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Study on Taiwan consumers' cost of living: an application of the additive Tornqvist price index formula.

I. INTRODUCTION

There are very few empirical studies on Taiwan consumers' cost of living; however, the issue is becoming increasingly important in Taiwan because many economic and social welfare policies already include escalator clauses related to cost of living in order to take the impact of inflation on consumers' real purchasing power into consideration. (1) Normally, the escalator clauses only use the officially published Consumer Price Index (CPI) as the basis for adjustments due to changes in the cost of living in Taiwan. Since the CPI, which is computed with the Laspeyres index formula, uses consumers' base-period commodity expenditure shares as the aggregate weights and fails to consider consumer optimal choice behavior, it will over-estimate consumes' cost of living and produce a "substitution bias" (2) into the measurement (Braithwait, 1980; Manser & McDonald, 1988). (3) Hence, the current approach would not only distort the distribution of income but would consequently also aggravate economic inequality in Taiwan.

In this paper, we have utilized the Tornqvist price index, in particular, with an additively decomposed formula suggested by Reinsdorf et al. (2002) to measure the growth level of Taiwan consumers' cost of living over the period of 1991-2006. Using the Tornqvist price index to measure consumers' cost of living standards has many advantages. First and most importantly, Diewert (1976) has shown that the Tornqvist price index approximates to the second order of the underlying Konyus true cost of living index (Konyus, 1924); hence, by using the Tornqvist price index instead of the Laspeyres price index one can avoid the problem of substitution bias. Additionally, with the Tornqvist price index, the cost of living can be directly calculated using consumers' commodity expenditure shares and price ratio data without involving complicated econometric methods for estimating the related demand function parameters necessary to compute the corresponding Konyus true cost of living index (Jorgenson & Slesnick, 1999). Furthermore, unlike the econometric method, the calculations of the Tornqvist price index are not limited to broad aggregated commodity groups.

The adoption of an additively decomposed Tornqvist price index formula has two purposes. First, it allows us to identify and evaluate the contribution of each commodity group to the total growth of Taiwan consumers' cost of living over the study period. In many practical applications, we are not interesting in merely knowing by how much the level of consumers' cost of living has grown; we might want to go a step further to know how much each commodity group has contributed to the total growth in the cost of living and why some commodity groups have made higher contributions than others. In this study, we found that nearly 85% of the total growth of cost of living derived mainly from seven commodity groups, these being supplementary food (5.35 ppts), medical care services (4.89 ppts), educational expense (4.31ppts), residential rent (4.30 ppts), fruits (2.48 ppts), oil and related services (1.99 ppts) and food away from home (1.98 ppts). The above findings may provide useful information for governmental officials. For example, in order to avoid the rapid growth in Taiwan consumers' cost of living, it would be more effective for the government to try to control the price increases of the commodity groups mentioned above than the others. We went on to use the Laspeyres price index to measure Taiwan consumers' cost of living. By comparing the estimates obtained from the Laspeyres price index with those from the additively decomposed Tornqvist price index formula, we can not only estimate the level of substitution bias and evaluate the appropriateness of using the Laspeyres price index to measure Taiwan consumers' cost of living over the sample period; we can also further investigate the composition of the substitution bias. In this study, we found that substitution behavior occurred to most commodity groups over the study period. In particular, strong substitution effects appeared in six commodity groups whose prices had experienced significant changes, these being supplementary food, fruits, educational expense, communication fees, personal care services, and main food.

In the following section, we explain why the Tornqvist price index would approximate to the true economic cost of living index, and then derive its corresponding additive decomposition formula following the approach of Reinsdorf et al. (2002). In Section III, we first describe the data used for computing Taiwan consumers' cost of living over the period of 1991-2006, and then analyze our empirical results. Our analysis focuses on explaining the growing sources or contributing factors of Taiwan consumers' cost of living over the period of 1991-2006. In addition, we also use the Laspeyres price index to measure Taiwan consumers' cost of living and investigate the level and composition of substitution bias over this period through comparison with the estimates from the Tornqvist price index. In Section IV, we summarize our major empirical findings and suggest that the Price Statistics Department in Taiwan start to compile and publish an alternative consumer price index using the Tornqvist price index.

