedonic good

with characteristics vector z. In fact in the zi( "space, the graphs of " represent a family ofindifference curves between the i-th characteristicand money or the amount of foregone aggregategood X. The partial derivative @"/@zi can beinterpreted as the inverse demand function for theamount of characteristic i. This implies that " isincreasing and concave in zi. For a given income, aconsumer’s utility is maximized when the demandcurve for each characteristic crosses its derivedmarket price and the overall willingness to paymatches the market package price of the hedonicgood. That is,

@""z&, u&, y#@zi

! @h"z&#@zi

"6#

for i ! 1, . . . , k and

""z&, u&, y# ! h"z&# "7#

where z* and u* are the optimum values. This meansthat utility is maximized at the point where "(z, u, y)and h(z) are tangent to each other.

On the producer side, assume that each firmproduces M units of a particular model withcharacteristics bundle z and has its own input factorprices and technology characterized by a parameter #.The cost function can be written as C(M, z, #), whichis increasing in M and z. Each firm is a price takerand given the market price h(z), it maximizes profit

! ! Mh"z# ( C"M, z,## "8#

by choosing M and z. Similar to the value functionsof the consumers, we can define an offer function,$ ! !"z,!,##, of a firm implicitly from

! ! M$( C"M, z,##

Notice that M has been eliminated from $ by thefirst-order condition with respect to M in maximizing! in (8), i.e.

$ ! @C"M, z,##=@M

Conditional on !, $ is the minimum price the firm iswilling to accept for producing the hedonic good withcharacteristics bundle z. Again the partial derivative@$=@zi can be interpreted as the inverse supplyfunction of characteristic i. Profit is maximized atthe point where the offer curve (or surface) is tangentto the hedonic function, i.e.

@!"z&,!&,##@zi

! @h"z&#@zi

"9#

for i ! 1, . . . , k and

!"z&,!&,## ! h"z&# "10#

where z* and !* denote the optimal values.



The market is populated by heterogeneous con-sumers with different taste and incomes on thedemand side and by firms with different technologiesand input endowments. Each firm finds its own nicheby producing a model with a particular characteristicsbundle z. Market equilibrium is achieved by equatingthe optimal conditions (6) with (9) and (7) with (10).The resulting equilibrium path is the market hedonicfunction h(z).

Since h(z) is the envelope of both the valuefunctions and the offer functions, there is norestriction on its functional form. Its determinationis entirely an empirical matter. Nevertheless, byadding identical and independently distributedrandom variables to the otherwise similar utilityfunctions of different consumers, Feenstra (1995)shows the existence of the aggregate expected demandfunction and social welfare function. Consequentlyan exact hedonic price index can be calculated.9 Healso shows that under some assumptions for therelationship between the marginal costs and productcharacteristics, the hedonic regression should beof linear form. A hedonic price index using the log-linear form will be upward biased. Once the hedonicfunction ht(z) in period t is determined, a theoreticalelementary price index or subindex for the hedonicgood can be defined as

P ! e1"z&#e0"z&#

where

et"z&# ! minzfht"z# : q"z# $ q"z&#g

is the period t sub-expenditure function with refer-ence characteristics bundle z*, usually taken to be theperiod 0 or period 1 characteristics.

The Internet service market is probably closerto the implicit market model than the other models.Findings from the Household Internet Use Surveysuggest that consumers have different needs on theirInternet usage. For example, one of the character-istics in the packages is the number of hours, whichrequires time input from the users and differentusers have different time allocations for accessing theInternet. Also, households have different needsfor the number of e-mails included in their account.On the producer side, the Industry Canada surveyindicates that providers differs in size, organizationstructure, location and technology (e.g. cable versusdial-up connections). Therefore, both consumers andfirms are heterogeneous and each is trying to find itsown niche in the market.

IV. Data Sources and Descriptive Statistics

Lists of ISP and their web site addresses in 1999 and2000 are obtained from three sources:

. The membership list of Canadian Associationof Internet Providers (CAIP), www.caip.ca/m-list.htm

. The membership list of Responsible InternetService Companies (RISC), www.risc.ca/membersa-g.htm

. The List web site, thelist.internet.com/canada.html

The prices of the packages offered, together withinformation on the various features were collectedon-line by accessing the web sites of individualcompanies. In addition to prices, 11 characteristicsare identified and used in the hedonic regression.

The prices and other information for the years 1993to 1995 are obtained from Carroll and Broadhead(1994, 1995, 1996). These are handbooks anddirectories published at the beginning of the yearand, therefore, the information on the prices andother features are from the previous year. Startingwith the 1997 edition, this information is no longeravailable from this source. After contacting theauthors, they admitted that the market had becometoo volatile, thus making it difficult to properly keeptrack of the rapidly changing information. Pricesand the limited amount of information applicableto our study are however available from BoardwatchMagazine (1996, 1997, 1999) for the year 1996,1997 and 1998 (hereafter called the Boardwatchdata.) Of the information available, two character-istics are identical to the variables used in other years.

Since most ISPs allow customers to register on-line,the listed prices reflect the true transaction pricesexclusive of taxes. Special offers targeted to particulargroups such as students are not included in thesample. Moreover, we do not include the servicesoffered by so-called free-nets for several reasons.First, free-nets in the early years offered only a text-based system instead of a full graphic environmentto the world wide web. Second, they have a very highuser-to-line ratio of 1800/1 instead of the usual 15/1to 30/1 offered by most commercial ISPs. Third, eachdial-up session is usually limited to one hour(Teleconsult Limited, 1994). For these reasons thenature and quality of services provided by free-netsis very different from that of the commercial ISPs. Inrecent years some providers have started to offer freeaccess with graphic capacity. But the trade-off is users

9 See Diewert (1976) for a definition of exact index numbers.



will be exposed to an advertisement panel on thecomputer screen, which cannot be turned off.Moreover, free internet services do not show up inthe expenditure survey. Truly free Internet services,however, do exist in some European countries andsometimes the services are subsidized by local phonecompanies.10 Unlike North American local telephoneservices, which are flat-fee based, many Europeancountries have metered rates for local calls.Therefore, an economic incentive exists forEuropean telephone companies to offer subsidies toproviders or even to provide free services of theirown.11

Table 1 gives the number of suppliers and thetotal number of packages included in eachof the sampled years. The price and 11 featuresof each package are collected. The BoardwatchMagazine data are grouped by area codes of phonenumbers so the numbers of companies are unavail-able. For comparison purposes, the prices are unitprices expressed as charge per hour of connectiontime. In Table 1, we also list the means, SDsand the coefficients of variation of the unit priceper hour in the sample years. We see that boththe means and the SDs decrease with time. Onepossible explanation is that the increasing numberof ISPs has made the market more competitiveso that prices are decreasing. But the coefficientof variation is fairly stable, indicating that the pricevariability has remained unchanged.

Next, we shall look at some descriptive statistics forthe characteristics of various packages. But first, welist the names and definitions of the variables asfollows.

Dependent variable:

PRICE the unit price per hour of connection timefor the various packages for each ISP.

Independent variables (real or integer):

MONTH number of the pre-paid or committedmonths for the unit price. (0 if bulkpackage).

BHOUR number of bulk hours pre-paid. Unlikemonthly packages, where the unusedhours cannot be transferred to the nextmonth, bulk hours have no time limit. (0for monthly package).

HOUR number of hours per month inthe package. Bulk hours are also includedin this variable, making BHOUR a slopedummy in the regression.

