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Working Paper Series Measurement Errors in Japanese Consumer Price Index Shigenori Shiratsuka Working Papers Series Research Department (WP-99-2) Federal Reserve Bank of Chicago Measurement Errors in Japanese Consumer Price Index Shigenori SHIRATSUKA Bank of Japan and Federal Reserve Bank of Chicago E-mail: Shigenori.Shiratsuka@chi.frb.org February 1999 Abstract In Japan, the Consumer Price Index (CPI) is widely used as a measure of inflation or the cost of living. The CPI is constructed by using a fixed-weight Laspeyres formula. This formula is used mainly because of its ease of calculation and comprehension, thus limiting the total cost of constructing the statistics. However, such simplicity makes it difficult for the CPI to reflect dynamic changes in economic activity such as changes in consumers’ behavior between goods in response to relative price fluctuation, the introduction of new goods, and the disappearance of old goods. As a result, measurement errors are introduced into the CPI. In this paper, I summarize the problems pertaining to measurement errors inherent in the Japanese CPI, and provide some quantitative assessment. Based on currently available information, I place the point estimate for overall bias in the CPI at about 0.90 percentage point per year. Although this is the best estimate taking into account all information currently available, it is true that the estimate was based on various, rather bold assumptions. In addition, it should be noted that accuracy of the estimate is not necessarily high due to the lack of existing studies in this field in Japan. Key Words: Consumer Price Index, Measurement Errors, Cost of Living Index, Quality Changes, Boskin Report JEL Classification Code: C43, E31 ________________________________________________________________________ This paper is based on the chapters on evaluating the measurement problems in the Japanese CPI of author’s monograph written in Japanese (Shiratsuka, 1998). The author is grateful to Erwin Diewert, David Marshall, and seminar participants at the Federal Reserve Bank of Chicago and Federal Reserve Board for their helpful comments; and to Michio Kitahara, Joel Spenner, and Laura Kutianski for their extensive assistance to make this paper more readable. The opinions expressed are those of author and do not necessarily reflect those of the Bank of Japan or the Federal Reserve Bank of Chicago. Table of Contents 1. 2. Introduction ............................................................................................ 1 Sources of Measurement Errors ........................................................... 2 (1) Limitation of the fixed-weight Laspeyres index formula .....................................2 (2) Substitution effects...............................................................................................4 (3) Effects of quality change ......................................................................................6 (4) The new goods effect............................................................................................8 (5) Technical problems in constructing the CPI statistics........................................10 3. Magnitude of the Measurement Error: A Quantitative Evaluation. 11 (1) The range of quantitative evaluation ..................................................................11 (2) Problems of index formulas ...............................................................................13 (3) Problems in aggregating individual sample prices into item level.....................15 (4) Problems in quality adjustment method .............................................................15 (a) Upward bias in durable goods ......................................................................16 (b) Quality adjustment for services in the CPI...................................................17 (c) Quality change bias in the total ....................................................................18 (5) Effects of the structural change in the retail market...........................................19 (4) The magnitude of measurement errors ...............................................................21 (a) Evaluation of upward bias in total................................................................21 (b) Reservations for the results of the estimates ................................................22 4. Comparison with the Boskin Report .................................................. 23 5. Economic Policy Implications............................................................. 24 (a) Measurement of price stability .....................................................................24 (b) Treatment of asset prices..............................................................................25 (c) The needs for exploring additional methods to gauge the underlying trend of inflation..........................................................................................................25 (d) Fiscal balance and implication on fiscal policy............................................26 6. Conclusion............................................................................................ 27 (a) Introduction of chained CES index formula.................................................28 (b) Introduction of hedonic approach as quality adjustment method.................29 (c) Review of survey samples ............................................................................29 Appendix 1. Index Formulas ................................................................... 29 Appendix 2. Theoretical Relationship between Laspeyres Price Index and Cost of Living Index ............................................................................ 31 Appendix 3. Application of the Hedonic Approach to Specification Changes....................................................................................................... 35 References .................................................................................................. 36 1. Introduction In this paper, I review issues pertaining to measurement errors inherent in the Japanese Consumer Price Index (hereafter CPI), and quantitatively evaluate the magnitude of its upward bias. The CPI, which is widely used as a measure of inflation or the cost of living in Japan, is constructed by using a fixed-weight Laspeyres formula. This formula has been used mainly because of the simplicity of its concept, which aggregates individual price quotations using weights fixed at the base period, thus limiting the total cost of constructing the statistics. At the same time, however, such simplicity makes it difficult for the CPI to reflect the dynamic nature of economic activity such as changes in consumers’ behavior between goods in response to relative price fluctuation, the introduction of new goods, and the disappearance of old goods. As a result, measurement errors are introduced into the CPI. In particular, quality changes brought in by technological innovation are a major cause of measurement errors, and the magnitude of such biases is crucial under the current trend of rapid technological innovation. Moreover, accuracy of inflation measures becomes a more important problem when considering whether to go further down from an already low inflation rate.1 In the 1970s, it is perfectly apparent whether it is desirable to cut the inflation rate because inflation is high and prices are rising in any inflation measures. However, with recent low and stable inflation rates in major countries, the issue of measurement problems in price statistics becomes much more important for monetary policymakers. Measurement errors in price indices are an especially important issue in a country like Japan where there is controversy as to whether the country is on the verge of deflation. 1 Such concern was explicitly pointed out in the speech of Chairman Greenspan (1996) of the Federal Reserve Board during the August 1996 Conference held by the Federal Reserve Bank of Kansas City. 1 This paper is constructed as follows. In Section 2, I examine the sources of measurement errors in the CPI, from the practical viewpoints of statistics compilation. Section 3, I make a quantitative evaluation of measurement errors in the CPI. sections, I specify four major causes of the upward bias in the CPI: In In these two (i) problems in the index formula, (ii) problems in aggregating individual prices into item levels, (iii) inappropriateness of the quality adjustment method, and (iv) effects of structural changes in retail markets. Then, each cause is quantitatively assessed and aggregated to get the point estimate of the magnitude of bias. In Section 4, I compare my estimate of the Japanese CPI with that in the US by the “Boskin Report.”2 implications of measurement errors in the CPI. In Section 5, I discuss some policy In Section 6, I will conclude the paper by proposing some possible measures to improve the accuracy of the CPI. 2. Sources of Measurement Errors In this section, I first show the limitation of the fixed-weight Laspeyres index formula used in constructing the CPI, and then examine various causes of measurement errors from the practical viewpoint of constructing the CPI statistics. (1) Limitation of the fixed-weight Laspeyres index formula The CPI is constructed by using a fixed-weight Laspeyres formula. This formula has been adopted because (i) it is a simple formula that calculates the weighted average of sample prices using weights fixed at those of the base period, and (ii) it is only necessary to 2 For the discussion in the US, see also Gordon (1993), Wynne and Sigalla (1994, 1996), Fixler (1993), and Shapiro and Wilcox (1996). Moulton (1997) summarized various estimates of the magnitude of upward bias in the US CPI in tabular form. Discussion on this issue between academia and BLS economists still continues, and the 1998 Winter issue of the Journal of Economic Perspectives, a special issue on the measurement errors in the US CPI, covers various contributions from members of the Boskin Report, BLS economists, and academia (Boskin et al., 1998; Abraham et al., 1998; Deaton, 1998; Diewert, 1998; Nordhaus, 1998; and Pollak, 1998). 2 survey the prices of the reference period in order to calculate the price index, thus making it possible to limit the total cost of constructing the statistics. At the same time, however, the adoption of the fixed-weight Laspeyres formula to compile the CPI is also a main cause of measurement error. Within the framework of the Laspeyres formula, it is difficult to cope with dynamic changes in economic activity such as changes in consumers’ choices in response to relative price changes, the introduction of new goods, and the disappearance of old goods. These problems would result in the introduction of measurement errors in the CPI through its three components: (i) accuracy of sample prices, (ii) accuracy of the weights, and (iii) appropriateness of the index formula. Specific problems which affect these components are, as examined below: (i) substitution effects induced by relative price changes, (ii) effects of quality changes, (iii) effects of the introduction of new products, and (iv) technical problems in constructing the statistics. When measurement errors in the CPI are discussed, the CPI is compared to the cost of living index, which represents the changes of total expenditure while holding the households’ utility level constant.3 In other words, measurement errors in the CPI can generally be expressed as: (Changes in the CPI) = (Changes in the cost of living index) + (measurement error). In this case, the problem of measurement error can be analyzed from the viewpoint of its size and variability. In the following, I focus on the size of the bias in the CPI, while also referring to its variability by discussing its upper and lower bounds. 3 See Appendix 2 for a detailed explanation of the relationship between the cost of living index and the CPI. The Laspeyres index indicates the upper bound of the cost of living index for the utility level at the base period. 