International Comparison Program
PPPs for Technology Products with Country Brand Model Dummy [CBMD] Method

Global Office

Operational Material
Introduction Technology products such as audio-video equipment, office and communication equipment present special challenges for price collection and PPP computation. Primarily this is related to short life cycles and fast changing nature of these products, as well as rapid technological progress occurring in the underlying technologies. Particular models of DVD players or TVs, for example, may become obsolete and get replaced in the course of one year. Price of these products often drops 30% or more during one year. To complicate the situation, introduction of new models may not be simultaneous across different markets. In general, regular ICP procedures cannot capture these properties and cannot produce satisfactory PPPs. In addition, consumer electronics companies often tend to create market fragmentation, introducing models with minor variations for groups of countries or even for individual countries. The procedure discussed in this note intends to address these issues. Description of the Country Brand Model Dummy [CBMD] Method The CBMD method can be seen as an extension of the regular CPD method [see the definition in the annex below]. The extension incorporates models into the regression along with countries and brands. There are two variants of the PPP estimation using the CBMD specification: (i) as a one-stage procedure, where BH PPPs are directly estimated along with dummies for brand-model combinations, and (ii) as a two-stage procedure, where brand [or product group] PPPs are estimated first, and then the brand PPPs are combined into the BH PPP, using the regular CPD method. The two-stage procedure thus consists out of a number of one-stage procedures to be combined to produce BH PPPs. The procedure deals with market segmentation and obsolescence by sampling players from the same manufacturer and from the same market segment, incorporating new models as soon as they appear on the market.
EXAMPLE BASIC HEADING: CD PLAYERS [TWO BRANDS/GROUPS] TWO VERSIONS: 1-stage and 2-stage
Description: CD players [two brands/product groups] 1 Sony MHC RG 330 or Sony MHC RG 550 [medium stratum] 2 JVC PK33 or JVC PK55 [low level stratum] Instructions: to country collect the indicated models, if not available, collect models from the same market segment of that brand/group collect data monthly/quarterly, do not collect if a model is difficult to find to RC RCs would need to cross-check the models collected by the countries on the internet Sample returns included 9 models for Sony and 10 models for JVC out of which 5 were left for Sony and 6 for JVC [other models were collected in one country only, and four models were merged into two because they were judged to be identical even though sold under different names in different markets]

SUBMITTED PRICES

SONY MHC RG 221/222 MHC RG 330 MHC RG 441 MHC RG 550 MHC RG 551 JAX PK10 JAX PK33 JAX PK5 JAX PK66 JAX PK7/PK77 JAX PK88

ARG Q1 1,260

ARG Q2 1,160 1,250 1,700 910

ARG Q3 1,086

ARG Q4

COL Q1 900,000 900,000

COL Q2

COL Q3

COL Q4
URY Q1 12,885 14,114 14,720
URY Q2 12,000 13,000 13,900
URY Q3 11,500 12,500 13,500
URY Q4 11,000 11,000 13,500
840,000 720,000 389,000 500,000 600,000 700,000
780,000 666,000 389,000 500,000 550,000 650,000

720,000

1,200 784,800 410,000 529,000 450,000 622,683 787,900 350,000 450,000 500,000 650,000

1,750 1,000

REFERENCE (product of country and brand-model coefficients from CBMD regression, two brands/groups together) GAPFILLED PRICES (1-stage) ARG Q1 ARG Q2 ARG Q3 ARG Q4 COL Q1 COL Q2 COL Q3 COL Q4 URY Q1

