Use of hedonic regression methods for quality adjustments in

Statistics NZ

Bhaskaran P. Nair Inflation Measures Division, Statistics New Zealand

Aorangi House, Molesworth Street, Wellington Tel: 04 931 4061; Fax: 04 931 4915

Bhaskaran.Nair@stats.govt.nz Abstract Several national statistical agencies have, in recent years, adopted hedonic regression

techniques to adjust for quality change in price indexes. Statistics NZ currently uses hedonics

to adjust for quality change in the used cars, refrigerator and fridge/freezers indexes of the

Consumers Price Index (CPI). Progress has also been made towards implementing hedonic

quality adjustment for video cameras.

This paper gives an introduction to the basic principles underlying hedonics and outlines

results to date of using New Zealand data collected in a CPI price-collection framework to

produce hedonic regression-based quality adjusted price indexes.

Issues on regression specification and selection of suitable hedonic method and practical

problems associated with the implementation of the method for quality adjustment are also

discussed.

JEL Classification: C43, C51

1. Background A price index, such as the CPI, intends to measure the effects of price changes while keeping

other economic factors, like the physical attributes of the goods, constant. In real life, we

experience those goods and services as ever changing in their physical characteristics. The

non-price aspects of consumer goods and services are often referred to as ‘quality

characteristics’ and can change in various ways.

Changes that take place over time in a rapid phase pose a fundamental problem in

constructing a robust CPI that measures only the pure price change. Separating pure price

change and the quality change components from the total price change is a major challenge

for the CPI’s producer. Traditionally, several methods are available for quality adjustments.

These include overlap pricing, direct quality adjustment using information from producers, and

linking methods. But all these methods potentially suffer from subjective biases in selecting

newly appeared products that most closely resemble the old ones.

A more objective way of dealing with quality change than the traditional methods was

recommended by the Price Statistics Review Committee (US) way back in 1961. This

committee suggested that statistical agencies explore hedonic methods, referring to a paper

on major hedonic study by Zvi Griliches (1961). Waugh (1928) and Court (1939) first used this

method to explain the relationship between price and quality characteristics. Works by

Griliches (1961) and Chow (1967) received much attention in the potential use of hedonics,

further supported by Lancaster (1971) and Rosen (1974). Rosen (1974) established the

theoretical relationship of the hedonic function to utility and production functions. He assumed

that the characteristics of the goods rather than the goods themselves are the true

components of the utility function (true inputs to the production function). It is an implication of

the hedonic hypothesis that heterogeneous goods are an aggregation of characteristics.

Triplett and McDonald (1977) studied hedonic quality adjustments to replacement items in the

refrigerator price index. Diewert (2001) developed a consumer theory approach to hedonic

regression as a simplification of Rosen’s (1974) theory.

Several European countries, US and Japan have adopted hedonic regression methodology in

their CPI quality control, particularly in areas which proved to be difficult for quality control

using traditional methods. The result has been quite successful in some areas like housing,

electronic goods, computers, clothing and cars (Pakes, 2001; Bascher and Lacroix, 1999;

Liegey and Shepler, 1999; Shiratsuka, 1999; Fixler et al, 1999; Okamoto and Sato, 2001).

The traditional index method for controlling quality change is known as the “matched model”

method. Prices are collected for a sample of models of selected products existing in period t,

and then the prices of these same matched models are collected in subsequent periods. The

matched model method is designed to control for quality changes by ensuring that ‘like is

compared with like’. The problem with the matched model method arises when new models

appear or old models disappear; the methods traditionally used to link the samples containing

the old and new models may overstate or understate the true quality differences. The matched

model method fails in situations where the quality of the product changes rapidly due to

technological changes. The matched model method ignores the non-observable aspects of

the transaction that may have significant influence on the price. For example, brand

reputation, after sales service, customer service and warranty are some of the non-observable

aspects not addressed by this method.

Implementation of hedonic methods in Statistics NZ

Statistics New Zealand (Statistics NZ) places a very high priority on the control of quality

change when calculating price indexes. Different sources for potential bias have been

identified in CPIs and it appears to be an accepted fact that the potential bias due to changes

in the quality of goods and services is the biggest challenge for price index compilers.

Although many other sources of potential bias exist, such as the index formula bias, outlet and

item selection bias and substitution bias, the quality adjustment process needs very much

attention.

Implementation of hedonic methods is now an integral part of the quality adjustment program

for CPIs. Statistics NZ has been conducting research into extending the use of hedonic

regression models for quality adjustment purposes to consumer items within the CPI. Hedonic

models estimate values for individual characteristics bundled together to form a good or

service. This allows the CPI to calculate the value of quality change between two items. The

CPI commodity analyst will use the parameter estimates obtained from the hedonic model to

adjust the price change used in index calculations in instances where the new item and old

item differ in quality. Household appliance and consumer electronics manufacturers are

constantly improving the quality of products in an effort to remain competitive. Quality change

often occurs at the time manufacturers introduce new models to replace previous models.

Currently the hedonic regression method is accepted as an alternative quality adjustment

method and has been implemented for used cars, refrigerators and fridge/ freezesr. Progress

has also been made towards implementation for video cameras.

In the September 2001 quarter, hedonic methods were introduced for the used car index

computation. The index is based on a regression approach estimated from a sample of used

cars sold in each quarter. The composition of the sample changes from quarter to quarter.

The regression coefficients are estimated from sample data obtained in the latest eight

quarters using five characteristics of used cars, and the most recent movement is linked to the

last published index number. The implementation of the hedonic price index has improved the

quality of the used cars index and is an improvement over the previously used ‘estimation cell

method’. The ‘estimation cell method’ had the limitations of being susceptible to quality shifts

and to the non-use of much of the data collected each quarter, since only common cells were

used in the calculation.

Subsequently in the September 2002 quarter, the hedonic regression approach was

developed and applied to refrigerators and fridge/ freezers. More research is being

undertaken into extending the use of hedonic regression methods for quality adjustment

purposes among consumer appliances and electronic items. An implementation process is

underway for video cameras. The methodology and data structures of each of these items are

discussed in section 2. Three methods of hedonic price index namely time dummy variable index, characteristics price index and hedonic double price imputation price index have

been studied on used cars, refrigerators, fridge/freezers and video cameras. The results are

discussed in the following section.

2. Methodology, Results and Discussion

2.1 What is a hedonic price index? A hedonic price index is a price index that makes use of a hedonic function. A hedonic

function is a relationship between the prices of different attributes of a product, such as the

attributes of various models of personal computers, and the quantities of characteristics in

them. The basic idea of a hedonic price index stems from the fact that there is an identifiable

relationship between prices and characteristics of heterogeneous products. The hedonic price

index is more appropriate for products which undergo rapid technological changes.

The hedonic function may be used in a number of ways to produce quality-adjusted price

indexes. The regression coefficients linked to the product attributes assign monetary value to

them which are also known as implicit prices or characteristics prices. These implicit prices

are used to construct quality adjusted hedonic price indexes.

2.2 Example of a hedonic function handling quality adjustment Assume that the price of a video camera model (call it ‘m’, and has a zoom rate ‘x’) is not

collected due to some reason in period ‘t’ , though this model was available in outlets. Under

the condition that the video camera was available, its price can be estimated in period t using

the hedonic function.

Similarly consider a scenario where a new model has appeared in the market (call it model ‘n’

with zoom rate ‘y’) and is treated as a replacement for model ‘m’. Assuming that the

introduction of a new video camera model does not change the price regime for video

cameras, the mean price of the new model in period t-1 could be estimated using the same

hedonic function. The difference in their quality characteristics is accounted for by computing

the estimated price of model ‘n’ in period t. Both the replaced and replacement models would

be included in computing the hedonic function.

2.3 Hedonic regression model specification

2.3.1 Time dummy variable index method

The hedonic method is basically a regression technique used to estimate the prices of

qualities or models. A time dummy hedonic regression model is specified with the

characteristics as independent variables and the natural log of the collected price as the

dependent variable. The regression model varies depending upon the hedonic method being

used. Model specification for the time dummy method look like this:

ln(pit ) = α t +∑ β=

k

i 1ik zik + δtDt + εitk (1)

For k set of observation and time period t and not all good appearing in all periods. pit is price of ith model in tth quarter expressed in natural logarithmic scale

α is the constant term

βk is the regression coefficient or implicit hedonic price

zitk is the value of the characteristics

δt is the regression coefficient for time dummy

Dt is the time dummy variable with a value of 1 in period t and 0 otherwise

εit error term

The quality-adjusted price index can be calculated directly by taking the exponential of the

time-dummy coefficients of interest after estimating the regression coefficients. In other words,

Index = exp (δt), where δt is the regression coefficient of the time dummy when the hedonic

functional form is semi-log. The justification for this is straightforward. If we compare the

relative price of a good, between say period t and period t-1, for any given quality

specification, say represented by z , then this ratio is equal to the relative exponential of the

time dummy variables (Melser, 2004). This is the simplest and most common approach. Many

statistical agencies world-wide use this method to calculate price indexes.