II. TORNQVIST PRICE INDEX AND CORRESPONDING ADDITIVE DECOMPOSITION FORMULA

Tremendous progress has been made in the field of economic price index number theory (4) in the last few decades (Samuelson & Swamy, 1974; Diewert, 1981). In particular, since Diewert (1976, 1978) developed the "superlative index number theory," it has become popular for economists to use superlative price indexes to measure and analyze consumers' cost of living standards (5) (Manser & McDonald, 1989; Aizcorbe & Jackman, 1993; Sharpiro & Wilcox, 1996; Cage & Jackman, 1997; Blow & Crawford, 2001). (6) Diewert (1976) defined a price index as superlative if it is exact for a "flexible" (unit) expenditure function c, where a "flexible" (unit) expenditure function c means that it is capable of providing a second-order approximation to an arbitrary twice differential (unit) expenditure function at any point in its domain.

Diewert (1976, p.122) showed that if the reference utility level is chosen to be [u.sup.*] = [([u.sup.0*][u.sup.1]).sup.1/2], the geometric mean of period 0 and period 1 utility levels, then the following Tornqvist price index [P.sup.T] ([P.sup.1], [P.sup.0], [Q.sup.1], [Q.sup.0]),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

which is a geometric average mean of price ratios with weights equal to ([s.sub.i.sup.0] + [s.sub.i.sup.1])/2, where [s.sub.i.sup.t] represents the expenditure ratio for commodity i at period t, t=0&1, is a superlative index number formula. Because it is exactly equal to Konyus true cost of living index (Konyus, 1924), i.e.,

[P.sup.T]([P.sup.1], [P.sup.0], [P.sup.1], [Q.sup.0]) = [P.sup.K] ([P.sup.1], [P.sup.0], [u.sup.*]) = c([p.sup.1], [u.sup.*])/c([P.sup.0], [u.sup.*])

where the c(P, u) has the "flexible" general translog functional form,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII];

where ln is the natural logarithm function and the parameter [[alpha].sub.i], [[alpha].sub.ij], and [[beta].sub.i] satisfying the following restrictions:

[[summation].sub.i][[alpha].sub.1] = 1; [[alpha].sub.ij] = [[alpha].sub.ji], [for all], j; [[summation].sub.j][[alpha].sub.ij] = 0; [[summation].sub.i][[beta].sub.i] = 0

Furthermore, it can be shown that c(P,u) can provide a second-order Taylor series approximation to an arbitrary cost function. (7)

However, when using the geometric Tornqvist price index formula (see Eq. (1)) to estimate consumers' cost of living, one is unable to directly identify the exact contribution of each individual commodity group to the total growth of the consumer's cost of living due to its non-additive index formula. Reinsdorf et al. (2002, p.5) have recently proved that any geometric mean index of price ratio [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be rewritten as the following additive formula: (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [P.sup.t] and [Q.sup.t] are the corresponding price and quantity vectors; the logarithmic mean function, m(a, b) is defined for positive a and b as (a-b)/(loga-logb), or as a if a = b; and where the additive weight

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Then, if we let [[sigma].sub.i] = ([s.sub.i.sup.0] + [s.sub.i.sup.1])/2, the above Tornqvist price index formula (Eq. (1)) can be expressed alternatively as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

where the additive weight

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

According to Eq. (4), the contribution of individual commodity group i to the level of the consumers' cost of living is determined by its corresponding aggregate weight [s.sub.i.sup.T] which is stated in terms determined by the average expenditure share that consumers have spent on it between the base and the current period together with price ratio ([P.sub.i.sup.1]/[P.sub.i.sup.0]). Therefore, a commodity group would contribute more to the total growth in the cost of living if it had a larger increase in its price level and consumers had spent more of their income on it. In the next section, our empirical analysis is based on the above transformed additive form of the Tornqvist price index formula.

We will also use the following Laspeyres price index formula to measure Taiwan consumers' cost of living over this period. (9) By comparing these results with the estimated results from the transformed Tornqvist price index, we will be able to evaluate the appropriateness of using the Laspeyres price index to measure Taiwan consumers' cost of living.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)

where the additive weight

[s.sub.i.sup.0] [equivalent to] [p.sub.i.sup.o][q.sub.i.sup.0]/ [[summation].sub.i][p.sub.i.sup.0][q.sub.i.sup.0].

III. EMPIRICAL RESULTS AND ANALYSIS

To calculate both the Tornqvist and Laspeyres price indexes used in the following empirical analysis, data on both Taiwan consumers' expenditure shares and prices are required. Data on commodity expenditure shares are taken from "The Survey of Family Income and Expenditure in Taiwan Area of the Republic of China, 1991 through 2006." The survey data, which includes expenditure data for more than 50 commodity groups, is on magnetic tape available from the Directorate-General of Budget, Accounting and Statistics (DGBAS), Executive Yuan, the Republic of China. For a detailed explanation about the number of sample household units and commodity groups contained in each survey year, please see APPENDIX 1. Data for [P.sub.it], are from 'The Monthly Commodity-Price Statistics in Taiwan Area of the Republic of China, 1991-2006 (1996=100), which includes price data for 42 commodity groups. This bulletin is also published by the DGBAS. Because of the somewhat different classifications of commodity groups in these two separate sets of data, we had to reclassify the data into 29 commodity groups in order to come up with a corresponding match for expenditure shares and commodity prices.

