Chapter Index numbers Index Numbers  Index numbers allow relative comparisons over time  It measures the percentage change in the value of some economic commodity over time  Index numbers are reported relative to a Base Period Index  Base period index = 100 by definition Notes    ‘Economic commodity’: used to describe anything measurable which has some economic relevance ‘Economic commodity’ can be: price, quantity, wage, productivity… Index numbers must always be related to some time period (i.e base time period and another time period) Examples  If the index number values are: 130 95 250 Index Relatives  Index relative or simple index number is an index number which measures the change in a single distinct commodity Index Relatives  Formula: yt I y  �100 y0 where Iy = index number of commodity ‘y’ yt = value of commodity ‘y’ at time t y0 = value of commodity ‘y’ in the base period Index Numbers: Example  Company orders from 1995 to 2003: Year Number of Orders 1995 272 1996 288 1997 295 1998 311 1999 322 2000 320 2001 348 2002 366 2003 384 Index (base year = 2000) Index Numbers: Interpretation Price relatives  Formula pt I p  �100 p0 Where: pt: price at time t p0: price in the base period I p (2003/ 2000) The price index for 2003,  120 based on 2000(as 100), is 120 Quantity relatives  Formula qt I q  �100 q0 Where: qt: quantity at time t q0: quantity in the base period I q (2003/2000)  150 The quantity index for 2003, based on 2000 (as 100), is 150 Time series deflation: example Year 2000 2001 2002 2003 2004 2005 Average daily wage (USD) 10 15 17 19 22 25 CPI 104.3 106.8 107.8 109.8 110.5 112.6 Real wage index Composite index numbers   A composite index number is an index number obtained by combining the information from a set of economic commodities It measure the percentage changes of a group of items (not one item) Weighting of components    Usually, a composite index can be calculated by weighting each component A weighting factor is an indicator of the importance of each component in calculating the composite index The need for weights (read in the textbook) Types of composite index number Weighted average of relatives Weighting the index relative calculated for each component Weighted aggregates Multiplying each component value by its corresponding weight and adding these products to form an aggregate Weighted average of relatives Formula: I AR wI �  �w Where: w: weighting factor of each component I: index relative of each component Weighted average of relatives Items Price p0 pt Standard quantity w A 2.0 2.2 10 B 1.8 2.4 15 C 10.2 12.5 Weighted average of relatives Items Price Standard quantity w p0 pt A 2.0 2.2 10 B 1.5 2.4 15 C 10.2 12.5 Totals 28 Price relative Ip wI Weighted average of relatives Weighted average of price index relatives Weighted aggregates  Formula I AG wy �  �wy t �100 where yt : Value of commodity at time t y0 : Value of commodity at base time point w: Weight factor Weighted aggregate: Example Items Price p0 pt Standard quantity w A 2.0 2.2 10 B 1.8 2.4 15 C 10.2 12.5 Weighted aggregates Items Price Standard quantity w p0 pt A 2.0 2.2 10 B 1.5 2.4 15 C 10.2 12.5 Totals wp0 wpt Weighted aggregates Weighted aggregate of price index: Weighted Aggregate Price Indexes  It Paasche index pq �  �p q t t (100) t A Paasche price index uses current time period quantities as weights  Laspeyres index It pq �  �p q t (100) 0 A Laspeyres price index uses base time period quantities as weights Weighted Aggregate Quantity Indexes  It Paasche index pq �  �p q t t (100) t A Paasche quantity index uses current time period prices as weights  It Laspeyres index pq �  �p q t (100) 0 A Laspeyres quantity index uses base time period prices as weights Example Item Uni s t Price (USD) Quantity (p0) (pt) (q0) (qt) A kg 3,0 4,5 1000 1100 B m 5,0 6,0 2000 2400 C l 2,0 2,2 4000 4200 Calculate the Pasache and Laspeyres price and quantity index? ... relative Year 2000 2001 2002 2003 2004 2005 Old Index (1980=100) 244 260 270 285 300 315 New Index (2000=100) 100 1 06. 56 110 .66 1 16. 80 122.95 129.10 Time series deflation  A technique used to obtain... Company orders from 1995 to 2003: Year Number of Orders 1995 272 19 96 288 1997 295 1998 311 1999 322 2000 320 2001 348 2002 366 2003 384 Index (base year = 2000) Index Numbers: Interpretation Price... 2000 2001 2002 2003 2004 2005 Average daily wage (USD) 10 15 17 19 22 25 CPI 104.3 1 06. 8 107.8 109.8 110.5 112 .6 What is the real wage index for 2005? Time series deflation: procedure  Step 1: