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Dikhanov Table - Chapter 7

By Joe Perkins,2014-05-07 17:17
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Dikhanov Table - Chapter 7

    Chapter 7a

    Dikhanov Table - New ToolPack Product Diagnostics Table

Two Approaches to Price Diagnosis in the Tool Pack

    1. The ICP Tool Pack, a comprehensive software package developed by the World Bank

    and designed for purposes of collecting, validating and processing price and expenditure

    data, includes a new tool for price diagnostics and data validation the Dikhanov Table

    (DT). While the Quaranta Table (QT), also included in the Tool Pack, is intended to serve

    as a diagnostic tool for prices at the basic heading level, the Dikhanov Table is geared

    toward an analysis of the whole tableau of price data in a compact form.

    2. Both QT and DT convey similar ideas and start off with similar concepts: studying

    product price deviations for each country in a two-dimensional space: that of products

    and countries (Figure 1 shows an example of QT with an explanation of computational

    flows; arithmetic operations used in QT are shown with geometric symbols; for a detailed

    discussion on the QT see Chapter 7 of ICP Handbook). Both tables work with price 1variations.

    3. Even though both QT and DT show measures of price variations by product and country, 2the QT is limited to the basic heading level in its analysis, whereas the DT can be

    processed at any level, starting from the total GDP down to the basic heading (the DT can

    also be processed for groups of products, such as goods, services etc.). Whereas the QT

    shows some additional information about product prices within a basic heading, such as

    the number of quotations, the price variance and average prices, as well as the exchange-3rate ratios (see Figure 1); the DT adds an emphasis on the between basic heading

    validation, adding facilities to detect anomalies across both countries and basic headings.

    4. In the QT, PPPs are computed using one of the four indexes: EKS, EKS-STAR, CPD or 4CPRD. However, in the DT case, only CPD is used in computations as EKS does not

     1 In the QT case, the methodology in summarizing product price deviations does not exactly correspond to the one in

    the country dimension (see Figure 1, the average CV at the basic heading level presented in the Summary

    Information section is calculated as a simple average of the CVs for individual products). The DT is consistent in

    that respect using the same principles in computing standard errors by row (product level) and by column (country

    level).

     2 We refer to the QT implementation in the ICP Tool Pack. S. Sergeev (Statistics Austria), for example, has

    extended the original QT to include processing above the BH level.

     3 The exchange rate ratios in the QT serve to establish a common denominator for prices across BHs, due to the fact

    that the QT produces PPPs only within the BH. On the other hand, the DT uses other facilities for a common across-

    BH denominator as it explicitly computes PPPs at the GDP level.

     4 CPRD could potentially be also used in the DT diagnostics, but only after the representativity information has

    been cleaned up, as wrong or missing representativity data may affect results greatly and mask real problems as it

    Chapter 7a. Dikhanov Table

    1

    generate the average product price, an important measure that enters in various

    computations in the DT. See ANNEX for an additional discussion of using CPD in price

    diagnostics.

has been demonstrated in processing actual ICP data for the 2005 round (representativity is a whole new dimension

    in this case, just as the product and item dimensions are, but, unfortunately, it is not given as much attention and scrutiny as the other two dimensions). In fact, based on our experience we are recommending using CPD for the

    Quaranta Table as well, at least initially.

    Interpreting the DT statistics becomes less obvious in the CPRD case. An additional consideration in favor of using CPD is the fact that normally the residuals are one or more orders of magnitude larger than any difference between CPD and CPRD. In fact, a large difference between CPD and CPRD would indicate data problems, in particular, in

    the representativity dimension. Indeed this difference has been used as a diagnostic tool for the representativity validation.

In studies, CPRD has been found to be the least biased of the CPD, CPRD, EKS and EKS-STAR elementary indices,

    with CPD being second in the group, but this analysis presumes having correct information on representativity

    which may be lacking in particular during the editing and validation stage. Thus, CPRD is reserved for the final processing in the aggregation as the recommended elementary index number.

