Transcript New Methodological Developments for the ICP W. Erwin Diewert Department of Economics University of British Columbia.

New Methodological
Developments for the ICP
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)
pcnk = acbnucnk ; c = 1,…,C; n = 1,…,N; k = 1,…,K
Taking logs of both sides of (1) leads to:
(2) ycnk = c + n + cnk ;
c = 1,…,C; n = 1,…,N; k = 1,…,K
where ycnk  ln pcnk, c  ln ac, n  ln bn and cnk  ln ucnk.
•
(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:
(24) ycnkr = c + n + r + cnkr ;
c = 1,…,C; n = 1,…,N;
k = 1,…,K(c,n) ; r = 1,2
where the c are the log country PPP’s, the n are the log
product price effects and the r are the two log
representativity effects and the cnkr are independently
distributed random variables with mean zero and constant
variances. In order to identify the parameters, we impose
the following normalizations:
(25) 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:
(27) prcnk  ar brc cn ;
(28) a1 = 1;
(29) br1 =1;
r = 1,…,5; c = 1,....,C(r);
n = 1,...,N; k = K(r,c,n) ;
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 (28) 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 (29) 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:
(33) ln prcnk ln brc = ln ar+ln cn + rcnk ;
r = 1,…,5;
c = 1,....,C(r); n = 1,...,N; k = K(r,c,n).
• The above model simplifies into:
(34) ln [prcnk/brc] = r + n + rcnk
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 Yuri
Dikhanov (1997), who generalized a bilateral method
due to Doris Iklé (1972).
• The DI method is a bit too complicated to explain
here; see the paper for the details.
• I believe that the DI additive method is a clear
improvement over the GK (Geary-Khamis) additive
method which was used in earlier rounds of the ICP.
• But any additive method suffers from substitution
bias (see Diewert (1999) on this) so use caution!
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:
(56) 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:
(57) 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 (56) and (57)
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!