Transcript Document

New Methodological Developments
for the International Comparison
Program
Presentation at the Tinbergen Institute at Erasmus University,
Rotterdam, October 3, 2008
W. Erwin Diewert
Department of Economics
University of British Columbia
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
• 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
• 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?
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.
The CPD method with a balanced panel of price data
works as follows:
(1) 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 a’s are the
country PPPs for the particular BH category under
consideration and the b’s are product premiums
that depend on the units of measurement
• 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 PPP’s, 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)
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 a’s are interregional PPPs
and (8) means that region 1 is chosen as the
numeraire region, the b’s 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 c’s are
commodity effects that depend on the units of
measurement for the products.
• 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 ar+ln 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.
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.
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yk]1/2
j = 1,...,K ; k = 1,...,K.
The aggregate PPP for country j, Pj, is defined as follows:
(18) Pj  k=1K [PF(pk,pj,yk,yj)]1/K ;
j = 1,...,K.
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/j=1K 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.
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 = k=1K [ynk/j=1K ynj][pnk/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 .
4.3 The Ikle Dikhanov Balk Method (IDB)
Dikhanov’s (1994; 9-12) equations that are the counterparts
to the GK equations (21) and (22) are the following ones:
(27) n = [k=1K snk [pnk/Pk]1/j=1K snj]1 ;
(28) Pk = [n=1N snk [pnk/n]1]1
n = 1,...,N
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.
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 c=1C(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.
• 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.
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.
 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.
• 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.
• 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.
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!
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.
Example 1 (continued)
Table 1: Fisher Star, GEKS, GK and IDB
Relative Volumes for Three Countries
Fisher 1
Y1 1.00
Y2 8.12
Y3 57.88
Fisher 2
1.00
8.12
81.25
Fisher 3 GEKS GK
1.00
1.00
1.00
5.79
7.26 47.42
57.88 64.81 57.35
IDB
1.00
33.67
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.
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: 1=Hong Kong, 2=Bangladesh;
3=India, 4=Indonesia; 5=Brazil; 6=Japan; 7=Canada and
8=US.
• The 5 commodity groups are: 1=durables; 2=food, alcohol
and tobacco; 3=other nondurables excluding food, alcohol,
tobacco and energy, 4=energy and 5=services
• The expenditure data (converted to US dollars) and the
quantity data for the 8 countries are on the next slide.
Example 2 (continued)
Expenditures by commodity (row) and country (column)
14320
10562
14951
2619
62124
1963
24835
5100
3094
11627
23207
8234
176782 83882
60748 15158
42126 17573
166826 61248
52722 307547 94121
105527 448995 82056
60798 272875 69461
39933 125835 43342
273669 1736977 379629
967374
778665
992761
524288
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.
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
Example 2 (continued)
A final method: Robert Hill’s 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.
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!