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Topic 3:Index Numbers and Times Series Part I: Index Numbers: What is an _____ number? Constructing Indices Choosing between Indices Using Price Indices The Canadian ___ Price Indices and the "Cost of Living" Reference: Chapter 16 DWe need to develop a measure that summarizes the characteristics of _____ data sets and is useful for period to period comparisons.
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DAn I____ number accomplishes this by aggregating information into a single measure that permits easy comparisons.
Definition: An INDEX NUMBER is a number which summarizes pieces of information in a _______ way, and forms the basis for comparative judgements. a An index number is a ratio of 2 numbers expressed as a percentage.
Used if we want to keep track of "______" price changes over time
or need to get an aggregate measure of output- different items have the own units. Examples: CPI (Consumer Price Index);
PPI (Producer Price Index)
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Basic Considerations for a "good" Index Number:
(i) Include information on ___ items. (ii) Combine in way which recognizes r______ importance of each
item. (iii) Need a "bench mark" value and period to provide reference
point for comparisons. *Base period required
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Price and Quantity Indices
Price Indices Two broad types: (and there are several variants of each) (i) A__________ Indices (ii) R________ Indices
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Looking at (i): Aggregative Indices
Example: Bundle of Two Goods
Item 1990 2010 Price ($)
(Q) Price ($)
(Q) Good 1 Good 2
We want to summarize overall price change from 1990 to 2010. (Base Year =1990.) Must be the same goods in each year! (Assumption)
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Type of Price Index
Price of the "ith" item in the year of interest.
Price of the "ith" item in
the base year.
Base Year Year of interest
The 100 indicates that we have a base value of 100 in the base year.
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S____ Aggregative Index: Let Pit= Price of the ith item at time "t".
(i= 1, 2,....,n; t=0, 1, 2,....,T) Construction of the Simple Price Index:
The simple price index from base year '0' to year 't' for items 1 to n.
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If t=0, index=100 (Base year value). Example: See previous data for 1990 and 2010:
Base Year =1990
0 1980 2000
180 2 70 0 75 0 50
× = ⇐