Whenever an item replacement takes place between the base and reference periods, quality

change potentially occurs. The change in quality due to item replacement is taken care of by

the associated characteristics, and the pure price change will be captured by the regression

coefficient of the time dummy variable. The time dummy hedonic index is not equal to the

matched model index as long as item replacement occurs. If no item replacements occur then

these two methods are expected to show the same index value (Triplett, 2001). The

disadvantage of the time dummy variable index is that it is sensitive to specification bias and

multi-collinearity. Multi-collinearity arises when the independent variables are correlated,

violating one of the basic assumptions of the multiple regression concept.

2.3.2 Characteristics price index method

An alternative approach for a comparison between period ‘t-1’ and ‘t’ is to estimate a hedonic

regression for period ‘t’, and insert the values of the characteristics of each item existing in

period ‘t-1’ into the period t regression to predict, for each item, its price. This would generate

predictions of the price of items existing in period ‘t-1’, at period ‘t’ shadow or implicit prices.

These prices (or an average) can be compared with (the average of) the actual prices of

models in period ‘t-1’. Similarly another set of implicit prices could be generated by inserting

the characteristics values of period ‘t’ into the period ‘t-1’ regression coefficients. These prices

are then compared with the actual prices of items in period ‘t’. The geometric mean of these

two indexes gives us the desired characteristics price index and a chain linked index is

developed from this.

ln(pit ) = β0t + β∑=

k

i 1it xit + εit (2)

xit = variable for characteristics i and β0 , βi are the partial regression coefficients.

Substituting average specification xit in the period t for variables itX in (2) we have

ln( p it ) = β0t + β∑=

k

i 1it X it + εit and ln( p it+1 ) = β0t + β∑

=

k

i 1it+1 X it + εit.

Chained hedonic index average specification in period t = ∏ ( p it+1 / p it) (3)

Where p it is the average unit price of an individual model in the period t.

Substituting average specification X it+1 in the period t+1 for variables itX in (2) we have

ln(p’it ) = β0t + β∑=

k

i 1it X it+1 + εit and ln(p’ it+1 ) = β0t + β∑

=

k

i 1it+1 X it+1 + εit.

Chained hedonic index average specification in period t = ∏ (p’it+1 / p’ it) (4)

And the chained hedonic index is the geometric mean of (3) and (4).

Geometric mean of (3) and (4) = √ ∏ ( p it+1 / p it )* ∏ (p’it+1 / p’ it).

In other words, this is nothing but the valuation of the typical base period (t-1) commodity by

the current period’s implicit prices, obtained from the current period’s hedonic function, and

compared with the same valuation for the base period. This is analogous to the Laspeyres

type price index. Similarly the alternative index is the comparison of typical current period’s

price with the hedonic function of the base period. The geometric mean of these two indexes

would give the desired characteristics price index (Okamoto and Sato, 2001; Triplett, 2001).

2.3.3 The Hedonic double imputation price index method

Sometimes the statistical agencies may be reluctant to change calculation methods for those models where the traditional approach is quite adequate. It is thus natural to use traditional matched model approaches to make price comparisons for the unchanged models, and to focus attention on devising an imputation for the missing item prices or a quality adjustment for the differences between item m and n. The hedonic double imputation method permits exactly that (Haan, 2003). Where matched model comparisons are possible, they are used. Where they are not possible, a hedonic time dummy index is computed and the geometric mean of these two indexes using expenditure shares as weights provide us with the hedonic double imputation price index. The methodology is similar to the matched model price index when a perfect match exists between periods. When there is a complete mismatch this method coincides with the time dummy index. The only difference between the characteristics price index and the hedonic double price

imputation method is that in the former we use the implicit prices to compute the price

relatives and in the latter method we use the actual price relatives whenever they are

available and merge them with the time dummy method. The time dummy price index for the

unmatched prices is computed using the regression expression:

Est. pit = exp (β0t +∑=

k

i 1βit xit +αt Dt + εit).

Where xit is the ith characteristics of vth model in period t and αt is the partial regression

coefficient associated with the time dummy Dt.