MHC RG 221/222 MHC RG 330 MHC RG 441 MHC RG 550 MHC RG 551 JAX PK10 JAX PK33 JAX PK5 JAX PK66 JAX PK7/PK77 JAX PK88 1,319 1,260 1,392 1,475 1,1,000 1,1,213 1,160 1,280 1,250 1,910 1,1,143 1,086 1,207 1,250 1,820 1,1,103 1,111 1,164 1,200 1,750 1,900,000 848,939 900,000 943,004 784,800 410,000 529,000 450,000 622,683 787,900 413,563 783,857 789,249 840,000 876,699 720,000 389,000 500,000 438,646 600,000 700,000 384,484 743,991 749,108 780,000 832,111 666,000 389,000 500,000 416,337 550,000 650,000 364,930 695,889 700,675 720,000 778,312 656,300 350,000 450,000 389,419 500,000 650,000 341,336 12,885 14,114 13,795 14,720 12,327 6,560 8,400 7,314 9,580 11,874 6,000
URY Q2 12,000 13,000 13,091 13,900 11,698 6,225 8,400 6,941 9,091 11,267 5,700
URY Q3 11,500 12,500 12,326 13,500 11,015 5,862 7,200 6,536 8,560 10,610 5,500
URY Q4 11,000 11,000 11,638 13,500 10,400 5,535 7,060 6,171 8,083 10,017 5,000
REFERENCE (product of country and brand-model coefficients from CBMD regression, two brands/groups separately) GAPFILLED PRICES (2-stage) ARG Q1 ARG Q2 ARG Q3 ARG Q4 COL Q1 COL Q2 COL Q3 COL Q4 URY Q1 URY Q2
MHC RG 221/222 MHC RG 330 MHC RG 441 MHC RG 550 MHC RG 551 JAX PK10 JAX PK33 JAX PK5 JAX PK66 JAX PK7/PK77 JAX PK88 1,263 1,260 1,423 1,445 1,1,000 1,1,141 1,160 1,285 1,250 1,910 1,1,075 1,086 1,210 1,250 1,820 1,1,050 1,079 1,182 1,200 1,600 900,000 850,635 900,000 945,855 784,800 410,000 529,000 450,000 622,683 787,900 429,115 733,960 754,669 840,000 839,146 720,000 389,000 500,000 436,844 600,000 700,000 404,608 680,222 699,415 780,000 777,707 666,000 389,000 500,000 419,597 550,000 650,000 388,635 639,422 657,464 720,000 731,060 637,544 350,000 450,000 388,664 500,000 650,000 359,984 12,885 14,114 14,814 14,720 13,117 6,155 8,400 6,834 8,963 11,140 6,000 12,000 13,000 13,809 13,900 12,228 5,999 8,400 6,661 8,736 10,858 5,700
URY Q3 11,500 12,500 13,308 13,500 11,784 5,456 7,200 6,058 7,945 9,875 5,500
URY Q4 11,000 11,000 12,565 13,500 11,126 4,862 6,289 5,398 7,080 8,800 5,000
DIAGNOSTICS [CPD RESIDUALS], 1-stage
ARG Q1 MHC RG 221/222 MHC RG 330 MHC RG 441 MHC RG 550 MHC RG 551 JAX PK10 JAX PK33 JAX PK5 JAX PK66 JAX PK7/PK77 JAX PK88 -0.05 ARG Q2 -0.05 -0.08 0.05 0.03 0.03 0.02 ARG Q3 -0.06 0.01 -0.02 -0.03 -0.01 -0.04 -0.02 0.15 -0.08 0.10 -0.03 -0.02 -0.05 0.01 0.03 -0.03 -0.01 0.00 0.04 -0.02 -0.05 0.04 0.05 0.01 -0.04 0.00 0.01 -0.02 0.03 -0.07 -0.07 -0.04 -0.08 0.00 0.06 -0.04 0.04 -0.04 0.02 0.03 0.02 -0.01 -0.02 0.01 0.00 0.03 0.09 ARG Q4 COL Q1 0.07 COL Q2 COL Q3 COL Q4 URY Q1 -0.01 0.07 URY Q2 -0.03 0.04 URY Q3 -0.02 0.06 URY Q4 0.00 -0.01

