scholarly journals A Practical Approach to choosing Formulae for Economic Index Numbers

Author(s):  
John Wood

Abstract Traditional axiomatic, economic and stochastic approaches to choosing a formula for economic index numbers are based on theoretical considerations, with little regard to whether they reflect the actual circumstances affecting the markets to which they relate. This paper presents an approach to index number formulation based on how markets operate and presents a general, parameter-based formula for price and quantity indices. Two variants of this general formula cater for the “substitution effect” in different ways and one of these variants provides a practical expression for an economic-theoretic index based on purchasers' revealed preferences. Another variant applies this approach to short-term inflation indices. A final variant provides a straightforward means of estimating purchasing power parities for spatial indices. The analysis also emphasises the importance in National Accounts of using coherent price and quantity indices, whose products generate the corresponding value indices.

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Wang Xingyuan ◽  
He Yijie ◽  
Sun Yuanyuan

This paper presents two methods for accurately computing the periodic regions' centers. One method fits for the general M-sets with integer index number, the other fits for the general M-sets with negative integer index number. Both methods improve the precision of computation by transforming the polynomial equations which determine the periodic regions' centers. We primarily discuss the general M-sets with negative integer index, and analyze the relationship between the number of periodic regions' centers on the principal symmetric axis and in the principal symmetric interior. We can get the centers' coordinates with at least 48 significant digits after the decimal point in both real and imaginary parts by applying the Newton's method to the transformed polynomial equation which determine the periodic regions' centers. In this paper, we list some centers' coordinates of general M-sets'k-periodic regions(k=3,4,5,6)for the index numbersα=−25,−24,…,−1, all of which have highly numerical accuracy.


1983 ◽  
Vol 65 (3) ◽  
pp. 520 ◽  
Author(s):  
Keith C. Brown ◽  
K. Rao Kadiyala
Keyword(s):  

2020 ◽  
Author(s):  
Mutia Zaroh ◽  
Fadila Raihani
Keyword(s):  

Abstract - Index numbers are a concept that can give you an idea of variable changes from one period to the next. Index numbers are divided into two methods, namely: The index number method is not orderly and the index number is weighted, both methods require a price and quantity of a group of goods and an item. from these methods are divided into several kinds, some consider in weight and some consider it, by using excel applications can facilitate our calculation of this index number.Keywords: numbers, indexes, methods


PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11843
Author(s):  
Carlos Prieto ◽  
Christophe Faynel ◽  
Robert Robbins ◽  
Axel Hausmann

Background With about 1,000 species in the Neotropics, the Eumaeini (Theclinae) are one of the most diverse butterfly tribes. Correct morphology-based identifications are challenging in many genera due to relatively little interspecific differences in wing patterns. Geographic infraspecific variation is sometimes more substantial than variation between species. In this paper we present a large DNA barcode dataset of South American Lycaenidae. We analyze how well DNA barcode BINs match morphologically delimited species. Methods We compare morphology-based species identifications with the clustering of molecular operational taxonomic units (MOTUs) delimitated by the RESL algorithm in BOLD, which assigns Barcode Index Numbers (BINs). We examine intra- and interspecific divergences for genera represented by at least four morphospecies. We discuss the existence of local barcode gaps in a genus by genus analysis. We also note differences in the percentage of species with barcode gaps in groups of lowland and high mountain genera. Results We identified 2,213 specimens and obtained 1,839 sequences of 512 species in 90 genera. Overall, the mean intraspecific divergence value of CO1 sequences was 1.20%, while the mean interspecific divergence between nearest congeneric neighbors was 4.89%, demonstrating the presence of a barcode gap. However, the gap seemed to disappear from the entire set when comparing the maximum intraspecific distance (8.40%) with the minimum interspecific distance (0.40%). Clear barcode gaps are present in many genera but absent in others. From the set of specimens that yielded COI fragment lengths of at least 650 bp, 75% of the a priori morphology-based identifications were unambiguously assigned to a single Barcode Index Number (BIN). However, after a taxonomic a posteriori review, the percentage of matched identifications rose to 85%. BIN splitting was observed for 17% of the species and BIN sharing for 9%. We found that genera that contain primarily lowland species show higher percentages of local barcode gaps and congruence between BINs and morphology than genera that contain exclusively high montane species. The divergence values to the nearest neighbors were significantly lower in high Andean species while the intra-specific divergence values were significantly lower in the lowland species. These results raise questions regarding the causes of observed low inter and high intraspecific genetic variation. We discuss incomplete lineage sorting and hybridization as most likely causes of this phenomenon, as the montane species concerned are relatively young and hybridization is probable. The release of our data set represents an essential baseline for a reference library for biological assessment studies of butterflies in mega diverse countries using modern high-throughput technologies an highlights the necessity of taxonomic revisions for various genera combining both molecular and morphological data.


1998 ◽  
Vol 2 (4) ◽  
pp. 456-471 ◽  
Author(s):  
W. Erwin Diewert

This paper studies the problems of measuring economic growth under conditions of high inflation. Traditional bilateral index number theory implicitly assumes that variations in the price of a commodity within a period can be ignored. To justify this assumption under conditions of high inflation, the accounting period must be shortened to a quarter, a month, or possibly a week. However, once the accounting period is less than a year, the problem of seasonal commodities is encountered; i.e., in some subannual periods, many seasonal commodities will be unavailable and hence the usual bilateral index number theory cannot be applied. The paper systematically reviews the problems of index number construction when there are seasonal commodities and high inflation. Various index number formulas are justified from the viewpoint of the economic approach to index number theory by making separability assumptions on consumers' intertemporal preferences. We find that accurate economic measurement under conditions of high inflation is very complex.


1995 ◽  
Vol 55 (3) ◽  
pp. 671-672 ◽  
Author(s):  
Patrick K. O’Brien ◽  
Trevor Griffiths ◽  
Philip Hunt

Historians and economists have long been in need of index numbers to measure both the volume (real value) of activity that is undertaken to produce process or product innovations over time, and also a counterpart index that might capture the outcome of that activity (the volume of inventions) that come on stream year after year. For purposes of measurement the first index can in principle be equated (within tolerable limits of accuracy) with the real annual expenditures on research and development as recorded (at least for recent times) in governmental, corporate, company, and other accounts. Alas, for years before 1914 national or even industry-wide research and development expenditures are very rarely recorded in a form that might allow for the construction of an index number.


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