SPEED maximum modem speed supported(kilobit per second).

EMAIL number of free e-mail accounts includedin the package.

WEB amount of free web page storage spaceincluded (MB).

SETUP amount of set-up fee required ($).

Dummy independent variables:

ROAM free roaming hours. (0! not included,1! included).

DEDIC dedicated connection, i.e. high speedphone or cable connection can free upthe phone line and there is no time limitfor each login session. (0! dial-up,1! dedicated).

TECH availability of technical support service.(0! normal hours, 1! 24/7).

FNBH free nonbusy hours access. (0! no,1! yes).

BULK (0!monthly package, 1! bulk hourspackage) generated by the variableBHOUR.

Table 2 lists the means of the characteristics from1993 to 2000. Notice that the maximum speedof modem (SPEED) and the memory providedfor personal web sites (WEB) are increasing. In factmost of the dial-up services in 1993 had the maximummodem speed of 14.4 kilobit per second (kbps), whilein 2000 broadband connections with phone linesand TV cable wires offered maximum speeds exceed-ing 1000 kbps. Also, average setup fees (SETUP) aredecreasing. The provision of 24 hours a day, 7 daysa week technical support services (TECH) are alsoincreasing, probably because as the customer base getslarger, more ISPs find this service more cost effectiveto run and at the same time there is increasing demandfor the service. The provision of free nonbusiness

Table 1. Sample information

YearNo. ofcompanies

No. ofpackages Mean SD.

Coef. ofvariation

1993 15 27 1.668 1.577 0.9461994 44 136 1.061 1.073 1.0111995 95 306 0.927 0.805 0.8681996 n.a. 257 0.766 0.753 0.9821997 n.a. 378 0.660 0.683 1.0351998 n.a. 522 0.573 0.575 1.0021999 96 559 0.383 0.390 1.0202000 109 590 0.306 0.295 0.996

10 See OECD (2000) for a comparison of Internet service price structure among OECD countries.11 See Haan (2000) for a theoretical analysis of free Internet access in European countries.



hour connection time (FNBH) first appeared in1995 but dropped to lower levels in 1999 and 2000.It is probably because more and more unlimited timepackages are available so that this bonus is no longerneeded to attract new customers. The Boardwatchdata set contains only monthly packages with 28.8 and56 kbps modem speed and all the other informationis missing. Therefore, the regressions are run with twoindependent variable, namely HOUR and a dummyfor speed for the year 1996 to 1998. For all packageshaving an unlimited access time, the monthly numberof hours is assumed to be 480, which is based on 16 hper day times 30 days a month.

Next, we compute the chain indices (annualpercentage change in parentheses) and the averageannual indices (AAI) for the unadjusted geometricmean (UGM) of the unit prices and the matchedmodel prices in Table 3. In matching the packages, wechoose the same packages from the same companiesso that there is no ‘brand name’ effect in the sample.12

Matches are not done on the Boardwatch data sopackages in 1995 are matched with those in 1999.The average annual change for the matched indexis (8.3% compared to (21.2% for the UGM index.This difference is probably due to the increasingnumber of unlimited monthly packages, which pullsdown the average price from year to year. It is forthis reason that we have to adjust the prices of thepackages for quality changes. Otherwise, the priceindex will be biased. Also, comparing the UGM indexwith the average price in Table 1, we see that thelatter is slightly upward biased. On the other hand,due to the small percentage of matched samples,

the matched model index can be unreliable as well.For these reasons, we now turn to the constructionof a hedonic price index.

V. A Hedonic Price Index

In Section III, we see that by using different theorieswith different assumptions as the underpinning of thehedonic approach, we can justify different functionalforms in the regression. Practically there is no a prioristructural restriction on the choice of functionalforms. A lot of studies done on durable goods usingthe hedonic method are based on the semilog andthe log-linear models. These log models have theadvantage or convenience that when pooled oradjacent-year regressions13 are carried out the timedummies can be interpreted as a ‘fixed-weightindex’.14 On the other hand, a simple log modelmay not be the correct specification due to thepossible nonlinear relationship between price andcharacteristics and interactions between characteris-tics. For these reasons, we use a battery of nestedmodels to find the right model with superior good-ness-of-fit but consideration will also be given to theease of use in routine production of an elementaryprice index for the CPI. In this section, we firstdiscuss an issue in choosing the unit of measurementof prices. Next, we define the various functionalforms used in the regression. Then, we carry outspecification tests to determine whether pooled dataor yearly data should be used in the regression. Theperformance of various functional forms is then

Table 2. Mean values of characteristics and prices of ISPs in Canada, 1993–2000

YEAR 1993 1994 1995 1996 1997 1998 1999 2000

N 27 136 306 257 378 522 559 590PRICE 1.67 1.06 0.93 0.77 0.66 0.57 0.38 0.31MONTH 2.74 3.71 4.03 1.00 1.00 1.00 4.43 4.42BHOUR 1.26 3.46 13.9 0 0 0 12.7 10.0HOUR 160 116 87 48 59 74 170 221SPEED 17.5 23.2 29.3 28.8 31.0 35.8 98.1 220EMAIL 1.11 0.93 1.10 n.a. n.a. n.a. 1.64 1.97WEB 0 0.04 2.14 n.a. n.a. n.a. 3.89 5.61SETUP 47.2 32.7 15.2 n.a. n.a. n.a. 12.5 16.0ROAM 0 0 0.07 n.a. n.a. n.a. 0.16 0.08DEDIC 0.19 0.13 0.03 n.a. n.a. n.a. 0.02 0.12TECH 0 0.01 0.03 n.a. n.a. n.a. 0.14 0.18FNBH 0 0 0.08 n.a. n.a. n.a. 0.03 0.04BULK 0.19 0.07 0.09 0 0 0 0.06 0.06

12We also use the Jevon index (geometric mean of the price ratios) in the matched model.13 Pooled and adjacent-year regression will be discussed in specification test for structural change.14 This term is used by Feenstra (1995).



Tab

le3.

Matched

mod

elpriceindexan

dun

adjusted

geom

etricmeanindexforISPsin

Can

ada

Year

1993

1994

1995

1996

1997

1998

1999

2000

AAI

N27

136

306

257

378

522

559

590

No.matched

617

––

–38

176

Percentage

matched

22.2

12.5

––

–12

.431

.5Matched

index

1.00

01.06

3(6.3%

)0.90

1((

15.2%

)–

––

0.55

8((

11.3%

)0.54

7((

2.0%

)0.91

7((

8.3%

)UGM

index

1.00

00.68

4((

31.6%

)0.60

5((

11.6%

)0.52

7((

12.9%

)0.44

8((

15.0%

)0.37

3((

16.6%

)0.23

8((

36.2%

)0.18

9((

20.7%

)0.78

8((

21.2%

)



compared, followed by an introduction to a straightforward computation of the three commonly usedelementary price indices. The often used Laspeyres-type and Paasche-type indices will also be computedfor comparison.15

The unit of measurement for prices

Monthly packages are quoted with various numbersof hours of connection time. Sometimes packagesmay vary in the number of months. For example,a typical monthly package is given a discountif the customer commits for a period of 6 monthsor 1 year. Therefore, we have to decide on theunit of price in the regression. There are threechoices: the whole package price, the monthly priceor the hourly rate.16 In this study, we first usethe hourly rate as the independent variable. Asthe following discussion shows, however, using thehourly rate may cause a bias in the regression.Therefore, we also use the monthly package priceas the dependent variable in a number of models.The resulting price indices from the two approacheswill be compared.

