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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 www.statistik.at 22.09.2019

Overview The Austrian price survey Initial Sampling The Neyman formula A numerical example Special cases Interpretation 22.09.2019

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 22.09.2019

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 22.09.2019

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% 22.09.2019

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 22.09.2019

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 22.09.2019

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 22.09.2019

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 15.2422 (Step 4) 2% * 0.2101 = 0.4202 16% * 0.2481 = 3.9696 Step 3: Compute the product of expenditure weights and the standard deviation Step 4: Compute the sum of the products 22.09.2019

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 15.2422 (Step 4) = 8.6292/ 15.2422 * 100 Step 5: Calculate percentage of products from Step 3 and 4 22.09.2019

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 15.2422 (Step 4) 56.61 * 469 = 266 Step 6: multiply percentage by total sample size 22.09.2019

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 15.2422 (Step 4) 266 - 185 = 81 Step 7: Compute the difference between estimated and observed number of prices 22.09.2019

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 22.09.2019

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 22.09.2019

für die Aufmerksamkeit VPI / HVPI Wir danken für die Aufmerksamkeit 22.09.2019

Österreich besser verstehen 22.09.2019