New Methodological Developments for the International Comparison Program Presentation at the Tinberg

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New Methodological Developments for the
International Comparison ProgramPresentation at
the Tinbergen Institute at Erasmus University,
Rotterdam, October 3, 2008

• W. Erwin Diewert
• Department of Economics
• University of British Columbia

2
Introduction

• The World Bank released the results for ICP 2005
  in February of this year
• 146 countries in 6 regions participated in the
  comparisons of prices and volumes (or real
  outputs) for the year 2005
• Each of the 6 regions made up its own list of
  about 1000 narrowly defined products to be priced
  within the region
• These individual prices were aggregated into 155
  Basic Headings

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• Each participating country also provided a GDP
  breakdown of its expenditures on these 155
  categories
• Thus if region r has C(r) countries, we have 2
  matrices of size 155 by C(r)
• One matrix has the country price levels
• The other matrix has the country expenditures by
  155 commodity classes
• Now international comparisons of prices and
  volumes within the region can be carried out
  using EKS or GK

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• But how were the regions linked together?
• Another commodity list was constructed the ring
  list and 18 countries across the regions priced
  out this list, enabling linking
• This is what led to new methodological
  developments we now have a 2 stage procedure for
  linking the 146 countries
• Sections 2 and 3 how to link the 155 BH prices
  across (a) countries within a region and (b)
  across regions?
• Sections 4 and 5 how to construct aggregate
  price and volume comparisons across (a) within a
  region and (b) across regions?

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2. Linking prices across countries within a region

• The Country Product Dummy (CPD) method (Summers
  (1973)) was used by African, Asian Pacific and
  West Asian regions
• The Extended (to include representativeness) CPD
  method (Cuthbert and Cuthbert (1988) was used by
  South America. Hill (2007) called this the CPRD
  method.
• The EKS method was used by the OECD and CIS
  regions.

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• The CPD method with a balanced panel of price
  data works as follows
• pcn acbnucn c 1,,C n 1,,N
• Taking logs of both sides of (1) leads to
• (2) ycn ?c ?n ?cn c 1,,C n
  1,,N
• where ycn ? ln pcn, ?c ? ln ac, ?n ? ln bn and
  ?cn ? ln ucn.
• (2) is a linear regression model. The as are
  the country PPPs for the particular BH category
  under consideration and the bs are product
  premiums that depend on the units of measurement

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• The Basic CPDR model is
• (5) ycnu ?c ?n ?u ?cnu c
  1,,C n 1,,N
• 
  u 1,2
• where the ?c are the log country PPPs, the ?n
  are the log product price effects and the ?u are
  the two log representativity effects and the ?cnu
  are independently distributed random variables
  with mean zero and constant variances. In order
  to identify the parameters, we impose the
  following normalizations
• (6) ?1 0 ?1 0.
• This is another linear regression model. In
  principle, it should work better than the CPD
  method.
• The EKS model is explained by Hill (2007)

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3. Comparing Prices Across Regions

• The model that was used to link BH price levels
  across regions was the following generalization
  of the CPD model
• (7) prcn ? ar brc cn r 1,,5 c
  1,....,C(r) n 1,...,N
• (8) a1 1
• (9) br1 1
  r 1,,5
• where the above model pertains only to the price
  data for the ring countries. There are C(r) ring
  countries in region r 1,2,3,4,5, the as are
  interregional PPPs and (8) means that region 1 is
  chosen as the numeraire region, the bs are the
  country PPPs for the countries in one of the 5
  regions and (9) means that country 1 in each
  region is chosen as the numeraire country in that
  region and the cs are commodity effects that
  depend on the units of measurement for the
  products.

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• In order to respect the parities that were
  estimated by the regions, the following
  modification of the basic model above was run by
  the World Bank
• (13) ln prcn? ln brc ln arln cn ?rcn
  r 1,,5
• c 1,....,C(r) n
  1,...,N.
• The above model simplifies into
• (14) ln prcn/brc ?r ?n ?rcn
• which is a linear regression model. The ?r are
  the logs of the interregional PPPs and the ?n are
  the individual product effects for the products
  within the basic heading category of commodities
  which were price out by the ring countries.