In hedonic studies, we try to adjust the priceof a commodity or service for its quality, notquantity. MONTH and HOUR are quantity vari-ables per se. We treat them as characteristics herebecause of nonlinear pricing. That is, we expect thehourly rate to go down as MONTH and HOURincrease. Therefore, if we use the package price in theregression, the linear method will be mis-specified andnonlinear terms must be added to the abovetwo variables. There are two consequences of thisspecification. First, the high R2 resulting fromthe highly correlated price and quantity will makemodel selection less clear. Second, the flexiblefunctional forms (to be described in functionalforms) will become less efficient because the second-order terms now have to accommodate nonlinearityin pricing and not nonlinearity in characteristics.Also, in collecting prices for elementary price indices,we require the prices to be in the same unitof measurement. This is because if the Dutot indexformula (ratio of arithmetic means) is employed, theindex will be biased otherwise (Diewert, 1995). In thisstudy, we will also compare the price indices based onthe Dutot formula with others. Therefore, itseems logical to use the same unit of measurementin price.

There is, however, a potential problem in usingthe hourly rate as the dependent variable. Incalculating the hourly rates for packages withunlimited access, we take the number of hours tobe 480 per month, based on the assumption of 16 hper day times 30 days per month. This number isnevertheless arbitrary and it is possible that theregression result will be different if another numberis chosen. Moreover, dividing the monthly packageprice with such a large number results in a smallhourly rate for the unlimited packages. As aconsequence, we may introduce a negative bias inthe estimated coefficient for the variable HOUR.For these reasons, we also use the monthly packageprice as the dependent variable in the linear,logarithmic and Box–Cox models. In order toaccommodate nonlinear pricing we employ thespline technique for the variable HOUR asrecommended by Diewert (2001). Instead of esti-mating one slope coefficient for the variableinvolved, it assumes a piecewise linear relationship.For example, if we break the variable x into threelinear segments, with break points at x1 and x2, theregression equation becomes

Y !

%0 ' %1x'P

#izi ' u if 0 ) x ) x1%0 ' %1x1 ' %2"x( x1#

'P

#izi ' u if x1 ) x ) x2%0 ' %1x1 ' %2"x2 ( x1#

'%3"x( x2# 'P

#izi ' u if x2 5 x

8>>>><

>>>>:

"11#

where Y is the monthly package price, the z’s areother dependent variables in the regression, the %’sand #’s are the coefficients to be estimated and u isthe disturbance term. Depending on the model inquestion, x can be the original monthly hour, its logvalue or that of the Box–Cox transformation. Thelast break point is at the maximum number of hours,xmax, for all the limited packages in the sample.In this way, the last segment of the spline functionwill be effectively a dummy variable for the unlimitedpackages. The value that we choose to representthese packages is immaterial as long as it is greaterthan xmax.

Functional forms

The functional forms used in this study are listed asfollows.

15 See, example, Berndt et al. (1995) in their study of computer price indices.16 There is some ambiguity between the whole package price and the monthly price. For example, if a package of $20 permonth is given a 10% discount on the condition of a 12 month commitment, we can either treat the package as $18 per monthfor 12 months or $216 for 12 months.



1. Linear Model:

Y ! #0 'XK

i!1

#iXi ' u

2. Semilog Model:

logY ! #0 'XK

i!1

#iXi ' u

3. Log-linear Model:

logY ! #0 'XK

i!1

#i logXi ' u

4. Box–Cox (BC) Model:

Y"&# ! #0 'XK

i!1

#iXi ' u

where the Box–Cox transformation is definedas

Y"&# !Y&(1& if & 6! 0

logY if & ! 0

!

5. Extended Box–Cox Model:

Y"&# ! #0 'XK

i!1

#iX"&#i ' u

6. Restricted Box–Cox–Tidwell (BCT) Model:

Y"&# ! #0 'XK

i!1

#i logXi ' u

7. Quadratic Model:

Y ! #0 'XK

i!1

#iXi '1

2

XK

i!1

XK

j!1

#ijXiXj ' u

8. Translog Model:

logY! #0'XK

i!1

#i logXi'1

2

XK

i!1

XK

j!1

#ij logXi logXj' u

9. Restricted Quadratic Box–Cox (RQBC)Model:

Y"&# ! #0 'XK

i!1

#i logXi '1

2

XK

i!1

XK

j!1

#ij logXi logXj ' u

10. Quadratic Box–Cox Model:

Y"&# ! #0 'XK

i!1

#iX"%#i ' 1

2

XK

i!1

XK

j!1

#ijX"%#i X"%#

j ' u

Model 7 is a second-order quadratic expansion of theindependent variables at the origin. In Models 6 and9, we restrict the independent variables so that &! 0in the Box–Cox transformation. This has theadvantage of being easy to converge during itera-tions. Models 7 to 10 are flexible functional formsas defined by Diewert (1993, p. 159). Model 10 is anunrestricted quadratic Box–Cox model suggested byHalvorsen and Pollakowski (1981). This is the mostgeneral flexible functional form since all the othernine models are nested in it.

Specification tests for structural change

In general, there are three ways to carry out theregression. First, we can estimate the coefficientsfor each individual year separately. Second, we canpool the observations for two adjacent years andestimate a common set of coefficients. And finally, wecan pool the observations for all years. Pooledregression should be used in the absence of structuralchange for two reasons. First, as discussed in simplerepacking above, the coefficients of the regressionare parameters in the consumer’s utility function andshould be stable in the medium term, if we base ouranalysis on the simple repackaging model. Mosthedonic studies implicitly assume this because theyare concerned with obtaining an elementary priceindex based on their own characteristics. Second,in constructing a price index from the results of yearlyregressions, we are in effect performing out of sampleprediction, which can pose a problem if the variancesof some estimated coefficients are large.

Chow (F) tests are commonly used to detect anystructural change during the adjacent years. The test,however, is only valid for models with a linearspecification. For the various Box–Cox models, theindividual regressions have different values for & and,therefore, different degrees of nonlinearity. Thetest statistic for the Chow test thus is not anF distribution.17 Also, the Chow test assumes thatthe variances for different periods are the same,otherwise the computed statistic is not exactly anF distribution. We, therefore, carry out a seriesof Goldfeld–Quandt tests on the adjacent-yearregressions. Results using a 99% confidence levelindicate that homoskedasticity is rejected for abouthalf of the models for at least some periods. Thismeans that the variances of the disturbance terms inthose adjacent periods are not the same. Since, wedo not know the source of heteroskedasticity,it is unlikely that we can correct the problem ina pooled regression. For these reasons, we turn to the

17 Preliminary results do show that some of the computed F statistics in the Box–Cox models are negative.



Wald test, which in essence tests the equality ofthe slope coefficients from two separate regressions.The test statistic is asymptotically a '2 distribution,even in the presence of heteroskedasticity. Table 4reports the results from the Chow test and the Waldtest for the three logarithmic models. The linear andquadratic models have low goodness-of-fit and,therefore, are not included. In the table, Y meansthe test is positive with a significance level of 99%except for 1993–1994, where we use 95% due tothe small sample size and Nmeans the test is negative.Conclusions drawn from the two tests are the sameexcept for 1993–1994, probably because the asymp-totic assumption does not hold for the Wald test. Wesee that for the 42 tests in total, 22 are positive. Bothtests are negative for 1997–1998 for the three models.

