Comparison of elementary price indices

Abstract

Most countries use the Dutot, Jevons or Carli index for the calculation of their Consumer Price Index (CPI) at the lowest (elementary) level of aggregation. The choice of the elementary formula for inflation measurement does matter and the effect of the change of the index formula was estimated by the Bureau of Labor Statistics. It has been shown that difference between elementary indices can be explained in terms of changes in price dispersion. In this article, we extend these results comparing both population and sample elementary indices. We assume that prices from two compared time moments are log-normally distributed and correlated. Under the above-mentioned assumption, we provide formulas for biases and mean-squared errors of main elementary indices.     

Relatioinships between economic and statistical price indices

In the following, the economic counterparts of Eichhorn's and Voeller's tests for statistical price indices will be studied. We will see that replacing the statistical Commensurability Axiom in the economic price index theory by a property which is only concerned with price changes leads to similar relationships between this one and several other tests as in the statistical price index theory.     

Hedonic price indices for the Paris housing market

Summary: In this paper, we calculate a transaction–based price index for apartments in Paris (France). The heterogeneous character of real estate is taken into account using an hedonic model. The functional form is specified using a general Box–Cox function. The data basis covers 84 686 transactions of the housing market in 1990:01–1999:12, which is one of the largest samples ever used in comparable studies. Low correlations of the price index with stock and bond indices (first differences) indicate diversification benefits from the inclusion of real estate in a mixed asset portfolio.*This paper has been developed at the Research Program Real Estate Finance at Goethe-University of Frankfurt/Main (Germany). We gratefully acknowledge iii Internationales Immobilien Institut, IVG Holding AG and Stiftung Rheinische Hypothekenbank for their financial support. For further information, see www.real-estate-finance.de. We thank the participants of the 8th Conference of the European Real Estate Society (ERES), the International Conference of the American Real Estate and Urban Economics Association (AREUEA), the 10th Global Finance Conference 2003 and the anonymous referees for helpful comments, which improved the paper substantially.     

Laplace random variables with application to price indices

Laplace distributions are becoming increasingly popular models in economics and finance. In this note, the exact distribution of the ratio Z=|X/Y| is derived when X and Y are independent Laplace random variables. This distribution arises when one is interested in comparing the performances of two economic or financial entities. We consider estimation issues of the distribution and illustrate an application for consumer price indices from the six major economics. Several computer programs are given for implementation of the methods used.     

A characterization of the price indices satisfying the Eichhorn-Voeller axioms

In [EiV1] and [EiV2] a set of axioms based on sound economic reasoning was introduced, which a function should satisfy in order to be called a price index. There the problem was already posed how to characterize these sets of functions in mathematical terms. After introducing, for mathematical reasons only, a slight generalization of the axioms this paper presents one possible solution of this problem.     

Some suggestions concerning an axiom system for statistical price and quantity indices

Starting from the axiom system for price indices given by Eichhorn, this paper intends t o suggest some new axioms. They seem useful from a theoretical of practical point of view. The reversal tests, introduced by Fisher i n 1922, are investigated systematically. This procedure leads to new reversal properties and to a group theoretical representation of these properties.     

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

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.     

Measuring price-induced changes in standard of living in least developed countries: economic validity of laspeyres price indices and some further suggestions

Usually, also in developing countries, price-induced changes in standard of living are measured by means of Laspeyres price indices. Looking at the special economic situation characterizing least developed countries, the economic validit of such indices is doubtful. The main theoretical results of this paper are derived on the basis of a special utility concept which may be considered typical for least developed countries. It is shown that, under certain conditions, a Laspeyres price index over- or underestimates respectively changes in standard of living. Furthermore, it does not sufficiently evaluate households’ supply positions. These theoretical results are motivated and illustrated by a special least developed country, the Republic of Niger. The paper closes with some further suggestions for measuring changes in standard of living in developing countries.     

Robust projection indices

Loosely speaking a robust projection index is one that prefers projections involving true clusters over projections consisting of a cluster and an outlier. We introduce a mathematical definition of one-dimensional index robustness and describe a numerical experiment to measure it. We design five new indices based on measuring divergence from Student's t -distribution which are intended to be especially robust: the experiment shows that they are more robust than several established indices. The experiment also reveals more generally that the robustness of moment indices depends on the number of approximation terms, providing additional practical guidance for existing projection pursuit implementations. We investigate the theoretical properties of one new Student t -index and Hall's index and show that the new index automatically adapts its robustness to the degree of outlier contamination. We conclude by outlining the possibilities for extending our experiments to both higher dimensions and other new indices.     

Asymmetric selection indices

In 1936, H. Fairfield Smith (A discriminant function for plant selection, Annalsof Eugenice (London) 7,240–260) suggested a linear selection index for selecting varieties with higher genotypic values. Since then, the idea has been extended in various directions such as restricted selection indices. In this paper, linear selection indices are considered when, unlike squared error, the loss function is asymmetric. In particular, a LINEX loss function is considered for this purpose. It is shown that under multivariate normality, this approach still leads to the usual selection indices. Certain computational aspects are indicated.     

Inequality restricted linear selection indices

The problem of construction of selection indices with arbitrary linear inequality constraints on covariances is considered. The selection indices suggested by Smith (1936), Kempthorne Nordskog (1959) Tall is (1962) are shown as special cases. A method of solution is presented and prediction errors of various indices are compared. The method is applied to the example given in Kempthorne Nordskog (1959).     

Fundamentals and asset price dynamics

The relation between fundamentals and asset returns is analyzed by means of Markov-switching regression models with time-varying transition probabilities. By referring to the Italian Stock Exchange over the 1973-2002 period, we find that (i) returns switch between a zero-expected return/low volatility state and a high expected return/high volatility state; (ii) states are persistent and hence state changes can be forecast to some extent; (iii) the probability of state changes can be explained in terms of changes in the fundamentals; (iv) fundamentals do not have a direct impact on the expected returns but they only affect the transition probability matrix. Overall, our results show that a non-linear relation between market price changes and market fundamentals can be caught within the framework of (Markov) switching regession models.A previous draft of the paper was presented at the XL Scientific Meeting of The Italian Statistical Society, Firenze, April 2000. We would like to thank Maurizio Vichi (the editor) and several anonymous referees for important suggestions. A special thank to Lorenzo Sevini for valuable research assistance. Partial financial support by Italian M.I.U.R. grants is gratefully acknowledged.     

Generalized-order statistics with random indices

In this paper, we study the asymptotic behavior of general sequence of extreme, intermediate and central generalized-order statistics (gos), as well as dual generalized-order statistics (dgos), which are connected asymptotically with some regularly varying functions. Moreover, the limit distribution functions of gos, as well as dgos, with random indices, are obtained under general conditions.