    Chapter 7a. Dikhanov Table

    2

Figure 1: Quaranta Table: Computation Order and Dependencies

    QUARANTA TABLE DIAGNOSTICS-Filters - Mushrooms and Garlic

    Time PeriodRun DateBasic Heading Code11011Quarter 1-200429-5-2005, 09:05:47Upper BoundLower BoundScope of CoverageCountry15050AggregationAggregationAveraging MethodArithmetic MeanCPDGeometric Mean

    Price AttributesNALocation AttributesNAProduct AttributesNA

    Summary Information

    3 out of 3205.0No of Items included in the AnalysisAverage weight of Basic Heading in Total Expenditure39.0No of Countries included in the Analysis3 out of 3Average Coefficient VariationBase CountryX

    Country Level Details

    CountryXRPPPPLI(%)Weight #ItemsVar.Co.Y1.001.6590165.9%105.03;*356.9X9.129.8517108.0%210.03;*333.1Z1.001.0000100.0%300.02;*122.9

    # Shares are multiplied by 10000.Item Level Details

    1101171021Var.Co.:57.0MushroomsCountryNC-PriceQuotationsVar.Co.XR-prXR-ratioCUP-priceCUP-ratioY*20.922612.720.92249.2512.61182.50X*43.917616.34.8257.374.4664.51Z5.87056.15.8769.935.8784.94

    8.396.91Geo Mean

    Mushrooms loose

     1101171022Var.Co.:30.1CountryNC-PriceQuotationsVar.Co.XR-prXR-ratioCUP-priceCUP-ratioGeo MeanY*4.500109.34.5099.822.7180.55X*41.18846.24.52100.184.18124.15Garlic4.513.371101171023Var.Co.:29.9CountryNC-PriceQuotationsVar.Co.XR-prXR-ratioCUP-priceCUP-ratioY*4.1701010.74.1792.912.5168.03Geo MeanX*45.4551019.44.98111.054.61124.87Z*4.3501124.84.3596.924.35117.73

    4.493.70LEGEND:

    RATIOELEMENTARY INDEX NUMBER

    GEO MEANVARIATION COEFFICIENT

    MEAN

    Chapter 7a. Dikhanov Table

    3

Connection between the Quaranta and Dikhanov Tables

    5. The main indicator in the QT is the CUP-Ratio. The CUP-Ratio is the double-normalized

    item price (one normalization is vs. the average country price level PPP, this is CUP-5price in the QT parlance, and another vs. the average of the country’s CUP-prices, see

    Figure 1).

    6. In the case of using CPD, the logarithm of the CUP-Ratio from the QT turns out to be the 6CPD residual from the DT as it is defined by expression 5 of Box 1 from below.

    However, this is only true for the DT processed at the basic heading level. It is no longer

    true for other cases.

    7. Both the QT and DT provide statistics based on price deviations, even though in

    somewhat different ways (see Footnote 1). The modus operandi of the two tables is

    similar as well: reducing deviations through price validation.

Description of the Dikhanov Table

    8. Figure 2 below contains a short description of the DT, also is shown an extract of a

    typical output with several basic headings and eight countries (only the upper part of the

    actual table is shown). The DT can be used at different levels of aggregation. Figure 3

    below exhibits the scopes of processing for various characteristics (for example, the

    country-specific characteristics such as the STD of CPD residuals and number of items

    prices are computed based on all items priced in that country see the gray out area

    under Cntr3) .

    9. The DT is organized in two sections: the general section at the top of the table and the

    item section at the bottom. The general section describes overall characteristics pertaining

    to the whole set of items under investigation: PPP, overall standard deviation of the CPD

    residuals, Price Level Index, Number of Items and Exchange Rate by country, and the

    overall STD of residuals and number of items for the whole price tableau. (Note that the

    GDP PPP is estimated here as the CPD PPP utilizing the whole set of prices and products,

    and, thus, does not take into account basic heading expenditures. The advantage of that is

    that the CPD PPP at the aggregate level can be estimated before the actual Basic Heading

    weights are known, and it will still provide a ball park estimate of the final PPP for the

    GDP).

    10. The lower section of the DT describes characteristics of the individual items: CPD

    Residual, standard deviation of CPD residuals by item, and Number of Countries pricing

    the item. The CPD computations are done at the level specified by the user (BH, class,

     5 I.e., the CUP-price is the price of the product in PPP terms; the CUP-ratio for any country is the ratio of the CUP-

    price for that country to the geo mean of the CUP-prices for individual countries.

     6 For a formal proof see (… ). The proof follows immediately from the following property of CPD index: if CPD

    index exists, then the CPD dummy coefficients for the original price matrix with some empty cells are identical to

    the coefficients of a new matrix which is obtained by adding to the original price matrix the prices which were gap-

    filled using the dummy coefficients for the original matrix.

