## Types of weighted aggregate index numbers

The ratio of the sum of weighted prices of current and base time periods multiplied by 100 is called weighted aggregate price index. This index is calculated after allocating weights to each commodity on the basis of their relative importance. Weights of these commodities are then multiplied by the prices of base and current time periods. There are three main types of indexes: price-weighted, value-weighted, and pure unweighted. Price Weighted Indexes With a price-weighted index, the index trading price is based on the trading prices of the individual securities (stocks) that comprise the index basket (known as components). A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base. Types of Index Numbers The following types of index numbers are usually used: price index numbers and quantity index numbers. Quantity Index Numbers: These types of index numbers are considered to measure changes in the physical quantity of goods produced, consumed or sold of an item or a group of items. Methods of constructing index numbers: There are two methods to construct index numbers: Price relative and aggregate methods (Srivastava, 1989). Unweighted Index: A simple arithmetic or geometric average used to calculate stock indexes. Equal weight is invested in each of the stocks in an index with equal dollar amounts invested in each

## This paper uses index number theory to disentangle changes in aggregate retail interest Laspeyres-type decomposition in 3 terms with extended weight effect.

The method in which sum of prices of all the commodities in the current period is divided by the total prices in the base period is called unweighted aggregate index. Since simple aggregate index does not give relative importance to the commodities therefore it is neither meaningful nor representative index. Weighted index numbers are also of two types (i) Weighted aggregative (ii) Weighted average of price relatives . 1. Weighted aggregate Index Numbers. In this method price of each commodity is weighted by the quantity sale either in the base year or in the current year. There are various methods of assigning weights and thus there are many In weighted index number each item is given weight according to the importance. There are two group methods to calculate index number of this category: Weighted aggregate method. Weighted average of price relative method. Here, two types of weighted aggregate method are used to calculate weighted index number: Capitalization-weighted index: You must have an historical database of the number of shares outstanding or the market capitalization of the index stock components. Equal-weighted index or Price-weighted index: This type of index gives the same weight to each stock in the index or composite. Small and large companies will have the same Definition: An index number in which the component items are weighted according to some system of weights reflecting their relative importance. In one sense nearly all index numbers are weighted by implication; for example, an index number of prices amalgamates prices per unit of quantity and the size of these units may vary from one commodity

### Weighted Aggregative Index Method. 1. Laspeyres Index. Under this type of index, the quantities in the base year are the values of weights. Formula – ( ∑P n Q o / ∑P o Q o )*100. 2. Passche’s Index. Under this type of Index, the quantities in the current year are the values of weights . Formula –

Unlike simple index numbers, weighted index numbers, as the name suggests, weigh items according to their importance with respect to the concerned variable. For example, when calculating the price index number if the price of a unit of rice is twice the price of a unit sugar then the rice will be weighed in as ‘2’ whereas sugar will be weighed in as ‘1’. (a) Simple index number and (b) Weighted index number. Simple index number again can be constructed either by – (i) Simple aggregate method, or by (ii) simple average of price relative’s method. Similarly, weighted index number can be constructed either by (i) weighted aggregative method, or by (ii) weighted average of price relative’s method. The ratio of the sum of weighted prices of current and base time periods multiplied by 100 is called weighted aggregate price index. This index is calculated after allocating weights to each commodity on the basis of their relative importance. Weights of these commodities are then multiplied by the prices of base and current time periods. There are three main types of indexes: price-weighted, value-weighted, and pure unweighted. Price Weighted Indexes With a price-weighted index, the index trading price is based on the trading prices of the individual securities (stocks) that comprise the index basket (known as components). A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base. Types of Index Numbers The following types of index numbers are usually used: price index numbers and quantity index numbers.

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Weighted index numbers These are those index numbers in which rational weights are assigned to various chains in an explicit fashion. (A)Weighted aggregative index numbers- These index numbers are the simple aggregative type with the fundamental difference that weights are assigned to the various items included in the index. Dorbish and bowley A number of different formulae, more than hundred, have been proposed as means of calculating price indexes. While price index formulae all use price and possibly quantity data, they aggregate these in different ways. A price index aggregates various combinations of base period prices ( p 0 {\displaystyle p_ {0}} ), later period prices (

## chain aggregation and then illustrates the usage of chain-aggregated data with three obscurity of index-number theory, perhaps because few economists spend time of a fixed-weight measure real GDP depends on the choice of base year. between these two types of series over short periods are usually very small.

elementary index of the type noted above (the Carli, Jevons and Dutot indexes) is compared to an elementary aggregate that was constructed using a weighted the various kinds of index number that are, or might be, used for CPI purposes. aggregates, or as an arithmetic weighted average of the price ratios, or price

There are two types of aggregate price indices: unweighted aggregate price indices and weighted aggregate price indices. An unweighted aggregate price index, defined in Equation (16.23), places equal weight on all the items in the market basket. UNWEIGHTED AGGREGATE PRICE INDEX (16.23) where number of items under consideration UNWEIGHTED PRICE INDEXES. The two most commonly used formulas for computing price indexes are the aggregate formula and the average of relatives formula. Each of these for mauls may involve an weighted or a weighted type of calculation. In this section we consider the unweighted versions of price index formulas. Meaning: Index numbers is a statistical tool for measuring relative change in a group of related variables over two or more different times. Index number expresses the relative change in price, quantity, or value compared to a base period. An index number is used to measure changes in prices paid for raw materials; numbers of employees and customers, annual income and profits, etc. Weighted index numbers These are those index numbers in which rational weights are assigned to various chains in an explicit fashion. (A)Weighted aggregative index numbers- These index numbers are the simple aggregative type with the fundamental difference that weights are assigned to the various items included in the index. Dorbish and bowley A number of different formulae, more than hundred, have been proposed as means of calculating price indexes. While price index formulae all use price and possibly quantity data, they aggregate these in different ways. A price index aggregates various combinations of base period prices ( p 0 {\displaystyle p_ {0}} ), later period prices ( Weighted Index Number of Prices: New types of commodities may be introduced and consumers may change over to these types of commodities which are not comparable with the similar types used in the base period. (b) Problem of Averaging of Prices: An index number is a summary measure. Thus, its usefulness decreases as it tries to describe a