Title: New Methodological Developments for the International Comparison Program Presentation at the Tinberg
1New 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
2Introduction
- 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
3- 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
4- 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?
52. 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.
6- 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
7- 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)
83. 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.
9- 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.
104. 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.
114. 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.
12GEKS (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. -
134.2 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 .
144.3 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.
155. 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.
16- 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.
176. 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.
18- 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.
19- 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.
20- 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.
217. 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!
22Appendix 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.
23Example 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.
24Example 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.
25Example 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.
26Example 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
27Example 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.
28Example 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!