3 (2) Substitution effects Since the CPI is constructed by surveying prices of specific goods and services at specific outlets for a fixed consumption basket at a specified base period, it does not thoroughly reflect changes in households’ purchase behavior in response to relative price changes (substitution effects). More specifically, substitution effects might be easier to understand when they are divided into (i) substitution among item levels, (ii) substitution in aggregating individual prices surveyed into item levels, (iii) substitution among brands within the same category, (iv) substitution among the outlets, and (v) substitution induced by the emergence of new discount outlets (outlet substitution effects). 1) Substitution among item levels: This bias is induced by the fact that the weight used to calculate the weighted average of prices is fixed at that of the base period. For example, fish and meat are generally thought to be substitutes, thus there will be a shift in household expenditure from meat to fish when the price of meat increases. Since the weights applied to meat and fish in the CPI are those of the base period, an upward bias is introduced by the overvaluation of the price increase of meat. 2) Substitution in aggregating individual prices into item levels: This bias is introduced at the stage of aggregating individual prices, which are at a lower level than the publicized items, into the item levels. 3) Substitution among brands within the same category: This bias is induced by the fact that there exist many goods other than those surveyed which are close substitutes. For example, the current CPI adopts a color television set of 21-inch multiplex-voice type with brand specified as the survey sample. However, electronics chain stores and supermarkets carry various television sets, ranging from large size color television sets with satellite tuners to compact low price television sets. Although the CPI price surveys are conducted while considering a product’s representativeness 4 in the market, most of the items surveyed are specified as one brand or specification, thus making it difficult in many cases to gauge the price changes in the product categories as a whole. 4) Substitution among outlets: This bias is induced by the inability to thoroughly grasp consumers’ price search activities. For example, many consumers are believed to shop around neighboring outlets such as supermarkets, department stores, and brand shops in order to purchase the cheapest product at the time of shopping. Since the CPI surveys the selling price on a specific date and at a specified shop, it fails to thoroughly reflect such activities. 5) Outlet substitution effects: This bias is induced by the structural change in retail stores that have been the focus of recent attention in relation to the so-called “price busting” phenomenon. The CPI price survey fails to cover most of the discount stores, thus insufficiently reflecting the consumers’ shift from retail shops and department stores to discount stores.4 These substitution effects are classified into the problem of index formulation ((i)), the problem of aggregating sampled prices into an item level ((ii)), and the problem of survey prices ((iii) -(v)).5 In addition, as years pass after the base period revision, the levels of the price index for various items differ substantially. Such differences will lead to an overvaluation of the items whose price has increased in the case of an arithmetic average index such as the 4 In order to incorporate the effects of advance in discount outlets into the CPI, it is necessary to examine whether price differences between existing outlets and discount outlets correspond to quality difference between them. One criterion is to observe changes in consumers’ behavior: if consumers are shifting from existing to new discount outlets, it can be assumed that the number of consumers who felt the products in discount outlets to be less expensive after taking account of quality differences is increasing. It should be noted that what is referred to here as quality differences are not only the differences in the “product itself,” but also the difference in “retail services” such as how easy it is to shop and how crowded the parking lot is. 5 In the Boskin Report, introduced in Section 4 of this paper, calls (i) “upper level substitution,” (ii) “lower level substitution,” and (v) “new outlet substitution.” 5 Laspeyres.6 (3) Effects of quality change The CPI surveys specific items continuously, which becomes difficult in many cases where the products surveyed have disappeared from the market or have lost representativeness as a result of structural changes in the economy or the development of technological innovations. Therefore, it becomes necessary to substitute survey samples (specifications) in line with the transition of product cycles in the market. In such cases, quality differences between new and old specifications are adjusted so that pure price changes are reflected in the price index: these adjustments are called specification changes. The current Japanese CPI mainly adopts the following three methods of specification changes. First, when the change does not involve any difference either in quantity or in quality, the price of the new specification is directly linked to that of the old one (direct comparison method). Second, when there is an apparent qualitative improvement as well as a price increase, the price index is automatically linked by assuming that the price index of both specifications are constant (price link method). Third, when there is no qualitative change and the difference between the new and the old specifications is attributable to the difference in quantity, the prices are linked after adjusting the ratio of the new and old quantities.7 As a price index is supposed to represent a price change of a product while keeping its quality constant, its rate of change should be equal to the rate of change in product price minus the rate of a quality change: 6 that is, See Shiratsuka (1995a) for details. 7 In the case of the Japanese Wholesale Price Index (WPI), besides the widely used “cost comparison method,” which is adjusted for quality changes based on the difference in production cost, the “hedonic approach” has also been used for some of the items. 6 D(Price Index) = D(Product Price) - D(Quality), where D(•) represents the rate of change of the variable in parentheses. This relationship is useful for explaining the above three methods for quality adjustment in the Japanese CPI. The direct comparison method assumes a “quality improvement rate equal to zero,” making the price index increase rate equal to the nominal price increase rate. The price link method, on the other hand, assumes a “nominal price increase rate equal to the quality improvement rate,” thus making the price index increase rate zero. However, both methods are not that realistic: in the real world, there might be quality changes, and such changes might not be equivalent to price changes. Thus, quality differences are appropriately adjusted only when the third method can be applied, that is, when quantity has changed without any qualitative changes. As a result, it is apparent that the CPI does not fully account for actual quality changes. Therefore, the quality adjustment methods in specification changes are a most likely source of measurement errors in the official CPI, especially in products subject to rapid technological innovation, such as electronic products. Shiratsuka (1995c) checks the accuracy of the quality adjustment method in the CPI through a simulation of specification changes for automobiles, and suggests that quality changes are likely to have caused a upward bias in the CPI. Some 13 Toyota and Nissan models were selected as simulation samples, and their quality changes from the models in the previous year are evaluated by the pre-estimated hedonic functions.8 The Table 1 presents the rate of changes in product price, quality, and quality-adjusted price indices. Toyota Corolla models, for example, changed in 1990-91 and product prices rose 20.5 percent. However, as the quality change computed by the hedonic function increased 17.1 percent, it follows that the quality-adjusted price index rose 8 See Appendix 2 for the details of the evaluation method for quality difference used in the simulation. 7 only 3.4 percent (20.5 percent minus 17.1 percent). In the 52 simulation samples (13 automobiles times four years), 28 cases are deemed to have some quality changes. Among these 28 cases, it is only with respect to the 1994 Toyota Camry that the rate of change in the quality-adjusted price index is less than two times the standard errors in the bottom row in the Table. Therefore, the other 27 cases have experienced a statistically significant change in the quality-adjusted price index. An increase in the quality-adjusted price index is found in 11 cases and a decrease in 16 cases. The above simulation used relatively continuous models to ensure consistency in terms of size and styling of the simulation samples. In practice, however, the construction of a price index is faced with product diversification in terms of sizes and stylings such as an increase in the number of standard and RV-type vehicles in the market. In such cases, the present construction methodology of the CPI is less than appropriate and a bias is likely to exist. Moreover, because quality changes are not properly taken into account, there is a high possibility that a specification change in the sample structure may miss the best timing. (4) The new goods effect Since new goods and services are not brought into the CPI basket immediately, but only after a time lag after their introduction to the markets, the impacts of the appearance of new goods and services on the CPI are not thoroughly reflected. When new products are introduced and come into wide use among households, they will create new demand as well as replace old products. This phenomenon suggests that households regard new products as relatively less expensive than old products on a quality-adjusted basis. In other words, unless the new products are included in the survey sample, the price of items included in the survey will become relatively more expensive than those excluded from the survey, thus resulting in an upward bias in the CPI. Figure 1 illustrates this point. As shown in Table 2, which lists the products newly adopted at the time of base year revision, new products are not introduced at the appropriate time. 8 In fact, new products included in the CPI basket after a certain time lag from the time they came into wide spread use in each household are compact cars (under 2,000cc engine displacement) and pianos (1970); fully-automatic washing machines, stereos, and tape recorders (1975); microwave ovens, and portable calculators (1980); room air conditioners (1985); word processors, and camcorders (1990); medium size cars (over 2,000cc engine displacement), and telephones (1995). In addition, personal computers, facsimile machines, and cellular phones are yet to be included in the survey range. Lags in introduction are also observed in the case of some services. For example, garage rental charges and amusement park fees are included from the 1985 base, and fast food prices such as hamburgers and rental fees for videotapes are included from the 1990 base. Telephone bills of the new telecommunication companies and rent-a-car fees are still not included, and various financial services such as credit card fees and account transfer fees are excluded from the survey range.9 Such lags are especially large in the case of products subject to rapid technological innovation and short product cycles. For such products it is difficult to measure quality changes, and this makes it very hard to construct and update quality-adjusted price indices using conventional methods. As a result, it has been decided to postpone introduction of these items into CPI basket until some time in the future. In addition, it has been pointed out that, since items are subdivided into lower disaggregation levels, newly adopted commodities are not always compared with existing ones with similar functions in the CPI basket. For example, when personal computers are included in the future, effects that stem from their substitution for word processors will not be taken into account.10 This implies that the appearance of new goods affects the 9 The Corporate Service Price Index (CSPI) already includes various financial service fees such as those of bank account transfers. 