The hedonic double imputation index is obtained from the geometric mean formula computed

from the expression:

[Pm] q. [exp (α)] 1-q

Where Pm is the matched model index component, α is the regression coefficient associated

with the time period in the model, ‘q’ is the expenditure share of matched products, and exp

(α) is the time dummy index for the mismatched products.

2.3.4. The matched model index If a good with the listed characteristics is found when the price collector revisits the outlet in

the reference period, the price of that good is recorded, and the ratio of the second period to

the first period becomes the price relative for the good. If no good with the listed

characteristics is found in the reference period, that good is dropped from the list of goods

used to form the index for that commodity group. These price relatives are averaged (either

arithmetic average or geometric average) to obtain the index for the particular commodity

group. However, the conventional method practised in Statistics NZ for quality adjustments of

item replacement namely ‘Overlap method’, ‘Link method’, ‘Class mean imputation’ and ‘Direct

adjustments’ are adopted depending upon the situation to compute the price index. The

problem with the matched model method arises when new models appear or old models

disappear; the methods traditionally used to link the samples containing the old and new

models may overstate or understate the true quality differences (Moulten, 2001).

3. The data structure Our aim is to produce a reliable CPI as efficiently as possible. For this the basic data has to be

of good quality. The significant problem in the CPI price collection and a source of potential

bias is the uncontrolled quality change occurring with each replacement. The potential bias

due to quality changes can be reduced by applying different quality adjustment methods for

different items and item groups. Hedonic regression is offered as one alternative but it

requires a lot of data.

3.1 Refrigerators Refrigerators are included in the CPI section ‘household appliances and equipment’ along

with other appliances like TVs, video cassette recorders, washing machines, clothes dryers,

microwaves, video cameras etc. Refrigerators have about one fifth of the weight given to

major household appliances and equipment. The underlying assumption is that fridge or

fridge/freezers buyers are looking for qualities such as capacity, durability, economy,

convenience, maneuverability, style, performance, energy efficiency and safety, and that the

value placed on these attributes is reflected in the price of the refrigerators.

The existing refrigerator sample data used in the hedonic model were collected in a

conventional framework of CPI calculation, covering 19 quarters beginning from June 99. The

primary sample data (price, model, brand and capacity) consisted of about 60 observations

each quarter collected through field survey from 15 regions. The quarterly data extends from

June 1999 to December 2003 for two commodities refrigerators and fridge/freezers.

Observations were collected for the two commodity categories: refrigerators and

fridge/freezers involving 370L capacity single door and 380L capacity double door models

respectively drawn from seven major brands of refrigerators marketed in New Zealand.

Though there are different colours of refrigerators (white, almond, beige and complete

stainless steel body), data on only standard white colour refrigerators are collected. The

characteristics included in the model are price, region, outlet, quarter, brand, volume (total

volume, refrigerator volume and freezer volume), type (number of doors), energy use

efficiency. Also included are qualitative features like butter conditioners, humidity drawers,

rollers and feet, electronic control, no-frost, automatic cyclic defrost, manual defrosting in

freezers, 3-temperature control, 1-temperature control. Wherever possible secondary sources

of information such as manufacturer web sites, consumer information magazines and product

brochures were used to verify the accuracy of the characteristics data collected on

refrigerators.

The variables involved in the Multi-collinearity were measured by VIF (variance inflation

factor), Eigenvalue and condition index. Variance inflation factor (VIF), tolerance (VIF-1) and

condition index measure the degree of Multi-collinearity in the model. In an ideal situation VIF

and condition index should be closer to 1. A condition index of around 30 indicates a great

deal of collinearity, enough to warrant corrective measures. For example it is observed that

some manufacturers make refrigerators that are then sold under different brand names,

leading to collinearity problems.

3.2 Video cameras Video cameras are included in the television and video equipment subsection under the

household appliances and Equipment section of the CPI along with video cassette recorders

(VCRs), DVD players and colour TV sets. Video cameras have about one twentieth of the

weight within Television and Video Equipment. The primary sample data (price, model, brand

and basic specification) consisted of about 60 observations in each quarter collected through

field survey from 15 regions in 19 quarterly periods starting from the June 1999 quarter.

Observations were collected for video camera models drawn from five major brands of video

camera marketed in New Zealand.

