Motivation for Writing this Manual
Consumer Price Index (CPI) measures changes in prices of goods and services. It is used for determining inflation and standard of living of persons in countries across the globe. CPI utilizes weights obtained from Household Expenditure Surveys (HES). Laspeyres’ index utilizes weights obtained in a base year, while Paasche’s index computes indices using current year weights. To compute an ideal index, such as the Fisher’s Ideal Index (FII), base and current year weights are needed, which then requires two surveys to be conducted – one in the base year and another at the time of index computation (in the current year). This way, consumption expenditures within the period are adequately captured. So, it is common knowledge in literature to have an ideal index bounded by the Laspeyres’ and Paasche’s indices. This solves the main problems associated with index numbers, which are formula and weight biases.
However, time and cost involved in attempting to generate weights for both current and base years make it almost impossible for practitioners to generate weights for base and current years, which is why the fixed base-year weighting approach is adopted, despite its known bias. The suggested remedy is to have weights reviewed frequently, but that further worsens the time and cost implications.
Meanwhile, a concept of multivariate analysis of price data provides a conduit to generate weights conveniently for consumer price indexing. This is possible because price datasets are usually multivariate in the first place. The approach will require that weights are generated from the same price data, making it possible to generate both base and current year weights conveniently at the same time without having to conduct HES. This will eliminate the widely reported weight and formula biases. The proposed method was developed in previous works led by this author, validated and proved to be most efficient when compared with the expenditure-based weighting system. An additional advantage of the suggested approach is that it helps to retain variability in the resultant index.
Objectives of this Manual
Hence, the objectives of this manual is to:
- Highlight the main problems of weight and formula biases in index numbers;
- Provide detail and historical background to the various index formulas;
- Establish the theoretical underpinning of the proposed multivariate weighting method for indexing;
- Provide R algorithms for computing index using the multivariate weighting method under stated scenarios. This is important since the computations involved in adopting the new weighting approach are laborious.
Significance of the New Weighting Approach
This manual provides an R algorithm for potential users of the proposed alternative weighting scheme to conveniently compute Consumer Price Index (CPI) using the new approach. The approach, apart from the fact that it is an attempt to fill the gap in literature created due to the weight and formula biases, also allows for variability in price items to be duly incorporated in the resultant index. This is important because the overarching essence of inflation, in the first place, is to measure changes in set of price variables whose variability differ.
Further, because weights would be computed from the same price data, there would not be the problem of having to deal with challenges associated with the credibility of expenditure data and/or the unrepresentativeness of same. Essentially, the new approach can be applied to price data at any time of the year, without having to conduct household expenditure survey with its accompanying time and financial commitments. Yet another advantage of the new approach is that the dilemma of re-basing and its associated challenges would no longer exist. Hence, the proposed multivariate approach to weighting would be beneficial to statistics practitioners, academia, governments and the research community in general.
To academia and practitioners, the new methodology adds to the knowledge in official statistics by introducing a new multivariate weighting scheme distinct from what exists currently. Additionally, the approach helps in pulling much information about the internal structures within price data and can better report inflation. Thus, the method sought to promote the overall essence of indexing for ranking and comparison purposes, especially where variations exist in data points.
To policy formulation and implementation by governments, the methodology proposed in this manual would serve as an alternative in the field of index numbers for large set of data and can be used by National Statistical Agencies for computing consumer price index. In addition to the core benefits stated hitherto, the method provides an opportunity to determine and label (if possible) factors that explain the correlation of price variables with additional information on possible latent price variables that affect price movements.
Lastly, the multivariate weighting approach can be adopted in other areas of life (for example in financial markets and in performance indexing) where weight are computed for indexing.
Key Features of This Manual
The manual consist of four chapters with each chapter having its own synopsis presented at the beginning of the chapter. Chapter one introduces the index number problem and a summary of the various problems associated with indexing and their implications. Chapter two presents detail historical backgrounds to index numbers, their associated problems, and the deduction of the consumer price index formula from popular index numbers. Chapter three introduces the various multivariate concepts and their linkage to indexing. All computations done in the manual were done with the help of the R statistical software programming language. The R codes and function written for the various computations and results are presented in chapter four.
