I S S N 統計学第 108 号 1 16 GDP GDP

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1 I S S N 統計学第 108 号 1 16 GDP GDP

2 CPI Consumer Price Index CPI CPI Lower Level of AggregationUpper Level of Aggregation 2 CPI suzuki-t@rikkyo.ac.jp 1 The advisory commission

3 2 Cost ofliving IndexCOLI CPI CPI G7 EU Harmonized Index of Consumer Prices HICPs CPIs HICPs HICPs Eurostat2013 Dutot Jevons 3 CPI CPI CPI CPI CPI 2 17

4 CPI 2010 CPI n tij,, = Ptijk,,, n k = 1 P tij kn 3 P 1 = P 0,, ij tij,, Mij, t 0M tij P 0, ij, Σ P w = Σ w t tij,, tij,, t tij,, w n P Σk= 1 Ptijk,,, tij,, Iij, = = n P 1 0, ij, ΣtPtij,, M ij, I Σ Σ i= 1 j= 1 tij,, 0, ij, t = Σi= 1Σj= 1 p0, ij, q0, ij, Σ Σ p p tij,, i= 1 j= 1 0, ij, p0, ij, i= 1 j= 1 0, ij, 100 = 100 Σ Σ w q w Ipq wpq ij0 t CPI

5 位集計下位集計上 Carli DutotJevons Carli Dutot Jevons 19

6 Carli I C n t 1 p i = 0 n i= 1 pi Dutot t pi Σ t n Σpi I D = = 0 0 pi Σ pi Σ n Jevons I J 1 1 n t t n n p i Π( pi) 0 1 i= 1 pi 0 n Π( pi ) = = G CPI Dutot CPI Dutot Jevons G Jevons Carli 8 Carli The advisory commission1996bls1997 BLS Dutot Carli EU Carli Dutot Eurostat2013 Dutot Jevons 9 Jevons 12 Dutot Carli 10 Dutot Dutot CPI CPI 11 CPI Dutot CPI HICPs Dutot 20

7 Dutot Carli CPI 1 1 Carli Carli Carli Dutot Carli EU Dutot EU HICPs Carli Dutot Jevons CPI CPIThe advisory commission1996 CPI CPI Cost of Goods Index COGI COLI CPI CPI COLI 12 COLI CPI CPI

8 ILO2014 The advisory commission1996 CPI 2 22

9 CPI 2 Carli Dutot Jevons ILO Fisher The advisory commission1996 CPI BLS Stigler et al The advisory commission

10 Diwert 2 q A q B A B 0t l l CPI COLI COLI A A A B m n q t A q t B C D q 0 A q 0 B m C n C n s C C C s COLI m C n C n r E s r m n E 0 D C I I O 0 24

11 CPI 25

12 A 2 2 A A A B A B a b A B A B a b A B A B a b A A A B AB AB AB

13 B B A B ab 3 A COLI CPI COLI 2 CPI COGI COLI 27

14 COGI a LaspeyresPaasche Lowe elementary aggregate 2007ap.4 2 The advisory commission The advisory commission1996 BLS1997 BLS a 3 Eurostat2013p p G7CPI Eurostat2013p ILO G7 CPI G CPI COLI 2014b p

15 CPI 2010p ILO2014pp BLS1997p Paasche Lowe ILO2014p.3 P LO Σ i = 1 pq i i 0 b pq i i n t b Σ b 0 t PaaschePaasche n t t Σ i = 1 pq i i PP Σ 0 t pq Paasche COLI COLI i i CPI CPI CPI aCPI BLS b CPI

16 No a b Bureau of Labor Statistics 1997, Measurement Issues In The Consumer Price Index. 20Bureau of Labor Statistics 2007, BLS Handbook of Methods, Chapter 17. Consumer price index, updated 2007http:// 2014/10/08 21Eurostat 2013, Compendium of HICP reference documents, methodology/compendium. 2015/03/06 22Eurostat 2004, Harmonized Indices of Consumer Prices HICPsA Short Guide for Users, ec.europa.eu/eurostat/web/productsmanualsandguidelines//ksbe /03/06 23ILO 2014, Consumer Price Index Manual : Theory and Practice, First Published Mcclelland, R Evaluating Formula Bias in Various Indexes Using Simulations, Bureau of Labor Statistics Working Paper Moulton, B.R A Comparison of Estimators for Elementary Aggregates of The CPI, To be presented at Western Economic Association International Conference, San Diego, CA, July 7, Schultze, C. and Mackie, C. 2002, At What Price?: Conceptualizing and Measuring CostofLiving and Price Indexes, The National Academies Press. 27Shapiro, M.D. and D.W. Wilcox 1997, Alternative strategies for aggregating prices in the CPI, ReviewFederal Reserve Bank of St. Louis, Vol. 79, No Shapiro, M.D. and D.W. Wilcox 1996, Mismeasurement in the Consumer Price Index: An Evaluation, NBER Macroeconomics Annual 1996, Volume Stigler, G.J. Chairman1961, The Price Statistics of the Federal Government, New York: National Bureau of Economic Reserch. 30The Advisory Commission To Study The Consumer Price Index 1996, Toward A More Accurate Measure Of The Cost Of Living, Final Report. 9 14http:// 2014/10/08 30

17 The Relationship between Price Variation and Bias in the Lower Level of Aggregation Suzuki TAKAHIRO The CPI is constructed in two stages, namely the lower level of aggregation and the upper level of aggregation. In these two stages, the upper level substitution bias and the lower level substitution bias are caused by not reflecting the consumers substitute across item categories or across items within an item category. Because the Laspeyres index formula, used in the upper level, holds the market basket fixed at base period quantities, the overstatement or understatement of weights incurs the upper level substitution bias upward biasthe lower level substitution bias differs from that in the upper level in two points. First, the bias in the lower level does not be caused by putting too much too littleweight on the relatively more expensive cheaperitems. Second, the calculated subindex overstates the index which accounts for consumers substitute when the relative price of item increases. The calculated subindex understates the index which accounts for consumers substitute when the relative price of item decreases. Consumer Price Index, Lower Level of Aggregation, Lower Level Substitution Bias, CostofLiving Index Graduate School Department of Economic Research, Rikkyo University. 31

CPI CPI CPI CPI 2008 CPI Goodhart 2001 CPI 2008a CPI Beatty et al CPI CPI CPI Beatty and Larsen 2005 Larsen 2007 CPI 2006a b

CPI CPI 1997 ~ 2010 1 2 CPI 3 4 2010 12 CPI Consumer Price Index CPI 837 100872 010-82500319 sunwk@ ruc. edu. cn CF40 09&ZD019 09&ZD018 10YJA790271 8 87 CPI CPI CPI CPI 2008 CPI Goodhart 2001 CPI 2008a

I S S N 統計学 第 108 号 1 16 GDP GDP

I S S N 統計学第 108 号 1 16 GDP GDP