For the Box–Cox model, we experiment witha two-stage test for structural change. In the firststage, a common value for & is obtained by anadjacent-year regression. Separate yearly regressionsare then run for each of the two years by restricting& to this common value. The separate regressions arerepeated without the restriction. A likelihood ratiotest is used to test the equality of the restricted& specification with the unrestricted one in each year.If equality is rejected in either of the two periods, weconclude that a structural change has occurred;otherwise, we go on to the second stage. In thesecond stage the Chow test and the Wald test areperformed with the common & from the adjacent-yearregressions. Our results show that in the first stage allbut three adjacent years, namely 1993–1994, 1994–1995 and 1996–1997, have unequal &’s. In the secondstage, the period 1994–1995 and 1996–1997 resultsfor the Chow and the Wald tests are positive.Therefore, the estimated coefficients are differentwhen we impose the same & in the transformation.For the period 1993 to 1994, the Chow test is positive,while the Wald test is negative. In what follows,we shall base our analysis on the yearly regressionsbecause that is the unrestricted specification.

But, we shall also calculate the indices fromadjacent-year regressions.

For the spline regressions using monthly packageprices, the variable HOUR is broken up into fivesegments, with the last one representing the unlimitedpackages. The break points are selected so thatapproximately the same number of observations fallwithin each segment. Wald tests are carried out forthe linear, semilog and log-linear models. Of the totalof 21 tests, 16 are positive using a 95% critical value.This indicates that structural changes occur moreoften when a spline function is used for the monthlyhour. For these reason only yearly regressions areused to calculate the price indices for the splinemodels. Besides the monthly packages, there are bulkpackages in the sample years 1994, 1995, 1999 and2000. Using dummy variables for the bulk packageson top of the spline function would make theregression equations too messy. Therefore, the twotypes of packages are treated differently. At first, weconsider using seemingly unrelated regressions (SUR)with unequal number of observation to increase theefficiency of the estimation (Zellner, 1962; Schmidt,1977). This technique, however, requires that theequal portions of the observations from the twodata sets to be ‘matched in time’ in order to satisfythe assumptions in the structure of the variance-covariance matrix of the disturbance terms. Since themonthly packages and bulk packages in the ISPdata are cross-sectional, the choice of the matchingobservations will certainly affect the estimationresults. Therefore, SUR is not used and insteadseparate regressions are run and the resulting indicesare aggregated using sample sizes as weights. Due tosmall sample sizes, only three spline segments areused in the regressions for the bulk packages.

Performance of alternative functional forms andregression results

A number of the models, we test here are nested, i.e.the simpler models can be obtained by restrictingthe parameters to specific values in the morecomplex models. It is natural that more unrestrictedmodels usually give a higher value for the adjustedcoefficient of determination, #R2. In this regard,the flexible functional forms often perform betterthan the various linear and Box–Cox models,with the exception of the quadratic model. Wealso use the Akaike Information Criterion (AIC) tocompare the various models. With this test, theflexible functional forms lose some of their apparentadvantage due the loss of degree of freedom withthe additional second-order terms. Table 5 lists thevalues of #R2, AIC and the Schwartz Criterion (SC)

Table 4. Chow and Wald tests for Structural change

Model 93–94 94–95 95–96 96–97 97–98 98–99 99–2000

SemilogChow N N Y Y N Y NWald N N Y Y N Y N

Log-linearChow Y Y N Y N N YWald N Y N Y N N Y

TranslogChow Y Y Y N N Y YWald N Y Y N N Y Y



for all the yearly regressions.18 Using #R2, the variousBox–Cox, the translog and the RQBC models allgive very good results. With the AIC, the translogand RQBC both perform very well in early yearsand in the years with the missing variables, becausein those years the number of second-order terms isnot too high. For the years 1999 and 2000, wherewe use almost the full set of second-order terms,the translog and RQBC models are penalized by theAIC and SC because of the extra terms (Greene,2000, p. 306). Compared with the #R2 criterion, AICand SC are heavily biased towards the linear and thelog models. Note that the commonly used semilogmodel is inferior to all the other models except thelinear one. The log-linear model, on the other hand,performs satisfactorily compared with the translogmodel. In future analysis with less severe samplesize restrictions, we expect the log-linear, Box–Cox,the translog and the RQBC models will all havesatisfactory goodness-of-fit.

As mentioned above, the quadratic Box–Coxregression fails to converge. Instead a Box–Cox–Tidwell regression (without the second order terms)is tried. In this model the transformation for

the independent variable (PRICE) is differentfrom the transformation for the dependent vari-ables. In other words, the transformation parameterA on the left-hand side of the regression equation isdifferent from % on the right-hand side. A non-linear iterative maximum likelihood method isused for the yearly regression for the years withthe full data set. The iterations converge except forthe year 1995. Therefore, we cannot compute thecorresponding price indices but it is interesting topoint out that in the 1999 regression the estimated& and % are (0.776 and 0.512 with t-ratios equal to(3.35 and 3.074 respectively. This implies that thelinear model with the values of & and % restrictedto (1, 1), the semilog model (0, 1), the log-linearmodel (0, 0), the Box-Cox model (&, 1), the extendedBox–Cox model (&, &) and the restricted Box–Cox–Tidwell Model (&, 0) should all be rejected.

To test for multicollinearity and sampling sensi-tivity, we randomly remove a small set of data andrepeat the regression. The estimated coefficientsare found to be stable for the logarithmic modelsand the Box–Cox models. Also, for the purpose ofcomputing the fitted prices and the price indices we,

Table 5. Model selection statistics for the hourly price models

Year Criterion Linear Semilog Log-linear Box–Cox Ex. BC BCT Translog RQBC

1993 #R2 0.07 0.11 0.32 0.11 0.32 0.33 0.40 0.41AIC 3.01 1.06 0.82 1.07 0.82 0.82 0.72 0.72SC 4.63 1.64 1.26 1.65 1.26 1.26 1.10 1.11

1994 #R2 0.29 0.53 0.80 0.57 0.80 0.80 0.81 0.80AIC 0.88 0.33 0.14 0.35 0.14 0.14 0.13 0.14SC 1.12 0.41 0.18 0.44 0.18 0.18 0.17 0.18

1995 #R2 0.26 0.59 0.74 0.67 0.74 0.74 0.76 0.76AIC 0.49 0.31 0.20 0.34 0.18 0.19 0.19 0.18SC 0.57 0.36 0.23 0.40 0.22 0.22 0.22 0.21

1996 #R2 0.19 0.62 0.64 0.80 0.68 0.64 0.75 0.77AIC 0.46 0.17 0.16 0.19 0.13 0.16 0.12 0.13SC 0.48 0.18 0.17 0.20 0.14 0.17 0.12 0.14

1997 #R2 0.14 0.62 0.77 0.89 0.78 0.77 0.80 0.81AIC 0.40 0.19 0.12 0.22 0.10 0.11 0.10 0.11SC 0.42 0.20 0.12 0.23 0.10 0.11 0.11 0.12

1998 #R2 0.17 0.65 0.77 0.74 0.79 0.77 0.81 0.81AIC 0.27 0.22 0.15 0.29 0.10 0.11 0.12 0.12SC 0.28 0.23 0.15 0.29 0.11 0.12 0.13 0.13

1999 #R2 0.37 0.82 0.89 0.91 0.90 0.90 0.91 0.91AIC 0.10 0.19 0.11 0.41 0.08 0.08 0.10 0.12SC 0.11 0.21 0.12 0.45 0.09 0.09 0.12 0.14

2000 #R2 0.57 0.85 0.89 0.88 0.91 0.91 0.91 0.91AIC 0.04 0.16 0.12 0.31 0.06 0.05 0.10 0.05SC 0.04 0.18 0.13 0.34 0.07 0.05 0.12 0.06

18 Both AIC and SC minimize a loss function of the sum of the square error, therefore, the lower the number the better thegoodness-of-fit.



re-estimate the coefficients without the extremelyinsignificant variables (those with a t-ratio 51).Due to large number of second-order cross termsin the translog and RQBC models, the regressionresults sometimes are sensitive to the choiceof omitted cross terms. This factor should beconsidered in choosing these models for futureregular production of the price index. Becauseof the additional effort required to fine tune theresults, sometimes involving the subjective judge-ment of the analyst, quality control in productionwill be more difficult.

