Approximation of the Fisher price index by using Lowe, Young, and AG Mean indices

ABSTRACT

The Consumer Price Index (CPI) approximates changes in the costs of household consumption assuming the constant utility (COLI, Cost of Living Index). In practice, the Laspeyres price index is used to measure the CPI despite the fact that many economists consider the superlative indices to be the best approximation of COLI. The Fisher index is one of the superlative indices and additionally it satisfies most of tests from the axiomatic price index theory. Nevertheless, the Fisher price index makes use of current-period expenditure data and its usefulness in CPI measurement is limited. In this article, we verify the utility of using the Lowe, Young, and AG Mean indices for Fisher price index approximation. We confirm this utility in a simulation study and we provide an empirical proof.

KEYWORDS:

• AG Mean index
• Fisher index
• Lowe index
• Price index theory
• Young index

JEL CLASSIFICATION:

• C43

Notes

1 The Fisher price index is a geometric mean of the Laspeyres (P_La) and Paasche (P_Pa) price indices.

2 It is typical for the analytical purposes to assume a linear or exponential change in quantities and prices (see for instance Vaninsky (2013)). Many countries' CPI price trends over time have rather exponential character due to the fact that inflation tends to be a multiplicative process, not an additive one. Thus, we decide to assume that prices change exponentially while quantities change linearly to better estimation of lags in price and quantity movements.

3 Taking a = 0, we obtain numbers assumed in Table 1.

4 In the case of Laspeyres and Paasche formulas, weights and base prices are always from the same, base period s = 0.

5 In Poland, the highest level of data aggregation consists of 12 categories. In our study, we use lower level of aggregation taking into consideration 40 categories of goods and services. The data are available on the following webpage (Tables 16 and 17).http://stat.gov.pl/obszary-tematyczne/ceny-handel/ceny/ceny-w-gospodarce-narodowej-lipiec2015-r-,1,38.html

6 Główny Urząd Statystyczny (GUS) in Poland.

7 When prices and quantities are positively correlated then ηis negative and when this correlation is negative then η is positive (see Figure 3).