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Homology of laspeyres and paasche index numbers.

GDP/GNP is the only indicator which reflects the working of the whole economy. The estimates of the GDP/GNP at current and constant prices provide a firm basis for the measurement of economic growth. To convert sectors of the GDP/GNP from current to constant and vice versa, various type of index numbers are used as deflators. Any error in the computation and use of index numbers will, therefore, effect the validity of the GDP/GNP.

The use of index numbers for economic analysis is not confined to a single aspect of the economy. The measurement of dynamic forces and economic phenomena including the variations in the purchasing power of money at different points of time owe much to the construction of index numbers. Due to inherent limitations of various dimensions, index numbers are criticised as widely as they are used. One of the important criticism against the use of index numbers for purpose of economic analysis is that they usually provide result which are not identical when applied to the same set of data-a situation which bewilders the users. Even then, index numbers are intensively used though half-heartedly because there is no tool other than index numbers available to users. Therefore, an attempt has been made in this paper to throw light on this proposition and to illustrate the homology of Laspeyres and Paasche-type index numbers when constructed on the same set of data.

The main concept of an index number is to measure the general level of magnitude of group of distinct, but related variables in two or more situations. Based on this concept, the preparation of index numbers has a long history and goes back to Edgeworth, who in 1887-89 was Secretary of a committee of the British Association set up to study methods of measuring variations in the value of money. Therefore, price indexes, whether constructed to measure the value of money on different points of time, or are indexes of wholesale prices, retail prices of agricultural and manufacturing products etc., all of them are widely used to compare changes over time and space.

Uses of Index Numbers

The purposes for which index numbers are computed and used are manifold. Different type of indexes are computed to meet certain needs e.g. WPI to measure the prices of goods and services sold in bulk, CPI to determine the cost of living etc. Among the main purposes for which index numbers are computed include the measurement of inflationary trend, growth rate and real product over time and space.

In most of the developed and developing countries, CPI is also used for wage adjustment. In US, for example, the construction of CPI was started during the World War-I when a need was felt to adjust wages with the high cost of living. Similarly in undivided India, on the recommendation of the Rau Court of Enquiry in 1944, data on retail prices were used by the Ministry of Labour to settle a dispute on the dearness allowance to be given to GIP Railways employees. In Pakistan too, a start has been made to calculate indexed-pay on the basis of the trend exhibited by CPI and its effect is given on the wages and salaries being paid to the employees of the federal and provincial governments' departments etc. Besides its use for wage-adjustment, price indexes are also used as deflators for sectors of GNP and flows of Expenditure on GNP respectively.

Some Basic Criticisms on Index Numbers

Index numbers are generally criticised because they merely reflect the level of magnitude attained and are indicators of trend only. Since index numbers suffer from limitation of various types they are simply a crude device to measure changes in cost and volume of production, trade and investment at base-year prices. The results obtained by applying index numbers to certain type of data may not be always close to reality. Moreover, inconsistent and different results derived from the same set of data when different type of index numbers are applied to it, reveal their greatest limitation. The other criticism is that index numbers usually possess element of bias. For example, at a time when prices are arising, laspeyres price index usually shows a higher trend than a Paasche index. This aspect of index numbers is termed as upward bias in Laspeyres index and downward bias in Paasche index. Fishers ideal approach to thread a way between the two, is also criticised on he ground that "the average of two wrong answers does not necessarily give one right answer.

Homology of Laspeyres and Paasche Index Numbers

The general conclusion that different type of index numbers when applied to certain data produce results which are not identical. This fact may not be always true. In certain cases, Laspeyres and Paasche index numbers are homologous in character and produce symmetric results. The homology of Laspeyres and Paasche index numbers may be visualized when the indexes are computed on the basis of same set of data. For purpose of illustration, different type of indexes have been constructed which are based on employment and wage data for scheduled banks of Pakistan for the year 1975-76 to 1979-80. The indexes so computed placed in Table-I exhibit the homology among each other. Column-2 of Table-I contains wage data at current prices while Column-5 contains wage data using 1975-76 average wage; Columns 7 and 8 contain wage indexes based on Laspeyres and Paasche-type price indexes respectively. Similarly, employment indexes (Columns 9 and 10) have been computed on the basis of Laspeyres and Paasche-type volume indexes. The symmetric figures under Columns-7 and 8 transpire homology of Laspeyres and Paasche indexes. Similar fact is focused by the figures under Columns 9 and 10. Therefore, the results (values) derived from the data after deflating wages at current prices either by Laspeyres and Paasche wage indexes will also be identical. Similarly, base-year values when extrapolated either by Laspeyres or Paasche employment volume indexes will be symmetrical with one another. Since index numbers being identical whether computed on the basis of Laspeyres or Paasche-type formulae the results (values) derived from these formulae are coherent showing their complete homology with one another as given in Columns 5 and 8 of the Table-2.


Index numbers play a key role in the measurement of inflationary trend, economic growth and change in cost of living besides their use to frame economic policies and planning. Therefore, the contributions made by index numbers for economic analysis cannot be ignored TABULAR DATA OMITTED though they contain element of various types of errors causing an equivalent error in the output measurement. Generally, index numbers are applied to assess the changes occurring in economic activities by valuing their products. For this purpose, either base-year prices or price indexes are used as deflators. But in most cases, resort to use conventional index numbers is usually made instead of constructing index numbers for specific purposes. Under such circumstances index numbers not being true representative of the situation fail to yield results which may be termed real. In order to rectify some of the deficiencies, it is being suggested that the index numbers be based on the components of flows involved and they should be directly factored into their own price and quantity TABULAR DATA OMITTED elements. This process of constructing index numbers is considered to focus a real picture and produce better results than one obtained by making indiscriminate use of conventional index numbers. Furthermore, a great deal of discussion on the system of national accounts has been made with regard to choice between Laspeyres and Paasche index numbers and quantity extrapolation and price deflation methods to obtain values at constant prices. Both Laspeyres and Paasche index numbers as well as extrapolation and deflation methods work equally well since all of them produce homologous and symmetrical results. This fact has been illustrated with the help of the figures given in Table-2 which show the homology of Laspeyres and Paasche index numbers.
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Author:Qadir, Syed Abdul
Publication:Economic Review
Date:Feb 1, 1993
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