Table 6 reports the regression result of the Box–Cox model for 2000. All the significant coefficientshave the expected signs. The negative coefficientsfor MONTH and HOUR confirm that pricing isnonlinear. BULK and BHOUR have positive coeffi-cients, meaning that consumers pay a premiumfor the bulk packages and prices for those packagesdecline less rapidly with hours purchased than themonthly packages. SPEED is positive, but insignif-icant as a continuous variable in this model, but issignificant in a number of other models such as log-linear and translog. Since high speed (broadband)Internet connections are gaining popularity in the last2 years and 56 kbps is the standard for most dial-upconnection services, we experiment with replacingSPEED with a dummy variable for the former.19 Theresulting coefficients for this dummy in 2000 arepositive and significant in most models. The coeffi-cients for EMAIL and WEB are insignificant,probably because these services can be obtained freeof charge on the Internet. The negative signs for fulltechnical support (TECH) and out of town roamingservices (ROAM), probably reflect a scale economyfor the industry. Large national companies canprovide those services at low costs and at the sametime charge low prices for the packages.

As for the spline models, Table 7 shows that in theearly years the performance of all the modelsare quite uniform according to the adjusted R2, butthe values drop for the linear model in latter years.The AIC and SC also indicate that the linear modelis inferior. The semilog model perform well in thiscase compared with the log-linear and the Box–Coxmodels. Goodness-of-fit among the Box–Cox modelsare very close in all years.

Elementary price indices

In each of the above regression models, the fittedprice of each observation can be calculated after the

coefficients have been estimated, not only for the yearthat the observation belongs to, but also for anotheryear using that year’s estimated coefficients. Forexample, the estimated coefficients for 1993, #93,in the yearly regression can be used to evaluate theprices, p93=94i , of the observed characteristics in 1994as if those packages were available in 1993. In otherwords, we calculate

p93=93i ! f"X93i , #93# p93=94i ! f"X93

i , #94#

where X93i is observation i of the vector of character-

istics in 1993 and f is the functional orm used in theregression. Similarly, we can calculate p94=94j andp94=93j for all j in 1994. In this way, we can come upwith the fitted prices of a package in the adjacentyears. Using these fitted prices, we can calculate thevalues of the three commonly used elementaryindices, namely the Carli index (arithmetic meanof the price ratios), the Dutot index (ratio of thearithmetic means) and the Jevons index (geometricmean of the ratios)20 The performance of theseindices can be compared and evaluated. In thisway, we actually infer the comparison period pricesof the products available in the reference period andvice versa. The symmetric treatment of the twoperiods makes the resulting index similar in natureto a Fisher-type index. Moreover, it avoidsthe controversy of the ‘dummy’ price index.(Triplett, 1990). In passing, we should mention thatin all the log models, the ordinary least squareassumptions imply that the estimated values for Yis the conditional median, M(Y/X), instead of the

Table 6. Regression results from the Box–Cox model, 2000

Variable Estimated Coefficient t-statistic 564 DF

MONTH (3.07* 10(2 (5.93BHOUR 5.84* 10(3 11.49HOUR (7.76* 10(3 (56.72SPEED 7.36* 10(5 0.89EMAIL (2.61* 10(2 (1.62WEB 3.60* 10(3 0.68SETUP (1.43* 10(3 (1.65ROAM (2.85* 10(2 (0.30DEDIC 1.301 9.18TECH (0.112 (1.74FNBH (0.187 (1.52BULK 0.444 3.30Constant (0.514 (9.55

Notes: Box–Cox regression for &!(0.41R2! 0.9085Adjusted R2! 0.9065.

19 Since all high speed connections are dedicated, we drop the dummy DEDIC to avoid multi-collinearity.20Note that it is also the ratio of the geometric means.



conditional mean, E(Y/X) (Goldberger, 1968). Thetwo estimators are related byM"YjX# ! E"YjX#e((2=2, where (2 is the disturbancevariance. Therefore, the estimations from the logmodels are not unbiased. We ignore this factor here,since the variances are small and the bias applies tothe base years and the comparison years.

Table 8 lists the three elementary chain indices(annual percentage change in parentheses) with theAAI from the semilog, Box–Cox, log-linear, translogand the RQBC models. For the extended BC andrestricted BCT models some values of the nontrans-formed fitted price are negative and so an indexcannot be computed. In Table 8, we see that the Carliindex is upwardly biased with respect to the JevonsIndices, as predicted by theory (Diewert, 1995).The Dutot index, on the other hand, is unstable.It fluctuates above and below the Carli index. Forexample, in the Box–Cox model, the 1995–1996Dutot index is 0.808, exceeding the Carli index at0.761. In the 1996–1997 indices, however, the reverseis true (0.932 vs 0.953). The Dutot index is sensitiveto departure from the homogeneity assumption andthe unit of measurement of the product (Diewert,1995, p. 15). Although the unit prices here are qualityadjusted they are far from homogeneous. Therefore,in hedonic pricing, the Jevons index is the most

suitable among the three. This result is in line with thechoice of most statistical agencies, which employ theJevons index to aggregate elementary prices.

We see in Table 8 that there is a commondownward trend for the ISP price index computedwith the different models. For example, if we lookat the Jevons index from the log-linear model, we seethat there is a rapid decline of prices from 1993to 1996. The decline exhibits a sudden drop in 1997of about 5% and picks up slowly in 1998 and 1999.In 2000, prices seem to have stabilized. The averageannual price decrease from 1993 to 2000 is 14.8%.In other words, the average Internet access hourlyrate in Canada in 2000 is about 33% of what theconsumers paid in 1993 (Fig. 1). We can also comparethe hedonic indices with the matched model indexand the unadjusted geometric mean index in Table 3.With average annual decreases of 8.3% and 21.2%,respectively, the matched model index is upwardbiased, while the UGM index is downward biasedrelative to the hedonic indices. The bias in thematched model is probably due to the low percentageof matching, albeit, we tried to match the companiesin 2000 with those in 1999. As a result, a lotof information for new discount packages is notincluded in the index. The UGM index is downwardbiased because the samples in adjacent periods are