As seen in Table 1, the price levels of 22 out of 29 commodity groups in Taiwan over the period of 1991-2006 show increasing trends. Among them, price levels of seven commodity groups have increased more than 50% over the study period, these being the fruits (increased by 104.66%), the alcoholic (74.13%), the educational expense (73.44%), the medical care services (66.11%), the personal care services (55.81%), the supplementary food (53.42%), and the household keeping services (50.38%); next, except for four commodity groups i.e. the tobacco (increased by 45.94%), the transportation fees (40.05%), the oil and related services (38.79%) and the main food (31.62%), the price levels of all other commodity groups had increased less than 30% over the study period, ranging from 29.76% (for the food away from home) to 1.40% (for the entertainment expense). In general, the price levels of the service groups grew faster than those of the goods groups in Taiwan over this period. In addition, price levels of both the alcoholic and the tobacco had increased significantly mainly because of the change of tax systems imposed on them in 2002. At the same time, there are seven commodity groups whose price levels showed a declining trend over this period, four of which had price levels decreased by more than 10%. In particular, price levels of both the communication fees and the medical supplies and appliances had decreased more than 20%, -21.21% and -20.54%, respectively. Price levels of both the transportation equipment and the footwear had decreased by around 11%. The reduction of import tariff is one of the main causes for the reduction of price levels of most of the manufacturing commodity groups, e.g. the medical supplies and appliances and the transportation equipment. Furthermore, the deregulation of the telecommunications industry during this period accounted for the significant decline in price level of communication fees in Taiwan.

First, according to the Tornqvist price index computed by the additive Eq. (4), Taiwan consumers' cost of living had increased 29.93% with a yearly (compound average) growth rate of 1.76% over the period of 1991-2006 (1991=100), (see Table 2). If the Laspeyres price index were used instead, it would show that the level of Taiwan consumers' cost of living had increased by 31.89% with a yearly growth rate of 1.86% over the period of 1991-2006 (see Table 2). Comparison with the estimates from the Tornqvist price index shows that the Laspeyres price index had overestimated the total growth of Taiwan consumers' cost of living by 1.96 percentage points (or ppts), or by a yearly average by 0.1 ppts over the same period. This level of overestimated substitution bias obtained using the Laspeyres price index is consistent with previous studies in the literature. Recently, Reinsdorf and Triplett (2004) reviewed the BLS research on substitution bias against the Laspeyres price index and concluded that "... these studies show that a COLI (Cost of Living Index) computed from an approximation to the true utility function suggests a small amount of substitution bias, on the order of 0.1 - 0.2 points per year." (See Reinsdorf & Triplett, 2004, pp. 24-27; Moulton, 1996)

We move on now to analyze the contribution of each commodity group to the total growth of Taiwan consumers' cost of living over the study period. From the additive decomposition results listed in Table 3, we find that according to the estimates computed by the Tornqvist price index there are seven commodity groups whose contributions to the estimated total growth of Taiwan consumers' cost of living over this period (1991-2006) are all greater than 1.9 ppts. These are supplementary food (5.35 ppts), medical care services (4.89 ppts), educational expense (4.31ppts), residential rent (4.30 ppts), fruits (2.48 ppts), oil and related services (1.99 ppts) and food away from home (1.98 ppts). Together their contributions to the estimated total growth of Taiwan consumers' cost of living amount to 25.30 ppts or around 85% of the total growth level. The individual contributions of the remaining 22 commodity groups to the estimated total growth of the cost of living over this period are all much smaller in comparison with the above seven commodity groups, ranging from 0.85 ppts (for water, electricity and gas supply) to -0.57 ppts (for communication fees).

