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Mick Silver and Saeed Heravi
The Consumer Price Index Manual (2004) provides guidelines for aggregation formulas that are promulgated at IMF training courses and technical assistance missions. This paper develops elementary level aggregation theory to better inform users and compilers. Most countries use either the Dutot or Jevons index formula. These formulas generally give different results; advice on choice of formula matters. Using an approach based on sample estimators, and an illustration based on scanner data, the paper shows how differences in these formulas can be explained by changes in price dispersion and, in turn, by product heterogeneity. Implications for choice of formula are considered.
Mick Silver and Saeed Heravi

section of the paper uses highly detailed scanner data from retailers’ barcode readers that amount to about 31,000 observations over 24 months on prices, characteristics, and brands of models of television sets (TVs) sold in different outlet types. The focus of the paper is on the difference between two lower-level formulas—the ratio of unweighted arithmetic means of prices (Dutot index) and the ratio of unweighted geometric means (Jevons index). Both formulas are commonly used, both can be justified under particular circumstances, but they can give quite different

International Monetary Fund

0 , p 0 ) . ( 21.5 ) This index number formula was first suggested by Fisher ( 1922 , p. 472) as his formula 101. Fisher also observed that, empirically for his data set, P CSW was very close to the Jevons index P J , and these two indices were his best unweighted index number formulas. In more recent times, Carruthers, Sellwood, and Ward ( 1980 , p. 25) and Dalén ( 1992 , p. 140) also proposed P CSW as an elementary index number formula. 21.31 Now that the most commonly used elementary

International Monetary Fund. Research Dept.

five years. A defining feature of these elementary indices is that they are unweighted. For CPI compilation there are three main aggregation methods used at the elementary level: the arithmetic mean of price changes (the Carli index), the change in arithmetic mean prices (the Dutot index), and the geometric mean of price changes, equal to the change in geometric means (the Jevons index). All three formulas have some intuition. Axiomatic index number theory clearly shows Carli to be biased and chained Carli, substantially so—the annual change in the CPI for Kenya

International Monetary Fund. Statistics Dept.
This Technical Assistance Report on Suriname constitutes technical advice provided by the staff of the IMF to the authorities of Suriname in response to their request for technical assistance. The mission discussed issues concerning the consumer price index (CPI), the producer price index (PPI) and export price index (XPI). On the CPI, the mission reviewed current practices and provided some recommendations. The main recommendations are to switch from a Dutot to a Jevons index on the elementary aggregate level and to start publishing the CPI according to the Classification of Individual Consumption according to Purpose on a class level provided the number of items permits. On the planned PPI and XPI, the discussion focused on available data sources and next steps for developing a PPI for Suriname. Reliable price statistics are essential for informed economic policymaking by the authorities. They also provide the private sector, foreign investors, rating agencies, and the public in general with important inputs in their decision-making, while informing both domestic economic policy and IMF surveillance.
International Monetary Fund. Statistics Dept.

mission reviewed current practices and provided some recommendations. The main recommendations are to switch from a Dutot to a Jevons index on the elementary aggregate level and to start publishing the CPI according to the Classification of Individual Consumption according to Purpose (COICOP) on a class level provided the number of items permits. On the planned PPI and XPI, the discussion focused on available data sources and next steps for developing a PPI for Suriname. Reliable price statistics are essential for informed economic policy-making by the authorities

Brian Graf

.45 4.45 5.32 4.84 L-T Price Relative 1.000 0.970 0.936 1.046 0.920 0.920 1.100 1.000 S-T Price Relative 0.970 0.965 1.117 0.880 1.000 1.196 0.909 Jevons Index (L-T ratio of geometric mean prices) 100.0 96.3 92.4 105.6 91.7 91.7 110.0 100.0 Dutot Index (L-T ratio of arithmetic mean prices) 100.0 97.0 93.6 104.6 92.0 92.0 110.0 100

Mick Silver and Saeed Heravi

Front Matter Page Statistics Department Authorized for distribution by Adriaan M. Bloem Contents I. Introduction II. Elementary Index Number Formulas, Their Use and Justification A. Elementary Index Number Formulas B. Their Use and Justification III. Differences Between the Jevons and Dutot Formulas A. Jevons, Dutot and Price Dispersion B. Jevons and Dutot Indexes and Hedonic Heterogeneity-Controlled Price Dispersion IV. Empirical Work A. Data and Variables B. Dutot and Jevons Indexes C. Heterogeneity-Controlled Dutot

International Monetary Fund

.25 113.21 100.07 Chained month-to-month index 100.00 112.50 122.54 124.81 113.89 128.93 129.02 Direct index on January 100.00 112.50 125.60 132.50 100.00 113.21 110.00 Dutot index—Ratio of arithmetic mean prices Month-to-month index 100.00 105.00 104.76 100.00 90.91 106.00 103.77 Chained month-to-month index 100.00 105.00 110.00 110.00 100.00 106.00 110.00 Direct index on January 100.00 105.00 110.00 110.00 100.00 106.00 110.00 Jevons index—Geometric mean

International Monetary Fund

index, defined as the ratio of the unweighted arithmetic mean prices: The third is the Jevons index, defined as the unweighted geometric mean of the price relative or ratio which is identical to the ratio of the unweighted geometric mean prices: I D 0 : t = 1 n Σ p i t 1 n Σ p i 0 ( 9.2 ) I j 0 : t = Π ( p i t p i 0