Table 7. Model selection statistics for the spline models

Year Criterion Linear Semilog Log–linear Box–Cox Ex. BC BCT

1993 #R2 0.90 0.82 0.86 0.89 0.89 0.90AIC 7.74 (0.87 (1.13 2.00 1.18 1.21SC 8.19 (0.42 (0.68 2.45 1.63 1.66

1994 #R2 0.85 0.88 0.88 0.88 0.88 0.88AIC 7.79 (1.85 (1.87 (1.85 (1.87 (1.87SC 8.08 (1.56 (1.58 (1.56 (1.58 (1.58

1995 #R2 0.78 0.65 0.67 0.62 0.64 0.65AIC 6.58 (1.71 (1.77 (2.58 (2.63 (2.57SC 6.75 (1.54 (1.60 (2.40 (2.46 (2.40

1996 #R2 0.50 0.54 0.65 0.56 0.58 0.60AIC 3.80 (1.68 (1.96 1.25 0.82 0.34SC 3.89 (1.60 (1.87 1.34 0.91 0.42

1997 #R2 0.58 0.64 0.65 0.63 0.63 0.63AIC 3.55 (2.37 (2.39 0.32 0.32 0.16SC 3.62 (2.30 (2.32 0.40 0.39 0.23

1998 #R2 0.47 0.51 0.54 0.51 0.53 0.54AIC 3.66 (2.07 (2.15 1.21 0.83 1.09SC 3.71 (2.01 (2.09 1.27 0.88 1.15

1999 #R2 0.63 0.75 0.74 0.75 0.74 0.74AIC 3.53 (2.91 (2.85 (2.91 (2.45 (2.91SC 3.64 (2.79 (2.74 (2.79 (2.33 (2.80

2000 #R2 0.54 0.77 0.76 0.80 0.79 0.79AIC 5.07 (2.59 (2.55 (5.02 (5.02 (5.24SC 5.18 (2.48 (2.44 (4.91 (4.91 (5.13



Tab

le8.

Hedon

icpriceindicesforinternet

services

inCan

ada

Model

1993

1994

1995

1996

1997

1998

1999

2000

AAI

Carliindices

Sem

ilog

1.00

00.71

8((

28.2%

)0.66

3((

7.7%

)0.51

2((

22.7%

)0.50

5((

1.3%

)0.47

6((

5.9%

)0.45

8((

3.7%

)0.44

9((

2.1%

)0.89

2((

10.8%

)Log-linear1.00

00.72

7((

27.4%

)0.66

9((

7.9%

)0.52

8((

21.1%

)0.50

5((

4.4%

)0.46

0((

8.8%

)0.39

3((

14.8%

)0.38

2((

2.8%

)0.87

1((

12.9%

)Box–

Cox

1.00

00.68

0((

32.1%

)0.63

8((

6.1%

)0.48

6((

23.9%

)0.46

3((

4.7%

)0.43

6((

5.9%

)0.39

7((

8.9%

)0.39

0((

1.7%

)0.87

4((

12.6%

)Translog

1.00

01.03

8(3.8%

)0.98

0((

5.6%

)0.77

3((

21.1%

)0.74

6((

3.5%

)0.68

9((

7.7%

)0.62

6((

9.2%

)0.62

0((

0.9%

)0.93

4((

6.6%

)RQBC

1.00

01.01

8(1.8%

)0.96

3((

5.4%

)0.74

2((

22.9%

)0.71

5((

3.7%

)0.66

5((

7.0%

)0.60

2((

9.4%

)0.60

4(0.2%

)0.93

0((

7.0%

)

Dutotindices

Sem

ilog

1.00

00.67

7((

32.3%

)0.60

3((

11.0%

)0.49

5((

17.8%

)0.44

9((

9.5%

)0.40

4((

10.0%

)0.33

9((

16.1%

)0.31

6((

6.6%

)0.84

8((

15.2%

)Log-linear1.00

00.75

6( (

24.4%

)0.66

2((

12.4%

)0.49

8((

24.7%

)0.50

7(1.8%

)0.47

5((

6.3%

)0.38

6((

18.9%

)0.36

5((

5.3%

)0.86

6((

13.4%

)Box–

Cox

1.00

00.63

9((

36.1%

0.58

5((

8.5%

0.47

2((

19.2%

0.44

0((

6.8%

0.39

2((

11.0%

)0.32

4((

17.2%

)0.30

4((

6.2%

)0.84

4((

15.6%

)Translog

1.00

00.77

0((

23.0%

)0.62

6((

18.8%

)0.47

6((

24.0%

)0.45

8((

3.7%

)0.42

5((

7.2%

)0.37

0((

13.1%

)0.34

6((

6.4%

)0.85

9((

14.1%

)RQBC

1.00

00.76

7((

23.3%

)0.62

4((

18.6%

)0.46

4((

25.8%

)0.44

4((

4.3%

)0.41

5((

6.3%

)0.36

2((

12.9%

)0.34

2((

5.6%

)0.85

8((

14.2%

)

Jevo

nsindices

Sem

ilog

1.00

00.67

1((

33.0%

)0.60

4((

9.9%

)0.41

7((

30.9%

)0.39

9((

4.3%

)0.37

0((

7.4%

)0.33

9((

8.4%

)0.32

9((

2.8%

)0.85

3((

14.7%

)Log-linear1.00

00.66

6((

33.5%

)0.58

6((

12.0%

)0.46

1((

21.3%

)0.43

9((

4.9%

)0.39

9((

9.1%

)0.33

8((

15.1%

)0.32

6((

3.8%

)0.85

2((

14.8%

)Box–

Cox

1.00

00.63

4( (

36.6%

)0.57

5((

9.3%

)0.41

1((

28.5%

)0.39

1((

4.9%

)0.36

4((

6.9%

)0.32

2((

11.6%

)0.31

5((

2.3%

)0.84

8((

15.2%

)Translog

1.00

00.73

5((

26.5%

)0.64

1((

12.8%

)0.49

3((

23.1%

)0.47

4((

3.7%

)0.43

7((

7.9%

)0.38

8((

11.3%

)0.37

8((

2.6%

)0.87

0((

13.0%

)RQBC

1.00

00.72

6((

27.4%

)0.63

4((

12.7%

)0.47

7((

24.8%

)0.45

9((

3.8%

)0.42

5((

7.3%

)0.37

7((

11.4%

)0.37

1((

1.6%

)0.86

8((

13.2%

)



not matched, therefore, an increase in the numberof unlimited packages in the comparison periodwould induce a bigger price drop.

Since a number of variables are missing in theregression from 1996 to 1998, the resulting indiceswill be biased. To assess the seriousness of this bias,we compute the same indices using 1995 as thebase year and 1999 as the reference year with a fullset of variables. These bilateral indices are thencompared with the chain indices computed withthe missing variable. Table 9 reports the compar-ison. Since the quality of the service improves overtime, we anticipate the chain indices with missingvariables be downward biased. But surprisingly mostvalues in Column 4 of Table 9 are positive,indicating an upward bias, although the differencesare small. For example, the Jevons chain index andbilateral index from the log-linear model are 0.578and 0.544, respectively, which differ by a 6% spread.This result can be explained by looking at theindividual regressions more closely. Table 10 lists theyearly regression results for the log-linear modelof the 2 years. We see that in 1999 the variablesHOUR and MONTH are highly significant, whileother variables such as SPEED, EMAIL, WEB,DEDIC and TECH either have the incorrect signsor are insignificant at the 95% level. The samplesfrom 1996 to 1998 contain monthly packages onlyand so the variables MONTH, BHOUR and BULKare irrelevant.21 And since the other variablesbesides HOUR do not have a lot of explanatorypower, the chain indices from the Boardwatch datawith the missing data give satisfactory results.22

From the economic perspective, this implies that

Internet service pricing, at least for the years from1995 to 1999, is largely determined by the packagingof the service. Most of the other characteristics areadd-ons that do not affect pricing strategy to a largedegree.