    Chapter 7a. Dikhanov Table

    4

    GDP etc). In addition, the cells in the report with CPD residuals are color-coded to

    facilitate visual diagnostics:

Chapter 7a. Dikhanov Table

    5

Figure 2. How to Read the Dikhanov Table

     Cntr1Cntr2Cntr3Cntr4Cntr5Cntr6Cntr7Cntr8STDCNT

    PPP 2.0401.000 1.026 239.754 886.041 0.342 1,701.13 1.189 STD 0.380.28 0.31 0.35 0.32 0.31 0.33 0.32 0.34Country NameGENERAL PART:N. of items priced401369396418369350400369571COMPUTED USING ALL PLI 0.721.00 1.11 1.19 1.10 1.00 0.78 1.07 Number of ItemsAVAILABLE ITEMS (571 in this example) AND ALL COUNTRIES (8)Exchange Rate 2.8231.000 0.927 200.77 806.20 0.342 2,191.1 1.115 Priced in the Regioncomputed at the selected levelER (LCU/US$)2.9238.2532.711586.922356.781.00006405.1503.259(PPP is computed at the GDP level)1101111_0101Premium rice #1(0.06) 0.00 0.24 (0.09) 0.21 - (0.53) (0.24) 0.25 9Overall STD of Residuals in the 1101111_0102Premium rice #2- (0.08) - - - 0.08 - (0.00) 0.07 3Region: uses whole tableau of 1101112_0101Wheat flour prepackaged0.66 (0.16) 0.07 (0.11) (0.03) (0.63) 0.32 (0.42) 0.35 10CPD residuals1101112_0102Wheat flour loose0.14 - (0.02) - - - (0.20) - 0.13 41101112_0103Wholemeal flour (Atta)- 0.30 0.24 (0.33) (0.57) 0.23 - (0.15) 0.32 7STD of Residuals1101112_0104Semolina (Suji)- - - - (0.19) - - - 0.19 21101112_0201Corn flour loose(0.12) - 0.06 0.09 - - (0.04) - 0.08 4for the Country1101112_0202Corn flour prepackaged- (0.35) - (0.07) (0.34) 0.57 (0.41) (0.07) 0.41 7

    STD of Residuals1101113_0101White bread sliced0.24 0.40 (0.30) 0.19 (0.37) (0.31) 0.31 (0.19) 0.27 101101113_0103White bread loose- - - - 0.20 (0.20) - - 0.20 2for the Product1101113_0104Roll or bun loose0.09 0.16 (0.16) (0.24) 0.13 - 0.11 (0.24) 0.17 8

    Number of Products1101114_0101Cup cakes- 0.24 0.17 - 0.01 0.18 - (0.31) 0.22 61101114_0102Sponge Cake boxed0.16 (0.08) 0.19 (0.05) (0.04) - (0.06) (0.22) 0.13 9Priced in that Country1101114_0103Plain Butter Cookies (bag)(0.13) - 0.10 (0.09) - - 0.23 - 0.14 5ITEM-SPECIFIC PART:1101114_0201Biscuits prepacked- 0.45 - (0.11) - - - (0.20) 0.26 4COMPUTATIONS FOR INDIVIDUAL 1101114_0202Soda crackers0.43 - - (0.16) - - (0.22) - 0.26 4ITEMS (PRODUCTS),1101121_0101Mince/ground beef- 0.25 (0.08) (0.09) (0.17) (0.19) - 0.00 0.18 7out of 571 lines in this example, first Price Level Index1101121_0102Round steak(0.02) 0.51 0.06 (0.54) (0.03) 0.13 0.53 (0.08) 0.32 101101121_0103Sirloin steak0.08 - 0.14 (0.37) - - 0.22 - 0.20 6(PPP/ER ratio)41 lines are shown, grouped by basic headings1101122_0101Pork loin chops0.37 (0.14) 0.31 (0.59) 0.01 (0.25) 0.47 (0.26) 0.32 10

    PPP based on CPD index1101123_0101Lamb leg0.07 0.04 0.13 (0.16) - (0.23) 0.40 0.15 0.22 9computed at the selected level (GDP 1101124_0101Fresh whole chicken(0.25) 0.40 (0.21) - - - - 0.06 0.26 4ran on all products and countriestotal in this case) 1101124_0102Live chicken0.05 - 0.20 (0.02) (0.33) - 0.01 - 0.15 7in the region1101124_0201Native house chicken- 0.17 - - - (0.19) - 0.03 0.15 3