According Eq.(4), the amount which a commodity group contributes to growth in the cost of living will be determined together by how much its price has increased over the period, and its aggregate weight, which depends on the consumers' average expenditure shares on that commodity group between the base and the current periods. By examining the price increases and the corresponding aggregate weights (and the average expenditure shares) of all commodity groups, we notice that both the price increases and the corresponding aggregate weights of the above seven commodity groups were in general all much larger than the averages of all commodity groups. In particular, we find that the reason supplementary food made the largest contribution to the growth of cost of living over the period was because its price had increased by as high as 53.42%, and Taiwan consumers had spent around one-tenth of their total income on it. Similarly, both the medical care services and the educational expense had made the second and third largest contributions to the growth of cost of living for the same reason. The prices of the medical care services and the educational expense had increased by 66.11% and 73.44%, respectively; and Taiwan consumers had also spent a lot of their income on them, the aggregate weights for the medical care services and the educational expense were 7.39% and 5.87%, respectively. The price of the fruits had increased by 104.66%, the highest among all the commodities and was nearly twice of that of the supplementary food, however since its aggregate weight was about one-fourth of the latter, its contribution to the growth of the cost of living was only 2.48 ppts, about half of the contribution made by the supplementary food. The prices of the alcoholic, the personal care services and the household keeping services had all increased more than 50%, higher than that of most of commodity groups over the period, but their corresponding aggregate weights were all less than 1%. In other words, Taiwan consumers had spent relatively much less of their income on them, hence, their contributions to the overall growth in the cost of living were all less than 1 ppts, ranging from 0.74 ppts (for the personal care services) to 0.34 ppts (for the alcoholic) (see also tobacco and transportation fees).

On the other hand, although the price of the residential rent had only increased by 21.5%, its contribution to the growth in the cost of living was 4.3 ppts and was almost as large as that of the educational expense, mainly because Taiwan consumers had spent more than one-fifth of their total income on it over the study period. Similar to the residential rent, the prices of the oil and related services and the food away from home had increased moderately by 38.79% and 29.76%, however both had also made significant contributions to the growth of cost of living due to that Taiwan consumers had also spent relatively more of their income on them, and the aggregate weights for the oil and related services and the food away from home were 5.12% and 6.66%. Although the aggregate weight for the entertainment expense is 6.77%, which was even higher than that of the food away from home, however its price level had only increased by 1.4%, hence its contribution to the total growth of cost of living was only 0.09 ppts over the study period.

We further examine the composition of substitution bias through comparison of the contribution of each commodity group to the overall growth in the cost of living estimated from both the Laspeyres price index and the additive Tornqvist price index formulas. In general, we find that the substitution behavior did occur to most commodity groups with significant price changes over the study period (see Table 3, column (8)). In particular, strong substitution effects appeared in the following six commodity groups: supplementary food, fruits, educational expense, communication fees, main food, and, personal care services. Five of them had prices increased significantly above the average (29.55%, see Table 1), these five being fruits (price increased by 104.66%), educational expense (73.44%), personal care services (55.81%), supplementary food (53.42%), and main food (31.62%); the price for communication fees had decreased the most, by -21.21%. Without having taken the substitution effects caused by the above six commodity groups into consideration, Taiwan consumers' cost of living would have been overestimated by 4.38 ppts according to the Laspeyres price index over the study period. In particular, the contributions of supplementary food and fruits to the growth of Taiwan consumers' cost of living had been overestimated by the Laspeyres index by 1.88 ppts and 1.31 ppts, respectively.

On the other hand, the prices of medical care services and oil and related services had increased more than the average level over the sample period; nevertheless, Taiwan consumers had increased, rather than decreased, their shares of expenditure on them. As a result, according to the Laspeyres price index, these two commodity groups together had underestimated Taiwan consumers' cost of living by 2.54 ppts in comparison with estimates made by the Tornqvist price index; in particular, medical care services alone had underestimated Taiwan consumers' cost of living by 2.08 ppts over the sample period. One possible explanation might be that Taiwan consumers' preference on these commodity groups may have changed over the study period.

IV. CONCLUSIONS

In this paper we have utilized the additive Tornqvist price index formula to analyze the growth of Taiwan consumers' cost of living and its contributing factors over the period of 1991-2006. In addition, we have also evaluated the appropriateness of using the Laspeyres price index to measure Taiwan consumers' cost of living over this period. We have reached the following important conclusions.