We also calculate the Laspeyres-type and Paasche-type indices using the sample (arithmetic) means Xwhere k! 0 for the reference year and k! 1 forthe comparison year. The Laspeyres-type index isdefined as

PL ! f" #X0, #1#f" #X0, #0#

whereas the Paasche-type index is defined as

PP ! f" #X1, #1#f" #X1, #0#

Table 11 lists the Laspeyres and Paasche-type chainindices (annual percentage change in parenthesis)with the average annual indices for some selectedmodels.

We see that the indices are sensitive to the choiceof the reference year.23 For example, the log-linear

Fig. 1. Price indices from the matched model and the yearlylog-linear models

Table 9. Comparison of the 1995/1999 bilateral indices withthe chain indices

Model Chain Bilateral Difference

SemilogCarli 0.691 0.579 0.113Dutot 0.562 0.532 0.030Jevons 0.561 0.554 0.007

Box–CoxCarli 0.621 0.627 (0.006Dutot 0.555 0.590 (0.035Jevons 0.560 0.609 (0.049

Log-linearCarli 0.587 0.592 (0.005Dutot 0.583 0.572 0.011Jevons 0.578 0.544 0.034

TranslogCarli 0.638 0.616 0.022Dutot 0.591 0.578 0.013Jevons 0.605 0.576 0.029

RQBCCarli 0.625 0.610 0.015Dutot 0.579 0.572 0.007Jevons 0.594 0.568 0.027

21 For this reason only subsets of the data from 1995 to 1999 are used in computing the 1995–1996 and 1998–1999 priceindices. The 1995–1999 bilateral indices, however, are computed using the full data set.22 The adjusted R2 is 0.89 with the full data set, compared with 0.86 with the missing variables.23 This is observed by Berndt et al. (1995) in their study of computer prices as well.



Laspeyres average annual change is (12.0%, butthe corresponding Paasche index changes by(16.9% annually. The gaps for individual yearsare sometimes even wider. There are three possibleproblems here. First, it is well known that theLaspeyres index is upwardly biased relative to thePaasche index. That is, going from one period tothe next, quantities (characteristics in this case) shifttowards those which have dropped the most inprice, resulting in a substitution bias in theLaspeyres index when the first-period characteristicsare used. Second, all the functional forms usedhere are nonlinear so that the fitted priceof the sample mean is not equal to the meanof the fitted prices. Third, by using the samplemeans of the reference year only, the price index,in a statistical sense, is not sufficient. That is,it does not make use of all available information.The Jevons index above avoids all threeproblems here and should be used for futurehedonic analysis.

As discussed in specification test for structuralchange, the results from the Chow and Wald testsindicate that structural change is rejected in slightlyless than half of the periods, we studied. Therefore,we also calculate the indices from the adjacent yearregressions. Table 12 reports the results. A timedummy is used in each regression to compute theprice index. In all the log models, the price indicesare simply the anti-log values of the time dummies.For the various Box–Cox models, however, theprice indices are functions of the time dummies,values of the characteristics and their estimatedcoefficients and &. Therefore, we can in principle

compute the three elementary price indices. But inlight of the above discussion, we report the Jevonsindices only. In Table 12, we see that the resultingindices from different models agree with each othermore than those from the yearly regressions.The pooled regressions force the slope coefficientsto be the same in the adjacent years andhence do not suffer the out of sample predictionproblem discussed above. Therefore, when produ-cing a monthly or quarterly price index of ISPfor the CPI, where structural change is unlikelyto happen, pooled adjacent period regressionsshould be used. The average annual percentagechange ranges from (11.2% for the translog andRQBC models to (13.2% from the BCT model. Inthe yearly regression, the Jevons index drops morewith average annual change, from (13.0% to(15.2% (Table 8).

Jevons indices computed from yearly regressionsusing the spline function for HOUR are shown inTable 13. These indices follow the similar trendsas those of the Jevons indices hedonic indices usinghourly prices. The average annual changes for thesemilog, log-linear and Box–Cox models are (14.2,(16.7 and (15.4%, compared with (14.7, (14.8and (15.2%, respectively, for the hourly prices.Therefore, it seems that the resulting indices arerobust with respect to the two different approaches.Figure 1 also plots the log-linear model index fromthe spline method.

The hedonic index vs. the cost-of-living index

In view of the discussions in Section III, thehedonic price index can be interpreted as a cost-of-living index. There are, however, two qualifica-tions of such an interpretation. First, in the theoryof the cost-of-living index, the preference structureof the consumer is assumed to be the samein the base period and comparison period. Butthe frequent structural changes, we observe hereimply that consumer tastes are not constant. This isnot an unreasonable result, given that technologyin this sector is rapidly changing and there havebeen high increases in the growth of Internetusers every year. Second, the hedonic analysisdoes not capture the increased utility fromnetwork effects. The increasing populationof Internet users induces the creation of morecontent on the world wide web and popularizesthe use of electronic mail as an importantmeans of communication. These extra benefitsof Internet use are the result of positiveexternalities but are not reflected in the priceindices that we constructed.

Table 10. Regression results from the log-linear model forthe years 1995 and 1999

1995 1999

VariableEstimatedcoefficient

t-statistic293 DF

Estimatedcoefficient

t-statistic546 DF

MONTH (0.149 (4.69 (0.115 (6.62BHOUR 0.568 9.05 0.421 7.38HOUR (0.661 (25.20 (0.716 (62.11SPEED (0.349 (3.38 0.039 0.51EMAIL 1.043 7.76 (0.018 (0.47WEB (0.076 (2.45 (0.025 (1.39SETUP (0.012 (0.76 0.012 1.27ROAM (0.040 -0.38 0.097 2.37DEDIC 1.474 8.36 (0.082 (0.25TECH (0.104 (0.71 0.051 1.17FNBH (0.121 (1.25 0.323 3.95BULK (1.389 (5.07 (0.755 (2.63Constant 2.624 6.96 1.683 5.43



Tab

le11

.Laspeyres

andpa

asche–type

hedo

nicpriceindices

Model

1993

1994

1995

1996

1997

1998

1999

2000

AAI

Laspeyres-typeIndices

Sem

ilog

1.00

00.68

8((

31.2%

)0.62

9((

8.7%

)0.37

8((

39.9%

)0.35

3((

6.5%

)0.32

6((

7.8%

)0.27

8((

14.7%

)0.26

6((

4.3%

)0.82

8((

17.2%

)Log-linear1.00

00.84

4((

15.6%

)0.74

0((

12.3%

)0.58

7((

20.8%

)0.56

4((

3.8%

)0.52

4((

7.1%

)0.43

5((

17.1%

)0.40

9((

5.9%

)0.88

0((

12.0%

)Box–

Cox

1.00

00.61

9((

38.1%

)0.58

8((

5.0%

)0.30

4((

48.2%

)0.28

8((

5.4%

)0.29

2(1.3%

)0.24

1((

17.4%

)0.25

4(5.3%

)0.82

2((

17.8%

)Translog

1.00

01.06

7(6.7%

)1.50

2(40.8%

)1.12

3((

25.3%

)1.07

9((

3.9%

)1.01

2((

6.2%

)0.84

6((

16.4%

)0.80

4((

4.9%

)0.96

9((

3.1%

)