    Number of Countries1101125_0101Beef liver(0.07) (0.15) 0.24 (0.04) (0.23) (0.05) 0.24 (0.20) 0.18 101101125_0201Pork liver0.48 (0.00) (0.03) - (0.52) - 0.72 (0.28) 0.42 8Pricing that Product1101125_0301Mutton/goat liver(0.16) - 0.27 (0.42) - - 0.51 - 0.34 51101125_0302Pork kidney(0.17) (0.40) 0.34 0.64 0.01 (0.43) 0.31 (0.49) 0.36 101101125_0303Bacon0.31 (0.56) 0.10 0.78 (0.02) (0.43) 0.20 0.15 0.39 101101131_0101Mud crab(0.19) - 0.19 0.24 - - (0.25) - 0.22 41101131_0102Sea Crab0.10 - 0.09 (0.15) (0.17) - - 0.21 0.17 7Exchange Rate1101131_0103Sea Lobster- - - 0.02 (0.04) 0.06 - (0.28) 0.17 51101131_0104Prawn/shrimp small0.27 - 0.23 (0.46) (0.75) - - - 0.53 5vs. base country1101131_0105Prawn/shrimp medium- (0.35) - (0.09) (0.22) - - 0.53 0.31 5Exchange Rate1101131_0106Squid0.20 (0.15) (0.09) - - - 0.05 - 0.13 4vs. US$

    Product Codeindividual Basic HeadingsCPD RESIDUALProduct Name

Chapter 7a. Dikhanov Table

    6

Figure 3. Scope of Data Processing in the DT

    Cntr1Cntr2Cntr3Cntr4Cntr5Cntr6Cntr7Cntr8Cntr9Cntr10STDCNT

    PPP 2.4801.000 1.176 294.69 1,206 0.411 2,131 1.675 11.013 935.65 SCOPE OF CPD STD 0.180.20 0.15 0.17 0.19 0.30 0.21 0.14 0.13 0.19 0.19REGRESSION FOR PPP -

    GDP level N. of items priced71110101188106816

    PLI 0.881.00 1.27 1.47 1.50 1.20 0.97 1.50 1.26 1.29

    Exchange Rate 2.8231.000 0.927 200.77 806.20 0.342 2,191 1.115 8.715 726.00

    ER (LCU/US$)2.9238.2532.711586.922356.781.00006405.23.25925.47812122.34

    1101111_0101Premium rice #1(0.00) 0.08 - (0.00) (0.00) - 0.00 (0.08) (0.00) - 0.04 9BASIC HEADING1101111_0102Premium rice #2- (0.08) - - - - - 0.08 - - 0.07 31101112_0101Wheat flour prepackaged0.40 0.01 (0.00) (0.07) 0.26 (0.66) 0.37 (0.27) 0.16 (0.19) 0.31 101101112_0102Wheat flour loose(0.01) - 0.01 - - - (0.05) - 0.05 - 0.04 41101112_0103Wholemeal flour (Atta)- 0.42 0.12 (0.35) (0.33) 0.15 - (0.05) - 0.04 0.25 71101112_0104Semolina (Suji)- - - - 0.05 - - - - (0.05) 0.05 21101112_0201Corn flour loose(0.32) - 0.05 0.19 - - 0.07 - - - 0.19 41101112_0202Corn flour prepackaged- (0.24) - (0.10) (0.12) 0.47 (0.43) 0.01 - 0.40 0.30 7 SCOPE OF ITEM-SPECIFIC 1101112_0203Rice flour- 0.10 (0.37) - - - - 0.27 - - 0.27 31101112_0301Cake mix(0.07) - 0.15 0.10 - - 0.04 - (0.21) - 0.13 5COMPUTATIONS (STD and 1101112_0302Oats- (0.17) 0.05 0.07 0.20 (0.08) - 0.04 - (0.10) 0.12 7CNT /N. of countries pricing 1101112_0303Cornflakes- (0.13) - 0.17 (0.06) 0.13 - - - (0.11) 0.12 5the item/ by item) 1101113_0101White bread sliced0.05 0.15 (0.19) 0.20 (0.33) (0.14) 0.08 0.07 (0.13) 0.24 0.18 101101113_0102White bread loose- - - - 0.14 (0.14) - - - - 0.14 21101113_0103Roll or bun loose(0.05) (0.05) (0.02) (0.20) 0.21 - (0.08) 0.06 0.13 - 0.12 81101113_0104Roll or bun prepacked- (0.09) 0.20 - (0.02) 0.28 - (0.13) - (0.24) 0.18 6