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2010 | OriginalPaper | Buchkapitel

Retrospective Approximations of Superlative Price Indexes for Years Where Expenditure Data Is Unavailable

verfasst von : Jan de Haan, Bert M. Balk, Carsten Boldsen Hansen

Erschienen in: Price Indexes in Time and Space

Verlag: Physica-Verlag HD

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Abstract

CPIs are typically fixed-weight or Lowe indexes. Several statistical agencies have recently been experimenting with retrospective computations of superlative price index numbers, to provide information on (upper level) substitution bias of their CPIs. This obviously requires expenditure data of all the periods compared. However, detailed expenditure data are often available only for fairly distant benchmark years, particularly for the “weight-reference periods” of consecutive CPI series. This chapter addresses the question of how to approximate a consistent time series of annual superlative price index numbers such that use is made of all the available data. We consider various approximation methods, all of which are based on linear combinations of expenditure shares from benchmark years. The methods are illustrated on a data set consisting of the elementary aggregate price index numbers and expenditure weights that have been used for the computation of the official Danish CPI from 1996 to 2006. We also compare the resulting index numbers with Lloyd–Moulton index numbers.

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Vorheriges Kapitel Are Integration and Comparison Between CPIs and PPPs Feasible?

Nächstes Kapitel Harmonized Cross Region and Cross Country CPI Time-Space Integration in the Euro-Zone

The Lloyd–Moulton index is a generalized mean of order \(1 - \sigma\), which is strictly increasing in \(1 - \sigma\) and thus strictly decreasing in \(\sigma\). Its “current-weight counterpart” can be written as the inverse of a generalized mean of order \(1 - \sigma\) and is thus strictly increasing in \(\sigma\). The solution \(\sigma ^{0t}\) must be obtained by some numerical method.

Yet, not all the superlative price indexes are necessarily numerically similar. The problem is that “as the parameter r increases in absolute value, the superlative price (quantity) index number formula becomes increasingly sensitive to outliers in the price-relatives (quantity-relatives) distribution” (Hill, 2006, p. 38). Anyway, for small absolute values of r, which is the usual case, we do expect small numerical differences between different superlative indexes.

Balk (2000) addressed substitution effects as well as the treatment of new and disappearing goods in a nested CES price index. See De Haan (2005), Melser (2006) and Ivancic (2007) for empirical evidence on these topics at the lower aggregation level.

This subsection draws heavily from an unpublished paper by Balk (1990a).

All indexes are “forward looking”; they are going from benchmark year 0 to year t. Retrospectively we could also calculate “backward looking” indexes going from benchmark year T to year t; see also Triplett (1989b). Given some approximation method, the product of the forward looking index going from 0 to t and the inverse of the backward looking index going from T to t will in general not be equal to the index going from 0 to T.

In some countries the CPI is a Young index, which results from replacing the price-updated expenditure shares in (17) by the actual shares of period 0. A Young index can be interpreted in different ways. For example, statistical agencies computing a Young index may target at a Laspeyres index with price and weight reference period b and use the period 0 shares as estimates of the period b shares. Essentially they assume that the elasticity of substitution between any two commodities is equal to 1. In Denmark the Young CPI is interpreted as an approximation of the (superlative) Walsh index (Boldsen Hansen, 2006, 2007). In Sect. 6 we present evidence for Denmark on the value of the elasticity of substitution.

Unfortunately their description is not entirely clear on this point. Quarterly index numbers can indeed be calculated using (27). However, the computation of quarterly or monthly (approximate) superlative indexes may not be very useful as seasonality disturbs their interpretation. Diewert (2000) discusses the problems faced when constructing annual superlative index numbers using monthly price data. The US Bureau of Labor Statistics publishes an experimental monthly superlative index (see Cage et al., 2003).

It should be mentioned that “in some cases adjustments were made to reflect quantity changes since 2003/2004” (Nimmo et al., 2007, p. 4).

For a discussion of the substitution bias of a Lowe price index, see Balk and Diewert (2004).

As will be explained in Sect. 6, our data have been adjusted to account for such changes.

The resulting 444 elementary aggregates account for over 98% of the total CPI weight. Boldsen Hansen (2007) has shown that re-calculating the Danish (Young) CPI with this data set produces index numbers that differ only marginally from the officially published figures.

These figures are in between the estimates of 0.2%-points per year on average by Shapiro and Wilcox (1997) for the US and 0.1 %-points per year by Balk (1990b) and De Haan (1999) for the Netherlands. The differences will be partly due to differences in the aggregation level. The Dutch figures are based on approximately 100 product categories, the US figures on more than 9,000 item-area strata.