First of all, according to the estimates from the Tornqvist price index, Taiwan consumers' true cost of living had grown 29.93% over the period of 1991-2006 (1991=100) with an average yearly growth rate of 1.76%. Furthermore, we found that nearly 85% of the total growth of cost of living derived mainly from seven commodity groups, these being supplementary food (5.35 ppts), medical care services (4.89 ppts), educational expense (4.31ppts), residential rent (4.30 ppts), fruits (2.48 ppts), oil and related services (1.99 ppts) and food away from home (1.98 ppts). The main reason was that both the price increases and the corresponding aggregate weights of the above seven commodity groups were in general all much larger in comparison with the average of all commodity groups over this period. In particular, supplementary food had made the largest contribution to the growth of cost of living over the period because its price had increased by as high as 53.42%, and Taiwan consumers had spent around one-tenth of their total income on it. Similarly, both the medical care services and the educational expense had made the second and third largest contributions to the growth of cost of living for the same reason. The price of the fruits had increased by 104.66%, the highest among all the commodities, and was nearly twice of that of the supplementary food, however since its aggregate weight was about one-fourth of the latter, its contribution to the growth of the cost of living was only 2.48 ppts, about half of the contribution made by the supplementary food. The individual contributions of the remaining 22 commodity groups to the estimated total growth of the cost of living over this period are all much smaller in comparison with the above seven commodity groups, ranging from 0.85 ppts (for water, electricity and gas supply) to -0.57 ppts (for communication fees).

Next, a comparison of the Tornqvist and Laspeyres price index estimates suggests that the Laspeyres price index had overestimated the growth of Taiwan consumers' cost of living by 1.96 ppts or in yearly average by 0.1 ppts over the sample period. The above finding is consistent with previous studies in the literature (see Reinsdorf & Triplett, 2004; Moulton, 1996). Without having taken the substitution effect caused by the price changes into consideration, six commodity groups, whose prices had changed significantly over the period, had together overestimated Taiwan consumers' cost of living by 4.38 ppts, according to the Laspeyres price index; in particular, in the supplementary food and fruits, the Laspeyres price index had overestimated Taiwan consumers' cost of living by 1.88 ppts and 1.31 ppts, respectively. On the other hand, the prices of medical care services and oil and related services had increased more than the average level over the study period; nevertheless, Taiwan consumers had increased, rather than decreased, their shares of expenditure on them. As a result, according to the Laspeyres price index, these two commodity groups together had underestimated Taiwan consumers' cost of living by 2.54 ppts in comparison with estimates made by the Tornqvist price index; in particular, medical care services alone had underestimated Taiwan consumers' cost of living by 2.08 ppts over the sample period. One possible explanation might be that Taiwan consumers' preference on these commodity groups may have changed over the study period.

Following the suggestion of the well-known Boskin Commission Report (1996, p. iii), which had recommended "that the CPI (Consumer Price Index) should move toward a COLI (Cost Of Living Index) concept by adopting a "superlative" index formula to account for the changing market baskets," (10) in August of 2002, the U.S. Bureau of Labor Statistics started to officially publish another new consumer price index, called Chained Consumer Price Index for All Urban Consumers or C-CPI-U, which is basically computed using the Tornqvist superlative price index formula. The new measure is designed to be a closer approximation to a cost of living index than the existing BLS measure (see Cage, Greenlees and Jackman (2003)). Recently, Triplett (2001, F331) had strongly contended that "the theory of the cost-of-living index does provide the underlying conceptual rationale for constructing a practical CPI." Furthermore, using the Laspeyres price index (or other fix-basket price indexes) in constructing a CPI will cause substitution bias in measurement. More importantly, Triplett (2003) argued that the Laspeyres price index (or any other fix-basket price index) fails to provide an underlying conceptual framework for resolving measurement issues within CPI detailed component indexes. Based on our empirical study, we would also like to suggest to the Price Statistics Department in Taiwan that it is about time for them to consider compiling and publishing an alternative consumer price index (CPI) using the Tornqvist price index in Taiwan.
APPENDIX 1
Sample units and detailed commodity groups included in
"The Survey of Family Income and Expenditure in Taiwan Area
of the Republic of China, 1991 through 2006."

Year Sample units Detailed commodity
 (Households) groups

1991 16,434 61
1992 16,434 61
1993 16,434 65
1994 16,434 50
1995 14,706 50
1996 13,702 51
1997 13,701 51
1998 14,031 51
1999 13,801 51
2000 13,801 51
2001 13,601 51
2002 13,681 51
2003 13,681 51
2004 13,681 51
2005 13,681 51
2006 13,776 51


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ENDNOTES

(1.) To name just a few of such public policies: income tax exemptions and tax bracket adjustments; inheritance and gift tax exemptions and tax bracket adjustments; land price adjustments for land value increment tax; and adjustments of the basic (minimum) wage.

(2.) Conceptually "substitution bias" can be divided into the "upper level substitution bias" and "lower level substitution bias." The "substitution bias" discussed in this paper is referred to the "upper level substitution bias," that occurs among basic commodity groups of the index (in the following analysis we have considered 29 commodity groups). In contrast to the former, the "lower level substitution bias" occurs between the detailed items and varieties within a specific commodity group.