10 Of course, since many of the new products provide new functions that are not available in the old products, there exists a limit for exact comparison. Correspondence by electronic mails on the Internet and usage of cellular phone are regarded as substitutes for communication based on existing telephones, facsimiles, 9 accuracy of the CPI through not only the improvement in quality but also the increase in the range of goods and services. (5) Technical problems in constructing the CPI statistics In addition to the aforementioned substitution bias, quality change bias, and new product bias, there are unique technical problems pertaining to the compilation methodology of the Japanese CPI. Such technical problems can be divided into the problems of price survey and those of weighting methods. There are two major problems in price survey. First, since price quotations are collected on a specific date, irregular factors such as bargain sales and seasonal prices are easily introduced. The CPI survey is, in principle, conducted every month on Wednesday, Thursday, or Friday in the week which includes the twelfth day of the month, thus the actual survey date will vary by a maximum of eight days (see Figure 2).11 As a result, the price quotation of some items can differ substantially depending on whether or not the survey date coincides with a special event such as a bargain sale.12 Second, monthly changes in private rents tend to differ substantially, since their price quotations have been collected only once every three months, and the number of samples is limited. With regards to the weights, a major source of the problem lies in the Family Income and Expenditure Survey (hereafter FIES), compiled by the Management and Coordination Agency, from which the CPI weights are calculated. Mizoguchi (1992) reviewed the past discussion of this issue and pointed out the following two points. and postal services, which also have strong features as new ways of communication. for the detailed discussion on this point. First, See Nordhaus (1997) 11 As an exception to the principle, hotel charges are collected every month on the weekend (Friday and Saturday) in the week that includes the fifth day of the month. In addition, price quotations of fresh foods, which often show big changes due to factors such as bad weather, are collected three times a month. 12 The CPI excludes, in principle, items sold at specially reduced prices from the viewpoint of collecting price samples of goods and services regularly sold; although the survey includes items sold at such special prices for more than 7 days at the time of the survey. As such, since the survey date is subject to differ by 8 days at the greatest, items sold at special prices will be sometimes included and sometimes excluded. 10 there is a bias in the process of selecting the household samples. Second, the survey is insufficient to gauge the total expenditure of the household since it excludes households with one person, and it collects information mainly through housewives who might not be fully aware of other family members’ expenditures.13 In addition, problems pertaining to the calculation of the weight of imputed rent have also been pointed out.14 3. Magnitude of the Measurement Error: A Quantitative Evaluation In this section, I will present a quantitative evaluation of the upward bias in the CPI. I will first specify, among the causes of the measurement errors we have discussed so far, which ones are suitable for quantitative evaluation at this stage. Then, I will calculate the point estimates for each of the individual causes specified, and estimate the overall bias by summing them up. (1) The range of quantitative evaluation As a starting point, I will rearrange the four causes of measurement errors --substitution effect, quality change, introduction of new products, and technical problems pertaining to the construction of the statistics --- from the viewpoint of the three components of the CPI --- index formula, accuracy of prices surveyed, and accuracy of the weights --- and specify the range for quantitative evaluation at this stage. First, as previously mentioned, there are four problems with the substitution effects: (i) the index formula for aggregating the upper level items, (ii) the substitution in 13 On September 8, 1996, the evening edition of Nihon Keizai Shinbun carried an article “Four problems of the Household Expenditure survey,” which pointed out the problems of the survey as: (i) it requires a great deal of time to fill it out, with small reward, and is prone to omission, (ii) it excludes households with only one person, (iii) the sample number is small, and (iv) uncertain expenditure such as pocket money and social expenses are increasing. 14 See Shiratsuka (1995a, 1996) for details. 11 aggregating prices surveyed into item levels, (iii) the substitution among brands within the same category, (iv) the substitution among existing outlets, and substitution due to the appearance of new outlets. Among these, the first two problems, i.e. the problems in index formula for aggregating the upper level items, and the substitution in aggregating prices surveyed into item levels, can be evaluated as problems in the index formula. The last problem of substitution due to the introduction of new discount outlets is relevant to the accuracy of price information. However, the other problems magnify monthly variability, but do not have a significant impact on the direction of measurement bias. Second, I will quantify the impact of quality change and the introduction of new goods and services together as problems in quality adjustment methods which substantially affect the accuracy of prices surveyed. Since quite limited quality adjustment methods have been adopted in Japan, the problem of quality adjustment is deemed to be significant. In the previous section, I have discussed quality changes and the introduction of new products separately: the former as the improvement of the quality of goods and services in the survey, and the latter as the introduction of new goods and services into the price survey. However, the difference between quality change and the introduction of new products depends heavily on how finely disaggregation levels of commodity classifications are subdivided. Thus, from the practical viewpoint of constructing statistics, it is quite difficult to separate them in an explicit way. In addition, the official CPI does not cover all products, because quality changes in some products are difficult to measure using the conventional methods. Finally, technical problems in constructing the statistics are excluded from the range of quantitative evaluation in this paper. This is because it is assumed that they may not have a substantial impact on the accuracy of the index when we consider a longer term such as a yearly average.15 Although these problems can be major causes of measurement 15 With regard to the accuracy of the weights, it is true that the possibility of remaining bias even on a yearly average basis cannot be denied. For example, if there is an item that shows a smaller increase than that of the 12 error, many of the technical problems are factors that lead to a magnification of the monthly variability of the price index. In summary, what I can quantitatively estimate at this stage are the effects of index formula; aggregating individual price samples into the item level; quality adjustment methods; and structural changes in the retail market. Figure 3 illustrates the relationship between causes of measurement error and quantitative evaluations to be shown in this paper. (2) Problems of index formulas As in previous studies, I will evaluate the problem of index formula by comparing fixed-weight Laspeyres index to the superlative indices such as the Fisher and Törnqvist indices (see Appendix 2 for the details on the index formula). To this end, I picked up, from the CPI data series, the lowest classification (88 commodities) available continuously from 1970 up to now; estimated the corresponding weights annually by using the FIES16 and composed the fixed-weight Laspeyres price index (corresponds to the CPI), as well as the chained Törnqvist and Fisher price indices. Figure 3 reports the estimation result: the fixed-weight Laspeyres index, the chained Törnqvist index, and the chained Fisher index (1970=1) are 3.011, 2.923, and 2.923, respectively. When converted into annual change rates, each index level corresponds to the annual inflation rate of 4.167, 4.053, and 4.053. Therefore, the fixed-weight Laspeyres index has upward biases over both the Törnqvist and Fisher indices in the rate of 0.114 total index and the weight of such an item is undervalued, then the total index incorporates an upward bias. In the Japanese CPI, weights of durable goods, which decline more sharply than the overall index, are deemed to be undervalued because of the low coverage of the expenditure pattern of family members other than the housewife. As such, it can also be considered from the viewpoint of the accuracy of weights that the Japanese CPI possibly inherits an upward bias. 16 Each index formula is composed by using the smallest 88 specifications for which a continuous series is available since 1970 in the CPI data, and by estimating the CPI weight from the FIES (Family Income and Expenditure Survey). It should be noted that imputed rents are excluded due to the difficulty of calculating the weight of each year. For the fixed base series, weights are modified every five years taking into account that the base year is revised every five years. 13 percent from 1970 to 1997. These figures are somewhat smaller than the US’s estimate of 0.2 percent, although bias can be expected to become larger once specifications are further divided into more detailed items.17 In Table 3, I further divide the series into time periods of five years and compare the divergence of the chained Törnqvist and Fisher price indices from the fixed-weight Laspeyres price index. It shows that the variability of biases varies according to periods and index formula. However, the divergence of chained Törnqvist and Fisher price indices are 0.025 and 0.030 percentage points per year, respectively, in the 1990s, which illustrate that substitution effects are almost negligible at the moment. One possible explanation for the recent decline in the impact of substitution effects is that the variability of relative prices was reduced under the low inflation rates, and, as a result, consumers might have had less scope for substitution recently. To test this hypothesis, following Shapiro and Wilcox (1997), I calculated an index of the cumulative change in relative prices, Jt, defined as follows: æp ö J t = å wi 0 lnçç it ÷÷ - ln P0Gt , i è pi 0 ø (1) where wi0 is the expenditure share in the base period, pit is the price of item i at time t, and PG0t is the fixed-weight geometric mean index that is defined in Appendix 1. The bottom row in Table 3, previously appeared, shows changes in the index J from the previous year. Except for the period from 1970 to 1975, when the first oil crises occurred, both the magnitude of substitution effects and the pace of relative price drift are mild. Taking into account the results, the size of upward bias caused by the index formula is in the range of 0.00-0.25 percent, although it differs according to the period 17 This point is suggested in Aizcorbe and Jackman (1993), employing the smallest specification CPI data in the US (44 regions and 207 item strata). 