Aggregation of Price Data Below the Basic Heading Level

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Aggregation of Price Data Below the Basic Heading
Level

• D.S. Prasada Rao
• School of Economics
• University of New Queensland
• Brisbane, Australia

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Outline

• Aggregation below the BH Level
• Main characteristics
• EKS-type Methods
• CPD Method and its variants

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Basic Data

• Transitivity
• BH Parities must satisfy transitivity and base
  country invariance

PPPHK,India PPPHK,Malaysia PPPMalaysia,India
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Data for Aggregation at the BH Level

• No expenditure share weights are available for
  items at this level.
• Price tableau may be
• Complete
• Incomplete
• Incomplete tableau (missing prices for some items
  in some countries) is more frequent.
• In the ICP 2005 round, each item is classified as
  representative (general ICP or for poverty work)
  or not representative

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Data for numerical illustration
R representative N non-representative
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Aggregation Methods at the BH Level

• Elteto-Koves-Szulc (EKS) method
• Four different alternatives
• For use in different situations
• Country-Product-Dummy Method (CPD)
• Unweighted
• Weighted
• Other variants of CPD method

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Aggregation Methods at the BH Level

• Elteto-Koves-Szulc (EKS) method
• For complete tableau with all commodities equally
  representative
• Incomplete tableau where all items are equally
  representative
• Incomplete tableau where some items are
  representative and some or not

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Elteto-Koves-Szulc (EKS) Method

• Price Tableau Complete
• All items are priced in all the countries

• This index is transitive
• PPPs from this method are the same as those we
  get from the CPD method if the tableau is
  complete and all items are equally representative.

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EKS Method Variant 1

• 2. Price Tableau is incomplete
• No information on representativeness is known.
  Then the EKS method is given by

Where njk number of items priced in both
countries j and k.

• We note that Ijk is not transitive, but can be
  made transitive.

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EKS Method Variant 2

• 3. Price Tableau is incomplete
• Information on representativeness is known. Data
  is similar to the table given above.
• We make an index based on all items
  representative in country j which are also priced
  in k and vice versa. Then take geometric mean of
  the two indexes.

Where nkj no. of representative items in k that
are also priced in j and njk no. of
representative items in j that are also priced in
k
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EKS Method Variant

• 3. Price Tableau is incomplete
• Information on representativeness is known. Data
  is similar to the table given above.
• Variant 3 is same as variant 2 except that when a
  priced item is representative in both countries j
  and k then it is given double the weight.

Note PPPs from Variants 2 and 3 of the EKS
method are not-transitive. But they can be made
transitive by using
When representativeness is known, EKS-Variant 3
is considered the best.
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Country-Product-Dummy (CPD) Method

• A method due to Summers (1973) used by Balk
  (1985) for the treatment of seasonality
• Used in ICP for
• Treatment of missing prices
• Computation of PPPs below basic headings
• The Basic Model

where Ds are country and product dummy variables
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Country-Product-Dummy (CPD) Method

• Some comments
• If the price tableau is complete, and if all
  items are equally representative, then the CPD
  method gives same PPPs as the EKS method.
• If weights are available, then we can use
  weighted CPD. For example, we may give weight 2
  for items that are representative.
• 3. If some items are representative, then we can
  handle it by including a representativeness
  dummy in CPD model. This is the CPRD method.

Where Ri 0 if item is representative and 1 if
it is not representative
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PPPs from different methods
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Comments on the results

• When some items are representative and others are
  not, then EKS- variant 3 and CPRD methods are
  preferable.
• The CPRD method also provides standard errors.
• The weighted CPRD method gives additional weight
  to prices of items that are representative.
• If item expenditure share weights are known then
  weighted CPD is adequate.
• We will use the CPD and CPRD methods with 1st and
  2nd Quarter data when items are representative
  of the consumption of the poor.