DIAGNOSTICS [CPD RESIDUALS], 2-stage
ARG Q1 MHC RG 221/222 MHC RG 330 MHC RG 441 MHC RG 550 MHC RG 551 JAX PK10 JAX PK33 JAX PK5 JAX PK66 JAX PK7/PK77 JAX PK88 -0.03 ARG Q2 -0.01 -0.04 0.05 -0.01 0.01 0.00 ARG Q3 -0.02 -0.03 0.02 -0.05 -0.07 -0.03 0.09 -0.06 0.06 -0.02 -0.02 -0.03 0.02 0.04 -0.02 -0.01 -0.02 0.05 -0.02 -0.02 0.03 0.02 0.00 -0.05 0.00 -0.01 -0.02 0.03 -0.05 -0.08 -0.02 0.05 0.08 0.02 0.03 -0.06 0.02 0.04 0.02 0.02 -0.02 -0.01 0.00 0.06 ARG Q4 COL Q1 0.08 COL Q2 COL Q3 COL Q4 URY Q1 -0.02 0.04 URY Q2 -0.02 0.03 URY Q3 -0.03 0.03 URY Q4 -0.01 -0.04

QUARTERLY AVERAGE PRICES

AVE. PRICE AVE. PRICE AVE. PRICE AVE. PRICE CD PLAYER SONY CD PLAYER JVC CD PLAYERS (1-stage) CD PLAYERS (2-stage) 1,1,030 1,053 1,1,1,874,505 523,352 658,397 676,516 775,846 493,463 612,104 618,750 719,042 473,982 580,973 583,792 675,913 439,040 543,411 544,750 13,907 7,720 10,207 10,361 12,964 7,524 9,686 9,877 12,493 6,843 9,120 9,246 11,796 6,098 8,611 8,481
QUARTERLY BASIC HEADING PARITIES (brand/group)
2-stage computation PPP CD PLAYER SONY PPP CD PLAYER JVC ARG Q1 1.00 1.00 ARG Q2 0.90 0.94 ARG Q3 0.85 0.87 ARG Q4 0.83 0.83 COL Q1 654.8 630.1 COL Q2 580.9 594.1 COL Q3 538.4 570.6 COL Q4 506.1 528.6 URY Q1 10.41 9.29 URY Q2 9.71 9.06 URY Q3 9.35 8.24 URY Q4 8.83 7.34
QUARTERLY BASIC HEADING PARITIES
Pooled CBMD on 11 models (1-stage) PPP CD PLAYER ALL CBMD on two brands/groups (2-stage) PPP CD PLAYER ALL 1.00 1.00 ARG 1,0.92 0.92 0.87 0.86 0.84 0.83 639.4 642.3 COL 757,785 481,480 597,240 604,035 594.4 587.5 564.2 554.3 527.7 517.2 9.91 9.84 URY 12,767 7,017 9,387 9,465 9.41 9.38 8.86 8.78 8.36 8.05

ANNUAL AVERAGE PRICES

CD PLAYER SONY CD PLAYER JVC CD PLAYERS (1-stage) CD PLAYERS (2-stage)
ANNUAL BASIC HEADING PARITIES
CD PLAYER SONY CD PLAYER JVC CD PLAYERS (1-stage) CD PLAYERS (2-stage) 1.00 1.00 1.00 1.00 634.9 638.2 641.8 636.5 10.70 9.30 10.09 9.97

ANNEX CBMD Procedure

There are two variants of the PPP estimation using the CBMD specification: (i) as a onestage procedure, where BH PPPs are directly estimated along with dummies for brandmodel combinations, and (ii) as a two-stage procedure, where brand PPPs are estimated first, and then the brand PPPs are combined into the BH PPP, using the regular CPD method. The two-stage procedure thus consists out of a number of one-stage procedures to be combined to produce BH PPPs. CBMD regression can be presented in two equivalent forms with intercept and without. Without intercept, the regression equation for the CBMD is written as:

ln pcbm ycbm xcbm cbm

where pcbm - price of model m of brand b in country c; (2) T 2. Nc 1 2. Nbm Dc j and Dbmi - country, brand/model dummies; Nc, Nbm number of countries, brand/model combinations respectively; In matrix notation, by stacking individual observations, this can be written as:
xcpm Dc2.DcNc Dbm1Dbm2.DbmNbm
Note that the first country dummy is dropped from the system because matrix X is of rank (Nc+Nb+Nm-1) [in fact, we can drop any variable from the system, dropping the first countrys dummy simply makes it the base country]. The solution is given (under the conditions of independently and identically distributed random disturbances) by

1 XT X XT y