(3.) In fact, the bias caused by using the CPI to estimate consumer's true cost of living is not limited to substitution bias only, other biases such as outlet substitution bias, new product and quality change bias would also occur. According to the Boskin Commission's Report (See Boskin et al., 1996), the U.S. CPI in 1995-96 was upward biased by 1.1 percentage points per year, and 0.15 percentage points was contributed by the upper-substitution bias. (See Boskin, et al., (1996)). Recently Lebow & Rudd (2003) have updated the study about the upward bias regard to U.S. CPI and concluded "that the CPI likely overstates the rate of increase in the "true" cost of living by about 0.9 percentage points per year." (See Lebow & Rudd (2003, p.192)) Furthermore, their study also indicated that the total bias in CPI contributed by the "upper level substitution bias" and the "lower level substitution bias" were 0.3 and 0.05 percentage points, respectively, and the rest was contributed by the outlet substitution bias, new product and quality change bias (Also see Gordon (2006)).

(4.) The economic price index number formula theory began with Byushgens (1925) and Konyus & Byushgens (1926) (See Diewert (1997, p.130)).

(5.) Two most widely used superlative price indexes, as strongly recommended by Diewert (1976, 1997) are the Tornqvist price index and the Fisher ideal price index (Also see Hill (2006)).

(6.) Beginning from 2002 (August), the U.S. Bureau of Labor Statistics started to officially publish another brand new consumer price index, called Chained Consumer Price Index for All Urban Consumers or C-CPI-U, which is basically computed using the Tornqvist superlative price index formula (see Cage, Greenlees & Jackman (2003)).

(7.) In addition, it can be shown if all of the?i = 0, and?00 = 0, then C(p,u) =u* c(p) becomes a unit cost or expenditure function, and we have homothetic preferences. Diewert (1976, p.121) has shown that the Tornqvist price index is also exact for a Translog unit cost function c(p). Diewert (1976, p.123) first pointed out the possibility that "the same price index PP 0 is exact for more than one functional form (and reference utility level) for the true cost of living."

(8.) Other alternative additive decomposition approaches for the Tornqvist and Fisher indexes had been proposed and compared in the literature. (See Hallerbach (2005); Balk (2004); and Dumagan (2002)).

(9.) Alternatively, Laspeyres price index can be treated as an exact price index by assuming that consumer has fixed coefficient Leontief-type preference structure.

(10.) The Boskin Commission's Report (See Boskin et al., 1996, p. iii) had recommended "that the CPI (Consumer Price Index) should move toward a COLI (Cost Of Living Index) concept by adopting a "superlative" index formula to account for the changing market baskets." This recommendation has recently been reaffirmed by the National of Sciences on Conceptualizing and Measuring Cost-of-Living and Price Indexes (known as the CNSTA) report that "The BLS should publish, contemporaneous with the real-time CPI, an advance estimate of the superlative index, utilizing either a constant--elasticity--of--substitution method or some other method." (See National Research Council, 2002, p.6).

Pang-Tien Lieu (a), Jui-Hui Chen (b), and Chih-jung Chang (c)

(a) Associate Professor, Department of Business Administration National Taiwan University of Science and Technology No. 43 Keelung Road, Section 4, Taipei, Taiwan. lieu@ba.ntust.edu.tw

(b) Assistant Professor, Department of Finance, China University of Technology No. 56, Hsing Lung Road, Section 3, Taipei, Taiwan. Jay95018@cute.edu.tw

(c) Assistant professor, Department of Finance, Vanung University No.1, Van-Nung Rd. Chung-Li, Tao-Yuan, Taiwan jrchang@msa.vnu.edu.tw
Table 1
Consumer price indexes for 29 commodity groups in Taiwan area,
1992-2006 (1991=180)

Commodity groups 1992 1996 2001

1. Main food 100.94 116.86 122.19
2. Supplementary food 111.10 134.30 133.28
3. Fruits 125.90 173.28 178.43
4. Dairy 101.17 105.34 114.73
5. Alcoholic 99.59 104.30 114.72
6. Non-alcoholic 102.31 105.70 102.85
7. Food away from home 103.11 117.23 126.80
8. Garments 101.60 102.63 96.34
9. Footwear 100.83 99.98 87.74
10. Apparel services and
 accessories 98.57 110.79 104.29
11. Residential rent 104.30 120.55 124.51
12. Maintenance and repairs 103.67 126.66 120.53
13. Household appliances 100.11 108.47 102.28
14. Household keeping
 services 104.70 132.05 152.36
15. Water, electricity and gas
 supply 102.01 107.71 114.47
16. Transportation equipment 97.86 100.90 96.12
17. Oil, parts and related
 services 99.07 102.54 116.91
18. Transportation fees 100.33 121.98 137.14
19. Communication fees 100.77 97.08 85.63
20. Medical care services 107.04 114.77 137.51
21. Medicines and health food 103.08 109.64 113.76
22. Medical supplies and
 appliances 99.19 100.40 86.10
23. Educational expense 107.12 143.27 172.94
24. Entertainment expense 101.42 106.77 106.77
25. Tobacco 100.09 104.38 106.78
26. Cosmetic items 99.34 102.21 102.28
27. Personal care services 106.52 137.93 153.86
28. Wedding and funeral
 expense 101.23 112.02 124.15
29. Others 102.63 109.30 114.20
Average 104.46 119.62 124.47