14 analyzed and the index formula adopted. In addition, such bias is deemed to be negligible for the latest period. (3) Problems in aggregating individual sample prices into item level Since the Management and Coordination Agency does not release the price index of those lower than the item level, problems in aggregating individual sample prices into item levels have not been estimated.18 However, taking into account the fact that (i) the increase in the Japanese CPI is now at a low rate, thus biases caused by the index formula are deemed to be almost negligible, and (ii) as the classification of Japanese CPI items is more detailed than the item strata used in the US, it can be safely assumed that biases caused in the process of aggregation of individual prices into item level are considerably smaller than the US estimate of 0.25 percent.19 In this paper, I will assume the bias stemming from the process of aggregating individual prices to item level to be 0.10 percent, a figure derived as the difference between upper level substitution and lower level substitution, which were both estimated in the Boskin Report. (4) Problems in quality adjustment method My previous research (Shiratsuka, 1995b, c, Shiratsuka and Kuroda, 1995) estimates hedonic functions for the quality-adjusted prices for durable goods such as personal computers, automobiles, and camcorders, and shows that their quality-adjusted 18 With respect to the WPI, the Bank of Japan (1998) begins to compile and release a reference index using a geometric mean formula since June 1998. In the reference index, geometric mean is partly used in the lower level aggregation, from “sample price” to “commodity class,” and Laspeyres formula is used in the upper level of aggregation, from “commodity class” to “all commodities.” Bank of Japan (1998) shows that the Laspeyres index has upward bias over the geometric mean index in the rate of 0.3 percent annually from 1995 to 1998. 19 See Advisory Commission to Study Consumer Price Index (1996) and Bureau of Labor Statistics (1977) for the details of the estimation. 15 prices indicate declining trends. In the official CPI, however, such quality adjustment is not sufficiently implemented, and thus appears to introduce an upward bias. (a) Upward bias in durable goods Shiratsuka (1995b, c), and Shiratsuka and Kuroda (1995) have estimated hedonic price indices for certain durable goods and calculated the upward bias by replacing the CPI item indices with their estimated indices. The results are summarized in Table 4. When hedonic price indices for automobiles, camcorders, and personal computers are included, the level of the overall CPI is lowered by 0.01, 0.01, and 0.02 percentage points respectively; and that of CPI durables is lowered by 0.16, 0.09, and 0.36 percentage points. By just adding up these figures, the upward bias reaches 0.04 percentage points for the overall index, and 0.6 percentage points for the durable goods index. Considering the fact that the relative importance in the CPI basket of these three goods totals just two percent, contribution of durable goods as a whole to the overall bias can well reach a substantial amount when such hedonic estimates are obtained for various other microelectronic products. It should also be noted that the magnitude of quality change bias also changes over time. For example, in the case of automobiles, the upward bias for the total CPI has increased from 0.01 to 0.02 percent during 1993 and 1994. In addition, among durable goods, microelectronic products such as personal computers are subject to rapid technological innovation and have short product cycles. This suggests that such products are subject to the problem of quality adjustment at the time of specification change. The prices of these products are difficult to track on a continual basis, and normally accompany lags in their inclusion in the CPI basket. In fact, personal computers are yet to be included in the CPI, and word processors are included only from the 1990 base CPI. 16 (b) Quality adjustment for services in the CPI With respect to services in the CPI, there have been many unresolved problems such as the difficulty in specifying “one unit for standard service,” and it is thought to be an area where price accuracy can be greatly improved.20 in this area are limited.21 In Japan, however, existing studies In the following, taking rent, the cost of privately owned houses, and medical care as examples, I will point out the problems inherent in quality adjustment in the CPI services. In the case of the CPI rent, the current compilation method is likely to introduce an upward bias because it fails to take account for the recent improvement in the structure and convenience of houses. The CPI surveys average rent per residential area on three classifications of houses: (i) wooden small size houses (residence area less than 30 square meters), (ii) wooden medium size houses (residence area over 30 square meters), and (iii) non-wooden houses. Table 5 illustrates how the structure and facilities of houses have developed over time. It shows that the structure of the houses has undergone a major shift from wooden to non-wooden, with an increasing share of reinforced-concrete and steel frame construction. substantially increased. In the wooden house category, that of fireproof houses has In addition, the state of facilities seems to have improved as the ratios of those houses with flush toilets in bathrooms increase year after year. With respect to the cost of privately owned houses, the Japanese CPI covers it as 20 For example, see Griliches (1992) and Kroch (1991). 21 With respect to the relation between changes in service price and changes in quality, Sawa et al. (1989) estimated a hedonic price index for hotel charges and showed that the increase rate of the CPI was bigger than that of the hedonic index. In addition, there are estimates such as Ito and Hirono (1993), Kasuga (1996) for house rent, and Nanbu et al. (1994) for medical expenses, although both studies are deemed as problematic for use in examining the impacts on the measurement errors in the CPI. Ito and Hirono (1993) derived price and specification data from the new contract rent carried in housing magazines, and those data are deemed to overestimate the average rent which should be gauged in the CPI. Nanbu et al. (1994) stated that explanation variables in the hedonic function were not sufficient to adjust for quality changes brought by technological innovation, and a substantial effect of quality changes was mingled in the estimate parameter of annual dummy variable. 17 an imputed rent. However, since there is a large difference in facilities and comfort between privately owned houses for rent and owner-occupied houses, the quality adjustment of the surveyed price becomes important. As shown in Figure 5, distribution of the amount of floor space, which can be deemed as a proxy for comfort of the house, differs substantially between privately-owned houses for rent and owner-occupied houses regardless of construction materials (wooden or non-wooden). Therefore, it has been questioned whether the current CPI appropriately gauges the actual owner’s equivalent rent, which are houses with large residential space. With regard to medical care in the CPI, gauging advances in medical technology has been a big problem.22 In Japan, however, the survey items are quite limited, and there has been great doubt whether the survey reflects overall medical expenditure appropriately (see Table 6). For example, only standard medicines sold over the counter in a drugstore are included, while medicines on provided prescriptions in hospitals are not. In regards to hospitalization expenses, the survey includes that for childbirth but not for others such as general medical treatment or operations. It should also be noted that the weight for medical expenses is underestimated, and the quality adjustment in this area can result in a large impact on the overall bias. The weight used in the CPI is calculated based on the FIES, which surveys medical expenses directly paid by the households. Considering the fact that most of such expenses are paid in an indirect way, through health insurance, the weight calculated only on the basis of direct payment would probably result in an underestimate of actual medical expenses. (c) Quality change bias in the total Table 7 shows the items that are thought to be difficult to adjust for quality changes, and their weights add up to about 30 percent of the overall CPI. 22 Shapiro and Wilcox (1996) examine the measurement issues in the medical service in detail. 18 In order to estimate the average upward bias for these items, I take an annual average of 1.0 to 1.5 percent for total durable goods (estimate in Gordon, 1990) as a starting point.23 Then, I assume the upper limit of the bias to be approximately three percent, taking into account the following three factors. First, the Japanese CPI does not employ the hedonic approach at all, and the quality adjustment methods for the current Japanese CPI do not account for the actual quality changes appropriately. Second, survey items of the Japanese CPI are fairly subdivided and their specifications are stipulated in detail, thus the introduction of formerly uncovered new products into the survey is limited at the time of the base year revision. Third, there is a time lag before the inclusion of products subject to rapid technological innovation in the survey sample. As a result, the impact of quality adjustment is estimated to be somewhere in the range of 0.30 to 0.90 percent. I assume the median to be about 0.70 percent, slightly higher than the mean value of the range.24 (5) Effects of the structural change in the retail market The effects of sampling are difficult to quantify because of the lack of appropriate statistical evidence. Admitting its extreme nature, I have made an examination of the case of the Great Southern Hyogo Earthquake that took place in January 1995.25 The CPI showed a very peculiar movement before and after the earthquake, which could be used to obtain a hint of the magnitude of the effects of the prevalence of discount stores on the CPI. 23 The declining pace of the price of durable goods is not very different between the US and Japan. According to the estimate of Shiratsuka (1995b), the hedonic price index for personal computers has been declining annually at the pace of about 30 percent, and this is almost equivalent to that in the US, estimated by Berndt and Griliches (1993). However, it should be noted that these estimates assume that the CPI for services inherits the same size of upward bias as that of durable goods. As aforementioned, the CPI for services is deemed as problematic from the viewpoint of price accuracy, although the size of such a problem is yet to be empirically examined. 24 The estimate here specifies the range affected by quality changes, and assumes an average upward bias within the range, and no bias without the range. This is an unavoidable treatment due to the lack of existing studies in judging to what extent individual goods and services contain upward bias. However, it is also reasonable to think that the size of upward bias differs for goods and services. This question awaits future study. 25 The Great Southern Hyogo Earthquake was the worst natural disaster in Japan in 70 years. More than 5,000 people died, and about 2 million people, including foreign residents in Japan, suffered from the disaster. 