Paa

sche-typeIndices

Sem

ilog

1.00

00.66

3((

33.7%

)0.20

2((

69.6%

)0.15

3((

24.3%

)0.14

8((

2.8%

)0.13

8((

7.1%

)0.14

4(4.3%

)0.14

2((

1.4%

)0.75

7((

24.3%

)Log-linear1.00

00.71

9((

28.1%

)0.47

2((

34.4%

)0.37

0((

21.6%

)0.34

9((

5.5%

)0.31

3((

10.6%

)0.27

8((

11.2%

)0.27

3((

1.8%

)0.83

1((

16.9%

)Box–

Cox

1.00

00.61

1((

38.9%

)0.38

9((

36.3%

)0.26

4( (

32.2%

)0.25

2((

4.4%

)0.26

0(3.0%

)0.24

5((

5.6%

)0.26

6(8.6%

)0.82

8((

17.2%

)Translog

1.00

00.89

3((

10.7%

)0.86

8((

2.9%

)0.68

0((

21.7%

)0.65

5((

3.6%

)0.59

6((

9.0%

)0.59

1((

0.9%

)0.51

9((

12.1%

)0.91

1((

8.9%

)



Tab

le12

.Hedon

icpriceindicesfrom

adjacent

year

regression

s

Model

1993

1994

1995

1996

1997

1998

1999

2000

AAI

Sem

ilog

1.00

00.67

1((

32.9%

)0.64

1((

4.6%

)0.46

7((

27.1%

)0.44

1((

5.6%

)0.40

6((

7.9%

)0.40

1((

1.3%

)0.38

6((

3.7%

)0.87

8((

12.7%

)Box–

Cox

1.00

00.67

7((

32.3%

)0.64

7((

4.4%

)0.47

2((

27.0%

)0.45

7((

3.2%

)0.42

1((

7.9%

)0.42

9(1.8%

)0.41

4((

3.5%

)0.88

6((

11.8%

)Log-linear

1.00

00.66

8((

33.2%

)0.64

5((

3.5%

)0.50

9((

21.1%

)0.48

5((

4.5%

)0.44

7((

8.0%

)0.39

4((

11.9%

)0.37

3((

5.3%

)0.87

5((

13.1%

)Ex.

Box–

Cox1.00

00.67

0((

33.0%

)0.64

6((

3.6%

)0.49

9((

22.8%

)0.47

9((

4.0%

)0.44

4((

7.1%

)0.40

6((

8.8%

)0.38

4((

5.4%

)0.87

9((

12.8%

)BCT

1.00

00.66

9((

33.1%

)0.64

4((

3.7%

)0.50

4((

21.8%

)0.48

1((

4.5%

)0.44

5((

7.6%

)0.39

4((

11.4%

)0.37

2((

5.6%

)0.87

5((

13.2%

)Translog

1.00

00.69

2((

30.8%

)0.71

1(2.7%

)0.54

9((

22.7%

)0.52

8((

3.9%

)0.49

2((

6.8%

)0.45

8((

6.8%

)0.43

6((

5.0%

)0.89

5((

11.2%

)RQBC

1.00

00.69

4( (

30.6%

)0.71

2(2.6%

)0.55

1((

22.7%

)0.52

9((

4.0%

)0.49

2((

6.8%

)0.46

0((

6.5%

)0.43

6((

5.2%

)0.89

5((

11.2%

)



Tab

le13

.Hedon

icindicesusingspline

function

s

Model

1993

1994

1995

1996

1997

1998

1999

2000

AAI

Sem

ilog

1.00

00.77

3((

22.69)

0.58

4((

24.5)

0.44

1((

24.5)

0.42

7((

3.3)

0.39

5((

7.5)

0.35

6((

9.9)

0.34

4((

3.4)

0.85

8((

14.2)

Log-linear

1.00

00.64

3((

35.7)

0.47

7((

25.8)

0.36

1((

24.4)

0.34

6((

4.2)

0.32

0((

7.4)

0.28

7((

10.2)

0.27

8((

3.3)

0.83

3((

16.7)

Box-Cox

1.00

00.70

9((

29.1)

0.52

3((

26.2)

0.42

5((

18.7)

0.40

3((

5.2)

0.37

6((

6.6)

0.32

5((

13.7)

0.31

1((

4.3)

0.84

6((

15.4)



VI. Recommendations and Conclusion

Based on the above findings, we recommend thefollowing actions for the treatment of Internetservices in the CPI:

. From the survey of household computer com-munication usage, the share of Internet servicesin total consumption has exceeded the recom-mended threshold of 0.1% in 1998. Therefore,this expenditure should be incorporated in theCPI soon.

. The hedonic method for the price index cansometimes be time consuming and expensive dueto the amount of information to be collected.The information for the Internet services, how-ever, is available on-line and relatively easyto get. Also, the list prices mostly represent thetransaction prices. We, therefore, recommendthe use of the hedonic method for constructingthe elementary price index.

. The observed prices listed on-line are not volatilein the medium term (month-to-month) com-pared to the prices of other commodities suchas grocery items or gasoline. We recommend thesurvey interval to be 3 to 6 months.

. A detailed set of instructions should be devel-oped regarding the procedure and methodologyof the whole process from sampling to comput-ing the price index. This will ensure consistencyand the reputation of the CPI and enhancepublic understanding of the indices.

. Specification tests for structural change shouldbe used to decide whether the regressions shouldbe pooled or separately conducted in eachperiod. Pooled regressions should be carriedout whenever possible.

. The log-linear, Box–Cox, translog and RQBCmodels give superior performance to the othermodels, we tested. Apart from the difficultyin testing for structural change, the Box–Coxmodel runs the risk of negative fitted prices,which would pose a problem for index computa-tion. The translog and RQBC have the bestgoodness-of-fit. In order to avoid the problemof multicollinearity, some second-order crossterms in these models are excluded in theregressions. The resulting index, however, canbe sensitive to the choice of the excluded crossterms. This can pose a quality control problemin the regular production of the price index. Thelog-linear model gives satisfactory results com-pared to the other three models. The simplicityof the computation procedure makes it anattractive choice in regular production.

. The Jevons index from yearly regressions of thelog-linear model shows that prices of Internetservice providers decreased from 1993 to2000 at an average rate of 14.8%. The corre-sponding indices from the adjacent year regres-sions and the matched model are 13.1 and 8.3%.Therefore, the matched model has an upwardbias on the average. Results using the splinefunction technique for the number of hoursin the packages are very close to the correspond-ing indices using hourly rates as the dependentvariable. The average annual decrease for thespline models is 15.9%.

. The Jevons index (geometric mean of price ratio)is the most stable index among the three mostcommonly used formulas and is, therefore,recommended. The Carli index is known tobe upward biased and Dutot index is foundto be unstable in our study. The Laspeyres-typeand Paasche-type indices commonly used inhedonic studies are sensitive to the selectedreference characteristics and are, therefore, notrecommended.

. Since the market is concentrated in a handful oflarge companies, it would be desirable to includemarket shares for weighting in the constructionof the index. But consideration must be given tothe fact that most other elementary price indicesare not weighted and market share informationis not always available. Also, to keep operatingcost to a reasonable level, it may be desirableto collect information from the large firms(say the top 10%) only. They represent overhalf of the market share in Internet services.

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