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I n f o r m a t i o n e n

2. Paper presented at the Joint UNECE/ILO Meeting on CPIs
Wir bewegen
Optimal allocation of prices in practice - using the Neyman formula as tool
Paper presented at the Joint UNECE/ILO Meeting on CPIs
I n f o r m a t i o n e n
Alexandra Beisteiner
8. May, 2008
© STATISTIK AUSTRIA

3. Overview The Austrian price survey Initial Sampling The Neyman formula
A numerical example
Special cases
Interpretation

4. Motivation cost efficiency
best results under given circumstances (budget constraint)
optimize the precision for stratified samples
take into account the weight and the price diversity for a given product
optimal allocation -> Neyman formula

5. Austrian price survey
prices are collected by STAT and by regional governments
monetary compensation is fixed in a national regulation
field survey is done by standardized questionnaires
survey is divided into national classification, e.g. all food items that are typically bought in one shop are on one questionnaire
"difficult" prices or prices that are the same for all over Austria are collected by STAT

6. Initial Sampling Item expenditure weights Option I Option II
Option III
47 convenience food 2% 25 2 5
48 whole milk
68% 68
170
49 milk cocktail
16% 16 40
50 sour cream
14% 14 35
100%
100
250
Option I: even distribution of prices independent of the weights
Option II: n = 100, dependent on expenditure weights; e.g. 68 = 100 * 68% or 16 = 100 * 16%
Option III: n = 250, dependent on expenditure weights ; e.g. 170 = 250 * 68% or 40 = 250 * 16%

7. Neyman Formula sample size for stratum h
abb.
meaning in formulae
meaning in CPI setting nh
sample size for stratum h
number of prices observed for weighted item in the basket of goods n
total sample size
number of prices observed for the whole CPI Nh
population size for stratum h
item weight (relative expenditure share) h
standard devi-ation for stratum h
standard deviation of price relatives for weighted item in the basket of goods ch
direct cost to sample an individual element from stratum h
cost to sample an individual price for a specific item in the basket of goods

8. A numerical example 2% 0.2101 68% 0.1269 16% 0.2481 14% 0.1588 100%
Step: 1
Item
exp. weight
std. dev.
47 convenience food 2%
0.2101
48 whole milk
68%
0.1269
49 milk cocktail
16%
0.2481
50 sour cream
14%
0.1588
100%
Step 1: compute the standard deviation of the individual index numbers
either price relatives in a given month or twelve month rate of change

9. A numerical example 2% 0.2101 90 68% 0.1269 185 16% 0.2481 97 14%
Step: 1 2
Item
exp. weight
std. dev.
# of prices
47 convenience food 2%
0.2101 90
48 whole milk
68%
0.1269
185
49 milk cocktail
16%
0.2481 97
50 sour cream
14%
0.1588
100%
469
Step 2: compute the absolute number of prices for each item

10. A numerical example 2% 0.2101 90 0.4202 68% 0.1269 185 8.6292 16%
Step: 1 2 3
Item
exp. weight
std. dev.
# of prices
weight * std.dev.
47 convenience food 2%
0.2101 90
0.4202
48 whole milk
68%
0.1269
185
8.6292
49 milk cocktail
16%
0.2481 97
3.9696
50 sour cream
14%
0.1588
2.2232
100%
469
(Step 4)
2% * =
16% * =
Step 3: Compute the product of expenditure weights and the standard deviation
Step 4: Compute the sum of the products

11. A numerical example
Step: 1 2 3 5
Item
exp. weight
std. dev.
# of prices
weight * std.dev.
% of Step 3
47 convenience food 2%
0.2101 90
0.4202
2.76
48 whole milk
68%
0.1269
185
8.6292
56.61
49 milk cocktail
16%
0.2481 97
3.9696
26.04
50 sour cream
14%
0.1588
2.2232
14.59
100%
469
(Step 4)
= / *
Step 5: Calculate percentage of products from Step 3 and 4

12. A numerical example
Step: 1 2 3 5 6
Item
exp. weight
std. dev.
# of prices
weight * std.dev.
% of Step 3
est. #
47 convenience food 2%
0.2101 90
0.4202
2.76 13
48 whole milk
68%
0.1269
185
8.6292
56.61
266
49 milk cocktail
16%
0.2481 97
3.9696
26.04
122
50 sour cream
14%
0.1588
2.2232
14.59 68
100%
469
(Step 4)
56.61 * 469 = 266
Step 6: multiply percentage by total sample size

13. A numerical example 2% 0.2101 90 0.4202 2.76 13 -77 68% 0.1269 185
Step: 1 2 3 5 6 7
Item
exp. weight
std. dev.
# of prices
weight * std.dev.
% of Step 3
est. #
differ-ence
47 convenience food 2%
0.2101 90
0.4202
2.76 13
-77
48 whole milk
68%
0.1269
185
8.6292
56.61
266
+81
49 milk cocktail
16%
0.2481 97
3.9696
26.04
122
+25
50 sour cream
14%
0.1588
2.2232
14.59 68
-29
100%
469
(Step 4)
= 81
Step 7: Compute the difference between estimated and observed number of prices

14. Special cases
own weighted elementary aggregate for single price observations
e.g. new and used cars and newspapers -> introduction of a new key to enable the computation of the standard deviation
computation of price development is done in a separate file
e.g. telecommunication or flight tickets -> standard deviation has to be imputed into the calculation
rents have to be excluded
only overall value is entered into the CPI database; standard deviation is not known; sample size of rent survey can not be influenced directly by CPI

15. Interpretation of results
increasing or decreasing number of observations
in Austrian survey it's only possible to change number of observations for whole branches of trade;
duplication of product descriptions on the price survey for one branches
use results as an indicative and not as an absolute value
changes in survey structure should not affect the index

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