19 In February 1995, the CPI of Hyogo prefecture, where Kobe city is situated, decreased by 2.3 percent from the previous month, falling substantially lower than the CPI decrease of 0.4 percent in the Tokyo Metropolitan area. Since the Great Southern Hyogo Earthquake broke out between the dates of CPI price survey in January and February, such irregular changes in prices may suggest some connection with the Earthquake. In practice, it is reported that reasons behind this phenomenon are (i) the price of fresh foods which need fire to cook have decreased, (ii) damaged shops made a discount sale of their stocks or pulled down the price of their products, and (iii) supermarkets which carried rather cheaper products were substituted for department stores and shops which were shut down.26 Table 8 compares the price movements of commodity groups between Hyogo prefecture and Tokyo Metropolitan area for the period before and after the earthquake. The table lists 19 commodity groups in which the Hyogo CPI declined two percentage points more than the Tokyo CPI in February 1995, and placed them in reverse order. Items normally believed to be discounted deeper in the discount stores such as liquors (beer, whiskeys, etc.), recreational goods (toys, sporting goods, etc.), and clothing accessories (ties, belts, etc.), rather than fresh foods, are ranked in the top class. The size of the decline compared with the previous month is far larger than the average change of the previous three years. Furthermore, if three categories --- fish, meat, eggs, and daily products, which are regarded as fresh foods --- are excluded from the above 19 commodity groups and the weighted average of the difference in the monthly change rate between the two areas is calculated using the Tokyo Metropolitan area weights, it is estimated that the overall index will be lowered by about 1.7 percentage points. Based on the above result, the downward bias caused by the substitution of the outlets surveyed is deemed as significant, taking into account the finding that commodity groups with large divergence were thought to be greatly affected by adding discount outlets 26 For example, see evening edition of Nihon Keizai Shinbun on March 3, 1995. 20 to the survey.27 Of course, it is true that this result should be interpreted carefully, since the divergence of the two areas is due partly to Hyogo’s unique factors such as stock clearance sales by shops which had suffered damage during the earthquake (for example, Japanese clothing). It should be noted that the expansion of new and low-priced outlets such as discounters and road-side shops, sometimes represented by the development expressed as “price busting,” does not progress at a constant pace. In particular, recent price development and consumer behavior suggest that the shift from department stores and specialty shops to discount outlets has largely subsided, and price differences between these outlets has settled down to a level consistent with the difference in retail service quality provided by them. This phenomenon implies that measurement errors induced by structural changes in the retail market have been diminishing in recent years. Bearing these points in mind, I will assume the upward bias of the CPI to be 0.10 percentage points for the median, 0.05 percentage points for the lower limit, and 0.60 percentage points for the upper limit, which corresponds to one-third of the above estimation result. (4) The magnitude of measurement errors (a) Evaluation of upward bias in total As discussed above, the measurement biases are introduced by way of index formula, aggregation of individual prices into item index, quality adjustment method, and price survey sampling. If I sum my point estimates measurement biases in those four sources, the total bias is, at this moment, judged to be some 0.90 percentage points, as 27 Of course, price differences between existing retail outlets and discount stores partly reflect the difference in the retail services provided, which also needs to be adjusted in the CPI. 21 shown in Table 8.28 However, it should be noted that a possible range of estimates will be as wide as from 0.35 to 2.00 percentage points, according to various conditions.29 (b) Reservations for the results of the estimates It should be noted that the method adopted in this paper, that is, the individual examination of the problems inherent in the Japanese CPI and the simple adding of the results, has the following limitations: 1) At present, available research results are quite limited in Japan. With respect to the effects of quality adjustment, for example, it has been proven that there is an upward bias for certain durable goods, especially for microelectronic products which are subject to rapid technological innovation. However, for non-durable goods and services, there is no accumulation of studies in Japan, which lead to an indecisive conclusion with respect to the impacts of quality adjustment on the price index. 2) The question of whether effects of the problems inherent in the CPI with regard to its accuracy can be correctly estimated by this simple adding has been noted. As already shown, sources of measurement errors in the CPI and the sources which introduce such error are mutually correlated and quite complicated. Adding them without any adjustment means that I assume no correlation among sources.30 3) I have shown that the point estimate of the upward bias in the Japanese CPI is judged 28 The size of measurement error is, as described later, less than one percent on an annual basis, although it is quite important to adjust appropriately for such errors taking into account the cumulative effect on assessing the general price level and productivity. 29 In this paper, I update the estimation results of the upward bias in the Japanese CPI shown in Shiratsuka (1998). The point estimate remains unchanged, while upper limit was lowered from 2.35 to 2.00 percentage points per year, based on the revised estimation results on the upper substitution bias. 30 In order to solve the problem of mutual dependence of sources of measurement errors, and that of estimates of measurement errors and credibility range, Shapiro and Wilcox (1996) specified the (subjective) probability distribution of biases for each source, and calculated the probability distribution of overall measurement errors taking into account such mutual relationships. 22 to be 0.9 percentage points on an annual basis with a possible range of 0.35-2.00 percentage points. However, this range does not refer to a statistical confidence interval. The point estimate itself is the most reliable “best shot” based on all the available information to date, although it is true that the calculation is also based on many assumptions. Therefore, it should be noted that the estimates shown in this paper are not necessarily ones with a high accuracy. 4. Comparison with the Boskin Report In the US, the Senate Finance Committee’s Advisory Commission for studying the CPI presented a report “Toward a more accurate measure of the cost of living” (the socalled “Boskin Report”) in December 1996.31 measurement error: The Report specified four sources of (i) upper level substitution, (ii) lower level substitution, (iii) new products/quality change, and (iv) new outlets. The Report examined past studies in detail for the above four sources, and presented its best estimate of the size of the upward bias as 1.10 percentage points per year (see Table 10 for details). If I roughly compare the four sources pointed out in this report with those of our study, they will correspond (i) to the index formula problem, (ii) to the problem of aggregation of individual prices, (iii) to quality adjustment methods problem, and (iv) to survey sample problem. Among these sources, lower level substitution has not been studied in Japan due to data availability, thus the estimate for this cause should be regarded as preliminary.32 31 Since the publication of the Boskin Report, there has been a lot of discussion on support for, and criticism of their estimation results. However, Boskin et al. (1998) takes the position that there are no reasons to change the original estimate of a 1.1 percentage points per annum upward bias in the US CPI. 32 As the range of plausible values of the upward bias in the Japan CPI, I have set 0.35 to 2.00 percentage points (0.8 to 1.6 in case of the Boskin Report) around the point estimate of 0.90 percentage points. Due to the lack of similar studies in Japan, the estimate is bound to be quite preliminary, thus taking quite a wide range. 23 5. Economic Policy Implications In this section, I will discuss the policy implication of measurement errors in the CPI. (a) Measurement of price stability As the measured inflation rate approaches zero, it is generally believed that measurement error portion increases within the observed inflation rate. Therefore, although the accuracy of the price index will not be that problematic in the process of lowering the inflation rate from, say, ten percent to three percent, it will become crucial in considering bringing down the rate from three percent to zero. In this sense, mismeasurement in the CPI matters a lot for the conduct of monetary policy. The existence of upward bias in the CPI means that pursuing a zero inflation rate is to conduct a deflationary policy, thus possibly resulting in a loss of economic welfare. This suggests that true price stability will not necessarily correspond to zero measured inflation. In addition, the time-varying nature of this problem in the short-run suggests that it is difficult to interpret movements in the measured inflation rate. In other words, to accept a certain inflation rate as an upward bias may also lead to the loss of economic welfare, since the magnitude of measurement error is deemed to change according to economic conditions. Bearing this point in mind, how measurement errors in the price index change over time in relation to the business cycle is an important issue awaiting solution. Furthermore, an overestimation of inflation is, to put it differently, an underestimation of productivity growth or economic growth. For example, if price decline is brought about by a downward shift of the aggregate supply curve as a result of an increase in productivity, it is possible to argue that such downward pressure on the general 24 price level is acceptable (Figure 6). Even if the price index incorporates an upward bias of the same magnitude, the implication for monetary policy will differ according to the source of such bias. (b) Treatment of asset prices As far as monetary policy tries to achieve the medium- to long-run sustainable price stability, it is not sufficient to monitor only the fluctuation of current price indices. Therefore, it is important for policy judgement to take into account the asset prices that implicitly reflect the future development of goods and service prices as well as current price indices. From the viewpoint of considering the dynamic nature of consumer behavior, it is important to extend the current price index concept in order to trace intertemporal changes in cost of living, depending on the future path of consumption. However, asset price information can only be used as a supplementary measure to price indices in making policy judgements on price developments because of the following two reasons. First, current asset prices are affected by various factors other than price expectations for future goods and services, thus current changes in asset prices do not necessarily indicate future changes in prices of goods and services. Second, the accuracy of such asset prices is quite low compared with those of existing price indices. Therefore, it is deemed as difficult to attach a central role to price indices, including asset prices, in the judgement of monetary policy.33 (c) The needs for exploring additional methods to gauge the underlying trend of inflation In order to conduct a preemptive monetary policy, it becomes necessary to gauge appropriately the changes in underlying inflation trends. To make use of the asset prices mentioned above can be one way, and to reexamine information contained in relative price 33 Treatment of asset prices in price indices is discussed in detail in Shiratsuka (1996). 