There are basically two kinds of video cameras viz., Analogue and Digital. Typically digital video cameras are more expensive than analogue models. Most of the video cameras available today in the New Zealand market are digital. The most important characteristics in the consumer’s mind are style, performance and versatility. The characteristics included in the model are price, region, outlet, quarter, brand, tape format, charged couple device (CCD), System (Analogue or Digital), LC Display screen, Zoom optical, Zoom digital, Built in light, Image stabiliser mode, Sound and dimension. Whenever possible secondary sources of information such as manufacturer web sites, consumer information magazines and product brochures were used to verify the accuracy of the characteristics data collected on video cameras. Video cameras are among the most expensive major household electronic high tech

appliance, both in terms of purchase price and operating cost. The list of characteristics

identified for video cameras are:

Storage Tape Format - VHS, VHS-C, SVHS-C, 8mm, Hi8, Digital, Digital8, Mini DV View finder - Black and White, Colour view finder, LCD electronic view finder Zoom quality - Optical, Digital Power Source - Batteries, AC adapter, Car adapter. Light - Standard, Built-in, External connectivity Image stabilizer - Electronic, Digital, Optical CCD - Charge coupled device- one CCD chip, three CCD chips. Exposure mode - Automatic, semi-manual, manual. Microphones - Built-in, External connectivity. Sound Type - Stereo, Mono Camera Control - Automatic, Manual. Low Light capacity - Given in Lux rating. Editing features - Digital special f/x recording, digital fades and wipes, 16x9 recording,

video dubbing, audio dubbing and Random assemble editing. Video camera size - Box size, Hand size and pocket size. Still image capability - Mostly found in Digital video cameras.

3.3 Used cars Used cars are included in the purchase of vehicles section under the private transport

subgroup of the CPI and constitute about 70% of weight within the section. The reason for

adopting hedonic methods in used cars is different from the reasons identified for refrigerators

and video cameras. The previous method of index computation did not utilise all the price

information collected (about 3,500 prices each quarter) and we sought a robust quality

adjustment method, given the importance of used cars in the CPI. It is also relatively volatile

and when combined with its high expenditure weight, this makes it an important contributor to

the CPI. Approximately 300 used car dealers are asked to provide data on all cars, up to 10

years old, sold to private buyers in the middle month of each quarter. For each car sold, they

are asked for the price (inc GST), year of manufacture, make and model, cc rating, odometer

reading (km) and whether or not the car is a Japanese import, a station wagon or automatic.

In this way we collect data for approximately 3,500 used cars.

The current hedonic method for used cars is modelled as a function of: Age of car,

This is derived from year of manufacture and quarter of collection, and expressed in

years and quarters - eg a car manufactured in 1998 and purchased in the March

quarter of 2000 would be given an age of 2.25 years.

Dummy variable on 2-digit category,

This variable is assigned at the data-capture stage based on the make and model of

the car, and the broad cc rating range – e.g. a Ford Laser with cc rating between 0801

and 1350 would be given a 2-digit category of 01, while a Ford Laser with cc rating

between 1351 and 1600 would be given a 2-digit category of 02. The base 2-digit

category is cat01.

Dummy variables for collection period:

This is the quarter that the car was purchased in and therefore the quarter that the

data was collected.

cc rating - Odometer reading -

Dummy variables for town of purchase: The base town is t27 (Invercargill).

Dummy variables are used for categorical variables. E.g. - a car purchased in quarter 2 of

1998 will have values of 0 for every collection period variable except that period, which will

have a value of 1. The parameter of the base category is set to 0 and the other parameter

estimates for the categorical variable are scaled to this. Setting another category as the

base (i.e. town 04 instead of town 27) would give equivalent results, and the calculated

index would be unaffected.

3.3.1 Calculation of the hedonic regression parameter method index Each quarter, the index is re-calculated right back to the previous eight quarters, and the most

recent movement is linked to the last published index number. If the calculation of the full

index was quite variable across time, this splicing would cause discontinuities, but

investigation has shown that any discontinuities are likely to be insignificant. In each quarter,

the index is calculated as follows:

Index number = modelled price for period x / modelled price for the base period * 1000. Where the modelled price for period x = age parameter*median age + cc rating parameter*median cc rating + odometer parameter*median odometer + 'average' 2-digit category parameter + 'average' town parameter + parameter for collection period x. The parameters for ‘age’, ‘cc rating’, ‘odometer reading’ and collection periods are straight

from the regression output (from the regression model run on latest eight quarters dataset).

The medians for age, odometer reading and cc rating are calculated from the full dataset.