 Growth rate (%)
Commodity groups 2006 (1991-2006)

1. Main food 131.62 31.62
2. Supplementary food 153.42 53.42
3. Fruits 204.66 104.66
4. Dairy 120.58 20.58
5. Alcoholic 174.13 74.13
6. Non-alcoholic 112.35 12.35
7. Food away from home 129.76 29.76
8. Garments 97.29 -2.71
9. Footwear 88.72 -11.28
10. Apparel services and
 accessories 112.84 12.84
11. Residential rent 121.50 21.50
12. Maintenance and repairs 128.34 28.34
13. Household appliances 97.54 -2.46
14. Household keeping
 services 150.38 50.38
15. Water, electricity and gas
 supply 122.44 22.44
16. Transportation equipment 88.14 -11.86
17. Oil, parts and related
 services 138.79 38.79
18. Transportation fees 140.05 40.05
19. Communication fees 78.79 -21.21
20. Medical care services 166.11 66.11
21. Medicines and health food 120.31 20.31
22. Medical supplies and
 appliances 79.46 -20.54
23. Educational expense 173.44 73.44
24. Entertainment expense 101.40 1.40
25. Tobacco 145.94 45.94
26. Cosmetic items 99.61 -0.39
27. Personal care services 155.81 55.81
28. Wedding and funeral
 expense 122.05 22.05
29. Others 112.91 12.91
Average 129.55 29.55

Note: In the table we have only reported consumer price indexes
for 29 commodity groups of every-five year over the study
period. The consumer price indexes of all years are available
from the authors upon request.

Data source: Commodity-Price Statistics Monthly in Taiwan Area
of the Republic of China

Table 2
Estimates of Taiwan consumers' cost of living based on
[P.sup.T] and [P.sup.L], 1991-2006

 Tornqvist price index ([P.sup.T])
Year
 Yearly growth
 Index rate
 (1991=100) (%)

1991 100 --
1992 104.59 4.59
1993 107.49 2.77
1994 111.49 3.72
1995 115.40 3.51
1996 118.70 2.85
1997 119.89 1.00
1998 122.06 1.81
1999 122.32 0.22
2000 123.98 1.36
2001 124.04 0.05
2002 123.26 -0.63
2003 123.35 0.07
2004 125.58 1.81
2005 128.91 2.65
2006 129.93 0.79

Annual compound 1.76%
growth rate (%)

 Laspeyres price index ([P.sup.L])
Year
 Yearly growth
 Index rate
 (1991=100) (%)

1991 100 --
1992 104.76 4.76
1993 107.82 2.92
1994 112.30 4.15
1995 116.48 3.73
1996 119.99 3.01
1997 121.03 0.87
1998 123.76 2.25
1999 123.82 0.05
2000 125.42 1.28
2001 125.32 -0.07
2002 124.42 -0.72
2003 124.18 -0.20
2004 126.99 2.26
2005 131.25 3.36
2006 131.89 0.49

Annual compound 1.86%
growth rate (%)

Table 3
The additive decomposition of total growth rate of Taiwan
consumers' cost of living (1991-2006) based on [P.sup.T]
and [P.sup.L]

Commodity groups Price
 growth Tornqvist
 rate price index ([P.sup.T])

 (1991-2006) [S.sub.i.sup.T] components

 (1) (2) (3)-(1)x(2)

1. Main food 31.62 2.47 0.78

2. Supplementary 53.42 10.02 5.35
 food

3. Fruits 104.66 2.37 2.48

4. Dairy 20.58 1.12 0.23

5. Alcoholic 74.13 0.46 0.34

6. Non-alcoholic 12.35 1.57 0.19

7. Food away from 29.76 6.66 1.98
 home

8. Garments -2.71 4.20 -0.11

9. Footwear -11.28 1.15 -0.13

10. Apparel 12.84 0.74 0.09
 services and
 accessories

11. Residential rent 21.50 20.00 4.30

12. Maintenance 28.34 1.16 0.33
 and repairs

13. Household -2.46 3.09 -0.08
 appliances

14. Household 50.38 1.10 0.55
 keeping services

15. Water, 22.44 3.77 0.85
 electricity and
 gas supply

16. Transportation -11.86 2.29 -0.27
 equipment

17. Oil, parts and 38.79 5.12 1.99
 related services

18. Transportation 40.05 1.31 0.53
 fees

19. Communication -21.21 2.67 -0.57
 fees

20. Medical care 66.11 7.39 4.89
 services

21. Medicines and 20.31 1.14 0.23
 health food

22. Medical -20.54 0.35 -0.07
 supplies and
 appliances

23. Educational 73.44 5.87 4.31
 expense

24. Entertainment 1.40 6.77 0.09
 expense

25. Tobacco 45.94 1.01 0.47

26. Cosmetic items -0.39 1.94 -0.01

27. Personal care 55.81 1.32 0.74
 services

28. Wedding and 22.05 0.72 0.16
 funeral expense

29. Others 12.91 2.21 0.29

Total growth rate, 29.93
1991-2006

Commodity groups Laspeyres
 price index index ([P.sup.L])

 [S.sub.i.sup.0] components

 (4) (5)-(1) x (4)

1. Main food 3.38 1.07

2. Supplementary 13.54 7.23
 food

3. Fruits 3.62 3.79

4. Dairy 1.16 0.24

5. Alcoholic 0.60 0.44

6. Non-alcoholic 1.58 0.20

7. Food away from 5.87 1.75
 home

8. Garments 4.98 -0.13

9. Footwear 0.97 -0.11

10. Apparel 0.89 0.11
 services and
 accessories

11. Residential rent 20.04 4.31

12. Maintenance 1.30 0.37
 and repairs

13. Household 3.15 -0.08
 appliances

14. Household 1.19 0.60
 keeping services

15. Water, 4.04 0.91
 electricity and
 gas supply

16. Transportation 2.46 -0.29
 equipment

17. Oil, parts and 3.94 1.53
 related services

18. Transportation 1.61 0.64
 fees

19. Communication 1.03 -0.22
 fees

20. Medical care 4.24 2.80
 services

21. Medicines and 0.99 0.20
 health food

22. Medical 0.24 -0.05
 supplies and
 appliances

23. Educational 6.37 4.68
 expense

24. Entertainment 6.45 0.09
 expense

25. Tobacco 1.27 0.58

26. Cosmetic items 1.60 -0.01

27. Personal care 1.67 0.93
 services

28. Wedding and 0.76 0.17
 funeral expense

29. Others 1.05 0.14

Total growth rate, 31.89
1991-2006

Commodity groups Substitution Bias

 [S.sub.i.sup.0]
 -
 [S.sub.i.sup.T] components

 (6)=(4)-(2) (7)=(5)-(3)

1. Main food 0.91 0.29

2. Supplementary 3.52 1.88
 food

3. Fruits 1.25 1.31

4. Dairy 0.04 0.01

5. Alcoholic 0.14 0.10

6. Non-alcoholic 0.01 0.00

7. Food away from -0.79 -0.23
 home

8. Garments 0.78 -0.02

9. Footwear -0.18 0.02

10. Apparel 0.15 0.02
 services and
 accessories

11. Residential rent 0.04 0.01

12. Maintenance 0.14 0.04
 and repairs

13. Household 0.06 -0.00
 appliances

14. Household 0.09 0.05
 keeping services

15. Water, 0.27 0.06
 electricity and
 gas supply

16. Transportation 0.17 -0.02
 equipment

17. Oil, parts and -1.18 -0.46
 related services

18. Transportation 0.30 0.12
 fees

19. Communication -1.64 0.35
 fees

20. Medical care -3.15 -2.08
 services

21. Medicines and -0.15 -0.03
 health food

22. Medical -0.11 0.02
 supplies and
 appliances

23. Educational 0.50 0.36
 expense

24. Entertainment -0.32 -0.00
 expense

25. Tobacco 0.26 0.12

26. Cosmetic items -0.34 0.00

27. Personal care 0.35 0.19
 services

28. Wedding and 0.04 0.01
 funeral expense

29. Others -1.16 -0.15

Total growth rate, 1.96
1991-2006
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Author:Lieu, Pang-Tien; Chen, Jui-Hui; Chang, Chih-jung
Publication:International Journal of Business
Date:Jan 1, 2009
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