25 changes across the various goods and services is another. What makes it difficult to trace the underlying inflation trends are not only the size and variability of biases in price indices, which both stem from measurement errors, but also the adjustment method pertaining to transitory or temporary fluctuations in the prices of individual items. In order to cope with the latter issue and to supplement the judgement of underlying inflation trends, central banks employ various devices. For example, Japan uses the CPI series that excludes fresh food items; New Zealand and the UK sometime employ a limited influence estimator, an index that excludes items located on both tails of the cross-sectional distribution of inflation. The limited influence estimator provides important information concerning changes in underlying inflation trends, and could well be a quite useful and powerful indicator for policy judgement. Shiratsuka (1997) shows that such an indicator is applicable to the Japanese economy, and points out that the indicator helps to (i) reveal the underlying trend in price changes by adjusting for temporary disturbance such as rapid yen appreciation and sudden rises in oil prices, and (ii) clarify the magnitude of upward pressure on prices by making use of monthly and yearly changes in the index. (d) Fiscal balance and implication on fiscal policy The major incentive for compiling the Boskin Report was that upward bias in the CPI had a great impact on the fiscal budget. In the US, upward bias in the CPI has been a major source of the increase in the federal budget, since about 30 percent of fiscal expenditure (such as Social Security and pension payments) and 45 percent of fiscal revenue (income tax) are tied to the CPI. According to the Boskin Report, the Congressional Budget Office (CBO) has estimated that if the change in the CPI was brought down by an average of 1.1 percentage points for the next decade, it would slash as much as $148 billion from projected federal deficits by the year 2006 (see Advisory Commission to 26 Study Consumer Price Index, 1996).34 When the fiscal system and inflation indexation are discussed, however, examination of the validity of the price basket is also important. In the case of pensions, it could well be the case that the average consumption basket of all households and that of pension recipients are quite different. 6. Conclusion In this paper, I have summarized the problems pertaining to measurement errors inherent in the Japanese CPI, and have provided some quantitative evaluations. Based on currently available information, I presented the point estimate of about 0.90 percentage points as the size of measurement error. Although this is the best estimate taking into account all information currently available, it is true that the estimate was based on various, rather bold assumptions. In addition, it should be noted that the accuracy of the estimate is not necessarily high due to the lack of existing studies in this field in Japan. Despite the efforts of many statistical institutions in constructing accurate statistics, measurement errors are unavoidable to some extent. Thus, the most important point is to ascertain whether they are small enough to be safely ignored in practice or serious enough to mislead users. The debate about the accuracy of CPI should therefore be aimed at investigating the sources of measurement errors and the extent to which they affect accuracy. Unfortunately, research on price index measurement errors has been limited in Japan, and further research in the area is necessary. In order to deal with the three problems quantitatively estimated in this paper --- 34 Pension payments constitute the only item in Japan’s fiscal budget which is tied to the CPI, and its weight is, in fiscal year 1994, about 13 percent of the total expenditure of the general government (current expenditure + total capital formation + acquisitions less disposal of land) in the System of National Accounts. 27 the index formula problem, the effects of quality changes, and the effects of structural change in retail markets --- can be somewhat clarified by adopting the following methods. (a) Introduction of chained CES index formula The superlative indices such as the chained Törnqvist and Fisher indices have more desirable features than the fixed-weight Laspeyres index formula currently used in the CPI as a measure of the cost of living. This is because the chained Törnqvist and Fisher indices reflect the substitution effect appropriately. However, such indices cannot be computed on as timely a basis as the current CPI due to the delays in the availability of the required expenditures data. Therefore, it is important to produce an approximation of the chained Törnqvist and Fisher indices with data available to the statistical agency when they compile the CPI. One possible answer to this question is application of the CES index formula, proposed by Shapiro and Wilcox (1997). More specific, I construct the version of the CES index that is defined as: Pt CES 1-s é æ pit ö ù ÷÷ ú = êå wit çç êë i è pi 0 ø úû 1 /(1-s ) , (2) where s is the elasticity of substitution between items (assumed to be identical for all possible pairs of goods and services in the CPI). Table 11 compares the annual rates of change in the cost of living indices, computed by the eight different index formulas. The first two rows use the Törnqvist and Fisher index formulas. The remaining rows apply Equation (2) for six different assumptions about the elasticity of substitution, that is, s = 0.3, 0.4, 0.5, 0.6, 0.7, and 1.0 (identical to the geometric mean formula with one-year lagged weight). This table shows that the elasticity of substitution, on average, lies between 0.4 and 0.5 from 1970 to 1997, 28 and between 0.5 and 0.6 in the 1990s. This estimate is a little lower than that in the United States of 0.7, reported in Shapiro and Wilcox (1997). (b) Introduction of hedonic approach as quality adjustment method Bias induced by quality changes can be made small enough by the introduction of the hedonic approach. I propose to adopt a framework of using a pre-estimated hedonic function in adjusting the quality difference between new and old products (for the details, see Appendix 3). This framework can avoid the cumbersome process of estimating the hedonic function every time the price index is constructed. In addition, this framework is deemed to be highly feasible since it is relatively compatible with the methodology of surveying specific prices every month. In fact, the Japanese WPI employs this framework for some computer items and has been constructing a price index on a monthly basis. (c) Review of survey outlets Whether the development of price busting has been appropriately reflected in the CPI is still an open question. However, judging from the case study of the Kobe earthquake, I believe that the effect of the expansion of discount outlets on price survey is substantial. Therefore, the review of survey outlets is worth considering in order to improve the accuracy of the CPI. Appendix 1. Index Formulas In Appendix 2, I practically summarize some basic price index formulas applied in the paper. The basic components of a price index are the price of item i in time t, denoted pit, and the quantity of this item purchased in time t, xit. Then, the fixed-weight version of Laspeyres (PL0t), Paasche (PP0t), Fisher (PF0t), Törnqvist (PT0t), geometric mean (PG0t) 29 indices are defined as follows: n P0Lt = å pit xi 0 n n i =1 i =1 å pi 0 xi 0 = å wi 0 ´ i =1 pit , pi 0 æ n p ö pi 0 xit = çç å wit ´ it ÷÷ å pi 0 ø i =1 è i =1 n n P = å pit xit P 0t i =1 P0Ft = P0Lt ´ P0Pt æp ö P0Tt = Õ çç it ÷÷ i =1 è pi 0 ø n (A-1) -1 , , (A-2) (A-3) ( wi 0 + wit 2 ) (A-4) , æp ö P = Õ çç it ÷÷ i =1 è pi 0 ø n wi 0 G 0t (A-5) . The chained index formula first aggregates individual prices in period-to-period basis to compute an intermediate period indices, and, then, chains these intermediate period In general, chained price index (CPk0t) is defined as indices to obtain a long-term index. follows: t -1 CP0kt = P01k ´ P12k ´ L´ Pt -k1,t = Õ Psk,s +1 (for k = L, P, F, T, G). s =0 (A-6) Therefore, chained Laspeyres (CPL0t), Paasche (CPP0t), Fisher (CPF0t), Törnqvist (CPT0t), geometric mean (CPG0t) indices are written as: t -1 t -1 s =0 s =0 i =1 n CP0Lt = Õ PsL,s+1 = Õå wis ´ t -1 P s ,s +1 s =0 t -1 t -1 s =0 s =0 (A-7) -1 p ö æ n = Õ çç å wis ´ i ,s +1 ÷÷ , pis ø s =0 è i =1 t -1 CP = Õ P P 0t pi ,s+1 , pis (A-8) CP0Ft = Õ PsF,s +1 = Õ PsL,s +1 ´ PsP,s +1 = CP0Lt ´ CP0Pt , t -1 CP = Õ P T 0t s =0 T s , s +1 æp ö = ÕÕ çç i ,s +1 ÷÷ s =0 i =1 è pis ø t -1 n 30 (A-9) ( wis + wi ,s +1 2 ) , (A-10) t -1 CP = Õ P G 0t s =0 Appendix 2. G s ,s +1 æp ö = ÕÕ çç it ÷÷ s =0 i =1 è pi 0 ø t -1 n wi 0 . (A-11) Theoretical Relationship between Laspeyres Price Index and Cost of Living Index The purpose of the CPI is to measure the average change in the prices paid by households for a fixed basket of marketable goods and services while keeping quality constant. According to the theory of consumer behavior, the CPI can be considered as an approximation to the “cost-of-living index” by the Laspeyres price index.35 The cost-of- living index is defined as the ratio of the minimum expenditure required to achieve a particular level of satisfaction, or utility level, between two points of time. Let u R be the constant utility level of a consumer and C (p t , u R ) be the amount of minimum expenditure necessary to realize this utility level under the price vector p t . Then the cost-of-living index at time 1 relative to time 0 is defined as P(p 1 , p 0 ; u R ) = C (p 1 , u R ) . C (p 0 , u R ) (A-12) The price index for a given consumption vector q R , which minimizes the household’s expenditure under the price vector of a reference period, while attaining the utility level u R , is defined as P(p 1 , p 0 ; q R ) = 35 p 1q R . p 0q R (A-13) See Deaton and Muelbauer (1980), Diewert (1987), Pollak (1989), and Morita (1989) for theoretical background for the price index. 31 Laspeyres and Paasche price indices are defined respectively as P(p 1 , p 0 ; q 0 ) = p 1q 0 , p0q0 (A-14) P(p 1 , p 0 ; q 1 ) = p1q1 . p 0 q1 (A-15) With these equations in hand, the relationship between these three price indices is derived. Between the Laspeyres and cost-of-living indices, the following equation holds, P(p 1 , p 0 ; q 0 ) = p 1q 0 > C (p 1 , u 0 ) = P(p 1 , p 0 ; u 0 ) . 0 0 = 0 0 C (p , u ) p q (A-16) First, the denominators of both sides of equation (A-16) are identical by definition. Second, looking at the numerators of both sides of equation (A-16), it is found that p 1q 0 is greater than or equal to C (p 1 , u 0 ) . This is because that: (i) on the one hand, the consumption vector q0 does not necessarily minimize the expenditure under the price vector p 1 , although it attains the utility level u 0 ; (ii) on the other hand, C (p 1 , u 0 ) is the amount of minimum expenditure necessary to realize the same utility level u0 under the price vector p 1 . By similar arguments, the following equation between the Paasche and the cost-ofliving indices are derived, p1q1 < C (p1 , u1 ) P(p , p ; q ) = 0 1 = = P(p1 , p 0 ; u1 ) . 0 1 C (p , u ) pq 1 0 1 (A-17) Figure A-1 and Figure A-2 make these relationships among three price indices even more intuitive in a two-goods problem. First, Figure A-1 shows the relationship between the cost-of-living index and the Laspeyres index. 