'Average parameters' are derived for 2-digit category and town by calculating the distribution

of 2-digit category and town across the full dataset and using these distributions to derive

weighted averages of the parameters for 2-digit category and town. Based on hedonic

regression calculated at standardised quality point a weighted Laspeyres index is constructed

using quarterly chaining.

The hedonic regression method adopted here is slightly different from the hedonic methods

that are in vogue. Unlike refrigerators or video cameras the used car samples in the

subsequent quarters are collected afresh without making any efforts to replace the price of the

models selected in the previous period. We have tried the time dummy, characteristics price

index and hedonic double imputation price index on the used car data and the results are

discussed in the following section.

4. Results and Discussion All the three hedonic based index methods namely, time dummy variable index, characteristics price index and double imputation price index use all of the data available in each period. If there is a new model observed in the new period it is included in the data set and its quality difference is controlled by the regression. Similarly the disappearing models are still included in the indexes for the period in which they existed. With the time dummy variable there is no explicit weighting associated and this is a serious disadvantage. Similarly there is no explicit weighting associated with the characteristics price index. However, the double imputation price index uses the expenditure share as the weights. In our present study we have used the observation counts as the weights in the absence of expenditure share information. The adjusted R-square obtained from pooled regression is presented in Appendix-I (Table 1).

The adjusted R-square value is significant for each product and this indicates the goodness of

fit of the regression models. The adjusted R-square obtained from single period regression for

each product is presented in Table 2. The result throws some light on the behaviour of data

and the instability of the regression coefficients when single period data are used in cases like

refrigerators and fridge/freezers. It may also be noted that the R-square values are more

consistent with used cars, where the sample size is very large compared to the other items.

Though the sample size for video cameras is small (Table 6) the adjusted R-squares were

more consistent and robust than refrigerators or fridge/freezers.

Refrigerators and fridge freezers showed volatile price movements in some quarters in spite of

the fact that the level of substitution (Table 4 and Table 5) is very small compared to either

video cameras (Table 3) or used cars (Table 6). Some qualitative characteristics that have

high correlation with the price were removed to reduce collinearity. The attributes that are left

in the regression models may not be showing strong correlation with the price. These factors

might have contributed to the volatile adjusted R-square. The result indicated that the hedonic

price index based on single period regression namely the characteristics price index may not

be a good method for items like refrigerators and fridge/freezers.

As the double imputation index is the geometric mean of matched model and time dummy

index, the contribution from the mismatch part of the data is rather minimal and hence is

actually representing a matched model index rather than a hedonic based index. Unlike other

electronic equipment such as computers, there are no rapid changes in the refrigerators and

fridge/freezers models and obsolescence is seldom a factor. The result indicated that the

double imputation price index also is not suitable for refrigerators and fridge/freezers under

the present condition. However, this method may be suitable for video cameras due to its high

level of substitution provided large sample size data are available.

When there is no systematic price effect of disappearing products, the time dummy index and

double imputation price index should be closer to a matched model geometric mean index

provided the parameters are constant. The double imputation price index would be more

appropriate for situations where the substitution frequency is substantial and the market share

of each model entered into the regression is available every quarter.

It may be very difficult to answer the question ‘which method is more appropriate for a given

commodity’, keeping in view of the complexity of the commodity and the data availability. The

time dummy variable method is simpler and utilises all the information available in the data

set. Its price indexes are derived on the basis of pooled regression models. The

characteristics price index method is more sensitive to item replacement and hence brings

forth the quality differences more accurately than the time dummy method. The characteristics

price index method could have been a better option if the number of observations per quarter

was substantial.

The time dummy variable approach assumes that all parameters are time independent but in reality they are not. In a long run the model might pose problems when new products with new features enter the market. The advantage of using the hedonic price index instead of the matched model index is the expected gain in efficiency. For the double imputation price index method, matched models are treated in a conventional manner and unmatched models are quality adjusted using the hedonic approach. Here the prices of newly introduced models are matched synthetically to the prices of the replaced models through hedonic quality adjustment. This index is a hybrid of the geometric mean index for the matched models and the synthetically matched model index. Concerns about index number formulas apply only to hedonic indexes estimated directly from the regression by the dummy variable method. Moreover, Hedonic double imputation indexes can account for systematic price effects of unmatched models whereas the time dummy cannot. This index is makes sense in respect of video cameras where the proportion of mismatched items is substantial.

