Aggregation of Price Data Below the Basic Heading Level

D.S. Prasada Rao

School of Economics University of New Queensland Brisbane, Australia

Outline



Aggregation below the BH Level

– Main characteristics 

EKS-type Methods



CPD Method and its variants

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Basic Data

Product i 1 2 . . n

•

Transitivity 1

p 11 p 21

. .

p n1

Country j

p p p

2

12 22

. .

n2 … …

…

…

c

p 1c p 2c

. .

p nc

PPP HK,India = PPP HK,Malaysia PPP Malaysia,India

•

BH Parities must satisfy transitivity and base country invariance

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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 4 4/30/2020

Data for numerical illustration

Product 1 2 3 4 5 6 Table: Incomplete Tableau with Representativity Country A Country B Country C Country D R 2 6 8 N 6 R – representative N – non-representative R 120 N 100 250 270 280 R 12 15 12 N 70 100 R 25 22 120 N 60 100 4/30/2020 5

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 4/30/2020 6

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 4/30/2020 7

Elteto-Koves-Szulc (EKS) Method

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

I jk



i n

  1   

p i k p i j

   1/

n

• 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 I jk  i n jk   1    p i p i k j    1 / n jk Where n jk = number of items priced in both countries j and k. • We note that I jk is not transitive, but can be made transitive.

I jk EKS   M   1  I j  I  k  1 / M 4/30/2020 9

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.

1 2

I jk

  

kj p i k p i j

1  

n kj



jk

 

p i k p i j

1  

n jk

Where n kj = no. of representative items in k that are also priced in j and n jk = no. of representative items in j that are also priced in k 4/30/2020 10

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: I jk EKS   M   1  I j  I  k  1 / M 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:

ln

p i j

  1

D

1   2

D

2  . . .

 

n D n

  1

D

1 *   2

D

* 2  . . .

 

M D

*

M



u i j

where D’s are country and product dummy variables 12 4/30/2020

Country-Product-Dummy (CPD) Method

Some comments: 1. If the price tableau is complete, and if all items are equally representative, then the CPD method gives same PPPs as the EKS method.

2. 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.

ln

p i j

  1

D

1   2

D

2  . . .

 

n D n

  1

D

1 *   2

D

* 2  . . .

 

M D

*

M

 

i R i



u i j

Where R i = 0 if item is representative and = 1 if it is not representative 4/30/2020 13

Method. EKS 2 EKS 3 CPD unw s.e. CPD wei s.e. CPRDunw s.e. CPRD wei s.e. 4/30/2020

PPPs from different methods

A 1 1 1 1 1 1 1 Estimated PPPs : data from Table 4 Country coefficients (PPPs) B 28.12 26.61 37.56 (1.51) 35.51 (1.50) 25.81 (1.36) 25.21 (1.37) C 2.96 3.17 3.96 (1.50) 3.57 (1.46) 3.82 (1.33) 3.47 (1.32) D 8.11 7.99 10.56 (1.51) 9.40 (1.46) 9.67 (1.34) 8.88 (1.32) 1 Representativity coefficients Rep Unrep 2.06 (1.24) 1 2.01 1.25 14

Comments on the results

1. When some items are representative and others are not, then EKS- variant 3 and CPRD methods are preferable.

2. The CPRD method also provides standard errors.

3. The weighted CPRD method gives additional weight to prices of items that are representative.

4. If item expenditure share weights are known then weighted CPD is adequate.

5. We will use the CPD and CPRD methods with 1 st and 2 nd Quarter data when items are “representative” of the consumption of the poor.

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