Mô hình Hedonic PC ứng dung trong đinh giá

Dr Stefan Linz (Diplom-Volkswirt) and Gudrun Eckert (Diplom-Kauffrau) Introducing hedonic methods in price statistics Hedonic methods have come to play a growing role in measuring price trends and economic growth in recent years Germany’s Federal Statistical Office has formulated a step-by-step plan for a detailed examination of the effects and practicability of applying hedonic methods This essay describes the Federal Statistical Office’s efforts to introduce hedonic methods into price statistics Apart from outlining framework conditions and plans for the future, it focuses in particular on the hedonic price index for personal computers implemented in June 2002 as part of the overall consumer price index The story so far When calculating price indexes, central importance is attached to how quality changes to observed goods can be taken into account The objective of official price statistics is to measure what we call “pure” price changes, i.e price movements purged of the adulterating influence of quality change Hedonic methods, as they are now known, are special techniques for quality adjustment that have recently been incorporated into official German price statistics They particularly lend themselves to technological goods which are subject to rapid progress and cannot be observed over a long period with the quality remaining unchanged For hedonic quality adjustment, a good is conceptually broken down into quality features and then the influence of these features on the price is determined using regression analysis In this way, those price changes that result only from qualitative changes to certain features can be mathematically separated from pure price changes and eliminated The United States has played a pioneering role in introducing hedonic methods into national price statistics, implementing a hedonic price index for computers in the mid-1980s Hedonic methods have since been applied to many more products in the USA, such as housing rent since 1987, clothing since 1991, multi-family homes since 1993, digital phone systems since 1997 and television sets since 19991 The German Federal Statistical Office also explored the subject at a very early stage In 1990 a study of the uses of the hedonic method concluded that this method was a promising alternative to conventional calculation methods, but that the difficulties of practical application should nevertheless not be overlooked2 At the time the costs and benefits of introducing hedonic techniques were compared and their use for official statistics was rejected Other European countries, with the exception of France, made similar decisions In France a hedonic producer price index was introduced for computer equipment in the early 1990s Further hedonic price indexes followed for clothing, household appliances and books In other European countries Cf MOULTON, Brent R., The Expanding Role of Hedonic Methods in the Official Statistics of the U.S., http://www.bea.doc.gov/bea/papers.htm (24.9.2002) Cf GNOSS, Dr Roland et al, Neue Ansätze zur Berechnung von Preisindizes, Empirische Analyse der sogenannten hedonic-Indizes zur Eliminierung der Qualitätskomponente bei der Berechnung von Preisindizes am Beispiel von Computern, no 13 in the series Ausgewählte Arbeitsunterlagen zur Bundesstatistik, Statistisches Bundesamt, Wiesbaden, 1990, p 43 (Sweden, Finland, Belgium and now Germany) hedonic indexes are so far only used for one or two products The hedonic method also plays an important part in measuring real gross domestic product For deflating purposes, nominal gross domestic product is recalculated into real figures using price indexes In principle this recalculation is carried out by dividing nominal values by the corresponding prices The lower the measured price trends are in a product category, the greater is the measured real growth in turnover in that sector Furthermore, price trends are lower when quality increases in a product category If, for example, a product’s directly observed prices remain more or less constant while its quality increases, then from an economic perspective this is a drop in prices and quality-adjusted price statistics will show declining prices Thus productivity gains make their mark on measuring real economic growth via quality adjustment The hedonic method is especially helpful in demonstrating these productivity gains adequately In certain cases, its use in price statistics can lead to increased measured price decline and therefore to greater increases in real gross domestic product than conventional quality adjustment techniques In this sense the isolated use of hedonic methods in individual countries adversely affects international comparability of economic growth figures The Ifo Institute expressed this as follows: "Hedonic techniques take quality changes into account to a greater extent than conventional adjustment methods, which leads to a more dynamic development of real investments and, insofar as domestic products are concerned, also raises real gross domestic product"3 However, the magnitude of these deviations is very difficult to measure It is impossible to make a general statement about whether reality is better expressed using hedonic methods or conventional ones These uncertainties leave plenty of room for speculation Doubts concerning international comparability of productivity figures – as they are