Divisia Price Research Articles

How do fossil energy prices affect the stock prices of new energy companies? Evidence from Divisia energy price index in China's market

With the shale gas revolution and the maturity of new energy technologies, the global oil-based energy pattern began to be remodeled worldwide. From the perspective of China, coal has played a dominant leading role in the energy structure. Therefore, it is becoming increasingly irrational to replace fossil fuels with oil. This paper considers the impact of fluctuations of three fossil energy (oil, coal and natural gas) prices on new energy companies stock prices to meet the needs of policy makers and investors in this rapidly developing field. Due to the incomplete substitution among fossil fuels, this paper uses the Divisia price synthesis method to synthesize these three prices into a composite price index. Furthermore, we use a variable vector autoregressive model to explore dynamic relationships among stock prices of new energy companies and technology companies, fossil energy prices and carbon futures prices. The results reveal that previous stock prices of new energy companies had the most significant impact on the current level. However, fossil energy prices account for only a small part of stock price fluctuations of new energy companies.

Bounds for the expected value of the stochastic Divisia's price index

ABSTRACTIn this article, we estimate bounds for the expected value of the stochastic Divisia's price index, that is, we assume that prices and quantities of the given commodities are stochastic processes with continuous time. We consider some special case of the stochastic model in which prices and quantities are described by the geometric Brownian motion. It is shown that the precision of this estimation depends rather on the volatility of prices than quantities volatilities.

Generalization of the Divisia Price and Quantity Indices in a Stochastic Model with Continuous Time

In this article, we present and discuss original price and quantity index formulas being a next step in Francois Divisia's index approach. We assume that prices and quantities of the given commodities are stochastic processes and we consider a continuous-time model. As a consequence, we obtain very general index formulas being random variables for any fixed time interval of observations. We present basic properties of the discussed formulas and show that, in the deterministic case, the general formulas lead to known classic Divisia indices.

SPATIAL COMPARISONS OF PRICES AND EXPENDITURE IN A HETEROGENEOUS COUNTRY: METHODOLOGY WITH APPLICATION TO INDIA

This study addresses two significant limitations in the literature on cross-country expenditure comparisons: (a) treatment of all countries, large and small, as single entities with no spatial differences inside the countries, and (b) use of Divisia price indices, rather than Rank 3 preference-based “exact price” indices, in the expenditure comparisons. This paper compares alternative preference consistent methods for estimating spatial price differences in a large heterogeneous country, namely India, that are benchmarked against the spatial prices generated by the Laspyeres and Tornqvist price indices. Unlike the use of conventional price indices, the use of demand-systems-based methods allows the incorporation of price-induced substitution effects between items. The paper illustrates the usefulness of the methodology by using the “exact” spatial price indices, in conjunction with the inequality-sensitive welfare measure due to Sen, to rank the Indian states and examine changes in ranking during one of the most significant periods in independent India. The results have methodological and empirical implications that extend far beyond India.

Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

We use the general form of hat matrix and DFBETA measures to detect the influential observations in order to estimate the Divisia price index number when the error structure is first order serial correlation. An example is presented with reference to price data of Pakistan. Hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates and are not affected by the parameter of autoregressive process AR(1). Whereas DFBETAs for Divisia index numbers depend on both the weights and autoregressive parameter.

Decomposing the Changes of the Divisia Price Index: Application to Inflation in the Philippines

We propose a method to decompose the logarithmic change of the Divisia price index into the pure price effect, the preference effect and the substitution effect. Our empirical results in the Philippines shows the effects of preference change on the Divisia price index are heterogeneous but positive across all regions and income deciles. However, they are dominated by the pure price effect.

Divisia price and quantity indices: 80 years after

This paper reviews and extends the theory of price and quantity indices which are defined as line integrals, the two types being those of Divisia and Montgomery. The properties of these indices are systematically explored, whereby in particular attention is paid to the path‐(in)dependency issue. Two sections discuss the problem of how to approximate the line integral indices when only data at discrete points of time are available. It appears that every bilateral index can be conceived as the outcome of a line integral index over a particular curve in price–quantity space. The classical position is that chained bilateral indices are rationalized by Divisia indices. This rationalization is only interesting when the Divisia indices themselves possess a proper foundation in economic theory. The final sections are therefore devoted to the role played by the Divisia indices in micro‐economic theory.

Is world metal consumption in disarray?

The consumption pattern of seven major metals—steel, aluminum, copper, lead, nickel, tin and zinc—has frequently violated the law of demand in the late 20th century. This paper examines the patterns of the major metal consumption in the world and seven particular regions and analyzes the disarray of metals consumption. Divisia price–quantity covariance indexes report that the price and quantity consumed moved frequently in the same direction, and the elasticity approach shows that the own-price elasticities are extremely small and insignificant, while income elasticities are significant. However, considering the parameters that are crucial in determining the own-price elasticity, this paper concludes that the apparent disarray in metals consumption is not in fact real.

