Measuring CPI's reliability: the stochastic approach to index numbers revisited

Abstract

The reliability measurement of the Consumer Price Index (CPI) has recently drawn much attention, as the index number has been criticized for its inaccuracy in accessing the degree of inflation. This article centers on providing a new regression specification that can help better gauge the CPI's reliability. More specifically, based on the stochastic approach to index numbers, we argue that the conventional treatment of the systematic changes in relative prices should be made time variant. We therefore propose a more comprehensive regression specification by including additional dummies that represent different general inflation rate levels and business cycle phases. Under this framework, we are more capable of avoiding possible misspecifications in the regression equation, as was experienced by Clements and Izan (1987). It also allows us to better answer the ‘Keynes’ critic’ regarding the stochastic approach to index numbers. The empirical results of Australia and the US are used to validate the merit of our specification.

Keywords:

• index numbers
• stochastic approach
• business cycles
• estimation

JEL Classification:

• C43
• E31
• E32
• C13

Notes

¹ According to the pioneering paper of Frisch (1936), there are two fundamentally different ways in which the problem of price index numbers may be approached – the atomistic and the functional approach. There are two major streams in the atomistic approach. The first is the test approach whereby indexes are judged on their ability to satisfy certain criteria (Fisher, 1922). This article focuses on the other methodology, which is the stochastic approach (Clements and Izan, 1987; Selvanathan and Prasada Rao, 1994; Crompton, 2000). More specifically, in the atomistic approach, the prices and quantities of the various goods are considered as two sets of independent variables, and the price index number can be defined as a certain function of these 2N variables. Accordingly, the price index number in the atomistic approach can be regarded as one kind of measure of location. The functional approach to index number also known as economic theoretical approach is also the function of various quantities and price. However, the index number functions are derived from economic consumer behaviour theory, and the derived index number functions will change as different assumed utility functions.

² ‘The hypothetical change in the price level, which would have occurred if there had been no changes in relative prices, is no longer relevant if relative prices have in fact changed – for the change in relative prices has in itself affected the price level. I conclude, therefore, that the unweighted (or rather the randomly weighted) index number of prices – Edgeworth's ‘indefinite’ index number –‘…has no place whatever in a rightly conceived discussion of the problems of price levels’. (Keynes, 1930, p. 30).

³ [T]he logical basis of the whole concept seems untenable. We cannot assume that the ‘monetary factor’ will manifest itself as a proportional change of all prices. I am, therefore, in agreement with Keynes when he vigorously criticizes the stochastic definition of the price level as being ‘root-and-branch erroneous’. (Frisch, 1936, p. 5).

⁴Since expenditure shares of consumer goods are stable over time, therefore we assume to be constant over the sample period which is the arithmetic mean of over the sample period.

⁵ Crompton (2000) illustrated the stochastic approach by estimating quarterly Australian consumer inflation rates using price series from categories, including food, clothing, housing, household equipment and operation, transportation, tobacco and alcohol, and health and personal care.

⁶ The price data and corresponding expenditure weights were obtained from the Australian Bureau of Statistics (www.abs.gov.au) and Bureau of Labor Statistics of the US (www.bls.gov).

⁷ National Bureau Economic Research (NBER) dated July 1990, March 2001 and December 2007 as business cycle peaks of the US. The Economic Cycle Research Institute (ECRI) dated January 1998 as a growth cycle peak of the US.

⁸ Note that the CF filter is applied, due to its generality in which the weights on the leads and lags are allowed to differ. Specifically, the band-pass filter is a linear filter that calculates a two-sided weighted moving average of the data wherein the cycles are in a ‘band’, given by a specified lower and upper bound. They are ‘passed’ through or extracted, and the remaining cycles are ‘filtered’ out. Furthermore, the filter is time-variant, with the weights depending on both the data and the changes in each observation.

⁹ The Australian CPI is quarterly-based data; the US CPI is monthly-based data. In the literature, among those using quarterly data, the GDP series is the most commonly used in the study of business cycles; while among those using monthly data, the industrial production series is the most commonly used. Therefore, in order to match the frequencies of the CPI data used in Australia and the US in the identification of business cycle phases, we shall use the Australian quarterly GDP and the US monthly industrial production series with CF filter to identify the phases of business cycle in each nation.

¹⁰ Since Kitchin cycles range between 3 and 5 years, and Juglar cycles range between 7 and 10 years (van Duijn, 1983), the period of 3–10 years that we choose includes the two most frequent periods of cyclic fluctuation.

¹¹ By definition,

and

and and turn out to be null matrices .