regularly aired in the press – have lead to palpable uncertainty among data users Users of statistical data have increasingly questioned the reliability of official economic growth figures This limited international comparability is merely a common launchpad for contradictory and often simplistic arguments about the introduction of hedonic methods For example, hedonic price measurement is often mistakenly equated with the principle of quality adjustment itself, overlooking the fact that quality adjustments have been used throughout the history of price statistics Furthermore the word “hedonic” is often understood to mean more than it actually does: the hedonic technique does not differ from other forms of quality adjustment conceptually so much as technically For some goods, the results obtained by different techniques are not as different as is often claimed For other goods, especially those with very short life cycles and improved price/performance ratios in new product generations, the variation can be significant The Federal Statistical Office believes it has a responsibility to place this debate on a more rational footing, and has decided to test the practicability and impact of introducing hedonic methods in a comprehensive programme The hedonic method will be tried out on specific goods NIERHAUS, Wolfgang, Wirtschaftswachstum in den Volkswirtschaftlichen Gesamtrechnungen: Ein Vergleich Deutschland – USA, p 47, in: ifo Schnelldienst 3/2001, pp 41-51 (Original text in German) where the technique has proved useful in the experience of other countries and by scientific studies To lay foundations for the work to come, the Federal Statistical Office joined with the Deutsche Bundesbank to convene a symposium on the use of hedonic methods in June 2001 Based on the discussions that took place there, the following conclusion was reached: "The experiences deliberated in this high-calibre symposium demonstrate that the very personnel-intensive hedonic techniques can, under certain circumstances, provide important additional insights, especially about goods subject to erratic waves of innovation, e.g personal computers Hedonic price measurements provide an opportunity for broadening and improving the basis of statistical information However, this information gain in certain fields must be weighed up against the significantly greater effort required in data collection and processing and the burden on enterprises."4 In a next step the Zentrum für Europäische Wirtschaftsforschung (ZEW – Centre for European Economic Research) in Mannheim was commissioned to carry out a study on the uses and effects of applying hedonic methods to official price statistics The ZEW had already gained experience of the problems faced in the implementation of hedonic methods by participating in the work of the European Hedonic Centre The European Hedonic Centre, a project funded by Eurostat, examines opportunities for European nations to use shared data for calculating hedonic price indexes5 The ZEW’s study for the Federal Statistical Office calculated hedonic price indexes for personal computers and private motor vehicles and compared them to conventional indexes Another task under this remit was a global survey of the use of hedonic methods by statistical agencies The results of the study were discussed at an international conference organised by the ZEW in Mannheim in April 20026 In its final report in September 2002 the ZEW reached the following conclusion: "The use of hedonic methods for price adjustment is very promising Therefore it is not surprising that our survey showed many institutions intending to use hedonic indexes, and those that already intending to extend the practice to further goods In the future we expect a tendency towards using hedonic methods for certain product categories, such as PCs or private cars The selection of goods where quality adjustment would be improved by hedonic methods should be based on criteria such as the frequency of product change, the speed of technological progress, the extent of quality changes and especially their consumption significance."7 Commencing in January 2001 the Federal Statistical Office had already introduced an interim solution for calculating a consumer price index for PCs Instead of assembled computers, PC FEDERAL STATISTICAL OFFICE, Press release on 22 June 2001, (Original text in German) http://www.destatis.de/presse/deutsch/pm2001/p2210051.htm (24.9.2002) On the goals of the European Hedonic Centre see http://www.zew.de/en/forschung/projekte.php3?action=detail&nr=261 (24.9.2002), and on the initial findings see the progress report by KONIJN, Paul (Eurostat); MOCH, Dietmar (ZEW); DALÉN, Jörgen (statistics consultant), Searching for the European Hedonic Function for PCs, available under http://www.statistics.gov.uk/iaoslondon2002/contributed_papers/IP_Konijn.asp (24.9.2002) Conference scripts can be found on the following website under the "Programm" link: www.zew.de/de/veranstaltungen/details.php?LFDNR=63&mi=VER&si=ARC (24.9.2002) MOCH, Dietmar et al, Einsatzmöglichkeiten hedonischer Techniken in der amtlichen Verbraucherpreisstatistik, Endbericht für das Statistische Bundesamt, Mannheim, September 2002, p 110 (Original text in German) components were observed In this manner the problem of short product cycles for assembled computers was reduced The result was a shift towards the principle of hedonic quality