32 At time 0, a consumer maximizes his or her utility at E, where the budget line AB and the indifference curve for the utility level u 0 are tangent to each other. When the price of x1 increases, the budget line shifts to AC. level u 1 . Now consumer equilibrium moves to F, which brings the lower utility In order to attain the initial utility level u 0 under this new set of relative prices with minimum expense, the combination G must be realized, and the new budget constraint intersects the y-axis at point J. On the other hand, if we were to realize the combination E to attain the same utility level u 0 under the new set of relative prices, the budget constraint can intersect the y-axis at point K. Since the price of good x2 is held constant, the ratio of distances to origin OJ/OK is the ratio of expenditure to realize the utility level u 0 with and without minimizing living expenses. In other words, the Laspeyres index and the cost-of-living index are respectively defined as p 1q 0 OK = , p 0 q 0 OA (A-18) C (p 1 , u 0 ) OJ = , C (p 0 , u 0 ) OA (A-19) P(p 1 , p 0 ; q 0 ) = P(p 1 , p 0 ; u 0 ) = and yielding OK OJ ³ . OA OA (A-20) Hence the Laspeyres index is larger than or equal to the cost-of-living index. As for the relationship between the cost-of-living index and the Paasche index in Figure A-2, and these two index formula are respectively defined as, P(p1 , p 0 ; q1 ) = 33 p1q1 OA = , p 0q1 OM (A-21) P(p 1 , p 0 ; u 1) = C (p1 , u1 ) OA = , C (p 0 , u1 ) OL (A-22) and yielding OA OA £ . OM OL (A-23) Hence the cost-of-living index is larger than or equal to the Paasche index. However, the combination of equations (A-20) and (A-23) does not necessarily mean that the cost-of-living index is located between the Laspeyres and Paasche indices. This is because there is no generally accepted relationship between the cost of living indices P(p1 , p 0 ; u 0 ) and P(p1 , p 0 ; u 1 ) at time 0 and 1 respectively. Impacts of changes in relative prices vary with the utility level. If preferences are homothetic, the cost-of-living index situated between the Laspeyres and Paasche indices.36 This implies that the income expansion path or Engel curve --- the resulting locus of utility-maximizing bundles when prices are held constant and income is allowed to vary --- must be a straight line through the origin. If this is the case, then the minimum expenditure function C (p, u ) will be written as a (p) ´ b(u ) . This implies that the minimum expenditure function is separable with respect to prices and utility, and depends only on the price vector at a constant utility level. Then the cost of living index can be written as 36 It should be noted that Diewert (1983) shows that the unobserved true cost of living index lay between the observable Paasche and Laspeyres price indices without assuming homothetic preferences. 34 C (p1 , u 0 ) a(p1 ) ´ b(u 0 ) a(p1 ) = = C (p 0 , u 0 ) a(p 0 ) ´ b(u 0 ) a(p 0 ) , a(p1 ) ´ b(u1 ) C (p1 , u1 ) 1 0 0 = = = P(p , p ; u ) a(p 0 ) ´ b(u1 ) C (p 0 , u1 ) P(p1 , p 0 ; u 0 ) = (A-24) thus giving 1 0 0 < P(p1, p0 ; u1 ) = P(p1, p0 ; u 0 )< P(p1, p0 ; q1 ) = = P(p , p ; q ) . (A-25) Appendix 3. Application of the Hedonic Approach to Specification Changes In Appendix 3, I present a practical method for constructing a reliable CPI by adjusting quality changes with the hedonic approach. This method is something of a compromise between the following two requirements. On the one hand, it is necessary to employ the hedonic approach to account for quality changes more adequately. On the other hand, it is also necessary to sustain the conventional methodology of surveying specific prices every month. Thus, it is not appropriate to use the anti-logarithm of the estimated parameter for the year dummy as a quality-adjusted price index. Figure A-3 describes the method for applying the hedonic approach to specification changes in the case of one performance characteristic (functional form for the hedonic function is assumed to be a semi-log linear). The x-axis measures the characteristic, and the y-axis measures the logarithm of the product price. A straight line with a constant (a) and a slope (b) represents the pre-estimated hedonic function. Let XO and XN represent the characteristic values of the exiting and new products, respectively. Then the theoretical price (that is, the estimated price based on the hedonic function) is given by the antilogarithm of ln P = a + bX, that is, P̂O and P̂N for the old and new products respectively. The quality change between the existing product and the new product is measured by the difference in the theoretical prices between the existing product and the new product, which is depicted by AB in Figure A-3. Let n be the observed prices for old and new products 35 PO and PN respectively. Then, CD measures the change in the product price. Therefore, the difference between CD and AB corresponds to the change in the quality-adjusted price index. In this particular example, the quality-adjusted price index rises with an introduction of the new product because CD > AB. With this methodology, the following relationships hold among rates of change in terms of product price, quality, and the quality-adjusted price index. D(Product Price) > D(Quality) ==> D(Price Index) > 0 D(Product Price) = D(Quality) ==> D(Price Index) = 0 D(Product Price) < D(Quality) ==> D(Price Index) < 0 References Abraham, Katharine G., John S. Greenlees, and Brent R. Moulton, “Working to Improve the Consumer Price Index,” Journal of Economic Perspectives, 12(1), 1998, pp. 2736. Advisory Commission to Study the Consumer Price Index, Toward a More Accurate Measure of the Cost of Living: Final Report, 1996. Aizcorbe, Ana M., and Patrick C. Jackman, “The Commodity Substitution Effect in CPI Data, 1982-91,” Monthly Labor Review, December 1993. Bank of Japan, “Release for a Reference Wholesale Price Index Using Geometric Mean Formula,” Bank of Japan Quarterly Bulletin, 6(3), 1998. Bank of Japan Price Index Study Group, Bukka no Chishiki, (Basics of Price Index), Nikkei Bunko, Nihon Keizai Shinbun Sha, 1992 (in Japanese). Berndt, Ernst R., and Zvi Griliches, “Price Indices for Microcomputers: An Explanatory Study,” in M. F. Foss, M. E. Manser, and A. H. Young, eds. Price Measurements and Their Uses, 1993. Boskin, Michael J., Ellen R. Dulberger, Robert J. Gordon, Zvi Griliches, and Dale W. Jorgenson, “Consumer Prices, the Consumer Price Index, and the Cost of Living,” 36 Journal of Economic Perspectives, 12(1), 1998, pp. 3-26. Bureau of Labor Statistics, “The Experimental CPI Using Geometric Mean (CPI-U-XG),” 1997. Deaton, Angus, “Getting Prices Right: What Should Be Done?” Journal of Economic Perspectives, 12(1), 1998, pp. 37-46. ______, and John Muellbauer, Economics and Consumer Behavior, Cambridge University Press, 1980. Diewert, W. Erwin, “Exact and Superlative Index Numbers,” Journal of Econometrics, 4(2), 1976, pp. 114-145. ______, “Superlative Index Numbers and Consistency in Aggregation,” Econometrica, 46(4), 1978, pp. 883-900. ______, “The Theory of the Cost of Living Index and the Measurement of Welfare Change,” in W. E. Diewert and C. Montmarquette, eds., Price Level Measurement, 1983, pp. 767-780. ______, “Index Numbers,” in John Eatwell, Murray Milgate, and Pete Newman eds., The New Palgrave: A Dictionary of Economics, vol. 2, 1987, pp. 767-780. ______, “Index Number Issues in the Consumer Price Index,” Journal of Economic Perspectives, 12(1), 1998, pp. 47-58. Fixler, Dennis, “The Consumer Rice Index: Underlying Concepts and Caveats,” Monthly Labor Review, December, 1993. Gordon, Robert J., The Measurement of Durable Goods Prices, University of Chicago Press, 1990. Greenspan, Alan, “Opening Remarks,” in Achieving Price Stability: A Symposium Sponsored by the Federal Reserve Bank of Kansas City, 1996. Griliches, Zvi, ed., Output Measurement in the Service Sector, Studies in Income and Wealth, vol. 56, University of Chicago Press, 1992. Ito, Takatoshi and Keiko Nosse Hirono (1993), “Efficiency of the Housing Market,” Bank of Japan Monetary and Economic Studies, 11(1), 1993. Kasuga, Yoshiyuki, “Shutoken ni okeru Juutaku no Kousatsu: Mikuro Deita ni yoru Jutaku Shijou no Kenshou,” (Housing Problems in Metropolitan Area: Examination of Housing Market by Micro Data), Chousa No. 211, Japan Development Bank, 1996 37 (in Japanese). Kroch, Eugene, “Tracking Inflation in the Service Sector,” Federal Reserve Bank of New York Quarterly Review, 16(2), 1991. Lebow, David E., John N. Roberts, and David J. Stockton, “Monetary Policy and ‘The Price Level’,” mimeo, Board of Governors of the Federal Reserve System, August, 1994. Mizoguchi, Toshiyuki, Wagakuni Toukei Chousa no Gendaiteki Kadai, (Current Problems for Japanese Statistical Surveys), Iwanami Shoten, 1992 (in Japanese). Morita, Yuuzou, Bukka Shisuu Riron no Tenkai, (Development of Price Index Theory), Touyou Shinpou Sha, 1989 (in Japanese). Moulton, Brent R., “Bias in the Consumer Price Index: What is the Evidence,” Journal of Economic perspectives, 10(4), 1996. Nanbu, Tsuruhiko et al., “Saabisu no Shitsu no Keisoku II: Byouin Saabisu no Hinshitsu Henkaritsu no Keisoku,” (Quality Measurement of Services: Estimation of the Rate of Changes in Hospital Services), Financial Review, vol. 31, Institute for Fiscal and Monetary Policy, Ministry of Finance, 1994 (in Japanese). Nordhaus, William D., “Do Real-Output and Real-Wage Measures Capture Reality?” Chapter 1 in T. F. Bresnahan and R. J. Gordon eds., The Economics of New Goods, 1997, pp. 29-66. ______, “Quality Change in Price Indices,” Journal of Economic Perspectives, 12(1), 1998, pp. 59-68. Ohta, Makoto, Hinshitsu to Kakaku (Quality and Prices), Soubun Sha, 1980 (in Japanese). Pollak, Robert A., The Theory of the Cost-of-Living Index, Oxford University Press, 1989. ______, “The Consumer Price Index: A Research Agenda and Three Proposals,” Journal of Economic Perspectives, 12(1), 1998, pp. 69-78. Reinsdorf, Marshall, “The Effect of Outlet Price Differentials on the U. S. Consumer Price Index,” Chapter 7 in M. F. Foss, M. E. Manser, and A. H. Young, eds. Price Measurements and Their Uses, 1993. Shapiro, Matthew D., and David W. Wilcox, “Mismeasurement in the Consumer Price Index: An Evaluation,” NBER Working Paper No.5590, 1996. Shiratsuka, Shigenori, “Shouhisha Bukka Shisuu to Keisoku Gosa,” (Consumer Price Index 38 and Measurement Errors: Their Causes and Improvement Measures), Kin’yu Kenkyu, 14(2), 1995a (in Japanese). ______, “Effects of Quality Changes on the Price Index: A Hedonic Approach to the Estimation of a Quality-adjusted Price Index for Personal Computers in Japan,” Bank of Japan Monetary and Economic Studies, 13(1), 1995b. ______, “Automobile Prices and Quality Changes: A Hedonic Price Analysis of the Japanese Automobile Market,” Bank of Japan Monetary and Economic Studies, 13(2), 1995c. ______, “Shisan Kakaku to Bukka Shisuu,” (Asset Price Fluctuation and Price Index), Kin’yu Kenkyu, 16(5), 1996 (in Japanese). ______, “Inflation Measures for Monetary Policy: Measuring the Underlying Inflation Trend and Its Implication for Monetary Policy Implementation,” Bank of Japan Monetary and Economic Studies, 15(2), 1997. ______, Bukka no Keizai Bunseki (Economic Analysis of Inflation Measures), University of Tokyo Press, 1998 (in Japanese). ______, and Sachiko Kuroda, “Bideo Kamera no Hedonikku Bunseki” (Hedonic Analysis for camcorder Prices), Kin’yu Kenkyu, 14(4), 1995 (in Japanese). ______, and ______, “Apareru Seihin Kakaku to Hinshitsu Sa: CPI Apareru no Kakaeru Mondaiten to Hedonic Aprochi ni yoru Kaizen no Kanousei” (Apparel Product Prices and Quality Differences), Kin’yu Kenkyu, 15(1), 1996 (in Japanese). Suzuki, Kenji, and Makoto Ohta, “A Hedonic Analysis of Land Prices and Rents in the Bubble: Kanagawa Prefecture in Japan for 1986-1988,” Economic Studies Quarterly, 45(1), 1994. Turvey, Ralph, Consumer Price Indices: An ILO Manual, International Labor Organization, 1989. Wynne, Mark A., and Fiona D. Sigalla, “The Consumer Price Index,” Federal Reserve Bank of Dallas Economic Review, 1994. ______, and ______, “A Survey of Measurement Biases in Price Indices,” Journal of Economic Survey, 10(1), 1996. 39 Table 1. Simulation for Specification Changes 1991 1992 1993 1994 (TOYOTA) Carolla Carina Corona Camry Mark II Crown Celsior Product price Quality Quality-adjusted price Product price Quality Quality-adjusted price Product price Quality Quality-adjusted price Product price Quality Quality-adjusted price Product price Quality Quality-adjusted price Product price Quality Quality-adjusted price Product price Quality Quality-adjusted price 20.5 17.3 3.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.8 14.1 -6.3 0.0 0.0 0.0 0.0 0.0 0.0 -9.5 -15.6 6.1 8.6 18.0 -9.5 11.9 9.7 2.2 0.0 0.0 0.0 0.0 0.0 0.0 5.3 0.0 5.3 1.4 0.0 1.