On the measurement of real R&D: Divisia price indices for UK business enterprise R&D

This paper argues that, to measure the quantity of R&D undertaken, it is necessary to deflate R&D spending by a measure of its cost. Based on Divisia weighted averages of proxy price series, price indices are constructed for R&D spending in UK manufacturing in eight sectors and as a whole for 1970–1992. These indices are a better guide to the cost of performing R&D than the GDP deflator, which overstates the rise in real business enterprise R&D in the 1980s, although year-on-year changes are less distorted. Divisia indices are theoretically and empirically better at capturing changes in the cost of R&D than are fixed weighted indices. An investigation of the rapidly rising level of pharmaceutical R&D in the UK concludes that the rise is genuine in that it has not been driven by rapid increases in research salaries. Copyright , Beech Tree Publishing.

Energy forecasting models, simulations and price sensitivity: New formulation

The top-down, two-stage optimization approach provides energy analysts with a powerful tool for both policy analysis and forecasting. This approach assumes that energy is weakly separable from other inputs to the production process. An aggregate energy Divisia Price Index (DPI) links the two stages. Although the DPI is necessary for the model estimation, it can distort the outcomes of price sensitivity analysis and forecasting exercises when the model is used for forecasting and simulations without adjusting the DPI. This deprives the two-stage optimization procedure of some of its virtues. The present study attempts to explain the reason for these distortions and to show that, by reformulating the same set of estimated coefficients, the simulation module will correct the shortcomings of the conventional formulation.

Auditing the Producer Price Index: Micro Evidence from Prescription Pharmaceutical Preparations

In this paper we focus on a mystery we uncovered while undertaking a detailed audit of the US Bureau of Labor Statistics producer price index (PPl). We summarize our puzzle as follows. From January 1984 through December 1989.the BLS price Index for SIC 28341 (prescription pharmaceutical preparations) grew at an annual rate of 9.09%. For purposes of comparison, we have obtained monthly price and quantity sales data on all prescription pharmaceutical preparation products sold by four major US pharmaceutical manufacturers, accounting for about 24% of total industry domestic sales in 1989. Using Laspeyres price index construction procedures on these data that mimic BLS methods, we find that over the same time period. the four-company price index increased at only 6.68% per year. Finally. when we employ a Divisia price index procedure with smoothed weights that incorporates new goods immediately, the aggregate price index for these four firms grows at a rate of only 6.03% per year. Why is it that the official BLS price index grows approximately 50% more rapidly (9.09% vs. 6.03%)than the Divisia price index? That mystery is the focal point of our paper.

PURCHASING POWER PARITY AND RELATIVE PRICE VARIABILITY: THE MISSING LINK?

The failure of strict purchasing power parity to hold in the 1970s can be explained by the preponderance of the real shocks which involve large changes in sectoral relative prices. Previous work has attempted to measure these effects by using proxies for the prices of traded and nontraded goods. In this study the author uses the Divisia price variance as a measure of changes in the structure of relative prices to reexamine the case for real shocks causing deviations from parity. Using data from 21 OECD countries, the results show that an increase in the variance of relative prices at home (in relation to that abroad) depreciates the currency. Copyright 1991 by Blackwell Publishers Ltd/University of Adelaide and Flinders University of South Australia

Numerical integration of the divisia price index and an application of the equation of measurement to prices

First the linear and the exponential paths are chosen as examples to show how the Divisia price and quantity index can be integrated numerically. Then the equation of measurement by Eichhorn and Gleissner is adapted to price measurement and used to formulate certain properties of indices. A special class of properties, the reversal tests describing certain symmetries, is considered especially, It turns out that the corresponding antitheses form a group of eight elements.

Analytic integration of the divisia price index on the exponential path for two commodities

The Divisia integral on the exponential line is evaluated analytically for two commodities. This is done by using software for symbolic computation.

Ideal Divisia moments, price dispersion and inflation

Ideal Divisia price and quantity index numbers are computed for 18 countries using per capita consumption data for the 1970's. Correlation matrices of general price change and price dispersion are computed and determinants of price dispersion are analyzed.

Divisia moments of U.S. consumption, 1929–1982

Using U.S. consumption data for 1929 to 1982, Divisia price and volume indexes are computed as well as Divisia variances and covariances. The quantity variances tend to be larger than the price variances, and the majority of the price-quantity covariances is negative.

Divisia moments of Australian consumption

Quarterly Australian consumption data, 1959–1978, are used to compute Divisia price and quantity indexes, together with Divisia variances and covariances. The quantity variances tend to exceed the price variances, and the price-quantity covariances are mostly negative. Estimates of the income flexibility are also presented.