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4. Relative Prices and Volumes for Countries
within a Region

• 5 of the 6 regions used the Gini (1924) (1931)
  EKS (1964) method to construct aggregate PPPs and
  relative volumes for the countries in their
  regions.
• But Africa used a new additive method due to
  Doris Iklé (1972) and Yuri Dikhanov (1994), who
  made her method intelligible. Bert Balk (1996)
  provided the first existence proof for the method
  so we will call the method the IDB system.
• We will explain these two methods in the next few
  slides along with the Geary Khamis (GK) method
• Both methods are implemented at the basic heading
  level where we have price and quantity data
  available for each country for the 155 basic
  headings.

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4. Relative Prices and Volumes for Countries
within a Region

• 4.1 The Gini EKS Method (GEKS)
• Define country vectors of BH prices as pk ?
  p1k,...,pNk, country vectors of BH quantities
  as yk ? y1k,...,yNk, country expenditure
  vectors as ek ? e1k,...,eNk and country
  expenditure share vectors as sk ? s1k,...,sNk
  for k 1,...,K.
• (17) PF(pk,pj,yk,yj) ? pj?yj pj?yk/pk?yj
  pk?yk1/2
• 
  j 1,...,K k 1,...,K.
• The aggregate PPP for country j, Pj, is defined
  as follows
• (18) Pj ? ?k1K PF(pk,pj,yk,yj)1/K
  j 1,...,K.

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GEKS (continued)

• GEKS country real outputs or volumes Yj can be
  defined as the country expenditures pj?yj in the
  reference year divided by the corresponding GEKS
  purchasing power parity Pj
• (19) Yj ? pj?yj/Pj
  j 1,...,K.
• The GEKS country shares of world product are
  defined as follows
• (20) Sk ? Yk/?j1K Yj
  k 1,...,K.
• Aside on exact and superlative indexes and the
  role of the Fisher indexes consistent with
  perfect substitutability and no substitution at
  all (Leontief preferences) but also consistent
  with flexible functional forms in the case of
  homothetic preferences.

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4.2 The Geary Khamis Method (GK)

• The GK system of equations involves K country
  price levels or PPPs, P1,...,PK, and N
  international commodity reference prices,
  ?1,...,?N. The equations which determine these
  unknowns (up to a scalar multiple) are the
  following ones
• (21) ?n ?k1K ynk/?j1K ynjpnk/Pk
  n 1,...,N
• (22) Pk pk?yk/??yk
  k 1,...,K.
• (24) Yk pk?yk/Pk
  k 1,...,K
• ??yk using (22).
• Problem Big countries get undue weight in the
  ?n .

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4.3 The Ikle Dikhanov Balk Method (IDB)

• Dikhanovs (1994 9-12) equations that are the
  counterparts to the GK equations (21) and (22)
  are the following ones
• (27) ?n ?k1K snk pnk/Pk?1/?j1K snj?1
  n 1,...,N
• (28) Pk ?n1N snk pnk/?n?1?1
  k 1,...,K.
• Note the use of share weighted harmonic means in
  (27) and (28). The use of share weights gives the
  IDB parities a more democratic flavour.
  Equations (24) are still used to define the
  country volumes Yk. Thus both GK and IDB are
  termed additive methods since both methods use a
  common set of international prices to value
  output components across countries.

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5. Aggregate price and Volume Comparisons Across
Regions

• Reorganize the countries into 5 regions (we
  regard the OECD/Eurostat/CIS countries as forming
  one region).
• Consider region r which has C(r) countries in it.
  Let pnrc denote the within region PPP for basic
  heading class n and country c in region r and let
  enrc denote the corresponding expenditure in
  local currency.
• The total regional expenditure on commodity group
  n in currency units of country 1 in each region,
  Enr, is defined as follows
• (31) Enr ? pnr1 ?c1C(r) enrc/pnrc
  r 1,...,5 n 1,...,155.
• The corresponding regional PPPs by region and
  commodity, Pnr, are defined to be the world BH
  parities for the numeraire country in each
  region
• (32) Pnr ? pnr
  r 1,...,5 n
  1,...,155.

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• Now each region can be treated as if it were a
  single supercountry with supercountry
  expenditures and basic heading PPPs defined by
  (31) and (32) respectively for the 5
  supercountries. The EKS method was used to link
  these supercountries.
• Once the interregional price and volumes have
  been determined, the regional price and volume
  aggregates can be used to provide world wide
  price and volume comparisons for each individual
  country. This method necessarily preserves all
  regional relative parities.
• Hill (2007e) shows that the overall procedure
  does not depend on the choice of numeraire
  countries, either within regions or between
  regions i.e., the relative country parities will
  be the same no matter what the choices are for
  the numeraire countries.