5. Advantage and disadvantages of hedonic methods

Our aim is to produce a reliable CPI as efficiently as possible. For this the basic data has to be

of good quality. The biggest problem in the CPI price collection and biggest source of potential

bias is the uncontrolled quality change occurring with each replacement. The potential bias

due to quality changes can be reduced by applying different quality adjustment methods for

different items and item groups. Hedonic regression is offered as one alternative but it

requires a lot of data.

While the hedonic methods take into consideration the quality characteristics and other non-

observable aspects while deriving the price index, which is not possible using conventional

matched model methods.

The strong interrelationship among independent variables (multi-collinearity) makes the

regression coefficients unstable with large variance resulting in non-significant parameter

estimation. Multi-collinearity is problematic when one’s purpose is explanation rather than

mere prediction.

Several national statistical agencies have, in recent years, conservatively adopted hedonic

regression techniques to adjust for quality change in price indexes. The hedonic approach has

not gained popularity among the prices statistician due to the following pragmatic

considerations.

• The type of the regression function (choice of the functional form). • To decide which and how many "characteristics" to take in order to capture enough

aspects of quality (or aspects in which the selected varieties differ) on the one hand and to avoid Multi-collinearity on the other.

• The detection of the appropriate source of data. • The constancy of regression coefficients over time, not allowing for changes in. • The marginal utility assigned to the selected "characteristics”. • Cost-benefit considerations and some practicalities on implementing the hedonic

approach. • Implications for sample design and data collection strategy. • Selection of techniques. • Requires high level of technical expertise in addition to good product knowledge. • Access to detailed, reliable information on product characteristics.

• Assigns equal weights to all the participating models. • Suitable organisation for collecting, checking and processing information.

6. Conclusion

This paper presents the preliminary results of employing the hedonic method as a quality

adjustment technique for four commodities namely used cars, refrigerators, fridge/freezers

and video cameras in Statistics New Zealand’s CPI. The results obtained from this study

showed that the hedonic method is desirable as a quality adjustment technique for these

consumer goods.

Basic concepts of constructing the three methods of hedonic price indexes namely, time

dummy price index, characteristics price index and hedonic double imputation price index are

described in this paper. These methods have been studied on the four consumer goods listed

above and the results compared with the traditional method. The result suggests several

interesting empirical issues worthy of further investigation.

The Time dummy regression uses data from both past and current periods but their properties

are likely to be different if the period included is too long. The time dummy variable index

computes the index directly from the regression equation. In particular if there are trends in

the values of characteristics (which are obvious in high tech products) the index constructed

from the past and current data would be less precise in the range of products currently being

evaluated. If new characteristics appear we would expect this index to be biased towards past

evaluations of those characteristics. One might expect to use a single set of coefficients which

are in fact changing over time. What the time dummy variable index is doing is to smooth out

the differences over years. The coefficients are lower than the characteristics price index and

the double imputation price index. There is an additional problem of using data whose central

tendencies are those of a year in the distant past and not of a year which is in the middle of

the sample.

It may be concluded that among the three hedonic methods, the time dummy variable method

is simpler and easier, utilises all the information available in the data set, and its price indexes

are derived on the basis of pooled regression models. In contrast, the characteristics price

index method utilises the information available for a specific quarter to fit into a regression

model. This method becomes less precise when the numbers of observations are very few,

but is more sensitive to item replacement and hence brings forth the quality differences more

accurately than the time dummy method. The characteristics price index method would be a

better option if the numbers of observations per quarter were substantial and the same sets of

characteristics descriptors are entered in the analysis.

Hedonic double price imputation is a hybrid between the matched model and the time dummy

index. This method utilises the matched model information wherever possible. Hedonic double

imputation indexes can account for systematic price effects of unmatched models whereas the

time dummy cannot. This index makes sense in respect of video cameras where the

proportion of mismatched items is substantial.

Further investigation should focus on issues such as the behaviour of the regression

coefficients in the dynamic market context, quality attributes that are not included in this study

due to Multi-collinearity, and the functional form of the model. In addition to these issues focus

should be on the effect of matched and mismatched sample size on the index development.

___________________________________________________________________

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REFERENCES

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Court, Andrew. (1939), “Hedonic Price Indexes with Automotive Examples”, in The Dynamics of Automobile Demand, pp.99-117, General Motors Corporation.

