I3' Index Numbers I31' Price Indexes

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I-3. Index NumbersI-3-1. Price Indexes

• When we want to see the change of price, rather
  than the level of price, it is more convenient to
  look at price indexes.
• A. Simple Index
• Pit current price of commodity i in year t
• Pi0 price of commodity i in the base period

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Example (WW pp. 665-666)
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I-3-1. Price Indexes

• Advantage
• It expresses the RELATIVE change in value from
  one period to another. An index is a convenient
  way to express a change in a heterogeneous group
  of items (e.g. Yen/ton and Yen/Km)
• What should we do if we want to know a general
  trend of prices which consumers face in an
  economy?
• Use Q consumed as weight to reflect the
  importance of each com. In your consumption
  basket.
• Two ways (base year consumption vs. current
  consmption)

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I-3-1. Price Indexes

• B. Laspeyres Price Indexes (LPI)
• Use base year quantities as weights
• n number of commodities
• Pit current price of commodity i in year t
• Pi0 price of commodity i in the base period
• Qi0 quantity of commodity i in the base period

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I-3-1. Price Indexes

• LPIs advantages
• Put heavier weight to the goods consumed more.
• Less data demanding. We need quantity data from
  only base period.
• The changes in the index can be attributed to
  changes in the price

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I-3-1. Price Indexes

• LPIs Disadvantages
• Does not reflect changes in buying pattern over
  time. It may overweight goods whose price
  increase (since consumption of such goods
  decrease). ? LPI overestimates the true
  inflation.
• The selection of base year is very critical.
  (base years quantities are weights for entire
  periods) ? Do not use the year with unusual
  consumption pattern as the base year (e.g. year
  of rice crises in 2008)

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I-3-1. Price Indexes

• Example LPI and base year
• Two series of the Laspeyres price index (LPI) are
  computed from the table of prices and quantities
  of a basket of goods.
• The first series uses 1960 as the base year
• LPI1960100, LPI198083, LPI200080. (base
  year1960)
• The second series uses 1980 as the base year
• LPI1960136, LPI1980100, LPI200092 (base
  year1980)

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I-3-1. Price Indexes

• C. Paasche Price Index (PPI)
• Use current year quantities as weights
• Qit quantity of commodity i in year t

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I-3-1. Price Indexes

• Advantage
• Reflects current buying habits.
• Disadvantage
• Requires quantity data for each year.
• Impossible to attribute changes in the index to
  changes in price alone.
• Tends to overweight the goods whose prices have
  declined, thus, underestimates the true
  inflation.

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I-3-1. Price Indexes

• Why does LPI (PPI) tend to overestimate
  (underestimate)?
• Law of demand (P ? ? Q?)
• Any treatment?
• FFI

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I-3-1. Price Indexes

• D. Fishers Ideal Index
• The Geometric Mean of LPI and PPI

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I-3-1. Price Indexes

• Geometric Mean
• The nth root of the product of n values.
• The GM is useful in finding the average of
  ratios. The GM is used in order to avoid giving
  undue importance on a few large values.
• (The GM is also useful to obtain accurate average
  growth rate).

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I-3-2. Quantity Index

• A. Laspeyres Quantity Index
• B. Paasche Quantity Index

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I-3-3. Value Index

• A. Value Index