adjustment Since June 2002 hedonic methods have been used for quality adjustment in the “personal computer” price index category The following project phases have been planned for the future: Project phase Scope Date of implementation Combination of hedonic methods and conventional quality adjustment for private cars sub-index 1/2003 Hedonic producer, import and export price indexes for data-processing equipment sub-indexes 4/2004 Hedonic price indexes for electrical household appliances and consumer electronics sub-indexes 10/2004 By the beginning of next year the intention is to combine conventional quality adjustment techniques with hedonic methods in the case of private cars Introducing hedonic producer, import and export price indexes for data-processing equipment is planned for the end of the first quarter of 2004 Finally, by the last quarter of 2004 hedonic methods are to be introduced for the categories “electrical household appliances” and “consumer electronics” The principle of hedonic quality adjustment 2.1 Quality adjustment techniques To elucidate the principle underlying the hedonic method, we must first address the basic problem of quality adjustment in price statistics Theoretically the price of an item at two separate times can only be usefully compared if the quality of the item remains constant As mentioned above, the objective of official price statistics is to measure “pure” price changes This is reflected in the basic Laspeyres principle of once defining a basket of goods and keeping it as constant as possible over a defined period of time8 This principle causes difficulties when products change frequently and certain goods in the basket are no longer available on the market in their initial form so that the prices of the original goods can no longer be observed In these cases official price statistics undertake quality adjustment This introduces the monetary value of an item’s quality change into price observation A typical example might be air conditioning for a car: if from a certain point in time air conditioning is included as a standard feature of the particular model – and thereby becomes part of the price – an attempt must be made to determine the monetary value of this additional feature A proportion of this value is then subtracted from the car’s selling price in order to permit comparison with the previous month, when air conditioning was not yet a standard feature Cf KUNZ, Dietrich, Ausgewählte methodische und praktische Probleme des zeitlichen Preisvergleichs, p 23, in: Allgemeines Statistisches Archiv; vol 55; no 1/1971, pp 23-38 The technique used in this example is called feature adjustment and is a widely used form of quality adjustment9 Another reliable quality adjustment technique is the overlapping link method (or simply overlap method), where the price of an alternative product is observed over time alongside the selected product This means that if the selected product changes the alternative can be included in the basket in its place However, this switch to an alternative item can only take place when both products are available in the market simultaneously at equilibrium prices Under these conditions it can be assumed that the observed difference in price between the old and the new product is due to a difference in quality This “monetary value of quality difference” can then be taken into account when splicing the old and new item Hedonic methods are quality adjustment techniques of a specific kind10 The central element of hedonic quality adjustment is regression analysis, which is used to determine a quantitative link between an item’s selling price and its quality features Following this, there is a choice between two different hedonic quality adjustment techniques, the “time dummy variable method” and the “imputation method” There are, in turn, several variations on both these procedures The following sections outline the variations tested by the Federal Statistical Office for the product category “personal computers” 2.2 Time dummy variable method In the time dummy variable method computer prices and quality features are summarised for two consecutive months and combined in regression analysis The procedure is demonstrated in Figure for the months of August and September Figure 1: Time dummy variable method August sample Prices and quality features September sample Regression August / September p = f(x1, x2 , t, ε) Prices and quality features In the regression equation the price p is explained by the computer’s quality features x1, x2 Quality features could be processing speed, hard disc storage capacity etc The time variable t differentiates August and September Finally, the random variable ε is used to indicate that not all influences on a computer’s price are measurable in reality For example, additional retailer services (home servicing, telephone hotline) are not considered in the data used here The monthly price index follows from the influence of the time variable on the price as calculated by regression analysis In a linear function the value of the time variables would denote the absolute For an overview of conventional quality adjustment techniques see KUNZ 1971, op cit., p 24 ff An overview of scientific articles on the development of the hedonic method can be found in HARHOFF, Dietmar, Methodik und Einsatz hedonischer Preisindizes – Ein Überblick, in: HARHOFF, Dietmar and Müller, Michael (eds.), Preismessung und technischer Fortschritt, ZEW Wirtschaftsanalysen, volume 2, Mannheim 1995, pp 37-60 10 quality-adjusted difference in prices between computers sold in August and those sold in September Following the procedure above, a separate regression is calculated for each of September/October, October/November and so on The price index is calculated from this sequence of month-on-month quality-adjusted price changes The time dummy variable method is a very simple technique for calculating hedonic indexes However, its disadvantage is that all data for regression analysis must be available on time to calculate an up-to-date index number each month As the regression analysis requires a comparatively large sample with many different product variants in order to ensure sufficient variation among quality features, a significant data effort is essential This disadvantage is less acute with the imputation method 2.3 Imputation method The imputation method does not calculate the index number directly from the product of the regression equation The regression function only serves to establish a link between the price and quality of the goods The regression equation is used to calculate how many monetary units consumers are willing to pay on average for a certain quality gain As with feature adjustment as described in section 2.1, this information can then be used for actual quality adjustment by subtracting the monetary value of the improvement in quality from the directly observed change in prices In this method, therefore, the regression equation contains no time variable (cf Figure 2) Figure 2: Imputation method Regression analysis Information about price/ quality link p = f(x1, x2 , ε) Quality adjustment The imputation method has the advantage that it does not require regression analysis data to be updated for the current month The use of regression analysis only serves to calculate a general link between price and quality which is valid for several months rather than just one Using a preceding month’s data is, therefore, acceptable With the imputation method quality adjustment can then take place based on a smaller sample around data which has been updated for the current month It is this advantage which prompted the Federal Statistical Office to adopt the imputation method for calculating its personal computer sub-index The technique has been used in official statistics since June 2002 and is described in the following section The hedonic sub-index for personal computers 3.1 Data sources Two separate samples are used to calculate the sub-index for personal computers The first sample contains data for the regression analysis The mathematical link between price and quality features derived from this regression analysis is used for the quality adjustment and for the actual index calculation based on the second sample Thus only the second sample contains the prices and quality features of the sold models which contribute to the index calculation The first sample consists of data which the Federal Statistical Office purchases from the market research company GfK (Gesellschaft für Konsumforschung) in Nuremberg The GfK provides monthly information on prices, quality features and sales figures for computers which it has gleaned from the merchandise information systems (so-called scanner data) of sample companies This data is used for a regression equation to determine which price differences are based on variations in computer quality within the sample The calculation of the actual index, i.e the quality-adjusted month-on-month price change, is based on the second sample taken from advertisements in professional publications and on the internet Only PCs for sale via mail order, and therefore at uniform prices across the country, are included Ideally all retailers would be considered, including regional ones Using mail order data is justified because it is much easier to collect, but it also seems to make sense from a technical point-of-view: mail order prices are transaction prices, i.e there are no significant differences between additional services offered via mail order, and market dominance based on special regional status can be ruled out Furthermore, mail order quotes are used by interested parties to compare prices even when they buy or sell computers via other channels 3.2 Index calculation When calculating the index the second sample is divided into three components: subset A consists of computer models observed in the previous month but no longer purchased in the present month Subset B includes computers which, apart from the price, were registered with exactly the same features in the previous month Subset C, to complete the picture, is composed of models which had not yet been observed in the previous month Figure 3: The second sample subsets Month Subset A: Month models no longer on sale Subset B: identical models to last month Subset C: new models The price index is now calculated in two steps: first the mean change in price on the previous month is calculated for all computers in subset B This mean value, referred to below as the direct month-on-month change (MCdirect), expresses the change in price of those computers which were also available in exactly the same form via mail order in the previous month The second step creates a link between the models in subset A, now withdrawn from stock, and the new models in subset