1. Index numbers Value-, price-, quantity indices

2. Measuring changes in time Indices: relative change in price, quantity and value of products or services in a given period Marking: p=unit price; q=quantity; v= value (p*q) Value is highly important in examining economic phenomena. Periods Object for comparison: current period (p1,q1,v1) Base for comparison: base period (p0,q0,v0)

3. Simple indices A simple index shows the relative change in price, quantity or value of a given product in the current period compared to the base period. Simple value index Simple price index Simple quantity index

4. Aggregate values Aggregation Fixed price aggregate: – At base price:  p 0 q 1 ---------  p 0 q 0 –At current price:  p 1 q 1 ---------  p 1 q 0

5. Aggregate indices An aggregate index shows the relative change in price, quantity or value of a given basket of goods (product group) in the current period compared to the base period. Value index: Iv Price index: Ip Quantity index: Iq

6. Value index Product group’s value change at current price Average value change of the products of a product group Mean of simple value indices Weigh: value A value index expresses the relative change of a phenomenon measured in value.

7. Problem of value index E.g.: Revenue growth is real performance increase? „Heterogeneous”: contains the price change and the quantity change as well The inflation, the change of prices occurs in value data. If we want to filter out of that, we have to count the relative change of prices: This is the price index

8. Solution: calculation of price- and quantity indices Price index – Average change of price level for a product group (more products) Quantity index – Average change of quantities for a product group (more products)

9. Price index There are a lot of cases when price changes should be calculated for different products. Therefore we consider the average price changes of each product. The weighted mean of the products’ price changes (simple indices) should be calculated. The weights are values. Which period’s values? – Base period weights – Current period weights

10. Price indices The average price change for the products of a product group Base period weights: Laspeyres' price index Current period weights: Paasche's price index Value change due to price changes

11. Price indices Geometric mean of the two indices: Fishers’ price index Average value change due to price changes

12. Special price index: Consumer Price Index (CPI) Based on 960 representative items of 141 product groups 35-150 prices/item, together 70000 prices/month Simple price index of representative items: ratio of average prices Consumer Price Index based on simple price indices: Laspeyres’ price index Weights: represents the ratio of product- and services groups in the consumption of households. (Source: consumption data of national accounts, household statistics surveys). Revision of weights happens on a yearly basis, based on the household consumption two years before the current year.

14. Index relationships Meaning: decomposition of the value index (value change ) for two components: Value change due to the price changes Value change dute to the quantity changes

15. Quantity indices If we divide the value index by the price index, we can filter out the price change resulting the quantity index. The quantity index reflects the change in quantities. Rearranging the index relationships: the quantity index expressing the changes in quantities is equal to the ratio of the value index and price index Base period weights: Laspeyres' quantity index Current period weights: Paasche's quantity index

16. Quantity indices The average quantity change for the products of a product group Value change of a product group at fixed price Value change due to quantity changes Current period weights: Paasche's quantity index Base period weights: Laspeyres' quantity index

17. Quantity indices Value change of a product group at fixed price Average value change due to quantity changes Geometric mean of the two indices: Fishers’ quantity index