Fixler, D., Fortuna, C., Greenlees, J and Wlater, L . (1999), “The Use of Hedonic Regressions to Handle Quality Change: The Experience in the US CPI”, paper presented at the Fifth Meeting of the International Working group of Price Indexes, Reykjavik, Iceland, August 1999.

Diewert W.E. (2001), “Hedonic Regressions: A Consumer Theory Approach”, Discussion Paper, Department of Economics, University of British Columbia.

Griliches, Z. (1961). “Hedonic Price Indexes for Automobiles: An econometric Analysis of Quality Change”, in The Price Statistics of federal Government, New York, the National Bureau of Economic Research.

Griliches, Z. (1971). Price Indexes and Quality Change, Studies in new method of measurement, Cambridge: Harvard University Press.

Haan, J. de (2003). “Time Dummy Approaches to Hedonic Price Measurement”, paper presented at the seventh meeting of the International Working Group on Price Indexes (Ottawa Group), Paris, 27-29, 2003.

Lancaster, K. (1971). “Consumer Demand: A New Approach”. Columbia University Press, New York.

Liegey, P.R. and Nichole Shepler. (1999), “Adjusting VCR Prices for Quality Change:A Study Using Hedonic Method”, Monthly Labor Review.

Moulten, B.R. (2001), “The Expanding Role of Hedonic Methods in the Official Statistics ot the United States”, Bureau of Economic Analysis, US Department of Commerce, Washington.

Okamoto, M and Tomohiko Sato. (2001), “Comparison of Hedonoc Method and Matched Models Methods using Scanner Data: The Case of PCs, TVs and Digital Cameras”, Paper presented at the Sixth Meeting of the International Working Group on Price Indexes, Canberra, Australia, 2-6 April 2001.

Pakes, A. (2001), “A Reconsideration of Hedonic Price Indexes with an Application to PC’s”, NBER working paper 8715, Cambridge MA.

Rosen, S. (1974), “Hedonic Prices and Implicit markets: Product Differentiation and Pure Competition”, Journal of Political Economy, 82, 34-49.

Triplett, J.E., and R.J. McDonald (1977), “Assessing the Quality Error in Output Measures: The Case of Refrigerators”, The Review of Income and Wealth 23:2, 137-156.

Triplett, J.E. (2001), “Handbook of Quality Adjustment of Price Indexes for Information and Communication Technology Products” (draft), OECD, Paris.

Waugh, Frederick, V. (1928), “Quality Factors Influencing Vegetable Prices”, Journal of Farm Economics, 10:2,185-196.

APPENDIX-1

Table 1: Adjusted R square for pooled regression

Product Adjusted R-square Used cars 0.75

Refrigerators 0.71 Fridge / freezers 0.67 Video cameras 0.75

Table 2: Adjusted R square for used cars, refrigerators,

Fridge freezers and video cameras

Quarter Used Car Refrigerator Fridge/freezers

Video cameras

Mar-02 0.73 0.34 0.37 0.79 Jun-02 0.75 0.43 0.50 0.92 Sep-02 0.72 0.59 0.77 0.81 Dec-02 0.74 0.18 0.26 0.72 Mar-03 0.76 0.48 0.68 0.69 Jun-03 0.76 0.56 0.69 0.69 Sep-03 0.78 0.48 0.59 0.86 Dec-03 0.75 0.45 0.63 0.82

Table 3: Substitution levels in used cars

Quarter Sample size Substitution

frequency Jun-02 3,879 2,976 Sep-02 3,866 2,773 Dec-02 3,704 2,645 Mar-03 3,378 2,541 Jun-03 3,675 3,029 Sep-03 4,011 3,213 Dec-03 4,170 2,978

Table 4: Item substitution frequency in refrigerators

Quarter Sample size Substitution

frequency Jun-02 64 5 Sep-02 64 7 Dec-02 64 0 Mar-03 64 1 Jun-03 64 1 Sep-03 64 1 Dec-03 64 1

Table 5: Item substitution frequency in fridge/freezers

Quarter Sample size Substitution

frequency Jun-02 64 2 Sep-02 64 2 Dec-02 64 1 Mar-03 64 5 Jun-03 64 3 Sep-03 64 2 Dec-03 64 0

Table 6: Item substitution frequency in video cameras

Quarter Sample size Substitution

frequency Jun-02 59 19 Sep-02 59 30 Dec-02 59 15 Mar-03 59 15 Jun-03 60 39 Sep-03 59 15 Dec-03 60 8