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.4 50.9 -40.5 1.8 -1.0 2.8 0.2 0.0 0.2 0.7 0.0 0.7 9.1 14.3 -5.2 0.9 0.0 0.9 -4.0 -4.3 0.3 2.6 -6.2 8.8 0.0 0.0 0.0 0.7 2.5 -1.8 3.0 0.0 3.0 3.0 9.8 -6.8 1.3 9.2 -7.9 11.6 9.7 1.9 13.8 27.1 -13.3 0.0 -7.0 7.0 7 3 4 0.7 2.9 0.0 2.9 4.7 9.7 -5.0 0.8 -8.9 9.7 0.0 0.0 0.0 0.0 -11.0 11.0 -0.7 -8.7 7.9 7 5 2 0.7 5.9 21.8 -15.9 0.8 0.0 0.8 1.8 0.0 1.8 -1.9 15.1 -17.0 5.8 12.1 -6.3 9.5 24.2 -14.6 6 1 5 0.7 -4.4 -16.5 12.1 1.7 5.0 -3.3 4.1 11.3 -7.1 14.0 23.0 -9.0 0.0 0.0 0.0 0.0 0.0 0.0 7 2 5 0.7 (NISSAN) Sunny Product price Quality Quality-adjusted price Primera Product price Quality Quality-adjusted price Bluebird Product price Quality Quality-adjusted price Skyline Product price Quality Quality-adjusted price Cedric Product price Quality Quality-adjusted price Cima Product price Quality Quality-adjusted price Inadequate quality adjustment case Increase in quality-adjusted price (shaded) Decrease in quality-adjusted price (squared) Standard errors for hedonic price index Source: Shiratsuka (1995c) Note: Squared areas, and squared and shaded areas are case of increase and decrease in qualityadjusted prices, respectively. Crossed area indicates that quality difference is insignificant. Table 2. Items Newly Introduced in the Base-Year Revision Base-year 1970 Durable goods Automobiles (661cc to Services 2,000cc engine displacement), Pianos, Room Lesson fees (driving school), Fire insurance premiums air-conditioners, Color TV sets 1975 Washing machines (fully automatic School lunches, Expressway tolls type), Stereo phonograph sets, Tape recorders, Gas water heaters 1980 Microwave ovens, Portable electronic Lunch plate for children, Women’s calculators hairdressing charges 1985 Room air-conditioners, Video tape Garage rental charges, Amusement recorders park fees, premiums Automotive insurance (optional), Sewerage charges 1990 Word processors, Camcorders Hamburgers, Video rental fees 1995 Automobiles (over 2,000cc in engine Pizzas, Karaoke fees displacement), Telephones Excluded items Personal computers and peripherals Telephone (e.g. telecommunication companies, Rent- printers), Faxes, Cellular bills for new a-car fees, Financial services, Internet telephones 41 Table 3. Comparison of Laspeyres, Törnqvist, and Fisher Price Indices 70-75 75-80 80-85 85-90 90-95 95-97 70-97 90-97 (Annual changes) Fixed-weight Laspeyres (a) 11.379 6.297 2.604 1.095 1.155 0.892 4.167 1.079 Chained Törnqvist (b) 11.052 6.194 2.534 0.994 1.137 0.849 4.053 1.055 Chained Fisher (c) 11.052 6.194 2.534 1.001 1.137 0.831 4.053 1.049 Chained Törnqvist (a)-(b) 0.327 0.103 0.070 0.101 0.017 0.043 0.114 0.025 Chained Fisher (a)-(c) 0.327 0.103 0.070 0.094 0.018 0.061 0.114 0.030 3.207 1.191 0.745 1.114 0.953 1.346 1.442 1.065 (Deviations) (Relative Price Changes) 42 Table 4. Upward Bias in Durable Goods Weight (%) Annual change (%) Hedonic CPI Difference Index Contribution (%) to Durables to Overall Automobiles 1.8 0.1 -0.4 -0.5 -0.16 -0.01 Camcorders 0.1 -4.0 -9.6 -5.6 -0.09 -0.01 Personal 0.1 n. a. -24.4 n. a. -0.36 -0.02 computers Sources: Author’s calculation based on Shiratsuka (1995b, c), and Shiratsuka and Kuroda (1995). Notes: 1. The estimates of upward bias are the average from 1991 to 1994. 2. The weights are on the basis of 1990. 3. Estimated on the assumption that half of the weight for word processors in CPI is replaced by personal computers. 43 Table 5. Construction Structure and the State of Facilities Unit: % 1973 ratio of wooden houses 1978 1983 1988 1993 86.2 81.7 77.4 73.0 68.1 19.7 25.4 31.3 31.7 34.0 ratio of non-wooden houses 13.8 18.3 22.6 27.0 31.9 (the ratio of ferroconcrete houses) 10.5 15.2 20.0 24.5 29.0 ratio of houses with flush toilets 31.4 45.9 58.2 66.4 75.6 ratio of houses with bathrooms 73.3 82.8 88.3 91.2 93.5 (the ratio of wooden and fireproofed houses) Sources: Management and Coordination Agency, The Housing Survey of Japan. 44 Table 6. List of CPI Items: Medical Care Item Weight Specification (Medicines) Medicines for cold (multipurpose) 0.0011 “Shin Lulu A” Medicines for cold (antipyretic and 0.0005 “Bufferin A” Gastroenteric medicines (digestive) 0.0002 “Ohta’s Isan” Gastroenteric medicines (combined) 0.0005 “New Pan Siron” Vitamin preparations, multivitamins 0.0012 “Panvitan Hi” Vitamin preparations, vitamins 0.0012 “ALINAMIN A” Health Drinks 0.0012 “Ripobitan D” Dermal medicines 0.0005 “MENTHOLATUM” Plasters 0.0004 “TOKUHON A” or “SALONPAS A” Breath fresheners 0.0007 “Jintan SILVER PILLS” Chinese medicines 0.0029 For women, decoction, “Chujoto” analgesic) compound (Medical services) Medical treatment 0.0128 Rate of charges shared by the insured Hospital charges 0.0032 Charges for ordinary delivery, 8 days hospital treatment Massage fees 0.0004 Except in the application of insurance, massage from head to foot, about one hour Source: Management and Coordination Agency, Annual Report on the Consumer Price Index. 45 Table 7. Weight affected by quality adjustment problem 0.51589 0.08663 0.13494 0.06544 0.02727 0.01864 0.01952 0.05462 0.00601 0.00446 0.01818 0.00972 0.00311 0.01315 0.11315 0.01043 0.10272 0.04377 0.01734 0.48411 0.03161 Weight affected by quality adjustment problem 0.09530 0.00000 0.00000 0.04592 0.02727 0.01864 0.00000 0.03911 0.00601 0.00446 0.01818 0.00883 0.00087 0.00076 0.01027 0.01043 0.00000 0.00000 0.00000 0.21568 0.03161 0.13401 0.13401 0.25077 0.01579 0.00381 0.01745 0.01340 0.20031 0.06773 1.00000 0.05007 0.01541 0.00381 0.01745 0.01340 0.00000 0.00000 0.31099 Weight Commodities Agricultural and aquatic products Food products Textiles Clothing Shirts and sweaters Others Durable goods Domestic durables Heating and cooling appliances Automobiles Recreational durables Toys Others Other industrial products Medicines others Electricity, gas, and water charges Publications Services Private house rent Imputed rent Public and personal services Medical charges Airplane fares Telephone charges Hotel charges Others Eating-out General 46 Note Microwave ovens, refrigerators, etc. Room air-conditioners, etc. TV sets, camcorders, etc. Household video game machines Telephones Excluding massage fees Table 8. Comparison of CPI Movements in Hyogo and Tokyo in February Unit: % 1992-94 (a) 1995 Difference (b) Notes (b)-(a) Alcoholic beverages 0.0 15.1 ( -0.2 ) -15.1 ( -0.2 ) Underwear 0.8 -14.0 ( -0.1 ) -14.8 ( -0.1 ) Japanese clothing -0.4 -11.4 ( -0.1 ) -11.0 ( 0.0 ) Recreational goods 2.8 -10.8 ( -0.3 ) -13.6 ( -0.3 ) Tutorial fees 0.0 -7.9 ( -0.1 ) -7.9 ( -0.1 ) Beer, wine Toys and sporting goods Eating-out -0.1 -6.2 ( -0.5 ) -6.1 ( -0.5 ) Other clothing -0.7 -5.8 ( 0.0 ) -5.1 ( 0.0 ) Neckties, belts Books and others -3.0 -5.5 ( -0.1 ) -2.5 ( 0.0 ) Newspapers, magazines Cakes and candies -0.2 -4.8 ( -0.1 ) -4.6 ( -0.1 ) Domestic utensils 0.0 -4.6 ( 0.0 ) -4.6 ( 0.0 ) Fish and shellfish -0.1 -3.8 ( -0.1 ) -3.7 ( -0.1 ) Tableware, kitchen utensils Personal effects 0.5 -3.4 ( 0.0 ) -3.9 ( -0.1 ) Medical supplies -0.2 -3.3 ( 0.0 ) -3.1 ( 0.0 ) Disposable diapers Personal care services -0.2 -3.3 ( 0.0 ) -3.1 ( 0.0 ) Men’s haircut charges Medicines -0.2 -2.9 ( 0.0 ) -2.7 ( 0.0 ) Communication 0.0 -2.7 ( -0.1 ) -2.7 ( -0.1 ) Meat -0.7 -2.6 ( -0.1 ) -1.9 ( 0.0 ) Dairy products and eggs 0.6 -2.5 ( 0.0 ) -3.1 ( 0.0 ) Repairs and maintenance -0.2 -2.3 ( 0.0 ) -2.1 ( 0.0 ) Total ( -1.9 ) ( -1.9 ) Excl. fresh food ( -1.7 ) ( -1.7 ) Bags, watches Postage, telephone charges Sources: Management and Coordination Agency, Consumer Price Index, Hyogo Prefecture Government, Hyogo-ken no Shouhisha bukkasisuu sokuhou. Notes: 1. The above figures are the difference between the rates of change from the previous year of CPI of Hyogo prefecture and Tokyo Metropolitan-area. 2. Contribution to the percent change of the overall CPI the weights of Tokyo Metropolitan area in parentheses 3. The items for which figures exceed 2% in 1995 are listed in the above table. 4. Fresh food consists of fish and shellfish, meat, Dairy products and eggs. 47 Table 9. Magnitude of Measurement Errors in CPI Source of bias lower-bound mid-point upper-bound Price index formula 0.00 0.00 0.25 Aggregation to item levels 0.00 0.10 0.25 Quality adjustment 0.30 0.70 0.90 Price sampling 0.05 0.10 0.60 Total 0.35 0.90 2.00 Table 10. Comparison with the Estimate in Boskin Report Source of measurement error United States (Boskin Report) Japan (our estimates) Upper level substitution 0.15 0.00 Lower level substitution 0.25 0.10 New products / quality change 0.60 0.70 New outlets Total 0.10 1.10 (0.80 - 1.60) 0.10 0.90 (0.35 - 2.00) Sources: Advisory Commission to Study the Consumer Price Index (1996) 48 Table 11. Introduction of the CES Index 70-75 75-80 80-85 85-90 90-95 95-97 70-97 90-97 (Superlative indices) Chained Törnqvist 11.052 6.194 2.534 0.994 1.137 0.849 4.053 1.055 Chained Fisher 11.052 6.194 2.534 1.001 1.137 0.831 4.053 1.049 s = 0.3 11.104 6.218 2.541 1.005 1.139 0.879 4.072 1.065 s = 0.4 11.078 6.197 2.539 1.000 1.135 0.865 4.060 1.058 s = 0.5 11.052 6.175 2.536 0.987 1.139 0.850 4.049 1.056 s = 0.6 11.026 6.154 2.533 0.982 1.127 0.852 4.037 1.049 s = 0.7 10.999 6.132 2.531 0.976 1.123 0.855 4.026 1.046 s = 1.0 (Geometric mean) 10.827 6.127 2.582 1.004 1.120 0.858 4.010 1.045 (Chained CES indices) 49 Figure 1. Impact of the Appearance of New Goods and Services Items excluded from the CPI survey Increase in demand ô Decrease in relative prices Items excluded from the CPI survey Items included in the CPI survey Items included in the CPI survey Decrease in demand ô Increase in relative prices Figure 2. Date of Price Survey SUN MON 6 13 20 27 7 14 21 28 (earliest case) TUE WED THU FRI SAT 1 2 3 4 5 8 9 10 11 12 15 16 17 18 19 22 23 24 25 26 29 30 31 SUN MON 5 12 19 26 6 13 20 27 Note: Price quotations are collected during the shaded dates. 50 (latest case) TUE WED THU FRI SAT 1 2 3 4 7 8 9 10 11 14 15 16 17 18 21 22 23 24 25 28 29 30 31 Figure 3. Range of Quantitative evaluation Pr i ce in d ex for mu l a Substitution effects Q u a l i t y ch a n g e s l Index formula for aggregating the upper level items l Aggregation of individual prices into item index g o o d s l l Technical problems in compilin g methodology quantitative estimates Accuracy of price information l l N e w Within the range of Quality adjustment method Structural changes in retail markets Substitution among retailers and brands Methodology of price survey Without the range of Accur a cy of we i g h t s l l Limited coverage of FIES Method in estimation of weight for imputed rent for owner-occupied house 51 quantitative estimate Figure 4. Comparison of Various Price Index Formulae (1970=1) 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 Fixed weight Laspeyres 1.6 Chained weight Tornqvist 1.4 Chained weight Fisher 1.2 1.0 0.8 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 Source: Author’s calculation from FIES and CPI Statistics. 52 Figure 5. Distribution of the amount of floor space (% ) 50 40 30 (1) W o od en h ous es wo o d en s mall s ize h wo o d en mid iu m s ize ho us e 20 own hou s e 10 ho us e fo r rent 0 2 -29m 30-49m 2 (% ) 50-69m 2 70-99m 2 100-149m 2 2 150m - (2) Non-wood en h ous es 50 own hou s e 40 ho us e fo r rent 30 20 10 0 2 -29m 30-49m 2 50-69m 2 70-99m 2 100-149m Sources: Management and Coordination Agency, The Housing Survey of Japan. 53 2 2 150m - Figure 6. Impact of Productivity Increase Caused by Technological Innovation General Price level Aggregate Demand Curve Aggregate Supply Curve Productivity Increase Caused by Technological Innovation P P’ Y’ Y 54 GDP Figure A-1. Cost of Living Index and Laspeyres Price Index Good x2 K J A G E F O U(q) = u0 B C U(q) = u1 Good x1 Figure A-2 Cost of Living Index and Paasche Price Index Good x2 A M L F E U(q) = u0 H O B C 55 U(q) = u1 Good x1 Figure A-3. Application of the Hedonic Approach to Specification Change ln P C lnP = a + bX PN A ^ PN P rice C hange Q uality C hange B ^ PO PO D b ¡ E stim ated P rice n A ctual P rice a O XO XN 56 X
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