C A hedonic quality adjustment is obtained by the following method: The mean price PMA and PMC and the mean feature vector XMA and XMC are now calculated for each sample The two mean prices are used first to calculate the observed price change on last month, MCobs Then the regression equation is used to calculate a hedonic rate of price difference MChed, obtained purely by calculation as a result of inserting first feature vector XMA and then feature vector XMC into the regression equation MChed expresses how the price would have changed if the models in subsets A and C had differed solely in quality without any other price variables taking effect (no inflation) In other words, MChed expresses the “monetary value” in percentage terms of the month-on-month quality change The “pure” price change between the old and new products, MCold/new, is calculated as the difference between the observed price change and the hedonically calculated monetary value change: (1) Month-on-month change for new models: MCold/new = MCobs – MChed Figure shows the links between the two subsets A and C As we might expect, observed prices alter only slightly as new models are introduced (MCobs is small), while the quality of the new products (XM) rises and the monetary value of the quality change increases with it (MChed is greater than MCobs) As a rule, then, the pure price change for new models compared with models no longer observed, MCold/new, will be negative Figure 4: Rates of change in subsets A and C Month PMA Month MCobs PMC Phed = f(X MC ) MChed Phed = f(X M A) XMC XMA The calculation for the resulting total index integrates both the direct month-on-month price change described above and the quality-adjusted “pure” month-on-month change: (2) hedonic total index: TMC = a ⋅ MCold/new + (1-a) ⋅ MCdirect where ≤ a ≤ Factor a weights the proportion of new models in the overall sample This factor represents the ratio of the frequency of sale of new models to the frequency of sale of existing models 3.3 Regression analysis In September the following quality features were included in the regression analysis as explanatory variables: Variable Symbol Scorecard value score Indicator for hard disc storage capacity (dummy variable) Dhdd Indicator for the FSC brand (dummy variable) DFSC Indicator for the Sony brand (dummy variable) DSony The scorecard value is a measure of processor performance carried out by a neutral body11 This determines performance when running a variety of software applications, attributing a score of 100 to the most powerful processor; all other processors are quantified in relation to this The indicator for hard disc storage capacity distinguishes between hard discs with a memory up to and including 60 GB and those over 60 GB Two further dummies were included to reflect particular brand names The brand dummies express quality differences perceived by consumers but which cannot be measured by other variables, such as the manufacturer’s reputation The choice of variables included here is founded on specific technical considerations and also on the empirically measured influence of the variables It is not necessary to use precisely the same dummies every month What is important each month is to consider whether the regression equation used in the previous month still describes present data optimally If not, it should be adjusted A log-log function was selected for calculating the regression equation: (3) ln(P) = ß0 + ß1⋅ln(score) + ß2⋅ Dhdd + ß3⋅DFSC + ß4⋅DSony + ε P is price and ß0 to ß4 symbolise the regression coefficients In the months June to September regression analysis led each time to a coefficient of determination between 0.72 and 0.8 Accordingly, about 70 – 80% of the observed price difference between computers in the sample could be attributed to quality characteristics The residual price difference was expressed by the random ε 3.4 Results In September 2002 the hedonically calculated sub-index for personal computers demonstrated a price change of –2.4% on the previous month Using conventional quality adjustment methods, the rate of price change for personal computers would have been determined as – 3.3%, i.e 0.9 percentage points lower Figure displays rates of price change month-on-month since the technique was introduced into official price statistics in June 2002 11 Cf www.cpuscorecard.com (25.9.2002) Figure 5: PC price index, month-on-month, conventional and hedonic calculation 0% -1% -2% -3% -4% -5% -6% Jun 02 Jul 02 conventional index Aug 02 Sep 02 hedonic index In June 2002, too, the hedonic index was higher than the one based on conventional adjustment In July and August 2002, however, the hedonic method revealed a sharper fall in prices than did the conventional technique Given that personal computers carry a low weight in the basket for private households and that there was only a slight quantitative difference between the results produced by the new and conventional method of quality adjustment, the overall inflation rate was not affected by the introduction of hedonic techniques In June and September 2002 the relationship between the hedonic and conventional computer price index did not follow the “typical” pattern: prior research had shown that a price index for personal computers using hedonic quality adjustment techniques would on average display sharper falls in price than using conventional quality adjustment techniques 10