Balk (1990a) employed Triplett’s (1989a) US data on office, computing and accounting machinery for 1972–1986. This data set had four benchmark (weight-reference) years, 1972, 1977, 1982, and 1986, so that there were three sub-periods: 1972–1977, 1977–1982, and 1982–1986. For the first sub-period the TGFI method actually yielded greater index numbers than the natural and Quasi Fisher methods, whereas for the second and third sub-periods the TGFI method produced smaller index numbers. Thus, though there are reasons to expect that the TGFI method in “normal circumstances” generates downward biased index numbers, this is not necessarily the case.

This is what Nimmo et al. (2007) apparently did (see footnote 8).

Balk, B. M. (1990a). Approximating a superlative price index when not all quantity data are available (Research paper, BPA no. 6236-90-E7). Voorburg: Statistics Netherlands.

Balk, B. M. (1990b). On calculating cost-of-living index numbers for arbitrary income levels. Econometrica, 58, 75–92.CrossRef

Balk, B. M. (2000). On curing the CPI’s substitution and new goods bias (Research paper 0005). Voorburg: Department of Statistical Methods, Statistics Netherlands.

Balk, B. M., & Diewert, W. E. (2004). The Lowe consumer price index and its substitution bias (Discussion Paper No. 04-07). Vancouver: Department of Economics, University of British Columbia.

Boldsen Hansen, C. (2006, May 10–12). Price-updating of weights in the CPI. Paper presented at the Joint ECE/ILO meeting on Consumer Price Indices, Geneva.

Boldsen Hansen, C. (2007, October 9–12). Recalculations of the Danish CPI 1996–2006. Paper presented at the tenth meeting of the Ottawa Group, Ottawa.

Cage, R., Greenlees J., & Jackman P. (2003, May 27–29). Introducing the chained consumer price index. Paper presented at the seventh meeting of the Ottawa Group, Paris.

Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4, 115–145.MATHCrossRefMathSciNet

Diewert, W. E. (1978). Superlative index numbers and consistency in aggregation. Econometrica, 46, 883–900.MATHCrossRefMathSciNet

Diewert, W. E. (2000). Notes on producing an annual superlative index using monthly price data (Discussion Paper no. 00-08). Vancouver: Department of Economics, University of British Columbia.

Haan, J. de (1999). Demographic change and upper level bias in consumer price indexes. In M. Silver & D. Fenwick (Eds.), Proceedings of the measurement of inflation conference. Cardiff: Cardiff University, 31 August – 1 September 1999.

Haan, J. de (2005, December 12–13). New and disappearing product varieties and the CES cost of living index. Paper presented at the fifth Economic Measurement Group Workshop, Sydney.

Hill, R. J. (2006). Superlative index numbers: Not all of them are super. Journal of Econometrics, 130, 25–43.CrossRefMathSciNet

International Labour Organization (ILO), IMF, OECD, Eurostat, United Nations, World Bank (2004). Consumer price index manual: Theory and practice. Geneva: ILO Publications.

Ivancic, L. (2007). Scanner data and the construction of price indices, PhD thesis, Sydney: University of New South Wales.

Lloyd, P. J. (1975). Substitution effects and biases in nontrue price indices. The American Economic Review, 65, 301–313.

Melser, D. (2006). Accounting for the effects of new and disappearing goods using scanner data. Review of Income and Wealth, 52, 547–568.CrossRef

Moulton, B. R. (1996). Constant elasticity cost-of-living index in share-relative form. Mimeo, Washington, DC: Bureau of Labor Statistics.

Nimmo, B., Hayes, S., & Pike, C. (2007, October 9–12). Consumers price index: Retrospective superlative index and impact of alternative housing weights. Paper presented at the tenth meeting of the Ottawa Group, Ottawa. Retrieved from http://www.stats.govt.nz/developments/price-index-developments.

Shapiro, M. D., & Wilcox, D. W. (1997). Alternative strategies for aggregating prices in the CPI. Federal Reserve Bank of St. Louis Review, 79(3), 113–125.

Triplett, J. E. (1989a). Superlative and quasi-superlative indexes of price and output for investment goods: Office, computing and accounting machinery (Discussion Paper 40). Washington, DC: Bureau of Economic Analysis.

Triplett, J. E. (1989b). Price and technological change in a capital good: A survey of research on computers. In D. W. Jorgenson & R. Landau (Eds.), Technology and capital formation. Cambridge/London: MIT Press.

Titel: Retrospective Approximations of Superlative Price Indexes for Years Where Expenditure Data Is Unavailable
verfasst von: Jan de Haan
Bert M. Balk
Carsten Boldsen Hansen
Verlag: Physica-Verlag HD
Buch: Price Indexes in Time and Space
Print ISBN: 978-3-7908-2139-0

Electronic ISBN: 978-3-7908-2140-6

Copyright-Jahr: 2010
DOI: https://doi.org/10.1007/978-3-7908-2140-6_2

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