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6. Problem Areas and Future Research

• The problem of pricing exports and imports. At
  present, exchange rates are taken as the price of
  exports and imports.
• Inaccurate expenditure weights can cause grave
  difficulties.
• Methodological difficulties with hard to measure
  areas of the accounts. There are particular
  problems with housing, financial services and
  nonmarket production. These are problem areas for
  regular country accounts as well due to the lack
  of consensus on an appropriate methodology.
• The fact that current System of National Accounts
  conventions do not allow an imputed interest
  charge for capital that is used in the nonmarket
  sector tends to understate the contribution of
  this sector and the degree of understatement will
  not be constant across rich and poor countries.

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• The lack of matching of products. The same
  problem occurs in the time series context due to
  the introduction of new products and the
  disappearance of old products but the lack of
  matching is much worse in the international
  context due to differences in tastes and big
  differences in the levels of development across
  countries, leading to very different consumption
  patterns.
• However, Structured Product Descriptions were
  introduced in the current ICP round and this does
  open up the possibility for undertaking hedonic
  regression exercises in the next round in order
  to improve the matching process.
• There are many problems to be addressed however,
  and it would be wise to undertake experimental
  hedonic studies well in advance of the next round.

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• The fact that the ring list of commodities to be
  priced was almost entirely different from the
  regional lists means that there is the
  possibility of anomalies in the final results
  i.e., if entirely different products are priced
  in the ring list, we cannot be sure the relative
  ring price levels really match up with the
  relative prices within the regions.
• Thus in the next ICP round, there should be at
  least some coordination in the determination of
  the ring product list with the regional product
  lists so that within each basic heading level,
  one or more products are on all of the lists.

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• It would be advisable to undertake some studies
  on alternative methods of aggregation at the
  higher levels of aggregation. In particular, the
  program of making comparisons based on the degree
  of similarity of the price and quantity data
  being compared that was initiated by Robert Hill
  seems to be sensible but users have not embraced
  it, perhaps due to the instability of the method.
  In any case, the World Bank now has a
  considerable data set based on the current ICP
  round that could be used to experiment with
  alternative methods of aggregation.
• Looking ahead into the more distant future, it
  would be desirable to integrate the ICP with the
  EU KLEMS project, which is assembling data on the
  producer side of the economy as opposed to the
  final demand side, which is the focus of the ICP.
  Producer data are required in order to calculate
  relative productivity levels across economies, a
  topic of great interest to policy makers.
• The data disclosure problem.

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7. Conclusion

• The regions liked the idea that they could define
  their own list of products for international
  pricing and this improved the quality of the
  data.
• The new methodology to link prices across the
  regions using ring countries also seems to be a
  clear improvement over previous rounds.
• The use of hand held computers and the structured
  product description methodology led to
  improvements in the production of national price
  statistics in many cases.
• Overall, ICP 2005 was a major success!

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Appendix Numerical Examples

• Example 1 from Diewert 1999
• This was a three country, two commodity example.
  
• (A84) p1 ? 1,1 p2 ? 10, 1/10 p3 ? 1/10,10
  y1 ? 1,2 y2 ? 1,100 y3 ? 1000,10.
• Note that the geometric average of the prices in
  each country is 1, so that average price levels
  are roughly comparable across countries, except
  that the price of commodity 1 is very high and
  the price of commodity 2 is very low in country 2
  and vice versa for country 3. As a result of
  these price differences, consumption of commodity
  1 is relatively low and consumption of commodity
  2 is relatively high in country 2 and vice versa
  in country 3. Country 1 can be regarded as a
  tiny country, with total expenditure (in national
  currency units) equal to 3, country 2 is a medium
  country with total expenditure equal to 20 and
  country 3 is a large country with expenditure
  equal to 200.

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Example 1 (continued)

• Table 1 Fisher Star, GEKS, GK and IDB Relative
  Volumes for Three Countries
• Fisher 1 Fisher 2 Fisher 3 GEKS
  GK IDB
• Y1 1.00 1.00 1.00
  1.00 1.00 1.00
• Y2 8.12 8.12 5.79
  7.26 47.42 33.67
• Y3 57.88 81.25 57.88
  64.81 57.35 336.67
• It can be seen that the GK parity for Y3/Y1,
  57.35, is reasonable but the parity for Y2/Y1,
  47.42, is too large. The cause of this
  unreasonable estimate for Y2 is the fact that the
  GK international price vector, ?1,?2, is equal
  to 1, 9.00 so that these relative prices are
  closest to the structure of relative prices in
  country 3, the large country.

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Example 2

• Yuri Dikhanov rightly objected to the previous
  example, noting that the amount of price
  variation across countries was too extreme
  compared to the actual amounts. He was nice
  enough to give me data (from the 2005 ICP) on 5
  consumption components for 8 countries.
• The 8 countries are 1Hong Kong, 2Bangladesh
  3India, 4Indonesia 5Brazil 6Japan 7Canada
  and 8US.
• The 5 commodity groups are 1durables 2food,
  alcohol and tobacco 3other nondurables
  excluding food, alcohol, tobacco and energy,
  4energy and 5services
• The expenditure data (converted to US dollars)
  and the quantity data for the 8 countries are on
  the next slide.

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Example 2 (continued)

• Expenditures by commodity (row) and country
  (column)
• 14320 1963 23207 8234 52722
  307547 94121 967374
• 10562 24835 176782 83882 105527
  448995 82056 778665
• 14951 5100 60748 15158 60798
  272875 69461 992761
• 2619 3094 42126 17573 39933
  125835 43342 524288
• 62124 11627 166826 61248 273669 1736977
  379629 5559458
• Quantities by commodity (row) and country
  (column)
• 15523 2312 30189 9781 46146 280001
  81021 967374
• 9164 47509 356756 138273 163868 251846
  63689 778665
• 17564 10588 180964 29879 65274 200614
  58261 992761
• 1095 3033 38377 22084 23963
  59439 35714 524288
• 81148 47611 786182 223588 541236 1695136
  417210 5559458
• We use the above data to compute various indexes.
  

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Example 2 (continued)

• The GEKS volumes turned out to be
• HK BGD INDIA INDO BRA JPN
  CAN US
• 0.01315    0.01332    0.15317    0.04966   
  0.09128    0.26556    0.07357    1.00
• The Market exchange rate volumes are
• 0.01185    0.00528    0.05324    0.02109   
  0.06037    0.32782    0.07578    1.00
• The GK volumes turned out to be
• 0.01386    0.01357    0.16258    0.05057   
  0.09613    0.27814    0.07431    1.00
• The IDB volumes turned out to be
• 0.01346    0.01392    0.16187    0.05143   
  0.09441    0.27076    0.07417    1.00
• Vector of percentage differences, (GK/GEKS) 1
• 0.05413    0.01898    0.06147    0.01841   
  0.05306    0.04737    0.01015    0.00
• Vector of percentage differences, (IDB/GEKS) 1
• 0.02332    0.04497    0.05685    0.03568   
  0.03429    0.01957    0.00823    0.00
• Conclusion IDB no better than GK relative to EKS

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Example 2 (continued)

• A final method Robert Hills spatial linking
  method
• Need a measure of similarity in the structure of
  relative prices across two countries see Diewert
  (2002) is basically a share weighted average of
  log price ratios, where the prices of one country
  are deflated by the Fisher price index between
  the two countries to eliminate the effects of
  absolute differences in price levels
• The Hill volumes turned out to be
• HK BGD INDIA INDO BRA JPN
  CAN US
• 0.01349    0.01310    0.14720    0.04779   
  0.09214    0.27596    0.07429    1.00
• The 8 countries grouped themselves into two
  groups that had similar price structures rich
  countries HK, JPN, CAN and US and poorer
  countries BGD, INDIA, INDO and BRA. The linking
  between the two groups took place via HK and
  BRAZIL.

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Example 2 (continued)

• My preferred method is the Hill spatial linking
  method
• The differences between GEKS, GK and IBD are as
  follows
• HK BGD INDIA INDO BRA JPN
  CAN US
• (GEKS/HILL) 1
• -0.02544    0.01713    0.04054    0.03907  
  -0.00934   -0.03768   -0.00980    0.0
• (GK/HILL) 1
• 0.02732    0.03643    0.10450    0.05820   
  0.04323    0.00790    0.00025    0.0
• (IDB/HILL) 1
• -0.00271    0.06287    0.09969    0.07614   
  0.02463   -0.01885   -0.00165    0.0
• For India, both GK and IDB overstate Hill by
  10.0, for Bangladesh, IDB overstates by 6.3 and
  GK overstates by 3.6 for Indonesia, IDB
  overstates by 7.6 and GK by 5.8 for Brazil,
  IDB overstates by 2.5 and GK by 4.3. These are
  very substantial differences.
• Conclusion the choice of multilateral method
  matters!